Nelson Maths Teacher's Resource: Sixth year of school

Nelson Maths (Books 1–7) provides creative, stimulating and open-ended tasks allowing children to work at a learning lev...

Author: Jenny Feely | Melissa Dash | Glenda Bradley | Tony Doyle | Pauline Rogers

129 downloads 1079 Views 19MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

Nelson Maths (Books 1–7) provides creative, stimulating and open-ended tasks allowing children to work at a learning level appropriate to their needs. This series supports the whole class — small group — whole class teaching approach.

Teacher’s Resource

Nelson

Maths

Each Teacher’s Resource Book contains:

Nelson

more than 520 activities over 40 weekly units of work ‘Plain Speak’ Statements (teaching focus), Resources and Maths Talk 80 unit and resource blackline masters 11 assessment and planning blackline masters ideas for setting up an effective mathematics classroom, parent participation, five-minute maths activities, and assessment and monitoring.

Maths J ENNY F EELY

Book

© Nelson Austr alia Pty Ltd, 2004. Jay Dale and Jenny Feely Minimum syst em requirem ents Microsof t® Windows ® 98 or later; MacOS 8.5–9.2. and OSX Adobe® Acro bat® Reader (supplied on CD-ROM) is required to view documents.

JENNY FEELY

N

son Mel aths

Installation instructions PC: Insert CDROM into CD drive for auto matic play, or navigate to CD-ROM with Windows® Explorer and double-click on Title. Mac: Insert CD-ROM into CD drive. Doub le-click on the Title icon, then double-click on Title.

If you experienc e difficultie s using this email Nelson product, Thomson Lear ning Australi helpdesk@th a on omsonlearnin g.com.au

Book

M RO ins

Planning Assessme and nt Tool + TRB

e id

CD -

The complete Teacher’s Resource Book is on CD-ROM and features time-saving and easy-to-use interactive planning and assessment software. The CD-ROM also features an Enabler function which allows teachers to plan across grade levels, and a Correlation Chart linking units in Nelson Maths to individual Education Department syllabuses.

has taught at all levels of the primary school,

with many years’ experience as a Curriculum Coordinator and Early Years Coordinator. She has written various resources for a number of curriculum areas, and has been published nationally and internationally. In Nelson Maths, Jenny has created a wealth of practical, enjoyable classroom activities based on her extensive

S ixt

of h Sc Ye ho a ol r

classroom experience.

Thomson Learning AUSTRALIA 102 Dodds Street Southbank 3006 Victoria Email [email protected] Website http://www.thomsonlearning.com.au First published in 2004 10 9 8 7 6 5 4 3 2 1 08 07 06 05 04 Text copyright © 2004 Nelson Australia Pty Ltd Illustrations copyright © 2004 Nelson Australia Pty Ltd Thomson Learning is a trademark used herein under license. Nelson Maths Teacher’s Resource — Book 6 ISBN 0 17012 233 6 The overall structure for Nelson Maths (Books 1–7) was designed and written by: Jay Dale, Anne Giulieri and Lynn Davie Project management by Upload Publishing Services (Jay Dale) Edited by Sarah Fitzherbert Cover and text design by Christine Deering Cover and title page adapted by Goanna Graphics (Vic) Pty Ltd Paged by Christine Deering and Alena Jencik (Grand Graphix Pty Ltd) Illustrated by Sue O’Loughlin Photography by Lindsay Edwards CD-ROM programmed by James Ward Typeset in Grotesque and Plantin Printed in Australia by Ligare Pty Ltd This title is published under the imprint of Thomson Nelson. Nelson Australia Pty Ltd ACN 058 280 149 (incorporated in Victoria) trading as Thomson Learning Australia. Acknowledgements The publishers would like to thank the teachers and students at Broadmeadows Primary School for their willing participation in the photographs on and throughout this book. ‘Zone of proximal development’ diagram on p. 4 is adapted from a diagram by Peter Hill and Carmel Crevola.


Nelson

Maths J ENNY F EELY

Book

Contents Introduction

4

How Nelson Maths Is Organised

5

Teacher’s Resource Book

6

Student Book

7

What We Know About Learning

8

The Classroom Environment

9

Setting Up Your Maths Classroom

9

Assessment and Monitoring

12

Why Assess? What to Assess? When to Assess? How to Assess? Planning

12

Parent Participation

13

Family Maths (BLMs and game boards)

15

Five-minute Maths

20

An Additional Resource

22

Nelson Maths Teacher’s Resource Book on CD-ROM

12 12 12 13

22

Forty Units of Work Number and patterns

Unit

1

Place Value

24

Unit

2

Fantastic Number Facts

27

Unit

3

Number Patterns

30

Chance and data

Unit

4

Choosing Graphs

33

Number and patterns

Unit

5

Positive and Negative Numbers

36

6

Lines and Angles

39

Space

Unit

Number and patterns

Unit

7

Addition

42

Unit

8

Subtraction

45

Chance and data

Unit

9

Space

Using Data to Answer Questions 48

Measurement

Unit

29

Reading Maps

108

Unit

30

Making Maps

111

Unit 10

Running on Time

51

Chance and data

Unit 11

Time

54

Unit

Number and patterns

Unit 12

Numbers, Numbers, Numbers!

Area and Perimeter

Exploring Chance

114

Number and patterns 57

Measurement

Unit 13

31

60

Number and patterns

Unit

32

Mental Computation

117

Unit

33

Multiplication and Division

120

Unit

34

Transformations

123

Unit

35

Symmetry and Tessellations

126

Space

Unit 14

Decimals

63

Unit 15

Fractions

66

Number and patterns

Unit 16

Counting and Number Order

69

Unit

36

Percentages

129

Unit

37

Adding and Subtracting Fractions

132

Revision

135

Space

Unit 17

Making 3D Shapes

72

Unit 18

Drawing 3D Objects

75

Revision

Unit

Number and patterns

38

Unit 19

Multiplication

78

Number and patterns

Unit 20

Division

81

Unit

39

Investigating Problems

138

Unit

40

Fermi Problems

141

Measurement

Unit 21

Volume and Capacity

84 Unit and Resource

Number and patterns

Unit 22

Exploring Patterns

87

Unit 23

Number Puzzles

90

Blackline Masters

144

Assessment and Planning Blackline Masters

224

Answers to Student Book Pages

235

Measurement

Unit 24

Mass

93

Chance and data

Unit 25

Environmental Data

96

Number and patterns

Unit

26

Adding Decimals

Unit

27

Subtracting Decimals

99 102

Measurement

Unit

28

Exploring Measurement

105

Introduction Nelson Maths aims to: • implement focused teaching • maintain ongoing assessment • assist students by scaffolding their learning • improve students’ mathematical understandings • develop students’ mental computation skills. Nelson Maths provides a daily mathematical framework, i.e. whole class – small group – whole class. By providing creative, stimulating and openended tasks students will be able to work at a learning level appropriate to their mathematical needs. Teachers of mathematics are committed to interacting with their students to find out the skills they have, and then planning accordingly to build upon those skills.The foundation of mathematics learning and teaching is where students make connections between prior knowledge and new experiences to develop more complex understandings.

children’s own skills and understandings

+

targeted learning experiences planned as part of a rich mathematics program

+

children’s formation of generalisations

=

a transfer of knowledge to develop more complex understandings

Zone of proximal development Focused teaching

Anxiety

What the learner will be able to achieve independently

Z o n e

o f

Level of challenge

Scaffolding occurs through the support of the ‘more knowing other’

p ro x im a ld e ve lo p m e n t

Targeted teaching needs to occur so students are working within their zone of proximal development.

What the learner can currently achieve independently

Boredom What the learner can achieve with assistance

Level of competence

4

Nelson Maths Teacher’s Resource — Book 6

The activities in Nelson Maths: • provide teachers with choices so they are able to meet the needs of individual students and/or groups of students • are open-ended and stimulating, allowing students to work at their appropriate developmental level • encourage students to develop mental computation skills • provide ongoing monitoring and assessment • allow for effective grouping of students.

How Nelson Maths Is Organised There is one Teacher’s Resource Book and one Student Book for each year level.

The program is based on 40 units of work for each year level. Each unit of work provides material for one teaching week. The 40 units can be taught sequentially, or teachers may choose a unit of work on a weekly basis according to the needs of their class and their individual programs. It should be noted that each unit of work provides more activities than could be taught in one teaching week. In other words, Nelson Maths offers teachers choices and teachers should choose only those activities that suit the needs of their class. The four strands of the mathematics curriculum have been covered in each year level. The ratio is approximately Number, 50 per cent; Measurement, 20 per cent; Chance and data, 10 per cent; and Space, 20 per cent.


5

Teacher’s Resource Book Each weekly unit is divided into three main sections that relate to the daily mathematics hour. • Whole Class Focus — Introducing the Concept • Small Group Focus — Applying the Concept • Whole Class Share Time. Each unit in the Teacher’s Resource Book provides:

Whole Class Focus

• ‘plain speak’ statements for teachers to refer to when monitoring and assessing students (see ‘During this week look for students who can:’ in each unit).

Independent Maths

• text in a grey panel highlighting the fact that teachers can choose activities for the week’s work that best suit the needs of their class and their mathematics program. It also explains that each common symbol used (e.g. the ‘sun’) in ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ links related activities. For example, if the teacher chooses an activity with the sun symbol in ‘Whole Class Focus’ then the linking activity they should choose in the ‘Independent Maths’ section will also have the sun symbol. This same symbol will carry through to ‘Whole Class Share Time’.

Whole Class Share Time

• Resources — materials needed to implement the unit. • Maths Talk — the vocabulary that the teacher may need to model and use in their teaching, and the language the students should be encouraged to use when discussing mathematical concepts. • Whole Class Focus — Introducing the Concept (10 to 15 minutes plus). This is the time when the whole class joins together to focus on the concept being taught in the unit.Teachers can choose from any of the five to six activities, and program them into their weekly timetable (see BLMs 81–84). During this session, the teacher sets the scene and motivates the students. There is interaction between the teacher and the whole class as they share their skills and understandings, and develop their understandings further. During this session the teacher uses a ‘shared’ teaching approach (see p. 7 for a definition). • Small Group Focus — Applying the Concept (30 to 35 minutes plus). In this session, the Focus Teaching Group and the Independent Maths (individual, pair, small group) occur at the same time. Focus Teaching Group During this session, the teacher works with a small number of ‘likeneeds’ students to teach level-appropriate concepts. The teacher chooses a modelled, shared or guided teaching approach depending on the level of support the students need (see p. 7 for a definition).The aim of this session is for the teacher to assist students at their point of need and then move them on. This is also an appropriate time to take anecdotal records on individual students. The session usually runs for 20 minutes or so. After this time, the students work on related independent tasks, while the teacher ‘roves’ among the class. During this ‘roving’ time, the teacher monitors and assesses students, and notes those individuals to be included in future Focus Teaching Groups. There are three suggested Focus Teaching Group activities provided in each unit.

6


Independent Maths (individual, pair, small group) During the independent maths activities, students work in small groups, with a partner or individually on more open-ended tasks specifically designed so students can work at their individual level of understanding. The concepts in these activities are linked to the activities introduced in ‘Whole Class Focus’. The majority of Student Book pages have been incorporated into this section. In Independent Maths, most units feature at least one activity that integrates the use of technology, i.e. computers and/or calculators. • Whole Class Share Time (10 to 15 minutes plus). This is a time for the class to regroup, reflect upon and celebrate their learning. This session also promotes the students’ use of mathematical language, and enables the teacher to gain valuable insights into the students’ mathematical thinking and the strategies they are using.

Student Book The Student Book promotes stimulating and open-ended activities where students can investigate tasks at their own level of understanding. The Student Book includes: • two to three Student Book pages corresponding to each unit in the Teacher’s Resource Book. These pages have been integrated into the ‘Small Group Focus’ section of the Teacher’s Resource Book. • between 25 and 30 ‘Check and Self-assessment’ pages, each page occurring after a one- to three-week block of units/work. These pages enable both the student and the teacher to monitor and assess the student’s mathematical understandings throughout the units of work. The students can complete the page independently or with the teacher. These pages promote a student–teacher partnership in the learning process. They allow students to self-assess and therefore have individual input into their mathematics.The resulting data will assist teachers with future planning and can be used as part of the student’s portfolio (for teacher–parent interviews). • a list of the appropriate ‘plain speak’ statements and cross-references to the Teacher’s Resource Book.

ata Chanc e and d

l Breakfast Cerea

_________ Date: ______

graphs show. _______________ these pie (sector) ________________ 1 Explain what _______________ _______________ _______________ _________________ ________________ _______________ _______________ _____ _ _____ ______ B A

• a ‘Maths Talk’ section (glossary of maths terms) at the back of the book for students to refer to.

Choco Pops Flaky Corn vitamins and minerals 1% fibre 3%

salt 1% fibre 1%

sugar 39% carbohydrate 79%

vitamins and minerals 3% protein 6%

salt 1%

carbohydrate 50%

sugar 8%

Teaching Approaches

fat 0%

fat 0%

protein 8%

_________ ? _______________ has the most sugar ___________ 2 a Which cereal _______________ least fibre? _____ b Which has the ________ _ Why? __________ _____ _____ _ e? __________ _______________ would you choos ________________ 3 Which cereal _______________ _______________ _______________ table. the in y the data | r) graph to displa (secto pie a | 4 Make | es Breakfast Choic |

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

| | |

|

|

15

|

10

Toast

|

25

Eggs

|

50

Fruit

|

Cereal

|

Numb er of people who eat it

|

Food

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

| |

| |

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

graphs pie (sector) graphs, line graphs, bar (column) • Read and analyse using pie (sector) graphs, • Represent data collected

|

Chance and data

|

33–35.) ’s Resource pp. graphs. Graphs (See Teacher graphs and picture Unit 4 Choosing and picture graphs. line graphs, bar (column)

12

Modelled — This approach is used with small groups. The teacher provides a strong level of support by modelling the learning experience, presenting effective strategies and illustrating how connections are made. The teacher also models the use of materials and how to record the mathematics involved. Students talk about the presentation and model what they experience. This is an approach where the teacher predominantly models the mathematical concepts. Shared — This approach is used with small groups and as part of a whole class focus. The teacher and the students work together to explore mathematical concepts and to make generalisations. Both the teacher and students use materials and record the mathematics to demonstrate their understandings. This is an approach where the teacher and the students work along side each other to make connections and form generalisations. Guided — This approach is used with small groups. The teacher removes himself or herself slightly from the group, while still gently ‘guiding’ the students and addressing issues as they arise. This is an approach where the teacher provides support while allowing students to make their own generalisations and connections.


7

What We Know About Learning • Children learn in different ways.

• Children learn from and with others.

• Children learn by teaching others.

• Children should have the opportunity to record in different ways. • Children can follow different pathways to reach the same learning milestones. • Children need to be encouraged to take risks in their learning. • Children learn by being actively involved. • Children need time to grasp the concepts introduced, i.e. time for thinking, reflecting, reacting and sharing the processes and answers in mathematics. • Children learn when they feel good about themselves — self-esteem is critical.

8

The Classroom Environment It is important that the classroom environment: • is stimulating and engaging and immerses students in a mathematical context • incorporates a variety of rich resources that engage students in making mathematical connections • is rich in the language of mathematics • has access to calculators • has access to information technology, which is an integral component of our world; this should be reflected in our mathematical classroom environment • has rich displays where students can make metacognitive links to their mathematics learning • is positive and encouraging, and allows students to take risks in their learning.

Setting Up Your Maths Classroom Here are some ideas on how you can set up your classroom.

Encourage students to record mathematical terms and concepts in a dictionary format.

Taskboards are an excellent way to let students know what is expected of them.

Display real-life problems for students to solve.


9

Displaying students’ work is important. Allow time to talk about and view maths tasks.

Use charts to display helpful information and promote mathematical language.

Display individual students’ expertise so others can learn from them.

Use resources and tasks that relate to real life.

10


Include students in upcoming mathematical learning and assessment.

Ensure technology is part of the everyday learning environment.

Set tasks that are openended and encourage problem-solving skills.

Assist students by providing reference charts.

Encourage group work and peer tutoring.


11

Assessment and Monitoring Assessment and monitoring is an ongoing process. It allows teachers to gain a clear picture of students’ understandings. This can then be used to influence planning, as well as to assist the teacher to group students for effective focus teaching. Teachers need to model mathematical language constantly. They need time to talk to and question students, and must allow time for students to respond. Teachers will thereby gain useful insights into how each student is learning and what thinking processes they are using. This information is invaluable for future planning.

Why Assess? To collect data on individual students so their needs can be met and targeted when planning future learning experiences. Teachers use a range of strategies (see ‘How to Assess?’ below) to collect data for their ongoing planning.

What to Assess? The student’s: • attitudes • mathematical understandings (verbal and recorded) • problem-solving abilities • confidence • ability to work with others.

When to Assess? • at the beginning of the school year • at the end of a unit (or block of units) • at the beginning of a unit • on an ongoing basis — during your daily maths sessions • as part of the ‘Whole Class Focus’, ‘Focus Teaching Group’, ‘Independent Maths’, while roving, and during ‘Whole Class Share Time’.

How to Assess? • teacher observations, e.g. anecdotal comments on post-it notes on an A3 list of names • student self-assessment (learning journals, smiley chart, etc.) • peer assessment • file cards, kept for each student • portfolio assessment • Nelson Numeracy Assessment Kit • ‘Check and Self-assessment’ pages in the Student Book

12


ata Chanc e and d

________ Date: _______

___________ ________________________ ________________________ Name: ________ Year: __________ Term: __________ __ Year Level: ________

Code: t NA not apparen B beginning C E

Week

consolidating established

ents ‘Plain Speak’ Statem

Unit

(Date)

1 Place Value

2 Fantastic Number Facts

to 99 999 to its place in a number of a numeral according 000 000 Explain the value to largest up to 1 in order from smallest Put whole numbers or as numerals to 99 999 in words Read and write numbers 1 000, etc. the nearest 10, 100, Round numbers to division facts and tion n, multiplica addition, subtractio n facts, and also between Automatically recall addition and subtractio relationship between Explain and use the division facts tical problems multiplication and when solving mathema te strategies to use Identify appropria

numeric problems Identify patterns in patterns Continue number works ding of how the pattern Explain number patterns based on an understan pattern will continue Predict how a number and picture graphs bar (column) graphs graphs, line graphs, using pie (sector) presented have collated and Represent data collected they 4 sets data findings about Analyse and present Choosing of different graphs to its purpose Identify the features Graphs present data according graphs te type of graph to graphs and picture Select the appropria line graphs, bar (column) pie (sector) graphs, Read and analyse line +10 on a number between –10 and positive numbers +10 Place negative and to 5 –10 from negative numbers Order positive and Positive and is +20 number and –10 negative between Explain what a Negative and negative numbers contains positive Analyse data that Numbers l, parallel, diagonal, (vertical, horizonta of a range of lines and explain the features Construct, identify 6 and zigzag lines) perpendicular, curved Lines and angles measure angles and acute (sharp) Use protractors to Angles obtuse (blunt) angles angles, right Identify and draw 999 add numbers to 999 and calculators to s, written methods Use mental processe everyday life 7 could be used in Identify when addition solve addition problems Addition processes used to Verbalise the thought 999 999 in the range 0 to numbers subtract and calculators to s, written methods, Use mental processe 8 everyday life n could be used in problems Identify when subtractio solve subtraction Subtraction processes used to Verbalise the thought

3

Number Patterns

9 Using Data to Answer Questions

10 Running on Time

224

© Thomson Learning,

means using mathematical that could be solved issues of concern Pose questions about collect data Suggest ways to to investigate questions ction techniques Use a range of data-colle varying types of the data meaning the for Create graphs of ts data, providing argumen Analyse and present timetables Read and interpret calendars information from Read and calculate event it will be until a specified Identify how long s and schedules Make own timetable

2004. This page from

Nelson Maths Teacher's

Resource — Book 6

may be photocopied

for educational use within

the purchasing institution.

-ass essm Che ck and Self

BLM 81

Unit 4

e Student Profil

ent

1 to make a graph. ation in the Table 1 Use the inform You will need to: data is about • decide what the graph the for • choose a title scale • work out the • add labels.

Table 1 Doritos Popcorn Twisties Chips Pretzels

20 15 12 10 3

_________ this data? ______ asked to collect n was most likely ________________ a Which questio __________________ __________________ __________________ appropriate most the is type of graph _______________ information, which __________________ b To present this ___________ Why? ________________ to use? ____________ __________________ __________________ __________________ _____________ __________________ ______ ______ Title: ______

would use them. Explain when you le of each graph. 2 Draw an examp Pie (sector) graph Bar (column) graph

__ use it: ____________ _ When I would it: ____________ _ When I would use _________________ __________________ ________________ __________________ 33–35.) Resource pp. Unit 4 (See Teacher’s Chance and data

14

graphs and picture line graphs, bar (column) using pie (sector) graphs, • Represent data collected of different graphs. to its purpose. • Identify the features type of graph to present data according • Select the appropriate

graphs.

• ‘During this week look for students who can:’ (see the first page of each unit in the Teacher’s Resource Book) is a list of ‘plain speak’ statements for teachers to refer to when observing students (these are also listed in checklist form on BLMs 81–84) • Student Profiles (see also BLMs 81–84).

Planning Mathematics planning is ongoing and depends on the needs of the class and individual students. Information obtained from monitoring and assessing students can be used for future planning. Nelson Maths Teacher’s Resource Book provides the following weekly, term and yearly planners to choose from: • four weekly planners (BLMs 85–88) • one term planner (BLM 89) • two yearly planners (BLMs 90 and 91). Please note: The Teacher’s Resource Book is also available on CD-ROM, which enables teachers to plan directly on screen. Student Profiles (BLMs 81–84) can also be recorded and filed on screen. Also available on the CD-ROM is the Enabler function which allows teachers to plan across two or more grade levels; and a ‘Correlation Chart’ linking the units in Nelson Maths to individual state and the New Zealand syllabuses.

Parent Participation Research shows that strengthening the partnership between school and home increases students’ chances of success in their education. Therefore, as teachers, we need to encourage parents to be active participants in their children’s learning and, in turn, we need to keep parents informed of the type of learning that is happening in our classroom. In summary, we need to highlight the connections between maths experiences at home and maths experiences at school. Schools need to understand their community, and provide a supportive environment where parents’ attitudes and goals for their children are respected. Teachers need to encourage parents to be partners in their children’s numeracy education. Parent Participation

13

Parents need to have a true picture of how maths is taught today, how current teaching practices are different from their own maths education, and why things have changed. Teachers need to communicate to parents the content of their mathematics program, and the teaching strategies and resources used. Teachers and parents need to work together to provide their children with additional assistance. Through the assessment and reporting program, parents can be informed of their child’s mathematical progress, and goals can be set to extend the child’s development. Teachers can provide parents with hints and a range of enjoyable, hands-on activities to do at home that will support children’s mathematical development (see ‘Family Maths’ BLM, p. 15). There are many strategies to keep parents informed and involved such as: • holding sessions to outline the current mathematics program, i.e. individual classroom teachers providing parents with information about the class mathematics program and/or school-based information nights where all teachers, staff and/or guest speakers are involved in the presentation • conducting sessions at which parents can discuss their child’s progress and the type of mathematics they are involved in — the Nelson Maths Student Book provides samples of the student’s work (see also ‘Check and Self-assessment’ pages in the Student Book) • giving parents the opportunity to complete some of the activities students are involved in, i.e. ask parents into the classroom to actively participate in the mathematics program • distributing newsletters to inform parents of the current mathematics program and/or providing open-ended tasks for parents to do with their children (see ‘Family Maths’ BLM, p. 15) • erecting display boards outside the classroom with family maths problems to solve (see ‘Family Maths’ BLM, p. 15), and/or maths tasks to be done at home or at school for the week • having open maths times during the week/term/year to which parents are invited to interact with and/or observe the class in action • making digital photo montages of maths activities to display outside the classroom • posting video footage of the class maths program on the school intranet or burning a CD for parents to view. It is very important to make parents aware that many of their day-to-day activities with their children involve mathematics, e.g. cooking, going shopping, carpeting or tiling floor spaces, building, collecting and sorting objects, etc. It is also very important that the lines of communication are open between home and school, and that parents are informed of the type of mathematics program their children are involved in. It is crucial that parents feel welcome to participate in the program in any way acceptable to them, e.g. working with a group of students; preparing, sorting and/or organising resources. Parents and teachers need to work as partners to enhance the education of their children.

14


• You can help your children at home by involving them in mathematical activities and talking to them about mathematics and its everyday uses. Be positive! Praise your child's success. Encourage your child to have a go at measuring, calculating, counting, estimating and solving problems. Invite children to investigate and make discoveries for themselves. Encourage them to find their own answers. Don't be too quick to tell them the answers. • Show children how you use maths in your everyday activities, e.g. measuring ingredients, estimating costs, calculating change, timing how long things take to cook, preparing shopping lists, using calibrated containers, using kitchen scales, tendering money, playing card and board games, telling the time, looking for patterns in the environment, reading road signs, reading number plates. Materials to have on hand: dice; dominoes; number cards 0–9; 100 chart; games such as UNO and Snakes and Ladders. • Cooking at Home Children can help you prepare shopping lists, work out the quantities of ingredients needed, weigh the ingredients and check on the cooking time. Involve children in selecting new recipes. • Keep the Calendar Up–to–date Mark any special events on the calendar, e.g. family and friends’ birthdays, outings, holidays, excursions etc. Look for patterns in the number squares. Encourage children to make their own calendars or to keep a diary. • Mass and Height Keep a record of your child's mass and height. See how much they have grown each year. Do this for everyone in the family. Graph the results using various types of graphs.

Family Maths Blackline Master 1

Cut out the snippets (suitable for the upper school) below and reproduce them in the school’s weekly newsletter.

• Mapping When travelling, provide children with a street directory or map and discuss directions. Point out speed limits, distances to towns, populations in towns, etc. When you are driving along in the car, ask children to guess how far it is to the next light post, the next town, etc. Calculate the distance travelled or the distance yet to travel. Involve the whole family. Measure the distances with your speedometer. • Make My Target Number? Play with a partner or a small group. Write down the numbers 1 to 9. In turn, select a target number, e.g. 65.The object of the game is to be the first person to use three of the numbers written down to make the target number using addition or multiplication or both. A number can only be used once. Each person must record their equation, e.g. 7 x 8 + 9 = 65.The first person to write down a correct equation wins that round. • Take One or Take Two Put out 11 blocks in a row between two players. In turn, remove one or two blocks at a time. The object of the game is to make your partner pick up the last block. • Tossing a Coin Ask, ‘How many times do you think a coin will land on heads if you toss it 30 times?’ Write down your guess.Test your guess and record how the coin lands. Compare results. • Weather Chart Keep a weather chart. Older children can record weather conditions and daily temperatures from the newspaper and graph the results over a month. • Dice Games Throw two dice and have children multiply them together to reinforce times tables. Throw two dice and have children add the numbers and multiply the total by 1 to 12 to reinforce times tables. Throw three or four dice and have children record the largest and smallest numbers they can. After a number of throws, have children order all the numbers from smallest to largest. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.


15


Cut out the snippets (suitable for the upper school) below and reproduce them in the school’s weekly newsletter. There are three take-home game boards (pp. 17–19) provided. All use simple equipment. Copy onto card and send home. • Bounce into Maths Many children love to play ball games. Help your child to learn their tables by playing a ball game with them. First, ask a tables question, e.g. 7 x 9. If your child answers correctly then they can have a shot at the basket or a kick for goal, etc. Ensure you score so effort is rewarded, e.g. a goal = two points; if the ball hits the ring without going inside, then score one point. Your child then asks you a tables question. You can also play in teams. • The Clock is Ticking You need a ball and a timer (the timer on the stove will do) for this game. Set the timer for five minutes, ask a tables question that your child should know and then throw the ball to them. After your child answers correctly, they ask you (or another player) a new question as they throw the ball to them. Questions and answers continue in this way until the timer rings.The person holding the ball at this time is out. • What Am I? When travelling long distances by train or by car use the time to play maths games. This game can be played anywhere without any equipment. Here’s how. One person thinks of ‘something’ to do with maths, e.g. they might think of the number: 1 984. They then give the other players two clues, e.g. ‘I am a number between 1 000 and 2 000. I am an even number.’ The other players must then ask questions that can be answered with a ‘Yes’ or ‘No’. The first player to correctly guess the answer, takes the next turn at choosing another maths idea. You could focus on numbers, shapes, distances, weights, etc. • Money, Money, Money When shopping at the supermarket, ask your child to keep track of how much you are spending. You might say, ‘I only have $30 to spend today. Can you please keep track of how much I have spent and let me know when I reach my limit.’ Encourage your child to round off prices, e.g. an item that costs $2.99 could be added onto the tally as $3.00. Have your child check their mental calculations against the final docket at the checkout. • Best Buy When out shopping, encourage your child to help work out what items are the best buy, e.g. is it cheaper to buy the 450 mL bottle of shampoo at $6.98 or the 900 mL bottle of shampoo at $15.89? Which of the two is better value? • The Big Half Ask you child to help when things need to be shared amongst the family, e.g. children could count out strawberries or pour drinks so that everyone has an equal share.Talk about ways of doing this, e.g. measuring cups next to each other, counting, cutting food in half and then in half again. It is often helpful to follow the rule that one child shares, while the other chooses which share they will take! • Read All About It If you look through the daily newspaper you will find many example of maths being used in an everyday context. Point out to your child such things as graphs, tables, sports ladders, percentages, maps, etc.Talk about what these things tell us and whether or not they are the best way of providing the information. • Playing Around Many childhood games involve lots of maths. Games with dice and cards often involve adding or subtracting. When playing such games talk about the maths being used. Encourage your children to check each other’s working out. Take turns to keep score. • Seeing Daylight Encourage your child to notice the changes that happen in the sky, e.g. What time is sunrise and sunset each day? When does the moon rise each day? What shape is the moon each night? If living near the sea, what happens to the tides? • Time on Your Hands Discuss different time zones with your child when making phone calls to different places around the world, or when watching events on TV that are actually occurring in a different time zone. Say, for example, ‘Why is it tea-time here, when it is just after lunch in Perth? When would be the best time to ring Auntie Jen in London?’ © Thomson Learning, 2004. This page from Nelson Maths Teacher’s Resource — Book 6 may be photocopied for educational use within the purchasing institution.

16



Three in a Row You will need : 2 dice, a number of counters (each player will need their own coloured counters — coloured beans could be used) A game to practice multiplication tables (for 2 to 4 players) How to play: • In turn, throw the two dice twice. Add the first two numbers thrown and the last two numbers thrown, e.g. 3 + 6 = 9, 2 + 4 = 6. Now multiply these numbers, e.g. 6 × 9 = 54 and cover that number on the game board. If the space is already covered, the turn is missed. • The first player to cover three numbers in row vertically, diagonally or horizontally wins.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 © Thomson Learning, 2004. This page from Nelson Maths Teacher’s Resource — Book 6 may be photocopied for educational use within the purchasing institution. Game board 1

17

Add It On You will need : 1 dice and a different-coloured counter per player (different coloured beans could be used) (For 2 to 4 players) How to play: • Agree on a ‘target total’, e.g. 1 000. • Each player puts their counter on a circle of their choice. • In turn, throw the dice. Move that many spaces in either direction. Each player must then add on the number in the circle they landed on to their running total. • The first player to reach the ‘target total’ wins.

Lose all points

4

2

11

13

13

Lose all points

8

100

15 6

12

1

2

33 51 42 82

87

Lose all points

Lose all points

50 25

17

14 45 67 37 0 9

Lose all points

99

© Thomson Learning, 2004. This page from Nelson Maths Teacher’s Resource — Book 6 may be photocopied for educational use within the purchasing institution.

18


Game board 2

Number Detective You will need : a number of counters (each player will need their own coloured counters — coloured beans could be used) (For 2 players) How to play: • In turn, each player gives the other player a ‘number clue’ that is answered by placing a counter on the appropriate number, e.g. ‘Put a counter on the number 100 more than 260.’ (360) Incorrectly-placed counters are removed. • The first player to get three counters in a row vertically, diagonally or horizontally wins.

245

9 999

12 672

40 912

8 670

8 067

8 067

26 001

31 454

13 545

100 000

30 003

85 671

90 909

23 123

12 345

34 567

98 765

56 123

10 101

23 232

75 057

101

87 231

23 871

10 324

22 222

87 092

14 567

39 412

75 235

28 431

143

1 983

4 912

9 999

© Thomson Learning, 2004. This page from Nelson Maths Teacher’s Resource — Book 6 may be photocopied for educational use within the purchasing institution. Game board 3

19

Five-minute Maths At the beginning of each maths session, or when time allows throughout the day, spend five minutes doing some quick and enjoyable maths activities to reinforce and revise concepts previously taught, and/or revise number facts, counting sequences, shapes, etc.Traditionally, Number has been the focus of the five-minute maths session. However, featured below is a range of activities across all maths strands to provide a broader classroom focus.

Number • Provide pairs of students with a dice and a calculator. In turn, players roll the dice and key in either the number rolled or the number multiplied by ten, e.g. if a 3 is rolled then the player may key in either 3 or 30.The number keyed in is added to the player’s total. After seven rounds, the player whose total is closest to, but less than 100, wins. If a player obtains 100 or more during the game, they immediately allow the other player to win. • Have students complete the following activity: Think of a double-digit number, e.g. 16. Multiply each of the digits by themselves and add to get a second number, e.g. 1 x 1 = 1 and 6 x 6 = 36, 1 + 36 = 37. Complete this cycle again, e.g. 3 x 3 = 9 and 7 x 7 = 49, 9 + 49 = 58. Continue to do this to create a sequence, e.g. 16, 58, 26, 40, 16 ... If the sequence reaches 1, then the original number is called ‘happy’ and if it doesn’t, it is called ‘sad’. Have students investigate different numbers. • Unit fractions have a numerator of 1. Have students (using calculators if necessary) investigate those unit fractions whose decimal equivalent recur, e.g. 1/3 = 0.3333… and 1/7 = 0.1428571428571… • In pairs, have students create a number grid, say 7 x 5 and write in the numbers 0 to 35. Provide students with three dice and coloured counters. In turn, students roll the three dice and use the numbers rolled and any operation to create a number featured on the grid. They can only use each number once, but can use brackets or any sign more than once, e.g. if 3, 2 and 6 are rolled, students could create any of the following: 6 + 3 + 2 = 11 or 6 + (3 x 2) = 12 or (6 – 3) x 2 = 6, and so on. The winner is the first player to get three counters in a line; horizontally, vertically or diagonally.

Measurement • Show students a centimetre cube. Ask them to picture the cube in their minds. Ask, ‘How many centimetres long is the perimeter of your table top? How many centimetres long is your right foot? How many centimetres long is your mathematics book?’ • Using only a piece of paper and a pencil, have students draw and label different lengths, e.g. 50 millimetres, 1 centimetre, 30 centimetres. Once a set number are completed, have students measure these lengths with a ruler. Ask them to share the accuracy of their estimations and any difficulties they had with the activity.

20


• Show students two different-shaped objects that have the same volume but different mass. Have them predict which of the objects is heavier/lighter, and which one has the greatest/least volume. Invite students to explain how they will accurately measure the two items and test their predictions. • Have students calculate the area and perimeter of the classroom. Invite groups of students to use different measuring equipment, e.g. meter ruler, measuring tape, 30 centimetre ruler. Have students compare answers and reflect on the most appropriate piece of equipment to use.

Space • Have students play ‘Can you draw this?’ by following instructions, e.g. ‘Draw a triangle inside a circle, inside a square, inside a pentagon.’ Students can then make up their own instructions for a friend to follow. • Again, have students play ‘Can you draw this?’ This time, secretly select a shape (either two-dimensional or three-dimensional). Describe the shape, e.g. a cube: ‘It has six faces. Each face has two sets of parallel lines, and all corner angles of each face are equal.The lengths of the two diagonals of each face are also equal.’ Have students draw the shape from your verbal description. • Provide students with a grid and have them draw an axis on the grid, e.g. letters A – M by the numbers 1–10. Read out a set of points, e.g. (A, 5), (B, 6) etc., to create a dot to dot image or shape. • Provide students with a grid and have them draw an axis on the grid, e.g. letters A – M by the numbers 1–10. On a similar grid of your own, mark on 10 points. Play the game as a ‘hangman’ style activity. Ask students to nominate coordinates, to locate your 10 points, recording guesses on their grids before they reach their maximum number of guesses.

Chance and data • Record the favourite songs of the class. Rank them in order to make a class ‘Top Ten’. • Collect graphs and tables from a newspaper. Over time, make a class display of the different types of graphs. Discuss the differences. • Ask students to work out on what day of the week their 100 th birthday would fall. Ask students to explain how they found this out, and if there is a process they could use. • Provide pairs of students with a different numbers of coins, e.g. one pair with five coins, one pair with seven coins, and so on. Invite students to place the coins on the table with all of the heads facing up.Turning three coins over at a time, have students try to get all of the coins with the tails facing up. Ask students to record the processes they used and share these with the class. • Obtain a line graph from a newspaper and cut off the heading; leave the labels on the axis. In small groups, have students create a story about the graph and present it to the rest of the class. Having more than one line on the graph could extend this activity, and then different lines could be allocated to different groups.

Five-minute Maths

21

An Additional Resource Nelson Maths Teacher’s Resource Book on CD-ROM A planning and assessment CD-ROM accompanies every Teacher’s Resource Book in the Nelson Maths series.Teachers will find that: • all 240 pages of the Teacher’s Resource Book can be viewed on screen • all blackline masters can be printed from the CD-ROM (including the ‘Overview’ on pp. 19–23) • a ‘Correlation Chart’ is available linking the units in Nelson Maths to individual state and the New Zealand syllabuses • the CD-ROM is interactive, allowing teachers to keep assessment records of individual students and plan their weekly, term and yearly maths program on screen.

Assessment Using the CD-ROM The ‘plain speak’ statements (included in each unit) are featured in the assessment section of the CD-ROM. Teachers select the ‘Student Administration’ button, and follow the options available. A Student Profile for each class member can then be developed by entering the student’s name, the unit being studied and selecting from NA (not apparent), B (beginning), C (consolidating) and E (established) for each ‘plain speak’ statement featured. Graphing facilities provide a summary of each student’s achievements.

Weekly, Term and Yearly Planning on CD-ROM By following the ‘Planning’ menus, teachers are able to plan their weekly, term and yearly maths program for one grade or multiple grades on CDROM.To plan their weekly program, the teacher selects the week, the term, the date, the unit to be explored, the teaching focus for the week and their choice of activities from Whole Class Focus, Independent Maths, Whole Class Share Time and the Focus Teaching Group section. All activities selected can then be edited and teachers may choose to key in favourite tasks and activities of their own. Term and yearly planners function in a similar way to the weekly planner; however, they feature only the units to be covered and their corresponding teaching focus. All three planners can be viewed on screen and/or printed out. The CDROM’s planning and assessment functions are very simple to use and will save teachers valuable time.

22


Nelson

Maths U NITS 1– 40

unit

Place Value

1 Number and patterns

Student Book pp. 5–6

BLMs 1, 2 & 43

During this week look for students who can: • explain the value of a numeral according to its place in a number up to 99 999 • put whole numbers in order from smallest to largest up to 1 000 000 • read and write numbers to 99 999 in words or as numerals • round numbers to the nearest 10, 100, 1 000, etc. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources card, Blu-Tack, masking tape, post-it notes, advertising brochures, playing cards, newspapers, magazines, three twenty-sided dice, Excel, BLM 43 ‘Number Expander’, BLM 1 ‘What Number Am I?’, BLM 2 ‘Lowest versus Highest’ Maths Talk Model the following vocabulary in discussion throughout the week: place value, digit, ones, tens, hundreds, thousands, tens of thousands, hundreds of thousands, a million, bigger than, smaller than

Whole Class Focus — Introducing the Concept Justifying Order Have students write down a number between 0 and 99 999 and hand it to another student. Form groups of eight to ten. Have each group line up to order the numbers from smallest to largest. Ask students to justify their order, focusing on aspects of place value. Have students in each group exchange cards and form different groups to repeat the activity. Show students a number expander (BLM 43). Ask one student to write their number on the whiteboard. Ask others to use the number expander to investigate the number. Ask, ‘Which digit is in the tens of thousands column? How do you know? What do digits in the fourth/sixth place in any number represent?’ Number Knowledge Have ten students write a three-digit number on a card. Use Blu-Tack to stick the cards to the whiteboard. Ask, ‘How do we know which is the biggest number?’ Discuss place value and involve students in ordering the numbers. Introduce thousands, tens of thousands and hundreds of thousands. Have students turn their three-digit numbers into six-digit numbers. Ask, ‘Which is the biggest/smallest number now? How do you know?’ Numbers to 999 999 Use masking tape to mark six columns on the floor to represent place value from ones to hundreds of thousands. Sit a student in each column and have each write down a single digit and hold it up. Ask,

24


‘How do we say this number? What do we need to think about to work out what the number is?’ Review place value. Ask, ‘What does the 2 in this number represent? What does the 6 represent? How do you know?’ Discuss the need to count places from the right, and the convention of grouping digits in threes. For example, ‘The last three digits in a non-decimal number are always hundreds, tens and ones. The next three numbers are always hundreds of thousands, tens of thousands and thousands.’ Have the six students swap their number cards. Ask, ‘How do we say this number?’ Repeat, focusing on the thought processes needed to identify the number. Expanding Numbers Give each student a post-it note displaying a sixdigit number. Ask, ‘What value does each digit in your number represent?’ Have students form small groups and select one of their numbers. Ask them to record all the information contained in the number, e.g. by expanding it, writing 253 492 as 200 000 + 50 000 + 3 000 + 400 + 90 + 2. Have groups share their recording methods. Then have each group order their numbers from highest to lowest, and a representative explain the order. Discuss any numbers with the same digit in the same place. Say, ‘Both these numbers have a 7 in the thousands column. How do you know which is the biggest?’ Rounding Up and Down Cut out products priced between $10 and $100 from advertising brochures, e.g. chocolate $1.79, shoes $82.50. Make a number line with ten intervals (using masking tape or the whiteboard) and mark $0 (free) and $100 at each end. Invite students to guess what each interval represents, i.e. $10. Direct students to place products on the number line closest to the nearest dollar. Ask, ‘Why is $2.21 closer to $0 than $10? What did you need to think about to work it out?’

Small Group Focus — Applying the Concept Focus Teaching Group • Number Expanders Give each student a number expander (BLM 43) and ask them to write a six-digit number on it. Ask, ‘How do you say this number? How many tens of thousands/hundreds of thousands are in Allow students who your number? What do you need to think about to be able to say find it difficult to identify place value to open the number expander to this number?’ Repeat. As an independent activity give each check. Have less advanced students write student a deck of playing cards (picture cards removed, Ace each of the numbers onto number expanders before they write represents one). Have students shuffle the cards, deal out six sixthem in words. digit numbers, then record these numbers in order from smallest to largest and write them in words. • Who Am I? Give each student a number expander (BLM 43). Ask students to listen to the following number story and to write on the expander the number they think you are talking about. Say, ‘I am a five-digit number less than 50 000. My tens place is occupied by the digit 3 and the digit in the ones place is 2 more than that in the tens place. My hundreds and thousands digits are the same and total six. All my digits add up to 17. What am I?’ (Answer: 33 335.) Discuss the thought processes needed to solve this puzzle. Have students work independently to write their own similar number puzzles to be collated into a class book. • Rounding Numbers Up or Down Give each student a deck of cards (10s and picture cards removed, Ace represents one). Have students shuffle the cards and deal out the first six cards to make a six-digit number. Have them say their numbers. Ask, ‘What would your number be if you rounded it to the nearest 10? How do you know?’Talk about the thought processes needed Unit 1 Place Value

25

to round a number up or down to the nearest 10, then the nearest 100, 1 000, 10 000, etc. Have students work independently to form other six-digit numbers with the playing cards and to round these up or down.

Independent Maths Individual, pair, small group

Put Them in Order Have students look through newspapers/magazines to find or make six-digit numbers, write these numbers in words and order them from smallest to largest. Partners then use these numbers to play ‘Guess My Number’. One player selects a number from the list without telling their partner. Partners then ask ten questions (answerable only with ‘Yes’ or ‘No’) to discover the number. If the first player successfully works out the number, partners change roles. If not, the first player selects a new number and the round is repeated. What Number Am I? (BLM 1) 1 to play the game.

Provide pairs with sets of cards from BLM

Number Facts Have students work in small groups taking it in turns to be the leader.The leader writes down a six-digit number and directs the others to read the number out aloud. The leader then asks the others to give four facts about the number and to discuss how far the number is from the nearest thousand.When everyone has been the leader, have the group order the numbers from lowest to highest and paste them onto paper. Have them also record the information they generated. Ordering Numbers (Student Book p. 5) Have students complete the Student Book page.Then provide small groups with three twenty-sided dice and BLM 2 ‘Lowest versus Highest’. Students could record their results on BLM 2 or on an Excel spreadsheet. How Far? (Student Book p. 6) Book page.

Have students complete the Student

Whole Class Share Time Have students view each other’s number charts and locate specific numbers as they go, e.g. the smallest number, largest number, number closest to 500 000, number with a 7 in the thousands column, etc.

Now I understand …

Have individuals share facts about their favourite six-digit number without revealing the number. Ask others to identify the number. Ask, ‘What did you need to think about to identify this number? Which clues gave you the most information?’ Choose a group to demonstrate how they ordered the numbers and to share any shortcuts they used. Ask, ‘Which part of the number did you look at first/last? Why? How did you know what to do with the number that had a zero in it?’ Have students suggest rules or ideas to help others read large numbers and determine their value. Write on the whiteboard the distance each cyclist had travelled after 20 days. Ask, ‘Which cyclist had travelled the furthest/least distance? Which part of the number tells you that? How far does each rider still need to travel?’

26


unit


Fantastic Number Facts Student Book pp. 7–8

BLMs 3, 44, 45, 46 & 47

During this week look for students who can: • automatically recall addition, subtraction, multiplication and division facts • explain and use the relationship between addition and subtraction facts, and also between multiplication and division facts • identify appropriate strategies to use when solving mathematical problems. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources paper folded into eighths, cards with ‘Yes’ on one side and ‘No’ on the other, paper to make class books, Word, PowerPoint, BLM 3 ‘10-minute Challenge’, BLM 44 ‘Tables Chart 1’, BLM 45 ‘Tables Chart 2’, BLM 46 ‘Tables Grid’, BLM 47 ‘100 Grid’ Maths Talk Model the following vocabulary in discussion throughout the week: plus, minus, multiplied by, divided by, brackets, order of operations, finaldigit patterns, BODMAS

Whole Class Focus — Introducing the Concept Number Fact Pairs Write a number fact on the whiteboard, e.g. 6 × 8 = 48. Ask, ‘What number fact could be a pair to this one?’Write out the range of eligible number facts, i.e. 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 48, 8 + 8 + 8 + 8 + 1 1 8 + 8 = 48, 8 × 6 = 48, 6 of 48 = 8, 8 of 48 = 6, 48 ÷ 6 = 8, 48 ÷ 8 = 6. Discuss how recognising relationships between number facts can help to solve 1 problems, e.g. knowing that 6 × 8 = 48 can help to solve 6 of 48. Give students a piece of A4 paper folded into eighths. Have them write a different multiplication or division fact in each square. Play ‘Bingo’. Hold up a number card between 0 and 100. If this number is the answer to a number fact a student has written down, the student can cross out the fact.The first student to cross out all their number facts wins. How Fast Are You? Give each student a copy of BLM 3 ‘10-minute Challenge’. Explain that students must solve all of the problems accurately in the shortest time they can. Have students time themselves and note down in the appropriate place the time they have taken. If any students need tables practice before undertaking the challenge, supply them with copies of tables charts on BLMs 44 and 45 and have them fill out BLM 46 ‘Tables Grid’. Unit 2 Fantastic Number Facts

27

Think about It Give each student a card with ‘Yes’ on one side and ‘No’ on the other. Invite two students to be the callers for this game. One caller 1 states a problem, e.g. 9 of 81, 7 lots of 8. The other gives the answer to the problem. The remaining students hold up their cards showing ‘Yes’ if the answer was correct and ‘No’ if it was incorrect. Change roles frequently. Discuss the strategies students have developed for quickly recalling the answers to tables facts. Operation Order Write this problem on the whiteboard: 3 × (4 + 6) – 16 ÷ 4 = ? Allow time for students to solve it. Invite individuals to show how they worked out their answers. Ask, ‘How did you know which part of the problem to solve first?’ Introduce or review the term BODMAS, an acronym of a rule for ordering the completion of operations in a problem, i.e. ‘Brackets Of Division, Multiplication, Addition, Subtraction’. The parts of the problem in brackets are always done first, followed by the multiplication and division (in either order), then the addition and subtraction (in either order.) Repeat with other problems, discussing which part of the problem to solve first in light of BODMAS. Using Tables Quickly review number facts by calling out a range of them and having students record the answers. (Vary the types of problems to include multiplication, addition, subtraction, and division.) Write on the whiteboard a story problem involving more than one operation. For example, ‘I made four trays of muffins. Each tray had eight muffins on it. I burned four of the muffins and had to throw them out. Six friends were coming for afternoon tea. We shared the muffins equally between us. How many muffins did each of us eat?’ Allow time for students to work out the answer in their heads. Ask, ‘Which tables could we use to help solve this problem?’ Invite a student to underline the part of the problem that tells them to use multiplication. Continue, focusing on other parts of the problem. Repeat.

Small Group Focus — Applying the Concept Focus Teaching Group • Reviewing BODMAS Review BODMAS. Guide students to solve problems using BODMAS. It could help to write solutions to different parts of a problem above the appropriate place in the problem (see margin). Have 15 – 5 = 10 students work independently in pairs to devise similar problems for their 12 + 3 – 5 = 10 partners to solve. 4 × 3 + 6 ÷ 2 – 5 = 10 • Tricky Tables Have students list any tables they have difficulty remembering. Promote group discussion about strategies that could help. Have students work independently to record on small cards the strategies they could use to help remember these tables. Invite them to keep these cards in their pockets and take them out every time the bell goes to remind themselves of the strategies. At the end of a week have students test each other to see how effective this strategy has been. • Tables Patterns Give each student a 100 grid (BLM 47). Ask students to shade all the numbers in the nine times multiplication table. Ask, ‘What pattern can you see in the final digits of the numbers you have shaded?’ Draw out the pattern, i.e. counting backwards from 9. Ask students to add both digits in each of the shaded numbers. Discuss the results. Ask, ‘What other final-digit patterns do you know in other tables? How could you use these patterns to remember the tables?’ Have students work independently to explore and record final-digit patterns in other multiplication tables.

28



Know Your Number Facts (Student Book p. 7) the Student Book page.

Have students complete

Tables Challenge Have students create their own 10-minute challenge using Word.They will need to complete both a problem page and an answer page.These can be collated to make a ‘Tables Practice’ file for all students to use to develop speed and proficiency with tables facts. Alternatively, 10minute challenges could be collated into a class book and copies stored in plastic pockets for students to access as needed. Concentrate Have students work in cooperative groups to make related number facts cards (e.g. 5 × 7 = 35, 35 ÷ 5 = 7) to use to play ‘Concentration’. Students shuffle the cards and place them face down in an array. They take turns to turn over two cards at a time. If the cards are a number-fact pair the student takes both cards and has another turn. If not, the cards are turned face down again. Play continues until all cards have been won. Players then count their cards and the player with the most cards wins. BODMAS (Student Book p. 8) Have students complete the Student Book page. When finished, students could make their own BODMAS problem cards for others to solve. Encourage those making the problem cards to demonstrate on the back of the card how the problem should be solved.The cards can be stored and used for quick practice sessions. Writing Problems Have students make slides for a PowerPoint slide show, each containing a story problem involving at least three operations. Students could include buttons on each slide with drop-down solutions and explanations of the problem. Or they could write their problems for inclusion in a class book.

Whole Class Share Time Discuss number facts that students find difficult to remember. Invite students to share their strategies for remembering them. (For example, student knows 8 × 8 = 64.They use this to work out 9 × 8 = 72 by adding 8 to 64.) Ask students to reflect on strategies they will use in the future. Now I know …

Discuss the strategies students used to develop their 10-minute challenges. Have groups exchange card sets and sort them into matching pairs. Talk about the pairs they have made, highlighting any interesting number facts used. Invite several students to pose to the class the problems they have written on cards. Have them explain which parts of the problems they would solve first and why. Review the slide show/book. Talk about the words students used to indicate the operation needed. List such words on a chart, e.g. some words that indicate multiplication are ‘lots of ’, ‘groups of ’ and ‘times’.

Unit 2 Fantastic Number Facts

29

unit

Number Patterns

3


Number and patterns

BLMs 4, 75, 76 & 77

During this week look for students who can: • identify patterns in numeric problems • continue number patterns • explain number patterns • predict how a number pattern will continue based on an understanding of how the pattern works. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources six-sided dice, wooden cubes marked ‘– – + + × ×’, ten-sided dice, twentysided dice, card, Word, Kid Pix Studio Deluxe, BLM 76 ‘Grid Paper’, 1 BLM 77 ‘ 2 -cm Grid Paper’, BLM 4 ‘Shortcuts to Patterns’, BLM 75 ‘Isometric Dot Paper’ Maths Talk Model the following vocabulary in discussion throughout the week: pattern, element, repeating, look for patterns, final-digit patterns, continue the pattern, explain the pattern

Whole Class Focus — Introducing the Concept

In

5

2

7

4

1

3

Out

9

3 13 7

1

5

In and Out Write a table on the board as shown in the margin. Say, ‘I had a number machine. The numbers in the top row of the table are the numbers that I put into the machine. It did the same thing to each of these numbers, and the numbers in the second row are the ones that came out. What did my number machine do?’ Allow time for students to think about the problem. Ask, ‘What could have been done to 5 so that it would come out as 9?’ Discuss some of the possibilities, e.g. 5 + 4 = 9. Say, ‘Could all these numbers have been generated by adding 4?’Test this theory on some of the other numbers. Try students’ other suggestions. (One way to generate these numbers is: double the input number and take away one to give the output number.) Pattern Tricks Write on the board, 0 + 1 + 2 =, 1 + 2 + 3 =, 2 + 3 + 4 =, 3 + 4 + 5 =. Allow time for students to solve the problems. Ask, ‘Can you see a pattern here? What is it?’ Direct students to consider any relationship they can see between the second addend and the answer to each problem, i.e. the answer is three times the second addend. Ask, ‘Why do you think this happens? Would it be true if we added any three consecutive numbers?’ Allow time for students to test this theory. Write, a + b + c = 300, or use shapes to represent each number. Ask, ‘What numbers would “a”, “b” and “c” represent to make this true?’ (Answer: 99, 100, 101.) Repeat.

30


1st 2nd 3rd 4th 5th 50th 100th 3

7

11

15

19

Teacher’s Rule Draw a table on the whiteboard as shown in the margin. Ask, ‘What is the sixth number in this pattern? How could you describe this pattern to someone else? How could you get the 50th number in this pattern as simply as possible?’ Draw out the need to find a pattern governing each number in the sequence, i.e. the first could be generated using the formula 1 × 4 – 1 = 3, the second 2 × 4 – 1 = 7, etc. Test this in the case of other numbers. Repeat for another similar pattern, e.g. 3, 6, 12, 24. Shape Patterns Using grid paper (BLM 76 or 77) create a pattern by shading in progressive shapes. Invite a student to continue your pattern. Ask, ‘How did you know what comes next?’ Have students work in pairs, each creating their own patterns for a partner to continue. Shaking Hands Ask, ‘If there were three people in the room and each person shook hands with everyone else, how many handshakes would there be?’ Have three students act this out. Model drawing a tree diagram to demonstrate the hand-shaking that would take place. Ask, ‘What would happen if there were four/five people in the room? Can you see a pattern to help us to work out how many handshakes there would be if everyone in our room today shook hands with everyone else?’

Small Group Focus — Applying the Concept Focus Teaching Group • Make a Pattern You will need a six-sided dice and a wooden block (dice) marked with ‘– – + + × ×’. Choose a starting number, e.g. 10. Roll the two dice twice, and use the number and symbol thrown each time to form a pattern beginning with your starting number, e.g. start with 10, throw ‘× 2’ and ‘– 6’ to make the pattern, 10, 14, 22, 38, 70, etc. Discuss this pattern. Have students work independently to make their own patterns in the same way. They could record these in individual pattern books with each pattern on a left-hand page and its explanation on the right. • No Two the Same Show students a numeric pattern with a level of difficulty appropriate to the group. Ask one student to continue the pattern. Ask another to explain how the pattern works. Ask a third student to begin a second different pattern. Have students work in cooperative pairs to play the ‘Pattern Game’. To play, students take turns to form a numeric pattern for their partner to continue. The partner then explains the pattern and begins a pattern of their own to be continued and explained by the first student. No two patterns may follow the same rule. For example, the pattern, 22, 24, 26, 28, follows the same rule as the pattern, 1, 3, 5, 7 (produced by adding two), so would be disallowed if the latter pattern had already been used. • Pattern Detectives Have students roll four ten-sided dice and record the numbers thrown, e.g. 1, 6, 7, 4. Ask, ‘Can you continue this number progression to create a pattern?’ (The progression begins with the following operations: + 1, + 5, + 1, – 3. Continue this pattern to make, 1, 6, 7, 4, 5, 10, 11, 8.) Ask, ‘What would come next in this pattern?’ Have students work independently to create their own patterns by rolling four ten-sided dice. Encourage them to use a range of operations to devise their patterns. More advanced students could work with twenty-sided dice. Unit 3 Number Patterns

31


Find the Rule (Student Book p. 9) Have students complete the Student Book page.When finished, they could record their own ‘In and Out’ number patterns to be collated and made into a class book. A team could work together to write an answer page to go in the back of the book. Shortcuts to Patterns (BLM 4) Copy BLM 4 onto card. Cut out the cards and place multiple copies of each at one of six work stations around the room. Have students work in cooperative teams to visit each work station and identify the shortcut to each pattern, i.e. the rule that creates it. Number Patterns (Student Book p. 10) Have students complete the Student Book page. When finished, students could generate their own patterns by shading cells in tables in Word, or using stamps in Kid Pix Studio Deluxe. Polygon Patterns Provide students with grid paper (BLM 76 or 77) or isometric dot paper (BLM 75) on which to create their own polygon patterns. Have them write a description of how their patterns work. Alternatively, students could create their patterns using the shading tools and tables in Word, or shape tools and stamps in Kid Pix Studio Deluxe. Pleased to Meet You Have students work in cooperative groups to work out how many handshakes would take place in the class if everyone shook hands with everyone else. Have them record their solutions. Units 1–3 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 11).

Whole Class Share Time Discuss the thought processes needed to generate ‘In and Out’ number patterns. Ask, ‘What was the first thing you had to decide? Then what did you do?’ Invite individuals to share their number cards. Ask the class to identify the rules used. Discuss each of the work station cards. Have students share their strategies, e.g. looking for a pattern, making up an equation. For each card ask, ‘Did anyone work out the rule that produced this pattern? How would you use this rule to make a later number in the pattern?’ Today I learnt …

Invite discussion about the patterns students identified on the Student Book page. Ask, ‘What did you need to think about to understand each number sequence? Could you use this to predict another number in the sequence?’ Have students display their patterns for other students to view. Talk about the range of patterns displayed. Have students comment on patterns they found interesting. Have each group share its strategies for solving the problem. Discuss any patterns observed. Ask, ‘Could we use this pattern to determine how many handshakes would take place if there were 50 people in our classroom?’

32


unit

4 Chance and data

Choosing Graphs Student Book pp. 12–13

BLMs 5, 60, 76 & 77

During this week look for students who can: • represent data collected using pie (sector) graphs, line graphs, bar (column) graphs and picture graphs • analyse and present findings about data sets they have collected and presented • identify the features of different graphs • select the appropriate type of graph to present data according to its purpose • read and analyse pie (sector) graphs, line graphs, bar (column) graphs and picture graphs. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources newspapers, a box of fruit juice, thermometers, coloured beads and bead thread, a range of brands of potato chips including ‘light’ chips, brown paper bags, grid paper (BLM 76 or 77) photocopied onto acetate sheets, flywire mesh, Excel, BLM 5 ‘Hourly Temperature’, BLM 60 ‘Graph Paper’ Maths Talk Model the following vocabulary in discussion throughout the week: graph, pie (sector) graph, line graph, bar (column) graph, picture graph, data, visual representation, axis, x-axis, y-axis, key, title, plotting points, scale

Whole Class Focus — Introducing the Concept Bar (Column) Graphs Show students a bar (column) graph from a recent newspaper, enlarged or copied onto an overhead projector transparency. Ask, ‘What does this graph tell us?’ Analyse the data. Ask, ‘What kind of data is best represented using a bar (column) graph?’ Have the class decide on a topic for investigation. Raw data can quickly be collected using a tally sheet, e.g. students’ favourite TV show/football team, etc. Model constructing a bar (column) graph using this data. Determine the scale of the axes first. Pie (Sector) Graphs Show students the nutritional information on a box of fruit juice. Demonstrate how to enter the data into a spreadsheet using Excel. Show students how to convert this into a pie (sector) graph. Print out the graph and discuss the information it gives. Ask, ‘What does this fruit juice contain most of? How much sugar does it contain?’ Repeat this, having students consider nutritional information on other lunch items. Have them use the information to make data tables and pie (sector) graphs in Excel. Unit 4 Choosing Graphs

33

Line Graphs Before class, have students measure the outside temperature at half-hourly intervals over a whole day. Videotape the weather segment from the previous night’s news. Show to students. Focus on the line graph giving the temperature range in the preceding 24 hours. Ask, ‘What was the lowest/highest temperature during this time? When was the greatest increase in temperature?’ Discuss the kind of data that is best represented using a line graph. Demonstrate plotting a line graph using the data found on BLM 5 ‘Hourly Temperature’. Analyse this. Picture graphs Enlarge a picture graph found in a recent newspaper or magazine. Ask, ‘What does a picture graph show us? Why is it helpful to use small pictures to represent this data? Why is there a half picture in this part of the graph? What does each picture on the graph represent?’ Comparing Graphs Review the range of graphs studied. Ask, ‘What are the features of a line/bar (column) graph? How does a picture graph present information?’ Discuss where and when different types of graphs are best used.

Small Group Focus — Applying the Concept Focus Teaching Group • Everyday Graphs Give each student a recent newspaper and have students browse for graphic material.Talk about the types of graphs found. Ask, ‘What does the information on the x-axis show you? What does the title of the graph tell you? Why has the writer chosen to use the graph as part of the article?’ Have students work independently to cut out and display a range of graphs from the newspapers, labelling them to show their features. • Making Pie (Sector) Graphs Have students take 100 beads at random from a bucket of mixed coloured beads. Have them sort the beads by colour and then thread them in colour groups on the one thread, e.g. all the blue beads, then the yellow beads, then the red beads, etc. Demonstrate how to make a circle with the beads and place this onto paper. Use it to create a pie (sector) graph by tracing around the circle, marking its centre and then drawing lines from the centre to the points on the circle where the colours change. Have students work independently to use their bead necklaces to make their own pie (sector) graphs, and to analyse the information contained in the graphs. Students could record this using spreadsheets and graphs in Excel. • Choosing a Format Refer students to data that the class has collected and entered into a spreadsheet on Excel. Have students present this data in a range of graphic forms, i.e. a pie (sector) graph, bar (column) graph, line graph, etc. Have them consider each of their graphs. Ask, ‘How easy is it to understand the data when it is presented as a pie (sector) graph? Which of the graphs presents the information most clearly? Why?’ Discuss the pros and cons of each type of graph. Have students work independently to present data about their own families using the most appropriate type of graph.


34

Potato Chips Provide a selection of different brands of potato chips, brown paper bags and grid paper photocopied onto acetate sheets. First, label individual paper bags with each brand and type of chip to be used in the experiment. Then have students select a potato chip of a similar size from each different brand and type, and place these chips correctly in the


labelled bags. The experiment involves comparing the area of fat stain produced when a single potato chip of each brand is crushed inside its paper bag. This can be measured by placing the acetate sheet over the stain and counting the squares on the grid. Have students create a bar (column) graph (BLM 60, 76 or 77) to display their data, then analyse and record it. Breakfast Cereal (Student Book p. 12) Have students complete the Student Book page. Students could then further explore nutritional information on food packaging. Or they could collect further data and use Excel to represent it as a pie (sector) graph. Daily Temperature (Student Book p. 13) Have students complete the Student Book page.Then have them use the data previously collected about daily temperature to create a line graph, providing graph paper from BLM 60.They should analyse and record their findings. Down the Drain Have students set up an experiment to measure the rubbish that would normally go down the drain at your school. Students could make a rubbish trap by placing flywire mesh over a drain opening to catch rubbish. Have students collect and measure the rubbish caught in this trap each day, tally the rubbish and use the data to create a picture graph. Have them analyse their picture graphs and record the information. Which One Will I Use? Have students work in small groups to investigate a question of interest. Have the group collect its own data and enter it onto an Excel spreadsheet. Students could then graph the data using the graph tool in Excel to produce a range of different types of graphs. Guide students to consider which of these graphs best communicates their data. Have them share their work with the class. Unit 4 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 14).

Whole Class Share Time Have individuals present their data. Compare and contrast their results. Ask, ‘Which of the potato chips had the most fat? Are light chips really low in fat? How do you feel about eating potato chips after examining this data?’

Now I can ...

Talk about the effectiveness of pie (sector) graphs. Ask, ‘What sort of data is most effectively represented in a pie (sector) graph? Why? Is a pie (sector) graph a good way to represent changing temperature throughout the day or types of food you eat in one day? Why or why not?’ Have students share their line graphs with the class. Discuss the data. Have students share their data. Ask, ‘Which type of rubbish is most likely to go down the drain? How much of it goes down our drain each week? How much rubbish goes down our drains altogether?’ Discuss strategies for reducing this amount. Have groups share their data. Question their choice of visual representation, e.g. ‘Why did you choose to use a pie (sector) graph? Why not a line graph?’

Unit 4 Choosing Graphs

35

unit




BLMs 6, 7 & 49

During this week look for students who can: • place negative and positive numbers between –10 and +10 on a number line • order positive and negative numbers from –10 to +10 • explain what a negative number is • analyse data that contains positive and negative numbers between –10 and +20. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources international weather reports (from websites or daily newspapers), paper or cloth bag, six-sided dice, coloured counters, BLM 6 ‘Positive and Negative Numbers’, BLM 49 ‘Blank Number Line’, BLM 7 ‘Finishing Order’ Maths Talk Model the following vocabulary in discussion throughout the week: positive number, negative number, integer, zero, less than, more than, number line, ones

Whole Class Focus — Introducing the Concept What Is a Negative Number? Draw a blank number line on the board with zero in the middle. Point to where a positive number would lie on the number line. Ask, ‘What would this number be? How do you know?’ Repeat with other positive numbers. Point to where –1 would be on the number line. Ask, ‘What might this number be? Are there any numbers smaller than zero?’ Allow time for students to offer their suggestions. Introduce the concept of negative numbers. Say, ‘There are just as many numbers with values less than zero as there are with values greater than zero. Numbers with values less than zero are called “negative numbers”.We write negative numbers by placing a minus sign in front of them.’ Write the negative numbers in descending order from zero on the number line. Before you fill in each number ask, ‘Which number comes next? How do we write this number?’ Talk about the importance of the negative and positive signs to indicate the values of the numbers. Ordering Numbers Review positive and negative numbers. Give each student a number card cut from BLM 6 ‘Positive and Negative Numbers’. Ask students to line up to order their numbers from smallest to largest. Ask, ‘Are you in the correct order? How do you know? Why does –5 come before –4?’ Have students move around the room and at a signal stand next to a

36


partner. Say, ‘Hold up your card if it is bigger than your partner’s.’ Ask, ‘How do you know that –6 is bigger than –8? How do you know that –4 is smaller than +1?’ Brrrrr, It’s Cold! Show students daily minimum temperatures of capital cities around the world (from daily newspapers or weather-related websites). Ask, ‘Which place had the highest/lowest temperature yesterday? How do you know? What is a negative temperature?’ Draw out that negative temperatures are temperatures below 0ºC (the temperature at which water freezes at sea level). Have students order the temperatures from lowest to highest. Discuss the need to take into account the negative sign. Talk about what it would be like to be in a place when the temperature is below 0ºC. Spending Money Say, ‘I have $35 in my cheque account. I write a cheque for $45. How much money do I have left in my cheque account? What does this mean? How could I show this on a number line?’ Promote discussion about the problem, drawing out that I now owe the bank $10. Explain that this can be described as having a negative balance in my cheque account. Repeat with other similar problems. Positive or Negative Place cards cut from BLM 6 ‘Positive and Negative Numbers’ in a bag. Ask one student to select a card from the bag. Have other students identify the number by asking questions answerable only with ‘Yes’ or ‘No’. Encourage questions like, ‘Is the number lower than zero?’

Small Group Focus — Applying the Concept Focus Teaching Group • Placing Negative Numbers Give each student a blank number line (BLM 49) with zero marked at the midpoint. Ask, ‘Which two numbers are five units from zero?’ Have students mark in these numbers. Ask, ‘Which is bigger, –5 or +5? Which number is seven units from +5?’ Have students independently play the game ‘Six in a Row’. Give each student a blank number line with zero marked at the midpoint. Players take turns to roll a six-sided dice. If an even number is rolled the player moves the corresponding number of spaces in the positive direction. If an odd number is rolled the player moves in the negative direction. Players write on the number line the number corresponding to the position they land on. (For example, a player starts at 0 and throws 3.The player moves three spaces in a negative direction and writes ‘–3’ on the number line.) Play continues until one player has written six numbers in order.This player wins. • Missing Numbers Show students a number line on which one number is masked with a post-it note. Ask, ‘Which number is covered? How do you know?’ Repeat, covering a different number. Ask, ‘Which of these numbers is the biggest?’ Give each student a blank number line with zero marked at the midpoint. Guide students to cover a position on the number line for their partner to identify, then work independently to make their own missing number book. • True or False Give students a number line displaying numbers from –10 to +10. Say, ‘I am going to make some statements about this number line. Tell me if each is true or false.’ Present students with statements such as, ‘The number that is eight units to the left of 3 is –5 (True). Minus 4 and +3 are seven units apart on the number line (True). Minus 6 and –3 are one unit apart on the number line (False).’ Talk about why each statement is true or Unit 5 Positive and Negative Numbers

37

false. Have students work independently to write their own true and false statements based on the number line, then exchange their statements with a partner who must pronounce them true or false.


Negative and Positive Numbers Provide students with a blank number line (BLM 49) and ask them to mark on it whole numbers from –10 to +10. Pairs can use this to play the game ‘Minus 10 to Plus 10’. Players need a sixsided dice and a different-coloured counter each. Players place their counter at zero on the number line and take turns to throw the dice. If an even number is thrown players move the corresponding number of steps towards +10; if an odd number is thrown players move towards –10. Players must say the name of each number as they land on it or forfeit their next turn. Play continues until one player reaches either –10 or +10 and wins. Ordering Positive and Negative Numbers (Student Book p. 15) students complete the Student Book page.

Have

Temperature (Student Book p. 16) Have students complete the Student Book page. Students may then like to explore websites that give information about world temperatures. Have students find the places that recorded the world’s lowest and highest temperatures. Alternatively, students could construct a model of a thermometer that could measure temperatures in the range discussed in the whole class activity. Profit or Loss Set up a mini market in your classroom. Have students design a product to sell, e.g. bookmarks, penholders, paper fans, etc. Establish with students the costs of the materials they will use to make their products, e.g. one sheet of paper costs 10 cents, sticky tape costs 20 cents per 20 cm, etc. Have them make their products, sell them at the market and complete a profit or loss sheet to record either their positive or negative totals. Finishing Order (BLM 7) Establish work stations around the room with the activities found on BLM 7. Unit 5 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 17).


Today I understood …

Review positive and negative numbers. Show students a blank number line with zero at the midpoint. Point to different places on the number line and ask, ‘What would this number be? Is it bigger or smaller than zero? How do we write this number? How do you know?’ Discuss what students have learned about negative numbers. Ask, ‘Why are negative numbers always smaller than positive numbers? Is zero a positive or negative number?’ Ask, ‘What was the lowest/highest temperature you found? How did you write this temperature? Do we ever have temperatures like this in Australia?’ Have students report to the class on their profit or loss at the market. Encourage them to use mathematical workings to show why they made a profit or loss. Discuss the roll of negative and positive numbers in this. Have all students report their final scores. As a class, order these from highest to lowest. Promote discussion about any negative scores.

38


unit

6 Space

Lines and Angles Student Book pp. 18–20

BLMs 8, 9 & 56

During this week look for students who can: • construct, identify and explain the features of a range of lines (vertical, horizontal, parallel, diagonal, perpendicular, curved and zigzag lines) • use protractors to measure angles • identify and draw right angles, obtuse (blunt) angles and acute (sharp) angles. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources cloth bag, overhead projector and overhead-projector protractor, pattern blocks, protractors, craft sticks, magazines, advertising material, computer image banks, rulers, chart paper, Kid Pix Studio Deluxe, Word, BLM 8 ‘Line and Angle Cards’, BLM 9 ‘Make a Protractor’, BLM 56 ‘Blank Clock Faces’ Maths Talk Model the following vocabulary in discussion throughout the week: lines, vertical line, horizontal line, parallel lines, diagonal line, curved line, zigzag line, right angle, obtuse (blunt) angle, acute (sharp) angle, degrees

Whole Class Focus — Introducing the Concept Lines Brainstorm words used to describe lines, i.e. vertical, horizontal, parallel, diagonal, curved, spiral, zigzag, perpendicular, etc. Hold up line cards from BLM 8 ‘Line and Angle Cards’ and have students try to represent these types of lines with their bodies. Give each student a line card and ask them to find ten things in the room that display or incorporate the type of line on their card. Ask, ‘How did you know whether or not a line was vertical? How could you be sure that line was horizontal?’ Brainstorm other objects that would incorporate the lines you have discussed. Copycat Have all students draw a series of different and intersecting lines. Have one student describe the lines they have drawn so that another can try to copy this design on the whiteboard. When finished, compare the two drawings.Talk about the language used to help the drawer to reproduce the original drawing. List appropriate instructions on the board. Have students form pairs and repeat the activity independently. Lucky Lines Cut up line cards from BLM 8 ‘Line and Angle Cards’ and place them in a cloth bag. Have students choose a type of line and find an example of it in the classroom, i.e. a student might stand next to a table leg, identifying its edge as a vertical line. Ask students at random to call out the type of line they have chosen and show where it is represented in the classroom. Ask, ‘How do you know that is a vertical line? What are the features of a vertical line?’ Take a card from the cloth bag. All students who Unit 6 Lines and Angles

39

have chosen the type of line written on the card win one point. Continue until one student has scored five points. Using a Protractor Review the types of angles students already know, e.g. right angles, acute (sharp) angles and obtuse (blunt) angles. Display an overhead-projector protractor. Explain how the protractor is used to measure angles and demonstrate this. After several demonstrations ask students to explain what to do as you measure. Ask, ‘Where do I place the protractor? How do I ensure that the protractor is in the correct position to measure the angle, i.e. centre of protractor lined up with the point of the angle, and zero line covering one line of the angle being measured. Measuring Corners Give students pattern blocks and protractors. Say, ‘Look at your pattern blocks. How big do you think are the angles of the corners?’ Have students record their predictions. Demonstrate measuring one such angle. Have students measure the angles of their pattern blocks and record them. Ask, ‘Which of these shapes have acute (sharp)/obtuse (blunt) angles? How many degrees were these angles?’ Making Angles Review the angles featured in the angle cards cut from BLM 8. Give each student two craft sticks. Hold up an angle card and have students form the angle using their craft sticks, then check it using protractors. Discuss their strategies for constructing particular angles, e.g. to make 45º you could form a right angle and then halve it.

Small Group Focus — Applying the Concept Focus Teaching Group • On Track Shuffle line cards from BLM 8. Turn over the first card and read it aloud. Ask, ‘What are the features of this type of line?’ Draw these out. (For example: a horizontal line always runs parallel to or level with the horizon; a vertical line always runs at right angles to the horizon; a diagonal line is not level with or at right angles to the horizon; parallel lines are two or more lines that go in exactly the same direction, are always exactly the same distance apart and never meet.) Have each student work independently to make a secret trail. Have students shuffle a set of line cards, turn them over and then use them as instructions for drawing the secret trail. Students then exchange their trails with a partner who must write the instructions for following the trail (i.e. list in order the sequence of lines reproduced). • Measuring Angles Before class make cards displaying drawn angles appropriate to students’ ability. Demonstrate the use of a protractor to For less advanced measure one of the angles. Ask, ‘Where do I place the protractor? Where students limit the angles to do I line up the zero line on the protractor? How do I write the multiples of 45º. For more advanced students include angles that are measurement and show that it is in degrees?’ Guide students to multiples of 5º or 10º. measure another of the angles, then have them work independently to measure and record the remaining angles. • Clocks Give each student a model analogue clock, or have students draw times on BLM 56 ‘Blank Clock Faces’. Ask them to show ‘3 o’clock’. Have students measure the angle formed by the clock hands at this time. Ask, ‘At which other times do the hands of the clock form a right angle?’ Allow time for students to explore this problem. Have them work independently to investigate and record the times at which the clock hands form angles of 45º degrees.

40



Finding Lines Have students browse through magazines, advertising material or computer image banks to find pictures featuring the types of lines discussed in the whole class activity. Paste these pictures onto charts, label the lines featured and display the charts. Looking at Lines (Student Book p. 18) Student Book page.

Have students complete the

Making Protractors Have students make their own simple protractors using BLM 9 ‘Make a Protractor’. Students can then use these protractors to measure and record the angles of various classroom objects. Angle Tangle (Student Book p. 19) Have students complete the Student Book page. Students could then construct lines using the line tool in Kid Pix Studio Deluxe or Word. Have them try to make angles of exactly 30º, 60º, 45º, 90º, and 135º. These could be printed out and measured using protractors. Or, students could measure lines or angles they have drawn by conventional means. Mystery Shapes (Student Book p. 20) Have students complete the Student Book page. Making a Masterpiece Then have students work in groups of four to create their own masterpieces with lines and angles. Give each group a set of cards made from BLM 8 and each student chart paper, ruler, protractor and felttipped pens. Have students shuffle the cards and place them face down. To begin, all students draw a vertical line. They then take turns to take a card from the pile. This card tells them the line or angle they must add to their masterpiece, and they may add only this line or angle on their turn. Have them record on a separate piece of paper what they have added. Once used, cards are returned to the bottom of the pile. When students believe their masterpiece is finished they may colour it in and give it a title. Display the masterpieces with labels giving the artist’s name, the title of the masterpiece and the lines and angles used. Unit 6 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 21).

Whole Class Share Time Review students’ charts. Ask, ‘What kinds of objects tended to have vertical and horizontal lines? What kinds were most likely to have curved lines? Which lines were hard to find?’ Today I could not understand …

Invite students to share their work from the Student Book. Ask about the lines they identified, e.g. ‘Where did you find a vertical line? How did you know it was a vertical line?’ Have students explain how to use their protractors. Record this as a set of instructions on a class chart. Have individuals share the shapes they made on the Student Book page using their protractors. Ask, ‘How many degrees are there in the angles of triangles?’ Draw a triangle on the board showing two of its angles, e.g. 90º and 25º. Ask, ‘How many degrees will the third angle measure?’ Have students view the class masterpieces. Talk about the lines and angles used in the pictures. Ask, ‘Which lines/angles made your masterpieces most interesting? Which were the most difficult to include?’ Unit 6 Lines and Angles

41

unit

Addition



BLMs 10 & 11

During this week look for students who can: • use mental processes, written methods and calculators to add numbers to 999 999 • identify when addition could be used in everyday life • verbalise the thought processes used to solve addition problems. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources classified sections from newspapers, ten-sided dice, travel brochures, chart paper, counters, PowerPoint, BLM 10 ‘Number Mat’, BLM 11 ‘Lucky Dice’ Maths Talk Model the following vocabulary in discussion throughout the week: addition, carry, sum, more, add, plus, increased, altogether, total

Whole Class Focus — Introducing the Concept Choosing Addition Ask, ‘When do we use addition in everyday life?’ List suggestions on the whiteboard. Ask students to think of one addition problem and its solution in an everyday context. (For example, Ms Moneybags bought a car for $12 374. Her insurance cost $1 345. How much did she have to pay altogether?) Have students share their problems in small groups. Have them list the words that tell them the problem will require the use of addition, e.g. ‘sum’, ‘more’, ‘add’, ‘plus’, ‘increased’, ‘altogether’, etc. How Will I Do It? Ask, ‘Which methods could you use to solve addition problems?’ List these. Ask, ‘When would you use each method?’ Draw out the need to select a method based on the type of numbers involved. Ways of Doing It 1 Mental methods: breaking Write 32 403 + 47 869 on the whiteboard. Ask, ‘Could you solve this numbers up, rounding numbers, problem mentally, or would you use a written method or a using known facts, etc. calculator?’ Draw out that different people approach the same 2 Written methods: vertical setting out, estimate then check, checking problem in different ways. Solve the problem mentally, talking using subtraction. students through the process. Demonstrate solving the problem by 3 Using a calculator. writing it vertically. Repeat, varying the size of the numbers. Targeting 10 000 Enlarge BLM 10 ‘Number Mat’. Stick the number mat on the whiteboard. Ask, ‘Which two of these numbers have a sum closest to 10 000?’ Discuss strategies for solving this problem, e.g. looking for numbers close to 5 000; identifying the difference between a chosen number and 10 000, and looking for a number close to that difference. Ask, ‘Which three of these numbers has a sum closest to 10 000?’ Model adding the numbers vertically. Explain what you do as you carry numbers. As you go, invite students to explain what you should do next and why.

42


+ ______ 19 473

The Answer Write on the whiteboard the unfinished equation shown in the margin. Say, ‘This is the answer. What could the missing numbers be?’ Allow time for students to work out a range of possible solutions. Invite individuals to share their solutions and discuss the thought processes they used. Repeat. Going Camping Say, ‘Imagine you are going camping for two days in the wilderness and must take everything you need with you.’ Brainstorm necessary items and list suggestions. Ask, ‘How much do you think each item would cost?’ Have students either research actual costs of camping equipment or estimate the cost of each item. Review the class equipment list. Ask, ‘How much will this equipment cost us altogether? How could we work it out?’ Model using formal vertical addition to work out the total cost of the tent, sleeping bag and sleeping mat. Have students work in pairs to calculate the rest of the camping costs. Review these as a class, focusing on the methods students used to work out the answer. Addition Stories Provide students with copies of the classified section of a daily newspaper including house auction results and cars for sale. Say, ‘I bought a car and house on the weekend. Altogether they cost me $375 000 (a sum worked out by using real details from the paper).Which car and house did I buy?’ Allow time for students to search the paper for the answer. Discuss their solutions, focusing on their use of operations such as addition and subtraction. Allow for students to come up with different solutions and discuss this. Ask, ‘What other addition stories could you make up from the classified section of the newspaper?’

Small Group Focus — Applying the Concept Focus Teaching Group • Lucky Dice – Addition Review the vertical addition process with students ensuring that they understand how to carry. Vary the Less advanced students range of numbers added according to their needs. Guide could use MAB blocks. More advanced students students to play ‘Lucky Dice – Addition’ in pairs. Pairs will could add decimal numbers. need a copy each of BLM 11 ‘Lucky Dice’ and a ten-sided dice. • My Overseas Trip Relate an addition story using numbers appropriate to students’ skill level. (For example, ‘I was planning a four-week trip to England. I found out that my airfare would cost $3 495, my accommodation would cost $10 349 and hiring a car would cost $4 025. I allowed $1 400 per week spending money. How much would my holiday cost?’) Guide students to solve the problem using formal vertical addition. Then have them work independently to write their own addition stories. Provide access to the Internet so that students can look up real everyday prices. Alternatively, provide the classified sections from newspapers, travel brochures, etc. Have students record their addition stories as PowerPoint slide shows or on charts. • Explaining Addition Write an addition problem vertically on the whiteboard. Ask, ‘How would you explain how to complete this problem to someone who had never done addition before?’ Brainstorm the types of words they could use, e.g. ‘put with’, ‘borrow’, ‘carry’, ‘estimate’, ‘doublecheck’. Have students work independently to pose their own addition problems and then work out how to explain the addition process to a novice. Encourage students to use diagrams and other visual representations as part of their explanation. Unit 7 Addition

43


Everyday Addition Have students work in small groups to create PowerPoint slide shows to demonstrate how addition is used in everyday life. Encourage them to provide examples of formal addition and to highlight the key words that tell them to use addition. Alternatively, groups could make their presentations on large charts or in class books. It All Adds Up (Student Book p. 22) Student Book page.


10 000 Have students play ‘10 000’ in pairs. Give each student a copy of BLM 10 ‘Number Mat’ and three round counters.To play, players take turns to use one of their counters to flip their other two counters, Vary the game by having students add three, four one at a time, onto the number mat (as in Tiddlywinks). The or more numbers. Or vary the target number, two numbers on which the counters land are then added.The e.g. if students were adding five numbers, player with the sum closest to 10 000 wins one point. (Note that the target number could be 40 000. the sum can be greater or less than 10 000). The player with the most points at the end of the game wins. Finding Answers (Student Book p. 23) Have students complete the Student Book page. They may then like to make up more missing-digit problems.These could be collated as a slide show or a class book. Going on Holidays Have students choose a holiday destination and work out how much it would cost to go there for one week. Have them use Internet sites to research the costs of airfares, accommodation, car hire, food and entertainment. Alternatively, provide students with travel brochures containing this information. Students should show their working out using formal vertical addition. Have them set out how much each aspect of the holiday would cost, e.g. travel expenses, food expenses, entertainment, etc. Spend $500 000 Have students use the newspaper classifieds to write their own shopping problems. They should spend about $500 000. Have them record these using formal addition.

Whole Class Share Time Ask, ‘Why do you need to be able to add numbers? When in your everyday life might you have to use this skill?’ View the slide shows or charts/class books students have made. Discuss their examples. 5_ _9 7 + ______ 48 3_ _ _ _ 53 5

Today I really liked …

Have students write a reflection on their preferred method of solving addition problems. Have individuals share their reflections with the class. Write on the whiteboard the equation in the margin. Ask, ‘How could you solve this problem? What do you need to think about? What known facts could you use?’ Discuss students’ experiences in completing the Student Book page and creating their slide show/class book page. Choose a range of students to share their holiday costings. Ask, ‘What did you need to consider when choosing a holiday? How much would your holiday cost? How much would it cost if you went for two weeks?’ Ask, ‘How many different ways did you find to spend $500 000?’ Promote discussion about the addition strategies students used. Have students share their shopping problems with the class.

44


unit


Subtraction Student Book pp. 24–25

BLMs 10 & 11

During this week look for students who can: • use mental processes, written methods, and calculators to subtract numbers in the range 0 to 999 999 • identify when subtraction could be used in everyday life • verbalise the thought processes used to solve subtraction problems. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources classified sections from daily newspapers, ten-sided dice, advertising brochures from furniture and electrical stores, magazines, chart paper, round counters, PowerPoint, BLM 10 ‘Number Mat’, BLM 11 ‘Lucky Dice’ Maths Talk Model the following vocabulary in discussion throughout the week: subtract, difference, less than, minus, decrease, fewer than, reduce, have left

Whole Class Focus — Introducing the Concept Choosing Subtraction Ask, ‘When do we use subtraction in everyday life?’ List suggestions on the whiteboard. Ask students to think of one subtraction problem and its solution in an everyday context. (For example, Mr Moneybags had $12 354. He went shopping and bought a wide-screen TV for $5 799 and a digital video camera for $4 278. How much money did he have left?) Have students share their problems in small groups. Have students list the words that tell them the problem will require the use of subtraction, e.g. take away, subtract, difference, less than, minus, decrease, fewer than, reduce, have left, etc. List these on the whiteboard. Choosing a Method Ask, ‘Which methods could you use to solve subtraction problems?’ List these on the whiteboard. (Examples: Mental methods: breaking numbers up, rounding numbers up or down, using known facts, counting on/back, etc. Written methods: vertical setting out, estimate then check, checking using addition facts. Using a calculator.) Ask, ‘When would you choose to use each method?’ Draw out the need to select a method based on the type of numbers involved and personal preference. Write 47 869 – 32 403 on the whiteboard. Ask, ‘Could you solve this problem in your head using a mental method? Or would you need to use a written method and write it down vertically? Should you use a calculator?’ Draw out that different people would approach the same problem in different ways. Solve the problem mentally, talking through the steps you take. Demonstrate solving the problem by writing it vertically. Repeat, varying the size of the numbers. Unit 8 Subtraction

45

5 000 Enlarge BLM 10 ‘Number Mat’. Stick the number mat on the whiteboard. Ask, ‘Which two of these numbers have a difference closest to 5 000?’ Talk about the strategies that could be used to solve this problem. Repeat with other like problems. Model subtracting the numbers on the whiteboard using vertical written subtraction method. Explain what you do as you decompose numbers. As you work invite students to explain what you should do next and why. Find the Number Say, ‘On my calculator I entered a five-digit number, then a subtraction sign, then another five-digit number. The answer was 36 508. What could my two numbers have been?’ Promote discussion about the thought processes needed to solve the problem. (For example, ask, ‘What is the biggest number that I could have entered? What number would I have to subtract from this to get the answer?’) Subtraction Stories Provide students with copies of the classified section of a daily newspaper including house auction results and cars for sale. Say, ‘I have $60 000. Could I spend it all without receiving any change? What could I buy?’ Allow time for students to search the paper to find out which items could be bought. Promote discussion about their solutions, focusing on their use of operations such as addition and subtraction to solve the problem. Allow for students to come up with different solutions and discuss these. Ask, ‘What other subtraction stories could you make up from the classified section of the newspaper?’

Small Group Focus — Applying the Concept Focus Teaching Group • Lucky Dice – Subtraction Review the vertical subtraction process with students ensuring that they understand how to decompose numbers when necessary. Vary the range of numbers subtracted according Less advanced students could use MAB blocks. More advanced to their needs. Guide students to play ‘Lucky Dice – Subtraction’ students could subtract decimal in pairs. Pairs will need a copy each of BLM 11 ‘Lucky Dice’ and a numbers. ten-sided dice. • My House Relate a subtraction story using numbers appropriate to students’ learning needs. (For example, I have saved $17 982. I need to furnish my house. I need to buy a fridge, washing machine, lounge suite, dining suite, bed and TV. Once I have bought all these items how much money will I have left?) Provide advertising brochures from white goods and furniture stores. Guide students to solve the problem using formal vertical subtraction and assist them with anything they find confusing.Then have students work independently to write their own subtraction stories. You could provide access to the Internet so that students can look up real everyday prices. Alternatively, provide the classified sections from newspapers, advertising brochures, magazines, etc. Have students record their subtraction stories as Powerpoint slide shows or on charts. • Explaining Subtraction Write a subtraction problem vertically on the whiteboard. Ask, ‘How would you explain how to complete this problem to someone who had never done subtraction before?’ Brainstorm the types of words they could use, e.g. subtract, difference, less than, minus, decrease, fewer than, reduce, have left. Have students work independently to pose their own subtraction problems and then work out how to explain the subtraction process to a novice. Encourage students to use the diagrams and other visual representations as part of their explanation.

46



Everyday Subtraction Have students work in small groups to create Powerpoint slide shows to demonstrate how subtraction is used in everyday life. Encourage them to provide examples of formal subtraction and to highlight the key words that tell them to use subtraction to solve the problems. Alternatively, groups could make their presentations on large charts or in class books. Aiming for Zero (Student Book p. 24) Student Book page.


Make a Difference (Student Book p. 25) Have students complete the Student Book page. Zero or Bust Have students play ‘Zero or Bust’ in pairs. Give each student a copy of BLM 10 ‘Number Mat’ and three round counters. To play, players take turns to use one of their counters to flip their other two counters, Vary the game by varying the target number according to the one at a time, onto the number mat (as in Tiddlywinks). The numbers needs of students. More advanced on which the counters land are subtracted one from the other. The students could work towards a player with the difference closest to zero wins one point. (Note that the negative target number. difference could be a negative number).The player with the most points at the end of the game wins. Missing Numbers Have students work in cooperative pairs to find as many solutions as they can to the problem, ‘Which two five-digit numbers have a difference of 36 508?’ Look for students who work systematically, using addition or other strategies to solve the problem. Spending $900 000 Have students use the newspaper classifieds to write their own subtraction problems showing how they would spend $900 000. Have them record these using formal subtraction notation. Units 7–8 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 26).

Whole Class Share Time Ask, ‘Why do you need to be able to subtract numbers? When in your everyday life might you use this skill?’ View the slide shows or the charts/class books students have made.Talk about the examples used. + ______ 51 947

Today I made …

Ask students to write a reflection on their preferred method of solving subtraction problems. Have individuals share their reflections with the class. Write on the whiteboard the equation in the margin. Say, ‘This is the answer. What could the missing numbers be?’ Allow time for students to work out possible solutions to this problem. Invite individuals to share their solutions with the class. Promote discussion about the experiences students had in completing the Student Book page. Choose a range of students to share the solutions they found. Discuss the various strategies used. Ask, ‘How many different ways did you find to spend $900 000? Promote discussion about the subtraction strategies students used to solve the problem.

Unit 8 Subtraction

47

unit

Using Data to Answer Questions

9 Chance and data


BLM 60 & 77

During this week look for students who can: • pose questions about issues of concern that could be solved using mathematical means • suggest ways to collect data • use a range of data-collection techniques to investigate questions • create graphs of varying types • analyse and present data, providing arguments for the meaning of the data. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources school canteen price list, sticky dots, Excel, Kid Pix Studio Deluxe, BLM 60 1 ‘Graph Paper’, BLM 77 ‘ 2 -cm Grid Paper’ Maths Talk Model the following vocabulary in discussion throughout the week: posing questions, collecting data, spreadsheet, graph, bar (column) graph, pie (sector) graph, line graph, data, interpreting data, presenting data, what does your data show?

Whole Class Focus — Introducing the Concept Playing Around Ask, ‘Do we have enough playground equipment for students in the school? How could we find out?’ Discuss ways of doing this. Ask, ‘What data would we need to collect to work this out? Who would we need to ask?’ Draw an action plan for collecting the data. Identify a range of tasks that small groups of students could undertake. A Fair Share Ask, ‘Is our playground used fairly by all students? How could we find out?’ Discuss what would constitute fair usage of the playground. Consider the data that needs to be collected. Draw out the need to identify who uses which area of the playground, for how long, and whether or not the users consider this fair. Discuss the need to consult different groups in the playground, e.g. ‘Do girls and boys have the same opinion? Do the younger students in the playground get a fair share?’ Assign tasks to groups. Have them collect the data over the course of several days. Please note: Some of this may have to be done during recess. Food for Thought Display an enlarged copy of the school canteen price list. Ask, ‘How could we classify the food on the canteen menu?’ e.g. healthy/junk, hot/cold food. Ask, ‘If we could add three new food items to our canteen menu, what should they be?’ Ask students to work in small groups to decide on the three new items, then present their

48


ideas to the class. List these on the whiteboard. Ask, ‘How could we find out which of these items would be the most popular?’ Choose a datacollection method. Measuring Usage Ask, ‘How could we work out who uses the computers in the school the most?’ List students’ suggestions. Discuss the merits of each data-collection method. Draw out the need to consider different aspects of the question, e.g. ‘Do we measure computer usage by the amount of time the computer is used, or by the amount of work done? Should we consider individual usage or class usage? To make a survey fair, over what period of time should data be collected?’ Posing Problems Have students work in small groups to list current issues they think need to be addressed by the school. Have each group report to the class. List all suggestions on a large piece of paper. Have each student vote by placing a sticky dot next to each of the two issues they feel are the most important. Ask, ‘Which of these issues is the most important to students in our class? How can we tell? Which is the next most important?’ Ask students to work in small groups to determine what questions might be asked and what data collected to further investigate these issues.

Whole Class Focus — Introducing the Concept Focus Teaching Group • Posing Questions Ask, ‘What things about our school do we need to find out more about? What questions could we pose to investigate these issues?’ Have students brainstorm possible subjects for investigation. List these on the whiteboard. Guide students to pose questions about one of these subjects. Have pairs work independently to pose questions about other subjects on the list. • Collecting Data Remind students of methods of data collection already used by the class. Discuss each of these. Ask, ‘When would you collect data using a survey? a questionnaire? What sort of data would you collect using a table? What other ways are there to collect data?’ Ask students to pose a question they would like to investigate, e.g. What is the most popular sport in our class? Have students work independently to develop and then use a data-collection method to further investigate their question. • Presenting Data Have students consider data collected by the class prior to the lesson. Show students how to enter this data onto an Excel spreadsheet. Guide them to explore the various ways to represent it graphically. Ask, ‘Which way of representing this data is the clearest? Why? When would you use a pie (sector) graph? a bar (column) graph? a line graph?’ Have students work independently to select the most appropriate visual representation to use to present other class data.


Playground Equipment Have students work in small groups to collect data about different aspects of playground equipment use. Have each group prepare their data to present to the class. Sharing the Playground Ask students to consider the data they have collected about playground usage. Have them work in small groups to explore various ways to present this data using spreadsheets and graphs in Excel. Have each group prepare a report on their findings, including a justification for using the form of visual representation they chose. Unit 9 Using Data to Answer Questions

49

Happy Valley Canteen (Student Book p. 27) Have students complete the Student Book page. When finished, they could explore, using a range of visual representations and spreadsheets (in Kid Pix Studio Deluxe or Excel), ways of presenting the data they collected about adding items to the canteen menu. Alternatively, students could make visual representations of the data on paper using drawing and art materials. Computer Usage (Student Book p. 28) Have students complete the Student Book page. They could also investigate the usage of classroom computers. Encourage them to collect and present the data, and then to use it to put an argument to the class. Finding out More Have students work in small groups to explore one of the issues raised in the whole-class investigation. Have groups collect data on this issue and present it in graphic form (BLM 60 or 77).They should also use the data to make recommendations about how to address the issue. Unit 9 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 29).

Whole Class Share Time Ask each small group to share its data. Ask, ‘How does this data answer our original question? Do we have enough playground equipment for students in the school?’Talk about how to present the data to the whole school. Ask, ‘Could we take any further action as a result of collecting and analysing this data? Allow time for each group to present its data. Ask, ‘What are your findings about playground usage? Is our playground used fairly by all students? If so, how do you know? If not, what could be done to make it fairer?’ Discuss the visual representations used to present the data. Ask, ‘Why have you chosen to use a line graph? How else could the data have been presented?’

Today I discovered …

Consider students’ graphs. Ask, ‘If we could add three items to our canteen menu, which would be the most popular? Is popularity the only issue to consider when adding items to a school canteen menu?’ Invite students to present their case on the subject of computer usage in the class/school, using the data they have collected to support it. Ask, ‘Why do you feel that the computers are fairly/unfairly shared in our class? What data do you have to support this opinion? What could be done to make computer usage fairer?’ Invite each group to share its data, its interpretation of the data and its recommendations. Ask, ‘What have we found out about this issue? What does the data show? What recommendations on this issue could we make to the Principal or the Junior School Council? How could we use the data we have collected to persuade people of the need to address this issue?’

50


unit

10 Measurement

Running on Time Student Book pp. 30–31

BLMs 57, 58 & 59

During this week look for students who can: • read and interpret timetables • read and calculate information from calendars • identify how long it will be until a specified event • make own timetables and schedules. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources local bus and train timetables, acetate sheets, calendars (including those for the next ten years), Publisher, Word, BLM 57 ‘Blank Calendar’, BLM 59 ‘My Timetable’, BLM 58 ‘Blank Month’ Maths Talk Model the following vocabulary in discussion throughout the week: date, timetable, rows and columns, scheduled, depart, arrive, time taken, duration

Whole Class Focus — Introducing the Concept Bus Timetables Photocopy a local bus timetable onto an overhead projector sheet. Show the timetable to students. Show them how to read and interpret the bus timetable. Explain how the timetable is organised into rows and columns, and demonstrate how to use it. Ask questions about the schedule, e.g. ‘Which bus would get me to school on time? What is the first bus I could catch after school? How long does it take to get from (place name) to school?’ Ask one student silently to choose a destination to which they would like to travel and the time they would want to catch the bus. Have the others ask questions to determine which bus the student is catching and to which destination. Encourage questions like, ‘Does it take more than twenty minutes to reach your destination? Would you be on the bus at lunchtime?’ The student may answer only ‘yes’ or ‘no’ to these questions. Going to Town Photocopy the local train timetable onto an overhead projector sheet. Show the timetable to students and demonstrate how to read it. Guide students to read the timetable for themselves and explain how it is organised. Ask, ‘If I wanted to get to Melbourne Central (or other appropriate destination) by 10.30 a.m., which train would I have to catch? If I caught the 3.30 p.m. train, how long would it take me to get to Flinders Street? If I caught the 6:45 a.m. train at Melbourne Central, at what time would I reach the station closest to school?’ Unit 10 Running on Time

51

Making Timetables With students, plan a maths activity session during which eight teams each complete six activities. Draw up a timetable. Ask, ‘How would we make sure that each team had time to complete each activity? How would our schedule change if the activities took different amounts of time to complete?’ Have students work in small groups to select some activities and draw up a timetable. Have groups share their timetables. Discuss the optimum layout of timetables for ease of reading. Using Calendars Show students a copy of the current year’s calendar. Ask, ‘For what purpose do we use calendars? What information do calendars contain?’ Give each student a copy of both the current and following years’ calendars. (These should be year-to-a-page calendars, which can be made quickly using Publisher, or fill in BLM 57 ‘Blank Calendar’.) Ask, ‘How many more weeks until your birthday? Whose birthday is less than 100 days away?’ Talk about quick ways to work out the answers to these questions without counting each day, such as adding the number of days in each month, adding 7 for each week that passes, etc. Repeat, searching out other information on the calendar, e.g. ‘How many more days are there in this term/year? How many more days until Christmas? What will be the date in exactly 150 days?’ Christmas Day Review how to read calendars. Ask, ‘On which date is Christmas Day each year? When is Anzac Day? When is Australia Day? Which other dates do we need to know?’ List them. Ask, ‘On which day does Christmas Day fall each year?’ Discuss students’ answers. Ask, ‘How can we use calendars to work this out?’ Show students how to make calendars for future years using Publisher or BLM 57 ‘Blank Calendar’. Talk about the pattern that emerges when investigating the day on which Christmas Day falls over subsequent years.

Small Group Focus — Applying the Concept Focus Teaching Group • Reading Timetables Provide students with a copy of the local train or bus timetable. Guide them to read the timetable. Point out the need to read across rows or down columns to find out how long a journey will take, when the train or bus will arrive at a given destination, etc. Have students ask each other questions about the timetable, e.g. ‘What time would you need to catch the train to be in the city by 10.30 a.m.?’ Have students work independently on their own to make a mystery travelling book in which they write clues, based on the train/bus timetable, to an imaginary train/bus they caught and its destination. Have them exchange books with a partner. Partners try to find out each other’s mystery train/bus and destination. • My Week Show students the class timetable. Ask, ‘How long is morning recess? Where is this information on the timetable?’ Guide students to work out the time allocated to other activities on the timetable, e.g.‘How long is art class? How much time is there between the end of lunchtime and the time you go home?’ Demonstrate drawing up a timetable for a different class. Focus on the need to show when each activity happens and how much time is allocated to it. Have students work independently to make a timetable showing everything they do in one week. They could do this using ‘Table’ in Word, or multiple copies of BLM 59 ‘My Timetable’. • Our School Calendar Have students list events that happen throughout the school year, e.g. the beginning and end of terms, the school fete,

52


graduation, the school sports, etc. Ask, ‘When do these events happen?’ Guide students to identify the dates of several of these events. Have students work independently to create their own school calendar. This can be done using multiple copies of BLM 58 ‘Blank Month’, using Publisher, or by conventional means.


On the Buses Have students plan and record an imaginary bus trip around the local neighbourhood. Provide each student with a copy of the local bus timetable. Students should record details of each leg of their journey: the time they will catch the bus, the amount of time they will spend at each destination and what they will do there, the time they will get home/back to school. Encourage students to work out how long the trip will take altogether, and its cost. Catching the Train (Student Book p. 30) Have students complete the Student Book page. When finished, students could use the local train timetable to plan a trip to the city. Encourage students to explain how their time will be spent during the day, including what time they will catch the train, arrive at their destination, leave their destination and arrive back at the station from which their journey began. If possible have the class go on a train journey to practise reading timetables. Going to the Movies (Student Book p. 31) Have students complete the Student Book page. When finished, students may like to research actual movie timetables using the Internet. Have students use this information to plan a movie marathon of their own. My Calendar Have students make their own calendars using Publisher, identifying special dates, e.g. family birthdays, sporting events, regular activities such as swimming lessons or scouts. Alternatively, students could make their calendars using multiple copies of BLM 58 ‘Blank Month’.They could also be encouraged to plan for significant events and write their plans on the calendar, e.g. ‘Mark on the calendar when you should start saving up for your mother’s birthday present? Mark the day on which you should go shopping to buy it or start making it.’ My Birthday Have students use Publisher to find out on which day their birthday will fall for the next ten years. Alternatively, provide students with calendars for the next ten years so that they can work out the date on which other specific events will fall in future years. Students could work in groups to find out in which year each person’s birthday will next fall on a Saturday.

Whole Class Share Time Have students share the trips they planned. Discuss the different methods they used to record their trips. Today I found out ...

Review how to read train timetables. Ask, ‘How can you work out when a train leaves a particular station? How can you work out how long the journey will take?’ Have individuals share their planned journeys. Ask, ‘Why are timetables useful? What is the most useful way to set out a timetable? Why?’ Have students share the movie marathon they planned. Talk about the use of calendars to plan and keep track of events. Promote discussion about why it might be useful to know on which day a specific date will fall. Have students share what they found out about their future birthdays. Unit 10 Running on Time

53

unit

Time

11 Measurement


BLM 56

During this week look for students who can: • read analogue and digital clocks to the nearest minute • convert 12-hour clock time to 24-hour time • use stopwatches to measure and compare time taken to complete a given task • rank times from fastest to slowest • calculate time elapsed. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources stopwatches, eggtimers (brought from home), a dozen eggs, analogue clock faces, flight schedules (from the Internet), dry sand, paper cups, bowls, calendars (year-to-a-page), model digital clock, BLM 56 ‘Blank Clock Faces’ Maths Talk Model the following vocabulary in discussion throughout the week: second, minute, hour, in 24-hour time, analogue clock, digital clock, time, quarter, o’clock, time elapsed

Whole Class Focus — Introducing the Concept How Fast? Show students how to use a stopwatch. Have them practise timing a partner standing up and sitting down ten times or reciting the alphabet backwards. Ask, ‘Why might we need to measure accurately how long it takes to complete an activity in everyday life?’ List students’ suggestions, e.g. sporting events, cooking, games. Ask, ‘Do people with longer legs run faster than people with shorter legs? How could we find out?’ Draw out the need to measure the length of each person’s legs and how fast they can run over a set distance. Cooked to Perfection Show students a range of eggtimers. Ask, ‘What period of time does each of these eggtimers measure?’ Allow time to check the duration of each eggtimer using a stopwatch or the second hand on an analogue clock. Ask, ‘Would these eggtimers help you to cook a perfect egg?’ Boil a dozen eggs. Use an eggtimer and an analogue clock to time them. Take one egg out of the boiling water every 30 seconds, use indelible pen to write on it its cooking time, then place it in cold water.When all the eggs are out, cut them open to see how much they have cooked. Ask, ‘Which egg is cooked the way you like it? How long does this take? Do these eggtimers measure the right amount of time?’ Discuss individual preferences for boiled eggs.

54


What’s the Time, Mr Wolf? Using an analogue clock, review telling the time to the nearest minute. Focus on strategies for telling the time quickly and easily, e.g. remembering that ‘35 past’ is also ‘25 to’, or that there are five minutes between each number on the clock. In pairs, have students play ‘What’s the Time?’. Give each student an analogue clock face, or have them fill in the clock faces on BLM 56 ‘Blank Clock Faces’. Students secretly set their own clocks to a time of their choice. They then take turns to ask a question (answerable only with ‘Yes’ or ‘No’) to identify the time shown on their partner’s clock.The first player to succeed wins a point. How Long Does It Take? Ask, ‘For how long are you awake each day?’ Discuss ways of working out the answer, taking into account 60 minutes to the hour. Ask, ‘Who is awake for the longest period of time? Who has the most sleep?’ Have students list everything they do from the moment they get up until they go to bed, and estimate how long each activity takes. Ask, ‘Are you awake for long enough to complete all these tasks?’ 24-hour Clocks Show students a flight schedule (from an airline company website). Focus on times after 12 noon. Ask, ‘What time is this plane leaving? Why is the time written as 13:07?’ Explain how the 24-hour clock works. Ask, ‘Why might we need to use a 24-hour clock?’ Demonstrate converting 24-hour time to 12-hour time and vice versa. Present problems like, ‘I went to meet my friend at the airport. She left Sydney at 12.00 and arrived in 1 Melbourne 1 2 hours later.What time did I see on the “Arrivals” board?’ Gaining Time Say, ‘One week ago I set my watch to the correct time. But I know that my watch gains three minutes each day. My watch now says the time is… (Show watch running 21 minutes fast.) How can I work out what the correct time is?’ Encourage students to share their strategies. Discuss the merits of each. Review aspects of time with students, e.g. seven days in a week, 60 minutes in an hour. Ask, ‘What time would my clock show if it had been losing four minutes each day?’

Small Group Focus — Applying the Concept Focus Teaching Group • Telling the Time Revise reading time to the nearest minute on an analogue clock. Discuss strategies students could use, e.g. counting on or back from ‘o’clock’, ‘quarter past’, ‘half past’ and ‘quarter to’; relating the time to the nearest five-minute interval and adding or subtracting the More advanced students could include on their written cards appropriate number of minutes. Have students work independently times from the 24-hour clock. with a partner to make pairs of clock cards, one card showing a time on a clock face, and the other, the same time in words. These cards could be used to play ‘Concentration’. • 24 Hours Review 24-hour time. Guide students to convert 12-hour time into 24-hour time. Ask, ‘What do I need to do to 19:30 to work out what time it would be on a 12-hour clock? How do I work out what 3:29 p.m. is in 24hour time?’ Have students work independently to find out how many places they can fly to in 24 hours, using the Internet to find out departure times from their nearest city airport and arrival times at these destinations. • 45 Seconds Review the use of the stopwatch. Have students work in pairs with a stopwatch to see if they can guess when 45 seconds have elapsed. One partner says ‘Go’ and starts the stopwatch; the other closes their eyes and says ‘Stop’ when they think 45 seconds are up. Have students work independently to measure and record the things they can do in 45 seconds. Unit 11 Time

55


Long Legs versus Short Legs Have students work in cooperative groups to measure the length of their legs and how quickly they can run over a distance of 50 metres. Give each group a stopwatch. When groups have finished timing each other, have individuals add to a class chart the length of their legs and their time over 50 metres. Eggtimers Provide students with sand, paper cups and stopwatches. Have them build their own eggtimers (as shown in margin) to measure the time it takes to cook their perfect egg. They can vary the length of time measured by varying the amount of sand in the cup. Have them check the duration of their timers using stopwatches or analogue clocks. Telling the Time (Student Book p. 32) Have students complete the Student Book page. Have them make their own ‘What Is the Time?’ quiz by writing the clue to a particular time on one side of a page, and drawing a clock showing this time on the back. Make a class book. My Day Have individuals work independently to create a chart showing all the things they do in 24 hours, including analogue clock faces to show what time they start and finish each activity, and its duration. Then have them check how long they actually do spend on each activity. Changing Times (Student Book p. 33) Have students complete the Student Book page. They could then use the Internet to explore the flight schedules of other airlines to plan an interstate or overseas trip, stating their departure and arrival times and how long the entire journey would take. Qantas can be contacted at Website 11 (BLM 79). Alternatively, students could log their daily activities using a 24-hour clock. Losing Time Have students explore this problem: ‘Hassan set his digital watch at noon on the 28th February. But Hassan’s watch loses 90 seconds every day.What time will his watch show at noon on the 28th March?’ Provide each student with a calendar and model of a digital clock to assist them.They could record their strategies.

Challenge students further! Ask them to work out what time Hassan’s watch would show if it had lost 11 seconds per hour since 28th February.

Units 10–11 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 34).

Whole Class Share Time Have students consider the data collected. Ask, ‘Do people with longer legs run faster than people with shorter legs? How do you know?’ Discuss. Have students demonstrate their eggtimers and explain how they ensured that the eggtimers would measure the right length of time. Share the class book with students. Discuss the clues they have used. Today I really liked …

Have students share their charts. Compare the time individuals spent on the same activity. Ask, ‘How did you work out how long you spent sleeping?’ Focus on the total amount of time students spent during the day on their activities. Ask, ‘Did your total activities take up exactly 24 hours?’ Discuss the reason for discrepancies, e.g. miscalculation of time taken. Ask, ‘Why do we need 24-hour clocks? How do we convert 12-hour time into 24-hour time and vice versa?’Talk about students’ international trips. Ask, ‘What do you know about time that helped solve this problem?’ List students’ suggestions. As they share their strategies, have them say which information about time they used.

56


unit


Numbers, Numbers, Numbers! Student Book pp. 35–37

BLMs 47 & 76

During this week look for students who can: • determine factors of numbers • identify prime numbers • identify and construct square numbers • identify and construct cube numbers • identify one-step, two-step and three-step palindromes. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources calculators, Centicubes, chart paper, Word, BLM 47 ‘100 Grid’ (enlarged), BLM 76 ‘Grid Paper’ Maths Talk Model the following vocabulary in discussion throughout the week: factors, prime number, square number, cube number, palindrome, factor of, multiple of, can be divided by

Whole Class Focus — Introducing the Concept Looking at Prime Numbers Introduce or review prime numbers, e.g. ‘A prime number is a counting number that can only be divided by itself and one.’ Ask, ‘Is one/two a prime number? Which other numbers between zero and 10 are prime numbers? How can you prove this?’ Have students explore numbers between 10 and 20. Provide calculators to assist. Looking at Factors Introduce or review the term ‘factors’, e.g. ‘The factors of a number are all the whole numbers that can be divided evenly into that number.’ Ask, ‘How many factors does 24 have? How could we work it out?’ Guide students to solve the problem. Draw out the need to be systematic. Examine factor pairs. Say, ‘If we know that 8 is a factor of 24, we also know that 3 is a factor of 24, because 8 × 3 = 24.’ Square Numbers Show students Centicube towers (4, 8, 12, 16). Ask, ‘Which of these towers can be arranged to make squares?’ Allow time for students to predict the answer and explain their predictions. Invite individuals to try to form the Centicube towers into squares. Examine the 4-Centicube square. Ask, ‘How many Centicubes high is the square? How many Centicubes wide is it?’ Record this on the whiteboard. Repeat with the 16-Centicube square. Ask, ‘What number do you think will be the next square number? Why?’ Cubes Show students cubes made with Centicubes (2 × 2 × 2, 3 × 3 × 3, 4 × 4 × 4). Ask, ‘How many Centicubes do you think I used to make each of Unit 12 Numbers, Numbers, Numbers!

57

these cubes?’ Allow time for students to work this out by making their own cubes. Re-examine each of the cubes. Ask, ‘How many Centicubes wide/high/deep is this cube?’ Record this in a table. Ask, ‘Can you see a pattern emerging?’ Discuss the relationship between the height, width and depth of the cubes and the number of Centicubes needed to make them. Palindromes Write on the whiteboard: 33, 141, 6226, 403 304. Ask, ‘What do these numbers have in common?’ i.e. they can all be reversed and remain the same number. Say, ‘These numbers are called palindromes. A palindrome is a number or word that reads the same backwards as forwards, e.g. 1991, radar, pop, 22, 89 655 698. Find other examples. What Am I? Review square numbers, cube numbers, prime numbers, factors and palindromes. Hold up a number card between 0 and 100. Ask, ‘Is this a square/cube/prime number? Is it a palindrome? What are its factors? How do you know?’ Hand out number cards between 20 and 100. Ask students to determine whether their number is a prime, square or cube number, or a palindrome. Say, ‘Stand up if your number is a prime number.’ Consider those numbers. Say, ‘Stand up if your number is a palindrome.’ Ask, ‘Did anyone stand up for both prime number and palindrome? Are there any other numbers that fit into more than one classification?’

Small Group Focus — Applying the Concept Focus Teaching Group • Finding Factors Give each student a 100 grid (BLM 47). Ask students to mark a coloured dot on every number with a factor of 2. Point out that all numbers said when counting by 2s can also be divided by 2, i.e. 2 is a More advanced students factor of these numbers. Now have students mark a coloured dot on could work with numbers higher numbers said when counting by 3s, 4s, 5s, etc. Have them consider the than 100. number 24. Ask, ‘How many factors does 24 have? What are they? Have students work independently to record the factors of other numbers. • Square Numbers Give each student a copy of BLM 76 ‘Grid Paper’. Ask them to shade a 2 × 2 square. Ask, ‘How many squares have you shaded?’ Guide students to write this as an equation (2 × 2 = 4). Repeat, asking More advanced students students to shade a 3 × 3 square. Ask, ‘How many squares would I shade could explore triangular numbers. if I made a 4 × 4 square?’ Discuss the thought processes needed to make this prediction. Have students work independently to shade and explain other square numbers. Provide extra grid paper as needed. • Favourite Numbers Have students write down their favourite number greater than 20. Ask, ‘What can you tell me about this number?’ Discuss what students already know. Ask, ‘Is it a prime number, square number, cube number or palindrome? Does it have other attributes?’ Ask them to think about its factors (if any). Have students work independently to make a poster about their favourite number to record all they know about it.


Prime Numbers to 100 (Student Book p. 35) Have students form groups to complete the Student Book page. Extend this activity by asking students to find prime numbers between 100 and 200. Factors (Student Book p. 36) Have students complete the Student Book page. Factor Factory Enlarge a 100 grid (BLM 47). Have each student write their name on a different number on the 100 grid. Have students investigate and

58


record the factors of this number. Then have them select and investigate a new number. Continue until all numbers have been investigated. Squares, Squares, Squares Have students work independently to find as many square numbers as they can, shade them on grid paper It may be useful to provide calculators to assist some students, and describe them using equations, e.g. 11 × 11 = 121. Alternatively, and concrete materials to students could create grids in Word and use the shading tool to create assist others. the square numbers. Curious Cubes Have students work independently to build and record other cube numbers. Encourage them to generate the numbers using a calculator, and to look for emerging patterns. Finding Palindromes (Student Book p. 37) Student Book page.


Five Numbers Have students play in groups of four with number cards from 1 to 100 (use BLM 47). One player shuffles the cards and deals five cards to each player. Players order their cards from lowest to highest number. Players then add consecutive numbers, i.e. the first and second numbers, second and third numbers, etc., to generate four new numbers. These numbers are scored, as follows: square numbers are worth two points; cube numbers, three points; prime numbers, two points; palindromes, one point. After each round, players add their score for that round to their running total. When the deck has been used up, cards can be reshuffled and used again.The first player to gain 50 points wins. Unit 12 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 38).

Whole Class Share Time Create a class chart of all the prime numbers students have found, ordered from smallest to largest. Ask, ‘What do you notice about this list? How many prime numbers do you think there would be from 100 to 200?’ Have students arrange their factors sheets in order from zero to 100. Ask, ‘Which of these numbers can be divided only by one and itself? What do we call these numbers?’ Remove the prime numbers from the display. Ask, ‘Which numbers have the most factors? Which numbers have 4 as a factor?’ Discuss strategies students used to answer these questions. Today I could not understand …

List in a table all the square numbers students found. Ask, ‘What is the smallest square number? What is the next square number?’ Examine the table. Ask, ‘How could we work out which number comes next on our list?’ Ask, ‘What is the smallest cube number? What is the largest cube number you found? How did you work it out? How do you work out any cube number?’ List the range of cube numbers found. Ask, ‘What is a palindrome? Which numbers reversed and added together make palindromes?’ Ask, ‘What was the highest score for one round? What was the lowest score? Which were the best numbers to get?’

Unit 12 Numbers, Numbers, Numbers!

59

unit

Area and Perimeter

13 Measurement


BLMs 12, 76 & 77

During this week look for students who can: • accurately measure lengths in millimetres, centimetres and metres • estimate and measure the perimeter of polygons • investigate area using square metres • use the working method of A = L × W to calculate the area of polygons. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources balls of string, metre rulers, 30-cm rulers, rope of various lengths, trundle wheels, masking tape, newspaper, card (10 × 10 cm, small cards and a variety of rectangles), tape measures, six-sided dice, BLM 12 ‘Guessathon’, 1 BLM 76 ‘Grid Paper’, BLM 77 ‘ 2 -cm Grid Paper’ Maths Talk Model the following vocabulary in discussion throughout the week: length, width, perimeter, area, spaces, distance around, square units, composite shapes, metres, centimetres, estimate, the regular polygons

Whole Class Focus — Introducing the Concept A Metre or Not? Pass a ball of string to four students and ask each student to estimate and then cut one metre of string from the ball. Lay the lengths of string next to each other on the floor and ask, ‘Why are there differences in the length of each piece of string? How could we ensure that each length of string was exactly one metre?’ Model measuring and cutting one metre of string using a metre ruler or 30-cm ruler. Compare this length to students’ estimated lengths. Ask the four students now to measure and cut new metre lengths of string. Rope It Up Place a 20-metre piece of rope on the floor. Ask one student to measure the length of the rope using a trundle wheel. Tape the ends of the rope together using masking tape. Ask another student to make a rectangle with the rope. Ask, ‘What do you estimate the length of each side to be? What do you think the total length of all sides is?’ Repeat, with rectangles of different proportions. Build up a table identifying patterns and relationships. It’s in the News Have students work in groups of four to make a square metre from newspaper. Provide 30-cm rulers and tape. Ask, ‘What measurement strategies did you use to construct your newspaper square metre?’ Talk about the processes each group used, and the most efficient way of measuring and constructing the square metre. Draw out the need to have right-angled corners.

60


Area = Length x Width Use masking tape to mark out a one-metre square on the floor. Ask, ‘How many students could stand in this space?’ Have as many students as possible stand in the square. Count them. Ask, ‘Is this a fair way to measure the area of the square, by the number of students who can stand in it? Why, or why not?’ Discuss fair ways of measuring area. Show students a 10 × 10 cm piece of card. Ask, ‘How could we use this card to measure the area of the square? How many card squares would it take?’ Invite students to measure the area using the cards. Emphasise the need for each piece of card to be butted up to, but not overlapping, the piece next to it. Have one student measure the length of the square and another its width. Ask, ‘How long is our square? How wide is it? Could we use this information to work out how many 10 × 10 cm squares we would need to measure its area?’ Comparing Area Draw on the whiteboard a rectangle 20 × 10 cm. Model working out the area of the rectangle using the formula ‘Area = Length × Width’. Rule lines 1 cm apart on the rectangle to demonstrate that each of the units is a square centimetre. Divide students into small groups and give them 30-cm rulers. Have each group draw a rectangle with an area of 200 cm2. Ask, ‘What did you need to think about to create a rectangle with exactly this area? What do you know about the factors of 200 that helped you to make the rectangle?’

Small Group Focus — Applying the Concept Focus Teaching Group • Measuring Area Ask students to draw a square or a rectangle with an area of exactly 24 cm2. Ask, ‘What number facts would help you to work out how long each side of the rectangle should be?’ Talk about the factors of 24 and how they could be used in the formula ‘Area = Length × Width’. Have students use their rulers to draw several rectangles with an area of 24 cm2. Have students work independently to make squares and rectangles with areas of 48 cm2, 82 cm2 and 100 cm2. • The Square Metre Give students a newspaper square metre. Have them measure the perimeter of the square. Ask, ‘What is the area of this square? What is the perimeter?’ Have them cut the newspaper into two pieces and use these to make a rectangle or irregular polygon. Ask, ‘What is the area of your rectangle/polygon? What is its perimeter?’ Have students measure the perimeter. Talk about why both shapes have the same area but different perimeters. Have students work independently to investigate and record different polygons with an area of one square metre, but different perimeters. • Irregular Polygons Supply a range of cardboard rectangles. Have students select three of these and place them on a piece of paper to make an irregular polygon. Have students trace around these shapes. Ask, ‘How Less advanced students could we work out the perimeter and area of the shapes by measuring could be provided with grid paper the sides with a ruler?’ Guide students to understand that the polygons to support them in working out the area and perimeter of the were made from rectangles and that the area of each rectangle can be polygons. calculated using the formula ‘Area = Length × Width’. Have students work independently to form and trace around other irregular polygons, and to work out their areas and perimeters. Unit 13 Area and Perimeter

61


Guessathon (BLM 12) Have students work in pairs to complete BLM 12. Give each pair a copy of the BLM, 30-cm rulers, tape measures, etc. When finished, have each student add to a list on the whiteboard the most challenging object they measured. String Swap Give each student a different length of string (between 20 and 40 cm, cut in even cm) and a piece of card. Have them measure the string and then draw on the card as many polygons as they can with a perimeter the same length as the string. Students then swap cards and use the cards to estimate the length of each other’s string. A Costly Business! (Student Book p. 39) Have students complete the Student Book page. When finished, have students work in pairs to play ‘Cover the Grid’. Give each pair a copy of BLM 76 ‘Grid Paper’ and two sixsided dice. Players take turns to roll the dice and multiply the two numbers rolled. The product becomes the area of the rectangle they colour on their grid.The game continues until one student has coloured the entire grid and is declared the winner. Composite Shapes Give each student four small pieces of rectangular card of different sizes and grid paper (BLM 76 or 77). Have each student use their pieces of card to make an irregular polygon, then accurately copy this shape onto their grid paper. Students swap papers with a partner. The partner then calculates the perimeter and area of their shape and records them on the paper. Partners check the accuracy of each other’s calculations. Polygons (Student Book p. 40) Have students investigate area and perimeter by completing the Student Book page. Unit 13 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 41).

Whole Class Share Time Discuss the list of students’ most challenging objects. Draw out why it was difficult to estimate their lengths. Today I discovered …

Have individuals share their strategies for finding a range of polygons with the same perimeter but different areas. Draw out that understanding the factors of a number (i.e. using known facts) can help in this process. Discuss area. Ask, ‘When might you need to calculate area? Do any jobs require you to be able to measure area accurately? Why would this be important?’ Have several students share their composite shape with the class. Ask them to show how they calculated the area and perimeter of their partner’s shape. Discuss the strategies students used to ensure that they accurately measured both the perimeter and area of the polygons in the Student Book.

62


unit


Decimals Student Book pp. 42–43

BLMs 43, 48 & 49

During this week look for students who can: • order decimal numbers from smallest to largest • round decimal numbers up or down to the nearest hundredth • place decimal numbers on a number line, including hundredths. • use a ruler to measure to the nearest hundredth • write decimal numbers in words and explore features of decimal numbers. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources number cards from 0 to 9 with decimal points on the back, plastic ruler, overhead projector, calculators, multiple copies of a newspaper, masking tape, ten-sided dice, playing cards (picture cards removed), six-sided dice, streamers, metre rulers, supermarket catalogues, BLM 43 ‘Number Expander’, BLM 48 ‘Blank 100 Grid’, BLM 49 ‘Blank Number Line’ Maths Talk Model the following vocabulary in discussion throughout the week: decimal, decimal number, decimal point, decimal place, tenths, hundredths, smaller than, bigger than, fraction, rounding up or down, rounded to the nearest tenth

Whole Class Focus — Introducing the Concept Number Order Have students form teams of five. Give each student a number card between zero and 9 with a decimal point on the reverse side. Ask each team to form a number with four digits and a decimal point, i.e. they must choose which number to sacrifice to make the decimal point. Have teams show their numbers to the class. Ask, ‘Which group has made the largest/smallest number? How do you know?’ Have each team use their cards to make the largest/smallest number possible. Have the class order these from smallest to largest. Discuss place value, e.g. ‘Both of these numbers have a nine in them.Why is one number bigger than the other?’ Decimals Rule Place a plastic ruler on an overhead projector. Point to various markers on the ruler. Ask, ‘What is the value of this marker? How would you write it as a decimal?’ Place an object like a pencil on the overhead projector. Ask, ‘How long is this pencil?’ How do you know?’ Draw out the need to start measuring at zero. Ask, ‘How would we write that as a fraction of a metre?’ On the whiteboard, record this in both centimetres and metres, as a decimal. Focus on reading the scale on the ruler. Repeat, recording the lengths of objects as decimals. Discuss why the decimal point moves when the unit of measurement changes. Unit 14 Decimals

63

Ensure that all students can read the decimal point on the calculator.

Showing Decimals Give each student a calculator to solve this problem: 54 ÷ 8. Have one student give the answer. Ask students to find another way to make the calculator show a decimal without having to press the decimal point button. Have individuals share their findings. Decimal Hunt Have students work in teams of four. Give each team a copy of the same newspaper. Teams take it in turns to call out clues to a number they find somewhere in the newspaper, e.g. a number with a 7 in 1 the hundredths column/that rounds to three dollars/exactly 10 bigger than 99.89, etc. Other teams compete to be the first to find a number in the newspaper to match the clue. The team that wins each round provides the clue for the next.

Decimal Places Mark on the floor with masking tape a blank number line showing whole numbers and tenths, e.g. 7.00 – 7.10 –7.20 … 8.00. Have a student stand somewhere on the number line. Ask, ‘What number is To cater for students’ needs, you could change the Tom standing at? How do you know? What is the closest tenth to that range or complexity of numbers on number? How do we write that?’ Repeat, focusing on the tenths and every second or third turn. hundredths places.

Small Group Focus — Applying the Concept Focus Teaching Group • Hundredths Review place value using a number expander (BLM 43). Review tenths. Introduce hundredths. Give each student a copy of a blank 100 grid (BLM 48). Ask, ‘If the total grid equalled one, what would each square represent?’ i.e. ‘one out of 100 equal parts’ of the total grid.Write this as a common fraction. Have students shade a given number of squares. Ask, ‘How many squares have you shaded? How could you describe this as a common fraction? a decimal?’ Repeat, focusing on place value. Have students work independently to use the hundredths grid to make and record models of decimal numbers. • Deducing Decimals Write on the whiteboard a number with two decimal places. Ask, ‘How else could we write this number?’ Draw out that the number 4.63, for example, could be written as 4 + 0.6 + 0.03, or (4 × 1) + 463 (6 × 0.1) + (3 × 0.01) or 100 or 5 – 0.37 or ‘four and sixty-three hundredths’ 9.26 or 2 , etc. Repeat with other numbers, focusing on place value. Have students work independently to form numbers with two decimal places by rolling a ten-sided dice three times, then record these numbers in as many different ways as they can. • Rounding Decimals Show students a blank number line (BLM 49).Write 6 at the beginning and 7 at the end. Ask, ‘Where would you put 6.73 on this number line?’ Have one student place a mark on the number line. Have the others verify its position. Review rounding up and down. Have students mark a blank number line 4.6 at one end and 4.7 at the other. Guide them to fill in the intervening numbers. Ask, ‘What number would we get if we rounded 4.63 to the nearest tenth?’ Repeat. Have students work independently to roll ten-sided dice to form numbers with two decimal places, and then to round these numbers to the nearest tenth. These could be displayed in a table under headings, ‘Number’, ‘Rounded up to …’, ‘Rounded down to …’.


64

Bigger Is Better Have students play ‘Bigger Is Better’ in groups of four. Each group needs a deck of cards (picture cards removed, Ace represents one) and a six-sided dice. Play as follows. The dealer turns over four cards.


Players use the four digits shown on the cards to record a number that includes a decimal point wherever they wish. The dealer then rolls the dice. If it is an odd number, the lowest number wins the round. If it is an even number, the highest number wins.The winner of the round scores one point. Players choose a new dealer for each round.When all cards have been dealt, players total their scores and roll the dice again. If it is an odd number, the lowest score wins; if even, the highest score wins. Measuring up Have students work in groups of four. Give each group a paper streamer. Have students take it in turns to estimate and cut off 2metre lengths of streamer. When the whole streamer has been cut up, have students measure each length and write on it its length in metres.Then have them order the lengths from shortest to longest and work out the difference in length between each streamer and the next longest one. Calculator Stand-off Have students play ‘Calculator Stand-off ’ with a partner. To play, each player writes on a card a number with two decimal places, e.g. 3.56.Their partner then finds as many ways as they can, without pressing the decimal point button, to bring up that number as the answer on the calculator. Equations are recorded and scored. As they put in each equation, players score one point each time an operation button is pressed, e.g. (78 + 100) ÷ 50 = 3.56 scores two points. Players need to agree on a time limit for each round. At the start of each new round, a new number is written on a card. Decimal Numbers (Student Book p. 42) Have students complete the Student Book page. They could then conduct their own ‘Decimal Hunt’ using supermarket catalogues, which could be kept in a file for rainyday activities. Decimal Number Lines (Student Book p. 43) the Student Book page.


Whole Class Share Time Have individuals share the numbers they recorded during the game. Ask, ‘Which number is the biggest? How do you know? Where did you put the decimal point when you wanted to make the biggest/smallest number? Why?’ Today I understood …

Have groups of students present their streamers. Discuss lengths with similar measurements, e.g. 2.10 and 2.01. Ask, ‘Which of these lengths is longer? How do you know?’ Promote discussion about the thought processes students used to work out how to have the chosen number come up on the calculator. Have students share their answers on the Student Book page. Then have individuals share the clues they invented to the decimals (prices) in the supermarket catalogue. Review the blank number line. Ask, ‘What do each of the marks represent?’ Ask students to stand at a designated point on the number line, e.g. 7.03.

Unit 14 Decimals

65

unit

Fractions



BLMs 13, 53 & 54

During this week look for students who can: • order common fractions from smallest to largest • simplify common fractions • add common fractions • identify equivalent common fractions • make models to demonstrate fraction size • identify common fractions that are bigger than/smaller than another common fraction. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources fraction kits, six-sided dice, ten-sided dice, twenty-sided dice, Word, BLM 53 ‘Fraction Cards’, BLM 54 ‘Fraction Wall’, BLM 13 ‘Making Simplified Fractions’ Maths Talk Model the following vocabulary in discussion throughout the week: numerator, denominator, equal parts, common fraction, simplified, equivalent, smaller than, larger than

Whole Class Focus — Introducing the Concept 1

Two Fractions Write 2 on the whiteboard. Say, ‘I added two fractions and got this answer.What could the two fractions be?’ Discuss the fractions that could be added to make one half. Have students work in small groups to make as many fraction pairs as they can with this sum. Repeat. A Sum of Two Say, ‘I discovered some numbers that have a sum of two. At least one of them is a fraction. None of my numbers has decimals. What might these numbers be?’ Provide fraction kits so that students can model 1 1 1 the numbers. Demonstrate recording this as an equation, e.g. 2 = 3 + 6 + 1 4 1 + 4 . Ask, ‘How many equations with the sum of two is it possible to make?’ Focus on why there are an unlimited number of equations with fractional parts that can be added to give this sum. Finding Equivalent Fractions Have students work in groups of four. Give each group a fraction card cut from BLM 53 ‘Fraction Cards’. Have each group quickly brainstorm and record as many fractions as they can think of equivalent to the fraction on their card. Have groups share their equivalent fractions. Discuss identifying equivalent fractions, e.g. by multiplying both the numerator and the denominator of the fraction by the same number.

66


Fractions in Order Have students form groups of four. Have each group throw two six-sided dice ten times and use the two numbers rolled each time to form a fraction. Groups then order their ten fractions from Provide fraction kits to assist less able students. smallest to largest. Promote discussion about the thought processes students used to work out the relative size of each fraction. ?

?

Find the Fraction Write on the whiteboard the equation 2 = ? . Ask, ‘What could the missing numbers be?’ Provide fraction kits or fraction walls to support students. Encourage a range of answers. 100

Simplifying Fractions Write 200 on the whiteboard. Ask, ‘How could we simplify this fraction?’ Discuss the relationship between the numerator and denominator in this case. Ask, ‘What do we know about 200 and 100?’ Ask a student to demonstrate simplifying the fraction. Repeat.

Small Group Focus — Applying the Concept Focus Teaching Group • Fraction Size Have each student throw two six-sided dice to form a fraction and write this fraction on a card. Ask the group, ‘Which of your fractions is the biggest? How do you know?’ Guide students to make Vary the dice according to students’ needs, e.g. less models of these fractions using a fraction wall or other fraction kits. advanced students could use six-sided Have students work independently to form ten fractions by dice; more advanced students could throwing dice. Ask students to make models of each of these and to use ten- or twenty-sided dice. order them from smallest to largest. • Equivalence Give students a set of fraction cards from BLM 53 ‘Fraction Cards’. Guide students to model several of the fractions on a fraction wall made using ‘Table’ in Word. (Make a table with one cell per row. Select each row and split it into fractional parts using the ‘Split Cell’ feature in the ‘Table’ menu. Shade the cells to show the numerator.) Alternatively, give each student a copy of BLM 54 ‘Fraction Wall’. Talk about the size of each fractional part. Ask, ‘What happens to the size of the fraction as the denominator gets bigger? How does the numerator affect the size of the fraction?’ Have students use this understanding to predict, and then check using the table, which of a pair of fractions is the larger. Have students work independently to shade cells in the table to show equivalent fractions. • Changing Fractions Review the terms ‘numerator’ and ‘denominator’. Give students a set of fraction cards (BLM 53). Ask, ‘Which of your fractions has a denominator of two? a numerator of three? Which fraction has the largest denominator? Does this make it the smallest or largest fraction?’ Choose a fraction card and ask, ‘What would happen if we added one to both the numerator and the denominator of this fraction? Would the fraction get smaller or bigger?’ (For example, adding one to the numer3 3 4 ator and denominator of 4 gives a new fraction, 5 . Is 4 bigger or smaller 4 than 5 ?’) Have students work independently to investigate this and draw conclusions.


Question and Answer Give each pair of students a set of fraction cards from BLM 53 (‘Fraction Cards’). Have pairs work together to write question cards, the answers to which are the fractions on the BLM cards. They then exchange question cards with another group. Students take the other group’s set of question cards and match them to the fraction cards. A Sum of 10 Have students work independently to investigate making equations with a sum of ten, in which at least one of the numbers is a Unit 15 Fractions

67

common fraction or a mixed number. Have students make models of these equations and formally record them. Alternatively, students could record their equations as tables in Word. (Fractional parts of tables can be made using ‘Split Cell’ in the ‘Table’ menu.) Equivalent Fractions (Student Book p. 44) Have students complete the Student Book page. Fraction Trains Students could make fraction trains using Word to create tables with two rows. Have students split and shade cells in each table (using ‘Split Cell’ in the ‘Table’ menu) to model a fraction, then make further tables representing fractions equivalent to the first. These tables could be cut out and pasted to form trains that demonstrate a range of equivalent fractions. Alternatively, students could cut up BLM 54 ‘Fraction Wall’. Ordering Fractions (Student Book p. 45) Have students complete the Student Book page.They could use a fraction wall (BLM 54) if necessary. Missing Numbers Have students find a range of possible solutions to the ? ? equation ? = ? in which all the digits are different. Fractions Are Simple Provide each student with a ten-sided dice. Have students throw the dice four times to form a common fraction with doubledigit numerator and denominator. Students then determine whether or not this fraction can be simplified. Have them repeat this a number of times recording their fractions on BLM 13 ‘Making Simplified Fractions’. Units 14–15 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 46).

Whole Class Share Time Choose a fraction card and ask pairs to share the questions they have written to which this fraction is the answer. Discuss the different questions. Ask, ‘How did you think up this question? How did your knowledge of number facts help you?’ Have students share the models and equations they made. Ask, ‘How can you be certain that your equation equals ten?’ Have students display their fraction trains. Allow time for the class to look at each other’s trains. Ask individuals to look for equivalent fractions that they find particularly interesting, and share these with the class. Today I worked out …

Write a range of fractions on the whiteboard, all with a numerator of one. Ask, ‘Which of these fractions is the biggest/smallest? How do you know? What happens to the size of a fraction as the denominator gets larger?’ Have students share their solutions to the missing-number equations. Promote discussion about their solutions. Ask, ‘What strategies did you use to solve the problems?’ Discuss students’ strategies for simplifying their fractions. Ask, ‘What known facts did you use to predict whether or not a fraction could be simplified?’ Focus on the denominators that could not be simplified. Ask, ‘How many factors does this denominator have?’ Draw out that fractions having denominators with few factors can be harder to simplify.

68


unit


Counting and Number Order Student Book pp. 47–48

BLMs 2, 14, 15 & 43

During this week look for students who can: • order numbers from 0.01 to 999 999.99 • use counting skills to count by multiples of 10, 100, 1 000 • write numbers from 0.01 to 999 999.99 in words • continue counting patterns and identify the rule. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources card, overhead projector, overhead projector calculator, calculators, classified sections from newspapers, stopwatches, twenty-sided dice, advertising material (from supermarkets and department stores), BLM 14 ‘High or Low’, BLM 43 ‘Number Expander’, BLM 15 ‘Counting Constant’, BLM 2 ‘Lowest versus Highest’ Maths Talk Model the following vocabulary in discussion throughout the week: unit, tens, hundreds, thousands, tens of thousands, hundreds of thousands, tenths, hundredths, decimal point, smallest, largest, in order, bigger than, smaller than, pattern

Whole Class Focus — Introducing the Concept Silent Order Have students write a number between 0.01 and 999 999.99 on a card, then line up silently to order the numbers from smallest to largest. Ask, ‘Why does this number go here? Which digit did you look at to decide which number was biggest?’ Attach the ordered cards to the whiteboard. Play ‘Five Questions’. To play, one student chooses a card without saying what it is. The others ask up to five questions (answerable only with ‘Yes’ or ‘No’) to identify it. Discuss strategies that enable the card to be found within five questions, e.g. ‘Is it bigger than 500 000?’ may eliminate half of the possible choices. Using Counting Skills Review counting by 7s. Using an overhead projector calculator, demonstrate how to use the constant addition function. Have students record the last digit of each number as you To use the constant go. Ask, ‘Is there a pattern emerging? What will the last digit of addition function, punch in the the next number be?’ Now use the constant addition function starting number, then ‘+’, then the number to to count by 70s. Have students focus on the second-last digit. be added repeatedly. Then hit ‘=’ repeatedly. This will add the number repeatedly to Ask, ‘How does knowing how to count by 7s help you to count a progressive total, e.g. by 70s? Would it help you to count by 700s or 7 000s?’ Give 5 + 7 = = = =. students calculators and have them explore counting by multiples of other numbers, e.g. 8, 80, 800, 8 000, etc. In pairs, have students play ‘Guess Unit 16 Counting and Number Order

69

My Final Number’. To play, one player chooses both the starting number and the number to be added constantly, then pushes ‘=’ while their partner counts how many times the constant key is used and works out what the final number will be. Discuss the thought processes needed. Best Value Give students a page from the classified section of a newspaper (pages/papers can be different). Say, ‘Find something for sale that costs more than $10 000/less than $43.’ As students share the items they find, highlight the digits in the price that show the number to be ‘greater than 10 000’ or ‘less than 43’. Have students cut out five items and order them from greatest to least value. Ask them to select their item of greatest value and to line up to order the values from greatest to least. Discuss the thought processes required. Ask, ‘Which part of a number do you look at first to determine if it is bigger or smaller than another number? How do you deal with the decimal point?’ School Raffle Review place value from hundredths to hundreds of thousands. Write numbers on the whiteboard and point to a digit in each number. Ask, ‘What does this digit represent? How do you know?’ Give students advertising material from department stores. Have them work in groups to select ten items as prizes in a school raffle and to order the prizes from most to least expensive. Practice Makes Perfect Have students form groups of four. Give each group a stopwatch. Have students time how long it takes them to say the alphabet backwards. Have each student repeat the activity Over the course of a week, you could have students practise three times and record their times from fastest to slowest. Ask, a range of tasks, record their times and note ‘Did your times improve with practice? Which part of the any improvement in their times, to decide numbers you recorded shows your improvement?’ Have each whether or not practice does indeed make perfect. group record all group members’ times from slowest to fastest. Discuss the use of place value in completing this task.

Small Group Focus — Applying the Concept Focus Teaching Group • Highest or Lowest Give each student a set of cards cut from BLM 14 ‘High or Low’. Ask, ‘What is the largest number with six digits you can make with these cards?’ Guide students to discuss the value of each place and use the decimal point to make the largest, then smallest, possible number. When students show understanding of place value, have them make numbers according to other criteria, e.g. greater than 10 000/smaller Provide number expanders from BLM 43 for students who are than 0.93, etc. Have students work independently, using the number uncertain of place value. cards to make and record 20 numbers, then order them from smallest to largest.They could then use these numbers to play ‘Guess My Number’ with a partner. To play, students choose a number from their partner’s list without telling their partner what it is. Partners ask questions (answerable only with ‘Yes’ or ‘No’) to find the hidden number. • Counting Give each student a calculator. Have all students punch in the same starting number, e.g. 249 307, and use the constant function on the calculator to count by 500s. Before they press the ‘=’ sign, guide students to predict the next number, e.g. ask, ‘Which number/s will change when you press “equals” this time?’ Talk about how known counting patterns can be used to count by numbers that are multiples of .01, 10, 100, 1 000, etc. Repeat with other counting constants. Have students work independently to complete BLM 15 ‘Counting Constant’.

70


• Decimal Counting Patterns Show students a decimal number pattern appropriate to their skill level, e.g. 0.09, 0.27, etc. Ask, ‘Which number comes next in this pattern? How do you know? What am I counting by?’ Repeat, guiding students to understand the thought processes needed to identify the patterns. Have students work independently to generate their own decimal number patterns.


Decimal Lowest vs. Highest (BLM 2) Give each student a copy of BLM 2 to play a decimal version of ‘Lowest versus Highest’. Have students roll the twenty-sided dice five times to make a number with two decimal places. Crafty Counting (Student Book p. 47) Student Book page.


Value for Money Set up work stations with pages from the classified sections of newspapers and advertising brochures. If possible, include one allowing access to on-line shopping sites. At each work station, ask students to read through the material and find the most and least expensive item in a particular category, e.g. in the real estate pages, students look for the most and least expensive house. Have students record their findings. After visiting all stations, have them order their recorded items from most to least expensive. All in Order (Student Book p. 48) Have students complete the Student Book page. When finished, students could create their own shopping lists using on-line resources, or newspaper classifieds and advertising material. Have them order the items on their list from most to least expensive. High or Low (BLM 14) Provide pairs with sets of cards cut from BLM 14. Have them play the game and record the numbers they make. Unit 16 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 49).

Whole Class Share Time List a range of numbers generated while playing ‘Lowest versus Highest’. Ask, ‘Which of these numbers is the smallest/biggest? How do you know?’ Review the problems on the Student Book page. Discuss students’ strategies for completing the number patterns. Today I investigated …

Ask individuals to share the items they recorded and list these on the whiteboard. Ask, ‘Which was the most/least expensive item found?’ Have students write a price tag that is higher than the highest one listed. Ask, ‘How do you know your price is higher?’ Discuss students’ work on the Student Book page. Then write on the whiteboard a series of numbers containing zeros, e.g. 30.03, 107.01, 3406.10. Ask, ‘What is the value of this zero? How do you know? Why are there zeros in these numbers? Would the numbers change if we took out the zeros?’ Have students look at the numbers they made while playing ‘High or Low’. Have the class stand up, then find the lowest number in the class by eliminating students using statements like, ‘Sit down if all your numbers are bigger than 100/bigger than 10,’ etc. When only one student remains standing, ask, ‘What is the lowest number on your sheet? How do you know?’

Unit 16 Counting and Number Order

71

unit

17 Space

Making 3D Shapes Student Book pp. 50–51

BLMs 60, 62, 63, 64, 65, 66 & 75

During this week look for students who can: • define and draw 3D shapes by their features • identify features shared by 3D shapes • use concrete materials to make 3D shapes such as cubes, prisms, cones, cylinders, pyramids and other polyhedra • match 3D shapes with their corresponding nets • make to size a net to build a cube, triangular or rectangular prism • follow plans and diagrams to make 3D models. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources set of 3D shapes, real estate section from local paper, digital camera, craft matchsticks, Blu-Tack, different-shaped boxes, graph paper, masking tape, cardboard, acetate sheets, playdough, Word, Kid Pix Studio Deluxe, BLM 60 ‘Graph Paper’, BLM 75 ‘Isometric Dot Paper’, BLM 62 ‘3D-shape Cards’, BLM 63 ‘Square Pyramid Net’, BLM 64 ‘Triangular Pyramid Net’, BLM 65 ‘Triangular Prism Net’, BLM 66 ‘Rectangular Prism Net’ Maths Talk Model the following vocabulary in discussion throughout the week: cylinder, cube, cone, prism, rectangular prism, triangular prism, tetrahedron, pyramid, sphere, face, edge, corner, side, vertices, point, vertex, intersect, parallel, curved surfaces, arc

Whole Class Focus — Introducing the Concept House Design Show students 3D shapes. Have them name each shape and describe its features. List these. Show students a house photo from the real estate section of the local paper. Ask, ‘Which 3D shapes can you see in the shape of this house?’ Repeat with other houses. Walk students around the school to observe the 3D shapes visible in the school buildings and nearby houses. Take digital photos. Ask, ‘Which 3D shapes are most often represented in architecture?’ Invite several students to draw these. Matchsticks Give each student 24 craft matchsticks and some Blu-Tack. Demonstrate joining the matchsticks, using Blu-Tack to anchor the corners. Ask, ‘If you were to use all these matchsticks to make a 3D shape, which one could you make?’ Allow time for students to experiment. Ask, ‘Which 3D shape did you make? How many faces/edges/corners does it have?’ Solid Features One by one, hold up 3D shapes from a plastic solids kit. Ask, ‘What is this 3D shape called? What features does it have?’ Hold up two

72


solids with a shared feature, e.g. a cone and a tetrahedron both have a point. Ask, ‘What is the same about these two 3D shapes?’ Allow time for discussion. Invite individuals to choose two other solids with a shared feature. Ask, ‘How are these 3D shapes the same/different?’ Provide students with picture cards from BLM 62 ‘3D-shape Cards’. Ask them to sort the cards into pairs with like features. Invite them to share their pairs. Mystery 3D Shapes Show students 3D shapes from the solids kit and review their names. Have students form small groups to play ‘Mystery 3D Shapes’. Each student in turn thinks of a 3D shape.The others ask questions (answerable only with ‘Yes’ or ‘No’) to identify it, e.g. ‘Does it have a curved surface? Is it the shape of a food can? Does it have fewer than eight corners?’ Discuss which questions were the most effective. Nifty Nets Show students a range of different-shaped food boxes, e.g. a Toblerone box, a circular cheese box. Choose one of the boxes. Provide graph paper (BLM 60) or isometric dot paper (BLM 75) and have students quickly sketch what they think a net for this box would look like. Carefully cut along suitable edges of the box to open it out into a net. Compare this with students’ drawings and allow time for them to make changes. Discuss the thought processes required to draw the nets, e.g. considering the shape of each face and where it will join on. Talk about where to place tabs so that the net can be assembled. Students could remind themselves about nets by making 3D shapes with the nets provided on BLMs 63-66.

Small Group Focus — Applying the Concept Focus Teaching Group • 3D-shapes Dictionary Place a set of geometric solids into a cloth bag. Have a student pick up a 3D shape, keeping it hidden in the bag. As the student describes its features, list these, e.g. faces, edges, vertices, curved surfaces, names of 2D shapes. Have others try to identify the shape. Give other students a turn to draw out a shape. Consider the features of 3D shapes and the meanings of the terms listed. Have students work independently to make their own ‘Dictionary of 3D Shapes’ as a slide show in PowerPoint or Kid Pix Studio Deluxe, or as a book. • Boxes Give students a range of different-shaped boxes. Ask, ‘How could you cut along the edges of your box to flatten it out?’ Guide students to predict by drawing along those edges in pen. Invite them to think about whether or not cutting along these lines would work. Cut the boxes. Discuss the results. Use masking tape to reattach pieces that were wrongly cut. Have students trace around these nets onto stiff card, draw in broken lines to show where to fold the nets, and draw tabs necessary for reassembly. Have students cut out and assemble their boxes. Discuss the results. Have students work independently to make a net for a box to hold a particular item, e.g. drink bottle, pencil case, book, etc. • Naming 3D Shapes Show students a card cut from BLM 62 ‘3D-shape Cards’, e.g. a cylinder. Ask, ‘Can you see anything in our room that has this shape? What features does it have? What is it called?’ Repeat. Look for students who can recognise the solids being discussed. Have students work independently to take digital photos of objects with the same shape as the various geometric solids, and to use these to create a slide show to define and explain the solids being discussed. Alternatively, students could illustrate a range of solid objects and use acetate overlays to trace their outlines. Unit 17 Making 3D Shapes

73


Building a House Have students choose three or four 3D shapes, construct them using cardboard, then use them to build a model house. They should label the geometric features of the house and draw it from different viewpoints, including an aerial view. Have students name their houses and display them in a model street. Matchstick 3D Shapes Have students explore the 3D shapes they can make with different numbers of craft matchsticks. Have them record these using the ‘Line’ tools in Word or Kid Pix Studio Deluxe. 3D-shape Chains In pairs, have students play ‘3D-shape Chains’ with several sets of cards cut from BLM 62 ‘3D-shape Cards’. The cards should be shuffled and dealt evenly between the players. One player chooses a starting card and places it face up on the table.Their partner finds a card in their hand that shares a feature with the shape on the tabled card. This is placed next to the first card. The first player then places a third card that shares a feature with the shape on the second card, to form a chain. Play continues until no more cards can be placed.The player who placed the last card wins. Have students record their chains, identifying the features common to consecutive 3D shapes. 3D Shapes (Student Book p. 50) Have students complete the Student Book page. Creating a Sculpture Students could make a range of 3D shapes out of playdough, and use these to create a sculpture. Have students write a description of their sculpture by describing the features of each 3D shape rather than naming it. They then give their description to a partner, challenging the partner to build an identical sculpture. Matching Up (Student Book p. 51) Have students complete the Student Book page. Making a Net Have students design their own chocolate bar (column) and make a model of it using playdough. Students then use their models as a template for designing a box that could be used to package the chocolate bar. Have students complete a design drawing showing both the chocolate bar (column) and the net they would need to use to construct the box.

Whole Class Share Time Have students view each other’s houses. Ask, ‘Which 3D shapes were used to make this house? How many vertices are there? From an aerial view, how many vertices can you see?’ Ask, ‘What is the least number of matches you can use to make a 3D shape? Can you make 3D shapes with odd numbers of matchsticks? What are these 3D shapes called?’View and discuss the solids that students made. Today I learnt …

Hold up a cone and a sphere. Ask, ‘Which features do these two 3D shapes share? Can you think of another 3D shape that shares this feature?’ Repeat with other pairs of solids. Display students’ sculptures around the room without identifying their creators. Read some of the descriptions of the sculptures and have students try to identify the sculpture being described. Discuss the elements of the description that helped. Have students share the chocolate bars they designed and the nets they drew. Discuss the thought processes they used to draw the nets.

74


unit

18 Space

Drawing 3D Objects Student Book pp. 52–53

BLMs 75 & 78

During this week look for students who can: • draw representations of solids such as cubes, prisms, cones, cylinders, pyramids and other polyhedra using isometric dot paper or graph paper • show the part of an object that is not seen when drawing a solid • draw what models look like from the front, side and top. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources a set of geometric solids, real estate section from a newspaper, acetate sheets, cardboard, overhead projector, Centicubes, cardboard food boxes, felt-tipped pens, rulers, Multilink blocks, Lego, wooden blocks, Word, isometric dot paper (BLM 75), BLM 78 ‘Drawing 3D Shapes’ Maths Talk Model the following vocabulary in discussion throughout the week: solid, face, edge, corner, vertex, vertices, point, shape, cube, rectangular prism, triangular prism, pyramid, tetrahedron, cylinder, cone, two dimensions, three dimensions, isometric paper, seen, unseen, point of view, top, front, side

Whole Class Focus — Introducing the Concept Draw a Cat Show students a set of geometric solids and review their names and features. Ask, ‘How could we put these solids together to make a cat?’ Challenge students to draw a diagram of the cat they would make, labelling each solid used. Have individuals share their drawings. Discuss the strategies students used to show 3D solids in 2D space. Houses Show students a photo of a house from the real-estate section of the local paper. Ask, ‘Which geometric solids can you see in this picture? Repeat, pointing out any solids evident. Overlay one house with an acetate sheet and have a student use a whiteboard marker to draw in the visible edges of the solids they can see. Remove the photo and place the acetate on the whiteboard. Ask, ‘Which edges of this solid can’t we see?’ Model marking in some of these edges using dotted lines. Invite individuals to mark in other lines. Discuss the use of dotted lines to indicate unseen sections of solids. Name That Solid Give each student three pieces of cardboard and have them select a classroom object. Ask students to draw that object from the front, top and side, indicating the shape of the object, but not including identifying features such as labels or colour. Then have students exchange Unit 18 Drawing 3D Objects

75

their cards with a partner who tries to identify the object. Have individuals show their cards to the class. Ask, ‘Which object would look like this from the top, side and front?’ Talk about how appearance changes depending on point of view. Point of View Mask an overhead projector screen so that students cannot see what has been placed on it, e.g. by taping stiff paper around the edge of the screen as a barrier. Place a 3D solid on the screen so that the image projected is what you would see if viewing the object from the front. Ask, ‘Which solid could this be? Why? From which point of view are we seeing it?’ List suggestions on the whiteboard and draw the image projected. Turn the solid so that it is seen from a different point of view. Ask, ‘What solid do you think this is now?’ Discuss previous suggestions in the light of the new information. Delete from the list any information that is no longer relevant and add new information. Ask questions such as, ‘Could this shape still be a cone? Why, or why not?’ Turn the object once more and ask students to identify it again. Show students the solid. Repeat. Can’t See It Display a set of geometric solids, and review their names and features. Choose one solid. Show students an enlarged copy of a card displaying this solid, cut from BLM 78 ‘Drawing 3D Shapes’. Ask, ‘Which part of the solid does this drawing show?’ Ask a student to trace with a finger the parts of the solid shown in the drawing. Then ask them to trace along the edges of the solid not shown in the drawing. Repeat with other shapes. Give each student a copy of BLM 78. Have students use dotted lines to draw in the parts of the solids that cannot be seen. Discuss the thought processes required.

Small Group Focus — Applying the Concept Focus Teaching Group • How to Draw It Have students make a model using five Centicubes, then provide them with isometric dot paper. Guide students to draw a diagram of their model as seen from above (top view), by standing up and looking down on it. Ask, ‘What do you see? What lines would you draw to represent the model from this viewpoint?’ Now look at the model from the front, then the side. Ensure that students draw what they see and not what they expect to see. Repeat with a different model. Have students work independently and secretly to make another model, then draw it from the front, side, and top. They then exchange drawings with a partner, who tries to recreate the model from the drawings. • Showing What Is Not Seen Give each student a small cardboard food box. Ask, ‘What do you see when you look at this box from this angle?’ Ask students to use a coloured felt-tipped pen to draw along all the edges of the box that they can see; and then a different colour to draw along the unseen edges. Ask, ‘How many edges could you see/not see? Have students look at their box from one point of view and observe the apparent angles the Less able students may need support to complete their coloured lines make on adjacent faces. Ask, ‘How would you draw drawings. these lines on paper?’ Guide students to use rulers to draw a diagram of the box on isometric dot paper (BLM 75), using unbroken lines to represent the visible edges. Ask, ‘How many lines will you need to draw?’ (Refer students back to the coloured lines they drew on the boxes.) Now guide students to draw in broken lines to represent the unseen edges. Ask, ‘How many lines will you need to draw?’ Have students work independently to draw a diagram of a different 3D solid.

76


• Different Views Have students observe everyday classroom items, e.g. a pencil. Ask, ‘What does a pencil look like from the side/top/end? Guide students to draw it from different points of view. Encourage them to really look at the shape and relative position of the pencil, rather than drawing what they expect to see. Repeat with other objects. Have students work independently to make a ‘What Am I?’ book. On right-hand pages they should illustrate an everyday object from different points of view, writing ‘What am I?’ underneath; on the back of the page they should draw the object conventionally and answer the question, e.g.‘I am a pencil sharpener’.


Draw an Animal Have students use playdough to make an animal from at least four different geometric solids. Have them record their animal on isometric dot paper (BLM 75). Students then exchange drawings and their partner tries to construct the animal from the drawing. Drawing the Unseen Provide students with isometric dot paper (BLM 75). Have them draw everyday classroom objects representing the seen edges with unbroken lines and the unseen edges with broken lines. What Do You See? (Student Book p. 52) Student Book page.


Cube Art (Student Book p. 53) Have students complete the Student Book page. Then have them create a work of art using construction materials, i.e. Lego, or Multilink or wooden blocks. Have them name their sculpture. Provide isometric dot paper (BLM 75) so that students can draw diagrams of it from the front, side, and top. (Artists should remain anonymous.) Computer Solids Using the ‘Drawing’ and ‘Line’ tools in Word, have students draw 3D solids showing their visible edges with unbroken lines and their unseen edges with broken lines, i.e. go to ‘View’, ‘Toolbar’, ‘Drawing’, ‘Line’ then ‘AutoShapes’. Or students could draw geometric solids on isometric dot paper (BLM 75). Units 17–18 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 54).

Whole Class Share Time Have individuals share their animal drawings. Ask, ‘ How did you show a cylinder/a cone? What did you have to think about to represent the parts of the solid that could not be seen?’

Today I did not understand …

Have individuals show their drawings to the class. Ask others to identify the object drawn. Ask ‘How many edges does this object have? How have they been shown on the diagram?’ Ask, ‘What did you need to think about to draw an object from above? How are these sorts of drawings different from illustrations?’Talk about how students overcame the challenges. Ask, ‘Where would such drawings be useful in everyday life?’ e.g. architectural drawings, building plans, garden layouts. Collect students’ drawings of their sculptures and display the sculptures around the room. Give each student someone else’s drawing to see if they can find the sculpture that inspired it. Discuss aspects of the drawings that assisted students to identify the sculptures. Talk about the challenges students faced in constructing their diagrams of 3D solids. Have them share their strategies for overcoming them. Unit 18 Drawing 3D Objects

77

unit

Multiplication



BLM 10

During this week look for students who can: • multiply whole numbers by two-digit numbers • identify when multiplication could be used in everyday life • use mental and written methods, and calculators, to multiply numbers to 999 999 • write and solve multiplication word problems • verbalise the thought processes used to solve multiplication problems. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources ten-sided dice, calculators, clock with a second hand, classified section of a newspaper, travel brochures, travel magazines, chart paper, playing cards (picture cards removed), Word, PowerPoint, Kid Pix Studio Deluxe, Microworlds, BLM 10 ‘Number Mat’ Maths Talk Model the following vocabulary in discussion throughout the week: multiply, multiple, sets of, lots of, groups of, product

Whole Class Focus — Introducing the Concept Choosing Multiplication Ask, ‘When do we use multiplication in everyday life?’ List suggestions on the whiteboard. Ask students to think of a multiplication problem and solution in an everyday context. (For example, ‘I have three children. I bought them all new shoes.The shoes cost $45 a pair. How much did I spend altogether?’) Have students share their problems in small groups. Ask them to note the words that indicate that multiplication should be used to solve the problems, e.g. ‘multiply’, ‘multiple’, ‘sets of ’, ‘lots of ’, ‘groups of ’, ‘product’, etc. List these on the whiteboard. Product Target Enlarge BLM 10 ‘Number Mat’. Stick the number mat on the whiteboard. Roll a ten-sided dice. Tell students the number rolled. Ask, ‘If we were to multiply one of the numbers on the number mat by the number on the dice, which of these numbers would give the answer closest to 100 000?’ Talk about strategies to solve this problem, e.g. rounding the number to the nearest thousand, dividing 100 000 by the number on the dice, etc. Model multiplying the numbers on the whiteboard using the vertical written method. Focus on the thought processes needed when multiplying the numbers in the tens, hundreds and thousands columns. Explain as you go. Invite students to explain what you should do next and why. Roll the dice again and repeat.

78


× _______ 200 000

The Answer Write on the whiteboard the unfinished equation in the margin. Say, ‘This is the answer. What could the missing numbers be?’ Provide calculators and allow students time to work out solutions. Have individuals share their solutions with the class. Talk about the thought processes required to solve the problem. Repeat with another like problem. C-A-T Spells Cat Pose this problem to students: ‘If all letters of the alphabet had a numeric value according to their position in the alphabet, e.g. a = 1, b = 2, c = 3, then words could have a numeric value too. If ‘cat’ = 60 and ‘dog’ = 420, how is the value of a word being calculated?’ Guide students to identify the value of each letter, i.e. c = 3, a = 1 and t = 20, and draw out that multiplying these numbers is the way to get the answer. Show students how to estimate and then work out the value of a word using long multiplication. Have one student check using a calculator. Ask students, ‘What is the value of your first name?’ Have them work it out. Heartbeat Ask, ‘How many times does your heart beat each hour? What information would you need to collect to find out? What mathematical operations would you use to find the answer?’ Allow time for students to brainstorm ideas for tackling the problem. Provide a clock with a second hand for students to use to measure their heart rate, making sure they know how to find their pulse. Encourage them to take their pulse for 15 seconds and then multiply by 4. Use your own heart rate to demonstrate solving this problem on the whiteboard by formal multiplication. Then have students work in pairs to work out their own heart rates, and report their findings to the class. Ask, ‘What did you do to find out how many times your heart beats in one hour? Why do different people have different answers?’

Small Group Focus — Applying the Concept Focus Teaching Group • Multiplication Stories Tell students an appropriate multiplication story. (For example, ‘To have fresh eggs I bought 12 chickens. The chickens cost $15 each. How much did I spend altogether?’) Guide students to solve the problem, focusing on the use of the multiplication algorithm. Have students work independently to write their own multiplication stories. Provide access to the Internet so that students can work with real prices. Alternatively, provide the classified section of a newspaper, travel brochures, travel magazines, etc. Have students record their multiplication stories as slide shows or charts in PowerPoint or Word. • Explaining Multiplication On the whiteboard, write a vertical multiplication problem appropriate to the needs of students. Ask, ‘How would you explain to someone who had never done multiplication before how to complete this problem?’ Brainstorm the words that could be used, e.g. ‘multiply’, ‘multiple’, ‘sets of ’, ‘lots of ’, ‘groups of ’, ‘product’, ‘double-check’. Have students work independently to pose their own multiplication problems and work out how to explain the multiplication process to a novice. Encourage them to use diagrams and other visual representations. • High Rollers Review the vertical multiplication process with students ensuring that they understand how to carry. Vary the range of numbers being multiplied according to students’ needs. Have students roll a tensided dice seven times to form both a five- and a two-digit number. Guide students to multiply these numbers. Ask, ‘Which numbers do you multiply first? Where do you write the answer? What do you do with the tens? Which Unit 19 Multiplication

79

number do you multiply next? What do you do when you are multiplying by zero?’ etc. Compare students’ answers. Ask, ‘Which of these products is closest to 100 000?’ Have students work independently to roll the dice seven times to form a five- and a two-digit number, choosing the order of the numbers so that when the two numbers are multiplied their product is as close to 100 000 as possible.

Vary the target number according to students’ needs. Less able students could be given a target number of 1 000.


Work It Out! (Student Book p. 55) Have students complete the Student Book page. Everyday Multiplication Have students work in small groups to create slide shows in PowerPoint or Kid Pix Studio Deluxe to demonstrate how multiplication is used in everyday life. Encourage them to provide mathematical examples of the uses of multiplication, and to highlight the key words that tell them to use multiplication to solve the problem. Multiplication High Have students play ‘Multiplication High’ in small groups. Each group needs a deck of playing cards (picture cards removed, Ace represents one). The dealer shuffles, and deals seven cards to each player. Players use their cards to make a five-digit whole number and a twodigit whole number, and multiply these to give the scoring number. The player with the highest scoring number wins ten points. Players must be able to show how they worked out their scoring number. All cards are then shuffled again and the player to the left of the dealer deals the next round. Play continues until one player has scored 100 points. Multiplication (Student Book p. 56) Student Book page.


Zoo Animals (Student Book p. 57) Have students complete the Student Book page. Valuable Words Student may like to use the letter code to find the most valuable three- and four-letter word. Have them record their findings. Millionth Heartbeat Ask, ‘If I started now to count my heartbeats, when would I be likely to reach a million?’ Have students work in pairs to propose a solution to this problem and to record it in various ways. Some could create multimedia displays using Micro-worlds, or make slide shows using Kid Pix Studio Deluxe. Alternatively, students could present their findings on charts or as interviews.

Whole Class Share Time Have students share their ideas on the use of multiplication in everyday life. Ask, ‘How would you work out that multiplication problem? Could you do it in your head/use a pencil and paper/use a calculator? Why is it important to know how to do multiplication?’ Today I created …

Discuss the strategies students used to calculate their scoring numbers. Discuss the strategies students used to create their own stepping-stones problem. Have several students share their problem with the class. Ask, ‘Which was the most expensive animal you could think of? How did you work it out? Do animals with shorter names always cost less than animals with long names?’ Ask, ‘How long would it have been before you counted a million of your own heartbeats? How did you work it out?’ Focus on the use of multiplication.

80


unit

Division



BLM 51

During this week look for students who can: • divide whole numbers to 100 000 by single-digit numbers • identify when division could be used in everyday life • write and solve division word problems • verbalise the thought processes used to solve division problems. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources calculators, chart paper, ten-sided dice, Kid Pix Studio Deluxe, BLM 51 ‘Divisibility Table’ Maths Talk Model the following vocabulary in discussion throughout the week: share, groups of, left over, remainder, factor, divisible by quotient, dividend, divisor, quotient, remainder

Whole Class Focus — Introducing the Concept Choosing Division Ask, ‘When do we use division in everyday life?’ List suggestions on the whiteboard. Ask students to think of a division problem and solution in an everyday context. (For example, I have $60 to spend on Christmas presents. I have to buy five presents. How much can I spend on each present?) Have students share their problems in small groups. Ask them to note the words that indicate that division should be used to solve the problem, e.g. ‘divide’, ‘share’, ‘groups of ’, ‘left over’, ‘remainder’, ‘factor’, ‘divisible by’, ‘quotient’, etc. List these on the whiteboard. Birthday Quotient Review the process of division, talking through the steps needed to complete a problem. Draw out that division problems are worked from left to right, unlike the other operations. Encourage students to verbalise each step. Discuss ‘remainders’ and their implications. Ask students to write down their date of birth as a four- to six-digit number. Have them divide this number by the number of letters in their name. Ask, ‘Who has the biggest quotient (answer)? Who has a remainder?’ Have a number of students demonstrate how they arrived at their answer. __7__ 3 ) 822 2__3 4 ) 9 7__

Lost Numbers Write on the whiteboard the problems in the margin. Ask, ‘What do we need to do to work out which numbers are missing?’ Allow time for students to solve the problems independently. Invite individuals to demonstrate their methods. Remainders Write a division problem on the whiteboard. Ask, ‘Will the answer to this problem have a remainder? How would you work it out?’ Unit 20 Division

81

Talk about why it is useful to predict whether or not there will be a remainder. Draw out that an odd number when divided by an even number will always have a remainder. Students may find useful the divisibility tests on BLM 51 ‘Divisibility Table’. Special Number Write the following instructions on the whiteboard and have students follow them to work out their own special number: ‘Do this in secret. Take the number of the month of your birth and add 32. Then add the difference between 12 and the number of your birth month. Support students Divide by 2 and add 3. This is your special number. Don’t tell who feel less confident about the task by suggesting that they work out a few special anyone.’ Allow time for students to work out their number. Ask, numbers using the numbers of different ‘Is there a way to work out what another person’s special months to see what happens. number is without knowing their birth month?’Talk about how this might be done. Have students work in groups of two or three to solve the problem. Have students share their solutions.

Small Group Focus — Applying the Concept Focus Teaching Group • Explaining Division On the whiteboard, write a division problem appropriate to the needs of students. Ask, ‘How would you explain to someone who had never done division before how to complete this problem?’ Brainstorm the types of words that could be used. Have students work independently to pose their own division problem and work out how to explain the division process to a novice. Encourage them to use diagrams and other visual representations in their explanation, as well as words and numbers. • Estimate Then Check Pose a simple division problem, e.g. 45 ÷ 7. (For more advanced students use a larger dividend.) Ask, ‘How would we set out this problem? What might the answer be?’ Guide students to solve the problem. Ask, ‘How could we check our answer to this problem using multiplication?’ Guide students to pose their own division problem, estimate the answer, solve the problem and then use a calculator to check their answer using multiplication.When students are comfortable with this, have them work independently to make their own division problems and solve them, demonstrating how they predict, and then check, the answers. • The Answer Is 5 Say, ‘The answer to my division question is 5. What might the question be?’ Guide students to find a range of equations using a calculator, and then to check them. Ask, ‘What do we already know about the largest number in the equation?’ (The last digit must be zero or 5.) How could we use the calculator to help? (Work backwards and use multiplication, e.g. 5 × 4 987 = 24 935, so the question could be 24 935 ÷ 4 987 = 5). Have students work independently to find and record other division questions having the answer 5.


Everyday Division Have students work in small groups to create slide shows in PowerPoint or Kid Pix Studio Deluxe to demonstrate the use of division in everyday life. Encourage them to provide mathematical examples, and to highlight the key words that tell them to use division to solve the problem. Alternatively, students could do this on large charts or in class books. Postcodes (Student Book p. 58) Have students complete the Student Book page. When finished, students may like to make up their own division

82


scenarios using other numbers in their life, e.g. phone numbers, house numbers, car registration numbers, etc. These could be collated in a class book. Number Find Have students make up their own missing-number division problems. Students could write each problem in large print and place it in a plastic display pocket. Problems could be collected into a class book. Provide whiteboard markers for students to use when solving the problems, and have users wipe the sheets clean for the next user when finished. Division (Student Book p. 59) Book page.


Students could play ‘Remainder Lotto’ in groups.To play, each group needs paper and pencils and a ten-sided dice. At the start of each round, students write down five single-digit numbers to be their lotto numbers for that round. The dice is then rolled six times. Each Vary the difficulty student uses the six numbers rolled to make a division problem, of the game by varying the number of digits used in the division problems, e.g. for e.g. 45 678 ÷ 3 =, trying to come up with a different problem less advanced students, work with four from the others in the group. Students then solve their problems digits (345 ÷ 4). and the group lists all the remainders. Players then consult their original Lotto pages. The student who has the highest representation of remainders on their Lotto page wins that round and is awarded 100 points. Play continues until one player has won 1 000 points. Remainder Lotto

Number Detectives Have students work out their own detective formula that uses division at least once to find a mystery number. Have them try out their formula on others. Units 19–20 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 60).

Whole Class Share Time Have students share their ideas on division in everyday life. Ask, ‘How would you work out that division problem? Could you do it in your head/use a pencil and paper/use a calculator? Why is it important to know how to do division?’


Invite a range of students to share their problems with the class. Ask, ‘What did you need to think about to make up this problem?’ Allow time for students to try out some of the problems. Look at several of the missing-number problems with the class. Discuss strategies for solving them. Ask, ‘How did you know that this missing number was a 7? What number fact did you use to work it out?’ Discuss the thought processes students used to create division problems with remainders. Ask, ‘How did you use your knowledge of tables facts to make up the problems? Which divisors were most likely to give remainders?’ Have individuals demonstrate using their detective formula to find a hidden number. Ask, ‘How did you work out your formula?’

Unit 20 Division

83

unit

Volume and Capacity

21 Measurement


BLM 16

During this week look for children who can: • estimate and measure the volumes of a range of 3D objects • choose appropriate measures to determine the capacity of various drink containers • measure the capacity of drink containers to the nearest 5 millilitres • read graduated scales accurately • estimate the volume or capacity of an object using standard units of measurement. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources Centicubes, apples, potatoes, empty plastic drink bottles, straight-sided measuring jugs, graduated flasks, eye-droppers, syringes, medicine glasses, capacity measuring kits, rain gauge, advertising brochures (white goods), unopened food tin, small cardboard boxes, string, water tray, sand tray, BLM 16 ‘Making a Rain Gauge’ Maths Talk Model the following vocabulary in discussion throughout the week: volume, capacity, litres, millilitres, cubic centimetres, full

Whole Class Focus — Introducing the Concept Measuring 3D Shapes Use Centicubes to make a cube of 3 × 3 × 3. Ask, ‘How many Centicubes have I used to make this cube? How could you work it out?’ Discuss students’ strategies. Draw out that each Centicube takes up exactly 1 cm3 and that this is a standard unit of measurement. Dismantle the cube to show how many Centicubes there were. Ask, ‘How could we write this number of cubes as a volume?’ e.g. 3 × 3 × 3 cm = 27 cm3. Ask, ‘Can you see a relationship between the number of Centicubes used, the length, width and height of the cube, and its total volume. Ask students to predict how many cubes it would take to make a 4 × 4 × 4 cube or a 5 × 5 × 5 cube. Potatoes and Apples Show students a potato and apple of much the same size. Ask, ‘Which of these will float/sink?’ Place them in a container of water and observe. Ask, ‘Why does the apple float and the potato sink when they are about the same size?’ List suggestions. Show students a straightsided jug containing 200 mL of water. Ask, ‘How much would the water level rise if I placed the apple/potato in the water?’ Conduct the experiment. Consider the results. Ask, ‘Why does the potato sink/apple float?’

84


Drink Bottles Show students a range of empty drink bottles. Ask, ‘What is the capacity in millilitres of each of these drink bottles? How could we find out?’ Record students’ predictions. Show them a range of devices used to measure liquids, e.g. measuring jug, graduated flasks, eye-droppers, syringes, etc. Ask, ‘Which of these is the most useful for our purpose?’ Discuss. Ask, ‘How must we use these devices to ensure measurement is fair and accurate?’ i.e. don’t spill any of the liquid, place the device on a flat surface, use the scale to take an accurate reading. Demonstrate measuring the capacity of one or more of the drink bottles. Have students consider their predictions. Ask, ‘Would you like to change any of your predictions? Why?’ Reading a Rain Gauge Show students a rain gauge. Ask, ‘What is this used to measure? Where would you put it? Why might you need it?’ Place some water in the gauge and model reading it. Point out gradations such as the nearest 5 or 10 mL marks. Ask, ‘How do we read the gauge?’ Have students explain their strategies, e.g. going to the nearest ten above the waterline and then counting back. Taking up Space Ask, ‘When might you need to know the volume of an object?’ e.g. how much luggage an aeroplane can carry, etc. Give students brochures advertising white goods. Have them consider the descriptions of different refrigerators. Ask, ‘Which of these fridges has the greatest/least capacity? How do you know?’ Show students an unopened food tin. Ask, ‘How much space does this tin take up?’ Discuss the meaning of this, i.e. ‘What is the volume of the tin?’ Tell students that the space an object takes up is measured in cubic centimetres or cubic metres, that 100 mL = 100 cm3. Demonstrate this by finding the volume of the tin, e.g. by placing it in a jug of water and measuring the rise in water level.

Small Group Focus — Applying the Concept Focus Teaching Group • Reading Scales Show students a range of devices used for measuring capacity and volume. Ask, ‘What do the numbers/lines on this scale tell you? Why are some lines longer than others? How do you read this scale? What would you measure with this device?’ Point out that in some cases units in a measurement scale are greater than one. Guide students to measure the capacity of everyday containers using these devices. Point out that answers should be recorded in the units displayed on the measurement scale, e.g. mL. Have students work independently to measure and record the capacities of other containers. • Choosing Units Ask, ‘Which units do we use to measure liquids?’ List these on the whiteboard, i.e. ‘millilitres’, ‘litres’, ‘kilolitres’. Have students brainstorm situations in which it is important to know the exact amount More advanced of liquid, e.g. the capacity of a swimming pool so that the correct students could explore the amount of chlorine can be added, etc. List students’ suggestions. prefixes used to denote proportional 1 Have them consider the list and suggest the units of measurement units of volume, i.e. milli = 1 000 , 1 most applicable in each case. Have students work independently to deci = 10 , kilo = 1 000, etc. draw up their own chart showing situations in which it is important to measure liquid accurately, and the most appropriate unit to use.They could cut out photos from magazines as illustration. • Filling Boxes Show students a range of small cardboard boxes. Ask, ‘What could the volume of each box be? How could we measure it?’ Guide Unit 21 Volume and Capacity

85

students to measure the volume of one box by stacking Centicubes More advanced students inside it. Draw out the need to use a standard unit of could measure the dimensions of the box measurement when measuring volume, reminding students first and use these measurements to predict the volume before checking with Centicubes. that a Centicube is a standard unit, i.e. 1 cm3. Have students MAB units could also be used. work independently to measure and record the volume of other

boxes, ordering them from least to greatest volume.


Volumes of 3D Shapes Have students predict how many Centicubes they would need to make cubes and rectangular prisms of given dimensions, and then build the prisms to check.

Displacing Water Have students measure how much water is displaced by a range of objects, e.g. by placing each object in a straight-sided To assist them to measuring container with 300 mL of water and observing the rise in lower each object into the water water level. Have students record their observations. They could then and then remove it, students could investigate how much water is displaced by a plasticene ball shaped as, tie a piece of string to each object. e.g. a ball, a boat, a pancake, noting which of the shapes float/sink. Drink-bottle Capacity (Student Book p. 61) Have students complete the Student Book page. When finished they could consider any disparity between the measured capacity of each bottle and the amount of liquid its label claims it contains. Rain Gauges (Student Book p. 62) Have students use rain gauges made from BLM 16 ‘Making a Rain Gauge’ to complete the Student Book page. Encourage them to calibrate their scales carefully. Rain gauges can be placed at various locations in the schoolyard and used to measure rainfall over a period of time. Alternatively, students could measure rainfall at home and keep records in standard units to share later with the class. Students could also explore rainfall patterns and records by visiting the Bureau of Meteorology website (see Website 21, BLM 79). Finding Volumes Have students measure and record the volumes of a range of everyday items. Provide measuring containers, water, sand and sand trays, Centicubes, boxes, etc. Items could be tied with string to make it easier to get them into and out of the water. Unit 21 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p. 63.


Today I learnt …

Ask, ‘Can you use information about the length, width and height of an object to predict its volume? Think of a formula to use to work this out.’ Draw out that H × W × L = V. Discuss the results of students’ experiments. Ask, ‘Why do some things float while others sink?’ Discuss students’ results. Ask, ‘Why does the label on this bottle say it holds 375 mL when you found that it holds 392 mL when full?’ Ask, ‘How did you calibrate the scale on your rain gauge? What intervals did you use? How accurate is the gauge? How could its accuracy be improved?’ Have individuals share their strategies for finding out the volumes of everyday items.Talk about the effectiveness of each strategy.

86


unit

Exploring Patterns

22


Number and patterns

BLM 17

During this week look for students who can: • identify patterns in numeric problems • continue number patterns • explain number patterns • predict further numbers patterns based on an understanding of how the patterns work. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources calculators, square counters, six-sided dice, card, Centicubes, computer calculators, BLM 17 ‘Pattern Strips’ Maths Talk Model the following vocabulary in discussion throughout the week: patterns, element, general rule, sequence, predict how many, experiments to test, how is a pattern generated?

Whole Class Focus — Introducing the Concept

51 = 1 × 5 52 = 5 × 5 53 = 5 × 5 × 5 54 = 5 × 5 × 5 × 5 55 = 5 × 5 × 5 × 5 × 5 etc.

Pattern 1 10c 5+5 11c 5+3+3 12c 3+3+3+3 13c 5+5+3 14c 5+3+3+3 15c 3+3+3+3+3

5 25 125 625 3125

The Power of Numbers Introduce or review numbers to the power of two, e.g. 102. List some of the square numbers students know, and talk about how to work these out. Provide each student with a calculator and ask them to work out what a given number (< 10) is to the power of 5.Write 518 on the whiteboard. Ask, ‘What would the last three digits of this number be?’ Allow time for students to work out the answer using calculators. Say, ‘Can you see a pattern? Could we use this pattern to work out the answer without using a calculator?’ Ask, ‘When five is raised to an even power, what do you notice about the last three digits of the numbers? When five is raised to an odd power, what do you notice about the last three digits? How could we use this to predict the last three digits of 518?’Talk about using the pattern to predict the last three digits of other numbers generated by raising five to an odd or even power. Selling Stamps Say, ‘The Melbourne Post Office has decided to sell only 3-cent and 5-cent stamps. It also wants to raise the cost of sending a letter but can’t decide whether to charge 51, 52 or 53 cents. The Post Office needs to work out if any of these amounts can be made using only 3-cent and 5cent stamps. How could it work out the problem?’ Guide students to solve the problem by looking for patterns. Work together to generate all values from 10 cents to 25 cents. Ask, ‘Could we use these values to work out if we can make 51, 52, or 53 cents?’ Allow time for students to come up with ideas. Ask, ‘What should the Post Office’s new charge be?’ Unit 22 Exploring Patterns

87

Please note: There are two patterns that emerge. Once you have generated three consecutive numbers, the next three numbers can be generated simply by adding 3 to each of the previous numbers (see Pattern 1 in margin on p. 87). Once you have generated five consecutive numbers, the next five numbers can be generated by adding 5 to each of the previous numbers (see Pattern 2 in margin).

Pattern 2 10c 5+5 11c 5+3+3 12c 3+3+3+3 13c 5+5+3 14c 5+3+3+3 15c 5+5+5 16c 5+3+3+5 17c 3+3+3+3+5 18c 5+5+3+5 19c 5+3+3+3+5

Eights Write on the whiteboard the equations in the margin. Provide students with calculators to work out solutions to these problems. Ask, ‘Can you see a pattern? What do you think the next problem in this pattern will be? What will its solution be?’

8 × 8 + 13 = 88 × 8 + 13 = 888 × 8 + 13 =

2

5

Squares With square counters, make the pattern in the margin. Ask, ‘How many squares do you need to make the first shape? The second? The third? How many squares would you need to make the 10th shape? The 12th? The 25th?’ Discuss strategies students could use to identify the rule governing this pattern. Allow them time to use counters to explore the pattern, recording their findings in a simple table, e.g. shape, number of counters. Have students report their findings. As a class, generate a rule to work out the number of counters needed to make any shape in this pattern. Please note: It is possible that more than one pattern begins in this way.

20

What Is My Rule? Give students strips of paper folded into five sections. Have them roll two six-sided dice and record the two numbers thrown in the first two squares of the number strip. Ask each child to generate a pattern beginning with those two numbers, but to fill in only the fifth number on the strip, as shown in margin. Have students exchange their number strips with a partner who tries to solve and explain the pattern. Invite a range of students to share their patterns with the class. Have the class identify the rule behind each pattern. (The pattern in the margin is: 2, 5, 9 , 14, 20, i.e. + 3, + 4, + 5, + 6.) Discuss the thought processes needed to identify the patterns.

Small Group Focus — Applying the Concept Focus Teaching Group • Understanding Patterns Say, ‘I have made a pattern. The first number in my pattern is 1. The sixth number in my pattern is 8. What could the second, third, and fourth numbers be?’ Guide students to think their way towards a solution. Ask, ‘Is the second number likely to be bigger or smaller than 8? Why? What rule might have been used to make this pattern?’ Encourage students to predict a rule and then test it. (One solution to this problem is 1, 1, 2, 3, 5, 8, the pattern being generated by adding the preceding two numbers to make the next number, i.e. 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, etc.) Have students work independently to complete the patterns on BLM 17 ‘Pattern Strips’ and explain the rules behind them. • Pattern Sequences Show the following: 0 + 1 + 2 =? , 1 + 2 + 3 = ?, 3 + 4 + 5 = ?. Have students solve the problems. Ask, ‘Can you see a pattern here that would help you to solve 234 + 235 + 236 = ?’ Guide students to solve several more problems in the sequence to establish a rule that would Support less able students enable them to work out any number in the sequence. Have students by providing them with calculators to assist them. work independently to generate their own similar problems and write these onto card. Have group members exchange cards so that other students can work out the rule that generates each pattern. • Centicube Patterns Provide students with Centicubes. Then show students the first three elements of a pattern you have made using

88


Centicubes, e.g. a 1-Centicube building, 3-Centicube building and 5Centicube building. (Choose the complexity of the pattern according to the needs of students.) Ask, ‘Can you make the next building in this pattern? Why is this the next building in the pattern? How many Centicubes would the 5th building in this pattern have? The 20th building?’ Promote discussion about the thought processes needed to determine the pattern and have students articulate the rule. Then have students work independently to build and record their own Centicube building patterns.


Powers of 7 Provide students with calculators and have them work in cooperative pairs to find the last digit of 7 to the power of 1 999. Encourage students to look for final-digit patterns in the numbers generated. Students may like to further explore final or final two-digit patterns that arise when other numbers less than 10 are raised to given powers. It may be helpful to have students conduct this investigation using the calculator on a computer, as much larger numbers can be generated than with handheld calculators. Posting a Letter Have students work in cooperative pairs to determine what the Post Office could charge for sending a letter if it had only 3-cent and 7-cent stamps.

44 × 4 + 13 = 444 × 4 + 13 = 4444 × 4 + 13 =

Finding Patterns Have students use the computer calculator to find out whether or not the ‘Eights’ pattern continues indefinitely. Students could then investigate whether or not like patterns exist in the case of other digits. See example in margin. Shapes (Student Book p. 64) Book page.


Pattern Rules (Student Book p. 65) Student Book page.


Whole Class Share Time Ask, ‘What do you predict the last three digits of 7 to the power of 1999 to be? What reasoning did you use? What pattern have you found?’ Invite students who have explored other numbers to share their findings. Ask several pairs to share their solutions. Ask, ‘Which postage prices could you make with 3- and 7-cent stamps? What patterns did you find?’ Today I worked out …

Ask, ‘How does this pattern work?’ You could examine the relationship between 64 and 13 (i.e. 8 × 8 + 13 =) and the influence of this relationship on the pattern’s development. Ask students to share other patterns they have discovered. Discuss the importance of adding 13 in generating these patterns. Discuss the patterns students explored on the Student Book page. Ask, ‘What rules did these patterns have? Focus on different interpretations of each pattern, e.g. some students may have seen a pattern as a simple arithmetic sequence, while others may have made it more complex. Talk about the patterns students generated on the Student Book page. Ask, ‘What did you need to think about to link the first number with the final number in each strip? What number relationships did you look for?

Unit 22 Exploring Patterns

89

unit

Number Puzzles



BLM 50

During this week look for students who can: • see relationships between numbers • correctly use the rules of order of operations (BODMAS) • identify patterns in number problems • use addition, subtraction, multiplication and division to solve problems • use known facts to solve problems. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources calculators, playing cards (picture cards removed), Word, PowerPoint, BLM 50 ‘Blank Number Squares’ Maths Talk Model the following vocabulary in discussion throughout the week: look for patterns, look for relationships, look for common factors, use what you know, order of operations, BODMAS (Brackets of Division, Multiplication, Addition, Subtraction)

Whole Class Focus — Introducing the Concept Use What You Know Draw two columns on the whiteboard. Say, ‘I’m going to think of a rule. You must find my rule.’ Invite students to give you ten ‘input’ numbers to write in the left-hand column. In the right-hand column write three ‘output’ numbers obtained by following your rule, e.g. input number 16, rule is ‘× 4’, output number 64. Say, ‘I want you silently to work out what my rule is. If you believe you know the rule you may write an output number on the whiteboard. Invite students to come up when they are ready. When the table is complete, ask, ‘What is my rule?’ Repeat with another rule. Discuss the thinking process needed to play this game. Draw out the benefits of using known number facts and testing these across the four operations. Broken Down Numbers Say, ‘Imagine that I have a calculator with a broken number button. Could I still use the calculator?’ Encourage discussion, seeking strategies for using a calculator without having to use one particular number key. Say, ‘I want to add 234 962 and 24 203 using my broken calculator. The ‘2’ button won’t work. How could I do it?’ Write the numbers on the whiteboard and give students calculators to test their strategies. Have them share their strategies with the class. Making Numbers On the whiteboard write 4 _ 4 _ 4 _ 4 = ?. Ask, ‘What could the answer to this problem be?’ Allow time for students to work out a

90


solution to the problem, then share the solutions, listing them in numerical order on the whiteboard. Focus on problems where students have needed to use their understanding of the order of operations (BODMAS) to find a solution. Choose an answer, between zero and 100, that has not already been suggested by students, e.g. 4 _ 4 _ 4 _ 4 = 75. Ask, ‘How could we solve this problem?’ Discuss students’ solutions. Find My Number Say, ‘I want you to find my number. Listen to these clues. My number is odd. It can be divided by 9.The hundreds digit is twice the thousands digit. The number has a 2 in it. What could my number be?’ Note that there are many answers to this problem. Encourage students to look for numbers up to one million with these characteristics. Ask questions to draw out the limitations placed on the number by the clues, e.g. ‘Which numbers could be in the hundreds and thousands columns?’ e.g. 12_ _, 24_ _. ‘Which numbers could the final digit be?’ i.e. odd numbers. Review the fact that numbers that can be divided by 9 have digits that add to multiples of 9. When students have found a number that they think works, have them check back to ensure that all the necessary criteria are met. Using BODMAS Review the order of operations (BODMAS).Write _ × _ + _ + (_ ÷ _) – _ = 100 on the whiteboard. Ask, ‘Which numbers could be placed in this number sentence to make it correct?’ Allow time for students to explore possible solutions. Promote discussion about the thought processes needed to solve the problem.

Small Group Focus — Applying the Concept Focus Teaching Group • Using Calculators Review the use of calculators, having students share what they know about the process and number keys. Review the use of the constant function. Ask, ‘When might you use a calculator to help you solve problems? How do you know the calculator answer is correct? What do you need to think about to check?’Write an equation on the whiteboard and have one student use a calculator to solve it and report the answer. Encourage more advanced Ask, ‘Is this a reasonable answer? Why, or why not?’ Repeat with students to work with larger or decimal numbers. Have less advanced students work other equations, focusing on estimation and rounding skills. with a more limited range of numbers Draw out the need to have estimated a reasonable answer appropriate to their needs. before using the calculator, as a safeguard against entering incorrect information. Have students work independently to play ‘Guess My Calculator Number’ in pairs. One player, watched by their partner, enters a number followed by the ‘+’ sign. The same player then secretly enters a second number followed by the ‘=’ button, and shows their partner the answer.The partner must work out the hidden number. • Operating Order Have students review the order of operations in an equation, i.e. BODMAS (Brackets of Division, Multiplication, Addition, Subtraction). Show students an appropriate equation, e.g. 34 + 7 × 4 – (7 + 2) + 24 ÷ 6 =. Ask, ‘Which part of the problem do we solve first? Why?’ Demonstrate solving the problem explaining your thought processes as you go. Write the answer to each part of the problem above the relevant part of the equation. Repeat with other problems. Have students work independently to create their own multi-operational problems for a partner to solve. • Seeing Relationships Write on the whiteboard 64 ÷ __ = 16. Ask, ‘What do you know about both 64 and 16? What do they have in common?’ i.e. both have 4 and 8 as factors. Ask, ‘How could this help us to solve this problem?’ Guide students to solve the problem. Repeat. Shuffle a deck of Unit 23 Number Puzzles

91

playing cards (picture cards removed, Ace represents one). Deal out four cards to form two two-digit numbers. Ask, ‘Do these two numbers have anything in common? What is it?’ Encourage students to look for common factors, square numbers, etc. Repeat with other two-digit numbers. Have students work independently to deal two two-digit numbers and identify whether or not they have a relationship. Students could record this in a table in Word.


Number Squares (Student Book p. 66) Have students complete the Student Book page. Then students could create their own number square puzzles using BLM 50 ‘Blank Number Squares’. Broken Down Calculator Ask students to find three different ways to solve 464 × 42 if the ‘4’ button on the calculator were broken. Students could record their results as a slide show in PowerPoint. Four 4s Have students find ways to generate all numbers between zero and 100 using four 4s and any combination of operations of their choice. Note that it is possible to generate all numbers. More advanced students could investigate using four of a different digit to see how many numbers between zero and 100 they can generate. What Is My Number? (Student Book p. 67) Student Book page.


Missing Number Problems Have students invent their own missing number problems that require an understanding of the correct order of operations. Have them demonstrate three possible solutions to these problems, and present their findings as PowerPoint slides. Alternatively, students could make pages for a class book. The book could be made available for rainy-day problem-solving. Units 22–23 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p. 68.

Whole Class Share Time Ask, ‘What did you need to think about to solve the number squares puzzles?’ Discuss the strategies students used, focusing on the benefit of using known facts. Today I really liked …

Have students share the strategies they used to solve the problem, e.g. renaming numbers using addition, breaking numbers down into smaller components, etc. Discuss these with the class. Invite students to share their solutions. Ask, ‘Which equations were the most challenging to work out? Which were the easiest? Why?’ Invite a range of students to share their criteria. Ask, ‘What did you need to keep in mind when looking for the answers to these number problems? What known facts did you use? What patterns could you see?’ Have students share with the class the problems they created. Ask, ‘Which part of the problem would you solve first? Why?’

92


unit

24 Measurement

Mass Student Book pp. 69–70

BLMs 18 & 19

During this week look for students who can: • accurately read measurements on kitchen and bathroom scales and spring balances • appropriately choose grams as a unit of measurement for light objects, and kilograms or tonnes for heavier objects • fairly and accurately measure weight to the nearest gram • calculate the weight of objects from known measurements. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources bathroom scales, kitchen scales, pan balances, spring balances, metric weights, stones, packaged food items, potatoes, paper bags, boxes, flour, tablespoons, salt, bucket with a lid, jumper, jar of marbles, suitcase, advertising material and magazines, chart paper, rubber bands, cardboard boxes, masking tape, string, water, cooking oil, mixing bowls, wooden spoons, digital camera, fruit and vegetables, PowerPoint, Word, BLM 18 ‘Building a Weighing Machine’, BLM 19 ‘It Weighs 1 Kilogram’ Maths Talk Model the following vocabulary in discussion throughout the week: measure, scale, kilogram, gram, heavier than, lighter than, weighs the same

Whole Class Focus — Introducing the Concept Reading Scales Show students a range of devices used to measure mass. Ask, ‘What do these have in common?’ Focus on the calibrations used. Ask, ‘Where on this weighing instrument would you find its unit of measurement? Is this grams or kilograms? In intervals of 5, 10, 20, etc?’ Draw out that we would be likely to use kitchen scales to weigh quantities < 10 kg, spring balances to weigh items < 1 kg and bathroom scales to weigh items > 10 kg. Stress the need The Kilogram Collect a range of objects weighing close to 1 for accuracy, ensuring that kg, e.g. stones, tinned fruit, food packets, potatoes, book. Conceal the kitchen scales are level and set to objects in paper bags or boxes and show these to students. Allow zero, placing the objects gently in the centre of the pan, waiting until the them time to heft the objects and estimate their mass. Ask, ‘Which pointer is stationary, and ensuring that of these objects weigh more/less than/exactly 1 kg?’ Demonstrate nothing else is touching weighing items using kitchen scales. Have students explain how to the pan.

check the accuracy of the procedure. Weighing Flour Ask, ‘How many spoonfuls of flour weigh exactly 50 grams?’ Have students predict. Guide one student to check by measuring out 50 g of flour. Discuss strategies needed to ensure accurate measurement, Unit 24 Mass

93

e.g. adding one spoonful of flour at a time, smaller amounts when nearing 50 g. Ask, ‘How many spoonfuls of salt weigh exactly 50 grams? Why do you think so?’ Have students discuss their predictions in light of experience. Guide another student to measure 50 g of salt. Compare the results. What’s in the Bucket? Fill a lidded bucket with something weighing about 500 g, like a jumper.Tell students that the bucket is full. Allow them to heft it. Ask them to predict the weight of the bucket in grams or kilograms. Have one student weigh it using kitchen or bathroom scales. Ask, ‘What could be in the bucket?’ Discuss. Losing Your Marbles Show students a jar of marbles. Ask, ‘In which unit of measurement would it be best to record the weight of this jar of marbles, grams or kilograms? Why?’ Allow students to heft the jar. Ask, ‘How much do you think it weighs?’ Record predictions. Invite one student to weigh the jar using a pan balance and set of metric weights. Ask, ‘How much of the total weight is made up by the marbles/by the jar?’ Discuss. Ask, ‘How would we work out the answer?’ Talk about when it is important to know the total weight of a full container, and when you need to know only the weight of the contents, e.g. when loading a delivery truck, which has load limits, you must know the total weight of a load of jam, but a consumer buying a jar of jam is interested only in the weight of jam in the jar. Packing Your Case Display a standard suitcase. Ask, ‘What would this suitcase weigh full of clothes? How could you work it out?’ Discuss, listing estimated weights for various clothing items. Demonstrate using bathroom scales to weigh your shoes by weighing yourself with shoes on and then shoes off.Talk about why limits on baggage weight apply when flying.

Small Group Focus — Applying the Concept Focus Teaching Group • What Does It Weigh? Ask, ‘What features do you expect to see on a weighing scale?’ List suggestions. Examine the graduated scale on some kitchen scales. Ask, ‘In which unit does the scale measure? How do you know? What does this number mean? What does each of these marks mean? How many grams does each mark measure?’ Guide students to weigh a range of everyday items ensuring that they read the scale accurately. Have students work independently to record, to the nearest gram, the weight of a range of classroom items, ordering these from lightest to heaviest. • A Fair Measure Give each student a washed and numbered potato. Ask, ‘Which of these potatoes is the heaviest?’ Allow students to heft them. Ask, ‘How could we weigh each of these potatoes fairly?’ Discuss, You could demonstrate the results of poor technique, e.g. by then demonstrate accurate measuring technique. Once students weighing a potato placed on the side of the can measure accurately, have them work independently to pan, not setting the scale to zero, jiggling weigh each of the potatoes to the nearest gram, ordering them the scale while reading the weight, etc. from heaviest to lightest. Less advanced students could work with a partner. • Deciding on Units Ask, ‘Which units do we use to measure weight?’ Draw out the use of grams, kilograms and tonnes, explaining their relationship, i.e. 1 tonne = 1 000 kg; 1 kg = 1 000 g. Ask, ‘What sorts of things do we usually measure in kilograms/tonnes/grams? Why is the choice of unit important?’ Have students work independently to cut out pictures of objects from advertising material, display these on a chart and estimate their weight in an appropriate unit, e.g. a truck, 40 tonnes; a feather, 1 g.

94



Building a Weighing Machine (BLM 18) Give students a copy each of BLM 18 and assist them to follow the instructions. It Weighs 1 Kilogram (BLM 19) Have pairs find objects that weigh about 1 kg. Have them estimate the weight of each object, then weigh it to the nearest 5 g. Provide weighing equipment and a range of everyday food items, e.g. rice, fruit, etc. Students could record their findings on BLM 19.

To keep the activity manageable have students make only small quantities of playdough at a time.

Making Playdough Have students work in groups to find the best recipe for uncooked playdough (by mixing flour, salt, water and a little oil). Encourage them to look for ratios of ingredients in grams, e.g. 100 g of flour to 50 g of salt. Have students accurately measure the quantities of ingredients they use.They could take digital photos of the different batches of playdough, and use them to create a PowerPoint report to record the experiment. How Much Does It Weigh? (Student Book p. 69) complete the Student Book page.

Have students

Weekly Shopping (Student Book p. 70) Have students complete the Student Book page. They could then work with packaged food items to investigate the weight of food in each package versus the total weight of the item. Have them record their findings in a Word table. It may be useful to complete this activity over several days to allow students to weigh at home the objects they wish to pack.

Overseas Trip Have students work in groups to identify items they would take in their suitcase if going on a three-week overseas trip. Explain that the suitcase has a weight limit of 20 kg. Have students explore the weight of each item to determine what they can take and how much the suitcase will weigh. Unit 24 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p 71.

Whole Class Share Time Have students demonstrate their weighing machines. Ask, ‘How did you calibrate the scale? How accurate is it? What could you measure?’


Discuss the items students have weighed. Ask, ‘What weighs one kilogram?’ Talk about the difference in volume between 1 kg of heavy items and 1 kg of lightweight items. Discuss students’ measuring techniques. Ask, ‘How did you ensure that your weighing was accurate?’ Ask, ‘What is the best recipe for uncooked playdough?’ Compare the recipes. Focus on apparent differences in quantities. Ask, ‘Why are these recipes different? Do they both work?’ Discuss items in terms of relative volume and weight. Discuss students’ investigations into packaged food. Ask, ‘What weighs more, the food or the packaging? Why do some foods have heavy packaging and others light packaging?’ Have groups share their packing lists. Discuss strategies for working out the weight of the suitcase without having to pack and weigh it.

Unit 24 Mass

95

unit

Environmental Data



BLMs 20 & 60

During this week look for students who can: • pose appropriate questions to investigate • represent data using pie (sector) graphs, line graphs, bar (column) graphs and picture graphs • analyse data sets they have collected and present their findings • identify the features of different types of graphs • select the type of graph appropriate to their purpose in presenting the data • read and analyse pie (sector) graphs, line graphs, bar (column) graphs and picture graphs. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources pie (sector) graphs and weather maps from daily newspapers, school population data (available from the school office), graph paper, rulers, chart paper, Excel, PowerPoint, BLM 20 ‘State Populations’, BLM 60 ‘Graph Paper’ Maths Talk Model the following vocabulary in discussion throughout the week: minimum, maximum, tables, chart, graph, pie (sector) chart, bar (column) chart, line graph, data, collecting information, tally, table, estimate, trend

Whole Class Focus — Introducing the Concept The Census Ask, ‘ How many people live in Australia? Which state has the biggest population? How could we find out?’Visit the Australian Bureau of Statistics website (see Website 25a, BLM 79) to look at the latest data or use statistics from the 2001 census provided on BLM 20 ‘State Populations’. Ask, ‘What question/s might have been asked to collect this data? Why would governments want this information?’ Discuss why and how the census is collected every five years. List other information a government might want to know, e.g. age, sex, location, occupation of population. Ask, ‘What questions would you ask to collect this information?’ Reading Pie (Sector) Graphs Collect pie (sector) graphs from a daily newspaper, and weather maps for the preceding seven days. Enlarge these for students. Review the reading of pie (sector) graphs. Ask, ‘What do these graphs tell us? How important is the title?’ Pose questions that draw students’ attention to the information contained in the graphs. Review making a pie (sector) graph in Excel using data from weather maps, e.g. hours of daylight.

96


Reservoirs Before class, download data about reservoir storage levels from your local water board’s website — or use Website 25b (BLM 79). Show this to students. Ask, ‘Which reservoirs are full? How many reservoirs are less than half full?’ Consider the data on the line graph. Ask, ‘How is this year’s data different from that of other years?’ Model using the data to make a bar (column) graph. Discuss the scale of the graph and how this alters the appearance of the data. Ask, ‘What affects the amount of water in our reservoirs?’ Classroom Energy Use Ask, ‘What do we use in our classroom every day that requires energy?’ List suggestions, e.g. lights, heat, computers, etc. Ask, ‘How much energy do we use? How could we find out? Could we use less?’ Discuss the feasibility of collecting data to find answers to these questions, e.g. keeping a log to show how long each appliance runs during the day, monitoring classroom temperature. Gather further information by visiting the Australian greenhouse website (see Website 25c, BLM 79). Analysing Data Have students consider the data they have collected and examined. Ask, ‘What does this data mean for the environment?’ Draw out that looking at a range of data sets gives a bigger picture of the state of the nation, e.g. knowing that there are 4 822 663 people living in your state/country who use about 250 000 L of water a year is more meaningful when considered in relation to the level of water in the reservoirs. Ask, ‘Do we have enough water to get through the year? What if there is no more rainfall?’

Small Group Focus — Applying the Concept Focus Teaching Group • Reading Graphs Give each student a copy of BLM 20 ‘State Populations’ to see the four ways the data is presented. Ask, ‘How do you read the data in the table? How has it been organised?’ Guide students to locate different pieces of information, e.g. which states have populations above two million. Refer to the bar (column) graph. Ask, ‘What does the scale on the y-axis tell us? What does the x-axis tell us? What can we tell from looking at the Please note: Line graphs are most appropriately relative heights of the bars?’ Consider the line graph. Ask, ‘What does used to indicate a changing each axis tell us? What does the line suggest? Is this an effective way to trend, rather than relative show relative population size?’ Consider the pie (sector) graph. Discuss sizes. its features and the information it conveys. Ask, ‘Which state has the biggest population? How do you know?’ Discuss the pros and cons of each form of data presentation. Have students use class-generated data sets to make a range of graphs in Excel. Have them compare their effectiveness. • Looking for Answers Ask students to think about environmental issues that concern them, e.g. pollution, water usage, greenhouse gas emissions. Ask, ‘What data could you collect to find out what is really happening in our Environmental data local area? e.g. counting cars that pass the school could provide data can be found easily on the about local air quality. Encourage students to pose questions of their Internet by visiting sites related to environment, energy use or own. Ask, ‘How would you collect this data?’ Guide them to formulate greenhouse gases. questionnaires or tally sheets. Have students work independently to collect data and present it.They could compare it with published data. • Making Bar (Column) Graphs Give students graph paper (BLM 60), rulers and data about the school population. Ask, ‘What does this data show? How many boys/girls are there at our school? How many students in Year 5?’ Guide students to make a bar (column) graph to present Unit 25 Environmental Data

97

information drawn from this data, e.g. the number of students at each year level. Ask, ‘What scale would we use on the y-axis? What is the biggest number we need to show? What intervals do we show on the scale?’ Mark in the axes and plot the first two bars on the graph. Have students work independently to finish the graph and then to make another to present different information drawn from the data, e.g. the number of boys and girls at each year level.


Our Population Have students use websites to investigate other questions about Australia’s population. (See Websites 25a, 25d and 25e, BLM 79.) Have students pose questions, find the data they need and present this in Excel as a chart or in PowerPoint as a slide show. Rainfall Ask, ‘What is the difference between a normal year’s rainfall and rainfall in an El Nino or La Nina year? Have students visit the Bureau of Meteorology website (see Website 25f, BLM 79) to compare and contrast rainfall expectations during a normal year, an El Nino year and a La Nina year. Have students record their findings in various ways. Water Wise (Student Book p. 72) Have students complete the Student Book page. They could then visit Website 25g (BLM 79) to calculate the amount of water used in their homes. Have students download the final data and use this to make a graphic representation of water usage in Excel. Saving Energy (Student Book p. 73) Have students collect and analyse data about current energy usage in the classroom. To calculate the amount of energy used, students could visit the TXU website (see Website 25h, BLM 79). Have students record their data and results on the Student Book page. Planning for the Future Have students work in teams to consider the class’s data about the environment. Have each group collect any necessary additional data and make predictions and recommendations about what needs to be done to address issues of energy and water use in Australia. Each group should support its position through analysis of the data, and could present its findings as slide shows, mock interviews, books or charts. Unit 25 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p. 74.



Have students share their work. Ask, ‘What do we know about Australia that we didn’t know before? How does knowledge of this data affect us?’ Discuss the ways students have presented their data. Ask, ‘Why have you used a pie (sector) graph here? How does this enhance understanding of the data?’ Discuss what students have learned from looking at graphs showing rainfall during different weather patterns. Have students share their graphs. Ask, ‘What surprised you about this data? Does your family have above- or below-average water consumption?’ Have students share their findings. Discuss any conflicting data. Set targets for a more energy-efficient class and monitor your progress. Discuss the need to consider a range of data when making decisions.

98


unit


Adding Decimals Student Book pp. 75–77

BLMs 14 & 52

During this week look for students who can: • add decimal numbers including numbers with zeros • use mental and written methods, and calculators, to add numbers to 999 999.99 • identify when addition of decimal numbers is used in everyday life • verbalise the thought processes used to solve addition problems involving decimals. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources stopwatch, bean bags, long measuring tape, advertising brochures, card, ten-sided dice, Lego blocks, chart paper, classified sections from daily newspapers/Trading Post, Internet access, PowerPoint, Kid Pix Studio Deluxe, BLM 14 ‘High or Low’, BLM 52 ‘Calculating Averages’ Maths Talk Model the following vocabulary in discussion throughout the week: addition, carry, sum, more, add, plus, increased, all together, total, decimal place, hundredth, tenths, unit, tens, hundreds, thousands

Whole Class Focus — Introducing the Concept Adding Decimals Write 10.69 + 4.5 on the whiteboard. Ask, ‘How would we write this vertically? What do we need to keep in mind when writing the numbers?’ Draw out the need to keep numbers in vertical columns according to the place value of each column. Model adding the two numbers, pointing out the value of each digit. Focus on the placement of the decimal point. Repeat with other like problems. Average Time Ensure that students know how to use a stopwatch. Time one student saying the alphabet backwards. Write this time on the whiteboard. Time a second student doing the same and write this time on the whiteboard underneath the first student’s time. Continue timing other students until there are 10 times recorded vertically on the whiteboard. Ask, ‘Who was quickest to say the alphabet backwards? Who had the next fastest time?’ Introduce the concept of an average time for the group. Say, ‘Sometimes when looking at a group’s performance it is helpful to look at the average performance of the group. An average is one score that represents a whole collection of scores. An average score is calculated by adding all of the scores and dividing the answer by the number of scores.’ Demonstrate finding the group’s average time for saying the alphabet backwards. Focus on adding the decimal numbers, demonstrating how to Unit 26 Adding Decimals

99

carry numbers from hundreds to tenths, tenths to units, etc. Discuss the position of the decimal point. Point out that when dividing a decimal number by 10, the decimal point is moved one place to the left. Bean Bag Flick Take students outside and have them measure how far they can flick a bean bag by standing on one foot, balancing the bean bag on the top of their other foot and then flicking it as far as they can with their raised foot. Provide a long measuring tape so that students can measure the distance of their flick in metres to the nearest centimetre, e.g. 7.52 m.When each student has had several practice flicks, take the final measurement. Return to the classroom and list all students’ scores. Say, ‘What if we divided the class into two teams, those with first names starting with A-J, and those with first names starting with K-Z. If we added up the individual scores of each team, which team would have the biggest total?’ Have students work it out. Discuss their strategies for adding the decimals. The Meaning of the Zero Within the range 0.01 - 99.99, write vertically a range of decimal numbers containing zeros, e.g. 35.06, 19.60, 30.96, 40. Ask, ‘Why do these numbers have zeros in them? What values do these zeros stand for? Could we leave them out? Why?’ Demonstrate adding the list of numbers, pointing out how to deal with the zeros as you go. Spend $100 Give students advertising brochures. Ask, ‘Can you find any two items with a total price of $100? How did you work it out?’ Allow time for students to share their strategies. Focus on the usefulness of rounding numbers to the nearest dollar or $10 to get a quick price check. Have individuals share their working out and explain how to add decimals.

Small Group Focus — Applying the Concept Focus Teaching Group • Addition with Decimals Before class, cut up a supermarket catalogue. Paste the items on cards. Give each student two cards. Ask, ‘How much money would you need to buy the items on your cards? How could you work it out? Discuss strategies, e.g. setting prices out vertically as an algorithm, rounding to the nearest 10 cents or dollar, making up to the nearest dollar or $10. Guide students to record and solve the problem focusing on carrying, especially across the decimal point. Have students work independently to sort the cards to show how they could spend $5, $10, $20, and record their findings. • Rounding in Decimal Addition Give students advertising brochures. Ask them to select one item that they would like to buy. Ask, ‘How would you round the price of this item up or down to the nearest dollar?’ Discuss the thought processes needed. Ask, ‘When would rounding be useful in adding decimal numbers?’ Guide students to round some decimals, e.g. 1.19 to the nearest tenth, 1.80 to the nearest one, 150.09 to the nearest hundredth. Have students work independently to round prices of other items in the supermarket catalogue and to record the results. Have them choose ten items they would like to buy, estimate how much they would cost by rounding, then work out the total cost. Students could record this as a shopping list. More advanced students could make numbers with more digits.

100

• All Lined up Provide students with sets of number and decimalpoint cards from BLM 14 ‘High or Low’. Have students shuffle the cards and deal them to form three- and four-digit numbers. Once students have made three numbers ask them to align the cards so that


they can be added vertically. Ensure that students take into account the position of the decimal point. Guide students to complete the addition. Have students work independently to make and solve other three-number addition problems using these cards.


Make or Break 10 Have students practise adding decimals by playing ‘Make or Break 10’ in groups of up to four players. To play, each player in turn rolls three ten-sided dice, using the numbers rolled to form a number with two decimal places, e.g. 5, 3, and 9 are rolled; number formed could be 5.39, 3.59, 9.53, etc. After each round, players add the new number to their progressive total. Play continues until one player has made exactly 10.00, or one player has a total of less than 10 when all other players have broken 10. The player who first achieves either of these outcomes wins. Average Score (Student Book p. 75) Have students complete the Student Book page. When finished students could work in groups to time each other completing a range of activities. Each student should complete each activity ten times and then work out the average time taken. Students could check to see if their times improve with daily practice. Students could record their findings on BLM 52 ‘Calculating Averages’. 100-metre Flick (Student Book p. 76) Have students complete the Student Book page. Assist them to record in metres (i.e. in decimal numbers) the distances measured in metres and centimetres. Adding Numbers with Zeros (Student Book p. 77) Have students complete the Student Book page. Students could then further investigate decimals by researching the history of the decimal system on the Internet or in the library.Website 26 (BLM 79) is a useful site. Spend $1 Million Have students create posters, or slide shows in PowerPoint or Kid Pix Studio Deluxe, to show how they would spend $1 million. Provide advertising material, the classified sections from newspapers, the Trading Post and Internet access so that students can research prices as they complete this task.


Today I really liked …

Review adding decimal numbers. Ask, ‘What do we need to keep in mind about place value when adding decimal numbers? What do zeros in decimal numbers indicate? How do you add a decimal number with two decimal places to a decimal number with one decimal place?’ Ask, ‘How do you work out an average score?’ Talk about the need to check that the addition is accurate before working out the average. Have students share their results. Ask, ‘Who had the highest total after five/ten turns?’ Discuss strategies students used to check their addition. Ask, ‘What do the zeros mean in decimal numbers. Why are they important? What have you learned about adding decimal numbers?’ Have students share their posters or slide shows. Ask, ‘How easy is it to spend exactly $1 million?’

Unit 26 Adding Decimals

101

unit

Subtracting Decimals



BLMs 21, 22, 23, 24 & 25

During this week look for students who can: • subtract decimal numbers including numbers with zeros • use mental and written methods, and calculators, to subtract numbers to 999 999.99 • identify when subtraction of decimal numbers is used in everyday life • verbalise the thought processes used to solve subtraction problems involving decimals. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources ten-sided dice, advertising material (including some containing electrical appliances), 10 m of wool or string per student, the classified sections of the daily newspapers/Trading Post, MAB blocks, chart paper, counters, PowerPoint, BLM 21 ‘Subtraction Talent Search’, BLM 22 ‘Decimal Number Mat’, BLM 23 ‘Subtraction Problems’, BLM 24 ‘Cheque Book’, BLM 25 ‘Minimal Differences’ Maths Talk Model the following vocabulary in discussion throughout the week: subtract, difference, less than, minus, decrease, fewer than, reduce, have left, decimal place, regroup

Whole Class Focus — Introducing the Concept Subtraction Talent Search Give each student a copy of BLM 21 ‘Subtraction Talent Search’. Explain to students the significance of signing the sheet, i.e. that their signature means that they can answer the question and explain their answer to the class. Have students quietly move around the classroom collecting ten different signatures; one may be their own. Gather the class and ask, ‘Who has a signature from someone who can answer the question, “What is a decimal point?”’ Ask the person who signed to explain the answer to the class. Discuss their answer. Continue until all questions have been answered and answers discussed. Focus on the strategies needed to subtract decimal numbers. Decimal Difference Enlarge BLM 22 ‘Decimal Number Mat’ and display it. Ask, ‘Which two numbers have the greatest difference?’ Allow students time to work it out, then invite individuals to demonstrate answers on the whiteboard. Ask, ‘What is the difference between the first two numbers on the number mat, i.e. 146.3 and 52.07? How could we work this out?’ Demonstrate setting out this problem vertically on the whiteboard, pointing out the need to line up digits according to their place value.

102


Complete the problem, explaining as you go, e.g. ‘When I write 146.3 I need to add a zero to indicate the hundredths place, because I will be subtracting a number with a digit in the hundredths place. Repeat with other problems. Change Roll a ten-sided dice six times and record the numbers that come up. Have students use these numbers to form a number with six digits including two decimal places. This number becomes the student’s ‘bank’. Using the same six digits with two decimal places, write a figure for the class ‘bank’ on the whiteboard. Provide students with brochures advertising electrical appliances. Choose one item from the catalogue for the class to buy from the class ‘bank’. Model subtracting the cost of the item from the class ‘bank’ number, first by estimating, then by working out exactly how much change there will be. Make explicit the steps to follow to accurately subtract the number, starting with the need to set out the problem so that digits with the same place value are vertically aligned, and discussing regrouping. Ask each student to select an item from the catalogue that they could afford to buy with their ‘bank’ money. Ask, ‘How much money would you have left if you bought this item?’ Allow time for students to work it out. Invite individuals to share their working out with the class. Why Subtract Decimals? Ask, ‘When might we need to be able to subtract decimal numbers?’ List suggestions, e.g. working out change, the difference in temperature over a day, etc. Ask students to give an example of a relevant subtraction problem in each context. All Tied Up Have each student measure out exactly 10 metres of wool or string. Ask, ‘How many metres of wool/string do you think you would use if you wrapped it around your body four times. How much would you have left?’ List students’ suggestions, then demonstrate the use of subtraction to solve the problems. Have students carry out the activity, measuring in metres how much string they use. Ask, ‘How could you work out how much string is left without measuring?’ Discuss writing 10 m as a decimal number (10.00 m). Guide students to solve the problem using subtraction.

Small Group Focus — Applying the Concept Focus Teaching Group • Finding the Difference Make cards from BLM 22 ‘Decimal Number Mat’. Give each student two cards. Ask, ‘What is the difference between these two numbers? How could you find out?’ Guide students to set out Provide concrete their problems, considering the place value of digits.Then guide them in materials such as MAB blocks to solving the problems, pointing out the thought processes needed for assist those students who each step. Repeat. Have students work independently to find other need them. differences and record their solutions using formal notation. • Subtraction Problems (BLM 23) Give each student a copy of BLM 23. Guide students to work through the problems in the first column. Demonstrate setting out the problems vertically. As students work out the problems, provide concrete materials to those who need them. When students are solving the problems competently, have them complete the other problems independently. • Cheque Book (BLM 24) Explain how a cheque book works. Provide students with a copy of BLM 24, advertising material and newspaper classifieds. Guide them to complete the activity, discussing the subtraction process used. Have students reflect on what they needed to know to perform the subtractions. Unit 27 Subtracting Decimals

103


Finding Talent Have pairs write their own ‘Subtraction Talent Searches’ based on BLM 21. Students could publish their talent searches on the class website. Other students could then sign in to indicate that they are able to explain the answers to the questions. Alternatively, talent searches could be posted on charts around the classroom. Invite students to read the charts and sign their names where they feel they can. Closest to Zero Have students play ‘Closest to Zero’ in pairs. To play, each pair will need a copy of BLM 22 ‘Decimal Number Mat’ and a counter. Each player starts with a score of 9 999. Players take it in turns to toss the counter onto the number mat and subtract the number they land on from the starting number. On the next round, players subtract the number they land on from their previous total. Play continues for ten rounds. The player with the score closest to zero after ten rounds is the winner. Players must record each round using formal written subtraction. Remaining Money Tell each student that they have $99 999.99 in the ‘bank’. Ask them to spend as much money as they can buying only ten items. Provide students with advertising material, the classified section from a newspaper and access to the Internet to look up prices. Have students prepare a chart or multimedia presentation to explain how they spent the money and how much money they will have remaining in the bank. Subtracting Numbers with Zeros (Student Book p. 78) Have students complete the Student Book page. Then students could create a PowerPoint or Kid Pix Studio Deluxe slide show, or chart with the heading, ‘101 Reasons for Needing to Know How to Subtract Decimal Numbers and How to Do It.’ How Much Change? (Student Book p. 79) Have students complete the Student Book page. When finished students could play the game ‘Minimal Differences’ on BLM 25. Units 26–27 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p 80.

Whole Class Share Time Invite different pairs to check that the signatories to their talent search can indeed explain the aspect of subtraction for which they have signed up. Discuss the thought processes needed to write the talent search. Today I found out …

Ask, ‘Which number was best to land on? Why?’ Invite students to share their working out for different rounds of the game. Have students present their projects to the class. Ask, ‘How did you work out how much money you had left after you bought the ten items?’ Have individuals demonstrate their subtractions. Ask, ‘Why might you need to subtract decimals?’ Have individuals share their ideas, and their explanations of how to do it. Ask, ‘What have you learned about subtracting decimal numbers today?’ List suggestions on the whiteboard.

104


unit

28 Measurement

Exploring Measurement Student Book pp. 81–82

BLMs 26, 27, 76 & 77

During this week look for students who can: • estimate and calculate length, area and volume • draw plans to a simple scale • work out approximate cost of materials based on the area to be covered. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources 10 × 10 cm cards, 30-cm and metre rulers, long tape measures, a collection of small cardboard boxes and bottles, card, cardboard shapes, Centicubes, grid paper (BLM 76 or 77), advertising material from flooring companies, BLM 26 ‘My Dream House’, BLM 27 ‘Estimate then Measure’ Maths Talk Model the following vocabulary in discussion throughout the week: area, perimeter, volume, metre, square metre, cubic metre, litre, cost, total area, scale, to scale, scaling up

Whole Class Focus — Introducing the Concept Please note: This series of learning experiences is part of a project in which students design the house of their dreams. Most aspects of the project will take more than one session to complete and could be regarded as a total project. See BLM 26 ‘My Dream House’. Designing to Scale Provide students with ten 10 x 10 cm cards. Have them arrange these as a floor plan for a building. Ask, ‘How could we draw a plan of this building on A4 paper when the model is much bigger than the paper?’ Draw out the need to use a scale. Guide students to make a scale drawing of their model. A useful scale would be 1 cm = 5 cm. The Sandpit Review working out volume using the formula ‘Height × Width × Depth = Volume’. Say, ‘The school needs new sand for the sandpit. How could we work out how much sand to order?’ Work through the problem with students, drawing out the need to work in metres and cubic metres. Work through other similar problems, e.g. how much water would we need to fill a rectangular swimming pool? Paint the Classroom Ask, ‘How much paint would we need to paint our classroom? How would we work it out?’ Draw out the need to know the area Please note: of the ceiling and each wall, the area of windows and doors, and the area a Dulux says that a 4-L tin of paint quantity of paint will cover. Work through the problem with students, will cover about 64 m2. ensuring that they know how to work out area. Unit 28 Exploring Measurement

105

Classroom Area Ask, ‘How much space do you need to work in our classroom? How could you work it out?’ Model working out the area taken up by your desk, including the space where you sit. Guide students to work out the area of their tables. Focus on the formula ‘H × W = A’. (Those sharing tables will only need to calculate the area of half the table.) Taking Up Space Show students a collection of boxes and bottles. Say, ‘I want to find a box just big enough to store all of these. How big will the box need to be?’ Have students work in small groups to solve the problem. Encourage them to estimate the sizes of the objects. Have them share their solutions and mark the dimensions of their storage box on the floor to see if the objects fit into the space. Discuss the importance of working out approximate storage needs when designing kitchen cupboards and wardrobes. Students could investigate the capacity of their own wardrobes. Scaling Up Demonstrate how to build a cardboard model of a box from a scale drawing. Craft books can provide useful models. Discuss your thought processes as you convert a 1 cm = 10 cm drawing into a model.

Small Group Focus — Applying the Concept Focus Teaching Group • Measuring Length Review measuring length. Point out the need to align the zero on the ruler with the edge of the object being measured and to read the scale from zero. Ensure that students understand the millimetre markings on the ruler. Ask, ‘Can you see something that is about 20 centimetres long? What is it?’ Have students measure to test their predictions. Have students work independently to complete BLM 27 ‘Estimate then Measure’. • Measuring Area Review calculating area. Provide cardboard shapes including squares, rectangles, L-shapes, H-shapes and other irregular shapes with right-angled corners. Give each student a shape. Ask, ‘How could you work out the area of your shape?’ Provide Centicubes and rulers. Have students estimate the area of their shape in cm2 and then work it out using rulers or Centicubes. In the case of irregular shapes, discuss the need to work out the areas of discrete sections and then add these to give the total area. Have students estimate, measure and record the areas of five other cardboard shapes. • Measuring Volume Review the definition of ‘volume’. Ask, ‘Which units do we use to measure volume?’ List these on the whiteboard, modelling how to write them, e.g. cm3. Give each student a small cardboard box. Ask, ‘What do you estimate the volume of your box to be? How did you work it out?’ Encourage students to refer to the estimated dimensions of the box. Provide Centicubes and rulers and guide students to measure their box and work out its volume. Ask, ‘Is the volume of the box greater or less than your estimate?’ Discuss how to calculate volume (H × W × D = V), using the dimensions of one of the boxes. When students are comfortable with this, have them work independently to calculate the volume of other boxes and record their findings.


106

Competition House (Student Book p. 81) Have students complete the Student Book page. Then have them design their own dream house and complete scale drawings of it. Provide grid paper (BLM 76 or 77) and have students work to a scale of 1 cm = 1 m. Students could visit websites to find out how house plans are drawn (see Website 28a, BLM 79).


My Backyard Have students draw a design for the backyard of their dream house, including a sandpit and a swimming pool. Have them work out how much sand to order, the capacity of the swimming pool, and how much concrete is needed for any paths. They could use the Internet to research building regulations on swimming pools and driveways. Painting the House (Student Book p. 82) Have students complete the Student Book page.When finished, they could work out the amount of paint they will need to paint their dream house. Students could check their calculations at Website 28b (BLM 79). Floor Coverings Have students work out what floor coverings they will need for their house. Provide advertising material from flooring/tile/carpet companies so that they can work out the cost of covering each room. Cupboards Have students design storage space for their dream house. They could research household needs by measuring storage space in their own homes and interviewing their parents. A Model House

Have students build a model of their dream house.

Unit 28 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p 83.

Whole Class Share Time Have individuals share their house plans. Discuss the features they have included. Ask, ‘How big is your bedroom? What could you fit in it? Discuss issues arising from drawing houses to scale. Ask, ‘How did you work out how much concrete you would need?’ Discuss students’ decisions about the thickness of the concrete and the width of the paths. Ask, ‘Would that driveway be strong enough for a car to drive on? Would your pool meet council regulations?’ Today I discovered …

Ask, ‘How much paint do you need to paint your dream house? How many coats of paint does this allow for? How much will it cost?’ Have several students present their budgets for floor coverings. Ask, ‘How did you work out how many tiles/how much carpet you will need? What will be the total cost of floor coverings?’ Ask, ‘How much storage space is enough for an average family? How have you included this in your dream house?’ Hold a dream-house exhibition. Invite parents and other classes to attend. Have each student explain to a group how they worked out the size of their house and the estimated costs of landscaping, paint and floor coverings.

Unit 28 Exploring Measurement

107

unit

29 Space

Reading Maps Student Book pp. 84–85

BLMs 28, 67 & 68

During this week look for students who can: • use distance and direction coordinates to read maps and give instructions for journeys • identify the scale used on a map and use this to calculate distance • use maps to plan trips. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources compasses, masking tape, maps, street directories, large world map, atlases, state map, map of the local area, counters, straws, Centicubes, card, rulers, Word, BLM 67 ‘Grid Coordinates’, BLM 68 ‘Coordinates Cards’, BLM 28 ‘Pirates’Treasure’ Maths Talk Model the following vocabulary in discussion throughout the week: north, south, east, west, equator, tropics, hemisphere, direction, scale, coordinates

Whole Class Focus — Introducing the Concept North, South, East and West Give each student a compass. Ask, ‘What features does a compass have? What do we use it for?’ List its features and uses. Make sure students know how to read the compass. Have students stand up and face north. Ask, ‘In what direction will you be facing if you turn 90° to the right?’ Have students predict then check using the compass. Repeat, asking them to turn 90° and 180° to the left or right. Coordinates Mark a large 10 × 10 grid on the floor with masking tape. Ask one student to turn their back while another student stands in a square on the grid.When the rest of the class is certain of the square the student is standing in, the student leaves the grid. The class must now direct the first student to stand in the correct square. After several turns, place coordinate cards along the edges of the grid. Show students how to read the coordinates (letters on the x-axis, then numbers on the y-axis). Repeat. Ask, ‘How did having coordinates help you to find the correct square?’ Provide a range of maps and street directories for students to examine. Ask, ‘Where are the coordinates on these maps?’ Where Am I? Show students a large world map, pointing out the equator, tropics, hemispheres, continents, etc. Show students how to read the lines of latitude and longitude. Ask, ‘Where is Australia/England/New York?’ etc. Guide students to find the coordinates of these places. Give each student an atlas containing a world map. Play ‘Where Am I?’. To play, select a place on

108


the map and give clues to its location, including directional information. (For example: I am in the Southern Hemisphere. I am south of Darwin and east of Alice Springs. I am about 500 km north of Sydney.) Where Will We Go? Give students a map of the state. Say, ‘My family wants to go on a three-week holiday. My partner wants to go surfing, my children want to go canoeing and I want to walk in the mountains, so we will visit three places. Where should we go?’ Discuss the issues. Ask, ‘Where could you go for good surf/canoeing/to walk in the mountains?’ Refer to the map, discussing the key and how to find particular features. Allow students time to select destinations that meet the criteria. Understanding Scale Give each student a map of the local area that includes the scale. Discuss the scale. Ask, ‘How far would I travel if I moved one centimetre (or other appropriate measure) on this map?’ Have students find the school on the map. Ask, ‘How far are the shops/is the police station from the school?’ Ask, ‘Where could I go if I could only travel about two kilometres from school?’

Small Group Focus — Applying the Concept Focus Teaching Group • Reading Coordinates Give each student a copy of BLM 67 and cards cut from BLM 68. Place a counter on the grid. Ask, ‘What is the location of this counter? How do we read the coordinates?’ Demonstrate finding the To help them find the letter coordinate and then the number coordinate. Give each square defined by the coordinates, student a letter- and number-coordinate card and guide them students could run their fingers along the row and column until they intersect, or use to place a counter on the appropriate square. Repeat. Have two straws, laying them on the row and students work independently to draw shapes on the grid and column to find the point of write their coordinates. The coordinates could then be given to a intersection. partner to plot the shape on another copy of the grid.This could also be done using ‘Table’ and ‘Line’ tools in Word. • Reading Maps Give students an atlas. Have them find a map of Australia. Point out the lines of latitude and longitude. Ask, ‘Where is Brisbane? Where is Sydney?’ Have students identify these locations using approximate lines of latitude and longitude. Have students locate the capital city of another country in the atlas. Have them create ‘Where Am I?’ cards to identify the location of different places in the world. Cards should have the coordinates of latitude and longitude on one side and the name of the place on the other. These can be used to play the game ‘Where Am I?’ (see above).The first person to locate each place is awarded a point; the person with the most points at the end of the game wins. • Using the Scale Provide students with rulers and a scale map of the local area. Have students find the scale on the map. Discuss its significance. Have students locate the school on the map. Guide them to use their rulers to find out what is, say, 1 km along the road from the school, adjusting the distance according to the scale. Have students work independently to plot their journey home from school or to a local venue such as the swimming pool, using the scale to work out the distance travelled.


Pirates’ Treasure (BLM 28) In groups of four, have students play ‘Pirates’ Treasure’. Give each group a copy of BLM 28 and two wooden cubes to use as dice (one marked ‘90° to right’, ‘90° to left’, ‘180°’, ‘360°’, ‘Straight ahead’ and ‘Straight back’; the other marked ‘10 km’, ‘20 km’, ‘30 km’, ‘40 km’, ‘50 km’ and ‘60 km’). To begin, each player chooses an island and colours in a Unit 29 Reading Maps

109

square next to it to represent their ship. Players take turns to throw Players may not cross both dice and follow the instructions, e.g. if dice say ‘90° right, 20 over an island, and have to miss a turn if km’, the player must turn their ship 90° to the right and move they attempt it. They must also follow exactly it 20 km (by colouring two squares to the right). But first, the the instructions on the dice. Other players may challenge if they believe a player player must name the direction in which they are travelling. has moved illegally. Each time a pirate reaches an island, they collect the treasure

(number of gold coins marked) and record it on a progressive tally. The first player with 1 000 pieces of gold wins. Find Your Way (Student Book p. 84) Have students complete the Student Book page. Four in a Row Have students play ‘Four in a Row’. Give each pair a copy of BLM 67 and cards cut from BLM 68. Have players sort the cards into two piles: numbers and letters. To play, students take it in turns to draw a card from each pile, and to write their name in the corresponding square on the grid. The first player to write their name in four squares in a row wins. If a player draws coordinates that have already been used, they miss a go. Virtual World Trip Have students plan a world trip to visit two countries on each continent. They must identify the location of the country and the direction of travel. Students should provide information about each country’s population and climate details, and record one other interesting fact about the country. Students could consult Website 29 (BLM 80). Going on Holiday (Student Book p. 85) Student Book page.


Spotto Have students work in small groups to make a set of clue cards to play ‘Spotto’. This game is played with a state map. Using their school as a reference point, students write clues to locations for others to work out, e.g. ‘This place is about 50 km south-east of the school’. Chosen locations (e.g. towns, rivers, mountains, national parks) must be clearly visible on the map. When cards are made, have each group read their clues to the class. Other teams write down what they think each location is. The team with the most correct answers wins.

Whole Class Share Time Today I created …

Have students discuss any difficulties they had in working out the direction in which they were travelling. Have them share their strategies for overcoming these. Ask, ‘How do you read coordinates? Why do maps have coordinates?’ Have students share their world trips with the class. Focus on the use of maps and their features. Have students share their planned holidays with the class. Discuss the directions they have given, focusing on the most effective words used. Ask, ‘Why do maps have scales? How does scale work? How does having a scale help us to use the map?’

110


unit

30 Space

Making Maps Student Book pp. 86–87

BLMs 60, 76 & 77

During this week look for students who can: • draw maps according to specific instructions • draw maps of familiar locations • use coordinates to locate key features on a map • draw maps of familiar locations to scale. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources maps having a key and a scale, card, aerial photos of local area, acetate sheets, jar of jelly beans (or alternative treasure), post-it notes, house plans drawn to scale, rulers, map of the local area, street directories, measuring tapes, compasses, digital camera, Word, grid paper (BLM 76 or 77), graph paper (BLM 60) Maths Talk Model the following vocabulary in discussion throughout the week: north, south, east, west, direction, scale, coordinates, key

Whole Class Focus — Introducing the Concept Features of Maps Provide a range of maps for students to review. Each map should feature a key and display a scale. Ask, ‘What do all of these maps have in common?’ Focus on the key and scale of each map, drawing out the various ways these have been presented. Discuss cases where symbols have been used instead of words. Making Maps Make cards displaying the names of a number of civic buildings and places for community use, e.g. town hall, library, church, school, shopping centre, swimming pool, football ground, playground. Say, ‘We have been appointed town planners. We have been asked to plan a new town from scratch. Where will we put each of these buildings/places?’ At students’ suggestions, lay out the cards around the room. Ask, ‘How can we show the mayor what our town will look like?’ Draw out the idea of making a map. Demonstrate making a map of the town you have created. Have students name the town. Aerial Photos Show students an aerial photo of the local area. Ask, ‘What does this photo show? What is its scale?’ Overlay the photo with an acetate sheet and trace over key features on the photo to make a rough map. Place the sheet on the whiteboard so that students can see the lines and shapes. Ask, ‘What do I need to add to this to make it into a map?’ i.e. names of roads, main features, arrow pointing north, etc. Talk about the use of aerial photos in map-making. Unit 30 Making Maps

111

Treasure Map Before class, hide some treasure (e.g. a jar of jelly beans) somewhere in the schoolyard. Make a treasure map showing where to find the treasure. Cut the map up into pieces. Organise the class into groups. Give each group a piece of the treasure map. Ask, ‘What does your part of the map show?’ Have students reassemble the map and follow it to the treasure. Share the treasure. My Town Read the description of the town on Student Book p. 87 ‘My Town Centre’. Ask, ‘What buildings are there in this town? Where are they?’ Have students write on post-it notes the names of the places mentioned and arrange these on their tables. Consider the different arrangements students have made. Ask, ‘Which of these arrangements are right?’ Draw out that many different arrangements would meet the stated criteria. House Plans Show students a set of house plans. Discuss the features of the plans including the use of scale and the way doors, windows and other fixtures are represented. Ask questions relating to the scale of the house such as, ‘How big is this house? How many metres long is the bedroom?’ etc.

Small GroFup Focus — Applying the Concept Focus Teaching Group • Drawing to Scale Show students a range of everyday items, including a book. Ask, ‘What would I need to know to make a scale drawing of this book?’ Draw out the need to know its measurements. Measure the book. Say, ‘I am going to use a scale of 1 cm = 10 cm.What does this mean? Using this scale, how long will the side of the book be in my drawing?’ Draw a table on the whiteboard showing the conversion, e.g. a 29 × 21 cm book would become a 2.9 × 2.1 cm book in the scale drawing. Guide students to draw this book to scale on grid paper (BLM 76 or 77) or graph paper (BLM 60). Then guide students to measure another object, scale down the measurements, and complete a scale drawing of the object. Have students work independently to make scale drawings of other objects. • My Bedroom Have students write on post-it notes the name of every piece of furniture in their bedrooms. Then have them arrange the notes to represent the placement of the furniture. Have students describe their bedrooms. (For example:The bed is under the window.The bookcase is next to the bed, etc.) Ask, ‘How could we make this an accurate map of your bedroom?’ List on the whiteboard the steps students would have to follow, e.g. measuring the room, drawing the room to scale, measuring each piece of furniture, drawing the furniture to scale, working out the exact position of the furniture in the room, labelling things on the map, creating a key, drawing a scale diagram, etc. Have students work independently to make an accurate map of their bedroom. • Visiting Friends Have students consult a map of the local area or street directory and locate the houses of some of their friends. Ask, ‘How would you travel from your house to visit one of your friends? Guide students to explain the route they would take, telling you some of the things they would pass on the way (e.g. shops, school, etc.). Point out how different these things look in reality from how they appear on the map. Have students work independently to make a map showing the way to two different friends’ houses.

112



Classroom Maps Have students make a map of the classroom to scale, and include a key. Provide measuring tapes, compasses, rulers and grid paper. Alternatively, students could make their map using tables and drawing tools in Word. Drawing Maps (Student Book p. 86) Have students complete the Student Book page.When they have finished, students could draw a map of their own town or local area, using a key and providing a scale. Photo Maps Have students take some bird’s-eye photos of areas of the school using a digital cameral. (Such photos could be taken from the top of the play equipment, or from an upstairs window.) Alternatively, provide other aerial photos for students. Have students use acetate sheets or tracing paper to make maps from these photos. Ask them to work out a rough scale for their maps. Hidden Treasure Have students make their own treasure maps for other students to use to find the ‘buried treasure’. Encourage students to draw their maps to scale and to include a key.These maps could be posted on the class website so that younger students could find the treasure. My Town Centre (Student Book p. 87) Student Book page.


My Ideal House Have students draw up a plan, to scale, of their ideal house. Provide grid paper. A useful scale could be 1 cm = 1 m. More advanced students could work with specified minimum room sizes. Units 29–30 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p. 88

Whole Class Share Time Invite a range of students to show their maps to the class. Ask, ‘What scale have you used? What have you included in your key?’ Ask, ‘What did you have to think about to make sure that each place was in the correct position on the map?’ Today I had problems with …

Compare the photos to the maps students have made. Ask, ‘What information is in the map but not in the photo?’ Discuss anything about the treasure maps that made them easy to follow, and anything that was confusing. Ask, ‘How could we improve our maps?’ Have students share the maps they made. Ask, ‘What would be the advantages of having the hospital here? Why have you chosen to put the school there?’ Have students display their house plans in the classroom. View these plans and discuss the features shown. Ask, ‘How did you show which way the doors opened? How did you make sure the shower was big enough to fit in? Did you leave enough room for the stove?’

Unit 30 Making Maps

113

unit

Exploring Chance

31 Chance and data


BLMs 29 & 30

During this week look for students who can: • identify possible outcomes using the language of chance • find and record all possible outcomes or combinations in simple chance experiments • explain why something is fair or unfair. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources playing cards, six-sided dice, card, coins, paper bags, jelly beans, counters, BLM 29 ‘Three-coin Toss’, BLM 30 ‘Two Spinners’ Maths Talk Model the following vocabulary in discussion throughout the week: chance, probability, likelihood, likely, unlikely, possible, impossible, no chance, little chance, some chance, certain, uncertain, probable, always, never, sometimes, might, maybe, even chance, one in two chance, 50–50 chance, guess, fair, unfair, lucky, unlucky

Whole Class Focus — Introducing the Concept Fair Games Ask, ‘What makes a game fair?’ List student responses. Refer to everyday games, e.g. ‘Snakes and Ladders’, and examine these in the light of the listed criteria. Ask, ‘Does everyone have the same chance of rolling a two? Is this game fair?’ Playing Cards Give each group of four a deck of playing cards (no jokers). Have the group work out how many of each suit and each number are in the deck. List these facts. Discuss the probability of turning over a given card. Ask, ‘How many cards are there in a pack? How many of these 4 1 52 cards are Aces? We can write this as 52 , simplified to 13 . If we dealt out 13 cards it is likely that one would be an Ace.’ Have students shuffle the cards and deal out thirteen. Discuss the results. Ask, ‘Why did some groups get no Aces and others get more than one?’ Draw out that a chance of something happening doesn’t mean that it will happen. Repeat with other numbers or suits. Discuss the chance as ‘___ out of ___’. Scissors, Paper, Rock Teach students to play ‘Scissors, Paper, Rock’. Divide the class into pairs (Player A and Player B) and have pairs play the game 18 times. When finished, total the number of wins by ‘A’ and then ‘B’ players. Plot these on a simple bar (column) graph. Compare the results. Ask, ‘Which player won the most games?’ Is this a fair game?’ Show students how to record the possible results of this game as a tree diagram. Ask, ‘How

114


If there is a difference between total wins for A and total wins for B, it may be that the sample size is not big enough.

many outcomes does the game have? How many times can Player A win? How many times can Player B win? Is the game fair? Do both players have an equal probability of winning in any round?’ Compare the tree diagram with what happened when students played the game. Discuss any differences noted.

Pig Teach students to play ‘Pig’. This is played with two dice and the winner is the first player to score 100. Players take it in turns to throw the two dice as often as they like, adding the total score for each throw to get the score for the turn. If a double 6 comes up, the player’s accumulated score goes back to zero and the player’s turn ends. If a single 6 comes up, the player’s turn ends, and they sit on their accumulated score. Have students play the game. Ask, ‘What strategy works with this game? Does limiting yourself to three throws each turn work? Is this a fair game?’ Discuss the element of chance associated with the game. Ask, ‘What would happen to the fairness of the game if one dice had two 6s? Likely or Unlikely? Give each student two blank cards. Ask students to write on one card something likely to happen today, and on the other, something unlikely to happen. Have students read out their ‘likely to happen today’ cards. Ask students to form a line to order these cards from most to least likely. Discuss their reasons for the order they chose. Repeat, with the ‘unlikely to happen’ cards. Discuss any events listed as both ‘likely’ and ‘unlikely’ to happen. List on the whiteboard words related to chance. Order these from most to least likely.

Small Group Focus — Applying the Concept Focus Teaching Group • Tree Diagrams Have students toss two coins 20 times and record the results. Ask, ‘What is more likely to come up: head and tails, or two heads, or two tails?’ Guide students to construct a tree diagram to model these outcomes. Ask, ‘In how many ways can two heads come up/a head and tail come up? What is the most likely result when we throw two coins?’ Have students work independently to construct tree diagrams for the possible outcomes when tossing three coins. Have students toss the coins 100 times, recording their findings on BLM 29 ‘Three-coin Toss’ and comparing these to the likely outcomes indicated by the tree diagram. • Jelly Beans in a Bag Show students a paper bag containing red, green and black jelly beans. Have them count the number of each colour in the bag. Ask, ‘If I take one jelly bean from the bag, what is the chance that it will be a red/green/black jelly bean? What about an orange jelly bean?’ As you For more able students, go, draw out that there is a chance of getting a red, green or black jelly have more jelly beans in the bag. bean from the bag, but not an orange jelly bean. Give each student a For less able students, limit the bag containing three different-coloured jelly beans. Have students work number of jelly beans. independently to write about the chance of drawing each colour. Encourage them to use the terminology, e.g. ‘There is a 2-in-5 chance of getting a red jelly bean.’ • Probability Ask, ‘When might we need to predict the likelihood of something happening?’ e.g. whether or not it will rain today/the next card will be a 7, etc. Ask, ‘What knowledge might you use when making a prediction?’ Discuss the need to draw on past experience (it rained last time the clouds looked like that), or know what the possibilities are (all the 7s are already on the table). Have students work independently to make a game that uses probability. Unit 31 Exploring Chance

115


Spinners (Student Book p. 89) Book page.


In pairs, have students experiment to find out whether or not the game ‘Two Spinners’ is fair. Give each pair a copy of BLM 30 ‘Two Spinners’.

Two Spinners

Odds On (Student Book p. 90) Book page.


Have students play ‘In the Middle’ in small groups. Give each group counters, and one suit from a pack of cards (Ace represents one).The dealer starts with 100 counters; the remaining players start with 20 counters each.The dealer shuffles the thirteen cards then turns over the two top cards. Each player then decides whether or not to bet on the probability that the next card turned over will have a number in between the two numbers already on the table, e.g. if 3 and 7 are on the table, then 4, 5, and 6 would be winning cards. If players do bet they may place up to five counters on the table. If they win the bet, the dealer gives them back their counters plus an equal number from the dealer’s bank. Encourage students to discuss the likelihood of winning with each pair of cards, e.g. if a 3 and a 7 are on the table, there is a 3 in 11 chance of getting a 4, 5 or 6. If a 2 and a King are on the table, there is a 10 in 11 chance of getting a card in between. In the Middle

Heads or Tails Have students investigate whether or not it is fair to decide who goes first by choosing heads in a coin toss. Have them include tree diagrams when presenting their arguments. Piggy Sixes Have students play the game ‘Pig’ at Website 31 (BLM 80). Alternatively, they could play it with a partner using conventional dice. A Probability Scale Have students construct their own probability scale using words that describe the likelihood of an event. Have them place events on their probability scale. Unit 31 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p 91.

Whole Class Share Time Ask, ‘Is “Two Spinners” a fair game? Why, or why not?’ Focus on the combinations of numbers that add to make even and odd numbers. Ask, ‘How many combinations have an even sum? How many have an odd sum?’ Today I found out …

Turn over two cards and ask, ‘What is the likelihood that the number on the next card is in between these two numbers?’ Repeat. Ask, ‘Is it easy to win at this game? What do you need to consider before placing your bets? Is there any such thing as a sure thing?’ Ask, ‘Is tossing a coin a fair way to choose who goes first? Why?’ Discuss. As, ‘Is there any strategy that makes one player certain to win?’ Discuss the fact that in games of chance there is no certain way to win. Have students view each other’s probability scales. Discuss any events to which different children have assigned different probabilities. Ask, ‘Who is right? How could we find out?’

116


unit


Mental Computation Student Book pp. 92–93

BLMs 31 & 32

During this week look for students who can: • use known facts to solve problems • use a range of mental strategies to carry out computations • calculate addition, subtraction, multiplication and division mentally. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources packs of playing cards, jar of jelly beans, streamers, calculators, card, ten-sided dice, metre rulers, BLM 31 ‘Operations Cards’, BLM 32 ‘Number Chain’ Maths Talk Model the following vocabulary in discussion throughout the week: addition, subtraction, multiplication, division, estimate, total, strategy, automatically recall

Whole Class Focus — Introducing the Concept Divide and Conquer Give each student a number card from a pack of cards as their starting number. Shuffle cards cut from BLM 31 ‘Operations Cards’. Draw a card from the top of the pile and read it to the class. Have students mentally complete the operation on their starting number. (For example: starting number is 4; operations card is ‘+ 5’. 4 + 5 = 9. The student’s new number is 9.) Draw another operations card and have students complete that operation. Continue until a division card is drawn. Have students say what their remainder is. Students with the highest remainders win a point. Review the operations carried out. Ask, ‘How did you keep track of your number? What number facts helped you?’ Repeat. Odd Numbers Write this problem on the whiteboard: ‘What are four consecutive odd numbers with a sum of 160?’ Ask, ‘What known facts could we use to solve this problem? What sub-questions should we solve first?’ e.g. 1 ‘What are consecutive odd numbers? What is 4 of 160?’ Have students work in small groups to solve the problem. Have groups present their solutions to the class, focusing on the strategies used. Number Chain Cut up cards from BLM 32 ‘Number Chain’. Hand them around to students in the class (some could have more than one). Have the student with the ‘Start’ card read out their card, i.e. ‘I am 100. You are 6 × 7 + 4.’ The student holding the card saying ‘I am 46’ should then read out their card (i.e. ‘I am 46.You are 42 ÷ 2 – 9.’). Again students work out the answer and the student with ‘I am 12’ reads next. Continue until the chain is complete. Discuss mental strategies used. Unit 32 Mental Computation

117

Hit the Target Review BODMAS. Demonstrate to the class how to play ‘Target Number’. Shuffle a deck of cards (picture cards removed, Ace represents one).Turn over two cards to form the target number, e.g. if 4 and Ace come up, target number is 41. Deal five cards to each player, e.g. 4, 7, Ace (1), 5, 2. Each player must use as many of their five numbers as possible to make an equation, the answer to which is the target number. Players may use any operation. (For class demonstration, have the class work on only one set of numbers, and encourage the use of BODMAS, e.g. [5 + 7 – 2] × 4 + 1 = 41.) Repeat several times. Discuss strategies. Jelly Bean Jar Fill a jar with jelly beans and seal it. Have students guess how many jelly beans are in the jar. Record their guesses. Ask, ‘How did you work out your estimate? What strategies did you use?’ Streamer Metres Give each student a length of streamer longer than a metre. Ask students to tear their streamers to a metre in length using estimation skills. Have them compare their streamer metres. Ask, ‘How did you estimate the length? Why are there variations? How long is a metre?’

Small Group Focus — Applying the Concept Focus Teaching Group • Stop or Dare Play ‘Stop or Dare’ with students. To play, shuffle a pack of 52 cards and place it face down. Set a target score for the game, e.g. 100.The first player turns over the top card and continues turning over cards, adding the cumulative value of each card (Jack = 11, Queen = 12.) until they decide to stop.The player’s total is then recorded as their score. However, if an Ace or King is turned over, no points are scored and the turn is finished. Now the Vary the target score second player turns over the cards, etc. Players continue taking turns and according to the needs building scores until someone reaches the target score. This player wins. If of students. all cards are turned over before the target number is reached, reshuffle the pack and continue. Ask, ‘Is there a strategy to increase your chances of winning? How many cards should you risk turning over before you stop? Does it pay to be daring? Does it matter how many people play or who goes first? What difference does the target score make to the game? • Making Whole Numbers Ask, ‘What are whole numbers?’ Shuffle a deck of cards (picture cards removed, Ace represents one). Deal two cards to each student. Ask, ‘Can you add, subtract, multiply or divide these two numbers to make a whole number?’ Guide students to use mental calculation. Ask, ‘Which operations always give you a whole number?’ Repeat. Have students play the game in small groups. Players score a point for making either an odd number, or a number that can be divided by 3.The player with the most points after five rounds wins. • Calculated Calculations Give each student a calculator. Have students enter 100. Ask, ‘What could you enter next to give an answer that ends with zero?’ Discuss the answers and the thought processes behind them. Repeat, asking students to calculate an answer that is an odd number. Have students independently play ‘Calculated Calculations’ in small groups. The group begins by entering 100 on the calculator. Players take turns to subtract any single-digit number (i.e. 1 to 9) of their choice. Then, leaving the answer on the screen, they give the calculator to the next player to take away another single-digit number. This continues until someone reaches exactly zero. Score as follows: 1 point for an odd answer; 2 points for an answer ending with zero; 3 points for a multiple of 6.The highest scorer wins.

118



Think It Out! (Student Book p. 92) Have students complete the Student Book page.They could then play ‘Divide and Conquer’ in small groups. Brain Power (Student Book p. 93) Have students complete the Student Book page. Then have students write their own like problems and publish these on the class website for other students to answer. Alternatively, students could visit Website 32 (BLM 80) to practise mental strategies by playing the games. Ask students to choose a game to teach to others. Make a Chain Have students make their own number chain using ‘Insert Text Box’ in Word. Once completed, the text boxes can be cut out and scrambled for other students to reassemble as a rainy-day activity. Or students could make their number chains on small cards. Target Number Have students play ‘Target Number’ in small groups. Score as follows: 10 points for making the target number with all five cards without help; 8 points for making the target number with less than five cards without help; 6 points for making the target number with help; 8 points for helping someone else to make the target number. How Many Jelly Beans? Have each student develop an argument to support their estimate of the number of jelly beans in the jar. Encourage students to make models and show their working out. Make a Metre Have students play ‘Make a Metre’. Students take turns to throw two ten-sided dice and generate new numbers, e.g. with 2 and 8 a player could make 2 + 8 = 10, 8 – 2 = 6, 8 × 2 = 16, 8 ÷ 2 = 4. The player then chooses one of these numbers (i.e. 10, 6, 16 or 4) and cuts a piece of streamer to this length in centimetres. After each turn, the student must say how many more centimetres they need to make a metre. Play continues until one student has enough lengths of streamer to make exactly one metre.

Whole Class Share Time Ask, ‘What mental strategies did you use to complete the student book page?’ Focus on a range of strategies, drawing out that different people favour different strategies. Today I worked out …

Discuss how mental strategies can be used in everyday life. Have students share their number chains with the class. Ask, ‘What did you need to think about to make sure that your chain was complete?’ Turn over five cards. Ask, ‘What numbers could we make with these cards? What do you need to think about to make the biggest/smallest number?’ Have students justify their estimates. They could vote for the most convincing argument.The prize could be the jar of jelly beans. Ask, ‘What strategies did you use to keep track of how many more centimetres you needed to make your metre?’ Discuss.

Unit 32 Mental Computation

119

unit

Multiplication and Division



During this week look for students who can: • explain the link between multiplication and division • solve multiplication and division problems • divide whole numbers to 100 000 by single-digit numbers • verbalise the thought processes used to solve division problems • use mental and written methods, and calculators, to multiply numbers to 999 999 • verbalise the thought processes used to solve multiplication problems. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources calculators, packet of biscuits, packet of cheese slices, card, playing cards (picture cards removed), ten-sided dice, chart paper, food for class lunch Maths Talk Model the following vocabulary in discussion throughout the week: divide, dividend, divisor, quotient, multiply, product, multiplicand, multiplier, lots of, groups of, divided by, remainder

Whole Class Focus — Introducing the Concept Complementary Facts Write this problem on the whiteboard: 354 × 7. Have students work out the answer. Now write: 2 478 ÷ 7. Ask, ‘Who can tell me the answer to this problem without doing a written calculation? How did you do it?’ Draw out the relationship between multiplication and division. Have students pose other multiplication and division problems for each other to solve. Have them record the complementary number facts. On the Trail Make an outdoor multiplication and division trail with about ten stations. Use local features to create the trail. (For example, with chalk, draw a rectangle on a brick wall and attach a sign saying, ‘How many bricks? Work it out without counting.’ Attach a sign to the first of a row of six trees, saying, ‘I have 240 lanterns. I want to put the lanterns in the trees. How many lanterns can I put in each tree?’) Set the cards up before class and have students follow the trail, calculating the answers to the problems as they go. When finished, discuss students’ solutions to each problem. Rough Estimates Say, ‘When you multiply or divide numbers, it is good to make a rough estimate of the answer first. Then check your estimate against the actual answer.’ Write 92 ÷ 3 on the whiteboard. Ask, ‘How could we approximate this? e.g. 90 ÷ 3 = 30. Then work out the answer. Repeat

120


with other problems, e.g. 354 × 56 (approximately 350 × 50 = 17 500); 143 ÷ 7 (approximately 140 ÷ 7 = 20). Ask, ‘How does making a rough estimate help us to check our work?’ Is It True? Ask, ‘What happens when we divide any number by 10? By 100?’ Provide calculators and allow time for students to test this. Write on the whiteboard, ‘To divide any number by 50, multiply by 2 and divide by 100.’ Ask, ‘Is this true? How could we find out?’ Have students work through examples to test it. Discuss the results. Dollars to Cents Review converting dollars to cents. Ask, ‘How many cents are there in $2.56?’ etc.Talk about how to work this out by multiplying the dollar amount by 100 or moving the decimal point two places to the right. Show students a packet of biscuits and tell them its cost. Ask, ‘How much does each biscuit cost? How could we work it out?’ Guide students to solve the problem. Note the need to round up to the nearest 5 cents. Repeat with another product, e.g. cheese slices.

Small Group Focus — Applying the Concept Focus Teaching Group • Working Backwards Pose a division problem, e.g. 4 655 ÷ 7, varying the dividend according to students’ ability. Ask, ‘How would we set out this problem? What might the answer be?’ Guide students to solve the problem. Ask, ‘How could we check our answer using multiplication?’ Repeat with a multiplication problem. Discuss the relationship between multiplication and division. Guide students to pose their own multiplication or division problem, estimate the answer, solve the problem and then work backwards to check.When students are comfortable with this, have them work to make pairs of cards showing related multiplication and division facts, e.g. 467 × 9 = 4203, 4203 ÷ 9 = 467.These cards could be used to play ‘Concentration’. • 100 000 Review vertical multiplication, ensuring that students understand how to carry. Give students a pack of playing cards (picture cards removed, Ace represents one) and have them deal out seven cards to form both a five- and a two-digit number. Guide students to multiply these Vary the range of numbers. Ask, ‘What is a reasonable estimate of the answer? numbers, number of cards being dealt and the target number, according to the Which number do you multiply first? Where do you write the needs of students. Less able students answer? What do you do with the tens? Which number do you might be more comfortable with a multiply next? What do you do when multiplying by zero?’ etc. target number of 1 000. Compare students’ products. Ask, ‘Which of these products is closest to 100 000?’ Have students work independently to deal the cards to generate other multiplication problems. Have them rearrange the cards to create numbers that will give them products as close as possible to 100 000. • 100 Review formal division. Have students roll a ten-sided dice five times to form a four-digit dividend and a single-digit divisor. Guide students to work out the quotient, asking, ‘What is a reasonable estimate of the answer to this problem?’ Compare students’ quotients. Ask, ‘Which of these quotients is closest to 100?’ Have students work independently to deal cards to make other division problems. Allow them to rearrange the numbers to aim for quotients as close as possible to 100. Vary the target number according to students’ capabilities.


PMI Have students work in small groups to draw up a PMI chart for multiplication and division. (PMI stands for ‘Plus, Minus, Interesting’ and is a De Bono thinking strategy.) Unit 33 Multiplication and Division

121

Multiplying and Dividing (Student Book p. 94) Have students complete the Student Book page. Maths Trail Have students work in small groups to write multiplication and division problems for a maths trail of their own. Vary the activity by having students set up their trail to start and end with the number of their choice. Estimates and Answers Have students play ‘Estimates and Answers’. Each student prepares ten multiplication and division question cards, and ten answer cards. The answer cards should give the answer plus acceptable estimations of it. Question cards are then shuffled and placed face down in the middle. Answer cards remain with the students who wrote them. Players take turns to draw a question card from the middle.They must first offer an estimate of the answer. Other players decide whether or not their estimate is reasonable, consulting the answer card if they wish, and award one point if it is. A further point is awarded if the player can work out the correct answer.The winner is the player with the most points once all cards have been used. Division Tricks (Student Book p. 95) Student Book page.


Let’s Do Lunch Have students work in teams to plan and cost a school lunch. Decide on a menu. Have students work in teams to set prices for each item on the menu, e.g. if the menu includes salami sandwiches, students need to cost the salami (i.e. price per kg, how many slices in a kg, cost per slice, number of slices per sandwich, etc.). When all prices have been decided, have individuals order their lunch and work out what it will cost. Hold the lunch and enjoy the food. Units 32–33 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p 96.



Have each group share their PMI charts. Celebrate the ‘pluses’. Discuss the ‘minuses’ and brainstorm ideas to overcome them. Discuss ways in which the interesting aspects of multiplication and division could be incorporated more often into the classroom. After each group has completed another group’s trail, discuss the experience. Ask, ‘Which questions made you think? Which were the most fun?’ Ask, ‘Why should we estimate answers before we work them out? How does this help when using a calculator?’ Have students share the division tricks they devised. Talk about why they work. Ask, ‘What ideas about numbers did you use to work out your tricks?’ Review the pricing structure of the lunch. Did you collect enough money to cover the cost of the food? Why, or why not? Would you cost the lunch the same way next time? What would you do differently?

122


unit

34 Space

Transformations Student Book pp. 97–98

BLMs 33, 69, 76 & 77

During this week look for students who can: • enlarge and reduce simple pictures • identify what a shape will look like when it is reflected • identify what a shape will look like when it is rotated • explain what movement has occurred when a shape is translated • use mathematical language to explain how shapes have been transformed, i.e. ‘rotated’, ‘reflected’, ‘translated’, ‘enlarged’, ‘reduced’. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources two identical digital photos (one enlarged), acetate sheets, overhead projector, pattern blocks, 10-cent coins, rectangular mirrors, small counters of different colours, long strips of paper, Word, BLM 69 ‘Reduce or Enlarge’, BLM 76 1 ‘Grid Paper’, BLM 77 ‘ 2 -cm Grid Paper’, BLM 33 ‘Translation Cards’ Maths Talk Model the following vocabulary in discussion throughout the week: transformation, rotation, reflection, translate, rotate, reflect, flip, slide, turn, turn 90°, turn 180°, turn 270°

Whole Class Focus — Introducing the Concept Enlargement and Reduction Show students two identical digital photos, one of which has been enlarged. Ask, ‘What is the difference between these two photos?’ Discuss the definitions of ‘enlarge’ and ‘reduce’. Say, ‘When an image or object is enlarged or reduced, the final image or object is the same as the original but a different size.’ Copy BLM 69 ‘Reduce or Enlarge’ onto an acetate sheet and place the sheet on an overhead projector. Place a pattern block on the small grid. Ask, ‘What would I need to look at to enlarge this shape?’ Draw out the need to look at where the sides of the shape intersect the grid lines. Demonstrate enlarging the shape. Then demonstrate reducing a different shape. Rolling Around Show students two 10-cent coins displaying the Queen’s head the right way up. Ask, ‘What would happen if I held the first coin still and rolled the second coin around until it was on the other side of the first coin? ‘Would the second coin be upside down, the right way up or side-on?’ Record students’ predictions. Give each student two 10-cent coins and have them experiment to find out what happens. Discuss students’ findings. Ask, ‘Why does the Queen’s head finish the right way up? How many rotations does the coin make? Does the same thing happen with other coins?’ Unit 34 Transformations

123

Introduce the language of rotation. Say, ‘When a shape is “rotated” it is turned around a fixed point. The final shape is the same as the first shape but it may be in a different position.’ In the Mirror Say, ‘When a shape is “reflected”, the final shape is the same as the first one but flipped over an imaginary line to give a mirror image.’ Have students cut an irregular shape from card and trace around the shape. Ask them to draw free-hand what they think the shape would look like reflected. Have students check their predictions by observing the shape reflected in a mirror. Have students repeat the exercise, reflecting the shape from a different side. Ask, ‘What do you need to think about to show the reflection of a shape?’ Translating Shapes Introduce the term ‘translation’. Say, ‘Translation moves a shape from one place to another by sliding it.The final shape is the same as the first shape, in the same relative position, but in a different place.’ Copy grid paper (BLM 76 or 77) onto acetate and place it on an overhead projector screen. Put a pattern block on the screen. Have students describe its position, e.g. ‘It is in the centre of the grid’. Have students close their eyes while you slide the block to a new position on the grid. Ask, ‘How has the position of the block changed?’ Focus on words that describe the move, e.g. ‘up 5 and across 3’, ‘up diagonally to the left’. Repeat with other translations. Transformations Show students a simple irregular shape. Ask, ‘How could we transform this shape?’ Draw out that a transformed shape could be enlarged, reduced, reflected, rotated or translated. Have different students use the irregular shape to demonstrate each of these transformations. Talk about the thought processes required to draw the shape that demonstrates each transformation.

Small Group Focus — Applying the Concept Focus Teaching Group • Translating Counters Give each student a counter and an enlarged copy of BLM 76 ‘Grid Paper’. Have them colour on the grid a square of their choice and place a counter on it. Hold up cards enlarged and cut from BLM 33 ‘Translation Cards’ and have students move their counters accordingly. After several moves ask, ‘What moves would you need to make to retrace your steps?’ Repeat.When students are translating their counters confidently, have them work independently to draw a path for their counter to move through and then retrace. Have students write instructions for following this path and then ask a partner to check its accuracy by following the instructions back to the original coloured square. • Mirror Image Take digital photos of students. Print them out in their original format and also in reflection. Show the photos to students. Ask, ‘Do you still look the same in your reflection?’ Have students annotate their photos and write about how reflecting something can change its appearance. • Made to Measure Provide each student with a copy of BLM 69 placed in a plastic pocket. Give each student an overhead projector pen. Have students rule a triangle on the small grid. Ask, ‘What must we note to enlarge this shape?’ As they enlarge the triangle, guide students to note the angles of the triangle and where its edges cross the grid lines. Repeat with other shapes, reducing and enlarging as needed. When students are confident, have them draw a simple line drawing and its enlargement.

124



Enlarge and Reduce In pairs, have students draw a simple line picture on one of the grids on BLM 69 ‘Reduce or Enlarge’. (Place the sheets in plastic pockets to allow multiple usage.) Partners then swap pages and either reduce or enlarge each other’s pictures. Repeat several times. Have students work independently to draw a picture on the small grid and then enlarge it on the large grid.These can be displayed in the classroom. Rotating Shapes (Student Book p. 97) Have students complete the Student Book page. When finished, students could explore the rotation of regular and irregular 2D shapes by using ‘AutoShapes’ in Word. (Once a shape is selected, click ‘Draw’ and select ‘Rotate or Flip’.) Students could also explore rotating large upper- and lower-case letters by typing them into a table and using the ‘Change Text Direction’ icon (go to ‘Format’ then ‘Borders and Shading’ and click on ‘Show Toolbar’). Alternatively, students could cut letters and shapes from card and rotate them manually. Reflections (Student Book p. 98) Have students complete the Student Book page. When finished, students could make their own ‘Find the Reflections’ page using the ‘AutoShapes’ and ‘Rotate or Flip’ functions in Word.These could be assembled into a class puzzle book.

Translation Tussle Have students play ‘Translation Tussle’ in groups of three or four. Each group needs a different-coloured counter per player, an enlarged copy of BLM 76 and a set of translation cards from BLM 33. To start, the translation cards are shuffled and placed face down. In turn, each player places their counter on a grid square of their choice Players may challenge a move if they believe it to be incorrect. (only one counter to a square). Players then take turns to draw If the challenger is right, the player who the top card from the pile and move their counter according to moved incorrectly misses a turn. If the its instructions. (Moves are made in relation to the player’s challenger is wrong, the challenger misses a turn. position facing the grid.) If one player lands on another player’s counter, the second player is eliminated from the game. Players are also eliminated if their counter is instructed to move off the grid. The last player left in the game wins. If all cards are used, shuffle them and continue playing. Transformation Patterns Have students make a pattern by transforming only one shape. This could be done using a drawing program or in Word, or students could simply draw on long strips of paper. Have students explain their pattern.

Whole Class Share Time View students’ drawings. Ask, ‘Which lines were easy to enlarge or reduce? Which were more difficult? Why? How did you use the grid lines to help you?’ Today I found out …

Discuss students’ findings on the effects of rotating shapes and letters. Ask, ‘Which shapes and letters did not change when rotated through 90°/180°? Which did change?’ Have individuals share the reflection puzzles they made. Ask other students to see if they can reproduce the shape that has been reflected. Ask, ‘How do you visualise what a shape will look like when it is reflected?’ Ask, ‘What did you need to think about to challenge another player’s move?’ View students’ patterns. Ask, ‘How would you explain your pattern?’

Unit 34 Transformations

125

unit

35 Space

Symmetry and Tessellations Student Book pp. 99–100

BLMs 34, 35, 61, 70, 71, 72, 73, 74, 75 & 76

During this week look for students who can: • identify lines of symmetry in 2D shapes • predict how many lines of symmetry a shape will have based on the number of sides it has • make tessellations using regular and irregular shapes. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources kinder squares, photos of faces, Escher prints displaying tessellation, square tiles, coloured paper, cardboard templates of 2D shapes, cardboard squares, scissors, pattern blocks, advertising brochures, magazines or prints showing tiled floors and mosaic patterns, chart paper, Word, Photoshop, BLM 70 ‘Blank Carroll Diagram’, BLM 61 ‘2D-shape Cards’, BLM 34 ‘Carroll Diagram’, BLM 75 ‘Isometric Dot Paper’, BLM 76 ‘Grid Paper’ or BLM 74 ‘Square Dot Paper’, BLM 71 ‘Tessellation Pattern 1’, BLM 72 ‘Tessellation Pattern 2’, BLM 73 ‘Tessellation Pattern 3’, BLM 35 ‘Pentominoes’ Maths Talk Model the following vocabulary in discussion throughout the week: tessellate, tessellation, reflect, flip, translate, slide, rotate, turn, symmetry, lines of symmetry

Whole Class Focus — Introducing the Concept Symmetry Give each student a small kinder square. Say, ‘I want you to cut the kinder square so that the two halves are exactly the same size and shape.’ Have students share the results. Say, ‘You have cut the square along a line of symmetry. A “line of symmetry” is an imaginary line along which one half of the shape is reflected to make the other half.’ Have students brainstorm other shapes and everyday objects that are symmetrical. Ask, ‘How many lines of symmetry does an equilateral triangle have? How many lines of symmetry does a heart have? What about a four-leafed clover?’ Asymmetry of Faces Ask, ‘Are people’s faces symmetrical? How could we find out?’ One way is to cut a photo of a face in half and then use a mirror to see what the face would look like if it were symmetrical. Alternatively, this could be done in Photoshop by cropping a face down the centre, copying the half face, flipping the copy vertically and joining the two halves together. (It is interesting to do this with both halves of a face, to see the difference in the two people that result.) Ask, ‘Do all geometric shapes have lines of symmetry? If so, how could we prove it? If not, which ones do not?’ List students’ predictions on the whiteboard.

126


Tessellations Take students for a walk around the schoolyard. Point out any tessellations that you see, e.g. brick walls, paving stones, tiled floors, etc. Take digital photos of these.When you return to class, review your findings. Say, ‘A tessellation is a pattern of shapes covering a surface that fit together without any gaps or overlapping. Where do you see tessellations?’ List student responses. Over the next days, students could collect examples of tessellations from magazines and advertising material, and take photos of examples from the local neighbourhood. Irregular Shapes Show students examples of Escher prints in which tessellation has been used. These can be downloaded from either Website 35a or 35b (BLM 80). Alternatively, Escher books and posters are readily available from libraries. Have students view the pictures. Ask, ‘How do these pictures work?’ Provide each student with a photocopy of part of one of the Escher tessellations. Copy it so that the tessellation is in the middle of the page with room around it for students to draw. Have students continue the tessellation beyond the boundaries of the picture. Pentominoes Give each student five square tiles. Ask, ‘How many different shapes can you make with just five squares?’ Have students investigate and record their findings. Ask, ‘Will any of the shapes you have made tessellate? What makes you think so?’ Boys

Not boys

Brown eyes

Sam Abdul Van

Wai Fatima Francesca

Not brown eyes

Steve Nick Jake

Hannah Samantha Alice

Symmetry and Tessellation Demonstrate the use of a Carroll Diagram using BLM 70 ‘Blank Carroll Diagram’. You could do this by looking for groups within the class, e.g. boys/not boys, or brown eyes/not brown eyes (see example in margin). Repeat until students understand how the diagram works. Ask, ‘Do all shapes that tessellate have at least one line of symmetry? How could we find out?’

Small Group Focus — Applying the Concept Focus Teaching Group • Halves Provide students with coloured paper and cardboard templates of a range of 2D shapes, which could be made by enlarging BLM 61 ‘2Dshape Cards’ onto card. Demonstrate how a square can be cut in half in four ways to give symmetrical halves. Have students work independently to find the lines of symmetry of other shapes. • Tessellating Pictures Review Escher’s pictures of tessellation. Discuss the images. Give each student a cardboard square. Demonstrate cutting a shape from one side of the square and sticking it onto the other side. Ask, ‘Will this shape tessellate? How could we find out?’ Model tracing around the shape with a pencil and cutting out the traced shape to see if it will tessellate with the original shape. Guide students to make their own cardboard template. Have students work independently to design and make their own picture with tessellation. • Using Tessellations Ask, ‘Why might people use tessellations?’ Discuss students’ responses, drawing out the need to cover surfaces without gaps and at the same time make places look attractive. Have Please note: Each shape in the pattern students browse through magazines and books to could be coloured by double-clicking on it and using the find examples of tessellation. Alternatively, they ‘Fill Colour’ function. Shapes that do not easily move to the could be given copies of the tessellation patterns required position can be moved in small increments by holding down the ‘Control’ key and using the arrow keys. on BLMs 71, 72 and 73 to examine and colour. Discuss the shapes used and the way colour could also Unit 35 Symmetry and Tessellations

127

be used to accentuate or enhance the tessellation. Have students work independently to design their own tessellating floor pattern. Provide isometric dot paper (BLM 75), and grid paper (BLM 76) or square dot paper (BLM 74). Alternatively, students could use the ‘Autoshapes’ tool in Word.


Symmetrical Objects Have students make posters showing a range of shapes and objects that have lines of symmetry. The shapes/objects should be grouped according to the number of lines of symmetry they have. Lines of Symmetry (Student Book p. 99) Have students complete the Student Book page. When finished, students could explore the asymmetry of most living things by cutting computer images in half and using mirrors to view the results. Shapes that Tessellate (Student Book p. 100) Have students complete the Student Book page. When they have finished, provide coloured paper and have students make their own tessellated patterns. Lines of Symmetry in Tessellation Provide students with a range of pictures of tile and mosaic patterns and Escher prints, all showing tessellation. A useful site to visit is Website 35c (BLM 80). Have students investigate the question, ‘Do all shapes that tessellate have lines of symmetry?’ Students could work on making their own Escher-like tessellations. Pentomino Tessellations Give each student a copy of BLM 35 ‘Pentominoes’ and have students explore the shapes that tessellate. When finished, students could create other pentomino tessellation patterns using the ‘Shading’ feature in ‘Table’ in Word. (Make a square table with 20 rows and 20 columns. Select the cells to be coloured. Select ‘Format’, ‘Borders and Shading’, ‘Shading’, and the colour.) These could be printed out and displayed in the classroom. Finding Out Provide small groups with a copy of BLM 34 ‘Carroll Diagram’ and have them sort a range of shapes. Ask students to summarise and draw conclusions from the information in the diagram. Units 34–35 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p 101.

Whole Class Share Time View students’ posters. Focus on the different groups. Ask, ‘What do the things that have three lines of symmetry have in common?’ Today I discovered …

Ask, ‘How could you predict the number of lines of symmetry a regular shape will have?’ Ask, ‘Do all regular shapes tessellate? Do shapes with an even number of sides tessellate?’ Allow time for students to discuss their findings. Have students present their findings to the class. Ask, ‘Do all shapes that tessellate have lines of symmetry?’ Discuss students’ findings. View students’ tessellations. Ask, ‘Do all pentominoes tessellate? Ask, ‘Do all shapes that tessellate have lines of symmetry?’ Encourage students to support their points of view with evidence.

128


unit


Percentages Student Book pp. 102–104

BLMs 36, 37, 48 & 55

During this week look for students who can: • convert common fractions to decimal fractions and percentages • calculate numeric values in relation to percentages • explain a percentage • identify when percentages are used in everyday life. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources packet of 100 Smarties, advertising material, daily newspapers, sticky dots of two different colours, calculators, MAB blocks, empty food boxes and other packaging, Excel, blank 100 grid (BLM 48), BLM 55 ‘Percentage Grids’, BLM 36 ‘Percentage Match-up’, BLM 37 ‘Best Buys’ Maths Talk Model the following vocabulary in discussion throughout the week: percent, percentage, fraction, %, hundredth, common fraction, decimal fraction, tally, greater than or less than

Whole Class Focus — Introducing the Concept Smart Smarties Have some students draw out 100 Smarties from a packet. As each Smartie is drawn, record its colour on a tally sheet on the whiteboard. Ask, ‘How many Smarties were red? How many were blue? How could we write this as a fraction?’ Draw out that the fraction can be 35 written as, e.g. 100 . Introduce the idea of a percentage being equivalent to a fraction. Say, ‘We could also write this fraction as 35%.’ Draw students’ attention to the ‘percent’ sign, explaining that it stands for ‘a number out of 100’. Guide the class to write the other Smarties’ colours as common fractions and percentages. Everyday Percentages Have students browse through advertising material and daily newspapers to find instances when percentages are used. Ask, ‘What does “10% off ” mean? What does “54% of our yearly rainfall” mean?’ Discuss students’ understandings. Ask, ‘If the price of this item were discounted by 10%, what percentage would I be paying?’ Draw out that when we talk about percentages of a whole, all these percentages add to 100%, i.e. a 10% discount means that I pay 90% of the usual price. Repeat. 50% and 25% Give students a blank 100 grid (BLM 48). Ask them to shade 1 2 of the grid. Ask, ‘How would we write this as a percentage? What 1 50 percentage of the grid is not shaded?’ Draw out that 2 is the same as 100 , i.e. 50%. Ask, ‘What is 50% of 40? What is 50% of 200?’ Repeat, focusing on 25%. Unit 36 Percentages

129

Have students shade 25% of the 100 grid. Ask, ‘What is 3 What is 25% as a fraction? What is 4 as a percentage?’

1 4

as a percentage?

Understanding Percentages Write this problem on the whiteboard: ‘A computer game cost $100. It was discounted by 30%. How much was it selling for then? When it still did not sell, it was discounted a further 50%. What did it cost then? I bought it. Did I get a discount of 80%? Why or why not?’ Promote discussion about the steps required to solve this problem? What sub-questions need to be answered? Work with students to solve the problem. Calculating Percentage Ask students to put forward ideas or issues on which they would like the class’s opinion. Have students use sticky dots to vote ‘Yes’ or ‘No’ to these things. Give the girls dots of one colour and the boys dots of a different colour, so that the data collected can be presented to reflect the opinions of both boys and girls. Show students how to use a calculator to work out a percentage. Ask, ‘What percentage of girls voted ‘Yes’ to this question? What percentage of boys voted ‘Yes’? What percentage of students voted ‘Yes’?

Small Group Focus — Applying the Concept Focus Teaching Group • What Is a Percentage? Give each student some MAB tens and ones. Say, 1 ‘If the ten were equal to one, how could you show 2 ?’ Guide students to show 1 2 using the ones. Ask, ‘How many ones have you used?’ Demonstrate writing 1 this as a common fraction ( 2 ) and as a decimal (0.5). Introduce the idea that another way to write this is as a percentage (50%). Repeat with other fractions. Have students work independently to model and record other percentages as decimals and common fractions. • Playing with Percentages Give students a copy of BLM 55 ‘Percentage Grids’ and common fraction cards cut from BLM 36 ‘Percentage Matchup’. Have students shade a grid to show each fraction. Ask, ‘How many cells have you shaded? What is this as a decimal? What is it as a percentage?’ Repeat with other numbers drawing out the relationship between decimal fractions and percentages. Have students play ‘Percentage Match-up’. To play, students shuffle cards cut from BLM 36 and place the cards face down in rows and columns. Players then take turns to turn over three cards 1 looking for matching trios, e.g. 2 , 0.5 and 50%. If a trio is turned over, the player has another turn. If not, it is the next player’s turn. Play continues until all cards have been won.The player with the most cards wins. • Our Class Show students how to use a calculator to work out percentages. Ask, ‘What percentage of our class is boys? How would we work this out using the calculator?’ Guide students through the necessary steps. Ask, ‘What percentage of the class is girls? How could you work this out without using the calculator?’ Repeat with other like problems until students are confident. Have students work independently to calculate other percentages of interest to them, e.g. the percentage of time they spend watching TV, percentage of the day/year they spend at school, etc. Some might like to find out how percentage scores are worked out in the AFL.


130

Percentages (Student Book p. 102) Have students complete the Student Book page. When finished, students could investigate other figures as percentages, e.g. the percentage of vowels in the first 100 letters of a story,


the percentage of certain shapes drawn out of a bag of 100 pattern blocks, etc. Encourage students to use only a sample of 100 at this stage. Percentage Chart Have students look through advertising material and daily newspapers to find more examples of percentages. Have them cut these out and display them on a chart, grouping them according to context. Students should write about each percentage and what it means, e.g. ‘If we have had 54% of our annual rainfall, this means we have received 46% less rainfall than usual.’ ‘A bottle of orange juice that contains 25% juice also contains 75% water.’ Showing Percentages (Student Book p. 103) Have students complete the Student Book page.When finished, students could investigate claims on food packaging. Have them draw diagrams to represent the percentage of a given substance contained in a product, e.g. have them represent 93% fat free. Bargains (Student Book p. 104) Have students complete the Student Book page. Best Buys (BLM 37) Have students complete BLM 37. When finished, have them write their own ‘Best Buy’ ads. These can be placed in plastic pockets for other students to work through on a rainy day. The Winning Vote In small groups, have students explore the following question. Say, ‘A class was deciding whether or not to shorten their recess time so that they could get more work done. They had a vote. Twenty-two percent of girls voted for a shortened recess. Thirty percent of boys did too. For the vote to be passed, more than 50 % of the class had to be in favour of the idea.Were more than 50% of students in favour? Prove that your answer is correct.’ Provide students with access to Excel to make models and graphs of this problem. Please note: To assist students, it may be helpful to point out that they do not know how many boys and girls are in the class. However, if the class were made up entirely of girls, the motion failed, as it 1 1 did if it were made up entirely of boys. If the class were 2 boys and 2 girls, the motion still failed. (What a surprise!) When finished, students may like to practise converting fractions into percentages by visiting the game ‘Converting Percentage’ on Website 36 (BLM 80).

Whole Class Share Time Ask, ‘What is a percentage? How can it be expressed as a fraction?’ Have students convert to percentages the data they have collected. Today I did not understand …

Ask, ‘What do percentages tell us?’ Discuss students’ findings and the information they have written on their charts. Ask, ‘What is 10% as a common fraction? What is 20%?’ How could we use this information to help us work out the value of percentages quickly? What do you need to think about when considering whether or not something is a ‘good buy’? Is it better to get a ‘percentage off ’ or a ‘discount’?’ Discuss the need to work out how much you actually save in each instance. Have students share their solutions to the problem. Ask, ‘What was your reasoning in reaching this conclusion? Would our class vote this way?’

Unit 36 Percentages

131

unit

Adding and Subtracting Fractions

37


Number and patterns

BLMs 38 & 53

During this week look for students who can: • add and subtract common fractions • simplify fractions • give fractions common denominators • convert mixed numbers to improper fractions • convert improper fractions to mixed numbers. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources fraction kits, playdough, plastic knives, Blu-Tack, pattern blocks, ten-sided dice, Word, Excel, BLM 53 ‘Fraction Cards’, BLM 38 ‘Fraction Squares’ Maths Talk Model the following vocabulary in discussion throughout the week: fraction, common fraction, proper fraction, simple fraction, improper fraction, compound fraction, equivalent fractions, mixed number, numerator, denominator, simplify

Whole Class Focus — Introducing the Concept ?

?

?

Filling in Fractions Write ? + ? + ? = 2 on the whiteboard. Ask, ‘What could the fractions be?’ Allow time for students to find a range of answers. Discuss students’ answers. Have students demonstrate that their solutions are viable, using fraction kits where needed. Ask, ‘What did you need to think about to work out the problem? What known facts did you use?’ 3

3 4

2 5

1

Subtracting Fractions Write 1 4 – 1 3 = ? on the whiteboard. Ask, ‘How can we solve this problem? Demonstrate the following steps: convert any 4 3 4 3 7 3 mixed numbers to improper fractions (1 = 4 , so 1 4 = 4 + 4 = 4 , and 1 = 3 , 1 3 1 4 so 1 3 = 3 + 3 = 3 ); find equivalent fractions with common denominators 7 3 21 4 4 16 21 16 5 ( 4 × 3 = 12 and 3 × 4 = 12 ); subtract the numerators ( 12 – 12 = 12 ); further simplify the fraction if necessary. Repeat with other like problems, sharing the working with students. Give each student a fraction card made from BLM 53 ‘Fraction Cards’. Have students form pairs and work out the difference between their fractions. Repeat, having students form new pairs. Eating Pizza Write this problem on the whiteboard: ‘There are four people in my family. My family bought three pizzas. The first pizza was cut into quarters, the second into sixths and the third into eighths. Each member of my family ate a different amount of pizza. How much could each person have eaten?’ Ask, ‘What questions do we need to ask to solve this problem? What information do we need to collect? What maths will we

132


Less advanced students may find it useful to have playdough and plastic knives to help them to work out a solution.

need to do?’ List questions and information on the whiteboard. Allow time for students to work out one of the many solutions. Discuss their solutions, focusing on the questions they considered and the Maths they did.

Pattern-block Fractions Use Blu-Tack to stick some pattern blocks to the whiteboard to form equations based on the relative areas of the shapes, 2 e.g. hexagon + trapezium = 1 (where the hexagon represents 3 and the 1 trapezium, 3 ). Ask, ‘What fraction is the hexagon? What fraction is the trapezium? If this is true, what fraction is this triangle?’ Discuss the problem. Encourage students to place the shapes over each other to see 1 fractional relationships, e.g. the trapezium is 2 of the hexagon; the triangle 1 is 6 of the hexagon. Repeat with other like problems, e.g. ‘If triangle + triangle = 1, what does the hexagon equal?’ Making Wholes Show students two cards from BLM 53 ‘Fraction Cards’. Ask, ‘Do these fractions have a sum that is a whole number?’ Guide students to work out the sum of the fractions. Hand each student a fraction card from the BLM. Ask students to form groups so that the sum of group members’ fractions is a whole number. Discuss their strategies.

Small Group Focus — Applying the Concept Focus Teaching Group • Reducing Simple Fractions Roll a ten-sided dice to form fractions with two-digit denominators and numerators. Ask, ‘Is this the simplest form for this fraction? How could we work it out?’ Draw out the need to look for the factors of both the numerator and the denominator. List the factors on the whiteboard. Ask, ‘Do these two numbers have factors in common? What are they? What is the largest common factor?’ Demonstrate dividing both the numerator and the denominator by this factor to simplify the fraction. Repeat with other fractions. Have students work independently to roll dice to make fractions with two-digit numerators and denominators and simplify them where possible. Have students list these on a chart under headings ‘Simplified’ and ‘Cannot be simplified’. • Common Denominators Give students two fraction cards cut from BLM 53 ‘Fraction Cards’, ensuring that each has a different denominator. Ask, ‘How could we give these fractions the same denominator?’ If some students are Demonstrate giving each fraction a common denominator confused about the terms ‘numerator’ and ‘denominator’ and cannot remember by multiplying each fraction by one, where one is a fraction which is which, a mnemonic may help. Tell made with the same denominator as the other fraction, e.g. them, ‘Ned rides on the Donkey; the Donkey 1 1 1 5 5 does not ride on Ned, i.e. Numerator 4 and 5 can be given a common denominator thus: 4 × 5 = 20 1 4 4 over Denominator.’ and 5 × 4 = 20 . When students are comfortable with this, have them use pairs of fraction cards to make fractions with common denominators. 3

• Mixed Numbers Show students a mixed number such a 3 4 . Ask, ‘If I have three and three-quarters pizzas cut into quarters how many quarters do I have? How could I work it out?’ Provide concrete materials such as playdough or fraction kits for students to use. Demonstrate working this out using 4 3 3 3 4 1 12 1 13 formal notation, e.g. 4 = 1 and 3 4 = 3 + 4 , so 3 4 = 3 × 4 + 4 = 4 + 4 = 4 . Repeat with other mixed numbers. Have students work independently to form mixed numbers by throwing a ten-sided dice three times. Have them convert the mixed numbers to improper fractions. Unit 37 Adding and Subtrtacting Fractions

133


Adding Fractions (Student Book p. 105) Have students complete the Student Book page.When finished, have students find a range of answers to ? ? ? ? + ? + ? = 2, and record them in tables in Word. To represent a fraction, select a cell and use the ‘Split Cells’ feature to split the cell into the required number of columns. Fraction Squares (BLM 38) Have students complete BLM 38. When finished, students could create their own fraction squares identifying the inside numbers.These could be placed in plastic pockets in a class book. Family Pizza Night Have students think about how many pizzas their family would need for a meal, and record how the pizzas could be shared if everyone had different amounts. Students could present their findings using pie (sector) graphs in Excel. Pattern-block Problems (Student Book p. 106) Have students complete the Student Book page. They may need your assistance to move from the concrete expression of fraction equations in the first set of problems to the abstract in the second set. They might also need to be reminded that, for the purposes of this activity, pattern blocks can have different values in different equations. When finished, students could use pattern blocks to make and record their own fraction problems.

Fraction Sets In groups of three or four, have students play ‘Fraction Sets’. To play, students shuffle two sets of cards cut from BLM 53 ‘Fraction Cards’. Five cards are then dealt to each player, with the remaining cards placed face down in the middle. Players take turns to lay down sets Players may challenge of cards that add to a whole number. They then replace these if they believe a set placed on the table cards from the pile in the middle. If a player is unable to make does not add up to a whole number. If the challenge is successful, the set of cards is a whole number, they may reject two cards from their hand, returned to the bottom of the pile. place these on the bottom of the pile and take two replacement cards from the top of the pile. When all cards have been used, or no more sets can be made, the player with the most cards face up on the table is the winner. Units 36–37 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p 107.

Whole Class Share Time Have students share the solutions they found to the problem and demonstrate the validity of these solutions. Ask, ‘What did you have to think about to find this solution?’ Focus on students who have used number relationships or looked for patterns. Today I discovered …

Promote discussion about the strategies students used to build a fraction square with one as the final answer. Ask, ‘Which strategies did you use?’ Focus on strategies such as working backwards, using known facts and looking for patterns. Have students discuss their findings with the class. Focus on students’ pie (sector) graphs and how these can be read. Invite a range of students to share their pattern-block fraction problems with the class. Discuss the changing relationships between the fractions and the pattern blocks depending on the problem. Ask, ‘Which cards were most easily used to make whole numbers? Why? Which cards were more difficult to match? Why?’

134


unit

38 All strands

Revision Student Book pp. 108–111

BLM 75

During this week look for students who can: • operate successfully with numbers in the range 0.01 to 999 999.99 • calculate area, perimeter, volume, mass and time elapsed • draw 2D shapes accurately and to scale • draw transformed shapes and explore symmetry • draw 3D shapes in 2D space showing what is seen and not seen. • explain chance in numerical terms • collect, display and interpret data

Resources chart paper; books, paint bottles, cups, boxes; rulers; kitchen scales; measuring jug; posters showing 3D shapes seen in houses, trucks, fire hydrants, high-rise buildings, etc.; six-sided dice; Centicubes; card; art materials; Kid Pix Studio Deluxe; BLM 75 ‘Isometric Dot Paper’ Maths Talk In discussion throughout the week, model language associated with number, space, measurement, and chance and data.

Whole Class Focus — Introducing the Concept Operating with Numbers Have students form four groups. Nominate each group to consider one of addition, subtraction, multiplication and division. Each group must prepare an explanation of how to carry out its assigned operation, including an analysis of the thought processes involved and helpful hints for solving typical problems. Presentation could be in any form, including slide shows, interviews, charts, books, help cards, puppet plays, etc. Have each group present their work. Consider overlaps in presentations. Draw out that operating with numbers involves many relationships. Ask, ‘What have we learned about operating with numbers this year that we didn’t know before?’ Brainstorm suggestions. Measuring Things Hold a quick quiz in which you hold up a range of objects and ask students to estimate their various measurable attributes. (For example, hold up a book and ask, ‘What is the mass of this book? How long is its spine? How much paper would I need to cover it? How many identical books would fit in this box?’) Have students record their estimates. Discuss the attributes of each object and have different students carry out accurate measurements. Ask questions related to the process of measuring, e.g. as the book is being weighed, ask, ‘In which unit of measurement would we weigh the book? How do you read the scale? How do you make sure that you are measuring accurately?’ Repeat with other objects. Review formulae for determining area, perimeter and volume. Unit 38 Revision

135

The Shape of Things Show students pictures of things such as houses, trucks, fire hydrants. Ask, ‘How many different geometric solids can you see represented here? What shaped faces does this object have? How would you describe the angle between these two faces?’ etc. Give students isometric dot paper (BLM 75) and ask them quickly to sketch one of the objects to show what is seen and what is not seen. Ask, ‘What do you need to think about to draw three-dimensional objects?’ Finding Out about Things Show students a six-sided dice. Say, ‘I am going to throw this dice three times. If three sixes come up we will have a game instead of doing Maths today. What is the likelihood of this?’ Discuss and then test. If three sixes do come up, have students play chance games. If not, ask, ‘Which organisations in our country collect data about the world? Why?’ Brainstorm answers. Consider an organisation listed, e.g. the police. Ask, ‘What questions might the police want answers to? What data might they collect? How might they collect it? How might they use it?’ Making Patterns Ask, ‘What is a pattern?’ Write a definition on the whiteboard. In pairs, have students quickly generate a pattern of their choice. Have pairs share their patterns with the class, asking other students to explain how their pattern works and then work out its next few elements.

Small Group Focus — Applying the Concept Focus Teaching Group • What Is Mathematics? Ask, ‘What is Mathematics?’ List students’ suggestions on the whiteboard. Ask, ‘Why do we learn Maths at school? When might we use it?’ List and discuss students’ suggestions. Have students work independently to make a poster called ‘Everyday Maths’. • Recognition and Help Ask, ‘What are you good at in Maths?’ Have students brainstorm their strengths.Work through different areas of Maths, asking, for example, ‘How do you feel about fractions/working out percentages?’ Celebrate students’ strengths and give feedback, e.g., ‘I have noticed that you are very good at drawing 3D objects.’ Have students choose two of their strengths to share with the group.Then ask, ‘What do you feel you need to do more work on?’ Allow time for students to make a list. Ask, ‘How will you go about this?’ Discuss. Have students work independently to set goals for improvement and make plans for achieving those goals. • Practising Maths Ask, ‘What sorts of things do you do to practise Maths skills?’ List these on the whiteboard, e.g. play games, do exercises, sing songs. Discuss the list, allowing time for students to explain why they do particular activities, how these activities enhance their skills, and whether or not they enjoy them. Have students make posters to present enjoyable ways to practise different aspects of Maths, e.g. ‘101 Fun Ways to Learn Tables’.


Revising Operations (Student Book p. 108) Have students complete the Student Book page. Students could then prepare their own page of problems for others to solve. This could be electronic and linked into the class website, or be on paper and be included in a class book. Revising Measurement (Student Book p. 109) Have students complete the Student Book page. When finished, students could set a measuring task for their partner to complete.

136


Revising Shapes (Student Book p. 110) Have students complete the Student Book page. Students could then draw diagrams of Centicube models for a partner to make. Alternatively, they could make pairs of Concentration cards, the first card describing a shape and the second card displaying a scale drawing of it, and use these to play ‘2D Concentration’. Revising Chance and Data (Student Book p. 111) Have students complete the Student Book page.When finished, students could investigate what sort of data is collected by one of the organisations listed during the class brainstorm. Students could download data and share their findings. Alternatively, students could use the library to conduct this research. Patterns Galore Have students generate numeric patterns using art materials or Kid Pix Studio Deluxe. These could be displayed around the classroom or published on the class website for others to continue. Unit 38 To monitor and assess students’ understandings use the Student book pages above. To gain insight into students’ perceptions of their competence in a range of mathematical areas, have them complete the ‘Check and Self-assessment’ page on Student Book p 112.

Whole Class Share Time Consider the Student Book page. Ask, ‘What skills did you need to solve the problems?’ Discuss each section of the page in turn. Today I learnt …

Question students about the strategies they used to complete the Student Book page. Ask, ‘How did you work out the volume of the pool?’ etc. Ask, ‘What does “two-dimensional” mean? What does “three-dimensional” mean? What do we know about 2D and 3D shapes?’ Invite a range of students to share the results of their research into organisations that collect data. Ask, ‘What did this organisation want to know? What data have they collected? How did they collect it?’ View the patterns students made. Ask individuals to point out patterns they found particularly interesting and to explain why.

Unit 38 Revision

137

unit

Investigating Problems

39


Number and patterns

BLMs 39 & 40

During this week look for students who can: • identify the information needed to solve problems • choose the appropriate mathematical methods to solve problems • express word problems using mathematical symbols • write word problems to match equations • make reasonable estimates • use a calculator to check estimates and solutions to problems. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources calculators, PowerPoint, Kid Pix Studio Deluxe, BLM 39 ‘Numbers and Symbols’, BLM 40 ‘How Could You Do It?’ Maths Talk Model the following vocabulary in discussion throughout the week: information, solve problems, solution, expressed in symbols, mathematical operation, estimate, process, in addition, multiplication, division, subtraction, sufficient information, What’s missing? How would you work it out? What is the problem you have to solve? Which information is important?

Whole Class Focus — Introducing the Concept What’s the Problem? Say, ‘There is a difference of seven students between Grade 5K and Grade 5W, which has 22 students. How many students could be in class 5K?’ Ask students to record the equation they would choose to solve the problem. Ask, ‘What key words helped you?’What mathematical information was in the problem?’ Discuss similar problems (using numbers less than 50 and involving up to two operations, but not including division and multiplication in the same problem). ___ = 28 + 17 $32 – $17.50 = ___ ___= 7 × 10 + 12 $24 – 4 × $2.25 = ___ ___ = 12m – 6m – 3m

What’s the Story? Write on the whiteboard the problems listed in the margin. Choose one of the problems and model writing it as a story problem. Think out aloud as you develop the story. Draw out the need for story problems to end with a question. Ask students to suggest story problems for two of the other number problems. Have several students share theirs with the class. Ask questions to draw out the key words in each story, e.g. ‘What words in James’s story told you to multiply then subtract?’ Red Herrings Discuss the phrase ‘a red herring’. Say, ‘Sometimes Maths problems include red herrings. Can you find the red herring in this problem?’ Provide pencils and paper for students to record mathematical information as you present the problems. Use problems such as, ‘A train ticket to the Show costs $12. A family of six all went to the Show. At the

138


Show, each of the four children bought a hotdog costing $2.30. How much did it cost the family to travel to the Show?’ Encourage students to note down the necessary information without transcribing the entire problem. Ask, ‘What is the problem you are asked to solve? Which information does not help you to solve the problem?’ Repeat with other problems. Ask students to write their own story problems containing unnecessary information. Have them read these to the class while other students identify the relevant and irrelevant information. What’s Missing? Pose problems, giving insufficient information, e.g. say, ‘Marie’s stamp album has 42 pages. Each page has space for 40 stamps. Her brother’s album has 50 pages. How many stamps do Marie and her brother have altogether?’ Ask students to try to solve the problem, and discuss their responses. Ask, ‘Why couldn’t you solve this problem? What other information did you need?’ Repeat with other like problems. Fermi Teasers Pose a Fermi-type problem such as, ‘I wonder how many slices of bread will be eaten at this school at lunchtime on Wednesday.’ Ask students to record an estimate. Ask, ‘How did you make your estimate? For an explanation What did you need to think about? Which mathematical operations did of Fermi problems, see Unit 40. you use as part of your thought processes? What information would help you to reach a more exact answer?’

Small Group Focus — Applying the Concept Focus Teaching Group • Tell Us the Story Have students sit in a circle. Sort the number and symbol cards from BLM 39 into ‘numbers’ and ‘symbols’ and place the two piles face down in the middle of the circle. Ask one child to turn over two or three cards from each pile. As a group, work out and record a story problem using those numbers and operations, and ending with a question. Question students to draw out what they need to think about to develop such story problems, e.g. ‘What do I need to think about to choose a setting for this problem? What do problems involving multiplication usually involve?’ etc. Have students work independently to take other number and symbol cards from the piles and write their own story problems. These could be collated to make a class book. • Do You Have a Problem? Write this problem on the board: ‘Anna went swimming at 7:10 a.m. She started school at 8:45 a.m. After school she worked at the supermarket where she helped to unload a truck carrying six crates. Each crate held 20 cartons and in each carton were four boxes of jam. How long did Anna spend swimming? How many boxes of jam were there? For how long did Anna work?’ Focus on one part of the question, e.g. ‘How long did Anna spend swimming?’ Ask, ‘Which operations would you use to solve this part of the problem? Are you given enough information to solve it? Could you solve other parts of the problem?’ Guide students to solve the problem. Have them work with partners to create like story problems with questions, for consideration by other members of the group. • What Number Was I? Write this problem on the board: ‘I was a number. I was multiplied by 3, then had 10 added, and 4 subtracted. Now I am 36. What number was I?’ Ask, ‘Would the starting number be less or greater than 36? Why do you think that? Which mathematical operations do we need to use?’ Guide students to develop appropriate number sentences to represent the problem. Have them work independently to write their own ‘What Number Was I?’ problems using numbers within an appropriate range. Unit 39 Investigating Problems

139


Money and Buses (Student Book p. 113) Have students complete the Student Book page. Storyteller Have students write several story problems involving up to three different operations. Have them swap problems with a partner and estimate the answers to their partner’s problems, recording their estimates. Have students then write equations to solve their partner’s problems. Provide calculators for students to use to check their answers. Maths Writer (Student Book p. 114) Have students complete the Student Book page.When finished, students could sort number and symbol cards cut from BLM 39, shuffle each set and place them face down in separate piles. Have students select number and symbol cards from each pile and use them to create their own equations. They should then write story problems to explain these. Problems with Problems Have students work in pairs to write story problems with up to three operations that contain unnecessary mathematical information.These could be recorded as a slide show in PowerPoint or Kid Pix Studio Deluxe, or collated as a class book. Have other students identify the unnecessary information by highlighting it on the slide show. What’s the Question? (Student Book p. 115) the Student Book page.


How Could You Do It? (BLM 40) Have students work in small groups to discuss and record strategies for dealing with the Fermi problems presented on BLM 40. Have them create their own Fermi-type problems using these problems as a model.

Whole Class Share Time Review the story problems on the Student Book page. Have individuals share their favourite stories with the class, asking other students to identify the operations involved. Ask, ‘Which words told you how to operate with the numbers? Which words told you to use division?’


Ask, ‘When you were checking your equations using the calculator, did you remember BODMAS when putting addition and multiplication in the same equation? If not, what happened?’ Have students share the equations they made with cards from the BLM. Encourage discussion to clarify the operations used. Ask, ‘Why do you think a card showing the division symbol was not included?’ Have students read aloud their problems, while the rest of the class identifies the unnecessary information. Ask, ‘How do you know that this information is unnecessary? What did you need to think about to make this decision?’ Have several students share with the class the problems they wrote. Ask, ‘What did you need to think about to ensure that you included enough information for someone to solve the problem?’ Ask several students to share their Fermi-type problems. Discuss strategies that could be used to solve them. Ask, ‘What information would make it easier to solve each problem? Are problems like these useful?’

140


unit


Fermi Problems Student Book pp. 116–117

BLMs 41, 42 & 80

During this week look for students who can: • identify and restate a problem • identify sub-questions that need to be addressed to solve complex problem • make models to explain and test ideas • make reasonable estimates based on relevant information • make reasonable assumptions based on information • present arguments for why a solution is plausible. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.

Resources drawing pins, a packet of jelly crystals, digital camera, jelly beans, stiff card, PowerPoint, BLM 41 ‘Estimating’, BLM 42 ‘Measuring the School’, BLM 80 ‘Websites’ Maths Talk Model the following vocabulary in discussion throughout the week: estimate, clarify the problem, look for sub-questions, make models, make assumptions, argue

Whole Class Focus — Introducing the Concept A Convincing Argument Ask, ‘How could you prove that your solution to a problem is correct?’ List students’ suggestions on the whiteboard, e.g. show how you worked it out, use a table, demonstrate a pattern. Pose this problem: ‘How many steps would you have to take if you walked from Sydney to Melbourne?’ Ask, ‘Would there be a right answer to this problem? How could you convince someone that you had made a reasonable estimate?’ Central Questions Write this problem on the whiteboard: ‘How many tins of cat food were eaten by cats in our neighbourhood last night?’ Ask, ‘What does this problem require us to think about? Which questions must we answer to find a solution?’ List questions central to answering this problem, e.g. ‘How many cats are there in the neighbourhood? How much does an average cat eat each night?’ Have students work in cooperative groups to estimate an answer to each question on the list. Have them use their estimates to develop a solution to the problem. Have each group present their solution to the class. Making a Model Ask, ‘How many drawing pins would I need to cover the entire back wall of the classroom with drawing pins?’ Demonstrate making a model to use in solving the problem. Mark a square of 10 cm2 on the pin Unit 40 Fermi Problems

141

board. Ask, ‘How many drawing pins do you think will fit in this square?’ Have two students place the drawing pins to fill the square, then count them. Ask, ‘How can we use this information to solve the problem?’ Using Estimation Write this question on the whiteboard: ‘What is the length in metres of all students in our school lying end to end?’ Ask, ‘How could we work out an answer to this problem without actually measuring the height of each student?’ Focus on using estimation. Ask, ‘How tall would an average Prep student be? What about a Grade 5 student? How could we use these estimates to solve the problem?’ Understanding Fermi Problems Review Fermi problems with students. Say, ‘All of the problems we have been considering are called Fermi Problems. What are the characteristics of Fermi Please note: Fermi problems Problems?’ List these, e.g. they often involve making are named after the Italian physicist Enrico Fermi (1901-1954), best known for his contribution to nuclear estimates; you need to make some assumptions; physics and the development of quantum theory, for which not all the information you need is handed to you; he was awarded the Nobel Prize. Fermi was also noted as a you need to ask and answer other questions before mathematician who liked to pose seemingly impossible questions. ‘Fermi Problems’ are problems that you can solve the problems. Have the students work celebrate his ability to estimate and play around in small groups to quickly brainstorm one of the with problem-solving. Fermi Problems from BLM 41 ‘Estimating’.

Small Group Focus — Applying the Concept Focus Teaching Group • Understanding the Problem Pose this problem to students: ‘What weight of jelly crystals would we need to turn a 25-metre swimming pool into a giant bowl of jelly?’ Ask, ‘What is this problem asking you to think about? e.g. ‘How many kilograms of jelly crystals would we need? How much water does it take to fill a 25-metre swimming pool? What is the correct ratio of jelly crystals to water?’ etc. What other information would we need to solve the problem?’ Guide students to develop a plan for solving the problem based on this new understanding. List questions that might be helpful and any information that should be sought, e.g. ‘How much water do you add to one packet of jelly? What does the packet weigh? How much jelly does this make?’ Have students work in cooperative pairs to develop a solution to the problem. • Making Guesstimates Ask, ‘What is an estimate?’ Draw out that an estimate is a probable solution that is based on relevant information but has not been worked out accurately. Some students will understand this as a ‘smart guess’. Ask, ‘When might it be helpful to make estimates?’ List suggestions on the whiteboard, e.g. estimating how many people will come to the school fete is helpful when deciding how many sausages to buy for the sausage sizzle. Discuss the issues, guiding students to think about what they need to consider to make a ‘smart guess’, e.g. ‘How many people come to the school fete? How many sausages were sold last year? How many sausages is each person likely to eat? What other food is being sold?’ etc. Have students work independently to estimate the answers to other questions listed on the whiteboard, explaining how they have worked out their estimates and which factors have influenced their decisions. • Presenting Solutions Review the question, ‘What weight of jelly crystals would you need to turn a 25-metre swimming pool into a giant bowl of jelly?’ Ask, ‘What would you expect to see in a solution to this problem?’ Draw out the need to explain which sub-questions have been asked, which

142


information has been used (e.g. the amount of water needed per packet of jelly), how the amount of water in the swimming pool has been calculated (by providing a diagram), etc. Guide students to work through a solution to the problem, then have students work independently to present their solution to the class. Encourage them to use digital photos, diagrams and PowerPoint displays.


Walking to Melbourne Have students work in cooperative groups to develop convincing solutions to the problem. Students could research distances between capital cities.Website 40 (BLM 80) may be useful. Choosing Questions (Student Book p. 116) Student Book page.


Jelly Beans Ask, ‘How many jelly beans would it take to fill our classroom?’ Provide jelly beans and stiff card with which students can make model containers. Have students use these models to develop solutions to the problem. Have them record their solutions using multimedia, e.g. a digital photo could be taken of a student’s model and used in a slide show to present their solution. Estimating Have students complete BLM 42 ‘Measuring the School’ to develop a solution to the problem. Solving Fermi Problems (Student Book p. 117) Have students complete the Student Book page.When finished, have students write their own Fermi Problems. These could be launched on the school website, with the school community invited to submit solutions. Students could review the answers submitted and give feedback on the solutions. Alternatively, a range of these problems could be used to run a school competition. Invite parents, teachers and other students to enter and present convincing arguments for their solutions. Units 39–40 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page on Student Book p 118.

Whole Class Share Time Have each group share their solution with the class. Discuss the most convincing aspects of the solution. Focus on why they were convincing.

Today I understood …

Invite students to share the questions they asked to solve the Student Book problem. Focus on questions with sub-questions, e.g. ‘What does a birthday card cost? What is the cheapest birthday card? What is the most expensive birthday card?’ Have students share their solutions to the problem. Ask, ‘How did making models help you to solve this problem? What other sorts of problems might you solve by making models?’ Enjoy eating the jelly beans. Have a range of students present their solutions to the problem. Promote discussion about the estimates made. Ask, ‘Is this estimate reasonable? Why or why not? Review the problems students have written.

Unit 40 Fermi Problems

143

BLM 1

What Number Am I? Play this game with a partner. • Cut out and then shuffle the cards below. Place them face down. • Take turns to pick a card and read the clues aloud. • Both players then try to guess the number. Whoever first guesses a number you both agree matches the clues on the card, wins the card. • When all the cards have been played, the player with the most cards wins. I am a three-digit number that is larger than 500, smaller than 700 and has a 4 in the tens place. My digits add up to a total of 10.

I am bigger than 1 000, but only just. My hundreds place is occupied by a 0. My digits add up to 5.

I am bigger than 1 000 and smaller than 2 000. My hundreds and tens digits add up to 12.

All of my five digits add up to 10 and I am bigger than 30 000.

I am halfway between 500 and 1 000. My digits total 12.

I am a four-digit number, but almost a five-digit number. I have a 9 and 8 in me.

If all my numbers were added together they would total 15. I am less than 3 000.

If you double me I am almost 10 000.

My three digits are the same and I am one less than a four-digit number.

My first three digits are the same as my second three digits. I am between 400 000 and 500 000.

My digits are 5, 3, 0, 6, 2, and 8. I am bigger than 600 000. I have a 0 in the hundreds place.

I am the biggest six-digit number.

I am a five-digit number. My digits get bigger as their place increases. My digits have a sum greater than 15.

I am the smallest six-digit number.

I am between 400 000 and 500 000. I have four 0s in me.

Teacher’s note: Copy onto card and cut out. Number and patterns (See Unit 1 pp. 24–26.)

144

© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

BLM 2

Lowest versus Highest You will need : a partner, a calculator, three 20-sided dice

• Take turns to roll three 20-sided dice and record the lowest number you can make with those numbers, and then the highest number. • After ten turns each, use a calculator to add up the total in each column to see who has the lowest score in the lowest column and the highest score in the highest column.

Digits rolled

Lowest number

Highest number

Example: 18, 13, 2

11 238

83 211

1 2 3 4 5 6 7 8 9 10 Total Teacher’s note: Give a copy to each student. When working with decimals (see Unit 16), the game can be varied by rolling five 20-sided dice and creating numbers with two decimal places. Number and patterns (See Units 1 and 16, pp. 24-26 and 69–71.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

145

BLM 3

10-minute Challenge You will need : a stopwatch or analogue clock

See how many of these equations you can complete in ten minutes. Time yourself with a stopwatch or analogue clock. 5 × 6 =

20 – 8 =

9 + 8 =

48 ÷∏ 8 =

72 ∏÷ 9 =

7 × 9 =

12 – 4 =

7 + 6 =

7 + 4 =

36 ÷∏ 6 =

3 × 4 =

15 – 7 =

18 – 9 =

4 + 9 =

42 ÷∏ 7 =

10 × 7 =

6 × 7 =

13 – 5 =

5 + 6 =

24 ÷∏ 8 =

25 ÷∏ 5 =

8 × 3 =

14 – 9 =

7 + 5 =

7 + 9 =

81 ÷∏ 9 =

5 × 7 =

16 – 7 =

15 – 6 =

8 + 3 =

49 ÷∏ 7 =

8 × 7 =

10 × 2 =

16 – 9 =

9 + 6 =

56 ÷∏ 8 =

27 ÷∏ 3 =

4 × 4 =

11 – 8 =

9 + 7 =

7 + 7 =

50 ÷∏ 2 =

5 × 8 =

19 – 10 =

16 – 8 =

9 + 9 =

100 ÷∏ 10 =

9 × 9 =

2 × 9 =

14 – 6 =

8 + 6 =

63 ÷∏ 9 =

18 ∏÷ 2 =

3 × 5 =

15 – 6 =

8 + 7 =

70 + 50 =

72 ÷∏ 8 =

7 × 5 =

16 – 9 =

12 – 7 =

400 + 300 =

48 ÷∏ 6 =

8 × 8 =

6 × 4 =

11 – 5 =

50 + 80 =

64 ÷∏ 8 =

25 ÷∏ 5 =

5 × 8 =

17 – 8 =

6 + 50 =

450 + 9 =

16 ÷∏ 4 =

3 × 9 =

14 – 0 =

17 – 7 =

34 + 5 =

35 ÷∏ 5 =

4 × 8 =

Number completed and correct: ______________

Time taken: ______________

Teacher’s note: Give a copy to each student. Have students repeat the exercise on a weekly basis and record their improvement. Number and patterns (See Unit 2 pp. 27–29.)

146


BLM 4

Shortcuts to Patterns Work Station 1 1 Follow these instructions to make a pattern. Start with 2. Add 4 each time. What pattern do you get? ___________________________________________________ 2 Find a shortcut to work out the 20th number in the pattern. _________________________________________________________________________________ Work Station 2 1 Continue this pattern. 1

4

9

16

25

_____

_____

_____

2 Find a shortcut to work out the 12th number in the pattern. _________________________________________________________________________________ Work Station 3 1 Explain the pattern,

3

9

15

21 etc.

_________________________________________________________________________________ 2 Find a shortcut to work out the 30th number in the pattern. _________________________________________________________________________________ Work Station 4 1 Make the pattern, + 3 – 7. Start at 5. _________________________________________________________________________________ 2 Find a shortcut to work out the 16th number in the pattern. _________________________________________________________________________________ Work Station 5 1 Fill in the missing numbers in this pattern. 100

105

110

_____

_____

125

_____

2 Find a shortcut to work out the 13th number in the pattern. _________________________________________________________________________________ Work Station 6 1 Make a pattern with shapes. 2 Find a shortcut to work out the 200th shape in the pattern. _________________________________________________________________________________ Teacher’s note: Make multiple copies, cut out the cards and place multiple copies at each work station. Number and patterns (See Unit 3 pp. 30–32.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

147

BLM 5

Hourly Temperature Use a line graph to represent the information in the table. Hourly Tem perature – Melbourne, 29–30th June 2002 Time 9:00 10:00 11:00 12:00 1:00 2:00 3:00 4:00 5:00

Temp. in ºC a.m. a.m. a.m. noon p.m. p.m. p.m. p.m. p.m.

7.2 7.5 9.6 11.5 13 15.3 14 11.3 9

Time 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. 10:00 p.m. 11:00 p.m. midnight 1:00 a.m. 2:00 a.m.

Temp. in ºC

Time

8.2 6.8 5 5.6 4.3 4.2 4.3 3.7 3.2

3:00 4:00 5:00 6:00 7:00 8:00 9:00

Temp. in ºC a.m. a.m. a.m. a.m. a.m. a.m. a.m.

3 2.3 1.3 0.2 1.6 4.7 8.3

Teacher’s note: Enlarge if using with the whole class. Chance and data (See Unit 4 pp. 33–35.)

148


BLM 6


10

9

8

7

6

5

4

3

2

1

0

–10

–9

–8

–7

–6

–5

–4

–3

–2

–1

Teacher’s note: Copy onto card and cut out. Number and patterns (See Unit 5 pp. 36–38.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

149

BLM 7

Finishing Order Work Station 2

Write the letters of the alphabet in reverse order in both upper and lower case.

Make a necklace with 45 beads.

Z

Work Station 1

Work Station 3

Work Station 4

Complete 50 sit-ups.

Make a tower with 10 wooden blocks. Use your non-preferred hand, i.e. the hand you don’t write with.

Work Station 5

Work Station 6

Write numbers from 10 to –10 on a number line.

Throw a beanbag into the air and catch it 50 times.

Teacher’s note: At each work station provide the materials required. Have students visit the work stations in small groups and compete to see who can complete each task first. Players are awarded points according to their placement in the task: first = 2 points, second = –1, third = –2, fourth = –3. Players keep track of their scores on a number line (see BLM 49). Number and patterns (See Unit 5 pp. 36–38.)

150


BLM 8

Line and Angle Cards Vertical line

Horizontal line

Parallel line

Diagonal line

Curved line

Spiral

Zigzag line

Perpendicular line

Right angle

Obtuse (blunt) angle

Acute angle

20º

30º

40º

50º

60º

70º

80º

90º

180º

Teacher’s note: Copy several times and cut out. Separate cards into two piles: lines (white) and angles (grey). Space (See Unit 6 pp. 39–41.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

151

BLM 9

Make a Protractor You will need : a split pin

How to assemble • Cut out around Pieces A and B. • Attach them with a split pin through both holes as shown below. ° 60

0°

70°

80° 90° 100° 110

° 12

0°

13

0°

5

°3 30

0° 2

40°

0° 180° 190° 20

0° 17

350° 0° 10° 20° 30 °

40 °

° 16 150 0° 14

A

3

32

0°

22

0°

10 °

hole 23

0°

°

10

°3

240

° 25

0° 26

° 30 0

0

0° 270° 280° 29

B

hole

0° ° 7

Attach with a split pin.

0°

80° 90° 100° 110

° 12

0°

60

13

0°

5 40

°

0° 14

3

0°

22

° 20

0°

33

° 21

0° 3

40°

0° 180° 190° 20 0

0° 17

° 16

350° 0° 10° 20° 30 °

150 23

0°

°

10

240

° 25

°3

00

0° 26

0° 270° 280°

290 °3

Teacher’s note: Copy onto acetate for each student. Provide split pins to assemble. Space (See Unit 6 pp. 39–41.)

152


BLM 10

Number Mat 1 463

5 207

493

1274

8 520

7 329

25

0

943

2 307

6 024

973

8 250 9 003 3 009

9 300 5 820 7 014 5 000

749

1 300

270

8 627

48

12

Teacher’s note: Copy for student use. Enlarge for whole-class use. Number and patterns (See Units 7, 8 and 19, pp. 42–47 and 78–80.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

153

BLM 11

Lucky Dice You will need : a partner, a copy each of this BLM, a 10-sided dice

Are you playing the addition game or the subtraction game? In the addition game, your aim is to create the highest total you can each time by throwing the dice and making two 5-digit numbers. In the subtraction game, your aim is to create the largest possible difference between the two 5-digit numbers. Here’s how to play. • Take turns to roll the dice. Write the number rolled in one of the ten boxes in the first blank equation. Choose its position carefully! • Continue throwing the dice and writing in numbers until the equation is complete. • Now add up the two 5-digit numbers (or subtract them). Compare your answer with your partner’s. Who has the biggest total? The player with the biggest total (or difference) wins that round. • Keep playing until all equations are complete. The player who has won the most rounds wins.

Teacher’s note: Give a copy to each student. For multiple use, place in plastic pockets and provide whiteboard markers. To increase the complexity of the problems, include decimal points. Number and patterns (See Units 7 and 8 pp.42–47.)

154


BLM 12

Guessathon You will need : a partner, a 30-cm ruler, a measuring tape

Take it in turns to do the following, and record your findings in the table. • Choose an object in the room. • Have your partner estimate the length of the object. • Together, measure the object and work out the difference between the estimated length and the actual length.

Classroom object

Estimated length

Actual length

Difference

Teacher’s note: Provide a copy for each pair of students. Measurement (See Unit 13 pp. 60–62.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

155

BLM 13

Making Simplified Fractions You will need : a 10-sided dice, a calculator

Follow the steps below and record your results in the table. • Throw a 10-sided dice four times to make a fraction with a double-digit numerator and double-digit denominator, e.g. 25 65 . Write it in the table. • Predict whether or not the fraction can be simplified, then use a calculator to work it out. Was your prediction correct? • Continue making double-digit fractions to complete the table. Fraction

Can it be Simplified fraction simplified? Yes/No

Was I correct? Yes/No

Number and patterns (See Unit 15 pp. 66–68.)

156


BLM 14

High or Low You will need: a partner, four sets of these cards, a 6-sided dice, extra paper

Here’s how to play. • Cut out the cards and shuffle them. Deal six cards to each player. Place the remaining cards face down. • Roll the dice to determine if the round is “high” (odd number) or “low” (even number). • Use your cards to make a six-digit number. (If you have one or more decimal point cards, discard all but one and make your number with fewer numbers and one decimal point.) • Compare your number with your partner’s. Whoever has the highest number in a “high” round, or the lowest number in a “low” round, wins a point. Keep a record of your numbers and your score. • At the end of each round, place the used cards in the discard pile. When all cards have been dealt, shuffle the discard pile, place it face down and continue playing. The first player to score 20 points wins.

.

1

2

3

.

1

2

3

4

5

6

7

4

5

6

7

8

9

0

0

8

9

0

0

.

1

2

3

.

1

2

3

4

5

6

7

4

5

6

7

8

9

0

.

8

9

0

.

Teacher’s note: Enlarge and copy. Have students record the numbers they make, and their scores, on a separate piece of paper. Number and patterns (See Units 16 and 26 pp. 69–71 and 99–101.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

157

BLM 15

Counting Constant You will need : a calculator

As you do this activity, record each step in the table. • Choose a starting number and punch it into the calculator. • Now choose a “counting constant” to add repeatedly to your starting number. (For your counting constant, choose a single-digit number that has been multiplied by 0.01, 0.10, 10, 100, 1 000, or 10 000.) Predict what the total will be when you add this number to your starting number. Press + on the calculator, then your chosen number, then =. Record the total. • Predict what the next total will be when you add your counting constant again. Press = to add it again. Record the next total. • Continue until you have filled in the first column in the table. • Now choose a new starting number and counting constant and fill in the second column, etc. 1st

2nd

3rd

4th

Starting number Counting constant I predict the total will be Actual total I predict the next total will be Actual total I predict the next total will be Actual total I predict the next total will be Actual total I predict the next total will be Actual total I predict the next total will be Actual total Number and patterns (See Unit 16 pp. 69–71.)

158


BLM 16

Making a Rain Gauge You will need : an empty 600mL plastic drink bottle, scissors, masking tape, a measuring jug, water

Follow these instructions to make your rain gauge. 1 Use scissors to cut the drink bottle where shown. Pinch it to get the scissors started.

2 Stick masking tape to the side of the bottle and mark “0 mL” as near to the end of the tape as you can.

3 Fill your bottle only as far as the 0 mL on the masking tape.

4 Calibrate your scale by adding 50 mL of water at a time, and marking each 50 mL on the masking tape. Then empty out the water.

5 Put the top of the bottle upside down inside the bottom of the bottle. Refill the bottle to “0 mL” on your scale.

6 Dig a shallow hole to put the rain gauge in. Check each day to see how much rain has fallen. Record the results.

Teacher’s note: In a true rain gauge, the rainfall is measured in millimetres, not millilitres, but for the purposes of this exercise students are asked to calibrate their scale and measure rainfall in millilitres. Measurement (See Unit 21 pp. 84–86.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

159

BLM 17

Pattern Strips 1 Work out the numbers missing from these patterns. Then record the rule for each pattern. The first one has been done for you. 1

2

3

5

0 + 1

1 + 1

1 + 2

2 + 3

8 3 + 5

Rule: Each number is made by adding the two numbers that come immediately before it. a

3

21

Rule: ___________________________________________________________________________ b

2

16

Rule: ___________________________________________________________________________ c

1

26

Rule: ___________________________________________________________________________ d

1

11

Rule: ___________________________________________________________________________ e

21

5

18

2 Make up your own pattern strips.

Rule: ___________________________________________________________________________

Rule: ___________________________________________________________________________

Rule: ___________________________________________________________________________

Rule: ___________________________________________________________________________ Number and patterns (See Unit 22 pp. 87–89.)

160


BLM 18

Building a Weighing Machine You will need : a thick rubber band, string, a ruler, some masking tape, a small box, metric weights

Follow these instructions to build your own weighing machine. 1 Use the string to suspend the box from the rubber band.

2 Attach masking tape down one edge of the ruler, leaving more than half the width of the tape free.

3 Use string to tie the rubber band to a door handle or to a hook on the wall.

4 Tape the ruler to the door (or wall) so that the top of the box sits level with the top of the ruler.

5 Work out how far the rubber band stretches when you place a 5 g weight in the box. On the ruler, mark “5 g” where the top of the box comes to now. Repeat with 10 g and 15 g weights, etc.

6 Continue until you have calibrated your scale. Test your weighing machine. How accurate is it? Adjust your markings if necessary.

Teacher’s note: Ensure that students use rubber bands safely, i.e. no flicking. Measurement (See Unit 24 pp. 93–95.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

161

BLM 19

It Weighs 1 Kilogram You will need : a set of kitchen scales/pan balance/spring balance, metric weights

Weigh a range of classroom objects and food items to find things that weigh about 1 kilogram.

Item

My estimate of its weight

Actual weight

Teacher’s note: Provide kitchen scales, pan balances and/or spring balances and metric weights for students to use. Measurement (See Unit 24 pp. 93–95.)

162


BLM 20

State Populations Examine the data and graphs and answer the questions below.

South Australia

1 514 854

Western Australia

1 906 114

5 000 000

1 514 854

4 000 000 3 000 000 2 000 000

Tasmania

472 931

Northern Territory

200 019

Australian Capital Territory

321 680

1 000 000

321 680

3 635 121

ACT

Queensland

6 000 000

200 019

4 822 663

NT

Victoria

7 000 000

472 931

6 609 304

1 906 114

New South Wales

3 635 121

Population

4 822 663

State

Australian State and Territory Populations, 2001 6 609 304

Australian State and Territory Populations, 2001

Australian State and Territory Populations, 2001

Tas

WA

SA

Qld

Vic

NSW

0

Australian State and Territory Populations, 2001 Northern Territory

7 000 000 Tasmania 6 000 000

Western Australia

5 000 000

Australian Capital Territory

4 000 000

New South Wales

South Australia

3 000 000 2 000 000

Queensland

1 000 000

ACT

NT

Tas

WA

SA

Qld

Vic

NSW

0 Victoria

1 Which type of graph is best to present this data? _____________________ Why? ______________________________________________________________________ _____________________________________________________________________________ 2 Which State or Territory has the most people? _________________________ 3 Which State or Territory has the fewest people? ________________________ 4 What is Australia’s total population? ____________________________________ Teacher’s note: Enlarge for whole class use. This data has been taken from the Australian Bureau of Statistics website (see Website 25a, BLM 79). Chance and data (See Unit 25 pp. 96–98.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

163

BLM 21

Subtraction Talent Search • Find someone who thinks they can explain the answer to the first question. Have them sign your talent search sheet alongside Question 1. • Now find nine other people who can explain the answers to the other nine questions. One of them may be you! You should have ten different signatures on your sheet. Question

Signature of person who can explain the answer

1 What is a decimal point? 2 What is the difference between $12 245.67 and $1 224.56? 3 What is a subtrahend? 4 How do you solve a subtraction problem in which the numbers contain zeros? 5 How do you subtract 356.78 from 2 650.07? 6 When might you need to subtract a decimal number from another decimal number? 7 What does the 5 represent in the number 24 640.85? 8 How many decimal places are there in the number 45.67? 9 What does “difference” mean? 10 What are four different ways of saying “minus”?


164


BLM 22

Decimal Number Mat 146.3 52.07

73.29

2.5

60.24

97.3

9.3

49.3

127.4 85.20

0

943.5 23.07

82.50 900.3 300.9

582.0 701.4 50.00

13.00 862.7

4.8

1.2

74.9

2.70

Teacher’s note: Copy for student use. Enlarge for whole-class use. Number and patterns (See Unit 27 pp. 102–104.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

165

BLM 23

Subtraction Problems 1 Look at these problems. How would you set them out? Work out the answers.

a 84.22 – 65.77 =

f 84.04 – 26.19 =

b 77.01 – 51.26 =

g 94.17 – 44.51 =

c 82.47 – 14.61 =

h 90.36 – 67.21 =

d 41.20 – 27.32 =

i 81.34 – 69.98 =

e 23.62 – 3.59 =

j 41.73 – 29.03 =

2 Make up ten more subtraction problems like these. Have your partner solve them. Check that your partner’s answers are correct.


166


BLM 24

Cheque Book You will need : advertising material, the classified section of a newspaper

You have $99 999 in your cheque account and you want to spend some of it. Use advertising material and the classified section of the newspaper to select the items you will buy. Since you will pay for everything by cheque, you need to keep an account balance. Fill in the table to show how you balance your cheque account. Balance

Item bought

Cost

New balance

$99 999

Number and patterns (See Unit 27 pp. 102–104.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

167

Minimal Differences You will need : a partner, a 10-sided dice

• Take turns to throw the dice to make numbers the numbers in the boxes carefully. Your aim is difference you can each round. • At the end of each round, the player with the ten points. • The player with the most points at the end of Round 1

.

Round 3

–

Round 5

. –

.

Round 6

. .

Round 7

. –

.

Round 8

. –

.

Round 4

.

–

eight rounds wins.

.

. –

smallest difference wins

Round 2

. –

for each round. Place to make the smallest

.

. –

.


168


My Dream House Design your dream house. To complete this project you must provide the following. 1 A plan (to scale) of your dream house.

2 A landscape design that includes a sandpit and a swimming pool, for your outside area.

3 A plan for painting your house showing how much paint of each colour you will need and what it will cost.

4 A plan for floor-coverings showing what you will use, how much you will need and what it will cost.

5 A plan for storage space in your house showing where it will be and how much it will hold.

6 A model of your dream house. Make sure that you include a record of how you calculated any areas, volumes and costs associated with planning your house.

Teacher’s note: Provide a copy for each student. You will need to allow an extended period of time for students to complete this project. Measurement (See Unit 28 pp. 105–107.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

169

BLM 27

Estimate then Measure You will need : 30-cm and metre rulers, a long tape measure

• Find objects that you think have the approximate lengths listed in the table. • Measure each object. • Work out how good your estimate was. The first one has been done for you Find something you think measures...

10 cm

Object

Actual length

Difference between predicted and actual lengths

1 tile above the sink

8 cm

2 cm

25 cm

30 cm

50 cm

75 cm

1 m

2 m

3 m

10 m

Teacher’s note: Give a copy to each student. Provide each student with a 30-cm and metre ruler, and have long tape measures available. Measurement (See Unit 28 pp. 105–107.)

170


BLM 28

Pirates’ Treasure You will need : three other players, a different coloured pencil each North 1 square = 10 km

89 gold coins

145 gold coins

278 gold coins 137 gold coins

45 gold coins

413 gold coins

s oin d c l o g 209

Teacher’s note: Have each student use a coloured pencil of their choice to record the path of their pirate ship. Space (See Unit 29 pp. 108–110.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

171

BLM 29

Three-coin Toss You will need : three coins

1 Toss the three coins 100 times and record the results in the table. Mark ‘H’ for heads and ‘T’ for tails. No. of throw

Result (coins)

1

2

3

No. of throw

Result (coins)

1

2

3

No. of throw

Result (coins)

1

2

3

No. of throw

1

26

51

76

2

27

52

77

3

28

53

78

4

29

54

79

5

30

55

80

6

31

56

81

7

32

57

82

8

33

58

83

9

34

59

84

10

35

60

85

11

36

61

86

12

37

62

87

13

38

63

88

14

39

64

89

15

40

65

90

16

41

66

91

17

42

67

92

18

43

68

93

19

44

69

94

20

45

70

95

21

46

71

96

22

47

72

97

23

48

73

98

24

49

74

99

25

50

75

100

Result (coins)

1

2

2 How many times did you record each of these combinations? a three heads _______ b two heads and a tail _______ c one head and two tails d three tails _______ Chance and data (See Unit 31 pp. 114–116.)

172


3

BLM 30

Two Spinners You will need : a partner, a paper clip and a pencil with a sharp point, extra paper

Play “Two Spinners”. Here’s how to play. • Decide who will be Player 1 and who will be Player 2. Take turns to spin both spinners and add the two numbers that come up. • If the sum is odd, Player 1 wins a point even if it is not their turn. If the sum is even, Player 2 wins a point even if it is not their turn. • Play continues until one player has ten points. 1 Play the game a number of times to see what happens.

4

3

5

2 1

6 9

8

5

4

7

6

3 2

7 1

9

8

2 a Is this a fair game? ________ b Who, if anyone, has a better chance of winning? _____________________ c Why? ______________________________________________ Justify your answer. __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ Teacher’s note: Have each student keep a record of their score on another piece of paper. Chance and data (See Unit 31 Teacher’s Book pp. 114–116.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

173

BLM 31

Operations Cards

÷ 9

+ 7

+ 9

+ 8

+ 6

+ 5

+ 4

– 9

– 8

– 7

– 6

– 5

– 4

– 3

×2

×3

×4

×6

×7

×8

×9

÷ 2

÷ 3

÷ 4

÷ 5

÷ 6

÷ 7

÷ 8

Teacher’s note: Copy onto stiff card and cut out. Number and patterns (See Unit 32 pp. 117–119.)

174


BLM 32

Number Chain Start I am 100.

I am 46.

I am 12.

I am 35.

You are 3 + 4 × 8.

You are 20 × 80.

You are 6 × 7 + 4.

You are 42 ÷ 2 – 9.

I am 1 600.

I am 60.

I am 32.

I am 10.

You are 4 200 ÷ 70.

You are 49 ÷ 7 + 25.

You are 4 × 25 ÷ 10

You are 2 of 84.

I am 42.

I am 9.

I am 64.

I am 80.

You are 1 4 of (4 × 9)

You are 82 – 18.

You are 75 + 25 ÷ 5.

You are 10 × 16.

I am 160.

I am 890.

I am 90.

I am 78.

You are 10 × 89.

You are 900 ÷ 10.

You are 10 × 7.8.

You are 200 ÷ 10.

I am 20.

I am 560.

I am 13.

I am 75.

You are 7 × 80.

You are 64 ÷ 8 + 5.

You are 25 + 25 + 25.

You are 25 + 25.

I am 50.

I am 11.

I am 28.

I am 56.

You are 3 of 33.

You are 49 – 7 – 7 – 7.

You are 14 + 14 + 14 + 14.

You are 2 of 28.

I am 14.

I am 1 000.

I am 10 000.

I am 80.

You are 100 × 10.

You are 9 999 + 1.

You are 34 + 46.

You are 47 + 53.

1

1

1

Teacher’s note: Enlarge, copy onto stiff card and cut out. Number and patterns (See Unit 32 pp. 117–119.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

175

BLM 33

Translation Cards Move left 3 and up 2 spaces.

Move right 4 and up 2 spaces.

Move down 5 spaces.

Move up 4 spaces.

Move left 2 spaces.

Move right 2 spaces.

Move left 3 and down 4 spaces.

Move right 3 and down 5 spaces.

Move up 4 and left 4 spaces.

Move up 3 and right 3 spaces.

Move down 3 and right 3 spaces.

Move down 4 and left 4 spaces.


Move right 3 and down 2 spaces.

Move left 4 and up 2 spaces.

Move up 5 spaces.


Move left 3 and up 5 spaces.

Move down 4 and right 4 spaces.

Move down 3 and left 3 spaces.

Teacher’s note: Copy onto card and cut out. Space (See Unit 34 pp. 123–125.)

176


BLM 34

Carroll Diagram Use this Carroll diagram to classify shapes. Symmetrical

Not symmetrical

Tessellates

Does not tessellate

Space (See Unit 35 pp. 126–128.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

177

BLM 35

Pentominoes

Which of these shapes will tessellate? Test them by drawing on the grid. Tick the ones that do.

Space (See Unit 35 pp. 126–128.)

178


BLM 36

Percentage Match-up 1 10

0.1

10%

1 2

0.5

50%

1 4

0.25

25%

1 5

0.2

20%

1 20

0.05

5%

1 100

0.01

1%

2 5

0.4

40%

3 10

0.3

30%

3 4

0.75

75%

Teacher’s note: Copy onto stiff card and cut out. Number and patterns (See Unit 36 pp. 129–131.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

179

BLM 37

Best Buys The following advertisements were found in the local paper. Which is the best buy? Why? 1a

b

Which would you buy? ______ Why? ________________________ _______________________________

2a

b


3a

b


4a

b


5a

b


6a

b


7a

b



180


BLM 38

Fraction Squares 1 Complete the four fraction squares by following the instructions. • Look at the mixed numbers on the outer corners of Squares A and B. • Work out the difference between each adjacent two numbers and write the answer in the circle that lies on the line between them. • Now do the same for the squares formed by these answers. • Complete the smallest squares in the centre in the same way. • When you come to Squares C and D, you will need to work backwards. A

1 23

2 34

2 14

3 12

C

B

2 12

3 34

1 23

1 14

D 1

1

1 2

1 2

1

1

1 2

1 2

2 Now make up your own fraction square for a friend to solve.


181

BLM 39

Numbers and Symbols • Cut out the cards and sort them into two piles — numbers and symbols. • Place the two piles face down. Turn over several cards from each pile to create a mathematical problem. • Write a story to match. Ask your partner to solve the problem.

+

+

×

×

–

–

18

12

8

6

10

9

20

30

14

5

Teacher's note: Photocopy onto firm card and cut out. Number and patterns (See Unit 39 pp. 138–140.)

182


BLM 40

How Could You Do It? • Discuss each of these problems in your group. Record the information you would need to gather to work out the problem. • Make a step-by-step list of the mathematical tasks you would carry out to find the answers. 1 a How many slices of bread were eaten by the families in our school last week? ______________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ b Could you work out an exact answer? Why or why not? ___________ __________________________________________________________________________ __________________________________________________________________________ 2 a How much would it cost to buy a month’s supply of pizza cartons for the take-away pizza shops in our area? __________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ b Could you work out an exact answer? Why or why not? ____________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ Number and patterns (See Unit 39 pp. 138–140.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

183

BLM 41

Estimating Use estimation skills to find solutions to these problems. Problem

What I need to estimate

My estimate

My solution

1 How many flat toothpicks will fit on the surface of a sheet of poster board?

2 How many hotdogs will be eaten at an AFL football game during the Grand Final?

3 How many minutes will be spent on the phone by Year 5 students in Australia?

4 How many pizzas will be ordered by families from our school this year?


184


BLM 42

Measuring the School Problem: “What is the length in metres of all the students in our school?” If everyone lay end to end, how far would the line of students go? Task: To work out an acceptable answer to this problem without actually measuring each student. You will need to use your estimation skills. See how you go! Year level

Estimated average height of a student at this year level

Number of students in year level

Estimated total length of year level, i.e. all students lying end to end

Prep

1

2

3

4

5

6

Total length of all students lying end to end: _______________________________


185

BLM 43

Paste here

Paste here

Number Expander

Hundreds of thousands

Tens of thousands

Thousands

Hundreds

Tens

Ones

Tenths

Hundredths

How to fold. H 6

T 4

O 2

Teacher’s note: Cut out, assemble and fold as shown. Use with Units 1, 14 and 16, and other number-related activities.

186


BLM 44

Tables Chart 1 1 x 1 =

1

1

x 2 =

2

1

x 3

=

3

2 x 1 =

2

2

x 2 =

4

2

x 3

=

6

3 x 1 =

3

3

x 2 =

6

3

x 3

=

9

4 x 1 =

4

4

x 2 =

8

4

x 3

= 12

5 x 1 =

5

5

x 2 = 10

5

x 3

= 15

6 x 1 =

6

6

x 2 = 12

6

x 3

= 18

7 x 1 =

7

7

x 2 = 14

7

x 3

= 21

8 x 1 =

8

8

x 2 = 16

8

x 3

= 24

9 x 1 =

9

9

x 2 = 18

9

x 3

= 27

10 x 1 = 10

10

x 2 = 20

10

x 3

= 30

11 x 1 = 11

11

x 2 = 22

11

x 3

= 33

12 x 1 = 12

12

x 2 = 24

12

x 3

= 36

1 x 4 =

4

1

x 5 =

5

1

x 6

=

6

2 x 4 =

8

2

x 5 = 10

2

x 6

= 12

3 x 4 = 12

3

x 5 = 15

3

x 6

= 18

4 x 4 = 16

4

x 5 = 20

4

x 6

= 24

5 x 4 = 20

5

x 5 = 25

5

x 6

= 30

6 x 4 = 24

6

x 5 = 30

6

x 6

= 36

7 x 4 = 28

7

x 5 = 35

7

x 6

= 42

8 x 4 = 32

8

x 5 = 40

8

x 6

= 48

9 x 4 = 36

9

x 5 = 45

9

x 6

= 54

10 x 4 = 40

10

x 5 = 50

10

x 6

= 60

11 x 4 = 44

11

x 5 = 55

11

x 6

= 66

12 x 4 = 48

12

x 5 = 60

12

x 6

= 72

Teacher’s note: Give a copy to each student who would benefit from revision of tables facts. Use with Unit 2 and other tables-related activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

187

BLM 45

Tables Chart 2 11 x 7 =

7

1

x 8 =

8

1

x 9

=

9

12 x 7 = 14

2

x 8 = 16

2

x 9

= 18

13 x 7 = 21

3

x 8 = 24

3

x 9

= 27

14 x 7 = 28

4

x 8 = 32

4

x 9

= 36

15 x 7 = 35

5

x 8 = 40

5

x 9

= 45

16 x 7 = 42

6

x 8 = 48

6

x 9

= 54

17 x 7 = 49

7

x 8 = 56

7

x 9

= 63

18 x 7 = 56

8

x 8 = 64

8

x 9

= 72

19 x 7 = 63

9

x 8 = 72

9

x 9

= 81

10 x 7 = 70

10

x 8 = 80

10

x 9

= 90

11 x 7 = 77

11

x 8 = 88

11

x 9

= 99

12 x 7 = 84

12

x 8 = 96

12

x 9

= 108

11 x 10 = 10

1

x 11 =

11

1 x 12 =

2

12 x 10 = 20

2

x 11 =

22

2 x 12 = 24

13 x 10 = 30

3

x 11 =

33

3 x 12 = 36

14 x 10 = 40

4

x 11 =

44

4 x 12 = 48

15 x 10 = 50

5

x 11 =

55

5 x 12 = 60

16 x 10 = 60

6

x 11 =

66

6 x 12 = 72

17 x 10 = 70

7

x 11 =

77

7 x 12 = 84

18 x 10 = 80

8

x 11 =

88

8 x 12 = 96

19 x 10 = 90

9

x 11 =

99

9 x 12 = 108

10 x 10 = 100

10

x 11 = 110

10 x 12 = 120

11 x 10 = 110

11

x 11 = 121

11 x 12 = 132

12 x 10 = 120

12

x 11 = 132

12 x 12 = 144

Teacher’s note: Give a copy to each student who would benefit from revision of tables facts. Use with Unit 2 and other tables-related activities.

188


BLM 46

Tables Grid ×

1

2

3

4

5

6

7

8

9

10

11

12

1 2 3 4 5 6 7 8 9 10 11 12 All finished … Just in time for lunch!

Teacher’s note: Give a copy to each student who would benefit from revision of tables facts. Use with Unit 2 and other tables-related activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

189

BLM 47

100 Grid 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99 100

Teacher’s note: This grid can be used to record numbers and patterns. Use with Units 2 and 12 and other number-related activities.

190


BLM 48

Blank 100 Grid

Teacher’s note: This grid can be used to record numbers and patterns. Use with Units 14 and 36, and other number-related activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

191

BLM 49

Blank Number Line

Paste here

Paste here

Paste here

Teacher’s note: Blank number lines can be used to strengthen students’ understanding of the counting sequence involving negative, positive and decimal numbers. Use with Units 5 and 14, and other number-related activities.

192


BLM 50

Blank Number Squares Fill in numbers, operation signs (+ – × ÷∏) and the = sign to complete the squares. Example: 16

×

4

= 64

Use with Unit 23, and other activities in which computation practice is required. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

193

BLM 51

Divisibility Table This table will help you in your mental calculation. If you know these division facts, you will be better able to estimate the answers to division problems. Divisible by…

If

Example

2

The last digit is even.

4 876 6 ÷∏ 2 = 3

3

The sum of all digits has 3 as a factor.

171 1 + 7 + 1 = 9 9 ÷ 3 = 3

4

The last two digits are divisible by 4.

2 536 36 ÷∏ 4 = 9

5

The last digit is a 0 or 5.

55 670, 43 655

6

The last digit is even and the sum of all digits has 3 as a factor.

63 534, 45 336

7

There is no test for divisibility by 7.

8

The last three digits can be divided evenly by 8.

34 392 392 ÷∏ 8 = 49

9

All digits have a sum that is divisible by 9.

5 643 5 + 6 + 4 + 3 = 18 18 ÷ 9 = 2

The number ends in 0.

194 870

10

Use with Unit 20, and other activities requiring mental calculation of division problems.

194


BLM 52

Calculating Averages You will need : a calculator

Activity: ________________________________________________

Attempt

Day 1 no. Result

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

Total

÷ 10

Average

Attempt

Attempt

Day 2 no. Result

1 2 3 4 5 6 7 8 9 10 Total Average

1 2 3 4 5 6 7 8 9 10

Total

÷ 10

Average

Day 4 no. Result

Attempt

Day 5 no. Result

Total

Total

÷ 10

Average

1 2 3 4 5 6 7 8 9 10 ÷ 10

Attempt

Day 3 no. Result

1 Did your time improve with practice? ______ 2 What was the difference between your average time on Day 1 and your average time on Day 5? ______________ 3 What was your average time for the week? _______________

÷ 10

Average

Use with Unit 26, and other activities involving the calculation of averages. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

195

BLM 53

Fraction Cards 1 2

1 3

1 4

1 5

1 6

2 3

2 4

3 4

2 5

3 5

4 5

2 6

3 6

4 6

5 6

1 7

2 7

5 7

6 7

1 8

2 8

3 8

4 8

5 8

6 8

7 8

3 2

4 3

8 3

6 5

8 5

8 7

10 20

10 15

5 25

7 21

14 21

4 24

8 24

16 24

1 2

1 3

1 4

1 5

1 6

2 3

2 4

3 4

2 5

3 5

4 5

2 6

3 6

4 6

5 6

2 8

3 8

4 8

5 8

6 8

Teacher's note: Enlarge, copy onto stiff card and cut out. Use with Units 15 and 37, and other activities involving fractions.

196


BLM 54

Fraction Wall Colour and name fractions on this wall.

Use with Unit 15, and other activities involving fractions. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

197

BLM 55

Percentage Grids

Fraction: ______ This is ____%






Use with Unit 36, and other activities involving equivalence of fractions and percentages.

198


BLM 56

Blank Clock Faces 11

12

11

1

10

3 8

11

6

12

8

1

11

9 8

8

11

11

12

1

11

8

6

12

5

1

10 3

4 6

4

8

2

7

3

7

9

1 2

5

10

12

5

9

4

8

6

10 3

6

4

1 2

7

3

7

9

1 2

5

10

12

9

4

12

6

5

10 3

11

4 7

2

6

3

5

10

7

2

9

4 7

1

10

2

9

12

5

2

9

3 8

4 7

6

5

Use with Units 6 and 11, and other time-related activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

199

BLM 57

Blank Calendar January S

M

T

W

T

February F

S

S

M

T

April S

M

T

W

M

T

W

T

F

S

S

M

M

T

W

F

S

S

M

T

T

W

T

F

S

S

M

T

T

W

T

F

S

S

M

S

S

M

T

W

T

F

S

T

T

T

W

T

F

S

F

S

F

S

September F

S

S

M

November F

W

June

August

October S

T

May

July S

W

March

T

W

T

December F

S

S

M

T

W

T

Teacher’s note: Give a copy to each student. Enlarge for whole class use. Use with Unit 10, and other time-related activities.

200


BLM 58

Blank Month

Monday Tuesday Wednesday

Month: _____________________________________

Sunday Thursday Friday Saturday

Teacher’s note: Give a copy to each student. Enlarge for whole class use. Use with Unit 10, and other time-related activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

201

BLM 59

My Timetable Title: ___________________________________________ Time

Event

Teacher’s note: Give a copy to each student. Enlarge for whole class use. Use with Unit 10, and other time-related activities.

202


BLM 60

Graph Paper

Use with Units 4, 9, 17, 25 and 30, and other data- and space-related activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

203

BLM 61

2D-shape Cards

equilateral triangle

square

oval

parallelogram

octagon

right-angled triangle

circle

decagon

hexagon

nonagon

scalene triangle

heptagon

trapezium

pentagon

rectangle

isosceles triangle

Teacher's note: Copy onto stiff card and cut out. Cards can be used for shape recognition or to play ‘2D-shape Concentration’.

204

Use with Unit 35 and other activities requiring recognition of 2D shapes. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

BLM 62

3D-shape Cards

cube

rectangular prism

triangular pyramid

hexagonal prism

hexagonal pyramid

cylinder

square pyramid

pentagonal prism

hexahedron

triangular prism

rectangular pyramid

cone

pentagonal pyramid

sphere

octagonal prism

hemisphere

Teacher's note: Copy onto stiff card and cut out. Cards can be used for shape recognition or to play ‘3D-shape Concentration’. Use with Unit 17, and other activities requiring recognition of 3D shapes. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

205

BLM 63

Square Pyramid Net

fold

fold

fold

fold Use with Unit 17, and other activities requiring an understanding of 3D shapes.

206


BLM 64

Triangular Pyramid Net

fold

fold

fold Use with Unit 17, and other activities requiring an understanding of 3D shapes. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

207

BLM 65

Triangular Prism Net fold

fold

fold

fold


208


BLM 66

Rectangular Prism Net

fold

fold fold

fold

fold

fold



209

BLM 67

Grid Coordinates A

B

C

D

E

F

G

H

I

1 2 3 4 5 6 7 8 9 10

Use with Unit 29, and other location activities.

210


BLM 68

Coordinates Cards

A

B

C

D

E

F

G

H

I

J

1

2

3

4

5

6

7

8

9

10

Teacher's note: Copy onto card and cut out. Use with Unit 29 and other location activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

211

BLM 69

Reduce or Enlarge

Teacher's note: Copy onto an acetate sheet to use in whole class demonstration. Use with Unit 34, and other activities involving transformation.

212


BLM 70

Blank Carroll Diagram

Use with Unit 35. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

213

BLM 71

Tessellation Pattern 1

Use with Unit 35.

214


BLM 72



215

BLM 73


Use with Unit 35.

216


BLM 74

Square Dot Paper


217

BLM 75

Isometric Dot Paper

Teacher's note: Copy for use when drawing 3D shapes or creating patterns. Use with Units 3, 17, 18, 35 and 38 and other activities related to pattern, shape and space.

218


BLM 76

Grid Paper

Teacher’s note: Copy onto an acetate sheet for classroom demonstrations. Use with Units 3, 4, 12, 13, 28, 34 and 35. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

219

BLM 77

1 -cm 2

Grid Paper

Teacher’s note: Can be used as an alternative to graph paper. Copy onto acetate sheet for classroom demonstrations.

220

Use with Units 3, 4, 9, 13, 28, 30 and 34. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

BLM 78

Drawing 3D Shapes

Teacher's note: Have students use dotted lines to draw in the edges ‘not seen’. Use with Unit 18, and other activities requiring recognition of 3D shapes. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

221

BLM 79

Websites Unit 11 – Airlines 11 http://www.qantas.com.au/regions/dyn/home/qualifier-region-au ________________________________________________________________________ ________________________________________________________________________ Unit 21 – Bureau of Meteorology 21 http://www.bom.gov.au ________________________________________________________________________ ________________________________________________________________________ Unit 25 – Environment, energy, population, local councils 25a http://www.abs.gov.au/ 25b http://conservewater.melbournewater.com.au/scripts/storage.asp 25c http://www.greenhouse.gov.au/pubs/gwci/index.html 25d http://www.nla.gov.au/guides/discoverguides/auscensus.html (and follow Electronic Resources) 25e http://library.trinity.wa.edu.au/subjects/sose/geography/population.html 25f http://www.bom.gov.au/lam/Students_Teachers/climprob/rainprbsec.shtml 25g http://www.conservewater.melbournewater.com.au/scripts/wizard/ 25h http://www.txu.com.au/residental/energycalculator/energycalculator.asp ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Unit 26 – Decimals 26 http://www.math.com/ ________________________________________________________________________ ________________________________________________________________________ Unit 28 – House plans, painting 28a http://www.avjennings.com.au/fsm_display_vt.html 28b http://www.dulux.com.au/fr_paintingyh.htm _______________________________________________________________________ _______________________________________________________________________

Teacher’s note: Copy and display in classroom as a convenient reference for both yourself and students who may wish to access certain websites. Update as necessary.

222


BLM 80

Websites (continued) _______________________________________________________________________ Unit 29 – World travel 29 http://www.virtualtourist.com/vt/ _______________________________________________________________________ _______________________________________________________________________ Unit 31 – The game ‘Pig’ 31 http://www.nrich.maths.org/mathsf/journalf/jun01/game1/index.html _______________________________________________________________________ _______________________________________________________________________ Unit 32 – Mental strategies games 32 http://nrich.maths.org/prime/lib_games.htm _______________________________________________________________________ _______________________________________________________________________ Unit 35 – Tessellation 35a http://www.escher-prints.com/tessellations.html 35b http://www.mathacademy.com/pr/minitext/escher/#tess 35c http://library.thinkquest.org/16661/of.regular.polygons/index.html _______________________________________________________________________ _______________________________________________________________________ Unit 36 – Percentages 36 http://www.mathgoodies.com/lessons/vol4/challenge_vol4.html _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ Unit 40 – Travelling distances 40 http://www.indo.com/distance/ _______________________________________________________________________ _______________________________________________________________________ Other Useful Sites _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ Teacher’s note: Copy and display in classroom as a convenient reference for both yourself and students who may wish to access certain websites. Update as necessary. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 6 may be photocopied for educational use within the purchasing institution.

223

BLM 81

Student Profile Code:

NA not apparent

Week

B

beginning

C

consolidating

E

established

Unit

Name: ___________________________________________________________________ Year Level: __________

Term: __________

Year: __________

‘Plain Speak’ Statements

(Date)

1 Place Value

2 Fantastic Number Facts

3 Number Patterns

4 Choosing Graphs

5 Positive and Negative Numbers

6 Lines and Angles

7 Addition

8 Subtraction

9 Using Data to Answer Questions

10 Running on Time

224

Explain the value of a numeral according to its place in a number to 99 999 Put whole numbers in order from smallest to largest up to 1 000 000 Read and write numbers to 99 999 in words or as numerals Round numbers to the nearest 10, 100, 1 000, etc. Automatically recall addition, subtraction, multiplication and division facts Explain and use the relationship between addition and subtraction facts, and also between multiplication and division facts Identify appropriate strategies to use when solving mathematical problems Identify patterns in numeric problems Continue number patterns Explain number patterns Predict how a number pattern will continue based on an understanding of how the pattern works Represent data collected using pie (sector) graphs, line graphs, bar (column) graphs and picture graphs Analyse and present findings about data sets they have collated and presented Identify the features of different graphs Select the appropriate type of graph to present data according to its purpose Read and analyse pie (sector) graphs, line graphs, bar (column) graphs and picture graphs Place negative and positive numbers between –10 and +10 on a number line Order positive and negative numbers from –10 to +10 Explain what a negative number is Analyse data that contains positive and negative numbers between –10 and +20 Construct, identify and explain the features of a range of lines (vertical, horizontal, parallel, diagonal, perpendicular, curved and zigzag lines) Use protractors to measure angles Identify and draw right angles, obtuse (blunt) angles and acute (sharp) angles Use mental processes, written methods and calculators to add numbers to 999 999 Identify when addition could be used in everyday life Verbalise the thought processes used to solve addition problems

Use mental processes, written methods, and calculators to subtract numbers in the range 0 to 999 999 Identify when subtraction could be used in everyday life Verbalise the thought processes used to solve subtraction problems

Pose questions about issues of concern that could be solved using mathematical means Suggest ways to collect data Use a range of data-collection techniques to investigate questions Create graphs of varying types Analyse and present data, providing arguments for the meaning of the data Read and interpret timetables Read and calculate information from calendars Identify how long it will be until a specified event Make own timetables and schedules


BLM 82


NA not apparent

Week (Date)

B

beginning

C

consolidating

E

established

Unit

11 Time

12 Numbers, Numbers, Numbers!

13 Area and Perimeter

14 Decimals

15 Fractions

16 Counting and Number Order

17 Making 3D Shapes

18 Drawing 3D Objects

19 Multiplication

20 Division

Name: ___________________________________________________________________ Year Level: __________

Term: __________

Year: __________

‘Plain Speak’ Statements Read analogue and digital clocks to the nearest minute Calculate time elapsed Convert 12-hour clock time to 24-hour time Use stopwatches to measure and compare time taken to complete a given task Rank times from fastest to slowest Determine factors of numbers Identify prime numbers Identify and construct square numbers Identify and construct cube numbers Identify one-step, two-step and three-step palindromes Accurately measure lengths in millimetres, centimetres and metres Estimate and measure the perimeter of polygons Investigate area using square metres Use the working method of A = L x W to calculate the area of polygons Order decimal numbers from smallest to largest Round decimal numbers up or down to the nearest hundredth Place decimal numbers on a number line, including hundredths Use a ruler to measure to the nearest hundredth Order common fractions from smallest to largest Simplify common fractions Add common fractions Identify equivalent common fractions Make models to demonstrate fraction size

Write decimal numbers in words and explore features of decimal numbers

Identify common fractions that are bigger than/smaller than another common fraction

Order numbers from 0.01 to 999 999.99 Use counting skills to count by multiples of 10, 100, 1 000 Write numbers from 0.01 to 999 999.99 in words Continue counting patterns and identify the rule Define and draw 3D shapes by their features Match 3D shapes with their corresponding nets Identify features shared by 3D shapes Use concrete materials to make 3D shapes such as cubes, prisms, cones, cylinders, pyramids and other polyhedra Make to size a net to build a cube, triangular or rectangular prism Follow plans and diagrams to make 3D models Draw representations of solids such as cubes, prisms, cones, cylinders, pyramids and other polyhedra using isometric dot paper or graph paper Show the part of an object that is not seen when drawing a solid Draw what models look like from the front, side and top Multiply whole numbers by two-digit numbers Write and solve multiplication Identify when multiplication could be used in everyday life word problems Use mental and written methods, and calculators, to multiply numbers to 999 999 Verbalise the thought processes used to solve multiplication problems Divide whole numbers to 100 000 by single-digit numbers Identify when division could be used in everyday life Verbalise the thought processes used to solve division problems

Write and solve division word problems


225

BLM 83


NA not apparent

Week (Date)

B

beginning

C

consolidating

E

established

Unit

21 Volume and Capacity

22 Exploring Patterns

23 Number Puzzles

24 Mass

25 Environmental Data

26 Adding Decimals

27 Subtracting Decimals

28 Exploring Measurement

29 Reading Maps

30 Making Maps

226

Name: ___________________________________________________________________ Year Level: __________

Term: __________

Year: __________

‘Plain Speak’ Statements Estimate and measure the volumes of a range of 3D objects Choose appropriate measures to determine the capacity of various drink containers Measure the capacity of drink containers to the nearest 5 millilitres Read graduated scales accurately Estimate the volume or capacity of an object using standard units of measurement Identify patterns in numeric problems Continue number patterns Explain number patterns Predict further numbers patterns based on an understanding of how the patterns work See relationships between numbers Correctly use the rules of order of operations (BODMAS) Identify patterns in number problems Use addition, subtraction, multiplication and division to solve problems Use known facts to solve problems Accurately read measurements on kitchen and bathroom scales and spring balances Appropriately choose grams as a unit of measurement for light objects, and kilograms or tonnes for heavier objects Calculate the weight of objects from known measurement Fairly and accurately measure weight to the nearest gram Pose appropriate questions to investigate Represent data using pie (sector) graphs, line graphs, bar (column) graphs and picture graphs Analyse data sets they have collected and present their findings Identify the features of different types of graphs Select the type of graph appropriate to their purpose in presenting the data Read and analyse pie (sector) graphs, line graphs, bar (column) graphs and picture graphs

Add decimal numbers including numbers with zeros Use mental and written methods, and calculators, to add numbers to 999 999.99 Identify when addition of decimal numbers is used in everyday life Verbalise the thought processes used to solve addition problems involving decimals

Subtract decimal numbers including numbers with zeros Use mental and written methods, and calculators, to subtract numbers to 999 999.99 Identify when subtraction of decimal numbers is used in everyday life Verbalise the thought processes used to solve subtraction problems involving decimals

Estimate and calculate length, area and volume Draw plans to a simple scale Work out approximate cost of materials based on the area to be covered Use distance and direction coordinates to read maps and give instructions for journeys Identify the scale used on a map and use this to calculate distance Use maps to plan trips

Draw maps of familiar locations Draw maps according to specific instructions Use coordinates to locate key features on a map Draw maps of familiar locations to scale


BLM 84


NA not apparent

Week (Date)

B

beginning

C

consolidating

E

established

Unit

31 Exploring Chance

32 Mental Computation

33 Multiplication and Division

34 Transformations

35 Symmetry and Tessellations

36 Percentages

37 Adding and Subtracting Fractions

38 Revision

39 Investigating Problems

40 Fermi Problems

Name: ___________________________________________________________________ Year Level: __________

Term: __________

Year: __________

‘Plain Speak’ Statements Identify possible outcomes using the language of chance Find and record all possible outcomes or combinations in simple chance experiments Explain why something is fair or unfair Use known facts to solve problems Use a range of mental strategies to carry out computations Calculate addition, subtraction, multiplication and division mentally Explain the link between multiplication and division Solve multiplication and division Divide whole numbers to 100 000 by single-digit numbers problems Verbalise the thought processes used to solve division problems Use mental and written methods, and calculators, to multiply numbers to 999 999 Verbalise the thought processes used to solve multiplication problems Enlarge and reduce simple pictures Identify what a shape will look like when it is reflected Identify what a shape will look like when it is rotated Explain what movement has occurred when a shape is translated Use mathematical language to explain how shapes have been transformed, i.e. ‘rotated’, ‘reflected’, ‘translated’, ‘enlarged’, ‘reduced’ Identify lines of symmetry in 2D shapes Predict how many lines of symmetry a shape will have based on the number of sides it has Make tessellations using regular and irregular shapes Convert common fractions to decimal fractions and percentages Calculate numeric values in relation to percentages Explain a percentage Identify when percentages are used in everyday life Add and subtract common fractions Simplify fractions Give fractions common denominators Convert mixed numbers to improper fractions Convert improper fractions to mixed numbers Operate successfully with numbers in the range 0.01 to 999 999.99 Calculate area, perimeter, volume, mass and time elapsed Draw 2D shapes accurately and to scale Draw transformed shapes and explore symmetry Draw 3D shapes in 2D space showing what is seen and not seen Explain chance in numerical terms Collect, display and interpret data Identify the information needed to solve problems Write word problems to match equations Choose the appropriate mathematical methods to solve problems Express word problems using mathematical symbols Make reasonable estimates Use a calculator to check estimates and solutions to problems Identify and restate a problem Identify sub-questions that need to be addressed to solve a complex problem Make models to explain and test ideas Make reasonable estimates based on relevant information Make reasonable assumptions based on information Present arguments for why a solution is plausible


227

BLM 85 Unit: _______

Weekly Maths Planner A Week: _______

Term: _______

Date: _______

Year Level: _______

Resources:

Monday

Tuesday

Wednesday

Thursday

Friday

Whole Class Focus

Small Group Focus

Focus Teaching Group

Independent Maths (individual, pair, small group)


228


BLM 86 Unit: _______

Weekly Maths Planner

Week: _______

Term: _______

B Date: _______

Year Level: ________

Resources:

Whole Class Focus (Shared) Learning Experience (activities)

Teaching Focus M T W Th F Small Group Focus Focus Teaching Group Teaching Approach: M (modelled) Approach/Teaching Focus

S (shared) G (guided)

Learning Experience (activities)

Independent Maths (individual, pair, small group) Independent Activities

M S G

M

Focus: Students: M S G

T


W


Th


F

Focus: Students: Whole Class Share Time

Other


229

BLM 87 Unit: _______


Week: _______

Term: _______

C Date: _______

Year Level: _______

Resources:

Whole Class Focus (Shared) Teaching Focus


M T W Th F Small Group Focus (Focus Teaching Group) Teaching Approach – Modelled Shared Guided

M

Teaching Focus: Learning Experience: Students: Teaching Approach – Modelled Shared Guided

T


W


Th


F

Teaching Focus: Learning Experience: Students:



230



231

M S G M S G M S G M S G M S G

Teaching Approach: Focus:




Week: ___________



Resources:

Unit: _____________


Other (reflection/future planning)


Students

Small Group Focus

Teaching Focus

D

Focus Teaching Group


Whole Class Focus (Shared)

BLM 88 Date: ___________

Year Level: ___________


Term: ___________

BLM 89

Term Maths Planner Year Level: __________

Week

232

Unit/Page no.

Term: __________

Year: __________

Major Learning Outcomes


Year: _____________

BLM 90 Term 1

Yearly Maths Planner A Year Level: _____________ Unit

Term 3

Week 1

Week 1

Week 2

Week 2

Week 3

Week 3

Week 4

Week 4

Week 5

Week 5

Week 6

Week 6

Week 7

Week 7

Week 8

Week 8

Week 9

Week 9

Week 10

Week 10

Term 2

Unit

Term 4

Week 1

Week 1

Week 2

Week 2

Week 3

Week 3

Week 4

Week 4

Week 5

Week 5

Week 6

Week 6

Week 7

Week 7

Week 8

Week 8

Week 9

Week 9

Week 10

Week 10

Unit

Unit


233

BLM 91 Unit/Page no.

Year: _____________

Yearly Maths Planner

B Year Level: _____________

Major Learning Outcomes

Term 1 Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10



Term 4 Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9

234


Answers to Student Book Pages Page 5

4

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

| |

|

|

| |

|

|

|

|

|

1 20 483, 64 907, 70 946, 100 314, 204 832, 240 382, 714 003 2 a sixty-four thousand, two hundred and seven b seven hundred and three thousand, nine hundred and ninety-nine c ninety-three thousand, two hundred and seventy-two. 3 a 46 020 b 60 890 c 168 460 d 798 130 4 a 496 000 b 19 000 c 561 000 d 556 000

|

| |

|

|

|

|

|

|

|

Fruit

|

|

|

|

|

|

|

| |

| |

|

Cereal

|

| |

|

|

|

|

|

Toast

|

|

|

|

|

|

|

|

|

|

|

|

| |

|

|

|

|

|

|

|

|

|

|

|

Eggs

|

|

|

|

|

|

|

|

|

|

|

|

|

|

Page 13 1 a 3 p.m. and 5 p.m. (or mid-afternoon) b 15°C c 28°C d 21°C e 3 p.m. and 5 p.m. 25 2 20 15 10

9 a.m.

7 a.m.

5 a.m.

3 a.m.

1 a.m.

9 p.m.

11 p.m.

7 p.m.

5 p.m.

1 p.m.

3 p.m.

5

11 a.m.

Degrees Celsius (°C)

1 Sam: ten thousand, two hundred and fifty; Pedro: thirteen thousand, eight hundred and five; Melanie: twenty thousand, nine hundred and sixty; Janelle: nineteen thousand, nine hundred and sixty; Bashar: nineteen thousand, six hundred and ninety; Georgia: eighteen thousand, three hundred and five; Pat: two thousand, nine hundred and sixty-six; Van: twenty-one thousand and ninety-six. 2 1st Van, 2nd Melanie, 3rd Janelle, 4th Bashar, 5th Georgia, 6th Pedro, 7th Sam, 8th Pat 3 Sam: 103 133; Pedro: 99 578; Melanie: 92 423; Janelle: 93 423; Bashar: 93 693; Georgia: 95 078; Pat: 110 417; Van: 92 287.

9 a.m.

Page 6

Page 15 Page 7 1 a 5 b 6 c 7 d 8 e 7 f 27 g 7 h 7 i 36 j 16 k 7 l 13 m 6 n 9 o 6 p 9 3 a 9 b 7 c 56 d 5 e 12 f 8 g 6 h 3 i 9 j 3 k 9 l 6 4 a 63 Related number facts: 7 × 9 = 63, 63 ÷ 7 = 9, 63 ÷ 9 = 7, 1 of 63 = 9, 7 1 of 63 = 7 9

b 7 Related number facts: 56 ÷ 7 = 8, 7 × 8 = 56, 8 × 7 = 56, 1 of 56 = 8, 7 1 of 56 = 7 8

c 8 Related number facts: 24 ÷ 8 = 3, 8 × 3 = 24, 3 × 8 = 24, 1 of 24 = 8, 1 of 3 8 24 = 3 5 a 42 b 2 c 20 d 9 e 48 f 3 g 27 h 3 i 10 j 7 k 24 l 7 m 45 n 8 o 14 p 5 q 15 r 4 s 45 t 10 u 35 v 7 w 18 x 6

Page 8 1 Brackets of Division Multiplication Addition Subtraction 2 a 22 (5 + 24 – 7) b 21 (6 + 21 – 6) c 65 (56 + 6 + 3) d 29 (11 × 2 + 7) e 34 (3 + 40 – 9) f 36 (7 + 6 + 3 + 20) 3 a 7 b 3 c 64 d 4

Page 9 1 a Rule: × 3 + 1 b Rule: – 3 c Rule: × 2 – 4

Page 10 1a b c d e f g h i j

64, 128, 256, 512, 1024, 2048, 4096 Rule: × 2 80, 85, 75, 80, 70, 75, 65 Rule: – 10 + 5 28, 36, 45, 55, 66, 78, 91 Rule: + 3 + 4 + 5 + 6, etc. 66, 61, 122, 117, 234, 229, 458 Rule: × 2 – 5 62, 56, 28, 22, 11, 5 Rule: – 6 × 1 2 36, 49, 64, 81, 100, 121, 144 Rule: square numbers 243, 729, 2187, 6561, 19683, 59049, 177147 Rule: × 3 14, 42, 41, 123, 122, 366, 365 Rule: × 3 – 1 505, 606, 707, 808, 909, 1010, 1111 Rule: + 101 851, 852, 802, 803, 753, 754, 704 Rule: – 50 + 1

Page 11 1a b 2a 3a b 4a 5a 6a

sixty thousand, nine hundred and eighty-seven five hundred and sixty-seven thousand and three 406 534 b 968 000 843 210, 843 201, 843 120, 843 102, 843 021, 843 012 843 210, 843 201, 843 120, 843 102, 843 021, 843 012 32 668 b 686 430 36 (5 + 40 – 9) b 25 (28 + 9 – 12) 16, 20, 18, 22 Rule: + 4 – 2 b 55, 75, 99, 127 Rule: + 4 + 8 +12 +16 + 20 + 24 + 28

1

–11 –10 –9 –8 –7 –6 –5 – 4 –3 –2 –1

0

1

2

–4 –3 –2 –1

7

8

9

0

1

1 Answers will vary. 2 a Choco Pops b Choco Pops

3

4

5

6

2 a – 1, 0, 1 b 2, 3, 4 c –4, –3, –2 d –10, –9, –8 e –8, –7, –6 f –7, –6, –5 3 a –4, –3, –2, –1, 0, 1, 2, 3, 4, 5 b –154, –153, –152, –151, –150, –149, –148, –147, –146, –145 c –260, –259, –258, –257, –256, –255, –254, –253, –252, –251 4 –10, –6, –4, –3, –1, 0, 1, 6, 7, 10

Page 16 1 Top to bottom: 13, 10, 6, –1, –4, –7 2 Mount Hotham: 11; Mount Buller: 3; Canberra: 11; Melbourne: 14; Falls Creek: 8; Mount Wellington: 2; Ararat: 10; Ballarat: 13; Mount Sterling: 8 3 a Melbourne b Mount Hotham c Hobart d Mount Wellington

Page 17 1 A number less than zero 4 –15, –10, –5, –4, 0, 1, 2, 5 5 a –9, –4, –2, –1, 0, 1 b –8, –6, –2, 2, 6, 8 c 6, 3, –3, –6, –12, –18

Page 18 1

Vertical lines

Horizontal lines

Diagonal lines

Parallel lines

Perpendicular lines

Obtuse angle

Acute angle

30° angle

60° angle

Page 19 1

Right angle

60°

30°

2a

R R R R

A O A A O

O A A O O A A O

OA A O OA A O

R R R R O O

b They total 360°. 3a

OA A O

R R RR AO

A O R R

OA A O

b

O

A

A

A

O A A O

60°

Page 12

2

c

O A R R

A

d

60°

50° 70°

90°

30°

60°

60°

90°

20°

40°

90°

180, 180, 180, 180 Answers to Student Book Pages

235

Page 20

Page 32

1a

b

c

1 a 3:36 b 12:55 c 9:36 d 6:34 e 9:18 f 2:20 g 4:40 h 7:47 2a b c d

d

11

12

1

11

10

2

2a b c d

Has three 60° angles. All sides measure 3 cm. Has six sides each 1.7 cm. All angles are 120°. Has four 90° angles. All sides measure 3 cm. Has two sides of 3 cm and two sides of 2 cm. One angle is 70°. There are no right angles.

3

7

7

6

1a

11

12

b

1

10

2

9

11

c

1 2

9

4

11

4

8 7

number QF627

2

7

6

time 17:10

11

12

11

12

18:35

19:45

6

11

12

1 a 39 654 b 146 447 c 80 180 d 40 334 e 138 592 f 96 541 g 165 039 h 110 440 i 163 719 j 55 343 k 101 557 l 36 747 m 61 247 n 114 556 o 60 643 p 140 140 q 40 027 r 123 551 5 4 7 4 4 0

9 1 1 4 4 3

2 5 9 0 7 9

2 5 3 3 6 2

7 4 6 1 2 4

9 3 9 4 1 5

8 3 5 0 4 7

4 1 4 4 7 8

8 1 4 1 4 1

0 4 0 0 0 6

1 5 3 1 2 0

8 5 3 5 5 6

0 6 4 5 4 4

3 1 1 7 4 3

6 4 2 3 0 3

7 0 3 5 0 4

4 1 5 0 2 7

7 4 5 9 7 0

4 0 1 6 6 9

2 a 4, 6, 29 784, 34 104, 34 709, 35 096, 40 254, 254 781 b 295 035 c 428 738 3 a 50 193 b 27 697 c 27 562 d 133 507 e 71 576 f 128 114 g 62 781 h 69 086 i 91 155 j 34 141 k 109 477 l 100 000

Page 23 1 a 1 463 + 9 300 b 5 820 + 5 207 c 7 014 + 493 d 1 274 + 5 000 e 8 627 + 25 f 9 003 + 0 g 3 009 + 943 h 7 329 + 1 300 3 a 37 b 26 930 c 24 959 (9 003 + 8 627 + 7 329) 1 463 5 207 493 1 274 8 520 4a b c d e + 3 009 _______ 4 472

+ 9 300 _______ 14 507

+ 5 820 _______ 6 313

+ 7 014 _______ 8 288

+ 8 627 _______ 17 147

Page 24 a & b Answers will vary c 4 968, 73 732, 68 594, 20 594, 20 498, 48 574, 13 847, 27 364, 3 347, 29 487, 39 485

Page 25 1 a 45 678, 45 231 b 165 354, 10 098 c 89 065, 59 078 d 78 357, 10 908 (67 449) 2 a 34 987 b 56 982 c 87 003 d 40 982 e 35 467 – 28 745 ________ 6 242

– 34 995 ________ 21 987

– 45 243 ________ 41 760

– 39 987 ________ 995

– 25 489 ________ 9 978

Page 26

Page 27 Pies, 238; Pasties, 232; Pizzas, 148; Cola drinks, 105; Bottles of water, 44; Icy-poles, 122; Chocolate ice-creams, 93; Apples, 93; Chips, 34; Popcorn, 19. 1 a Pies b Popcorn

Page 28 Logged off 9:45 10:30 11:20 12:30 2:30 3:00 3:30 10:00 10:30

Duration of session 40 min 45 min 20 min 70 min 60 min 30 min 30 min 45 min 30 min

Name Luke Ahmed Fiona Hannah Ryan Hannah Luke Tara Tara

20:10

15:50

2

10

6

11

12

11

2

10

7

QF453

Mackay

16:25

19:50

6

11

12

2

10

7

6

4 7

3

4 hrs 20 min 2

11

4

5

1

3 8

9

6

12

9

4 5

8

4

11

1

10

1 hr 10 min 2

7

5

3

5

1

3 8

9

6 12

9

4

1

8

4 7

5

1

10

2

6 12

5

3 hrs 25 min

1 2

9

3 4

8 7

5

6

5

Page 34 1 13:55

11

12

1

10

11 2

9 4

8 7

6

12

1

10 3

2

9

3 4

8 7

5

6

5

2 a For all hours after 12 noon, add 12. 3 a 10:30, 12:10, 1:50, 3:30, 5:10 b My Mother Was a Beauty Queen, Which Witch Is Which? c Which Witch Is Which? d A Tale of Two Teachers, My Mother Was a Beauty Queen

Page 35 1 A number only divisible by itself and one. 2 1 2 3 4 5 6 7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

Page 36

1 a 89 912 b 21 937 2 a $30 797 b 749 406

Logged on 9:05 9:45 11:00 11:20 1:30 2:30 3:00 9:15 10:00

Cairns

1 hr 15 min

1

3 8

3

7

QF629

12

5

9

4

9

6

10 3

7

Canberra

3 4

11 2

8

2

8

1

10

Duration of f light 2 hrs 20 min

1

10

7

9

12

9

5

8

Logged on 11:00 12:00 1:30 2:30 9:00 9:45 11:00 11:15 1:30

Logged off 12:00 12:30 2:30 3:00 9:45 10:30 11:15 12:00 3:30

1 a Tara, 4 hrs 15 min b Ali, 20 min c girls

Page 30 1 a 6:36 b 7:35 c 27 minutes d Spencer Street and Flinders Street, 4 min apart e 10 f 28 min

236

11

3

17:20

Arrival time

4 6

5

6

1 2

7

Page 22

Luke Tara Ali Luke Ryan Ahmed Jodie Tara Ben

3 4

Departure time

8

16:05

2

7

5

10

Sydney

1

8

9

QF447

12

11 10

10

8 5 3 0 6 5

5

6

9

4

8

time 14:50

Brisbane

d

1

3

5

6

12

9

2 a 15:45 b 20:30 c 12:00 d 16:36 3 Flight From: Departure Arrival

QF819

Name

3 4 7

5

10

3

5

6

12

10

3 8

A line that runs at right angles to the horizon. A line that runs parallel to the horizon. A line, other than a side, that connects two vertices of a polygon. Lines that intersect to make right angles. e An angle measuring 90°. An angle greater than 90°. g An angle less than 90°. vertical b parallel c horizontal d diagonal e curved, wavy 90° right b 45° acute c 30° acute d 60° acute e 135° obtuse

3 6 6 1 4 6

2

8

Page 33

7

1 9 1 1 1 1

1

10 9

4 7

12

11

2

8

5

6

1

3

4

8

12

10 9

3 a 50 min b 5:40 c 6:27 d 3:09

Page 21 1a b c d f 2a 3a

11

2 3

5

6

1

9

4

8

12

10

9


Duration of session 60 min 30 min 60 min 30 min 45 min 45 min 15 min 45 min 120 min

1 A whole number that can be divided evenly into another number. 2 a No. A prime number can only be divided by itself and one. b 13, 37, 47, 17, 23, 41 3 b 2, 5, 5 (50); 2, 2, 3, 5 (60); 2, 2, 5, 5 (100) c 96

Page 37 1 A number (or word) that is the same whether read forwards or backwards. 2 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292

Page 38 1 a A number divisible only by itself and one b 3, 17, 23, 37 2 a A number that can be represented by counters in the shape of a square, e.g. 42 = 4 × 4 = 16 b 25, 49, 64, 81, 144 3 a A number that can be represented by Centicubes in the shape of a cube, e.g. 43 = 4 × 4 × 4 = 64 b 8, 27, 64, 125, 1000

4 a A whole number that can be divided evenly into another number. b 36: factors: 1, 2, 3, 4, 6, 9, 12, 36; prime factors: 1, 2, 3; 48: factors: 1, 2, 3, 4, 6, 8, 12, 24, 48; prime factors: 1, 2, 3; 82: factors: 1, 2, 41, 82; prime factors: 1, 2, 41 5 a A number (or word) that is the same whether read forwards or backwards.

Page 39 1 a Dining Room: A: 36 m2, C: $1 080; Kitchen: A: 24 m2, C: $240; Living Room: A: 104 m2, C: $3 120; Hall: A: 48 m2, C: $1 440; Bedroom 3: A: 48 m2, C: $1 440; Bedroom 2: A: 48 m2, C: $1 440; Bathroom: A: 32 m2, C: $640; Bedroom 1: A: 80 m2, C: $2400 b $11 800 2 Patio: A: 32 m2, C: $480

Page 40 1 A Area: 6 cm2, Perimeter: 10 cm; B Area: 22 cm2, Perimeter: 26 cm C Area: 84 cm2, Perimeter: 38 cm D Area: 36 cm2, Perimeter: 26 cm E Area: 18 cm2, Perimeter: 18 cm F Area: 24 cm2, Perimeter: 20 cm

Page 41 1a b 2a b 3a c 4a

The size of a surface or the amount of space within a shape Length × Width The distance around the edges of a 2D shape (Length + Width) × 2, or (Length × 2) + (Width × 2) Area: 144 m2, Perimeter: 54 m b Area: 162 m2, Perimeter: 66 m Area: 144 m2, Perimeter: 66 m d Area: 198 m2, Perimeter: 90 m Shape d b Shapes a and c

six point four three b twenty-five point eight seven thirty point zero four d two point zero eight e eight point six three 63.79, 63.88 b 4.03, 4.12 c 10.47, 10.56 d 0.6, 0.69 e 4.09, 4.18 6.59 e 639 f 7.99 g 8.00

1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47

b

9.95 9.96 9.97 9.98 9.99 10.00 10.01 10.02 10.03 10.04 10.05 10.06 10.07 10.08

c

4 2 25 1 1 14 3 5 , , , 6 2 25 4

4

6

6 A part of a whole number or quantity

Page 47 1a c d e f h 2a 3a 4a c d

34 159, 34 229, 34 299, 34 369, 34 439 b 46 689, 47 589, 48 489, 49 389, 50 289 51 890, 59 890, 67 890, 75 890, 83 890 127 897, 187 897, 247 897, 307 897, 367 897 116 987, 156 987, 196 987, 236 987, 276 987 778 477, 779 177, 779 877, 780 577, 781 277 g 1 110, 1 220, 1 330, 1 440, 1 550 11 200, 12 400, 13 600, 14 800, 16 000 + 800 b + 9000 4 056 b 13 746 c 50 165 3.00, 3.05, 3.10, 3.15, 3.20, 3.25, 3.30 b 3.52, 3.56, 3.60, 3.64, 3.68, 3.72, 3.76 10.58, 10.65, 10.72, 10.79, 10.86, 10.93, 11.00 22.64, 22.72, 22.80, 22.88, 22.96, 23.04, 23.12

Page 49 1 a twenty-four thousand five hundred and ninety-six point seven zero b three hundred thousand and eighty point zero six c four hundred and ten thousand four hundred and sixty point seven three 2 a 155 637.05 b 6 003.8 c 50 417.45 Smallest to biggest: 6 003.8, 50 417.45, 155 637.05 3 a 45.94, 46.03, 46.12, 46.21 Rule: + 0.09 b 1 000.01, 1 000.09, 1 000.17, 1 000.25 Rule: + 0.08 4 a 1 023.45, 23.40, 400 023.45, 22.35 b 1 204.56, 204.51, 400 204.56, 203.46 c 1 540.32, 540.27, 400 540.32, 539.22 d 877 984.65, 876 984.60, 1 276 984.65, 876 983.55

9.91 9.92 9.93 9.94 9.95 9.96 9.97 9.98 9.99 10.00 10.01 10.02 10.03 10.04

d

99.94

e

99.95

99.96

99.97

99.98

99.99 100.00 100.01 100.02 100.03 100.04 100.05 100.06 100.07

Page 50 1 Cone

, Cube

, Square pyramid

, Triangular prism

,

0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05

f

Cylinder

g

100.07 100.08 100.09 101.00 101.01 101.02 101.03 101.04 101.05 101.06 101.07 101.08 101.09 101.10

h

23.90

23.91

23.92

23.93

23.94

23.95

23.96

23.97

23.98

23.99

24.00

24.01

24.02

24.03

Page 44 1

4 a 3 b 1 c 14 d 3 e 1

1 Shopping spree, Bike, Food hamper, CD player, Dinner for two, Zoo entry, Meat tray, Gift voucher, Haircut, CD. 2 34 675.78, 34 675.87, 34 756.78, 34 765.87, 34 766.87, 37 465.87, 37 677.8, 37 678.57

Page 43 a

5.90 5.91 5.92 5.93 5.94 5.95 5.96 5.97 5.98 5.99 6.00 6.01 6.02 6.03

1 2 1.01, 1.10, 10.01, 10.10, 10.11, 100.10, 110.01, 1 000.10 3 a 0.08 m b 0.11 m c 0.04 m

Page 48

Page 42 1a c 2a 3b

Page 46

Fraction

Equivalent fraction shaded

Equation 1 3 1 2 1 4 4 5 3 4 2 7 2 3 3 4 1 2 3 5 6 7

1 3 1 2 1 4 4 5 3 4 2 7 2 3 3 4 1 2 3 5 6 7

2 a 10 , 5 , 1

2

20

6

b 3, 1

= 6 = 12 3

= 12 8

= 10 12

10 2

9 3 c 7, 6, 1 35 30 5

2 Rectangular prism: a 3D shape with 12 edges, 6 faces and 8 corners Triangular pyramid: a 3D shape with 4 triangular faces Sphere: a 3D shape with a curved surface and no edges or corners 3 A shape with three dimensions.

Page 51 1 Cube:

Pyramid

= 16 = = = = = =

4 14 6 9 6 8 6 12 9 15 12 14

2 a Triangular pyramid

Cylinder: Cone b Rectangular prism

c Triangular prism

Page 54 1

2

Page 45 1a d 2 a d

1 2 2 < 3

5 6 6
3

5 6 6 >

b e b e

3 3 , 1, 3, 2, 3, 4 10 2 5 3 4 5

3 4 4

3 4 > 5

c f c f

2 8 < 10

1 3 2
10

Page 55 2 a 144 000 b 1 008 000 4 30 CDs; otherwise Lee gets only 21 or 22 CDs. 5 $1 off the price of a dozen ($4).

Page 56 1 3 2 >

1 a 1 694 784 b 3 121 605 c 9 150 430 d 936 024 e 616 835 f 3 670 225 g 1 099 989 h 6 487 503 2 a 43 960 b 2 025 3 2, 5, 15, 17, 23


237

Page 57

5

1 lion: $22 680; frog: $11 340; bear: $180; owl: $4 140; emu: $1 365; snake: $14 630 2 frog, owl and snake

Page 59 1 a 586 r 1 b 1 130 r 5 c 811 r 2 d 952 r 4 e 406 r 4 f 4 893 g 347 r 1 h 493 r 4 i 497 r 2 j 963 r 4 2 a 15 b 44 r 4 3 ÷ 2 ÷ 8 ÷ 5

Starting number: 21 440 ÷ 7

Finishing number: 134

÷ 9 ÷ 6 ÷ 3 ÷ 4

21 440 ÷ 8 = 2 680 ÷ 4 = 670 ÷ 5 = 134

Input number Output number 56 158 194 296 307 409 34 136 934 1036 125 227 4 098 4200 The rule is... + 102

Input number 4 12 8 10 6 2 9 The rule is... × 9

Output number 36 108 72 90 54 18 81

Page 69 1 a 765 g b 46 kg c 6 kg d 3 g

Page 70 1a b c d e f 2a

Total: 600 g; One apple: approx. 150 g Total: 825 g; One potato; approx. 165 g Total: 480 g; One banana: approx. 80 g Total: 930 g; One orange: approx. 155 g Total: 450 g; One carrot: approx. 150 g Total: 850g; One pear: approx. 170 g 1.1 kg b 1.6 kg c 1.1 kg d 1.6 kg

Page 71

Page 60 1 a 996 r 3 b 772 r 3 c 1 292 d 574 r 4 e 748 606 f 5 726 400 g 1 360 058 h 802 326 2 a 111 636 b 831 r 1

1 a 465 g b 10.5 tonnes c 24 kg d 2 kg 3 Set the scale to zero. Place object in centre of scale. Wait until scale is still. Read weight.

Page 72

Page 61

1 a You use a quarter of the water if a bucket is used. b 300 L 2 a 100 L e

2 a 75 mL, 100 mL, 750 mL, 1.25 L, 1500 mL, 3 L

Having a Shower

Page 62

200 180

1 a Sun: 5 mm, Mon: 32 mm, Tues: 52 mm, Wed: 46 mm, Thurs: 18 mm, Fri: 0 mm, Sat: 28 mm b Tuesday c Friday d 181 mm 2 80

80

80

80

80

80

70

70

70

70

70

70

70

60

60

60

60

60

60

60

50

50

50

50

50

50

50

40

40

40

40

40

40

40

30

30

30

30

30

30

30

20

20

20

20

20

20

20

10

10

10

10

10

10

10

litres of water used

80

160 140 120 100 80 60 40 20 0 1

a 194 mm b 375 mm

Page 63

2

3

4 5 6 7 minutes’ duration

8

9

3 a 220 000 L b 49 000 L c 331 263 L

1 a 1.4 L, 40 mL, 15 mL, 5 mL

Page 75

Page 65

1 a Jets (37.06) b Zhane (123.01 m) 2 a 3.3 m

1

Page 77 1 a 5 835.25 b 212.75 c 2 434.12 d 2 332.54 e 3 250.47 f 4 641 g 7 689.29 h 2400.05, 340.35, 254.05 (2 994.45) i 7 724.89

Each new shape has four more shaded squares.

Page 78

2

1 a 2 365.98 b 1.53 c 2 365.98 d 2 400.05, 1 430.5 (969.55) e 1 970.63 f 1 430.5, 902.04 (528.46) g 1.53 h 395.35

Page 79 1 Sale price: tea towel $8.91, curtain rod $11.62, bath mat $23.66, shirt $24.39, dress $36.91, jeans $34.91, hammer $16.96, saw $17.52, drill $20.92 2 bath mat, jeans, saw and hammer

Each new shape has six more shaded squares.

Page 80 Each new shape has 3 times the number of shaded squares.

Page 81

× ÷

4 – 4 = 0

= = =

64 ÷ 8 = 8

7 + 2 = 9 24 + 20 = 44

18 × 2 = 36

÷ + –

6 + 6 = 12

= = =

3 × 8 = 24

– ÷ ÷

16 – 5 = 11

= = =

× + +

6 – 1 = 5

= = =

42 ÷ 3 = 14

8 – 4 = 4

6 m

Laundry

1

2m

Kitchen

A = 12 m2

2m

Bathroom 2

2m

A = 12 m

2 428 m2 3 104 m2

Study 8 m

A = 64 m2

8 m

Family room

A = 56 m2

×

A = 48 m2

6 m

8 m

Bedroom 2 A = 60 m2

6 m

8 m

8 + 8 = 16

× × +

A = 64 m2

8 × 3 = 24

= = =

64 – 24 = 40

28 m

16 ÷ 2 = 8

Hall

Page 66 1

1 a 11088.28 b 2310.77

8 m

10 m

Bedroom 3 A = 48 m2

6 m

8 m

Bedroom 1

Page 68 A = 64 m2

2 15, 24, 36; Rule: + 3 + 6 + 9 + 12 + 15 3 A sequence of numbers or objects that follows a rule.

238


2m

8 m

8 m

2 a l, o, s, x, z b H, I, O, S, X, Z

Page 82 1

Ceiling Litres Area of paint Kitchen 64 m2 4 Family room 128 m2 8 Bathroom 12 m2 0.75 Bedroom 1 80 m2 5 Bedroom 2 60 m2 3.75 Bedroom 3 48 m2 3 Hall 44 m2 2.75 Total 436 m2 27.25 Room

Inside walls Litres Area of paint 4 × 32 m2 = 128 m2 8 2 × 64 m2 + 2 × 32 m2 = 192 m2 12 2 × 8 m2 + 2 × 24 m2 = 64 m2 4 2 × 32 m2 + 2 × 40 m2 = 144 m2 9 2 × 24 m2 + 2 × 40 m2 = 128 m2 8 2 × 24 m2 + 2 × 32 m2 = 112 m2 7 2 × 88 m2 + 2 × 8 m2 = 192 m2 12 960 m2 60

2 87.25 L

1

BB

A W

P u S hh KK u

aa bb zz yy

Page 99

Page 83 2 1 800 cm3

Page 84 1a d f 2a

Page 98

Flinders Street Station b General Post Office c State Library St. Pauls Cathedral, or Federation Square e Law Courts Melbourne Town Hall G5 b D4 c G2

Page 85

1 a No. of sides 3, No. of lines of symmetry 3 b No. of sides 4, No. of lines of symmetry 4 c No. of sides 5, No. of lines of symmetry 5 d No. of sides 6, No. of lines of symmetry 6 e No. of sides 7, No. of lines of symmetry 7 f No. of sides 8, No. of lines of symmetry 8 g No. of sides 9, No. of lines of symmetry 9 2 Number of lines of symmetry is equal to the number of sides. 3 20

1 a Travel south-west to Geelong (D5) then west to Warrnambool (B5). b Travel north-west to Bendigo (D4), north-east to Echuca (D3) then north-west to Swan Hill (C2). c Travel north-west to Bendigo (D4) then Ouyen (B2). Travel north to Mildura (B1).

Page 100

Page 89

1 A line drawn through the centre of a shape so that each half of the shape is the mirror image of the other. 2a b c d

1 a 3, 2 b 5, 2 c 1, 2 d 2, 5 or 4 or 1

2

✓

✓

✓

Page 101

Page 90 1a

Card

Ace

Red card

Heart

Three

Chance

1 in 13

1 in 2

1 in 4

1 in 13

2 Deal 1: 5, 6, 7, 8; 8 in 25. Deal 2: 3, 4, 5, 6, 7, 8, 9; 14 in 25. Deal 3: none; no chance. 3 a 1 in 42 b 2 in 21 c 1 in 14 4 a No b In four shots, the most goals the player is likely to get is three.

3 a B to C: Translated two spaces to the right, and two spaces down. C to D: Translated one space to the right and one space up. D to E: Translated two spaces up. E to F: Translated two spaces to the right, and two spaces down. b No

Page 91 3 Coin 1 Coin 2 Coin 3 H H H H H T H T T T T T 4 a In six attempts, it is most likely that only one attempt will give desired result. b The likelihood or the chance

Page 102 2 Red: 25 or 1 , 25%; Black: 13 , 13%; White: 41 , 41%; Blue: 16 or 4 , 16%; 100

Page 93

4

100

100

100

25

Green: 4 or 1 , 4%; Yellow: 1 , 1%; Total: 100 100 25 100

1 a 56, 57, 58, 59

Page 94

Page 103

1 24 cm by 36 cm 2 4 weeks 5 Examples: 56, 60, 72 6 93 people

a

Page 96

1

b

1

d

Shade 2 50 Unshaded is ___% 50 Shaded is ___%

1


1 a 3114 b 32 r 4 c 7 000 d 3 025 3 a 360 000 b $303 750

Page 97 1

Shape by 90°

Rotation by 180°

by 270°

c


1

Shade 5 80 20 Unshaded is ___% Shaded is ___%


239

e

3

Shade 4 75 25 Shaded is ___% Unshaded is ___%

f

1

Shade 20 5 95 Shaded is ___% Unshaded is ___%

Page 108 1 2 3 4 6

564 098.36, 389 574.55, 109 983.45, 24 536.90, 2 543.56, 354.46 b 389 574.55, 109 983.45, 24 536.90 c 109 983.45, 2 543.56, 354.46 b 109 983.45, 24 536.90 c 564 098.36, 389 574.55 a 199 752, 29, 979 r 2, 3 653 5 $9.15 a 44 b 506

Page 109 Page 104 2 Cost without discount Final cost with discount Saving in dollars

Shopping List A $349 $222.50 $126.50

Shopping List B $250 $152 $98

Shopping List C $209 $134.50 $74.50

9

1 a 4, b 4, c 2, d 1 5

3

2

7

8 2 3 5 1 5 8 3 a 1 , b 2 , c 2 , d 4 4 e 4 13 , f 4 1 , g 4 1 , h 7 1 , i 7 5 6 12 15 15 20 12 15 3 12

= 1

= 1

+

= 1

+

+

1 2 3 + 3 = 1

7

6

5

60°

60°

2nd table: Answers will vary.

d

60°

60° 60°

Square

Parallelogram

60°

Equilateral triangle

e

= 1

= 1

2 1 3 + 3 = 1

= 2

1 + 1 = 2

+

= 3

3 3 2 + 2 = 3

Pentagon 3

1 A proportion of 100. 2a

Draw in lines of symmetry

Reflect

Rotate 90º

Page 111

4 2 3 + 3 = 2

1 a 1 in 3 b 5 in 12 c 1 in 4 2a b

Page 107

1

2

6

b 60%

2

3

1

3 5

4

4 5

6

Page 113 3 a $5 b 50 c $16 5 a 3, b 6, c 1, d 2 5 7 2 3 3 2 2 6 a 3 , b5 , c1 , d1 7 7 5 3 16 7 a 1 5 , b 21, c 1 1 , d 1 12 6 12 12 8 a Change all fractions to the lowest common denominator, then add the numerators. Simplify if necessary. b Change all fractions to the lowest common denominator, then subtract the numerators. Simplify if necessary.

240

c

60°

Equilateral triangle

1 1 2 + 2 = 1

1 1 2 + 2 = 1

= 2

b 60°

1 1 2 + 2 = 1

+

+

6

3 4

8

1a

Page 106

+

9

5

Page 110

2 a 31, b 31, c 12, d 41

+

3 4

8

4 250 m 5 Shimmer; Uses 1 kg per 2 000 L. Is cheaper than True Blue which uses 1 kg per 1500 L.

Page 105 5

1 a 100 000, 28 000 b 2 000 m3 2 172 m 12 12 11 1 3 a 10 11 1 2 b 9 hrs 35 min. 10 2


1 a $46.22 b $32.50 c Gained $10 d 24

Rotate 180°

Nelson Maths (Books 1–7) provides creative, stimulating and open-ended tasks allowing children to work at a learning level appropriate to their needs. This series supports the whole class — small group — whole class teaching approach.


Nelson

Maths

Each Teacher’s Resource Book contains:

Nelson

more than 520 activities over 40 weekly units of work ‘Plain Speak’ Statements (teaching focus), Resources and Maths Talk 80 unit and resource blackline masters 11 assessment and planning blackline masters ideas for setting up an effective mathematics classroom, parent participation, five-minute maths activities, and assessment and monitoring.

Maths J ENNY F EELY

Book

© Nelson Austr alia Pty Ltd, 2004. Jay Dale and Jenny Feely Minimum syst em requirem ents Microsof t® Windows ® 98 or later; MacOS 8.5–9.2. and OSX Adobe® Acro bat® Reader (supplied on CD-ROM) is required to view documents.

JENNY FEELY

N

son Mel aths

Installation instructions PC: Insert CDROM into CD drive for auto matic play, or navigate to CD-ROM with Windows® Explorer and double-click on Title. Mac: Insert CD-ROM into CD drive. Doub le-click on the Title icon, then double-click on Title.

If you experienc e difficultie s using this email Nelson product, Thomson Lear ning Australi helpdesk@th a on omsonlearnin g.com.au

Book

M RO ins

Planning Assessme and nt Tool + TRB

e id

CD -

The complete Teacher’s Resource Book is on CD-ROM and features time-saving and easy-to-use interactive planning and assessment software. The CD-ROM also features an Enabler function which allows teachers to plan across grade levels, and a Correlation Chart linking units in Nelson Maths to individual Education Department syllabuses.

has taught at all levels of the primary school,

with many years’ experience as a Curriculum Coordinator and Early Years Coordinator. She has written various resources for a number of curriculum areas, and has been published nationally and internationally. In Nelson Maths, Jenny has created a wealth of practical, enjoyable classroom activities based on her extensive

S ixt

of h Sc Ye ho a ol r

classroom experience.

Nelson Maths Teacher's Resource: Sixth year of school

Nelson Maths Teacher's Resource: Fifth year of school

Learning through art: a resource book for primary school teachers

The Teachers Calendar, School Year 2010-2011 (Teacher's Calendar)

Listening (Resource Books for Teachers)

Conversation (Resource Books for Teachers)

Homework (Resource Books for Teachers)

Letters (Resource Books for Teachers)

Pronunciation (Resource Books for Teachers)

Newspapers (Resource Books for Teachers)

Science for Primary School Teachers

Science for Primary School Teachers

Interactive Maths Teaching in the Primary School

Elementary Communication Games (Teachers Resource Materials)

Grammar Dictation (Resource Books for Teachers Series)

RBT: Writing (Resource Books for Teachers)

Cultural Awareness (Resource Books for Teachers)

Primary Teachers' Resource (Junior English Timesavers)

Games for Children (Resource Books for Teachers)

Sharing Maths Cultures: IMPACT: Inventing Maths For Parents And Children And Teachers

Nelson Textbook of Pediatrics

Auguste Rodin: The Burghers of Calais : A Resource for Teachers

Active Maths - Problem Solving Maths for 10 - 12 Year Old Students

Questions Dictionary of Maths

Auguste Rodin: The Burghers of Calais : A Resource for Teachers

Foundation Maths

The Teacher's Calendar School Year 2006-2007

AS Maths

Nelson Rodney

Nelson observed

Losing Nelson

Nelson Maths Teacher's Resource: Sixth year of school

Nelson Maths Teacher's Resource: Fifth year of school

Learning through art: a resource book for primary school teachers

The Teachers Calendar, School Year 2010-2011 (Teacher's Calendar)

Listening (Resource Books for Teachers)

Conversation (Resource Books for Teachers)

Homework (Resource Books for Teachers)

Letters (Resource Books for Teachers)

Pronunciation (Resource Books for Teachers)

Newspapers (Resource Books for Teachers)

Science for Primary School Teachers

Science for Primary School Teachers

Interactive Maths Teaching in the Primary School

Elementary Communication Games (Teachers Resource Materials)

Grammar Dictation (Resource Books for Teachers Series)

RBT: Writing (Resource Books for Teachers)

Cultural Awareness (Resource Books for Teachers)

Primary Teachers' Resource (Junior English Timesavers)

Games for Children (Resource Books for Teachers)

Sharing Maths Cultures: IMPACT: Inventing Maths For Parents And Children And Teachers

Nelson Textbook of Pediatrics

Auguste Rodin: The Burghers of Calais : A Resource for Teachers

Active Maths - Problem Solving Maths for 10 - 12 Year Old Students

Questions Dictionary of Maths

Auguste Rodin: The Burghers of Calais : A Resource for Teachers

Foundation Maths

The Teacher's Calendar School Year 2006-2007

AS Maths

Nelson Rodney

Nelson observed

Losing Nelson

Recommend Documents