targeting maths for victoria year4 - wikispacestg+yr+4.pdftargeting maths for victoria year 4...

Robyn Hurley

Teaching Guide

Year4Year4

PASCALPRESS

Targeting Maths for VictoriaTargeting Maths for Victoria

Contents

Introduction Planning and Assessment Records

Term 1

Term 2 Term 3 Term 4

Student Book Answers BLMs Term Planners

Robyn Hurley

Teaching Guide

Year4Year4

PASCALPRESS

Targeting Maths for VictoriaTargeting Maths for Victoria

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Targeting Maths for Victoria Year 4 Teaching GuideWritten by Robyn HurleyCopyright © Blake Publishing 2006

ISBN: 1-74020-172-8ISBN: 978-1-74020-172-8

Published by Pascal PressPO Box 250Glebe NSW 2037(02) 8585 4044www.pascalpress.com.au

Publisher: Katy PikeManaging Editor: Garda TurnerSeries editor: Amanda Santamaria

Designed and typeset by The Modern Art Production GroupCover illustration by Nahum ZierschPrinted by Green Giant Press

iii

About the program iv

Introduction v

Using the 4-page Teaching Guide unit vi

Year Planners – Scope and Sequence viii

Outcomes xii

Assessment Record Sheets xiv

Topic Student pages

Term 1Numbers (2 – 5) 2

Addition (6 – 9) 6

Subtraction (10 – 13) 10

Fractions and Decimals (14 – 17) 14

Patterns (20 – 23) 18

Length (24 – 26) 22

Calendar and Time (37 – 29) 26

3D Objects (30 – 33) 30

Data and Chance (34 – 37) 34

Term 2Four-digit Numbers (40 – 44) 38

Multiplication (46 – 49) 42

Division (50 – 53) 46

Money (54 – 57) 50

Decimals (58 – 60) 54

Patterns (61 – 63) 58

Volume and Capacity (64 – 66) 62

2D Space (67 – 69) 66

Position (70 – 72) 70

Chance and Data (73 – 75) 74

Topic Student pages

Term 3Numbers to 9 999 (78 – 80) 78

Addition (81 – 83) 82

Multiplication (84 – 87) 86

Division (88 – 91) 90

Fractions and Decimals (92 – 95) 94

Money (69 – 98) 98

Patterns (99 – 101) 102

Mass and Time (102 – 105) 106

2D Space (106 – 109) 110

Chance and Data (110 – 113) 114

Term 4Numbers to 9 999 (116 – 118) 118

Multiplication and Division (119 – 123) 122

Subtraction (124 – 127) 126

Addition and Subtraction (128 – 131) 130

Fractions (132 – 134) 134

Special Number Patterns (135 – 137) 138

Area and Time (138 – 141) 142

Angles (142 – 144) 146

Position (145 – 147) 150

Chance (148 – 149) 154

Student Book Answers 158

Targeting Maths Teaching Guide Year 4

Contents

iv Targeting Maths Teaching Guide Year 4

In creating the Targeting Maths scheme, we set out to do three things. 1 Provide a resource that is completely VELS compliant and that enables

teachers to fully implement the CSF II syllabus.2 Create child-friendly workbooks that are exciting and motivational for all

children, whatever their abilities.3 Provide teachers with a program that is easy-to-use, thorough in its coverage

and comprehensive in the extra resources that it provides.

A program that is truly enjoyable for all.

Using the Targeting Maths program for Years 3-6

Topic-based term programsThe student books from Year 3 to Year 6 are laid out as four terms of topic-based units of work. Each unit is 3 or 4 pages long. Grouping topics togetherallows the class to work on a topic solidly, giving better continuity. It is alsoeasier for the teacher to individualise programs to suit the needs of students.Having clearly defined terms of work makes it easier to assess the progress ofstudents.

The contents pages in the student books clearly show the 4 terms ofwork. The topics are in bold. Many teachers told us they wanted topicsto be easy to find, so they could alter the program to suit their needs.

Features of the student book• Topic-based units of work• Easy to follow instructions• Exciting, colourful pages and creative activities that appeal to all

ability levels • Dictionary of mathematical terms in each student book• Problem solving activities• Easy to achieve measurement activities• Regular challenging extension activities

Maths Lab CD-Rom — more than 20 motivating maths games and activities toreinforce essential maths concepts. Lab Icons indicate which game will helpstudents understand the concept being taught.

The Targeting Maths for Victoria Planning CD-ROM contains: • The complete Teaching Guide to make programming easier.• Additional Blackline Masters, 44 in all.• Student book answers in an easy-to-print format.

The Targeting Maths program

vTargeting Maths Teaching Guide Year 4

Student book units of workThe focus page Each unit begins with a focus page. The large focus picture grabs children'sattention with a high-interest or real-life situation. • Focus pages are good for all ability levels as they include open-ended

questions and active participation. Even the weakest student can performthe task because the visual image is so helpful.

• Focus pages are also useful for revision. Return to the page and use it formental warm-ups before a lesson.

Photos • Photos of real things are an exciting feature of the scheme and

serve to connect maths to real life.

Outcomes • The outcome number and the relevant skills and indicators are

written in full at the base of each page.

Mathematical language • Information notes reinforce mathematical language and

important facts.

Problem solving • Problem solving strategies such as looking for patterns appear

regularly. The other strategies covered include drawing a diagram, trial and error and working backwards.

Teaching Guide unitsEach unit of work in the student book is matched by a 4-page TeachingGuide unit. The teaching resources include:- • Syllabus outcomes, skills and indicators clearly stated for each unit• Teach and discuss section introduces each topic with a class discussion• Teaching notes for the other pages in the unit• Oral and mental activities — mental strategies give students a sound

base for their problem solving• Activity bank of extra hands-on and group activities• List of easily located resources needed for the unit • Two photocopiable activity cards for individual, pairs or group work —

especially useful for extension or fast-finishers• An assessment blackline master at the end of each unit.Every unit is cross-referenced to the Targeting Maths Blackline Master seriesfor all the additional materials you may need for consolidation, extension orextra assessment.

Assessment• Revision assessment page at the end of every unit of the Teaching Guide.• Term assessments in the student book.

The teaching guide is broken into units of work. Each unit is laid out in the sameformat for ease of use and is directly linked to 3 – 5 pages of the student book. Theteaching resources provided, as part of each unit, include teaching notes, oral, mentaland hands-on activities, two activity cards and an assessment blackline master.The sequence of units provides a guide to the order of presentation. This follows thesame order as suggested in the year and term planners. However, this is flexible andteachers can choose their own progression through the course.

vi Targeting Maths Teaching Guide Year 4

Using the 4-page teaching guide unit

The large illustration on the focuspage is the basis for a classdiscussion of the topic.

Outcomes and Standards covered inthis unit.

The key words that students need tounderstand.

A list of all extra materials used inany of the activities.

Additional work sheets in TargetingMaths blackline master books.

Answers to the assessment page inthe Teaching Guide.

Relevant Student Book pages.Teaching notes for the focuspage and other pages in theStudent Book.

viiTargeting Maths Teaching Guide Year 4

The two Activity Cards can be used asreinforcement; for fast-finishers; forhomework or for fun.

Activity Cards are designed for individuals,pairs or small groups. This information isclearly marked on each card.

Mental and oral strategies that can be used tointroduce the lesson, or as mental warm-ups thatreinforce previous learning and basic facts.

The Activity Bank provides a range of practicalactivities for the unit that present the mathematicalcontent in a variety of ways. Changing the presentationof a topic can support students with different learningstyles or who are struggling with the concept.

The Assessment page can be used toassess students’ understanding of atopic and to determine areas whichneed reinforcement.

viii Targeting Maths Teaching Guide Year 4

Year Planner — Term 1

Number pp 2–5Bridging 1 000Numbers on an abacusThousandsNumbers to 9 999

Bingo; Abacus shop; Find me; Making a poster;Smallest and largest; Looking at numbers indistances

Counting in hundreds;Writing numbers

Large abacus, MAB blocks,photocopies of abacus,calculators, magazines

Teaching Focus (student pages) Supporting Activities from Teaching Guide Mental and OralStrategies Resources

Addition pp 6–9AdditionAddition strategiesAddition using a number lineAddition with trading

MAB maths; Number lines; Columns, rows anddiagonals; Algorithms; Number grids;Numeral arrangements

Quick to 20; A gameof ‘Be the teacher’

Calculators; MAB blocks

Subtraction pp 10–13Two-digit subtractionSubtraction strategiesSubtraction on a number lineThree-digit subtraction

Secret numbers; Abacus numbers; Subtraction sign;Using our algorithms; Finding the differencebetween numbers; Subtraction using money

Two missing signs;Subtraction stories

Dice for each child,envelope, art paper,class abacus

Fractions and Decimals pp 14–17Animal fractionsNaming fractionsHundredthsAdding and subtracting decimals

Everyday fractions; Pairing numbers;Fraction words; Picture fractions;Making groups of numbers;Adding money

Which is more?;Tables practice

Cardboard, magazines,MAB ones, counters

Patterns pp 18–23Tables revision 1–6Tables revisionPatterns on a hundred squareChanging numbersCalculator patternsPatterns with one

Number in, number out; Y patterns; Find thepattern; Making patterns; Money patterns;Thinking game

Number patterns;Climbing ladders

Class copies of hundredsquares, calculators,1 cm grid paper, classcopies of Australiancoins BLM, counters

Length pp 24–26Lengthmm, cm, mPerimeter

Long jump; Measuring devices; Different shapes;Longest letter; Creating a room layout

Different names;Perimeter game

Trundle wheels, tapemeasures, calipers, string,A4 paper, ruler markedin mm, scissors

Calendar and Time pp 27–29CalendarSecondsComparing time

Counting seconds; Abbreviations; Making a clock;Reading a calendar; Estimating the length ofeveryday events; Sorting race results

Time facts;Months

Large class calendar,classroom calendars,popsticks, classroomanalogue and digitalclocks, clocks and watcheswith second hands,stopwatches, paper plates,matchsticks, pipe cleaners

3D Objects pp 30–33Pyramids3D objects3D drawingNets

Net patterns; Cross-sections; Real life 3D objects;Labeling objects; Net working; Drawing 3D objectsand their nets

Guess the shape;3D vocabulary

Models of prisms andpyramids, cones, spheres,cylinders, sharp pencils,1 cm square dot paper,isometric dot paper,textas, plasticine,cardboard, glue, ruler,blank cards, oldmagazines, oldphotographs,greeting cards

Data and Chance pp 34–37Bar graphA surveyChance experiment

Graphing an experiment; Hand spans; Hand span bar graph; Dice predictions; Year 2 picture graph; Using spinners to work out chance

Sometimes, always,never; Subtractionpractice – to 20

1 cm grid paper, dice,old magazines, stickers,cardboard

ixTargeting Maths Teaching Guide Year 4

Four-digit Numbers pp 40–44Four-digit numbersUsing numeral expandersPlace valueOrdinal numbersRoman numerals

Numeral expanders; Guessing game; Marathonnames; Place value Bingo; Choosing cards game;Using four digits in relation to dates

Counting in 10s and100s; Expanded notation

Large class numeralexpander, individualnumeral expanders, blank cards

Multiplication pp 45–49Tables revisionMultiplication in the warehouseDoubling strategyFactors and multiplesMultiple algorithm

Beating time; Shop orders; Factor trees;Problem numbers; Multiplication wheel;Moving numbers

Double quantities;Multiple clapping

Squared paper (5 mm x 5 mm)

Division pp 50–53Division in the cake shopHow many?RemaindersDivision and multiplication

String experiment; Please explain; Problems;Remainder game; Division circles; Peanut Huntusing different operations

Tables; Game ofguessing division rule

Counters, centicubes,string, class die,calculators

Money pp 54–57Spending moneyCosts and changeNotes and coinsProblem solving

Ways of writing money; Research; Shopping;Sorting coins; Graphing use of pocket money

Money chant;Doubling money

Australian play money,real coins and notes,catalogues, oldmagazines, scissors, glue,cardboard, calculators

Decimals pp 58–60TenthsWriting tenthsTenths and hundredths

Numeral expanders; Calculation; Groups of 10;Matching circles; Decimal towers; Using the < and > symbols

Tenths practice; Readingand writing decimals

Interlocking blocks, small hundreds squares,calculators, class numeralexpanders, MABs, blank cards

Patterns pp 61–63Patterns with 10Two-step rulesAddition and multiplication

2-step patterns; Patterns in life; Associativepatterns; Tables competition week; Calculator patterns; Triangle patterns

Quick mentals; Tables practice

Calculators, oldmagazines, newspapers,distinction award

Volume and Capacity pp 64–66CapacityMillilitresMeasuring volume

The first cup; Capacity collection; More capacity;Looking at litres; Finding capacities; Finding thevolume of different shapes

Capacity questions;Addition practice

Large clear plastic bottle,100 ml measure,permanent marking pen,ice-cream container andlarger bowl, 3 objects thatfit in ice-cream containere.g. a stone, clearcontainer, medicine glass,standard 250 ml cup,interlocking cubes

2D Space pp 67–69Flip, slide, turnLines and shapes2D shapes

2D patterns; Parallel and perpendicular lines; Shape word beginnings; Shape facts; Shape patterns

Shape guessing; Time revision

Transparency for OHP,pattern block, centimetregrid paper, 2D shapes,dictionaries, scissors

Position pp 70–72PositionCompass pointsGrids

Compass findings; Grids; Atlas; Map of the school;Mapping activity

Compass positions;Length revision

Magnetic compass,centimetre grid paper,atlases, school maps with grid lines

Chance and Data pp 73–75 OutcomesLanguage of chanceTravel graph

Bar graphs; Lucky book; Spinners; Chance vocabulary; Heads and Tails game; Possibility activity

Language of chance;Quick addition

Cardboard, BLMs ofhexagon spinners, librarybooks, coins — 5c, 10c,and 20c



x Targeting Maths Teaching Guide Year 4


Numbers to 9 999 pp 78–80Writing four-digit numbersLess than and more thanRounding thousands

Eliminating numbers; Guessing numbers; Abacus and calculator; Listening carefully; Calculator challenge; Working backwards

Less than or greaterthan; Ascending order

Class abacus, calculators

Addition pp 81–83Addition with trading Addition algorithmEstimation with addition

Refocusing; Grids; Problems; Algorithms; 3-digit dice; Star pairs

Estimating numbers;Mental problems

Calculators, class additiongrids, square grid paper,class grid

Multiplication pp 84–87FactorsMultiplication of tensMultiplying two-digit numbersSquare numbers

Showing factors; Factor competition; Writing problems; Square numbers; Multiplying numbers; Odd numbers and square numbers

Patterns; Square numbers

Calculators, MAB blocks,interlocking blocks, smallhundreds squares, scissors,glue, numeral cards 1-9

Division pp 88–91Division algorithmsEstimationDivision with remaindersTwo-digit division

Algorithms; Real life remainders; Missing digits;Game; Finding division facts; Pathways

Remainders; Ways of saying division

MAB blocks, algorithmphotocopies, calculators

Fractions and Decimals pp 92–95DenominatorsMixed fractionsEquivalent fractionsRounding

Prices; Equivalent shapes; Number line; Calculator check; Rounding prices; Fraction pattern

Denominators; Rounding

Cardboard 2D shapes,calculators, old magazinesand catalogues, glue,scissors

Money pp 96–98Values of notes and coinsEquivalent coinsSpending money

Coin combination; Dollar combinations; More spending money; New money; Rounding game; Rounding prices

Rounding money; Whole number rounding

Australian play money,real coins and notes, dice,calculators, glue, scissors

Patterns pp 99–101Related numbersMissing valuesEqual terms

Multiplication practice; Pattern display; Star numbers; True statements; Related numbers; Find the pattern

Completing sequences; Is equal to, is not equal to

BLM multiplication circles,blank cards

Mass/Time pp 102–105Mass at the greengrocerGrams and kilogramsUsing scalesCalendar

Guessing weights; Ordering mass; Bar graphs;Research; Mass in grams; Leap year land

Grams and kilograms;Time

Balance scales, dialscales, objects of varyinggram mass, largecalendar, 1 cm grid paper,gram labels from jars andboxes, scissors, glue

2D Space pp 106–109SymmetryAxis of symmetryTessellating shapesMaking a shape

Tessellations; Tessellating shape; Symmetricalnames; Pattern blocks; Symmetrical pictures;Drawing tessellating shapes

Revision ofmeasurement; Symmetry search

Mirrors, 4 cm squares ofcardboard, scissors, stickytape, magazines, scrapdress materials, M.C.Escher references, patternblocks, grid paper

Chance/Data pp 110–113Different paths SurveyMystery graphInterpreting data

Class survey; Different paths; Group survey; Group graph; Shopping; Mystery graph

Multiplicationcompetition; Place value revision

Coloured pencils, clip boards


xiTargeting Maths Teaching Guide Year 4

Numbers to 9 999 pp 116–118Four-digit numbers in wordsPlace value with four-digit numbersPosition on a number line

Four-digit number research; Numerical order;Number line; Card numbers; Distance on numberline; Choosing numbers

Spelling number words;Writing four-digitnumbers

Newspapers, magazines,old telephone books,blank cards, calculators



Multiplication and Divisionpp 119–123Prime numbersPrimes and compositesExtended multiplicationEstimation with divisionProblem solving

Calculator race; Number names; Problems; Prime game; Multiple colouring in game; Making multiplication algorithms

Composite or prime;Multiplication anddivision link

Calculators, dice, spinners,coloured pencils

Subtraction pp 124–127Four-digit subtractionTrading tensMore subtraction with tradingProblem solving using subtraction

Car prices; Real-life subtraction; Real-life continued; Cross numbers; Trading subtraction; Subtraction practice

Quick response; Linkingaddition and subtraction

Calculators, 1 cm gridpaper, MAB blocks,magazines, catalogues,newspapers

Addition and Subtractionpp 128–131Addition and subtractionPatterns in addition and subtractionEstimation and problem solvingMoney – addition and subtraction

Circles; Problem solving; Distances; Subtraction check; Garage sale; Number clowns

+ and –; Calculator Calculators, preparedaddition and subtractioncircles, blank cards, metre ruler

Fractions pp 132–134Add and subtract fractionsWorking with fractionsAncient Egyptian numbers

Collage; Toothpick fractions; Class charts; Shading fractions; Other numbers; Fraction survey; Fraction to fraction

Fractions; Multiplicationand division practice

Calculator, old magazinesand newspapers,toothpicks, small 100squares, chart paper

Special Number Patternspp 135–137Square and triangular numbersTriangular numbersTables patterns

Triangular numbers; Calculator; Circle patterns;Tables game; Triangular and square numbers; Finding numbers

Square numbers; Speed tests

Counters, rulers,calculators, circlepatterns, spinners

Area and Time pp 138–141Garden areaArea and perimeterSquare metresTimetable

Estimating areas; Favourite day timetable; Thesquare metre; Time stories; Enlarging area

Length measurements;Time

Centimetre grid paper, oldnewspapers; cloth; stickytape; metre measures,clock face, BLM of digitaland analogue clocks

Angles pp 142–144 Angle typesAcute, right, obtuseVertex and arms

Clockface angles; Angle tester; Drawing angles;Poster; Triangles in a dodecagon; Angles in 2D shapes

Time revision; 2D shape revision

2D shapes; BLM ofanalogue clocks, cardboardstrips and fasteners,newspapers, magazines,art books, cardboard

Position pp 145–147Map readingFollow the pathVenn diagrams

Locating objects; Book of mazes; Plotting game; Playground maze; Plot the shape; Fun for year four

Classroom “I spy”;Position words

1 cm grid paper,compasses, A4 paper,sports equipment, boxes

Chance pp 148–149Predicting outcomesCertainty of events

Increasing chances; Line predictions; Organisingoutcomes; Improve your chances; Counters;Predictions

Place value revision;Money revision

Coins (real or play),coloured pencils, container,bag, counters, dice

xii Targeting Maths Teaching Guide Year 4

Outcomes

Outcome Pages in student book

NUMBERNumbers, counting and numeration

3.1 Recognise the structure of whole numbers up to 5 digits, including place value. 2, 4, 5, 40, 41, 42, 43, 78, 79, 80, 116, 117, 118, 119, 130

3.2 Skip-count by numbers of increasing size. 2, 3, 6, 81

3.3 Represent, find, compare and order fractional parts of objects and collections of objects. 6, 14, 15, 92, 96, 94

3.4 Use decimal notation to represent and compare simple decimal fractions including those resulting from calculator computations. 16, 58, 59, 60, 65, 133

Mental computation and estimation

3.1 Recall or mentally determine basic multiplication and division facts. 8, 18, 45, 50, 51, 52, 53, 84, 85, 87, 88, 89

3.2 Use place value ideas and the properties of numbers and operations to assist mental computation. 7, 8, 9, 11, 47, 48, 53, 82, 85, 89, 129, 131,

3.3 Make estimates to check the reasonableness of the results of written computation and calculator use. 56, 57, 83, 95, 98, 121, 122, 130

Computation and applying number

3.1 Use knowledge of place value to solve and record solutions to addition, subtraction, multiplication and division problems. 10, 13, 81

3.2 Select the appropriate operations and computation methods to solve problems involving whole numbers and money. 12, 46, 49, 54, 55, 57, 83, 86, 90, 91, 96, 97, 98, 123, 124,

125, 126, 127, 128

3.3 State equivalence statements and addition and subtraction facts involving simple common fractions and carry out calculations involving tenths and hundredths. 13, 17, 61, 92, 94, 131, 132, 133

Number patterns and relationships

3.1 Use rules involving addition, subtraction and multiplication to devise, describe, extend and test number patterns. 10, 20, 21, 22, 23, 52, 61, 62, 86, 100, 101, 129, 135, 136

3.2 Detect similarities and differences in the nature of the operations of addition, subtraction and multiplication. 19, 63, 99, 100, 101, 120

3.3 Construct and complete simple statements of equality involving whole numbers and fractions. 11, 94, 100, 118

SPACEShape and space

3.1 Recognise, describe and represent straight, curved, diagonal, horizontal and vertical lines, and angles as rotations of lines. 31, 32, 68, 69

3.2 Use simple conventional spatial language when describing shapes, parts of shapes, objects, parts of objects and simple cross-sections. 30, 31, 69, 106, 143, 144

3.3 Explain and compare the spatial properties of shapes and objects. 30, 69

3.4 Visualise and describe some of 'what is not seen' of simple objects. 30, 31

3.5 Interpret, recognise and name three-dimensional objects from drawings and photographs and make recognisable models and sketches of simple shapes and objects. 30, 31, 32, 33

3.6 Copy and create simple patterns involving translating, rotating and reflecting multiple copies of a shape and informally describe the transformations used. 108, 109

3.7 Identify symmetry in regular two-dimensional shapes. 106, 107

Location

3.1 Use and understand conventional location language to follow and give directions and describe position. 70, 72, 146

3.2 Visualise, find and compare alternative paths on simple maps, grids and mazes. 70, 110

3.3 Interpret and describe location and direction using grid references and cardinal compass points. 71, 72, 145

3.4 Interpret and clearly record features when reading and making formal maps and plans of familiar environments. 145


Outcomes

Outcome Pages in student book

xiii

MEASUREMENTMeasuring and estimating

3.1 Make increasingly accurate estimates of measurements using informal units and standard units. 24, 64, 66, 140

3.2 Measure and compare using appropriate informal units. 26, 66, 138, 139

3.3 Estimate and accurately measure length, mass, volume and temperature using formal units and standard units. 24, 25, 65, 68, 102, 103, 104, 140

3.4 Demonstrate understanding of the concept of angle. 142, 143, 144

3.5 Use appropriate instruments to measure physical quantities. 25, 65, 66, 104

Time

3.1 Estimate short and long periods of time, describe duration of time, and make and use timetables, schedules and calendars. 27, 29, 105, 141

3.2 Tell the time using digital and analogue clocks. 28, 29, 141

Using relationships

3.1 Describe the relationship between attributes. 104

CHANCE AND DATAChance

3.1 Identify and record outcomes from simple chance experiments. 36, 73, 74, 148

3.2 Compare and order the likelihood of outcomes of simple chance experiments and of everyday events, and choose appropriate methods for random selection. 37, 149

Posing questions and collecting data

3.1 Identify information required to answer questions or test conjectures, refining the questions where necessary. 111, 112

3.2 Determine appropriate procedures to collect information relevant to questions and conjectures of interest. 36

3.3 Modify the method of data collection and classification to refine a question or investigate a further question. 112

Summarising and presenting data

3.1 Organise and summarise category and whole number data. 34, 35, 36

3.2 Use diagrams and two-way tables to summarise and display discrete data. 35, 36, 147

3.3 Use graphical methods involving scale to display discrete and continuous data. 34, 111, 113

Interpreting data

3.1 Extract specific information from data summarised in diagrams and tables. 57, 75, 112, 113, 147

3.2 Describe and interpret data displayed in simple scaled graphs. 36, 75, 111

REASONING AND STRATEGIESMathematical reasoning

3.1 Make and test simple conjectures. 20, 44, 67, 75, 130, 134, 139, 148

3.2 Make judgments about the accuracy of reasoning and results. 12, 36, 53, 66, 100, 110, 149

Strategies for investigation

3.1 Generate mathematical questions from presented data and from familiar contexts. 81, 101, 131, 134

3.2 Clarify the essential nature of a task or problem and identify key information infamiliar situations. 13, 62, 139

3.3 Use familiar representations, processes and concepts to explore unfamiliar tasks and problems. 4, 22, 23, 35, 51, 99, 109, 112, 127, 144

3.4 Use the guess-check-improve process in appropriate contexts. 83

xiv Targeting Maths Teaching Guide Year 4

Assessment of Outcomes Record Sheets

Outcomes Stage 3

NUMBERNumbers, counting and numeration3.1 Recognise the structure of whole numbers up to 5 digits, including place value.3.2 Skip-count by numbers of increasing size.

3.3 Represent, find, compare and order fractional parts of objects and collections of objects.

3.4 Use decimal notation to represent and compare simple decimal fractions including those resulting from calculator computations.

Mental computation and estimation3.1 Recall or mentally determine basic multiplication and division facts.3.2 Use place-value ideas and the properties of numbers and operations to assist mental

computation.3.3 Make estimates to check the reasonableness of the results of written computation

and calculator use. Computation and applying number 3.1 Use knowledge of place value to solve and record solutions to addition, subtraction,

multiplication and division problems.3.2 Select the appropriate operations and computation methods to solve problems

involving whole numbers and money. 3.3 State equivalence statements and addition and subtraction facts involving simple

common fractions and carry out calculations involving tenths and hundredths.Number patterns and relationships 3.1 Use rules involving addition, subtraction and multiplication to devise, describe,

extend and test number patterns. 3.2 Detect similarities and differences in the nature of the operations of addition,

subtraction and multiplication.3.3 Construct and complete simple statements of equality involving whole numbers and

fractions.SPACEShape and space3.1 Recognise, describe and represent straight, curved, diagonal, horizontal and vertical

lines, and angles as rotations of lines.3.2 Use simple conventional spatial language when describing shapes, parts of shapes,

objects, parts of objects and simple cross-sections.3.3 Explain and compare the spatial properties of shapes and objects.

3.4 Visualise and describe some of 'what is not seen' of simple objects.

3.5 Interpret, recognise and name three-dimensional objects from drawings and photographs and make recognisable models and sketches of simple shapes and objects.

3.6 Copy and create simple patterns involving translating, rotating and reflecting multiple copies of a shape and informally describe the transformations used.

3.7 Identify symmetry in regular two-dimensional shapes.

Location3.1 Use and understand conventional location language to follow and give directions and

describe position. 3.2 Visualise, find and compare alternative paths on simple maps, grids and mazes.

3.3 Interpret and describe location and direction using grid references and cardinal compass points.

3.4 Interpret and clearly record features when reading and making formal maps and plans of familiar environments.

Student name _________________________________________________________________ Date ______________________________________

xvTargeting Maths Teaching Guide Year 4

Student name _________________________________________________________________ Date ______________________________________

MEASUREMENTMeasuring and estimating3.1 Make increasingly accurate estimates of measurements using informal units and

standard units.3.2 Measure and compare using appropriate informal units.

3.3 Estimate and accurately measure length, mass, volume and temperature using formal units and standard units.

3.4 Demonstrate understanding of the concept of angle.

3.5 Use appropriate instruments to measure physical quantities.

Time3.1 Estimate short and long periods of time, describe duration of time, and make and use

timetables, schedules and calendars. 3.2 Tell the time using digital and analogue clocks.

Using relationships3.1 Describe the relationship between attributes. CHANCE AND DATAChance3.1 Identify and record outcomes from simple chance experiments.3.2 Compare and order the likelihood of outcomes of simple chance experiments and of

everyday events, and choose appropriate methods for random selection.Posing questions and summarising data3.1 Identify information required to answer questions or test conjectures, refining the

questions where necessary. 3.2 Determine appropriate procedures to collect information relevant to questions and

conjectures of interest. 3.3 Modify the method of data collection and classification to refine a question or

investigate a further question. Summarising and presenting data3.1 Organise and summarise category and whole number data. 3.2 Use diagrams and two-way tables to summarise and display discrete data.

3.3 Use graphical methods involving scale to display discrete and continuous data.

Interpreting data3.1 Extract specific information from data summarised in diagrams and tables. 3.2 Describe and interpret data displayed in simple scaled graphs.

REASONING AND STRATEGIESMathematical reasoning 3.1 Make and test simple conjectures. 3.2 Make judgments about the accuracy of reasoning and results.

Strategies for investigation3.1 Generate mathematical questions from presented data and from familiar contexts. 3.2 Clarify the essential nature of a task or problem and identify key information in

familiar situations. 3.3 Use familiar representations, processes and concepts to explore unfamiliar tasks and

problems. 3.4 Use the guess-check-improve process in appropriate contexts.

Outcomes Stage 3

2

Learning focus• Discuss the wallets and have the children read the amount in

each. Which wallet/purse would you most want to own? Why?Which would you least want to own?

• Point out the space between the thousands number andthe hundreds number. Remind them that even thoughthey may see a comma used in large numbers that weuse spaces instead.

• What does ‘closest to’ mean?• Ask questions similar to questions 7 and 8. Children orally give

their answers and explain why they chose a particular wallet.

Student page 3• Use a large abacus to explain the positions of the beads.• Make several abacus numbers. Children read the numbers.• State numbers and have children demonstrate the numbers

on the abacus.

Student page 4• Remind the class about the use of spaces — no commas to be

used. Practise writing numbers on the board using spaces.• Revise the spelling of difficult numbers (especially forty).• Ensure the children know to use a hyphen when writing

tens and units in words, eg twenty-six.

Student page 5• Demonstrate the values of MAB blocks.• Have the blocks available for children to use if they wish.• Make the first number (1a). Class reads the number.

If necessary break it down to — cube is 1 000, 2 flats are2 hundreds or 200, 3 longs are 3 tens or thirty, 5 shorts are5 ones or 5: 1 235

Answers for assessment page 51 a A b A c C 2 D, E, B, C, F, A3 a $35 b $1 256 c $1 009 e $1 6514 b $1 146, c $899, d $2 921, f $1045 wallet D6 a twenty-five dollars b one thousand two hundred and forty-

six dollars c nine hundred and ninety-nine dollars d threethousand and twenty-one dollars e one thousand six hundredand forty-one dollars f two hundred and four dollars

7 a 436 b 3 721 c 4 5028 a 207 b 1 004 c 879 d 1219 a 3 000 b 3 00010 a 1 500 b 2 750

VELS: NUMBER Outcomes and StandardsNumeration 3.1 Recognise the structure ofwhole numbers up to 5 digits, including place value. 3.2 Skip-count by numbers ofincreasing size. Investigation 3.3 Usefamiliar representations, processes andconcepts to explore unfamiliar tasks andproblems.• Reads, writes and orders whole 4-digit

numbers.• Counts forwards and backwards by tens

and hundreds.• Recognises and repeats different forms of

a number.• Orders numbers in ascending and

descending order.• Chooses and uses relevant and familiar

representations.

Key wordsmost, least, abacus, diagram, hundred,thousand, halfway between, digit, distance

Resourceslarge abacus, MAB blocks, photocopiesof abacus, calculators, magazines

Additional work sheetsTargeting Maths Middle Primary Numeration and Fractions• Numbers to 9 999 — Unit 2 BLM 2, BLM 6,

BLM 7


Student pages 2–5

Numbers

3

Counting in hundreds

Count around the classroom in 100s and 1 000s first forwards and then backwards.

Ask a child to choose a four-digit numberand instruct the class to count forwards orbackwards by 100s or 1 000s from thatnumber. I choose the number 2 257.You count forwards by 100s.

Writing numbers

Write four-digit numbers on the blackboard.Have the children read the numbers. Makesure some numbers have a zero in thehundreds and/or tens place.

Choose some children to come to theblackboard and write the numbers inexpanded form, eg 1 321 = 1 000 + 300 + 20 + 1.

Bingo

Have each child write 5 four-digit numberson a piece of paper, eg 2 897,

3 8049 4612 2223 061

Spin a spinner with numbers 0 to 9. Childrencross out numbers as they are called. The firstwith all numbers crossed calls Bingo. Theyread out their five numbers and then becomethe spinner.

Abacus shop

Children cut out 8 items worth four-digitwhole dollar amounts from old magazines.They show the amounts on photocopiesof an abacus.

Mental and Oral Strategies

Activity Bank


Find me

Discuss where you see four-digit numbers,eg house numbers in long streets. Make a list.This could be a homework exercise, anda class list could be compiled.

Make a poster

Discuss the number of ways you know to showa four-digit number, eg 2 671 (numbers),words (two thousand six hundred andseventy-one), using MAB blocks, modellingon an abacus, in another language,heiroglyphics etc.

Make a poster to advertise your favouritefour-digit number.

© Blake Publishing — Targeting Maths Teaching Guide 4This page may be reproduced by the original purchaser for non-commercial classroom use.

4

✎

✎

Activity Card 1

Activity Card 2

Smallest and LargestUse the four numerals to write the smallest number and largest number you can in numerals and words.

Smallest ___________________________ Smallest _________________________________________________________________ ______________________________________Largest ___________________________ Largest _________________________________________________________________ ______________________________________Remember: Whole numbers never start with zero.

÷ X _

+

Travelling AboutWhich distance is closest to:

2 000 km? _________________________

500 km? _________________________

1 000 km? _________________________

2 500 km? _________________________

Which would be longer — a single trip to Adelaide

or a return trip to Brisbane? _________________________

Distance by road from Sydney

To Kilometres

Melbourne 1 068

Adelaide 1 669

Brisbane 975

Darwin 3 959

4 6 8 2 00 5 3


Assessment Name __________________________________________

Date _____________________________Hundreds and thousands

5

$25A

$1 246 $999C

$3 021D

$1 641E

$204FB

1 Which is:a the least amount? _____ b closest to $100? _____ c closest to $1 000? _____

2 Order the amounts from largest to smallest.

___________ ___________ ___________ ___________ ___________ ___________

3 Add $10 to A ___________ B ___________ C ___________ E ___________

4 Take $100 from B ___________ C ___________ D ___________ F ___________

5 Would you rather have D, or C and F together? ____________

6 Write each number in words.

A ____________________________________________________________________________________

B ____________________________________________________________________________________

C ____________________________________________________________________________________

D ____________________________________________________________________________________

E ____________________________________________________________________________________

F ____________________________________________________________________________________

7 Write the numbers in numerals.

8 Circle the smaller number.

a 207 702 b 1 004 4 010 c 987 879 d 121 211

9 What number is:

a 1 000 more than 2 000? __________ b 1 000 less than 4 000? __________

10 Write the number halfway between:

a 1 000 and 2 000. __________ b 2 500 and 3 000. __________

a b c

6

Learning focus• Revise addition facts to 10 and 20. Let some children

use calculators.• Ensure children understand the meaning of vertically,

horizontally and diagonally. Have a quick game of ‘noughtsand crosses’ to reinforce.

• Work some examples on the board. Give a hint: if answer endsin 7 look for ones combinations that give 7, eg 9 + 8 or 3 + 4.

• Revise rounding to the nearest ten.• Allow use of calculators.

Student page 7• Thoroughly revise the three strategies. Allow for much board

work before text exercises.

Student page 8• Revise the use of number lines. Stress that all methods are

correct and encourage the children to use whatever worksfor them. eg 127 + 146 =

127 227 267 273or =

127 227 267 270 273• Set out an algorithm on the board. Talk about numbers being

in correct columns.

Student page 9• Allow for much hands on practice with MAB blocks.• Demonstrate many examples of written algorithms on

the board. Show trading under tens to help with accuracy.• Encourage reading from top down — helps when coming

to subtraction. More practice sheets need to be worked.

Answers for assessment page 91 a 53, 26 b 15, 53 c 86, 53 d 26, 9, 13 e 15, 53, 13

f 86, 53, 92 a 109 b 124 c 483 a 9 b 15 c 534 a 75 b 54 c 93 d 82 e 1155 a 62 + 40 + 1 = 103 b 83 + 30 + 2 = 115 c 216 + 50 – 3 = 2636 a 27 b 38 c 25 d 317 a 89 b 497 c 879 d 598 e 1 879

VELS: NUMBEROutcomes and StandardsCounting 3.2 Skip-count by numbers ofincreasing size. 3.3 Represent, find,compare and order fractional parts ofobjects and collections of objects. Mental Computation 3.2 Use place-valueideas and the properties of numbers andoperations to assist mental computation.3.3 Make estimates to check thereasonableness of the results of writtencomputation and calculator use.• Chooses appropriate methods to carry out

addition calculations.• Constructs simple statements of equality.• Uses appropriate strategies for mental

addition.• Uses written methods to solve addition

problems involving 3-digit whole numbers.• Selects appropriate computation methods.

Key wordsvertically, horizontally, diagonally, rows,columns, strategy, compensation, trading

Resourcescalculators, MAB blocks

Additional work sheetsTargeting Maths Middle Primary Operations and Number Patterns• Addition — Unit 2 BLM 1, BLM 3


Student pages 6–9

Addition

7

Quick to 20

Practise number facts to 20.

Children can:

(a) call out the answer.

(b) show the answer using fingers. eg 6 + 5, show 10 fingers and then 1 finger.

(c) write answers in work book.

Be the teacher

Ask the class to write a 2-digit plus 2-digitalgorithm, eg 27 + 34. Choose a child tocome to the front to ask their question. The“teacher” asks the first student with theirhand up the answer and the strategy theyused. If correct this child becomes theteacher.

MAB maths

Children work in pairs using MAB blocks.One child sets out an algorithm involvingtrading. The other child demonstrates theanswer. Children then reverse roles.(Refer to question 1, page 9 of text.)

Number lines

How many ways can you show 120 + 85on a number line?

If necessary demonstrate several wayson the board.

Ask the children to continue making as manyways as possible using a different colourfor each new line.

Who has the most? How many have the classmade in total?

Columns, rows and diagonals

Use the number grid on page 6. Remindchildren they have totalled the columns.

Ask children to total the rows and diagonals.

Calculators may be used.

Algorithms

Ask the children to use the numbers fromquestion 4, page 8 to make their ownalgorithms.eg, Take 231 from d and 783 from j to make

231+ 783

Have children work in pairs to find theanswers to each others algorithms.

Check with calculators.


Activity Bank



Activity Card 3

Activity Card 4

8

✎

Number GridsRemember the work you did on page 6?

Put your own one–digit and two–digit numbers

in this grid.

Using the grid put numbers in each box below.

(Be sure you know the answers.)

__________________ + __________________

__________________ + __________________

__________________ + __________________ + __________________ Give your card to a friend to work out.

Numeral Arrangements

Here are four numerals.

They have been arranged six ways.

Which arrangement has the highest total? ___________Which has the smallest total? ___________Make 6 other arrangements.___________________ ___________________ ___________________ ___________________ ___________________ ___________________ Total your arrangements. Check with a calculator.

÷ X _

+�

✎ �

7 2 8 6

2 + 7 + 6 + 8

27 + 68

276 + 8

76 + 28

86 + 7 + 2

278 + 6


1 Adding vertically, horizontally or diagonally find twonumbers that total:a 79 _____ + _____b 68 _____ + _____c 139 _____ + _____

Add three numbers that total:d 48 _____ + _____ + _____e 81 _____ + _____ + _____f 148 _____ + _____ + _____

2 Total each column. a _______________ b _______________ c _______________3 Find the missing numbers.

a 26 + _____ = 35 b 53 + _____ = 68 c _____ + 86 = 1394 Write the answers.

a Tens Ones b Tens Ones c Tens Ones d Tens Ones e Tens Ones

6 8 4 6 4 6 3 5 8 6+ 7 + 8 + 4 7 + 4 7 + 2 9

5 Use the compensation strategy to add these.a 62 + 41 = 62 + 40 + _____ = _____b 83 + 32 = _____ + _____ + _____ = _____c 216 + 47 = _____ + _____ + _____ = _____

6 Use doubles to help you add these.a 14 + 13 = ______ b 20 + 18 = _____ c 13 + 12 = _____ d 15 + 16 = _____

7

a 69 b 241 c 773 d 515 e 1 833+ 20 + 256 + 106 + 83 + 46

Assessment Name __________________________________________

Date _____________________________Addition

9

15 7 26

86 53 9

8 64 13

Learning focus• Revise 2-digit, no trading subtraction on the board.• Discuss why patterns help, eg 9 – 4 =

90 – 40 =900 – 400 =

• On the board practise similar examples to 6 – 3, 16 – 3, 26 – 3, 46 – 3 etc.

Student page 11• Have children discuss how they’d mentally work 72 – 49.

Write down all methods that are correct. Stress they arecorrect if they achieve the correct answer.

• Show strategy A. Why does it work? Repeat with strategy B.• After working the Challenge let children read their problems

to the class.

Student page 12• Revise number lines on the board. Work one example many

ways. –10 –10 eg 63 – 27 63

36 43 53–20

6336 43

–4 –3 –2063

36 40 43 53

Student page 13• Practise using a hundred square. How can we use it with $1?• Practise examples of 3-digit minus 3-digit numbers on the

board.

Answers for assessment page 131 a 27 b 19 c 352 a 133 b 370 c 363 d 304 e 6543 a 6, 60, 600 b 4, 70 – 30 = 40,700 – 300 = 400 c 13, 23, 73

d 4, 14, 24, 844 a 65, 65 b 13, 13 c 83, 83 d 84c e 53c f 45c5 a 46 b Teacher check c Teacher check

VELS: NUMBEROutcomes and StandardsMental Computation 3.1 Recall or mentallydetermine basic multiplication and divisionfacts. 3.2 Use place-value ideas and theproperties of numbers and operations toassist mental computation. 3.3 Makeestimates to check the reasonableness ofthe results. Patterns and Relationships 3.1 Use rulesinvolving addition, subtraction andmultiplication to devise, describe, extendand test number patterns. 3.3 Construct andcomplete simple statements of equalityinvolving whole numbers and fractions.Reasoning 3.2 Make judgments about theaccuracy of reasoning and results.Investigation 3.2 Clarify the essentialnature of a task or problem and identify keyinformation in familiar situations.• Selects appropriate operation and

computation method.• Solves subtraction problems including those

involving money.• Selects appropriate computation method to

solve problems.• Generates word problems using specified

operations.• Uses rules involving subtraction and

addition to devise number patterns.• Generates mathematical questions from

presented data.• Uses written methods and empty number

lines to solve subtraction problems.

Key wordssubtraction, minus, how many left, difference,strategy, vertical, horizontal

Resourcesdice for each child, envelope, art paper,class abacus

Additional work sheetsTargeting Maths Middle Primary Operations and Number Patterns• Subtraction — Unit 2 BLM 3, BLM 6

Student pages 10–13

Subtraction


Two missing signs

On the board write four sets of numbers withthe signs missing. Children tell what the signsare and why, eg 16 12 2 = 2

27 6 5 = 38Children decide on the sign and say thealgorithm to the class. If class ability allowsboth + and – signs may be used in onealgorithm, eg 36 12 6 = 42

Subtraction stories

Children take turns to ask the class a shortproblem involving subtraction but not usingnumbers over 100. eg I had 85c for lunchbut lost 23c. How much do I have now?

Remind the class of the strategies theycan use.

Secret numbers

Put a secret number less than 60 in anenvelope. Each child throws a die twiceto make a 2-digit number. They throw againto make another 2-digit number. They thensubtract the smaller number from the largerusing a number line. The child with thenumber closest to the secret number putsthe next secret number in the envelope.

Abacus numbersOn a class abacus demonstrate a 3- or 4-digitnumber and ask the children to write it down.Demonstrate another 3- or 4-digit number andask the children to subtract the smaller fromthe larger number and write the answer innumerals and then in words. Write the answeron the board. Children carefully check theirwork. Repeat using different numbers.Be careful not to involve trading.

Subtraction sign

The take away sign is —. It means takeaway, subtract, difference between, minusor less. Write these words to display in theclassroom. Brainstorm with the class to findwhen we might have to take away, eg moneywhen shopping, time when ringing overseas,sharing lollies, distance to go when travellingetc. Compile a class list. Children canillustrate different examples on art paperwith an appropriate number story and makea class display.

Using our algorithms

Look at the answers to the algorithms onpage 13, question 3. Check that the childrenall have the correct answers. Ask the childrento write the answers from the largest to thesmallest and(a) subtract the smallest (120) from the

largest (842).

(b) find the middle number.


Activity Bank

Targeting Maths Teaching Guide Year 4 11

✎✎

✎Lucky MoneyYou have won $100. You buy 5 people a gift but each gift mustcost less than $20. Fill in the chart. The first one is done for you.

NAME GIFT COST MONEY LEFTMum book $18 $100 – $18 = $82

$82 – = – = – = – =

What could you buy yourself? ____________________________

Check your answers with a calculator.

Activity Card 5

Activity Card 6


What’s The Difference?

12

50 37 6 32 19

8 24 12 45 18

18 4 19 57 44

5 17 46 12 31

30 17 33 8 21

Find pairs of horizonal or verticalnumbers with a difference of 13.

Colour them blue.

One has been done for you.There are 10 more pairs. Somenumbers belong to two pairs.

How many unused numbers arethere? ___________________

Colour them your favourite colour.

÷ X _

+

AssessmentName __________________________________________

Date _____________________________


1 Use the number lines.a 83 – 56 = ____b 68 – 49 = ____c 70 – 35 = ____

2

5 Ali used 36 of his mother’s pegs to make aeroplanes. His mother had 82 pegs.a How many has she now? ______b Show how you worked out your answer.

c Can you show another way?

3 a 9 – 3 = ____90 – 30 = ____900 – 300 = ____

b 7 – 3 = ____70 – ____ = ____700 – ____=____

c 6 – 3 = ____16 – 3 = ____26 – 3 = ____76 – 3 = ____

d 9 – 5 = ____19 – 5 = ____29 – 5 = ____89 – 5 = ____

4 Use the hundred square to help.a 100 – 35 = ____ 35 + ____ = 100b 100 – 87 = ____ 87 + ____ = 100c 100 – 17 = ____ 17 + ____ = 100Find the change from $1 if I spend:d 16c ______e 47c ______f 55c ______

a 3 5 9– 2 2 6

b 7 9 0– 4 2 0

c 6 9 4–3 3 3

d 8 0 7– 5 0 3

e 6 8 5– 3 1

Subtraction

83

68

70

13

82

82

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 5 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

14

Learning focus• How do we find half of a group?• Practise finding half of given numbers. Can we find half of five

cats? Why not?• How do you think we'll find a quarter of a group? Divide by 4.• Tell the class that the denominator tells us what to divide by

when finding a fraction (part) of a group.• Brainstorm: When do we need to find parts of a group?

Page 15• Revise purpose and use of numerator and denominator.• Draw some diagrams on the board similar to question 2. Work

these together.

Page 16• 100 parts =1 whole. How would you write this as a decimal?• Revise 29 = 0.29. Discuss the place values.

100• Why do we use decimals for $ and c? 100c = $1• Stress that the way of saying 0.57 is nought point five seven

not nought point fifty-seven.

Page 17• Work lots of addition and subtraction of money on the board.• Don't forget the decimal point in the answer.• Remind the children that we don't use $ and c together,

eg $3.75 not $3.75c.

Answers for assessment page 171 red 5 blue 4 yellow 6 black 142 Teacher check3 a 3

10 b 710

4 b red 0.35 c yellow 0.03 d black 0.255 0.05 0.15 0.35 0.50 0.99 1.006 a 11.58 b 9.90 c 8.62 d 6.21 e 6.54

VELS: NUMBER Outcomes and StandardsNumeration 3.3 Represent, find, compareand order fractional parts of objects andcollections of objects. Counting and Numeration 3.3 Represent,find, compare and order fractional parts ofobjects and collections of objects. 3.4 Usedecimal notation to represent and comparesimple decimal fractions including thoseresulting from calculator computations.• Represents and finds fractional parts of

collections.• Finds and compares fractional parts of

objects and collections.• Uses decimal notation to represent simple

decimal fractions.• Orders numbers with two decimal places.• Adds and subtracts numbers involving

tenths and hundredths.

Key wordsnumerator, denominator, hundredths,quarters, halves, fifths, eighths, tenths,decimal

Resourcescardboard, magazines, MAB ones, counters

Additional work sheetsTargeting Maths Middle PrimaryNumeration and Fractions• Fractions — Unit 2• Decimal Fractions — Unit 2



Fractions and Decimals

15

Which is more?

Would you rather have 12 a pie or 35 of a pie?Why?

Ask the children to the board to demonstrateon a pie graph or a number line. Childrenpose similar questions.

Tables practice

Children orally answer questions. How manytimes does 6 go into 36?

Children write answers to ten similar quickmentals each day. What was your personalbest for the week?

Everyday fractions

Discuss where we use fractions in daily life,eg the clock, half fill the bath, quarter of asandwich, half way there etc. Compile a classlist. Use the list to make fraction sentences.eg At half-time I sat on the quarter lineand ate three quarters of an orange.

Putting in pairs

Have the children pair these numbers ona long number line.

This can be done individually or as a classexercise depending on children's abilities.

Fraction words

Make a display of fraction words such ashundredths, numerator etc. These words canbe used in a spelling game. Children standand spell a word one letter at a time aroundthe class, if they make a mistake they sit.The winner is the last standing.

Picture fractions

Look in magazines and find pictures thatcould be divided into 12,

14,

18,

15,

110 .

Label each picture with its fraction anddisplay them around the classroom.


Activity Bank



3 47 62=

✎ �Activity Card 7

16

÷ X _

+

Lots of Groups

• Collect 36 counters or MAB ones.How many equal groups can you dividethe blocks into? eg 2 groups of 18

Activity Card 8

✎ � ÷ X _

+

• Give a friend an even number of your counters,eg 20. How many groups can they make?

Party Time

$1.39 $4.69 $1.23 $3.29 65cYou are allowed to choose 2 bags of lollies for your party. What would it cost if you choose:a M&Ms + Mars Bars? ________ + ________ = ________b Jelly Beans + Jaffas? ________ + ________ = ________c Freddos + Jelly Beans? ________ + ________ = ________d the two most expensive? ________ + ________ = ________e the two least expensive? ________ + ________ = ________What is the difference in cost between:

b and e? ________ + ________ = ________d and e? ________ + ________ = ________Check your answers with a calculator.

Freddos Mars bars M&Ms Jaffas Jelly beans

Assessment Name __________________________________________

Date _____________________________

1

2 3

Shade: a 12 b

34 c

58 d

18 What fraction:

a is shaded? _______b is unshaded? _______

Colour:a

14 of the cats red.

b 15 of the cats red.

c 310 of the cats red.

d The rest of the cats black.

e What fraction is black? _______


17© Blake Publishing — Targeting Maths Teaching Guide 4This page may be reproduced by the original purchaser for non-commercial classroom use.

5 Write these decimals from the smallest to the largest.

6

4 Colour this hundred square and finish the chart.

a

b

c

d

a 7.31+ 4.27

b 6.89+ 3.01

c 8.05+ 0.57

d 8.84– 2.63

e 6.87– 0.33

0.99 0.15 0.35 1.00 0.50 0.05

colour

shaded

red

yellow

black

fraction decimal

0.10

________

________

________

35100

110

3100 14

18

Learning focus• Look at the patterns. Determine it is a hundred square.• Are there only two patterns you can draw? Are there any

other patterns you could draw to show 4? etc.• Have blank hundred squares for children to practise their

patterns before committing to their textbook.

Page 21• Revise number in — number out. Work out how the number

is being changed.

Page 22• Teach how to use the constant factor on the calculator.

eg Rule , 1.78, 6.78, _____ _____ _____ _____

On calculator then keep pressing

to write each term.

• Ensure the children have a calculator each and have plentyof practice.

Page 23• Stop after Q1 and Q2. Discuss implications.• In Q3 look carefully at each pattern. Suggest children know

exactly what is happening each time before completing.

Answers for assessment page 211 a Teacher check

b 8, 8 16, 16 322 Teacher check3 Either, both the same4 c 12 spots

f 3 spots 5 2.86, 2.98, 3.10, 3.22, 3.34

=

=5++1.78

+ 5

VELS: NUMBER Outcomes and StandardsNumber Patterns 3.1 Use rules involvingaddition, subtraction and multiplication todevise, describe, extend and test numberpatterns. Strategies for Investigation 3.3 Use familiarrepresentations, processes and concepts toexplore unfamiliar tasks and problems.Reasoning 3.1 Make and test simpleconjectures.• Explains patterns on a hundred chart.• Puts forwards assertions about what might

be true.• Identifies simple patterns involving

numbers.• Works out a rule for a number pattern.• Models and recalls number patterns in a

hundreds chart.• Uses familiar concepts to explore unfamiliar

tasks.• Uses a given rule to generate a sequence of

numbers.• Predicts the value of a given term in a

sequence.

Key wordspatterns, rule, number in, number out,constant factor, identical

Resourcesclass copies of hundred squares, calculators,1 cm grid paper, class copies of Australiancoins BLM, counters

Additional work sheetsTargeting Maths Middle PrimaryOperations and Number Patterns: • Number Patterns — Unit 2



Patterns

19

Number patterns

Count patterns forwards and backwards froma given number. eg Count on by 3 from 17;count back by 4 from 32.

Increase difficulty to counting forwards orbackwards by two different numbers. eg Countfrom 17 by 3 and then 2,3 and then 2 etc[17 + 3 + 2 + 3 + 2 + 3 + 2= 20, 22, 25, 27,30, 32 etc.]

Count back from 28 by 4 and then 3, 4 and3 etc. [28 – 4 – 3 – 4 – 3 – 4 – 3 = 24,21, 17, 14, 10, 7 etc.]

Climbing ladders

Divide the children into four or five groupsand ask them to put their heads on theirdesks. Put four or five identical ladderson the board, eg

etc

Ask a child from each group to come forwardand climb the ladder. The first child finishedwith all correct, gains a team point. Headsdown again, change the numbers and repeatthe exercise until every child has had a turn.

Number in, number out

On the board put a number grid,eg

Children work orally. Change the numbersseveral times and ask the children to writethe answers in their books.

Y patterns

Put a Y pattern on the board.eg

Discuss the pattern with the children.Ask them to write their own Y pattern.Remind them they can add, subtract, multiplyor divide numbers on their pattern. Childrencome to the board and share their patternswith the class.

Find the pattern

(a) 1 1 2 3 5 8 __ __ __ __(b) 2 4 6 10 __ __ __ __Allow children time to work out the patterns.Let a child explain the rule to the class.The more able children could make similarextra patterns.

Making patterns

Ask the children to cut a pattern from 1cmgrid paper. They then turn the pattern anddraw their pattern on paper. How could you continue this pattern?


Activity Bank


4 π 6 =4 π 9 =4 π 2 =

INOUT 24 60 18

π62

3

53

5

146

4

233

6

?


$

20

✎ �

Thinking!

Activity Card 9

Activity Card 10

c c

Put the 4 counters on the grid so thatno two of them are in the same row,column or diagonal.

Is there only one solution? _____

$$ c$ c$

c c$ c$ $ c c$ $ c c$

c

$c

$

c

$c

$c

$

Money PatternsWork with a friend. You need a sheet of Australian coins. Cut them out.Here is a number pattern.

a What is the rule? ___________________b Make this pattern on your desk. Continue it for as long

as you are able with your coins.c Paste it onto art paper and write the rule. d How many different patterns can you make? _____

Glue�


Assessment Name __________________________________________

Date _____________________________

1

a Draw a number patern for the rule . The first pattern is done for you.

b Write the numbers in the boxes.

2 Make a number pattern using the rule .

Show 6 terms.____ ____ ____ ____ ____ ____

3 Would you rather have $64 π 1 or $64 ÷ 1? ____

Why?

4

7–

π 2

Patterns

21

Draw the right number of spots on cat c and cat f.

5 Use a calculator to find the next 5 terms.

Rule

2.62, 2.74, __________ , __________ , __________ , __________ , __________

+ 0.12

a b c d

a b c

d e f

2 2π 4= 4 2π = 2π = 2π =

22

Learning focus• Revise cm as

1 100 of m.

• Practise examples such as 2 m 36 cm = 2.36 m on the board.• Practise changing metres to centimetres and decimals,

eg 1 m 15 cm = 115 cm = 1.15 m.• Practise adding and subtracting cm.• Reinforce that there is a space left between the number

and the letter when writing a measurement, eg 4 cm.

Page 25• Discuss the difference between mm / cm / m.• Give measuring references, eg mm = diameter of a hair;

cm = width of thumbnail; m = distance from fingertip to …• Point out that the door is approximately 2 m high.• Look at a ruler and discuss mm/cm marks.• Use a ruler to measure a metre (30 cm + 30 cm + 30 cm

+ 10 cm). About how many steps? … hand spans?• What would you use to measure the length of a car (m),

a birthday card (cm), length of a pin (mm)?

Page 26• Revise measurement chart and abbreviations (see fact note).• Teach perimeter. Practise many examples on the board.

Answers for assessment page 251 a Father 1 m 85 cm 185 cm 1.85 m

Mother 1 m 65 cm 165 cm 1.65 mGrandma 1 m 58 cm 158 cm 1.58 mElana 1 m 49 cm 149 cm 1.49 mSasha 1 m 36 cm 136 cm 1.36 mJosef 82 cm 82 cm 0.82 m

b 1 cm c 1 m 3 cm2 Teacher check3 a 3 + 3 + 3 + 3 = 12 cm

b 7 + 2 + 7 + 2 = 18 cm c 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16 cmd Teacher check

4 20 m

VELS: MEASUREMENT Outcomes and StandardsMeasuring and Estimating 3.1 Makeincreasingly accurate estimates ofmeasurements using informal units andstandard units. 3.2 Measure and compareusing appropriate informal units. 3.3Estimate and accurately measure length,mass, volume and temperature using formalunits and standard units. 3.5 Useappropriate instruments to measure physicalquantities.• Makes sensible numerical estimates of

length.• Compares and orders length.• Chooses the appropriate formal unit to

estimate lengths.• Uses measuring equipment such as rulers

and tapes.• Compares format units of length.• Adds lengths to find perimeter.

Key wordsmillimetre, centimetre, metre, perimeter,measure, estimate

Resourcestrundle wheels, tape measures, calipers,string, A4 paper, ruler marked in mm, scissors

Additional work sheetsTargeting Maths Middle Primary Measurement• Length — Unit 2



Length

23

Different names

Write a measurement on the board.Have children say it as many different waysas possible,eg 20 cm = 200 mm = 0.20 m = 15 m.

150 cm = 1 500 mm = 1.50 m = 1 12 m = 1 m 50 cm.Allow more able children to extend answersbeyond syllabus requirements, but keepdiscussion at class level.

Perimeter game

I am thinking of something that has aperimeter of about 100 cm. What could it be?(Maths text). Ask the child who answers thequestion to pose another perimeter problem.Restrict objects to the classroom.

Long jump

Ask children to estimate the length they canjump. Working with a friend, have each childmeasure their longest jump (three triespermitted) using a tape measure or a trundlewheel.

What is the difference in mm between yourbest jumps?

Measuring devices

Compile a list of devices used for measuringlength, eg rulers, dressmakers’ tapes, builders’(steel) tapes, trundle wheels, calipers, handspans, depth gauges etc.

This could be a homework or extensionresearch topic.

Ask children to illustrate the measuringdevices and make a class display.


Activity Bank


Different shapes

Have children work in pairs. Give each paira 40 cm length of string. Ask them to makean interesting 2D shape, eg

then measure each side and total themeasurements. Repeat this exercise severaltimes making different shapes.

Why is the perimeter always the same?

Longest letter

Fold a piece of paper into four equal pieces.

Write your initials, or name, or nickname,as big as possible, in each section. Estimatethe longest letter and then take a pieceof string and measure each letter.

Who has the longest letter in the class?What is the longest letter in the alphabet?

J OH N


24

✎ �Activity Card 11

÷ X _

+

My Ideal Bedroom

1 What is the perimeter of:a the room? ________ m b the drawers? ________ mc the bed? ________ m d the bookcase? ________ me the desk? ________ m

2 Trace and cut out the plan furniture. Arrange it in the room.3 Draw some more furniture to scale, eg bedside tables, rug,

computer and table. Arrange them in the room with other furniture and then paste them all on your plan.

4 Pretend you are standing at the door.Draw a colourful picture of your room.

4m

Win

dow

3 m 2 m

1 mDoor

bed

1 m

0.5 mdesk

0.75 m

0.5 mchest ofdrawers

1 m

0.25 mbookcase

Glue �

Assessment Name __________________________________________

Date _____________________________

1 Sasha’s Family

2 Estimate and then measure: Estimate Measurea The length of your thumb. ______ mm ______ mmb The width of this paper. ______ cm ______ cm

3 What is the perimeter of these shapes?

d Draw a shape with a perimeter of 8 cm.Write the measurement on the sides.

4 The local swimming pool is a rectangle and it is 55 m long. The perimeter is 150 m.What is the width? ________

a Complete the height measurements.

b How much does Elena need to grow

to reach 1.50 m? ________

c What is the difference in height

between Dad and Josef? ________ m

Length


Name

Father

Mother

Grandma

Elena

Sasha

Josef

Height

1 m 65 cm

1 m 58 cm

1 m 49 cm

in cm

185 cm

158 cm

82 cm

in m

1.58 m

1.36 cm

3 cm

a P = _____ + _____ + _____ + _____ b P = _____ + _____ + _____ + _____

= _____ cm = _____ cm

c P = _____ + _____ + _____ + _____ + _____ + _____ + _____ + _____

= _____ cm

2 cm7 cm

2 cma b c

26

Learning focus• Discuss days of the week — names and how many.• Discus months of the year — names and how many.• Where do we see calendars? What do we use them for?• Discuss the varying lengths of different months.

Thirty days has September,April, June and November.All the rest have thirty-one,Excepting February clearWhich has twenty-eight and twenty-nine days each leap year.

Page 28• Show the class a clock with a second hand.• Teach 60 seconds in 1 minute. Explain that the second hand

moves right around the clock every minute, the minute handmoves right around the clock every hour, and the hour handmoves around the clock every 12 hours.

• Ensure every child has a popstick and a pencil to use asa minute and second hand. Work question 1 and question 2 asa class.

Page 29• Revise time facts.• Talk about quick actions (blinking), slow actions (sleeping)

and different time units used to measure the actions.• Revise reading a clock. Discuss how hands move as the minute

hand goes from one hour to the next.

Answers for assessment page 291 a Sunday

b Tuesday c Wednesday d Thursday e Saturday

2 a Tuesday b Friday c Saturdayd Saturday e Wednesday, Thursday, Friday

3 Teacher check4 a 20 to 5 b 5 past 1 c 23 minutes to 12

d quarter past 7 e 4:40 f 1:05g 11:37 h 7:15

5 Teacher check

VELS: MEASUREMENT Outcomes and StandardsTime 3.1 Estimate short and long periods oftime, describe duration of time, and makeand use timetables, schedules andcalendars. 3.2 Tell the time using digitaland analogue clocks.• Locates dates on a calendar.• Interprets simple calendars to find

information.• Tells the time on an analogue clock.• Relates time facts to each other.• Estimates short periods of time.• Classifies events according to time taken.

Key wordscalendar, days of week, months of year,abbreviations, seconds, digital, analogue

Resourceslarge class calendar, classroom calendars,popsticks, classroom analogue and digitalclocks, clocks and watches with secondhands, stopwatches, paper plates, pipecleaners, matchsticks

Additional work sheetsTargeting Maths Middle Primary Measurement• Time — Unit 2, BLMs 1, 2, 3, 4, 5



Calendar and Time

27

Time facts

Ask time questions and children write thefact. How many days in 6 weeks?

How many minutes between 1:15 and 1:32?

Months

Ask children month questions. What is themonth before…?, What is the month after …?

How many months in 2 years? ... 3 12 years?

... 14 year?

How many months to Easter? … Anzac Day?

Counting seconds

Have a clock with a second hand. Count onethousand, two thousand … ten thousand.

Was this close to 10 seconds?

Repeat with other times, eg half a minute.

Abbreviations

Discuss and record on the board abbreviationsfor days of the week and months of the year.

Why do we do this? Where do you see this?

Look at calendars from other countries.What abbreviations do they use? Is it stilleasy for us to know what day it is?

Make a clock

Refer to the clock on p28 of the studentbook. Using paper plates, matches, pencils,popsticks, pipe cleaners etc, have childrenmake a clock showing the hour, minute andsecond hands. Children demonstrate timeson their clocks.

Show me 10 mins and 30 secs past 7 o'clock.

This clock could be made as a homeworkexercise and children encouraged to beimaginative in the use of materials.

Reading a calendar

Children work in pairs sharing a calendar. Ask questions and children find the answerson the calendar.

What was the date of Easter Sunday?How many months had 5 Tuesdays? … 5Wednesdays? How many days werein February?


Activity Bank



28

✎ �

Activity Card 12

Activity Card 13

✎ � ▲

▲

It Takes Less Than A Minute

Write down 10 activities that take you less than one minute (60 seconds).

Estimate the time for each, eg wink — 1 second, tie shoelaces — 7 seconds.

Discuss your list with a friend. If you disagree about some activities,

check the time using a clock with a second hand, a stopwatch or count — one thousand, two thousand … etc.

Tess 34 hr

Tony61 min 50 sec

Tam1 hr 2 min

Tilly47 min

Tom1 1

2 hrs

Tahlia70 min 10 sec

Toby1 hr 32 min

Tiffany75 min 12 sec

Tim39 min 59 sec

Terri45 min 15 sec

Cross Country10 children went in a cross-country race. When they finished, eachwrote their name and time on a piece of paper and gave it to thejudge. Can you help place them from fastest to slowest.

Assessment Name __________________________________________

Date _____________________________

1 What do the letters stand for?a Su _____________ b T _____________c W _____________ d Th _____________e S _____________

2 What day is:a 14th July? _________________b 31st July? _________________c 4th July? _________________

d On what day will the 1st August fall? _________________e Which days in July have 5 dates? _________________ , _________________

and _________________ .

3 Using a lead pencil for the minute hand and a red pencil for the second hand, show thesetimes on the clocks.

a 5 min 20 sec b 10 min 55 sec c 50 min 25 sec d 30 min 45 sec

Calendar


e f g h

a b c d

ac

bd

Write the digital times.

5 If these clocks show p.m. time, what activity would you be doing at each time?

: : : :

MTWThFSSu

12345

6789101112

13141516171819

20212223242526

2728293031

JULY

4 Write the times.

30

Learning focus• Revise pyramids, prisms, cones, spheres and cylinders.• Define prisms (a 3D object with two identical ends, all other

faces being rectangles).• Define pyramids (a 3D object with a base, all other faces

being triangles).• Remind children that prisms are named by the shape of their

ends and pyramids by the shape of their base.

Page 31• Discuss cross-sections — what they are.• Demonstrate with a plasticine model. Cut to show cross-

sections.• Note that cross-sections of both prisms and pyramids are

identical in shape to their ends. Pyramid cross-sectionsbecome smaller as they approach the apex.

Page 32• Show children the two types of dot paper.• Insist on use of rulers and sharp pencils.• After completing page 32 have children try 3D drawings

on blank paper.

Page 33• Full nets are on pages 103 – 110 of Targeting Maths Middle

Primary: Space.• Explain what a net is and how one is made.• If using nets from Targeting Maths Space book explain that

the tabs are only to make joining the sides easy, not partof the net.

Answers for assessment page 331 a square pyramid, 5

b rectangular pyramid, 5c triangular pyramid, 4 d pentagonal pyramid, 6 Cross-sections, Teacher check

2 Teacher check3 a hexagonal pyramid

b Teacher check4 a Teacher check

b rectangular prism 5 Teacher check

VELS: SHAPE Outcomes and StandardsShape 3.1 Recognise, describe and representstraight, curved, diagonal, horizontal andvertical lines, and angles as rotations oflines. 3.2 Use simple conventional spatiallanguage when describing shapes, parts ofshapes, objects, parts of objects and simplecross-sections. 3.4 Visualise and describesome of 'what is not seen' of simple objects.3.5 Interpret, recognise and name three-dimensional objects from drawings andphotographs and make recognisable modelsand sketches of simple shapes and objects.Investigation 3.3 Use familiarrepresentations, processes and concepts toexplore unfamiliar tasks and problems.• Recognises and names 2D shapes and 3D

objects.• Uses conventional terms.• Identifies plain shapes.• Predicts and sketches the shape of a simple

cross section.• Draws congruent copies of shapes.• Uses a ruler to draw lines and shapes.• Makes prisms and pyramids from nets.• Translates a new task into a learnt process.

Key wordspyramids, prisms, cross-section, sphere,cylinder, cone, hexagonal, pentagonal,triangular, net

Resourcesmodels of prisms and pyramids, cones,spheres, cylinders, sharp pencils, 1 cmsquare dot paper, isometric dot paper,plasticine, cardboard, textas, glue, rulers,blank cards, old magazines, old photographs,greeting cards

Additional work sheetsTargeting Maths Middle PrimarySpace • 3D — Unit 1; Unit 2



3D Objects

31

Guess the shape

Put a 3D object in a container or undera cloth. Allow a child to feel, but not see theobject. The child describes the object and theclass takes turns in guessing what it is.

Repeat the exercise with as many different3D objects as possible.

3D vocabulary

Expand children's vocabulary by using3D words for description, eg a conical hat,an hexagonal pattern, a cylindrical rollof paper.

Build a list to display in the classroom.

Encourage children to use some of theseexpressions in creative writing.

Real life 3D objects

Children look for 3D objects in the'real' world. Collect pictures from magazines,old photographs, birthday cards etc of3D objects.

In the art class children make a collage usingthese objects.

Labelling objects

Have as many models of 3D objects aspossible displayed in the room. Make cardswith the names of all these models on them.Shuffle the cards. Have a child take a cardand place it on the correct model.


Activity Bank


Net patterns

Tell children to choose a 3D object and usetheir imaginations to make as many patternsas they can from the faces and ends (or base)of the object. eg square pyramid

Cross-sections

Using modelling clay or plasticine model the3D objects in this unit. Children cut cross-sections of the objects and make a displaywith labels.

etc


32

3x3Work in groups of 3.

One person describes a 3D object.

The next person makes a sketch of the described object.

The third person draws the net.

Repeat this activity so everybody has a turn at a ,

and and you have different drawings

and 3 different nets to show to the class.

Activity Card 14

Activity Card 15

Net Working!!• Find a small cardboard box, eg biscuit packet,

tea packet, Toblerone packet.

• Carefully pull the box apart andlay it out flat to display the net.

• Place the net on cardboard and draw around the edges, put dotted lines where the folds are. Cut out the net.

• Decorate the outside of your net.

• Fold and glue your net to remake the 3D shape.

✎ �

� ✎

A

B

CA B

C 3

5 Marzo has just arrived from Mars. Explain to him what a net is.

Assessment Name __________________________________________

Date _____________________________

1 Name each object and count its faces.

Name

2 Draw a cross-section of each shape in question 1.

3D Objects


3 a Name this object. b Copy the drawing.

a b c d

Faces

a b c d

4 a Finish this net of a pentagonal pyramid.

b This is the net of a ________________ .

34

VELS: DATA and CHANCEOutcomes and StandardsSummarising and Presenting Data 3.1Organise and summarise category and wholenumber data. 3.2 Use diagrams and two-waytables to summarise and display discretedata. 3.3 Use graphical methods involvingscale to display discrete and continuous data. Interpreting Data 3.2 Describe and interpretdata displayed in simple scaled graphs.Chance 3.2 Compare and order thelikelihood of outcomes of simple chanceexperiments and of everyday events, andchoose appropriate methods for randomselection. Reasoning 3.1 Make and test simpleconjectures.• Summarises data obtained by tallying.• Displays data in bar graphs with number

scales.• Uses graphs and two way tables to

summarise and display data.• Displays data in bar graphs with suggested

scales.• Collects relevant information.• Comments on predictions made in light of

results collected.• Makes judgements about the accuracy of

results.• Compares the likelihood of outcomes in a

simple chance experiment.• Predicts possible outcomes.

Key wordstable, bar graph, tally, survey, chance, 50-50 chance

Resources1 cm grid paper, dice, old magazines,stickers, cardboard

Additional work sheetsTargeting Maths Middle Primary Space • Chance and Data — Unit 2



Data and Chance

Learning focus• Discuss why data is collected. Why would the canteen keep

track of the drinks they sell? Where would the informationbe used?

• Discuss why it would be better to have the information in agraph. What is easier to interpret — a table or a graph? Why?

• Remind children how to use tally marks.• Point out the need for labels in question 3 — one for the title

and one each for the horizontal and vertical axes.

Page 35• Discuss what constitutes a picture graph. How is a picture

graph different from other graphs?• Explain the use of keys, including the use of half a picture.

eg= 10 = 5

• Discuss the advantages/disadvantages of picture graphscompared to bar graphs.

• Discuss the two tally tables. Which tells more? Are there usesfor both?

Page 36• Make sure the children predict first.• Discuss findings as a class.• Discuss final answers.

Page 37• Revise labels.• Discuss possible scales for the side axis in question 1.• Use a ruler.• Read question 2 using the language of chance — probably,

likely, even chance, 50-50 etc.• After working question 3 go through the answers as a class.• Questions 4 and 5 need careful analysis at the end of the

lesson.

Answers for assessment page 371 a Teacher check b Teacher check c sandals

d high heels e Teacher check2 a Teacher check b Teacher check3 2 in 6 chance

35

Sometimes, always, never

Divide the class into 3 groups.

Group A writes something that always happens,group B something that sometimes happens,group C something that never happens.

On the board put these headings:

Always Nearly always 50-50 chanceAlmost never Never

Have children read their happenings anddecide in which column they belong. Allowplenty of class discussion.

Subtraction practice to 20

Do some subtractions orally.

Change the numbers and have childrenquickly write answers.

Repeat this exercise several times.

Hand spans

Have children measure their hand spans tothe nearest 0.5 cm.

Orally predict the range of hand-span sizes inthe class.

On the board make a class tally of thechildren's hand spans.

Hand span bar graph

Use the information from the hand-span tableto make a bar graph. Give the graph a titleand discuss names for the axes.

If class ability allows, let children make theirown bar graph using 1 cm grid paper,otherwise make a class graph on cardboard.Ask the children to pose questions aboutthe graph.

Dice predictions

Give each child a die and have them work inpairs. Ask the children to predict theirchances of rolling a total of 2 or 9. Each pairrolls their dice 20 times and records thenumber of times they totalled 2 or 9. Make aclass tally and follow with a class discussion

Year 2 picture graph

Arrange with the year 2 teacher for the year 4children to do a survey of the pets in year 2.Be careful to survey the pet categories only,not number. eg How many children own fish?

not How many fish are owned by year 2?.Discuss with year 4 the most efficient wayto do this. The year 4 children discuss thetitle, names of the axes and type of keythey will use.

Children could use stickers or magazine cut-outs for the keys or alternatively have artisticchildren draw suitable keys. The childrenmake a picture graph on cardboard andpresent it to year 2. Choose some childrento explain the graph to year 2. Allow year 2children to ask and answer questions aboutthe graph.


Activity Bank


Span Tally Total10 cm 7

6

From 19 –

9 14 7 12


Activity Card 16

36

Chances with Spinners

a Never blue. b Very unlikely chance of blue.

✎ �

c 50-50 chance of blue. b Very likely chance of blue.

d Always blue.

1 Colour the spinners to match the decsriptions.

2 Cut out the spinners.3 Working with your partner

spin each spinner 10 timesand record the results.

a Never

b Unlikely

c 50-50

d Very Likely

e Always

Chances Spins No. of Blue

Compare your resultswith other pairs.�✎


1 This week the shoe shop sold these shoes.

2 Lena made a survey of people on the beach early in the morning.

a Finish her tally table. b Use the tally to make a picture graph.

3 What chance has Rollo of rolling a number of morethan 4 on his die? ______________

Use this information to make a bar graph.

a Write a title.

b Name the axes.

c What shoes sold the second most?

d What shoes sold the least?

e What time of the year might it be?

Why

Assessment Name __________________________________________

Date _____________________________Data and Chance

37

11109876543210

b __

____

____

____

____

_

c _____________________

a _____________________

Sandal

s

High Heel

s

Sneake

rs

School

Shoes

Day Tally Total

Monday 15

Tuesday

Wednesday 20

Thursday

Friday 15

5 5 5

5 5 5 5 5

5

Mon

Tues

Wed

Thurs

Fri

= 10 peopleKey

38

Learning focus• Remind children that whole numbers do not start with zero —

0 is only a place holder.• Write four-digit numbers on the board and have children

read them. The and comes between hundreds and tens,eg two thousand six hundred and three.

• Put 4 digits on the board and give children practice at writingfour-digit numbers. What is the largest? … the smallest? …number closest to? … 10 more than? … 100 less than?

• Point out the digit cards are to be used for all questions.• Before question 3 remind children to put a hyphen between

the tens and ones when writing in words.

Page 41• Ensure the children have lots of practice using the large

class numeral expander.• After completing the numeral expanders have the children

read the numbers orally.

Page 42• Teach the difference between What place? and What value?

eg In 7 615 the 6 is in the hundreds column but its hasa value of 600.

• Remind children about ascending (up) and descending(down) order.

Page 43• Teach abbreviations for all ordinal positions — 1st, 2nd,

3rd etc.• Discuss: What is a marathon? How many people can run?

Page 44• Teach Roman numerals to 20.• Show how they build on 3 like symbols and then a change.• After the children have completed the Challenge discuss their

findings.

Answers for assessment page 411 a Teacher check b Teacher check c 8 730

d 3 078 e Teacher check f Teacher check 2 a Teacher check b 92, 921, 9 2173 a 5 000 + 400 + 80 + 5 b 7 000 + 900 + 20 + 5

c 6 000 + 300 + 14 a 700 b 3 000 c 80 d 15 a 24th b 2nd c 19th, 20th, 21st, 22nd, 23rd

d 9th, 11th

VELS: NUMBER Outcomes and StandardsCounting and Numeration 3.1 Recognise thestructure of whole numbers up to 5 digits,including place value. Mathematical Reasoning 3.1 Generatesmathematical questions from presented dataand from familiar contexts.• Reads, writes and places in order whole

numbers up to 5-digits.• Recognises the structure of whole numbers

up to 5-digits including place value.• Recognises and represents different forms of

the same number.• Orders numbers in ascending order.• Explains position using ordinal numbers.• Recognises simple differences between our

number system and that of an earliercivilization.

Key wordssmallest, longest, digit, thousands, Hindu-Arabic, hundreds, value, position, ordinal,marathon, Roman

Resourceslarge class numeral expander, individualnumeral expanders, blank cards

Additional work sheetsTargeting Maths Middle Primary Numeration and Fractions • Numbers to 9 999 — Unit 2



Four-digit Numbers

39

Counting in 10s and 100s

Have the children count backwards andforwards from a given four-digit numberin 10s and 100s, on and off decades.

What are the numbers between … ?

Expanded notation

Write some numbers in expanded notation onthe board eg 4 000 + 300 + 70 + 5 =

Have a child come to the board and writethe number, then the class says the number.Choose another child to write the numberin words.

Marathon names

Tell, or have children research, the story ofPheidippides the ancient Athenian who ranabout 40 kilometres (the original marathon)to get help from Sparta in the battle againstthe Persians.

Write PHEIDIPPIDES on the board.

Ask ordinal questions. In what position is theH? What positions are the Ps? What letteris in the 12th position?

Elicit the longest names from the classincluding first names. Write them on theboard and ask ordinal questions about theletters.

Place-value Bingo

Ask the children to use the numbers on page40 to write down 3 different four-digitnumbers. Call a number and say a placevalue, eg 2 with a value of 20. 9 with a valueof 900. If the child has the number in theright column they cross it out. The first onefinished calls Bingo and becomes the caller.


Activity Bank


Numeral expanders

One child says a four-digit number andeach child writes it on their own numeralexpander.

Fold the numeral expander to show howmany hundreds? … tens? … ones?

Repeat the exercise many times.

Guessing game

One child writes a four-digit numberand shows the teacher. The others have20 guesses with only 'yes', 'no' answers.eg Does it use a 4? Is the 4 in the thousandsplace? The child who guesses the numberchooses a new number.


✎ �

✎ �Important Four-digit datesThis is the year 2 0 0 ____.

Write: the year you were born.

the year of the last Olympics.

Use the library or Internet to find 3 more importantdates. Write them down.

Choose one to research and tell the class about it.

Year What happened

Activity Card 17

Activity Card 18

40

Choosing CardsWrite the numbers 0 – 9 on 10 blank cards. Ask your partner to shuffle the cards and then you select 4. Write the numbers in the boxes.

Place the numbers to make:

• the largest number possible.

• the smallest number possible.

• the two smallest even numbers.

• the two largest odd numbers.

• the number closest to 5 000.

10 blankcards

Don’t forget to let your partner have a turn.

Assessment Name __________________________________________

Date _____________________________

1 Use these digit cards.

a Make 4 different four-digit numbers.

_____________ _____________ _____________ _____________

b Put the numbers in descending order.

_____________ _____________ _____________ _____________

c Make the largest 4-digit number. _________________

d Make the smallest 4-digit number. _________________

e Make a number between 7 000 and 8 000. _________________

f Write this number in words. _________________________________________________

2 a Write 9 217 in the numeral expander.

b In this number there are:

_____________ hundreds _____________ tens _____________ ones

3 Write these numbers in expanded notation.

a 5 485 = 5000 + 400 + _______ + _______

b 7 925 = ___________ + __________ + _______ + _______

c 6 301 = ___________ + __________ + _______ + _______

4 What is the value of the underlined numeral?

a 2758 _________ b 3064 _________ c 189 _____ d 6621 _____

5 30 snails had a race. On the way 4 went to sleep and 2 ate snail bait and died.Write the position of:

a the snail who came last. _______ b the snail just behind the winner. _______

c the snails between 18th and 24th.

_______ , _______ , _______ , _______ , _______

d the snail just before and just after the 10th. _______ , _______

Four-digit Numbers


8 0 7 3

Thousands Hundreds Tens Ones

42

Learning focus• Talk about buying in multiples from a warehouse.• Discuss how to work out how many boxes would be needed.

We can + or π . Which is easier? Why?• Have a quick tables drill. Remind the children of the π sign.

Page 47• Define strategy. Why do we use strategies? Remind children

of strategies they used in addition (page 7 student pages).Now we'll use some for multiplication.

• Practise doubling numbers around the class.• Explain: 4 = double, double (2 π 2)

8 = double, double, double (2 π 2 π 2) not 6.• Read the fact box with the class. Give extra oral examples

to ensure children all understand.

Page 48• Ensure each child has a sheet of squared paper. 5 mm π 5 mm

is acceptable.• Reteach words factor and multiple — discuss the difference

between them. A factor is a number which can be multipliedwith another number to make a given number. eg 3 π 4 = 12,therefore 3 and 4 are factors of 12.A multiple is any number which can be divided equally byanother number. eg 28 is a multiple of 4. 28 divided by 4 = 7.

• Multiples are infinite in number.

Page 49• On the board demonstrate a written algorithm. Have children

practise on the board.• Revise place value.• Remind children any number π 0 = 0.

Answers for assessment page 451 a 48 b 0 c 30 d 56 e 72 f 28 2 a 6 lots of 9, 54

b 6 + 6 + 6 + 6 + 6, 30 dotsc 7 π 8, 7 lots of 8, 8 + 8 + 8 + 8 + 8 + 8 + 8d 6 π 4, 6 lots of 4, 24 dots, 24

3 a 26, 52 b 60, 120 c 28, 56, 112 4 a 1, 16, 2, 8, 4, 4 b 1, 12, 2, 6, 3, 4 c 1, 18, 2, 9, 3, 6

d 1, 2, 4, 5, 10, 205 Teacher check 6 Teacher check

VELS: NUMBER Outcomes and Standards Applying Number 3.2 Select the appropriateoperations and computation methods tosolve problems involving whole numbers andmoney. Mental Computation 3.2 Use place-valueideas and the properties of numbers andoperations to assist mental computation.• Solves simple multiplication problems in

familiar context.• Uses the properties of numbers to assist

mental multiplication.• Extends multiplication facts.• Selects appropriate operation to solve

multiplication problems.

Key wordsmultiply, multiples, factors, multiplication

Resourcessquared paper (5 mm π 5 mm)

Additional work sheetsTargeting Maths Middle Primary Operations and Number Patterns• Multiplication — Unit 2



Multiplication

43

Double quantities

Double numbers and quantities.

eg Double 40 cm is …Double 23 minutes is …

Proceed to double doubles orally.

If class capabilities allow, encourage childrento convert quantity to next measurement,eg double, double 40 cm is 160 cm

= 1 m 60 cm.

Multiple clapping

The class stands. Say the number 4 and havechildren take turns around the class sayingconsecutive numbers and clapping on themultiples until they reach (4 π 10) 40,eg 4, 5, 6, 7, clap, 9, 10, 11, clap …… 37,38, 39, clap.

Children are out if they clap on a wrongnumber or fail to clap on a multiple. Continuewith new starting numbers. When only a fewchildren are left standing increase the speed.

Beating time

Put a circle on the board withnumbers placed randomly.

Put a number in the box andallow the children 1 minuteto write the answers around the circle. Children stand as they finish. Thewinner is the first finished with all correct.

Repeat with different numbers in the box.

Shop orders

Change the numbers in the boxes on page 46.Make up new shopkeepers and repeat theactivity. Do as a class exercise. Then childrencould change the numbers again and have apartner check their answers with a calculator.

Factor trees

On the board show the children how to writefactor trees, eg

Ask the children to make factor trees with 12,24 … etc. Discuss the possibilities.

Problem numbers

Ask the children to write a problem usinga given number. Give an example, eg usingthe number 8.

John was training for the cross-country.He trained 6 days a week and ran 8 km eachtime. How far did he run in a week?

More capable children could be encouragedto write 2 step problems. eg 5 childrentrained for 6 days a week and ran 8 km eachtime. What was the total number of kms runby the children in a week?

Children exchange and solve eachother's problems.


Activity Bank


9

6 04

17

3

108

25

π

36

49 π

2 π 23 π 3

36

66 π

3 π 23 π 2


✎

✎Moving Numbers

2 π 3 π 4 = 2 π 4 π 3 =

Write these numbers in four more different ways. Work out the answers.

____ π ____ π ____ = ____ π ____ π ____ =

____ π ____ π ____ = ____ π ____ π ____ =

What answer do you get?________Choose three different numbers. Multiply them in six different ways.You may use a calculator. Discuss your results with a friend.

Write the rule.

Activity Card 19

Activity Card 20

Each One Teach One

Choose a number > 2 and < 10. Ask your friends to put the numberin one circle and complete the multiplications.

44

÷ X _

+

÷ X _

+

Make sure everyone has a turn at being the “teacher”.

When they have all finished, use a calculator to mark the answers.

π ___

6 08

49

3

25 7 1

10π ___

6 08

49

3

25 7 1

10π ___

6 08

49

3

25 7 1

10


Assessment Name __________________________________________

Date _____________________________Multiplication

45

1

2 Fill in the spaces.

3 Use doubles to find:

a 4 π 13 b 30 π 4 c 8 π 14

double 13 = _____ double 30 = _____ double 14 = _____

double _____ = _____ double _____ = _____ double _____ = _____

4 π 13 = _____ 30 π 4 = _____ double ____= _____

8 π 14 = _____4 What are the factors of:

a 16? _____ _____ _____ _____ _____ b 12? ____ ____ ____ ____ ____ ____

c 18? ____ ____ ____ ____ ____ ____ d 20? ____ ____ ____ ____ ____ ____

5 Write 5 multiples of:

a 6. _____ _____ _____ _____ _____ b 8. _____ _____ _____ _____ _____

c 5. _____ _____ _____ _____ _____ d 10. _____ _____ _____ _____ _____

6 Write a question: ________________________________________________________________

9 π _____ = Answer 45 fish.

a 8π 6

b 7π 0

c 6π 5

d 8π 7

e 9π 8

f 7π 4

6 π 9 9 + 9 + 9 + 9 + 9 + 9

4 + 4 + 4 + 4 + 4 + 4

5 π 6 5 lots of 6 30

56

a

b

c

d

46

Learning focus• Discuss the names and types of cakes.• Why might Mr Dough want to package his cakes?• How can we do it?• Take suggestions from the children and discuss all possible

ways, eg circles around, using counters etc.• Have concrete materials (counters, centicubes) available

for children to use.

Page 51• Revise ÷ sign. What does it mean?• Ask the children to use the division sign to make a number

story, eg 6 ÷ 2.• For question 2 remind children of the link between division

and multiplication.• For the Challenge stress that there must be an equal number

of monkeys in each cage.

Page 52• When do we have leftovers? Why?• Introduce the term remainder. Is there always a remainder?

When is there no remainder?• Patterns often help in maths. Look at this pattern.

Write 8 ÷ 4 = 280 ÷ 4 = 20800 ÷ 4 = 200

• Build up more patterns, be careful not to use the onesin the book.

Page 53• Introduce . Stress that the answer goes on top. • Work many examples on the board.• Pay particular attention to placing the answer in 2-digit

numbers, eg 7 into 49. 49, not 4 is being divided by 7.• Keep stressing the inverse relationship between π and ÷.

Answers for assessment page 491 a Teacher check, 9 b 6 c 3r2, 5, 6r4, 8r22 a 8 b 7 c 6 d 8 e 1 f 93 a 45 b 60 c 7 d 6 e 36 f 11 g 49 h 8

i 7 j 9 k 8 l 144 a 2, 200 b 5, 50, 3 500, 500 c 48, 480, 6, 4 800, 8005 a 3 b 4 c 4 d 6 e 66 a 13 ÷ 6 = 2r1 b 45 ÷ 7 = 6r3 c 30 ÷ 5 = 6 d 3 π 6 = 18

VELS: NUMBER Outcomes and StandardsMental Computation 3.1 Recall or mentallydetermine basic multiplication and divisionfacts. 3.2 Use place-value ideas and theproperties of numbers and operations toassist mental computation. Number Patterns 3.1 Use rules involvingaddition, subtraction and multiplication todevise, describe, extend and test numberpatterns. Investigation 3.3 Use familiarrepresentations, processes and concepts toexplore unfamiliar tasks and problems.Reasoning 3.2 Make judgments about theaccuracy of reasoning and results.• Mentally determines basic division facts.• Recalls division number facts to 100.• Uses familiar representations to explore

unfamiliar tasks.• Recalls basic division facts.• Identifies simple patterns using division

facts.• Selects appropriate operations to solve

division problems.• Checks answers by using an alternative

approach.

Key wordsdivision, remainder, different ways, divide,division sign, equal groups, left over

Resourcescounters, centicubes, string, class die,calculators

Additional work sheetsTargeting Maths Middle Primary Operations and Number Patterns• Division — Unit 1, Unit 2



Division

47

Tables

Revise and drill multiplication tables. Give a πfact and the children give a ÷ fact,eg 7 π 9 = 63

63 ÷ 7 = 963 ÷ 9 = 7

Also extend to using 10s and 100s,eg 120 ÷ 4.

Game

Child writes down a division fact and thengives the class the answer.

I am thinking of a division fact wherethe answer is 7.

Class guesses the answer using the fullwording each time, eg Is it 42 ÷ 6 = 7? No, it is not 42 ÷ 6 = 7.

String experiments

Give each child a piece of string 75 cm long.If a string 75 cm long is cut into 5 equalpieces, how long is each piece?Ask the children to:a write a number sentence 75 ÷ 5 = .b use the sign. c write on a number line

Ask the children to cut the string into 5 equalpieces and measure each piece.

Please explain

Ask the children to explain different divisionconcepts to the class.

What is a remainder? … fair share? Whatdoes divide mean? How are multiplicationand division related?

As a class compile a list of division wordswith explanations. Make a class display.

Problems

Write a related multiplication and divisionsentence, eg 63 ÷ 9 = 7; 7 π 9 = 63.

Ask the children to write a problem tocorrespond with each sentence. Discuss withthe class.

Follow this activity by giving each childa different multiplication or division sentenceand asking them to write a correspondingsentence and two problems with answerson the back.

Remainder game

Divide the class into groups of approximately5 and give each group 2 normal dice and one10-sided die. One child throws the two diceand the other children write the answer as atwo-digit number in whichever way theychoose, eg 3 and 6 could be 36 or 63. Thesame child then throws the other die andthat number is used as the divisor. So 36 ÷ 7 = 5(r1), and 63 ÷ 7 = 9(r0). Eachchild writes down their remainder. Continuethis until one child has the highest remaindertotal over 20. This child then becomes thedie thrower.


Activity Bank


5 10 15 75


✎

✎

Activity Card 21

Activity Card 22

Division Circles• Finish the division circle. Check your answers

with a calculator.• Choose 2 other divisions for the other circles.• Write multiples of these numbers in the circles.• Give your circles to a friend to work.

48

÷4

24 032

16836

2028 4 12

40

÷ X _

+

Always check answers!

Peanut HuntMrs Monkey sent her 3 children on a peanut hunt. They had to follow theinstructions on their paths. Which lucky monkey ended up with the most peanuts?

_______________

÷ 6

80÷10 π 4

÷ 8+ 10

– 6π 6 ÷ 8

÷ 7

π 9+ 9 ÷ 6

π 9

÷ 9+ 6

49 ÷ 7 π 9– 9 π 4

÷ 6 π 8

35

Hilly

Marvin

Molly

Assessment Name __________________________________________

Date _____________________________

1 Luigi had 54 marbles. a Draw the number he could put in each bagif he divided them equally.

b If he put 8 in each bag, how many would

he have left over? ______

c Write the number, showing any remainders, that he could put in each bag if he had:

20 marbles ______ , 30 marbles ______ , 40 marbles ______ , 50 marbles ______.

2

3 Fill in the boxes.

4 Follow the pattern.

5

6 Write a number sentence and answer. Show the operation you will use and any remainders.

a 24 ÷ 3 = ______

d 64 ÷ 8 = ______

b 63 ÷ 9 = ______

e 7 ÷ 7 = ______

c 24 ÷ 4 = ______

f 45 ÷ 5 = ______

a ÷ 5 = 9

e ÷ 9 = 4

i 21 ÷ = 3

b ÷ 6 = 10

f 55 ÷ 5 =

j 54 ÷ = 6

c 56 ÷ = 8

g ÷ 7 = 7

k 72 ÷ 9 =

d 6 ÷ = 1

h 72 ÷ = 9

l ÷ 2 = 7

Division


a 6 ÷ 3 = ______

60 ÷ 3 = 20

600 ÷ 3 = ______

b 35 ÷ 7 = ______

350 ÷ 7 = ______

______ ÷ 7 = ______

c ______ ÷ 6 = 8

______ ÷ ______ = 80

______ ÷ 6 = ______

a 13 apples were shared by 6 people.How many each?

b 45 lollies were shared by 7 children.How many each?

c The zookeeper had 30 monkeysto put in 5 cages. How manymonkeys in each?

d The zookeeper had 3 pools and put6 seals in each. How many seals altogether?

a 3 9 b 2 8 c 8 32 d 5 30 e 7 42

50

Learning focus• Discuss how we now deal with money ending in 1c, 2c, 3c,

4c, 6c, 7c, 8c, and 9c.• Practise rounding to the nearest 5c. Draw children's attention

to the fact box on p56.• Why do we still have all these cents in the prices of items?

Why did we get rid of 1c and 2c coins?• Why do we need a note larger than the price of the gifts?• What are our notes? Make a list of our notes and coins

on the board.

Page 55• Remind children that they round to the nearest 5c before

calculating change and then count on from the price to workout the change.

• For question 4 remind children that to multiply by 10 we add a 0.• Stress c, (not ¢), $ (not S)• Remind children to use the c or $ sign in answers for questions

5 and 6.• For Challenge remind children to write the money in the

correct hundreds, tens and ones columns before adding.Practise on the board with different numbers.

Page 56• If possible have all the notes and coins for the children

to look at. Also have the Australian play money inequivalent amounts.

• Discuss the people, animals and buildings on the notesand coins.

• Explain question 5. Children name the coins that make theleast possible number, eg 35c = 20c, 10c, 5c.

Page 57• Allow time for oral estimation practice.• Discuss the Charity Collection table before attempting

questions 2, 3 and 4.• Discuss the meaning of total amount and difference.

Answers for assessment page 531 a $4.55, $14.55, $44.55 b $0.50, $10.50, $40.50

c $3.10, $13.10, $43.10 d $7.40, $17.40, $47.40 2 a $5, $1, 50c, 20c, 20c b $5, $2, $2, 50c

c $5, 20c, 20c, 5c d $2, 50c, 10c 3 a $6.89 + $9.50 = $16.39 b $5.45 + $2.62 = $8.07

c $9.50 + $5.45 + $6.89 = $21.84 4 a $4.05 b $1.44 5 a 45c b 70c c 20c d 15c e 35c 6 Teacher check 7 $12.75

VELS: NUMBER and DATAOutcomes and Standards Computation and Applying Number 3.2Select the appropriate operations andcomputation methods to solve problemsinvolving whole numbers and money. Mental Computation and Estimation 3.2 Useplace-value ideas and the properties ofnumbers and operations to assist mentalcomputation. 3.3 Make estimates to checkthe reasonableness of the results of writtencomputation and calculator use. Interpreting Data 3.1 Extract specificinformation from data summarised indiagrams and tables.• Selects appropriate operations and

computation methods to solve problemsinvolving money.

• Rounds money amounts to determine givenlimits.

• Recognises value of given notes and coins.• Uses front end estimation to find

approximate values.• Uses appropriate computation methods.• Extracts specific information summarised in

tables.

Key wordsexact amount, change, round, value,total amount

ResourcesAustralian play money, real coins and notes,catalogues, old magazines, scissors, glue,cardboard, calculators

Additional work sheetsTargeting Maths Middle Primary Numeration and Fractions• Money — Unit 2



Money

51

Money chant

Have children practise rounding moneyamounts and calculating change bydeveloping a chanting pattern.

eg Costs … $6.49

(class) … rounds to $6.50

Change from $10.00?

(class) … $3.50

Doubling money

Call out the cost of an item and have childrencall back the cost of buying 2 items,

eg one pen 55c … two pens $1.10

one book $1.24 … two books $2.50

Remind children of the need to round offto the nearest 5c. If the class ability allows,discuss what the cost would be of buyingthree items.

Writing money

On the board write amounts of moneyas cents. In their workbooks have childrenwrite the cent money in dollars and words,

eg 215 cents … $2.15 … two dollarsand fifteen cents

35 cents … $0.35 … thirty-five cents

Research

Children use the library or the Internet tofind out about one of the people or animalson the Australian coins.

Ask the children to either give a short classtalk or present a poster about their research.

Extension: More capable children couldbe asked to research Australian money priorto decimal currency.

Shopping

Working in pairs children make a poster for ashop — Fruit shop, Shoe shop etc. Childrencut out items from catalogues or oldmagazines and paste onto cardboard. Theyput price tags on the shop items. Unless classability allows, restrict money to prices endingin 5c or 10c.

Have another pair visit the shop and writea shopping list. Both pairs calculate the costof items bought and the change needed fromthe tendered amount. Encourage childrento buy some items in multiples.

If the children agree on the cost and changereverse the process. Otherwise have thechildren check with a calculator beforeproceeding.

Sorting coins

Children make several tracings of the differentcoins and cut them out. Ask them to arrangethe coins by value, size and colour. They canpaste their arrangements into theirworkbooks.


Activity Bank



Activity Card 23

52

Pocket MoneyThe children have been saving their pocket money.

1 Complete the bar graph to show the data.

2 Who has saved:

a the most? ____________ b the least? ____________

c What is the difference? ____________

d What is the total amount saved by the children? ____________

3 Which child has exactly double the money of one other?

________________

4 If two children put their money together they will have as much

as one other child. Who are they?

_______________________ and _______________________.

8

7

6

5

4

3

2

1

AmountSaved ($)

Pocket Money Graph

$5.50

$7.50$2.50$3.00

$6.00 $6.50

✎

Peter Maria Saul

Gabby Tessa Vince

Assessment Name __________________________________________

Date _____________________________

1 Write the change you would receive if you bought the following items from the toy shop.

2 Write the least number of coins and notes you would use to pay the exact amount.

a plane __________________________ b teddy bear ________________________

c doll ____________________________ d paint set _________________________

3 Write an algorithm and answer to show the cost of:

a plane + teddy bear.

b doll + paint set.

c teddy bear + doll + plane.

4 What is the difference in price between:

a the teddy bear and the doll? ________________

b the plane and the doll? ________________

5 Round to the nearest 5c.

6 Join the value to its coin.

7 Hugo had $20. He spent $4.75 and $2.50. What did he have left? ___________

Money


a 47c b 68c c 22c d 16c e 34c

5c

20c

50c

$210c $1

Toy

a doll

b teddy bear

c plane

d paint set

Change from $10 Change from $20 Change from $50

$6.89 $9.50

$5.45

$2.62

a b

Working

c

$5 + $1 +

54

Learning focus• Have coloured interlocking blocks for children to build models.

Each tower represents 10 blocks.• Teach: If 10 blocks = 1, then 1 block =

110 .

• Teach how to write tenths as a decimal.• Ensure that the children have much practice verbally and

visually before working p58.• Revise decimal place value — ones, tenths, hundredths.• Why do we use a decimal point? To separate whole numbers

from fractions. Stress that the decimal point does not havea place-value column.

• Stress writing the point in the middle of the numbers —not on the line. 0.3 NOT 0.3.

Page 59• Have many spare hundred squares for class practice.

Children can work in pairs to colour and record. • Demonstrate the placing of tenths on the number line

and reading places from the number line.

Page 60• Revise < and >.• Give a practical demonstration of

110 =

10100 using MABs.

• Have lots of hands on and board work before doing this page.• Mark and discuss question 2 before starting question 3.

Answers for assessment page 571 Teacher check 2 a 20 b 60 c 30 d 80 e 50

3 a 1.3, 1310 b 2.5, 2

510 c 3.7, 3

710

d 5.1, 5 110 e 5.9, 5

910

4 5.9, 5.1, 3.7, 2.5, 1.35 a = b > c > d < e < f <6 a $2.70 b $8.80 c $4.40 d $9.50

7 a 4 510, 4.5 b Teacher check

VELS: NUMBER Outcomes and StandardsCounting and Numeration 3.4 Use decimalnotation to represent and compare simpledecimal fractions including those resultingfrom calculator computations. Estimation 3.3 Make estimates to check thereasonableness of the results of writtencomputation and calculator use.• Models and names tenths.• Writes decimal notation for tenths.• Writes, compares and orders numbers with

up to two decimal places.• Interprets the results of calculator

computation.

Key wordsfraction, decimal, tenths, hundredths,decimal point, greater than, less than,place values

Resourcesinterlocking blocks, small hundred squares,calculators, class numeral expanders, MABs,blank cards

Additional work sheetsTargeting Maths Middle PrimaryNumeration and Fractions• Decimals — Unit 2


Decimals


55

Tenths practice

How many tenths in 1 310 , 4.7 etc.?

Write the decimal for 6 tenths, 17 tenths etc.

Have the class give oral and quick writtenanswers.

Allow for lots of practice.

Reading and writing decimals

Revise reading decimals — nought pointthree four (not nought point thirty-four);

nought point seven (the same as noughtpoint seven 0).

Write tenths on the board, eg 610 .

Tell children other ways to write it,

eg 6 out of 10, 0.6, 60 hundredths, 60100 .

Allow children practice in writing tenthsand hundredths.

Numeral expanders

Reinforce the relationship between tenths andhundredths by using numeral expanders.

Demonstrate a decimal fraction on MABblocks and ask children to show it on anumeral expander. Repeat many times.

Calculation

Revise the use of the constant factor on thecalculator.

Ask the children to press0.1 + + 0.1 = = = etc.9.9 + + 0.1 = = = etc.2.2 + + 0.5 = = = etc.

Allow children to explore other combinations.Discuss what happens.

Groups of 10

What comes in tens?

Ten flowers in a bunch, therefore 1 flower

is 110 of a bunch.

10 tea bags in a small pack, therefore …

10 decades in a century, therefore …

Build up a list of articles which come in tens.

Ask children to write stories about them.eg My aunty lived for 90 years.

That is 9 decades, or 910 of a century.

Read stories to the class.

Matching circles

Chose a decimal, eg 0.2, and in a circleon the board write it in different ways.

In their workbooks, ask children to makesimilar circles using other decimals.


Activity Bank


0.2

210

2 tenths

20 out of 100

20100

✎ �< = >• On the cards one person writes the fractions

110 ,

210 , up to

910 .

• The other person writes the decimals 0.1, 0.2 up to 0.9.

• Together make the signs .

• Shuffle your cards.

• Take turns to take a card and a sign to put with it, eg .

• The other person takes a card to complete the statement,

eg

• Score 1 point for every correct statement.

• Use all the cards.

0.6>

>

>=<

Activity Card 24

Activity Card 25

Decimal Towers

Look at the towers on page 58.

These towers represent the decimal 3.6.

Use blocks to build it.

Build more towers to represent:

5.7, 6.1, 2.9, 8.6, 4.5, 3.8.

56 © Blake Publishing — Targeting Maths Teaching Guide 4This page may be reproduced by the original purchaser for non-commercial classroom use.

Blankcards

810

810

Assessment Name __________________________________________

Date _____________________________

1 Colour to show the fraction and decimals.

a b c d e

2 How many hundredths have you coloured?

a b c d e

4 Write the decimals in question 3 in decending order.

a b c d e

5 Write to make each statement correct.

7

a 1.8 _____ 1.80d 0.9 _____ 1.1

b 0.9 _____ 0.7e 6.7 _____ 6.65

c 2.8 _____ 2.08f 3.19 _____ 3.2

6

3 Write each position on the number line as a decimal and fraction.

a decimalfraction

b decimalfraction

c decimalfraction

d decimalfraction

e decimalfraction

Decimals


a $ c0 . 60

+ 2 . 10

b $ c6 . 30

+ 2 . 50

c $ c1 . 15

+ 3 . 25

d $ c4 . 35

+ 5 . 15

a Write the blocks as: a fraction. __________a decimal. __________

b Write a story about them.

210 6 out of 10 0.3

810 0.5

1 2 3 4 5 6

< = >

58

Learning focus• Practise ÷ and π numbers by 10 using a calculator.• Read answers, eg one point two seven (not one point

twenty-seven).• Children make up patterns and write them on the board.

The class guesses what pattern was used.• In question 3 decipher the instructions, eg use numbers like

1.1 ÷ 10, 2.2 ÷ 10 or 1.1 π 10, 1.2 π 10 etc.

Page 62• Remind children that patterns can be made by using

any of the four operations (+ – ÷ π).• For question 2 allow use of calculators if you think fit.

Children can work in pairs.• Practise some 2-step patterns on the board. You write

a pattern and class guesses what it is. Encourage childrento write the patterns too.

• Children can use calculators to make patterns more exciting,eg + 4 π 4.

• For Trial and error allow children who worked it out to explaintheir methods to the class.

Page 63• Tell children to observe the + and π signs.• When complete children read their rules. Write the rule(s)

on the board and children write them into their books.• Have children give examples which are written on the board

and worked by the class to verify the rules.

Answers for assessment page 611 a 63.2, 53.2, 43.2, 33.2, 23.2, 13.2

b 11, 12, 13, 14, 15, 16, 172 a 12, 12, 12

b 26, 26, Teacher checkc 84, 84, Teacher check

3 a +4b +10 +9 +8 +7 + 6 etc

4 a 9, 12, 15, 18, 21b 14, 30, 62, 126, 154

5 Teacher check6 a 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

b 6, 12, 18, 24, 30, 36, 42, 48, 54, 60c Teacher check

VELS: NUMBEROutcomes and StandardsComputation 3.3 State equivalencestatements and addition and subtractionfacts involving simple common fractions andcarry out calculations involving tenths andhundredths. Number Patterns and relationships 3.1 Userules involving addition, subtraction andmultiplication to devise, describe, extendand test number patterns. 3.2 Detectsimilarities and differences in the nature ofthe operations of addition, subtraction andmultiplication. Investigation 3.2 Clarify the essentialnature of a task or problem and identify keyinformation in familiar situations.• Adds and subtracts numbers involving

tenths.• Uses a given rule to generate a sequence of

numbers.• Clarifies the essential nature of a task and

identifies key information.• Recognises that addition and multiplication

are associative.

Key wordspatterns, whole numbers, decimals, two-step rules

Resourcescalculators, old magazines, newspapers,distinction award

Additional work sheetsTargeting Maths Middle Primary Operations and Number Patterns• Patterns — Unit 2



Patterns

59

Quick mentals

Have children orally add 3 or multiply by3 starting at different numbers, eg 3 (…5, 8, 11, 14 etc, 3 π (2, 3, 4, 5) etc.

Give mental practice in using the associateproperty, eg 5 π 7 π 2 = 5 x 2 x 7

(10 π 7 = 70); 13 + 16 + 7 = (20 + 16 = 36).

Tables practice

On the board put numbers in a square.Put a π number in a smaller square.

Point to the numbers at random and havechildren give the answers orally.

Change the numbers in the smaller squareand let children take turns at pointing tothe numbers.

2-step patterns

Have children write a 2-step pattern with5 terms on the board. The class guesses thepattern and states the next 3 terms,eg 3, 5, 8, 13, 21ie (π 2 – 1), (π 2 – 2), (π 2 – 3), (π 2 – 4)

Patterns in life

Children make a list of patterns that are usedor occur in real life, eg weather patterns,patterns in nature etc.

They look in old magazines, newspapers etc.to find any patterns.

Discuss patterns found and make a displayfor the classroom.

Associative patterns

Ask children to look at page 63, question 6 intheir books. Discuss the fact that in eachcase two of the ones when added result in anumber ending in 0.

Ask children to make up 10 similaralgorithms. Children then exchange theiralgorithms, work each other's and checkanswers on a calculator.

Tables competition week

On Monday, tell children to practise all tablesfor homework.

Give a tables test with 20 written answerson Tuesday and Wednesday.

On Thursday select 3 - 5 children with thebest scores, and put identical table circleson the board. Time the children in completingthe circles. Change the multiplier severaltimes. The class champion is the one whocorrectly completes the most roundsin the fastest times.


Activity Bank


✎

Triangle PatternsCount the small triangles in each term.

Activity Card 26

Activity Card 27

Calculator Patterns

Check this on a calculator. 1 ÷ 11 = 0.09090909Do these.

Write the rule for this pattern.

Rule

a _____ b _____ c _____ d _____

e How many triangles would be in the next two terms?_____________ , _____________

Challenge!Put in the

triangles forthe next

term.

Rule

2 ÷ 11 =

4 ÷ 11 =

6 ÷ 11 =

8 ÷ 11 =

3 ÷ 11 =

5 ÷ 11 =

7 ÷ 11 =

9 ÷ 11 =


÷ X _

+

An interestingpattern!

✎


1.1 π 10 1.2 π 10 1.3 π 10 1.4 π 10 1.5 π 10 1.6 π 10 1.7 π 10

– 10 – 10– 10 – 10 – 10 – 10 – 10

73.2

Assessment Name __________________________________________

Date _____________________________

2 Complete the patterns.

3 Write the rule for each pattern.a 4 8 12 16 20 Rule:b 5 15 24 32 39 Rule:

4 Write the next five terms in these 2-step patterns.

a Rule 0, 3, 6, ____ , ____ , ____ , ____ , ____

b Rule 0, 2, 6, ____ , ____ , ____ , ____ , ____

5 Make up 2-step rules and write your patterns.

a Rule

b Rule

6 Finish the table.

a

b

c How are the 3π and 6π tables related?

+ 1 π 2

π 1 + 3

a 2 + 4 + 6 = ____4 + 6 + 2 = ____6 + 2 + 4 = ____

b 15 + 7 + 4 = ____7 + 4 + 15 = _______ + ___ + ___ = ____

c 6 π 7 π 2 = ____7 π 6 π 2 = _______ π ___ π ___ = ____

Patterns

61

π

3

6

1 2 3 4 5 6 7 8 9 10

1 Complete the patterns.a

b

62

Learning focus• Discuss the meaning of capacity — the amount a container

can hold.• What measurement do we use to measure milk, water,

soft drink?• Write the word litre on the board (and millilitre if mentioned

by the students).• Children give examples of things measured in litres

(and millilitres). Make a list on the board.• Ask students to name containers holding many litres and

a few litres.• Look at p64. Discuss each item. Ensure the children know

photos are not to scale.

Page 65• Discuss the abbreviations L and mL.• Let children practise writing mL with the gap between

the number and the abbreviation — 6 mL.

• Revise 0.5 = 12 , 0.25 =

14 .

Page 66• Discuss volume as being the amount of space something

takes up.• Why do we measure volume? Give examples of when you

need to know volume.• Questions 3 and 4 could be worked as a class, preferably in

groups.• Ensure children know what to do. If necessary give

a demonstration.• Tell children when using a calibrated measure to look at eye

level (not down) to read the measure. Have water in a clearmeasuring container and allow each child to note thedifference in measurement when reading the measure at eyelevel or looking down or up to it.

Answers for assessment page 651 a bath b teacup c thimble d milk carton2 milk carton would be quickest3 a 3 L b 5 L c 7.25 L4 a 2 500 b 4 500 c 1 2505 a 1 L 600 mL b 4 L 850 mL c 6 L 130 mL6 Teacher check7 a rise to 900 mL b overflow c rise to 600 mL

VELS: MEASUREMENT Outcomes and Standards Measuring and Estimating 3.1 Makeincreasingly accurate estimates ofmeasurements using informal units andstandard units. 3.2 Measure and compareusing appropriate informal units. 3.3Estimate and accurately measure length,mass, volume and temperature using formalunits and standard units. Numeration 3.4 Use decimal notation torepresent and compare simple decimalfractions including those resulting fromcalculator computations. Reasoning 3.2 Make judgments about theaccuracy of reasoning and results. • Makes sensible numerical estimates for

capacity.• Estimates capacity using the litre.• Chooses appropriate formal units for volume.• Records volume and capacity using decimal

notation.• Displays a degree of confidence in estimates.• Compares capacities.• Makes judgements about measurements using

reasoning.

Key wordslitres, millilitres, holds most, holds least,overflow, capacity, volume, calibrated

Resourceslarge clear plastic bottle, 100 mL measure,permanent marking pen, ice-cream containerand larger bowl, 3 objects to fit in an ice-cream container eg a stone, clear container,medicine spoon, class collection of plasticcontainers, medicine glass, standard 250 mLcup, interlocking cubes, plastic cups

Additional work sheetsTargeting Maths Middle PrimaryMeasurement• Capacity and Volume — Unit 2



Volume and Capacity

63

Capacity questions

A cup holds 250 mL. How much will 2, 12 ,

14 cup(s) hold?

The milk carton has 500 mL … 250 mL …750 mL left. What has been drunk?

Obtain quick oral responses.

Encourage the children to pose similarquestions.

Addition practice

Say a number and ask the children to countforwards by another number but not amultiple of the given number, eg 4 + 3 + 3 + 3 etc.

Set a limit, eg stop at the first numberover 60.

Allow oral practice as a class, then proceedwith written responses. Gradually decreasethe time allowed to finish.

The first cup

Tell the children to make a cup with theirhands and carefully tip the water intoa suitable calibrated container, eg a jug.Measure the handful. Alternatively usea medicine spoon (5 mL) to measure outthe water.

Capacity collection

Ask the children to make a class collectionof all the plastic containers they can find.They order the containers in ascendingcapacity. Put containers with the samecapacity behind one another.Discuss the different shapes which holdthe same capacity.

Discuss why we have different sizedcontainers. Why not put salad dressingin a 1.25 L container?

More capacity

Make use of the containers collected in theprevious activity. Have children work in smallgroups. Pose questions.

How many medicine glasses does it taketo fill the 300 mL salad bottle?

How many times could you tip a 300 mLbottle into a 1.25 L soft drink bottle?How much space would be left?

Children estimate their answers and measureto find out. This activity is best outside.

Have children share their experiments withthe class.

The litre

Take a collection of 1 litre containers andcompare their sizes. Do they look the same?

Use a litre measure and check that theyare all correct.

How many cups (a standard is 250 mL)will fill a litre? How many medicine spoons(5 mL)?

Discuss that cups and spoons may vary butthat we do have standard measurements.

For homework children find recipes that usestandard measurements.


Activity Bank


✎

✎VolumeTake 8 interlocking cubes and make an interesting shape.

eg

• Submerge your shape in a container which is full to the brim

and standing on a tray.

• Collect the overflow. Pour it into a clear plastic cup and mask

the level with a permanent marker.

• Change the shape of the 8 cubes several times and mark the level

in the cup each time.

What did you find?

Activity Card 28

Activity Card 29

CapacityCapacityUse a cup — any size. Find 5 containers bigger than the cup.

Estimate thenmeasure howmany of yourcups will beneeded to filleach container.Fill in thechart.


permanent

Container

a

b

c

d

e

Estimated Cups Actual Cups

Assessment Name __________________________________________

Date _____________________________

1

Name the container which holds:

a more than 10 litres.

b about !4 litre.

c about 2 mL.

d 1 000 mL.

2 If you had to fill the bath, which container would you use?

3 Write as litres:

Volume and Capacity


01002003004005006007008009001000mL

01002003004005006007008009001000mL

01002003004005006007008009001000mL

01002003004005006007008009001000mL

a 3 000 mL. _________ b 5 000 mL. _________ c 7 250 mL. _________

a 2.5 L? _________ b 4.5 L? _________ c 1.25 L? _________

4 How many mL in:

a 1 600 mL. _________ b 4 850 mL. _________ c 6 130 mL. _________

5 Write as litres and millilitres:

a 300 mL b 750 mL c 900 mL d 450 mL

6 Draw a line and colour to show the amount.

7 Nick put a stone in container a and the water level rose to 450 mL. If he put thestone in the other containers, what would happen to the water level in:

b?

c?

d?

66

Learning focus• Discuss the patterns.• Demonstrate flip, slide, turn on OHP or board.• Have children use pattern blocks on their desks to flip,

slide and turn identical pattern blocks. Draw the results.• Do all patterns flip, slide and turn? Why?• Tell children that when a shape flips, slides or turns it remains

the same size and shape, but has changed its position.

Page 68• Revise parallel lines, parallelogram and trapezium.• A parallelogram is a four-sided figure where each pair

of opposite sides are parallel and of equal length.• A trapezium is a four-sided figure with only one pair

of parallel sides.• Introduce perpendicular lines — refer to fact note.

Find examples in the classroom.• Remind children of signs: arrows to show parallel lines.

parallel perpendicular

• For Challenge, centimetre grid paper would be useful.

Page 69• Revise 2D names and spelling.• After question 2 have children read their explanations to the

class and discuss.

Answers for assessment page 691 Teacher check2 a hexagon, 6, 6

b octagon, 8, 8 c oval, 1, 0

3 a trapezium b a parallelogram is a four-sided figure where the opposite

sides are equal and parallel4 Circle c, e, g; colour a, f

VELS: MEASUREMENT and SPACEOutcomes and Standards Measuring 3.3 Estimate and accuratelymeasure length, mass, volume andtemperature using formal units and standardunits. 3.5 Use appropriate instruments tomeasure physical quantities. Reasoning 3.1 Make and test simpleconjectures. Shape and Space 3.1 Recognise, describeand represent straight, curved, diagonal,horizontal and vertical lines, and angles asrotations of lines.3.2 Use simpleconventional spatial language whendescribing shapes, parts of shapes, objects,parts of objects and simple cross-sections. • Uses measuring equipment to measure

capacity.• Puts forward assertions about what might

be true.• Measures length using centimetres.• Recognises and describes types of lines.• Recognises and describes 2D shapes.• Describes angles in shapes.

Key wordsflip, slide, turn, parallel lines, perpendicularlines, parallelogram, trapeziums, hexagon,pentagon, octagon

Resourcestransparency for OHP, pattern blocks,centimetre grid paper, 2D shapes,dictionaries, scissors

Additional work sheetsTargeting Maths Middle Primary Space• Space 2D – Unit 1 BLM 1, BLM2, BLM3,

BLM4– Unit 2 BLM6



2D Space

>>

>>

>>

67

Shape guessing

Hold a 2D shape hidden behind a screen (pileof books etc). Gradually lift a small part intoview. Let’s write down all the shapes we thinkthis could be. Choose a child to act asa scribe and put the children's suggestionson the board.

Slowly pull the shape up and ask the childrento eliminate shapes from their list. Discussthe properties of the shape. Hold the shapeat tilted angles to increase difficulty.

Time revision

How many seconds in a minute? How manyminutes in an hour? How many hours in aday? etc.

Have the children give quick oral responses.

Increase the difficulty to How many seconds

in 3 minutes? How many hours in 14 day?

How many days in September and October?etc.

2D patterns

Children use cardboard templates or patternblocks of 2D shapes to make patterns.Encourage them to use flip, slide and turnor a combination to make their patternsinteresting.

Patterns can be pasted onto cardboardto make a class display.

Parallel and perpendicular lines

In small groups (3- 4) children look forparallel and perpendicular lines in theclassroom and playground. Tell them tosketch and label each example. Have childrenshare their discoveries.

Make a class display of the sketches.

Shape word beginnings

Discuss the fact that many shape words havea beginning element (sometimes a prefix)that has a specific meaning, eg poly (many),octa (eight), tri (three) etc.

Children build lists of these words usingdictionaries.

This is a good research extension activity.

Shape facts

On the board make a list of 2D shapes andhave children build up facts about eachshape, eg name of shape; number of angles;types of angles; symmetry; diagonals;anything else of interest.

This could later be written on a chartand displayed in the classroom.


Activity Bank


Activity Card 30


Shape PatternsMake an interesting and attractive pattern using 2D shapes.

Use different shapes together and overlap some shapes.When you overlap colour the new shape you have made.

Cut out your pattern. Pin all the patterns around the room to make a frieze.

�✎

Assessment Name __________________________________________

Date _____________________________

1 Use this shape and:

2

3 a What is this?

b Complete the statement: A parallelogram is

4 Circle the parallel lines. Colour the perpendicular lines.

2D Space


a flip it. b slide it. c turn it.

Shape

a

b

c

Name Number of sides Number of angles

a b c

e f g>

>

>

>

>>

d

70

Learning focus• Revise the four main compass points.• Use a magnetic compass to find north in the classroom.• Find direction of other objects in relation to north.• Have children show left and right hands, ears, feet etc.• Why do we have to know directions? Who uses directions

in their work?• Have children stand and face N … S … E … W. • What is on your left? … right? … to the East? … West? etc.

Page71• Introduce NE … NW … SE … SW.• Write on the board with hyphens — put abbreviations next

to each; south-east (SE)• Point out that N or S always come first (main points).• Have the children point out objects in the classroom

or playground to the NE, SE, SW and NW.

Page 72• Draw grids on the board and label the axes.• Stress the use of the x axis (bottom) symbol first and y axis

(side) symbol second. Point out that they may see maps wherethis does not happen but to be mathematically correct the xaxis number/letter always comes first.

1 2 3Can be labelled in different ways but bottom symbol alwayscomes first.

Answers for assessment page 731 a big sister, mother, b big brother, father

c baby bird, father2 a north, north-east, east, south-east, south, south-west,

west, north-west. b NE, SW

3 a 4A b 2B c 3C d 1D e, f, g, h Teacher checki 1A, 2A, 3A, 1B, 4B, 2C, 4C, 3D

VELS: SPACEOutcomes and StandardsLocation 3.1 Use and understandconventional location language to followand give directions and describe position.3.2 Visualise, find and compare alternativepaths on simple maps, grids and mazes. 3.3Interpret and describe location and directionusing grid references and cardinal compasspoints. • Uses and understands conventional location

language.• Interprets and describes location and

direction.• Uses compass points to describe location

and direction.• Places an object accurately on a simple

grid.• Uses regions on a grid to locate places.

Key wordsposition, north, north-east, north-west,south, south-east, south-west, west,directions

Resourcesmagnetic compass, centimetre grid paper,atlases, school maps with grid lines

Additional work sheetsTargeting Maths Middle Primary Space• Position Mapping — Unit 1



Position

C 2C

B 3B

A 1A

71

Compass positions

In the classroom establish the directionof north. Have the children stand and facenorth. Call out the other compass points andthe children point in that direction. Pointto the south-west etc.

Children sit if they make an error.

To increase the difficulty children canbe asked to turn to face the direction.

Length revision

Revise length measurements. Ask quickand varied questions. eg Change 1 m 10 cmto cm. (110 cm) … decimals. (1.1 m).

Use measurements such as 25 cm, 14 m,

250 mm etc.

Name something approximately 30 cm long(ruler), 2.0 m high (door), 50.0 m long(swimming pool).

Compass findings

In the playground mark the eight compassdirections on the ground in chalk.

Children work in pairs and write down undereight headings (N, NE, E, SE, S, SW, W, NW)three interesting items they find in eachdirection.

Come together as a class to discuss eachpair's findings.

Grid

Children rule up 5 π 5 squares using centimetregrid paper and label the horizontal axis 1-5and the vertical axis A-E. They draw symbols inany 20 of the squares.

Call out the coordinates at random. Childrencross out symbols which are in the squarescalled. The first one with all their squarescrossed out becomes the caller. Tell the callerto mark off each coordinate they call ona blank grid.

Atlas

Ensure that each child (or pair) has a clearlymarked atlas. They find the eight compassbearings for the map.

Choose a town or city which has a fairlycentral location and ask the children to findlandmarks in specific directions. eg Pointto Canberra. What towns would you passif you travelled N? … NE?

Map of the school

Superimpose grid lines on a map of theschool. Give each child a copy.

Ask children to label the verticaland horizontal axes.

Children then find places on the planand give the coordinates.

They write questions about their mapand ask a friend to answer them.


Activity Bank


✎Activity Card 31

What direction does Pirate Pete travelwhen he leaves Ghost Town to go to:

a Treasure Trove? ______________

b Hide-away Camp? ______________

c Dark Forest? ______________

d Skull Lake? ______________

e Stinger Beach Club? ______________

f Shark Bay Wharf? ______________

Which direction would he gofrom Treasure Trove to:

a Spool Cave? __________

b Snake River? __________

Write down some other journeys Pirate Pete couldtake and ask a friend for thedirections.


N

S

ENENW

SESW

W

Snake River

Shark Bay

Wharf

Treasure

Trove

Skull

Lake

Spook Cave

Hide-away CampDark Forest

Stinger Beach Club

Ghost Town

Assessment Name __________________________________________

Date _____________________________

1 These birds are flying south.

a Who is flying to the left of big brother?

_________________

b Who is beside little sister? _________________

mother? _________________

c Who is north of big brother? _________________

south of big brother? _________________

2 Write in the eight compass points.

a

b What is the abbreviation for north-east? ______________ south-west? ___________

3

Position


N

Write the position of the:

Draw:e cherries in 3B.f a lemon in 1C.g a pineapple in 2D.h a peach in 4D.i Name all the blank spaces.

a pear. ________

c banana. ________

b grapes. ________

d apple. ________

D

C

B

A

1 2 3 4

North

South

EastWest

babybig sister

big brother

little sister

motherfather

74

Learning focus• Discuss combinations. Write names of four days on the board.

You can only go to the library on two of the days. Write allthe possible combinations.What is your chance of going on Tuesday and Wednesday?

• Repeat with another combination, eg apples, oranges,bananas, peaches and cherries are on special. Mum buystwo types of fruit. Write all the combinations.

• What is the chance that Mum will buy bananas and peaches?

Page74• Read the possible outcomes. Make up more.• Give some examples. eg Grandad will visit one day next week.

There is a one in seven chance it will be a Friday.There is one in six chance of throwing a 2 on a die.

• Encourage children to make up examples of chance, eg a one in four chance.

Page 75• Revise bar graphs.• Put a bar graph on the board, eg favourite holidays

in 4H — camping, beach, overseas travel, resort. • Do a tally.• Label both axes, give the graph a title. Reinforce the necessity

for the title and labels on all graphs.• Read the table.• When questions 2 and 3 are completed have a class discussion.

Answers for assessment page 771 a red & white, red & yellow, red & black, blue & white,

blue & yellow, blue & black, white & yellow, white & black,yellow & black

b 102 a unlikely b likely c no3 a 1 in 7 b impossible c fifty-fifty 4 Teacher check

VELS: CHANCE and DATAOutcomes and StandardsChance 3.1 Identify and record outcomesfrom simple chance experiments.Interpreting Data 3.1 Extract specificinformation from data summarised indiagrams and tables. 3.2 Describe andinterpret data displayed in simple scaledgraphs. Reasoning 3.1 Make and test simpleconjectures.• Identifies and records all possible

outcomes.• Identifies likely outcomes in simple

experiments.• Extracts specific information from data

given.• Interprets information contained in bar

graphs.• Puts forward ideas about what might be

true.

Key wordscombinations, possible, fifty-fifty,equal chances

Resourcescardboard, BLMs of hexagonal spinners,library books, coins — 5c, 10c, 20c

Additional work sheetsTargeting Maths Middle Primary Space• Chance and Data — Unit 2



Chance and Data

75

Language of chance

Ask the children to finish the sentence:It is probable that …It is unlikely …There is a fifty-fifty chance …

Have a class discussion. Ensure that thechildren understand the difference betweenwhat is probable or likely and what is wishfulthinking.

Quick additions

Write a number on the board and thenin quick succession write other single-digitnumbers on the board. Ask the childrento add mentally and silently as you write.Finish with a ? (question mark). The firstchild to call out the correct answer wins.Gear the speed and difficulty to class ability.

Bar graph

Predict — the number of children in the classwho have a name starting with each letterof the alphabet.Tally — make an A-Z tally.Discuss — the best way to make a bar graph.Do we need to show all the letters? What sort of number scale will work?Name of graph? Name of axes? etc.On cardboard make a bar graph to display inthe classroom.

Lucky book

Elicit the titles of five books that are popularwith the class and that they would like youto read to them. Put the names on the board.Tell the class you are going to choose two toread soon.Each child writes down the two they wouldlike and then work out the chances of gettingtheir choice. Discuss. Read one book. How many children actually got their choice?

Was this about 110 of the class?

What might happen if we did this again? etc.

Spinners

• Working in small groups (3-4) let thechildren make spinners similar to thosein question 3 on page 74.

• Children predict what is likely to happenon each spinner.

• Children spin each spinner 10 timesand keep a tally.What actually happened? Come togetherfor a class discussion.

Chance vocabulary

As a class make a list of all the words thechildren know that are associated with thelanguage of chance. Children could keep thislist in their workbooks and add to it throughthe year. At the end of the year they couldput the words in alphabetical order andperhaps write meanings.


Activity Bank


Activity Card 32

Activity Card 33


✎Heads and Tails

If 2 coins are thrown what are the chances of landing:head and head (HH)? ___ head and tail (HT)? ___ tail and tail (TT)___?Throw the coins 20 times. Write down what happens.

Which result occurred most often? ________________

Will this always happen? _______ Why? _________________________

Throw

1

2

3

4

5

Result Throw

6

7

8

9

10

Result Throw

11

12

13

14

15

Result Throw

16

17

18

19

20

Result

The chocolate blocks come in packs of 3.

On a piece of paper write all the possible combinations there could be.

How many are there? __________

What is the chance of you choosing a pack with

a friend’s 3 favourites? __________

YUM!YUM!YUM!

Dark Chocolate

Milk Chocolate

White Chocolate

Choc-mintChocolate

✎ �

coin coin

Assessment Name __________________________________________

Date _____________________________

1 T-shirts are 2 for the price of one.

a Finish the list of all the combinations you could choose.

b How many combinations are there? _____________2 What are the chances of the spinner landing on:

a green? _____________b red? _____________c Is this a fair spinner? _____________

3 What are the chances of:a my birthday being on a Saturday this year? _____________b throwing 2 dice and getting a total of 14? _____________c the kitten being a female? _____________

4 Cars owned in 4H Cars owned in 4H

a Use the information in the first graph to complete the second graph.b Does one graph tell you more than the other?c Write an easy question about this graph.

d Write a hard question.

Chance and Data


Red and BlueRed and

Holden

Honda

Toyota

Ford

Others

Type

of

car

Number of cars owned2 4 6 8 10

Num

ber

of c

ars

owne

d

Holde

nHo

nda

Toyo

taFo

rdOt

hers

R

R

R R

G G

red bluewhite

Yellow black

Type of car

10

8

6

4

2

Learning focus• Revise the place value in four-digit numbers.• Write four separate numerals on the board, one being 0,

eg 3 081. Ask children to write as many different numbersas possible. Emphasise 0 is a place holder and never startsa whole number.

• Read the numbers on page 78 aloud several times.• Discuss Which is the biggest?…smallest?• Revise ascending/descending order.• For question 3 tell children the number closest to can be

bigger or smaller than the given number. Practise a couple ofexamples on the board.

Page 79• Revise < and > .• Look at back of left hand. Thumb and forefinger form L for

less than. L — Left — Less.• For question 3 remind children of what place and what value.

eg In 9 254 the 9 is in the thousands column but has a valueof 9 000.

• Remind children of placing a space between thousandsand hundreds column, eg 9 254.

• Before question 6 discuss reasonable estimates.

Page 80• Reinforce place names — thousands, hundreds, tens, ones.• Why do we sometimes need to round numbers?• Refer to the fact box. Revise 1, 2, 3, 4 round down to the

nearest 10 — 5, 6, 7, 8, 9 round up.• For Work Backwards tell children to read the whole question

before attempting an answer.

Answers for assessment page 811 a three thousand two hundred and ten

b three thousand and twelvec two thousand nine hundred and nined five thousand two hundred and foure six thousand and forty-five

2 2 909, 3 012, 3 210, 5 204, 6 0453 a 3 012 b 3 209 c 2 910 4 a 3 504 > 3405 b 8 775 > 8 757 c 4 019 < 4 030 5 a 8 000 b 80 c 8 d 8006 a 5 000 b 5 000 c 4 000 d 2 0007 a 8 102, 8 082, 8 192, 7 992

b 2 116, 2 096, 2 206, 2 006, 8 1928 Teacher check9 a T b F c F d T e F f F

VELS: NUMBER Outcomes and Standards Numeration 3.1 Recognise the structure ofwhole numbers up to 5 digits, includingplace value. 3.2 Skip-count by numbers ofincreasing size.• Reads, writes and places in order whole

numbers up to 5-digits.• Recognises place value of numerals in whole

numbers up to 5-digits.• Represents different forms of the same

number.• Understands place value of digits in a 4-

digit number.• Counts forwards and backwards by tens and

hundreds.

Key wordsascending, descending, closest to,rounding off, estimate

Resourcesclass abacus, calculators

Additional work sheetsTargeting Maths Middle PrimaryNumeration and Fractions• Numbers to 9 999 — Unit 2


Numbers to 9 999

78 Targeting Maths Teaching Guide Year 4

Less than or greater than

Write the < and > signs on the board.

Write down pairs of four-digit numbersand ask children to decide which sign to usebetween the numbers.

Choose a child to write the sign.

Say a number and the children write thenumber one more or one less using the signs.

Ascending order

Look at the numbers on the board fromthe preceding < and > activity

Ask the children to sort all the numbersinto ascending/descending order.

Put a ladder on the board and ask thechildren to write the numbers.

Insist the children leave a space betweenthe thousands and hundreds column. Keepthe numbers in correct place-value columns.

Eliminating numbers

Ask the children to enter a four-digit numberon their calculators, eg 6 821. They eliminateone number by changing it to 0. eg toeliminate 8 would require the number to bechanged to 6 021, which is done bysubtracting 800.

Repeat many times, eliminating numberswith different place values.

Guessing numbers

Ask a child to write a four-digit numberon a card. The child chooses a classmateto guess the number.

My guess is 2 781.

No, my number is greater than/less than 2 781.

The game continues until the class guessesthe correct answer.

If this is too time consuming, restrictthe boundaries for the number card,eg between 2 000 and 4 000.

Abacus and calculators

Put a four-digit number on a class abacus.Ask children to enter it in their calculatorsand press the + key. After four entries theypress the = key to find the total.

If correct they score a point. The winner(s)has the highest score after ten rounds.

Listening carefully

Say a four-digit number slowly and clearly butdo not repeat it. Ask the children to write itand then round it to the nearest thousand.

The children then read back their answers.Put the answers on the board.

Repeat this exercise many times.


Activity Bank

79Targeting Maths Teaching Guide Year 4

✎ �

Activity Card 34

Activity Card 35

Calculator ChallengeLook at Challenge on page 79.

Are there any other upside-down numbers that look like letters?

Make as many words on the calculator as you can.

Keep a list.

Who has the most?

�✎÷ X _

+

14

7738335

3704+7

x 5

- 1

+8 -9x2

x3Working BackwardsWhat am I?My thousands digit is 3 more than my tens digit.My tens digit is 2 less than my hundreds digit.My hundreds digit is 7 more than my ones digit which is 1.

I am ____ ____ ____ ____

Write your own ‘What number am I?’Swap with a partner and work out each other’s.


÷ X_

+

÷X_

+


Assessment Name __________________________________________

Date _____________________________

Write each number in words.1 a

bcde

2 Write the numbers in ascending order.

a b c d e

a is closest to 3 000? ____________

c comes after 2 909? ____________

b comes before 3 210? ____________

3 Which number:

a 3 504 _______ 3 405 b 8 775 _______ 8 757 c 4 019 _______ 4 030

4 Use the < and > signs.

a 8 327. _______ b 7 682. _______ c 3 028. _______ d 9 801. _______

5 Write the value of the 8 in:

a 4 689 _______ b 5 327 _______ c 3 508 _______ d 2 072 _______

a people watching a football match? _______ b cents in $20? _______

c friends of Sam? _______ d books in the local library? _______

e mice in the pantry? _______ f days in 10 years? _______

6 Round to the nearest thousand.

a 8 092

b 2 106

____________

____________

____________

____________

____________

____________

____________

____________

10 more 10 less 100 more 100 less7 Write the number:

8 Write a number with:a a thousands digit of 6 and a ones digit of 3. ____________

b a thousands digit of 4 and a ones digit of 0. ____________

9 True or false. Could there be 5 000:

Numbers to 9 999

3 210 3 012 2 909 5 204 6 045

81

Learning focus• Discuss reasons for counting stock.• Ask questions about the stock. Why would there be more

chess sets and telescopes than paint palettes? Accept a varietyof answers.

• Revise number lines and for question 2 tell the children to usenumber lines in their workbooks if necessary.

• For question 3 the children use the setting guide lines.Suggest they can check their answers by using a number line.

• When question 4 has been completed ask how it was done.There will be a variety of answers. Ensure that the childrenaccept that there are many ways to tackle an additionproblem.

Page 82• Much board practice is required. Also demonstrate trading

with MABs.• Give practice in carrying in ones column, carrying in ones

and tens column and carrying only in tens.• Tell the children to put the carry number under the H T O

signs. Encourage children to add down the column — referto “fact box”.

• Allow the children to check the Challenge on a calculator.

Page 83• Discuss estimation. It is not the exact answer. How can we

estimate? Teach how to get approximate numbers to usefor estimating. Start with some easy examples. Never acceptexact answers when children are estimating.

• For question 1 let children use algorithms or number linesin workbooks.

• After question 2 have a class discussion.

Answers for assessment page 811 a Children’s b Gardening2 a 63

b 1253 a 132

b 1834 Gardening and Adult5 a Est 170 Ans 175

b Est 690 Ans 682 c Est 1 000 Ans 984

6 Est 430 Ans 436 km7 Teacher check

VELS: NUMBER Outcomes and StandardsComputation and Applying Number 3.1 Useknowledge of place-value to solve andrecord solutions to addition, subtraction,multiplication and division problems. 3.2Select the appropriate operations andcomputation methods to solve problemsinvolving whole numbers and money. Mental Estimation 3.3 Make estimates tocheck the reasonableness of the results ofwritten computation and calculator use.Investigation 3.4 Use the guess-check-improve process in appropriate contexts.• Uses knowledge of place value to solve and

record addition problems.• Applies appropriate computation methods

to solve addition problems.• Uses front end estimation to find

approximate values.• Selects appropriate computation methods to

solve addition problems.• Makes judgements about the reasonableness

of methods used.

Key wordsgroup, trading, total number, estimate,items, vertical, horizontal, sum

Resourcescalculators, class addition grids, spare paper,class dice

Additional work sheetsTargeting Maths Middle PrimaryOperations and Number Patterns• Addition — Unit 2


Addition


Estimating numbers

Say a number to the children and havethem write the number they would useif estimating.

eg 36. Children write 40.259. Children write 300 (if asked for hundreds) or 260.

Mental problems

Ask the children oral questions and havethem estimate and then give the answer. eg I bought 18 bananas and 24 oranges.

How many pieces of fruit?Estimation — 20 bananas + 20 oranges = 40 pieces of fruit.Answer — 18 + 24 = 42.

How did you do it?Revise the different strategies that canbe used, including + and – compensationstrategy.

Refocusing

Ask the children to look at the work theydid on page 81.

On the board put different, harder numbersfor each item and ask the children to alterthem in their books.

Change the sums for question 4. Ask thechildren to rework the page.

Ask quick workers to find the total numberof all the items and check on a calculator.

Grids

Give out BLM of addition grids.

On the board write 2-digit addendshorizontally and vertically and ask thechildren to write them on their grid.

Read the numbers and ask children to checkthey have written them correctly.

Have the children complete the grid andstand as they finish. The first finished withall correct is the “Addition Champion”.

Problems

Children write an addition problem on a pieceof paper. They work out the estimate andanswer on another piece of paper and thenswap problems with a friend. When both havefinished they check answers. If they disagreethey ask the class to discuss.

Algorithms

Write a 3-digit number on the board, eg 387.Children write down two numbers that willtotal the written number, eg 263 + 124 = 387

Tell them to work out the ones column first,then tens, then hundreds.

Increase the difficulty by telling the childrenthey must use trading in the ones and/ortens column.


Activity Bank


Star PairsJoin the pairs of stars that total .

Activity Card 36

Activity Card 37

�✎

+

+

+

3-digit Dice3 players throw the dice in turn and the fourth player

writes the number made by the dice.

eg = 5 2 3

Repeat and add the two numbers.

Keep adding for 4 turns. Everybody has a turn at adding.

The person with the largest number is the winner.

Do it again. This time the winner is the person with the smallest number.

✎

130 107 47119

72

6566

59

15991216813

69 87 3562

27

4

75

134



Assessment Name __________________________________________

Date _____________________________

1 In the bookshop which type of books are there:

2 Group these books.

a Gardening + Sport = ________________ + ________________ = ________________

b Children’s + Gardening = _______________ + _______________ = _______________

3 Set these out as an algorithm.

a Children’s + Sport

b Children’s + Adult fiction

4 Which two types of books total 114?

5 Estimate the answer, then work it out.

a 82 + 93 Est ___________ Ans ___________

b 295 + 389 Est ___________ Ans ___________

c 421 + 563 Est ___________ Ans ___________

6 Estimate the answer first.

Wendy drove 253 km one day and 183 km the next. How far did she drive altogether?

Est ___________ Ans ___________

7 Write a problem for this estimation and answer. Est – 540 Ans – 546

a the most of? _____________________ b the least of? _____________________

Addition

a Tens Ones b Tens Ones

Gardening 28 Children’s

Books97 Sport 35 Adult

Fiction86

85

Learning focus• Revise factors — numbers that multiply together to give

a product. Remind children that factors are finite.• Revise multiples. Remind children that multiples are infinite.• Practise many examples of factors and multiples orally.

List them on the board.• Point out that some numbers have many factors and

others only 2.

Page 85• Have MAB blocks available for children’s use.• Demonstrate using them to add and to multiply.• Allow class time for practice.

Page 86• Put patterns on the board,

eg 7 π 3 = 2170 π 3 = 210 (3 times 7 tens = 21 tens)700 π 3 = 2 100 (3 times 7 hundreds = 21 hundreds)

Work many with the children.• Teach multiplication as two steps. Write many examples

on the board. Work one at a time in workbooks, correctingas you go, until the children are confident.

Page 87• Define square numbers — refer to fact box.• Look at the patterns at the top of the page. Introduce

indices but only for interest. Write 32, 42 etc.• This is an easy way to write square numbers. Don’t expect

children to use or remember indices at this stage

Answers for assessment page 891 a 1, 5, missing 25

b 1, 2, 3, 10, 6, 5, missing 15, 30c 1, 2, 3, 4, 6, 12 missing 8 d 1, 3, 5 missing 15

2 a 63 b 18 c 64 d 42 e 0 f 20 g 72 h 323 a 268 b 392 c 8374 Teacher check

VELS: NUMBER Outcomes and StandardsMental Computation 3.1 Recall or mentallydetermine basic multiplication and divisionfacts. 3.2 Use place-value ideas and theproperties of numbers and operations toassist mental computation. Number Patterns 3.1 Use rules involvingaddition, subtraction and multiplication todevise, describe, extend and test numberpatterns.• Mentally determines basic multiplication

facts.• Selects appropriate operation to solve

multiplication problems.• Uses rules involving multiplication to extend

patterns.• Uses appropriate computation method for

multiplication.

Key wordsfactors, multiple, product, multiplying,square numbers

Resources calculators, MAB blocks, interlocking blocks,small hundreds squares, scissors, glue,numeral cards 1–9

Additional work sheetsTargeting Maths Middle Primary Operations and Number Patterns• Multiplication — Unit 2


Multiplication


Patterns

Practise multiplication patterns orally, eg 6 π 4 = 60 π 4 = 6 π 40 =

6 π 4 00 = 6 00 π 4 =

This could be a team game between bothsides of the class, one team asking the othera question. If a team answers correctly theyscore a point, if incorrectly the team askingthe question scores the point. The first teamto score ten points becomes the winner.

Square numbers

Ask many questions about square numbers.eg What is a square number larger than 20?… smaller than 40? etc.List the square numbers between 25 and 100.Nine squared? What number squared makes 81?etc. This can be done orally or children canwrite quick answers.

Showing factors

Children work in pairs. Give each pair 24interlocking blocks and ask them to make asmany rectangles as possible using the blocks.They record the dimensions as they go,eg 4 lots of 6 blocks.

On the board record the results undera heading “Factors of 24”.

Repeat this exercise to find the factorsof other numbers.

Factor competition

Look at the factor table in question 2 page85 (student pages).

Put two similar tables on the board.The children form two teams.

Choose a child from each team to fill in thegrid. First finished with all correct, scores ateam point. Repeat many times, changing thenumbers. Keep a tally of the points and dothis activity over a week so that each childhas a turn.

Writing problems

On the board write a problem involvingmultiplication of a two-digit number by aone-digit number. eg The principal gave the7 classes in our school 27 merit awards each.How many did he give altogether?

Ask the children to write their own problemson paper and write the answer on the back.Display them on a board. Have a problemsolving session, making sure every problemis solved.

Square numbers

Give the children a page of small hundredsquares. Refer to question 2 students page87. Discuss. Look at question 3 and ask thechildren to draw the block patterns for 81and 100 in two of the hundred squares.

As an extension activity refer to Challengepage 81. How could you draw the blockpatterns to show a square number between100 and 300? Children to cut out the numberof hundred squares they will need and pastethem together in their workbooks beforedrawing the pattern.


Activity Bank


✎

Odd Numbersand Square NumbersAdding the next odd number makes the next square number.Complete the pattern.

1 + 3 = 4 = 2 π 2 (22)

1 + 3 + 5 = 9 = 3 π 3 (32)

1 + 3 + 5 + 7 = 16 = _________

1 + 3 + 5 + 7 + 9 = ______ = _________

1 + 3 + 5 + 7 + 9 + _____ = ______ = _________

Continue this pattern up to 225 in your workbook.

Activity Card 38

Activity Card 39

Check your answers with a calculator.

43

�

✎ �

÷ X _

+

6 5 9 7

62 84 75 98

Stars and CirclesMultiply each star number by each cloud number.



Assessment Name __________________________________________

Date _____________________________

Number Factors from the bag Missing factors

a 25

b 30

c 24

d 15

1 Choose the factors from the bag which belong to each number.

Multiplication

a 7 and 9? _________

d 6 and 7? _________

g 8 and 9? _________

b 6 and 3? _________

e 9 and 0? _________

h 4 and 8? _________

c 8 and 8? _________

f 5 and 4? _________

2 What is the product of:

3 Complete these algorithms.

a 16 b 36 c 814 Draw block patterns to show these numbers.

a H T O6 7π 4

7 π 4

60 π 4

67 π 4

b H T O5 6π 7

6 π 7

50 π 7

56 π 7

c H T O9 3π 9

3 π 9

90 π 9

93 π 9

Factor Bag

101

4 5 3

126225 30

24 15

89

Learning focus• Discuss fun fairs. Talk about rides and standing in queues.

Look at and discuss the rides shown.• Do all rides hold the same number of people? How can you

work out how many rides/boats/trains etc. before your turn?What operation do you use?

• Read the questions and discuss before the children attemptthem.

• Remind the class of all the ways that division can be shown— especially the sign used.

Page 89• Have lots of oral estimation. Explain strategies — rounding off

to the nearest ten, using multiplication, too big or too littleetc. Insist that the ‘right’ answer is not acceptable as anestimate.

• Read question 4 — These are all different ways of sayingdivide. Make a list and display it as a memory jogger.

• For question 6 explain that the answers are cumulative.

Page 90• As π and ÷ are opposites we can use one to check the other.• On the board demonstrate. 42 ÷ 7 = 6. As 6 π 7 = 42,

the answer is correct.• Insist on written algorithms for question 2. Use workbooks.

Page 91• Demonstrate with MAB blocks and ensure the children have

lots of practice.• Explain carefully with much repetition because understanding

at this stage will prevent difficulties later on.• Demonstrate and allow practice in trading in one ten and

trading in more than one ten.• Have the children work some examples one at a time in their

workbooks. This may take a whole lesson before attemptingpage 91.

Answers for assessment page 931 a 6 b 9 c 8 d 3 2 a 40 b 29 c 533 Teacher check 4 a 7r4 b 48 c 6 d 10r55 a 4r2; check 6 π 4 = 24, 24 + 2 = 26

b 7r2; check 7 π 8 = 56, 56+ 2 = 58c 9r3; check 9 π 9 = 81, 81+ 3 = 84

6 a 31 b 24 c 15 d 12 e 12 f 15g 18 h 16 i 13 j 19

7 Teacher check

VELS: NUMBER Outcomes and StandardsMental Computation and Estimation 3.1Recall or mentally determine basicmultiplication and division facts. 3.2 Useplace-value ideas and the properties ofnumbers and operations to assist mentalcomputation. • Mentally determine basic multiplication

facts.• Makes estimates to check reasonableness of

results.• Uses appropriate computation methods to

solve division problems.

Key wordsdivision, divide, remainders, exchange,trade, estimate

Resources MAB blocks, algorithm photocopies,calculators

Additional work sheetsTargeting Maths Middle PrimaryOperations and Number Patterns• Division — Unit 2


Division


Remainders

Practise division tables with remainders.

What am I? When divided by 6 the answeris 5r2. Answer 32.

Teacher starts and then children can posequestions.

Ways of saying division

Put a division table on the board and askthe class how many ways they can say it,eg 64 ÷ 8 How many 8s in 64?

Share 64 equally between 8.Divide 64 by 8.How many groups of 8 in 64? etc.

Repeat with other division tables.

Algorithms

Prepare photocopies of 2 different sets of 10algorithms similar to page 91 in the studentbook. The children work in pairs, each oneworking a different set. When finished,children check each other’s work. When allthe children have finished, read the answersto the class.

Real-life remainders

Ask children to explain what remainders are.Ask them to give examples of real situationswhere there could be remainders, eg sharingsweets, money etc.

Pose questions. What would you do if you hadto divide: … 50 flowers between 6 bunches?

… 38 birds between 4 cages?

Elicit as many solutions as possible.

Missing digits

On the board put a set of algorithms withmissing digits.

Grade the algorithms from easy to difficult.Give the children time to work them out andcheck their answers. Make sure the algorithmsare within the class ability range.

Game

Ask division tables with remainders, eg 65 ÷ 8 = 8r1.

Children write down the remainders. Afterfive questions children total the remainders.If they have the correct total they scorea point.

Repeat many times. Who has the most points?


Activity Bank


Make your own division and multiplication path.Try to use at least 3 division signs.

Give your path to a friend to work out.

Activity Card 40

Activity Card 41

Finding

Division

Facts

For each number write as many divisionfacts as you can in your workbooks.

eg

30 ÷ 6 = 5

25 ÷ = 55

40 ÷ 8 = 5

35 ÷ 7 = 5

50 ÷ 10 = 5

45 ÷ 9 = 5

✎ � ÷ X _

+


5start with 50

8start with 80

9start with 90

6start with 60

✎Pathways

Help Cyril complete the path.

72 ÷ 9 = ÷ 2 = π 9 = ÷ 4 =÷ 3 =

60 ÷ = ÷ ==

= =

etc.


Assessment Name __________________________________________

Date _____________________________

1 The fruit bowl holds 6 oranges.How many bowls are needed for:

3 Write down 3 different ways of saying 45 ÷ 5.

a

b

c

4 Fill in the boxes.

2 Write the number of bowls needed for:

Division

a 36 oranges? b 54 oranges? c 48 oranges? d 18 oranges?

a 236 oranges. ________ b 172 oranges. ________ c 316 oranges. ________

5 Check your answers.

7 Write a problem where the answer is 49 ÷ 7 = 7.

a 46 ÷ 6 = r

d 53 ÷ = 8r5

b ÷ 5 = 9r3

e 85 ÷ 8 = r

c 73 ÷ = 9r1

f 41 ÷ 7 = r

a6 26

check ________

________

b8 58

check ________

________

c9 84

check ________

________

6

a3 93

f5 75

b2 48

g4 72

c3 45

h6 96

d6 72

i7 91

e8 96

j3 57

93

94

Learning focus• Discuss the terms numerator and denominator —

1 numerator

4 denominator

The 1 stands for 1 part out of 4 equal parts.

• Point out the fraction bar (–) is like the ÷ sign,

eg 23 means 2 ÷ 3.

• Before attempting question 5 discuss What is one whole?If one whole apple is cut into 4 equal parts, then each is

14 .

4 quarters make a whole.

Page 93• Draw different shapes to show the same fraction.

Emphasise that the parts in each shape must be equal.

• After completing question 2 discuss calling fractions by theirsimplest name, eg

24 =

12 .

Page 94• Revise tenths. Remind children of the place values of

decimals — ones (decimal point), tenths, hundredths.

• Revise 210 =

20100 = 0.2

• Draw a number line on the board and have lots of practicebefore attempting question 1.

Page 95• Revise rounding to the nearest whole number.

Remind children that 5 rounds up to the next number.

• Practise orally rounding with tenths and show positionson a number line.

• Discuss rounding with money. Again have lots of oral practice.

Answers for assessment page 971 a 2, 4, 10, 8 b

12 ,

14 ,

310 ,

78

c 12 +

12 = 1,

34 +

14 = 1,

310 +

710 = 1,

78 +

18 = 1

2 Teacher check

3 Teacher check

4 a 12 =

510 = 0.5 b

35 =

610 = 0.6 c

15 =

210 = 0.2

5 a 10 b 1 c 16 d 37 e $7.00 f $5.00 g $2.00

h $12

6 Teacher check

VELS: NUMBEROutcomes and StandardsNumeration 3.3 Represent, find, compare andorder fractional parts of objects andcollections of objects. Mental Computation 3.3 Make estimates tocheck the reasonableness of the results ofwritten computation and calculator use.Number Patterns and Relationships3.3Construct and complete simple statements ofequality involving whole numbers andfractions. • Represents fractional parts of objects.• States addition facts involving simple

fractions.• Represents fractional parts of objects and

groups.• Compares simple fractions and decimals.• States equivalence between fractions in

words and symbols.• Rounds numbers as appropriate.• Rounds decimals to the nearest whole

number.

Key wordsnumerator, denominator, whole, equivalent,rounding, nearest, closest

Resources cardboard 2D shapes, calculators, oldmagazines and catalogues, glue, scissors

Additional work sheetsTargeting Maths Middle Primary Operations and Number Patterns• Fractions – Unit 2• Decimals — Unit 2




95

Denominators

Quick written answers to denominatorquestions.

Write a number with a denominator of 5.

In 34 what is the denominator?… numerator?

What would be the denominator when thereare 3 equal parts?

Rounding

Ask children to round decimal numbers to thenearest whole number, eg 3.2 to 3, 5.5 to 6,3.9 to 4 etc. Include some money questions,eg $7.21 to $7.00 etc.

Answers can be given orally or writtenon the board.

Prices

On the board write 8 prices in dollars andcents. Ask the children to write down theactual prices and total the numbers. Thenask the children to round the prices to thenearest dollar and again total the prices.

What is the difference?

Children may use a calculator if needed.

Equivalent shapes

Divide the class into small groups (3-4).Give each group a set of identical cardboard,2D shapes, eg group 1 — red circles, group 2 — blue hexagons etc.

Give each group a different fraction and havethe group write the fraction clearly on oneshape. The group then writes an equivalentfraction on as many shapes as possible.Make a class display under the headingEquivalent Shapes.

Number line

On the board draw a long number lineshowing eight to ten whole numbers, withten divisions between each whole number.

Say a whole number with a fraction ordecimal, eg 3.4 or 3

410 and have a child place

it on the number line. Ask another child towrite an equivalent fraction above thisnumber, eg 3

25 . Repeat with different

numbers.

Finish this activity by asking the childrento round all the decimal numbers.

Calculator check

Say six decimal numbers, eg 2.4, 3.5, 6.9,8.7, 2.1, 6.4. Make sure the decimals rangefairly evenly from 0.0 to 0.9.

Ask half the class to add the numbers ontheir calculators as you say them. Have theother half round the numbers before adding.Compare the results and have a classdiscussion.

What happened? What does this mean? Whatwould happen with a different set of numbers?


Activity Bank


3 47 62=

✎ �

✎ �

Activity Card 42

Activity Card 43

Rounding PricesLook in magazines, catalogues or newspapers and cut out

10 items with cent prices, eg 68c or $3.89 etc.Paste your items on a sheet of paper.

Choose 5 items from your list and add the prices.Round the prices and add again. Use a calculator.

What happened? __________________________________________

Make another list of items. Give it to another pair to do.

÷ X _

+

Fraction Pattern1 Colour

12 of the pattern red.

2 Colour 110 of the pattern green.

3 Colour 15 of the pattern yellow.

4 a How many squares are left?

_________

b What fraction of the pattern

is left? _________


98c $5.63 82c $7.46

Assessment Name __________________________________________

Date _____________________________

1 a What is the denominator for:

2 Draw lines and colour to show the fraction.

3 On this number line show:

a 12 on top, 0.5 on the bottom.

b 25 on top, 0.4 on the bottom.

c 45 on top, 0.8 on the bottom.

4 Write as a fraction and a decimal:

5 Write to the nearest whole number or nearest dollar.

6 Draw a diagram to show 24 =

48 .

A ? _________ B ? _________ C ? _________ D ? _________

b Write the fraction for the coloured section of each shape.

A _________ B _________ C _________ D _________

c Make 1 whole.

A 12 + 2 = 1 B

34 + 4 = 1 C

310 + 10 = 1 D

78 + 8 = 1

a 12 = 10 = 0. ___ b

35 = 10 = 0. ___ c

15 = 10 = 0. ___

3 12 2 3

4 2 25

a 10.2 _________

e $7.39 _________

b 0.6 _________

f $4.55 _________

c 15.5 _________

g $2.49 _________

d 37.4 _________

h $12.09 _________



A B C D

0 1

98

Learning focus• Have real notes and coins available if possible, for children

to handle and look at.• Discuss value. What is it worth?• Discuss colours, people represented etc.• Does every country have the same money? Discuss.• Before questions 5 and 6 do similar exercises orally.• Have play money available for children to use when working

pages 96, 97 and 98.

Page 97• After question 1 discuss all the possible ways to make the

equivalent coins, eg$3 = $1 + $1 + 50c + 50c or $1 + $1 + 50c + 20c + 20c + 10c etc.

• For question 2 again discuss all the possible coincombinations.

Page 98• Discuss fully why money is rounded to the nearest 5c.• Allow for plenty of oral practice in rounding money to the

nearest 5c and nearest $1.• For Challenge ensure children understand that the cost of the

items is totalled and then rounded, ie don’t round each itembefore totalling.

Answers for assessment page 1011 a 20 b 2 c 5 d 10 2 a 20 b 10 c 40 d 43 Teacher check4 Teacher check 5 a bananas $4, oranges $6, peaches $6

b bananas $4.50, oranges $5.85, peaches $6.25 c bananas $5.50, oranges $4.15, peaches $4.75d $16.58, $3.40

VELS: NUMBEROutcomes and StandardsApplying Number 3.2 Select the appropriateoperations and computation methods tosolve problems involving whole numbers andmoney. Mental Computation 3.3 Make estimates tocheck the reasonableness of the results ofwritten computation and calculator use.• Makes mental and written calculations

involving money.• Solves addition and subtraction problems

including those involving money.• Rounds money amounts to determine given

limit.• Makes mental and written calculations

involving money.

Key wordsvalue, equivalent, change, round, nearest

Resources Australian play money, real coins and notes,dice, calculators, glue, scissors

Additional work sheetsTargeting Maths Middle PrimaryOperations and Number Patterns• Money — Unit 2



Money

99

Rounding money

State an amount of money and ask childrento round to the nearest dollar/nearest5 cents.

Do the reverse. Start with an amount,eg 75c and ask the children to write twoamounts that would round to 75c, suchas 77c, 74c or for $7, children write $6.83or $7.25 etc.

Whole number rounding

Give practice at rounding to the nearest 10,nearest 100.

Introduce rounding of fractions.

eg Is 11

3 closer to 1 or 2?

Coin combinations

Have the children working in pairs. Sayan amount of money and ask the childrento list the coins they could use to make upthe amount,eg 75c — 50c + 20c + 5c or

20c + 20c + 20c + 10c + 5c etc.

List all possible ways.How many combinations are there?Which way used the most/least coins?

Dollar combinations

Similar to coin combinations.

Which ways could you change $100 usingonly notes?

Again list all the combinations and havea class discussion.

Extend this activity to include calculating change. eg I had $100 and spent $45. What notes could I get for the change?, eg $55change – $50 + $5

– $20 + $10 + $10 + $10 + $5 etc.

More spending money

Alter the cents prices in the Super Sale onpage 98 and have the children rework thepage. Allow them to check their answerson a calculator wherever possible.

Ask children to pose different questions andhave the class work the answers. eg Whatwould be the cost of buying 3 spanners andwhat would be the change from $10?

New money

Ask class to design some “new” Australiannotes and coins.

Have a class discussion about who wouldbe suitable people/animals to put on thecurrency. Discuss the shape/size of the notesand coins.

Should we have more/less notes and coins?

Children could work in groups and choosewhich notes/coins they are going to design.

Have the groups present their new moneyto the class.


Activity Bank


✎Activity Card 44

Activity Card 45


�Glue

�÷ X _

+

Rounding GameThrow 2 dice and multiply the numbers.Call the answer cents and round to the nearest 5c.

eg = 3 π 3 = 9c; rounds to 10c.

= 6 π 2 = 12c; rounds to 10c.

Subtract your answer from $5 (500c).$5 – 10c = $4.90.Use a calculator if you need to.Throw the dice 10 times and keep subtracting the money.Let your partner have 10 turns. The winner has the most money left.

✎

Rounding PricesLook in magazines, catalogues and newspapers

to find 8 items with dollar and cent pricesnot ending in 0 or 5, eg $5.78, $2.32 etc.

Paste your items on a sheet of paper. On another sheet of paper round all the itemsand write the change from the nearest dollar.

eg $3.78 — rounds to $3.80.Change from $4.00 = 20c.

Give your sheet to a friend to do. Check your answers together.

$9.54


Assessment Name __________________________________________

Date _____________________________Money

101

1 How many make $100?

a $5 notes _______

c $20 notes _______

b $50 notes _______

d $10 notes _______

2 How many make $2?

a 10c coins _______

c 5c coins _______

b 20c coins _______

d 50c coins _______

a Round each price to the nearest dollar.

bananas ____________ oranges ____________ peaches ____________

b Round each price to the nearest five cents.


c How much change would you get from $10?

d Sarah bought all of them. What did it cost? _________ .

What change did she get from $20? _________ .


3 Make $50 four different ways.

a

c

b

d

4 List 3 ways of making $3.50 from the coins in the box.

a

b

c

5

bananas $4.49 Oranges $5.86 peaches $6.23

FRUIT

SHOP

102

Learning focus• On the board write some numbers, eg 10, 2, 14, 8, 6

and show some combinations, eg 10 π 2 = 14 + 6

14 – 6 = 10 – 214 – 10 = 8 ÷ 2

• After children complete question 1 check the answers. Makesure that they understand that a number can only be usedonce in a combination.

Page 100• Revise sequences. Put some simple sequences on the board,

eg 3, 5, 7, 9… 100, 90, 80, 70…Do the numbers increase/decrease? By how much?How was the sequence formed?

• Before question 2 remind children of the associative propertyof + and π.eg 2 + 4 + 6 = 6 + 4 + 2 2 π 5 π 3 = 3 π 5 π 2

• Encourage children to work out each answer before statingtrue or false.

Page 101• Teach = means not equal to. Work some examples on the board.• Revise meaning of order of term and term.• When question 2 is completed, have a child draw the 10th

term on the board. Let children read their descriptions.• After question 4 ask children to share their patterns with the

class.

Answers for assessment page 1051 a 10 b 8 c 12 2 Teacher check 3 a 1.8, 2.0, 2.2, 2.4, 2.6 b

58 ,

48 ,

38 ,

28 ,

18

4 a T b T c F d F e T f T5 a 2 b 2 c 20 d 4 6 a = b = c = d =7 a 8, 10, 12

b 0 . 0 . 0 . 0 . 0 .

0 . 0 . 0 . 0 . 0 .

VELS: NUMBER Outcomes and StandardsNumber Relationships and Relationships 3.1Use rules involving addition, subtraction andmultiplication to devise, describe, extendand test number patterns. 3.2 Detectsimilarities and differences in the nature ofthe operations of addition, subtraction andmultiplication. 3.3 Construct and completesimple statements of equality involvingwhole numbers and fractions. Investigations 3.1 Generate mathematicalquestions from presented data and fromfamiliar contexts. 3.3 Generatemathematical questions from presented dataand from familiar contexts. Reasoning 3.2 Make judgments about theaccuracy of reasoning and results.• Detects similarities and differences in the

nature of operations.• Uses familiar representations and processes

to explore unfamiliar problems.• Uses rules to extend number patterns.• Obtains a missing number in a number

sentence.• Makes judgements about accuracy.• Uses rules to extend and describe number

patterns.• Relates information in given context to a

similar situation.

Key wordsexpressions, related, sequences, pattern,order of term, term

Resources BLM multiplication circles, blank cards

Additional work sheetsTargeting Maths Middle PrimaryOperations and Number Patterns• Number Patterns — Unit 2



Patterns

103

Completing sequences

Say the first 3 numbers in a sequence andask the children to continue orally,

eg 18 ,

28 ,

38 … ; 1

12 , 3, 4

12 , 6 …;

0.75, 0.70, 0.65 … etc.

Is equal to, is not equal to

Give each child two blank cards. Ask themto put = on one card and =/ on the other.

State two operations and ask the childrento show the sign which should be placedbetween them.eg 6 π 5 and 3 π 10, children show =.

28 ÷ 7 and 5 π 3, children show =/ .

Multiplication practice

Give each child a photocopy of 6 – 8multiplication circles. Tell them a multiplierto put in each circle.

Children stand when they have completed thepage. Check answers and the first finishedwith all correct is the winner.

Alternatively work the circles one by oneand give points to the first three finishedand correct. Total the points at the endto find the winner.

Pattern display

Ask the children to look at question 4 page101. Talk about the patterns that they sharedwith the class.

Ask the children to make another patternshowing the first four terms and put it neatlyon paper. Make a display of all the patterns.Children choose a pattern to complete byadding 5 more terms.

Show the patterns again and have a classdiscussion.

Star numbers

Ask the children to work in pairs and makeStar numbers as in question 3 page 100.

Tell them to make 4 expressions using the4 operations (+ π – ÷).

If ability allows, encourage them to makea “Challenge” star. Have the class work outthe answers.

True statements

Write expressions on the board and askchildren to place the signs to make correctstatements.eg 10 = 40 __ 4 (10 = 40 ÷ 4)

12 = 6 __ 8 __ 4 (12 = 6 π 8 ÷ 4)2 = 4 __ 2 __ 1 (2 = 4 ÷ 2 π 1) etc.


Activity Bank


✎ �

✎Find The PatternsWork out the patterns and complete the tables.

You will need to think hard here!

Activity Card 46

Activity Card 47


Related Numbers

Put any number on the other six members of the card family.The numbers must all be different.

Write as many expressions as you can using the numbers.Put two numbers and an operation sign on each side

Swap with a friend. Check each other’s work. See if you can find more expressions.

of the = ( ).

Mother

1Father Brother Grandma Sister

Aunty Cousin=

+–π÷

+–π÷

Order of term

Term

1

87

2

79

3

71

4 5

55

6 7 8 9 10

Order of term

Term

1

1

2

4

3

9

4 5

16 64

6 7 8 9 10

Order of term

Term

1

1

2

3

3

6 8

4 5

13

6 7 8 9 10


a Look at the pattern to complete the table. b Draw the 10th term.

Assessment

Patterns

105

Order of term

Term

1

2

2

4

3

6

4 5 6

1 Use the numbers to complete.

3 Complete these sequences.

a

b

4 True or false?

2 Write four more expressions using the numbers.Remember to put two numbers and an operation sign on each side of =.

a 8 + 4 = + 2 b 12 + = 10 π 2 c 8 ÷ 4 = – 10

5 What is the value of the star?

a 16 = 32 ÷ ★

★ = _______

b 50 ÷ ★ ÷ 5 = 5

★ = _______

c ★ – 7 = 13

★ = _______

d 8 π ★ π 2 = 64

★ = _______

6 Write or .

7

a 100 – 51 _____ 7 π 6

c 7 + 9 _____ 4 π 4

b 9 π 5 _____ 12 π 4

d 81 ÷ 9 _____ 3 π 3

a 3 π 5 = 5 π 3 __________

c 20 ÷ 5 = 5 ÷ 20 __________

e 5 π 3 π 0 = 4 π 0 π 5 __________

b 14 + 6 + 5 = 5 + 6 + 14 __________

d 27 – 12 = 12 – 27 __________

f 15 + 4 + 9 = 14 + 5 + 9 __________

a _____ = _____

c _____ = _____

b _____ = _____

d _____ = _____

Name __________________________________________

Date _____________________________

84

212

106

1

1.2

88

1.4

78

1.6

68

= =

106

Learning focus• Is it possible to weigh everything in kg? Why not? Discuss.• We need a smaller unit. Does anyone know what it is? • Teach 1 000 g = 1 kg.• Remind children that when writing measurements to leave

a space between the number and measure, eg 700 g— space between the 700 and g.

• Have the children orally name things which are > and < 1 kg.• List items, eg an egg, pepper, sack of potatoes, large dog.

Would we use kg or g to measure the mass of these?

Page 103• Revise 1 000 g = 1 kg. How many g in 2 kg? … 3 kg?

How many kg in 1 000 g? … 2 000 g?

• Discuss 12 kg,

14 kg. What is weighed in

12 kg,

14 kg etc?

How many grams in each?

• Revise 14 =

25100 = 0.25,

12 =

50100 = 0.5,

34 =

75100 = 0.75

Page 104• Teach how to use scales — both balance and dial.• Make sure there are enough scales for each child to be able

to have practice. • Work pages 103 and 104 together so some children are using

the scales (p 104) while others work page 103.• Discuss how objects can be ordered differently by using other

attributes, eg height instead of mass.

Page 105• Have a large calendar to look at with the class.• Read the rhyme in the fact box. Whose birthdays are in months

with 30/31 days?• Whose birthday is on 29th February? Why do we have leap years?• Explain that a year is actually 365

14 days, so to keep moons

and months right an extra day is added every 4 years.

Answers for assessment page 1091 a B, A b A, D, C, B c C, D

d A 3 kg B 110 kg C 1 500 g D 2.5 kge C f Teacher check

2 a 6 kg b 3 kg 200 g c 4 kg 125 g3 a 5 000 g b 2 150 g c 3 750 g4 a 3 kg b 300 g c 2 kg d 3.5 kg5 a Teacher check b 28 days and 29 in a leap year

c Teacher check d 24, 36

VELS: MEASUREMENTOutcomes and StandardsMeasuring and Estimating 3.3 Estimate andaccurately measure length, mass, volumeand temperature using formal units andstandard units. 3.5 Use appropriateinstruments to measure physical quantities.Time 3.1 Estimate short and long periods oftime, describe duration of time, and makeand use timetables, schedules andcalendars.• Measures and compares mass using

appropriate formal units.• Estimates mass using formal units.• Uses appropriate instruments to measure

mass.• Uses calendars to locate dates.• Relates time facts to each other.

MS2.5 Reads and records time in one-minuteintervals and makes comparisons betweentime units.• Relates time facts to each other.

Key wordsattribute, heaviest, lightest, weigh, kilogram,gram, calendar

Resources balance scales, dial scales, objects of varyinggram mass, large calendar,1 cm grid paper,gram labels from jars and boxes, scissors,glue

Additional work sheetsTargeting Maths Middle Primary Measurement• Mass — Unit 2



Mass and Time

107

Grams and kilograms

Ask gram questions and elicit quickoral responses.

How many grams in 3 kg? … 3 12 kg?

… 3.5 kg?

How many kg in 2 000 g? … 2 750 g? Which is heavier — 1 520 g or 1.5 kg?

Time

Ask children to tell all the facts theyknow about time. Put a list on the board,eg 60 seconds in 1 minute; 365 days in ayear etc. Include any the children suggest, eg2 weeks equals 1 fortnight, 10 years equals1 decade etc.

Make a chart to display in the classroom.

Guessing weights

Ask the children to bring an object from home(maximum 2 kg), whose mass they think willbe hard to guess, eg a small but heavy pieceof wood, a golf ball etc.

The children:(a) look at the object and guess the mass.(b) heft the object and estimate the mass.(c) weigh the object and note the mass.What was the hardest object to guess?Were you close in estimating? etc.

Ordering mass

Use the objects from the previous activityand arrange them in order from lightestto heaviest. Children can find other objectsin the classroom that they think have thesame mass as some of the ones on display.Ask questions. Which two objects togetherweigh the same as the wood? What is thedifference in mass between the lightestand heaviest? etc.

Bar graphs

Gather 6 – 8 objects with masses from 50 gto 1 kg. The objects need to have exact 50 gor 100 g masses, eg 150 g, 700 g etc.

Discuss how to make a bar graph using thisdata.

Name of the graph? How will we label thehorizontal and vertical axes? How will wemark the axes? etc.

Make a class graph on the board or if capablethe children can make their own graphs using1 cm grid paper. Have them make upquestions about the graph.

Research

Use the library or the Internet to research theorigins of the days of the week and monthsof the year, eg January — named afterJanus, the Roman deity with two headslooking both ways. Thursday — named afterthe Scandinavian God of Thunder who wieldsa great hammer.

Children could work in groups and choosehow to present their information, eg a brieftalk, display chart, short play etc.


Activity Bank


✎ �

Activity Card 48

Activity Card 49

Mass in GramsLook at home to find jars and packets of items

with their mass written in grams.

Make a collection of as many different labels as you can.

Order the labels from the lightest to heaviest.

Paste the labels onto a sheet of paper.

Make a display.


Glue�

Leap LandIn the land of Leap babies are always born on the29th February and have a birthday every four years.The twins, Lottie and Lexie, were born in 1992.

In what year:

was their first birthday? ___________

will they be five and go to school? _____

Draw the twins celebrating their 20th birthday. What will they look like? What games will they play? What food will they eat?

Lottie Lexie


Assessment Name __________________________________________

Date _____________________________Mass/Time

109

1 a Which box is the lightest? ______ heaviest? ______

b Order the boxes from heaviest to lightest. ______ ______ ______ ______

c Which two boxes together weigh 2 kg? ______ ______

d What would 2 of each weigh?

A ______ B ______ C ______ D ______

e Which box weighs more than half a kilogram but less than 1 kg? ______

f Give reason why A might be heavier than D.

2 Change to kilograms.

a 6 000 g _______ kg

c 4 125 g _______ kg _______ g

b 3 200 g _______ kg _______ g

d 1 090 g _______ kg _______ g

a 5 kg _________ g b 2 kg 150 g _________ g c 3.75 kg _________ g

3 Change to grams.

A B C D

a b c d

4 Write the mass of each object.

5 a Write your birthday month in full.

b What is special about February?

c Is this a leap year? __________

d How many hours in: 1 day? __________ 1 12 days? __________

A B C D

1.5 kg 1.25 kg55 g 750 g

8

4 500g

17

3

kg1kg

56 2

4

2

kg3 1

4 kg

2

3 1

110

Learning focus• Discuss patterns. What makes a pattern? Point to some

patterns in the room.• Discuss tiling and other patterns which use symmetrical

shapes. • Have some large shapes prepared on coloured paper. Ask some

children to fold these on the line of symmetry in front of theclass. NB Include some shapes that are not symmetrical.Introduce the word asymmetrical.

Page 107• Have all the capital letters displayed in the classroom,

A B C D … etc.• Refer to the fact box and teach axis of symmetry, and the

plural axes.• Encourage use of mirrors to either complete or check the

patterns in question 1.

Page 108• Look at tiling patterns and define what makes a tessellating

shape — identical shapes which fit together without overlapsor spaces. Some triangles tessellate but circles do not.

Page 109• Have 4 cm squares of cardboard prepared — could be done in

another lesson.• Ensure each desk has access to sticky tape and each child has

a pair of scissors.• Start with a very simple shape as a practice,

eg

• Capable children can cut from top and side.

Answers for assessment page 1131 a Teacher check

b B, D 2 Teacher check3 B, C, D, E4 Teacher check

VELS: SPACE Outcomes and StandardsShape and Space 3.2 Use simpleconventional spatial language whendescribing shapes, parts of shapes, objects,parts of objects and simple cross-sections.3.6 Copy and create simple patternsinvolving translating, rotating and reflectingmultiple copies of a shape and informallydescribe the transformations used. 3.7Identify symmetry in regular two-dimensional shapes. Investigation 3.3 Use familiarrepresentations, processes and concepts toexplore unfamiliar tasks and problems.• Uses simple conventional spatial language.• Identifies symmetry in 2D shapes.• Draws lines of symmetry.• Completes a symmetrical pattern on a line

of symmetry.• Decides if a shape will or will not tessellate.• Draws tessellation patterns. • Constructs a tessellating shape to make a

pattern.• Chooses and uses relevant processes.

Key wordssymmetrical, line of symmetry, axis (axes)of symmetry, tessellate, tessellating shape

Resources mirrors, 4 cm squares of cardboard, scissors,sticky tape, magazines, scrap dress materials,M. C. Escher references, pattern blocks,grid paper

Additional work sheetsTargeting Maths Middle Primary Space• Transformation and Symmetry – Unit 2


2D Space


111

Revision of measurement

Revise length — mm, cm, m and perimeter,

eg 1 cm = 1100 of m.

2 m 36 cm = 2.36 m. Perimeter of blackboard?etc.

Revise volume and capacity. 1 000 mL = 1 L,

250 mL = 14 L,

14 L = 0.25 L etc .

Include estimation. How many cups to fill a1 litre jar?

Symmetry search

Look for symmetrical shapes in the classroomand playground.

What objects have you used today thatare symmetrical?—clock face, tennis ball,scissors etc. Brainstorm and make a liston the board.

Tessellations

Look at magazines, wallpaper samples, olddress materials etc. to find tessellatingpatterns. Ask children to look at home andmake a copy of tessellating patterns to bringto school. Make a collection of all thesetessellations to display in the classroom.

Tessellating shape

Repeat the activity on page 109.

Encourage the children to make as difficulta shape as they are able. Have childrentessellate their shape on art paper andmake a classroom display.

Before this activity do a library searchand introduce children to the work of M. C.Escher, a Dutch graphic artist (1898-1970).Look at his work for inspiration intessellating.

Symmetrical names

Look at all the capital letters and discussletters which are symmetrical.

Ask the children to write their names in largecapitals on a piece of paper. Children thendraw in all the axes of symmetry they canfind in their names.

Who has the name with the most symmetricalletters? Does anyone have no symmetricalletters?

Pattern blocks

Children work in small groups and usethe pattern blocks to create tessellatingpatterns. Ask them to draw their patternson grid paper.

Make a display of the patterns.


Activity Bank


Tessellating ShapesStart a tessellating pattern in the grid. Ask a friend to complete it. Colour it.

Activity Card 50

Activity Card 51

Symmetrical PicturesPut an axis of symmetry in the space and draw half a picture

on the axis of symmetry. Ask a friend to complete it.

Use patterns and colour to make your picture attractive.


✎

✎

Assessment Name __________________________________________

Date _____________________________

1 a Draw in all the axes of symmetry.

b Which of the shapes are not symmetrical?2 Complete to make symmetrical drawings.

A B C D

3 Colour the shapes which will tessellate.A B C D E

a b

4 a Finish this tessellating pattern. b Draw your own tessellating pattern.

2D Space


114

Learning focus• What is an outcome? Revise.• Point out that there are sometimes many different ways

to do the same thing. Have children suggest some instances.You can paint a wall from side to side or from the ceilingto the floor.

• How can John walk to my desk? How can you walk home?Is one way the correct one? Which is the shortest? etc

• Do we need to know all the possible outcomes in orderto choose the best? Discuss.

Page 111• Revise tally marks – groups of 5. Remind children that the 5th

mark crosses the others and makes a bundle so we can countin fives.

• Discuss how to conduct a survey. Who will we survey?What questions will we ask? How will we record the results?

• Ensure the children understand the need to ask a cross-sectionof people and why.

• Discuss the survey.• Revise bar and picture graphs (need not be a picture

— can use a symbol, eg ✦ = 2).

• Let children choose the type of graph even though a bar graphwould be easier in this instance.

Page 112• What could the graph be about? List some ideas.• Talk about asking “good” questions – give some examples.

(Must be possible from the data; some to make youthink hard.)

• Revise labels, axes etc.

Page 113• Read the table together with the class. Why are the questions

split into boys and girls?• Before attempting the picture graph ensure class knows the

need for two symbols in the key to show boys and girls.

Answers for assessment page 1171 a Teacher check b 4 c 6 2 a boys-black 8, white 0, red 6, green 2,

girls-black 1, white 3, red 7, green 3b 30 c black, red d 9, 5

3 Teacher check

VELS: NUMBEROutcomes and StandardsLocation 3.2 Visualise, find and comparealternative paths on simple maps, grids andmazes. Reasoning 3.2 Make judgmentsabout the accuracy of reasoning and results.Posing Questions and Collecting Data 3.1Identify information required to answerquestions or test conjectures, refining thequestions where necessary. 3.3 Modify themethod of data collection and classificationto refine a question or investigate a furtherquestion. Presenting Data 3.3 Use graphical methodsinvolving scale to display discrete andcontinuous data. Interpreting Data 3.1Extract specific information from datasummarised in diagrams and tables. 3.2Describe and interpret data displayed insimple scaled graphs. Investigation 3.3 Use familiarrepresentations, processes and concepts toexplore unfamiliar tasks and problems.• Finds alternate paths on simple maps.• Makes judgements about the accuracy of

reasoning.• Identifies information needed.• Uses graphical methods to display data.• Interprets information.• Clarifies questions to decide what data is

collected.• Uses familiar representations to explore

unfamiliar tasks.• Extracts specific facts from a table.

Key wordsdifferent, outcomes, likely, unlikely, survey,interpreting, data

Resources coloured pencils, clip boards

Additional work sheetsTargeting Maths Middle Primary Space• Chance and Data – Unit 2



Data

115

Multiplication competition

Divide the class into four teams and put fouridentical multiplication wheels on the board.One child from each team completes a wheel.The first finished, providing they are correct,scores a team point. Change the numberin the centre and repeat until everyonehas a turn.

Place value revision

Prepare ten numbers. Give the class placevalue instructions, eg this number has 3in the tens place, 0 in the hundreds place,4 in the ones place and 7 in the thousandsplace. The children then write the numberdown. When the exercise is completed askdifferent children to read the answers back.

Class survey

Survey the class on a suitable topic,eg school lunches.

Who has sandwiches, pies, salads, pita bread,rice …? etc.

Make a list of the class lunches on the boardand use tally marks to show the number.

Ask questions. Is it a good sample?What would happen if we surveyed the wholeschool? … another school? etc.

Different paths

Pose questions about different paths thatcould be taken around the school.

How many ways to the principal’s office? …oval? … year 2? etc.

Which is the shortest? … easiest? … bestin wet weather? etc.

Extend to possible ways to walk home,to walk to the shops etc.

Group survey

Organise the children into small groups (2-3).They conduct a survey on a topic of their ownchoice, eg favourite desserts, best TV shows,most popular sport etc. Encourage children tochoose something that interests them.Children plan how to conduct the survey.

Who are you going to survey? … our class?… boys only? … another class? … adults?Will you ask people orally? … give outa questionnaire? How will you keep a tally?… write up a table?

Children collate the data and have a classdiscussion about their results.

Group graph

Following the group survey the childrenpresent their data in a graph. They discussthe type of graph they will use and how theywill do it.

Ask them to present their graph neatlywritten on a piece of paper and to writesuitable questions about the graph. Displaythe graphs and have a class discussion.Allow constructive criticism. Children canswap graphs and work each other’s.


Activity Bank


✎

Mystery Graph

Activity Card 52

Activity Card 53

Shopping

Bruno and his mother went to the mall.They needed to visit the Pet Shop, Sport Shop, Hair Salon and Pharmacy. They didn’t care in which order they went

to the shops but wanted to start and finish at the Pet Shop. Use different colours to show the ways they could go.

Each draw a mystery graph. Swap. Make up 6 questions, a title and label the axes for your friend’s graph.

✎


Bank

Dress Boutique

Sport’s Shop

Pet Shop Cafe Pharmacy Shoe Shop

Supermarket

Hair S

alon


Assessment Name __________________________________________

Date _____________________________

a Fill in the totals for boys and girls.

b How many children are in the class? ______

c What is the most popular sock colour with boys? __________ with girls? __________

d How many children chose black? ______ green? ______

3 Use the data from question 2.a Give the graph a title.b Label the axes.c Choose colours for the key and

complete the graph.d Make up a question about the graph.

Key: boys girls

Chance and Data

117

Sock colours

Black

White

Red

Green

Tally for boys Total Tally for girls Total

1 a Start at A and show all the ways you can go to B. You must pass through the triangle every time. Use a different colour for each path.

b How many paths did you find? ________

c Draw another path from A to the triangle. How many ways from A to B now? ________

2 Year 4 surveyed their favourite sock colours.

5 111

5 1

11

1

111

5 11

111

109876543210

black white red greenB G B G B G B G

BA

118

Learning focus• Construct a spelling list of difficult words, eg forty, eighty etc.• Remind children to only use “and” between the hundreds

and tens.• Put a list of four-digit numbers on the board and have

children practise saying them.• Revise place value of four-digit numbers.• Read the stories with the class before they attempt

to link them.• After completing page 116 have the children read back all the

numbers to ensure plenty of practice in reading numbers.

Page 117• Discuss zero. What place does it have? Why is it used?• Talk about our number system – the Hindu-Arabic devised from

the Hindus and Arabs – the only system to use zero.• Put a place-value chart on the board and practise writing

numbers in it.

Page 118• Discuss strategies for estimating. Look at the number line.

Where is 12 way? What is

12 way between 0 and 10 000?

What is 12 way between 3 000 and 9 000? etc

• Practise stories about numbers orally. eg Write 2 074 on theboard and say the story Farmer Jones owned 2 074 sheepor I counted 2 074 peanuts in the large bag.

Answers for assessment page 1211 a 95 b 1 542 c 6 270 d 6 3022 Teacher check3 a 5 362 b 1 4204 a 8 430 b 3 048 c Teacher check d Teacher check

e Teacher check f 4 830 or 4 8035 Teacher check6 a 501 b 5 039 c 7 007

VELS: NUMBER Outcomes and Standards Numbers and Numeration 3.1 Recognise thestructure of whole numbers up to 5 digits,including place value. Number Patterns 3.3 Construct and completesimple statements of equality involving wholenumbers and fractions.• Reads and writes whole numbers up to

5-digits.• Recognises structure of whole numbers up

to 5-digits.• Demonstrates knowledge of place value.• Places, in order, whole numbers up to

5-digits.• Generates equations for specific numbers.

Key wordsfour-digit, place value, more than, less than,even, odd, position

Resources newspapers, magazines, old telephone books,blank cards, calculators

Additional work sheetsTargeting Maths Middle PrimaryNumeration and Fractions• Numbers to 9 999 – Unit 2



Numbers to 9 999

119

Spelling number words

Revise the list of difficult number words.

Play spelling guessing games. I am thinkingof a number word. Are you thinking of forty – F-O-R-T-Y? No, I am not thinking of forty, F-O-R-T-Y.

Child who guesses and spells the wordcorrectly picks a new word to ask the class.

Writing four-digit numbers

Say four-digit numbers slowly and clearlyto the class. Have the children write thenumbers in the correct value columns as theyare said. Be sure to include zero.

Four-digit number search

Ask the children to find four-digit numbersin newspapers and magazines. Each childchooses one and tells the class a storyabout it.

Make a display of the numbers and discussplaces where we often see these numbers,eg sporting events, theatre etc.

Numerical order

Ask the children to bring some old telephonebooks or catalogues. Have the children workin small groups. Tear pages out in sectionsand shuffle them randomly. Ask the childrento put them in correct numerical order.Children can then re-shuffle and repeatthe exercise.

Children can also estimate how many namesin a column, how many on a page etc.

Number line

Put a number line, starting at 0 and endingat 10 000, on the board. Put five marks alongthe line and ask the children to estimate thevalue of each mark. Have a class discussion.Select several children to put extra markson the line and the class estimates the value.Ask questions about the number line.eg Which card is closest in number to 8 000?What is the difference in number betweenthe 2nd and 3rd cards? Write the numbersin ascending order. Put the numbers ona place-value chart etc.

Card numbers

Give each child a set of blank cards andask them to write the numbers 0-9 on them.Say four-digit numbers and ask the childrento make them. Ask questions about the placevalue of different numbers.

What is the value of the 6? What number isin the tens column? The cards can be usedfor many activities. eg Write thesmallest/largest number possible; write anumber between 3 070 and 4 000; a number10 less than/100 more than 5 999 etc.

Children can also hold up a four-digit numberand ask another child to tell a story about it.


Activity Bank


✎

✎Choosing NumbersChoose numerals to put in the boxes.

Write your number. ________

Choose another four numerals. , , ,

Write the largest number. ______ Write the smallest number. ______

What is their difference? _______

Total your numbers. __________ + __________ = __________

Estimate a number halfway between your numbers. _______

in the hundreds, in the ones, in the tens,

in the thousands.

Activity Card 54

Activity Card 55

Mountain Climbing

The climbers can rest when they see signs which say they have climbed these distances:

Start

Write the signs at the correct places on their climb.


÷ X _

+

3 000 m 500 m 9 750 m 710 of the way

13 of the way

34 of the way

110 of the way

12 way

10 000 m


Assessment Name __________________________________________

Date _____________________________

1 Write these numbers correctly on the place-value chart.

a ninety-five

b one thousand five hundred and forty-two

c six thousand two hundred and seventy

d six thousand three hundred and two

2 Write a story about each number.

a b

3 What number is this?

a 6 in the tens, 5 in the thousands, 2 in the ones, 3 in the hundreds. __________

b 2 in the tens, 4 in the hundreds, 1 in the thousands. __________

4

Use these numerals to write:

a the largest number. __________ b the smallest number. __________

c a number less than 4 000. __________ d a number more than 8 000. __________

e an odd number. __________

f a number between 4 500 and 5 000. __________

5

Draw cards on the line to represent:

Numbers to 9 999

121

4 3 0 8

2 003 6 400

a 2 500 b 9 990 c 700 d 5 000 e 8 000

6 Write these numbers with zeros in their correct places.

a five hundred and one

b five thousand and thirty-nine

c seven thousand and seven 77

539

51

0 10 000

TH H T O

122

Learning focus• Ensure each child has a calculator.

Practise ÷ on the calculator.• Make sure the children start at the number 4 in question 2.• What are we looking for? (multiples of 2, 3, 5 etc.)

How do we find them? (by ÷).• Remind children of the link between ÷ and π — they are

inverse operations.

Page 120• If you think it necessary allow the children to use a calculator

for question 1.• Revise the term factor.• Introduce the terms prime and composite. Read the fact boxes.

Give plenty of practice at finding primes and composites usingeasy numbers.

• Highlight the number 2. Two is the only even prime number.Why?

Page 121• Revise 3-digit π 1-digit multiplication on the board.• Tell the children to use their workbooks to write the algorithm

for question 2.

Page 122• Put many estimation examples on the board and allow the

children to practise orally. Ask yourself if your answer is silly.• STRESS that the exact answer is not an estimate.• Keep pointing out how to find multiples.

To find if π is a multiple of y we divide π by y.

Page 123• Point out that the problems involve mixed operations.

Children must decide what to use.• Tell the children to write the operation sign in the box

and if they need more space for the algorithms to usetheir workbooks.

Answers for assessment page 1251 a, b, c, d Teacher check e 13, 17, 19, 23, prime2 a 1, 26, 2, 13 b 1, 29 c 1, 28, 2, 14, 4, 7

d 1, 54, 2, 27, 3,18, 6, 9 e 1, 32, 2, 16, 4, 8 f 1, 313 a 20 b 63 c 0 d 64

240 210 540 3201200 700 2400 16001460 973 2940 1984

4 a 40 ÷ 4, est. 10 b 100 ÷ 5, est. 20 c 90 ÷ 3, est. 30d 90 ÷ 9, est. 9

5 a 10r3 b 19r1 c 29r1 d 10r76 a ÷ 7 days b – 185 m

VELS: NUMBEROutcomes and StandardsNumeration 3.1 Recognise the structure ofwhole numbers up to 5 digits, includingplace value. Mental Computation 3.1 Recall or mentallydetermine basic multiplication and divisionfacts. 3.3 Make estimates to check thereasonableness of the results of writtencomputation and calculator use. Number Relationships 3.2 Detect similaritiesand differences in the nature of theoperations of addition, subtraction andmultiplication. Computation and Applying Number 3.2Select the appropriate operations andcomputation methods to solve problemsinvolving whole numbers and money.• Recognisies the structure of whole numbers.• Uses a calculator to determine divisibility.• Recalls multiplication facts up to 10 x 10.• Determines whether a number is prime or

composite.• Uses written computation methods to solve

multiplication problems.• Estimates results by rounding numbers to

the nearest ten or hundred.• Selects appropriate operation and

computation methods to solve problems.

Key wordsprime number, composite number, multiples,factor

Resources calculators, dice, spinners, coloured pencils

Additional work sheetsTargeting Maths Middle PrimaryOperations and Number Patterns• Multiplication – Unit 2• Division – Unit 2



Multiplication and Division

123

Composite or prime

Ask the class to stand. Start at 1 and goround the class saying consecutive numbersand whether they are prime or composite,eg 5 prime, next 6 composite. If wrong thechild sits down. When the numbers becometoo high start again at 1.

Multiplication and division link

Write three related numbers on the board,eg 8, 72, 9. The children write π and ÷ factsusing these numbers, eg 8 π 9 = 72; 72 ÷ 9 = 8; 9 π 8 = 72, 72 ÷ 8 = 9; there arenine 8s in 72; 72 shared 8 ways = 9 etc.

Continue until all possibilities are completed.Repeat using a different three numbers.

Calculator race

Children work in pairs. Put 10 divisionalgorithms on the board.

One child works the answer out on paperand the other uses the calculator.

Who finished first? Who had all correct?

Repeat with different algorithms and thechildren swapping activities.

Number names

Discuss the fact that numbers can be givenspecial names, eg prime, composite, ordinal,cardinal, odd, even, whole, rational andsquare.

Put these names as headings on the boardand build up a list of examples. Ensure thechildren understand that some numbers couldbe under many headings. This list can bewritten on cardboard and displayed in theclassroom.

Problems

Children work in groups of four. One childin each group writes a ÷ problem, anothera π problem, another an + problem andanother a – problem. Children swap problemsand work each other’s. Encourage them todiscuss any difficulties they encounter.

Prime game

Have the children in pairs and give eachpair two dice (nine-sided if possible) or usespinners. One child throws both dice andchooses a number. eg If a 1 and 5 are thrownthe child can choose 51 which is prime.

If the number chosen is a prime number thechild scores 1 point. Children take turns andkeep score until they have had ten turns.


Activity Bank


a

d

g

j

b

e

h

c

f

i

Activity Card 56

Activity Card 57

Multiple Colours

Colour all the multiples of 3 yellow.

Colour all the multiples of 6 blue.

Why are some green? ______________

Colour all the multiples of 4 red.

Colour all the multiples of 8 blue.

Why are some purple? ______________

✎✎✎

✎Making Multiplication Algorithms

Throw a die 3 times. Write the numerals as a 3-digit number.

eg = 625.

Throw again, eg 4.

Make an algorithm, eg 625 π 4 = 2 500. Use the die to make some of your own.


�÷ X _

+

* Work these in your workbook.* Use a calculator to check answers.

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

10

20

30

40

50

60

70

80

90

100

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

10

20

30

40

50

60

70

80

90

100

Assessment Name __________________________________________

Date _____________________________

1 a Cross out every number divisible by 2.

b Cross out any number left which is divisible by 3.

c Cross out any number left which is divisible by 4.

d Cross out any number left which is divisible by 5.

e Write down the numbers which remain.

They are called ________________ numbers.

Multiplication/Division


2 Write all the factors of these numbers.

3 Work these algorithms.

a 26

c 28

e 32

b 29

d 54

f 31

4 Write estimations for these.

a 43 ÷ 4 Est. _____ b 96 ÷ 5 Est. _____ c 88 ÷ 3 Est. _____ d 97 ÷ 9 Est. _____

6 Write the operation sign in the box and work out the answer.

a John walks 6 km every day. How many days does he take to walk 42 km?

Answer __________

b Sally swims 650 metres every morning. Today she has swum 465 metres. How far does she have to go?

Answer __________

5 Work out the exact answers.

13 14 15 16

17 18 19 20

21 22 23 24

25 26 27 28

a H T O3 6 5

π 4

b H T O1 3 9

π 7

c H T O4 9 0

π 6

d H T O2 4 8

π 8

4 π 5

4 π 60

4 π 300

4 43 5 96 3 88 9 97a b c d

126

Learning focus• On the board revise 2-digit minus 2-digit and 3-digit minus 3-

digit subtraction without trading. • Demonstrate that 4-digit minus 4-digit (no trading) is just as

easy. Have some children work examples on the board withhelp from the class.

• Make up some word problems involving 4-digits and write themon the board. eg In a jar of 6 385 hundreds and thousands 1 263 were yellow. How many were other colours?

Page 125• Ensure the class has much practice in trading down.• Demonstrate with MAB blocks.• Before the lesson have children work in pairs and play trading

games.• Give plenty of oral practice in trading down tens.• Write an algorithm very clearly on the board and demonstrate

how to show trading. Repeat as often as necessary to ensureall the children understand. It is very important that everychild grasps the concept at this stage.

• Work in stages and help strugglers.

Page 126• Again practise trading tens.• Write algorithms with heading Tens and Ones. Can we write

them without headings?• Insist that trading numbers are still clearly shown.

Page 127• Explain how to work the cross-number puzzle.• For questions 13 - 15 use blank space for working.

Answers for assessment page 1291 a $2 355 b $1 120 c $1 251 d $2 371

e $3 475 table & cabinet f $1 104 drawers & table 2 $1 5003 a 28 b 26 c 54 d 24 e 49 f 67 g 18

h 24 i 48 j 274

5 43

VELS: NUMBER Outcomes and StandardsComputation and Applying Number 3.2Select the appropriate operations andcomputation methods to solve problemsinvolving whole numbers and money. Mental Computation and Estimation 3.1Recall or mentally determine basicmultiplication and division facts.Investigation 3.3 Use familiarrepresentations, processes and concepts toexplore unfamiliar tasks and problems.• Selects appropriate operation and

computation methods to solve problemsinvolving money.

• Uses appropriate methods to carry outwritten subtraction calculations.

• Uses properties of numbers to assistcomputation.

• Uses familiar representations to exploreunfamiliar tasks.

Key wordsdifference, subtraction, trading down,estimate, more than, less than

Resources calculators, 1 cm grid paper, MAB blocks,magazines, catalogues, newspapers

Additional work sheetsTargeting Maths Middle Primary Operations and Number Patterns• Subtraction – Unit 2



Subtraction

72 24 48

38 22 16

34 2 32

a 71 33 38

23 18 5

48 15 33

b 68 33 35

29 25 4

39 8 31

c 87 28 59

52 17 35

35 11 24

d

127

Quick responses

Ask lots of mental subtractions and practiseto obtain quick responses.

Practise patterns, eg 15–825–835–8 etc.

Linking addition and subtraction

Ask the children to stand and state a number.Take turns around the class for children tosay a + or – fact about the number. If wrongthey sit down. When children start to havedifficulty with responses, state a new number.

eg State 27;responses 19 + 8, 30–3, 39–12, etc.

Car prices

Look at student page 124. Alter the prices ofthe cars. Ask the children to use a calculatorto work out the differences in prices betweenall the cars, eg Toyota and Ford, Toyota andHonda, Toyota and Mercedes and Toyota andPulsar. Then Ford and Honda etc. Encouragethe children to make up their own questionsabout the cars.

Real-life subtraction

Children look in magazines, cataloguesand newspapers and cut out advertisements forarticles which cost 4-digit figures, eg computersand sound systems, TV monitors, furniture, highfashion, air fares and holidays etc.

Ask the children to make a poster using theiradvertisement and make sure the prices areclearly marked. Have a class discussion aboutthe posters and suggest subtraction questionsthat might be asked about the prices. eg How much cheaper would it be to fly toRome than London?

Real life continued

After the class discussion about the postersask the children to write five questions abouttheir poster. The children work in pairs andanswer each other’s questions. They can thenpose extra questions for their friend’s poster.

Cross number

Have the children work in pairs and give eachpair 1 cm grid paper. They make a cross-number puzzle similar to that on studentpage 127. If children find this difficultsuggest they use a 1-across 1-down, 2-across2-down, etc. pattern.

Ask the children to swap with another pairand work each other’s number puzzle.


Activity Bank



Activity Card 58

Activity Card 59

✎Trading Subtraction

Use MAB blocks to work this subtraction. 453 – 249Put out 453, then take away 249.

To take away 9 ones trade a long for 10 ones.453 – 249 = 204

Use your MAB blocks to work these.a 328 – 219 = ________c 486 – 328 = ________e 625 – 517 = ________

b 333 – 226 = ________d 537 – 228 = ________f 435 – 317 = ________

Take the sunbeam numbers awayfrom the sun number.

Sunbeams ✎ �

MAB

95

76

29

43

88

20

47 73

54

27

49

65

36

48

Assessment Name __________________________________________

Date _____________________________

1 Find the difference in price between the:

a table and bed. ______________

b bed and cabinet. ______________

c bed and drawers. ______________

d drawers and cabinet. ______________

Use a calculator to find which two prices have:

e the greatest difference. ______________ f the least difference. ______________

2 Estimate the change from $5 000 if you bought the bed. ______________

3 Show the trading.

4 Complete these subtraction squares.

5 There were 82 oranges in a case. The children ate 39. How many were left? ___________

a b c d

Subtraction


a Tens Ones8 6

– 5 8

f 82– 15

g 57– 39

h 70– 46

i 85– 37

j 44– 17

72 24

38 22

71 33

23 18

68 33

29 25

87 28

52 17

b Tens Ones5 4

– 2 8

c Tens Ones9 0

– 3 6

d Tens Ones7 1

– 4 7

e Tens Ones9 5

– 4 6

$4 695$1 220$3 575

$2 324

– – – –

Woodies Handmade Furniture

130

Learning focus• Talk about hot-air balloons. • What’s a gala day? — a competition to fly the greatest

distance in a set time etc.• Encourage correct setting out in workbooks. Stress correct

columns, recording trading numbers and adding from the topdown the column.

• Suggest to the children that they estimate the answer first.

Page 129• Practise building patterns on the board.• Discuss the four facts from one expression,

eg 8 + 7 = 15, 7 + 8 = 15, 15 – 8 = 7, 15 – 7 = 8. • Why do we check answers? How do we check answers?

Show that we use opposites to check answers; for additionwe use subtraction, and vice versa. Give plenty of examples. 20 + 6 = 26, 26 – 20 = 6, 26 – 6 = 20 etc.

• Refer to question 3a. 8 + 7 = 15. What do you expect everyanswer to end in? Why?

Page 130• Put a number into calculators and change the digits

several times.• Revise estimation for question 3.• Children must use workbooks for question 4.

Page 131• Explain that the same rules apply for addition and subtraction

when using money.• Remind children to remember the signs $ or c and the point

separating them.• Children need to use workbooks for question 1b.

Answers for assessment page 1331 a 561 b 506 c 274 d 329 2 a 53 b 108 c 124 d 179 3 a B & C b A, C & D 4 205 a 8 + 14 = 22, 22 – 14 = 8, 22 – 8 = 14

b 18, 27 – 18 = 9, 18 + 9 = 27, 9 + 18 = 27 6 a 842 b 9057 a A $3.46, $7.96, $97.46 B 28c, $4.78, $94.28

C $1.45, $5.95, $95.45b $8.26, $10.27, $7.09c $3.18, $1.17, $2.01d $13, $7, $10

VELS: NUMBER Outcomes and StandardsMental Computation and Estimation 3.2 Useplace-value ideas and the properties ofnumbers and operations to assist mentalcomputation. 3.3 Make estimates to checkthe reasonableness of the results of writtencomputation and calculator use. Number Patterns 3.1 Use rules involvingaddition, subtraction and multiplication todevise, describe, extend and test numberpatterns. Reasoning 3.1 Make and testsimple conjectures. Computation 3.3 State equivalencestatements and addition and subtractionfacts involving simple common fractions andcarry out calculations involving tenths andhundredths.• Uses appropriate operations and

computation methods to solve addition andsubtraction problems.

• Extends addition and subtractions facts tocomplete a pattern.

• Uses properties of numbers to assist mentalcomputation.

• Applies inverse relationship of addition andsubtraction to check solutions.

• Recognises place value in 4-digit numbers.• Makes estimates to check reasonableness.• Puts forward assertions about what might

be true or false.• Adds and subtracts numbers involving

tenths and hundredths.• Estimates the results of a computation.

Key wordstotal distance, difference between,subtraction, addition

Resources calculators, prepared addition andsubtraction circles, blank cards, metre rule

Additional work sheetsTargeting Maths Middle Primary Operations and Number Patterns• Addition — Unit 2• Subtraction — Unit 2



Addition and Subtraction

131

+ and –

Ask the children to give quick oral responsesto mixed + and – expressions, eg 6 + 4 – 3 = 7, 18 – 5 + 4 = 17.

This can be extended to longer expressionswith the children giving answers as a class,eg 18 – 5 = 13; + 4 = 17; – 9 = 8; + 25 = 33

etc.

Calculator

Ask the children to display 4-digit numberson their calculators. Change digits intodifferent numbers, eg for 6 385 change the8 into 9. What did you do?

Circles

Prepare a page of addition and subtractioncircles similar to page 129, student book.Ask the children to complete the page ina set time. Children score a point for eachcircle correct and extra points if they finish intime.

Problem solving

Children write a problem on a piece of paperwhich involves both + and – . eg Elan had$5.95 and spent $2.73. He found 85c on theway home. How much does he have now?

Ask the children to put a number sentenceand the answer on the back. They then solveeach other’s problems.

Distances

Use a metre rule to represent a sign post inthe city centre. Have the children make signsstating destinations and distances to attachto the sign post.

Children ask one another distance questions.eg How far from Birds’ Nest to the city

and then to Sleepy Hollow?How much closer is Birds’ Nest to the city than Sleepy Hollow? etc.

Subtraction check

Emphasise the importance of checking writtenwork. Look at page 129, student book.

Put a number of similar addition algorithmson the board and ask the children to workthem in their workbooks.

Ask the children to double check them bydoing two subtractions,eg 386 591 591

+ 205 – 205 or – 386


Activity Bank


Activity Card 60

Activity Card 61


✎

Write the new prices in the blank labels.You have $20. You need 3 items for presents.

Which 3 could you buy? _____________ _____________ _____________Estimate the cost of buying all the items. __________

Use your calculator to total the cost of all the items. __________

Draw three clown faces with numbers and make rectangle expressionsfor a friend to work out.

Number ClownsPlace the numbers from the triangles in the rectangles so they equalthe number in the circle.

___ + ___ – ___ = 41 ___ – ___ + ___ = 26 ___ + ___ – ___ = 37

✎ �

÷ X _

+

41

36

27 22

26

15

18 23

37

43

12 18

$9.99$6.55

$3.84

$6.55

$8.72

Garage SaleLast hour specials! Everything marked down 50c!

Assessment Name __________________________________________

Date _____________________________

4 jars are filled with M&Ms for guessing competitions.A B C D

1 What is the total number in:

a A and B? ______ b B and C? ______ c C and D? ______ d A and D? ______

2 What is the difference in number between:

3 a Which 2 jars together total 506? ______________

b Which 3 jars together total 528? ______________

4 Josie won jar A and Bill won both C and D. How many more M&Ms did Bill have? ______

5 Write 3 more facts.

a 14 + 8 = 22, ____ + ____ = ____ , ____ + ____ = ____ , ____ + ____ = ____

b 27 – 9 = ____ , ____ + ____ = ____ , ____ + ____ = ____ , ____ + ____ = ____

6 Add then use subtraction to check your answers.

a A and B? ______ b B and C? ______ c C and D? ______ d A and D? ______

Addition/Subtraction


7 A

C

B

b How much money in A + B? _________ B + C? ________ A + C? _________

c What is the difference in money between A and B? _________ B and C? _________

A and C? _________

d Estimate: A + B + C _________ A + C _________ B + C _________

a 6 2 4+ 2 1 8 –

b 5 0 9+ 3 9 6 –

254 307 19975

a How much must be added to each wallet to make:

ABC

$6.00 $10.50 $100$2.54

$5.72

$4.55

Learning focus• Draw diagrams on the board to revise halves and quarters.

• Show that !2 = @4.

• Discuss how to write 1 whole in fraction form, eg $4.

• Use diagrams other than circles to practise simple additionand subtraction.

• Stress that when writing fractions the fraction bar should behorizontal not diagonal and the fraction is approximately thesame height as the whole number.

Page 133• Have the children count the jelly babies.• Work question 1. Discuss their answers. At this stage some

children will be able to say that the bigger the denominatorthe smaller the fraction.

• For question 4 encourage the drawing of diagrams for thosewho are still unsure.

• A diagram could also be useful for question 5 (20 dots).

Page 134• As children have already seen Roman numerals as a different

number system spend a few minutes talking about them beforeintroducing the ancient Egyptian numerals.

• Point out that this system is no longer in use.• They also worked on a ten system but symbols were drawn in

groups of ten and then changed.• Have children practise drawing the symbols on the board.• Show how long a number such as 9 999 would have been.

Have fun!• Assure the children that they do not have to learn the system;

it is there for interest.

Answers for assessment page 1371 a !2 b !2 = 8, !4 = 4

2 a 8 b 4 c 16 d 12 e 16

3 a #4 b !2 c @2 or 1 d $4 or 1 e !2 f !44 a !2 b #4 c !4 d !2 Teacher check diagrams

5 a 1!4 b 1 or $4 c 1!4 d 1#4 e #4 f !4g 0 h !4

VELS: NUMBEROutcomes and StandardsNumeration and Computation 3.3 Represent,find, compare and order fractional parts ofobjects and collections of objects. 3.4 Usedecimal notation to represent and comparesimple decimal fractions including thoseresulting from calculator computations.Reasoning 3.1 Generate mathematicalquestions from presented data and fromfamiliar contexts.• Uses words and symbols to express simple

addition and subtractions involvingfractions.

• States equivalence between fractions inwords and symbols.

• Interprets the results of a calculatorcomputation.

• Describes and uses simple, different numbersystems.

Key wordsadd, diagram, fraction, half, Hindu-Arabic,quarter, subtract, symbol, whole

Resources coloured pencils

Additional work sheetsTargeting Maths Middle PrimaryNumeration and Fractions • Fractions — Unit 2


Fractions


Fractions

Find fractions of given numbers, eg !2 of 50, !4 of 16.

What fraction is 5 out of 10?

Have children identify fractions that are drawndiagrammatically on the board.

Multiplication and division practice gameChild writes down a division or multiplicationfact and then makes a statement. Eg I amthinking of 3 related numbers. Two of thenumbers are 4 and 28.

The class must guess. Insist that the childrenuse the full wording o reinforce the facts.

Could it be 4 π 7 = 28? No it is not 4 π 7 = 28.

Could it be 7 π 4 = 28?

Could it be 28 ÷ 4 = 7?

Could it be 28 ÷ 7 = 4?

Collage

Ask children to look in newspapers andmagazines to find advertisements usingfractions. Discuss the meanings of theadvertisements.

Make a class collage for display.

Toothpick fractions

Children are in groups of four. Give each group 100 toothpicks. Ask them to show !2, !4,

#4, $4, @2 etc. of the toothpicks.

Children are in pairs and each pair has 80toothpicks. Again the children show thefractions.

This can be repeated with other numbers.

Shading fractions

Give each child a page of small hundredsquares.

They colour !2, !4, #4, $4.

Each time ask what fraction remains.

Children can cut to reduce some squares to 40, 80 etc. They then colour the givenfractions on the smaller squares.

If the class is capable other fractions can beintroduced, eg !5, !0 etc.

Other numbers

Children have now seen (and used) Romannumerals and ancient Egyptian numerals. They can use the Internet or library toresearch other systems. They present theirfindings to the class.

An alternative would be to find the numbersone to ten in different languages. They make a chart of the words and the symbols used.


Activity Bank


✎

Activity Card 62

Activity Card 63

Fraction Survey�✎

1 2

1 4

2 6

5 5

3 6

1 2

2 10

2 6 1

5

5 10

1 3 6

8

2 4

4 4

3 4

1010


Fraction to FractionDraw line to join equivalent fractions.Draw diagrams if you need help.

• Make up 10 questions for a class survey.eg Do you like vanilla ice-cream?

Do you play the piano?

• Work out the approximate fraction of “yes” answers for each question. eg 21 children out of 26 like ice-cream.

That is about #4. 4 children play the piano.

That is about a !4.


Assessment

1 a Would you choose !2 of the sweets

or !4 of the sweets? _________

b Why? __________________________________

________________________________________

________________________________________

2 How many sweets in:

a !2 ? ________ b !4 ? ________ c @2 ? ________ d #4 ? ________ e $4 ? ________3 What fraction is shaded?

a b c

________ ________ ________

d e f

________ ________ ________

4 Answer the question and colour the diagram.

a b

c d

Fractions

137

Name __________________________________________

Date _____________________________

5 a 1 + !4 = ________ b #4 + !4 = ________ c !2 + #4 = ________ d #4 + 1 = ________

e 1 – !4 = ________ f #4 – !2 = ________ g !2 – !2 = ________ h 1 – #4 = ________

+ = + =

– = – =

!4 + !4 = ________ !4 + !2 = ________

!2 – !4 = ________ #4 – !4 = ________

Learning focus• Have enough counters available for children to make

the patterns and extend them if necessary. • Discuss on completion of the exercises.

Why are the numbers called square numbers? …triangular numbers?

• When the page is completed let children explain whatis happening in their own words.

• Encourage children to “test” the rule by continuingthe pattern in 2d.

Page 136• For question 2 allow children to act out each step and record

their findings.• Practise with other numbers,

eg

• Point out that as they all equal 48 they must all equal eachother, eg 2 π 24 = 6 π 8

Page 137• Ensure children understand it’s the pattern of the last digits

only. Children rule lines in turn starting at zero each time. • Insist the children use rulers and rule carefully. When the page

is finished discuss patterns, Why is there no pattern for 10?

Answers for assessment page 1411 a 49, 81, 121, 144; square

b 28, 45, 55; triangular2 a 1 π 16, 2 π 8, 4 π 4

b 1 π 18, 2 π 9, 3 π 6c 1 π 48, 2 π 24, 3 π 16, 4 π 12, 6 π 8

3 a T b T c F d T e F f T

4 a 10 b 155 Teacher check

VELS: NUMBER Outcomes and StandardsNumber Patterns and Relationships 3.1 Usesrules involving addition, subtraction andmultiplication to devise, describe, extendand test number patterns.Mental Computation 3.1 Recall or mentallydetermine basic multiplication and divisionfacts.• Uses a given rule to generate a sequence of

numbers.• Uses rules to describe and extend number

patterns.• Recalls basic multiplication facts.

Key wordssquare numbers, triangular numbers,multiplication

Resources counters, rulers, calculators, circle patterns,spinners

Additional work sheetsTargeting Maths Middle Primary Operations and Number Patterns• Number Patterns — Unit 2


Special Number Patterns


481 π 48

2 π 24

3 π 166 π 8

4 π 12

Square numbers

Remind children of index notation, eg 6 π 6 = 62.

Ask “square” questions. eg What is 8 squared? ... 9 squared?Extend to How many is 8 squared + 2squared? … 6 squared – 5 squared? etc.Answers can be written or oral.

Speed tests

Emphasise the need for both speed andaccuracy with multiplication tables. Ask 20multiplications, eg 6 π 9, 8 π 7 etc. and allowchildren time to write the answers quickly.

This can be repeated each day of the weekand children record their score and noteimprovement.

Triangular numbers

How big a triangle could we make usingthe children in the class?

In the playground make a “giant” triangleusing a triangular number pattern.

Ask questions. How many terms did we make?How many more children are needed to makethe next term?How big a pattern could we make using … 2,… 3, classes? etc.

Calculator

Allow children to work out the squares ofnumbers bigger than 12 on a calculator. Havethe children record the squared numbers, eg

13 π 13 = 16914 π 14 = 19615 π 15 = 22516 π 16 = 256

Children discover that the difference betweenthe squared numbers increases by consecutiveodd numbers, eg 196 – 169 = 27, 225 – 196 = 29, 256 – 225 = 31.

Circle patterns

Look at page 137 of the student book.

Give the class copies of circle patterns.Allow children to use a calculator if necessaryto work out patterns for π11 and π12.

Ask children to discuss what happenedin making the π11 and π9 patterns.

Discuss why the π12 pattern is the sameas the π2.

Tables game

Children are in groups of four and play in pairs.

First pair spins 2 spinners numbered 1 to 10and multiply the numbers, eg 6 π 8 = 48.Each child on the other team records thenumber on a calculator.

The first pair spins again and the other pairadds this number to the first number. Repeatfor 5 turns and write down the total.

The second pair now has a turn at spinningand the first team adds the numbers.

The pair with the highest (or lowest) totalis the winner.


Activity Bank


Finding Numbers1 Find the number in

the rhyme.“I’m a number andhere’s the fix.Five times me is mysquare less six.”________

2 Find the specialnumber. Use dots toshow square numbers.Use dots to showtriangular numbers.What number is both a square and triangular number?________

3 Write all themultiplication facts for:

Activity Card 64

Activity Card 65

�✎

• Draw a square around the square numbers.• Draw a triangle around the triangular numbers.• Multiply every square number by every triangular number.

You may use a calculator.• Write the answers in ascending order.

✎


÷ X _

+

72

84

49

253

10 16

6

15

Triangular and Square Numbers

1 4 9

1

etc.

etc.3 6


Assessment Name __________________________________________

Date _____________________________

1 Write the missing terms:a b

2 Write as many multiplication facts as you can for these numbers.a b c

3 True or false?

5 a

Start at zero, make the pattern for the last digits. Rule your lines.

4 a A family of 5 people met at the airport. They all hugged each other.

How many hugs? _________

b If their grandmother had come too and they all hugged each other,

how many hugs? _________

a 6 π 6 = 3 π 12 ________

d 7 π 0 = 8 π 0 ________

b 4 π 3 = 2 π 6 ________

e 6 π 9 = 8 π 8 ________

c 6 π 9 = 7 π 8 ________

f 6 π 7 = 2 π 21 ________

a These numbers are called b These numbers are called

________________ numbers ________________ numbers.

Number Patterns

141

π4 π6 π9

16 18 48

Order of term

Term

6

36

7 8

64

9 10

100

11 12 Order of term

Term

4

10

5

15

6

21

7 8

36

9 10

b c

Learning focus• Define area as being the size of a surface. • Discuss acres and hectares. Ask the children for examples

of hectares — parks, farms etc.• Why do we need a measurement for smaller areas? Again,

ask the children for examples — table tops, small rugs etc.• Look at the illustration. We need measurements for a plan so

we can draw it up in square metres. Stress one square = 1 m2

• Discuss how to estimate half and quarter squares when findingan area.

Page 139• Revise cm2 from year 3.• Revise perimeter. Look at the fact box.• When question 3 is finished ask the children to read their

statements (part c) and discuss their findings.• Have centimetre grid paper for each child to attempt

the Challenge.

Page 140• Have plenty of newspapers, sticky tape and metre measures. • Allow a lesson for making square metres. Encourage the

children to discuss how they have made their square metres.(N.B. It can be handy to have spare square metres madefrom cloth — the newspaper ones will tear).

Page 141• Revise a.m., p.m., analogue and digital time.• Tell children to use the capital letters to place activities on

the time line.• Read and discuss the word bank before attempting question 2.

Answers for assessment page 1451 a 2 m2 b

12 m2 c 3 m2

2 shed3 the paved area4 24 m2

5 11 12 m2

6 a 6 cm2, 10 cm b 7 cm2, 12 cm c 6 cm2, 14 cm7 Teacher check8 Teacher check

VELS: MEASUREMENTOutcomes and StandardsMeasuring and Estimating 3.1 Makeincreasingly accurate estimates ofmeasurements using informal units andstandard units. 3.2 Measure and compareusing appropriate informal units. 3.3Estimate and accurately measure length,mass, volume and temperature using formalunits and standard units. Investigation 3.2 Clarify the essentialnature of a task or problem and identify keyinformation in familiar situations. Time 3.1 Estimate short and long periods oftime, describe duration of time, and makeand use timetables, schedules andcalendars. 3.2 Tell the time using digitaland analogue clocks.• Uses direct comparison and uniform units to

determine area.• Measures area of regular shapes by counting

squares.• Identifies key information in familiar

situations.• Estimates area by comparing with one

square metre.• Understands the importance of standard

units.• Reads simple timetables.• Shows digital time on an analogue clock

and vice versa.

Key wordssquare metre, area, perimeter, squarecentimetre, timetable

Resources centimetre grid paper, old newspapers, cloth,sticky tape, metre measures, clock face, BLMof digital and analogue clocks

Additional work sheetsTargeting Maths Middle Primary Measurement• Area — Unit 2


Area and Time


Length measurements

Revise changing cm to mm, cm to m andm to mm.

Ask children to estimate lengths and widthsof items in the classroom, eg desk, board etc.Have some children use measures to checkestimations. Give the measurements in mm,cm and m.

Time

Revise a.m. and p.m. time.

Children can list activities they mightbe doing at given times.

Have a large clock face and revise analoguetime. Demonstrate times and have childrentell the time. eg It is 25 to 9 or 8:35.

Estimating area

Children list items in the room which theyestimate to have an approximate surfacearea of 1 cm2, 5 cm2, 10 cm2 etc.

Children can cut out templates from 1 cm gridpaper and use them to check theirestimations.

Favourite day timetable

Children keep a diary for their favouriteschool day of the week. They record the timesthey started important activities to make atimetable, and enter them on a timelinesimilar to page 141 of the student book.

Give the children a BLM of analogue anddigital clocks and have them record the timesfrom their timetable. These are then pastedinto their workbooks.

The square metre

Children use their newspaper square metres.

How many shoes, hands, workbooks etc.can we fit on a square metre?

Keep a record of results and have a classdiscussion.

Which item needed the least number to covera square metre? etc.

Draw conclusions about the differencesin areas of the items.

Time stories

Increase the word bank on page 141 of thestudent book to include other measurementsof time, eg fortnight, decade etc.

Ask the children to write a short story usingas many words as possible from the wordbank. eg Sasha was born a decade ago in thefirst hour after midnight during the monthof July. A fortnight later … etc.

Have children share stories with the class.


Activity Bank


✎Activity Card 66

Draw your own picture on 1 cm grid paper and ask a friend to enlarge it on 2 cm grid paper.

What is the area of each picture?

Enlarge the worm on the1 cm grid to fit on the2 cm grid.What is the area of the

small worm? __________

big worm? ___________

Enlarging Area



Assessment

Area and Time

a A = _____ P = _____ b A = _____ P = _____ c A = _____ P = _____

Find the area and perimeter of these shapes.

a 12:25 p.m. b 8:45 p.m. c 7:05 a.m.

7 In space d draw a 5 cm2 shape. What is its perimeter? ___________

8 Write these times on the clocks.

145

Name __________________________________________

Date _____________________________

This is a small city garden.

1 How many square metres is:

a the flower bed? ____________

b the kennel? ____________

c the vegie patch? ____________

2 What has the same area as the flower bed?

____________________

3 What has an area of 5 square metres? _________

4 What is the area of the whole garden? _________

5 What is the area of the lawn? _________

Key:

: : :

c

d

a b

Fido’s KennelShed

Vegie Patch

Paved Area

Flowers

1 square metre Paved Area Lawn

6

Learning focus• Revise that an angle occurs when two straight lines meet. • Explain that we measure the size of an angle in degrees.

Teach that 90 degrees is written 900.• Teach that a right angle = 900,

an acute angle = less than 900 (sharp angle),an obtuse angle = more than 900 (blunt angle).

• Find angles of each type in the room. • Put many different acute, obtuse and right angles on

the board. Ask the children to label them.

Page 143• Show how an angle is made — two straight arms that meet at

a point called a vertex.• Revise right, acute and obtuse angles.• Make a right angle tester.

Fold a piece of paper, then fold again.• Encourage the use of the right angle tester for question 1.

Page 144• Teach vertex (plural vertices) and arms. • Look at the triangle descriptor. Discuss that this is not the

only way we label triangles. • Some children may mention scalene, equilateral, and isosceles.

Point out that at the moment we are only looking at theangles.

Answers for assessment page 1491 Teacher check2 Teacher check3 Teacher check4 Teacher check5 a A b O c R d R e A f O6 a right angle

b acute angle c obtuse angle

7 Teacher check

VELS: MEASUREMENT and SHAPEOutcomes and StandardsMeasuring and Estimating 3.4 Demonstrateunderstanding of the concept of angle.Shape and Space 3.2 Use simpleconventional spatial language whendescribing shapes, parts of shapes, objects,parts of objects and simple cross-sections.Investigation 3.3 Use familiarrepresentations, processes and concepts toexplore unfamiliar tasks and problems.• Demonstrates an understanding of the

concept of angle.• Identifies and orders angles according to

size.• Uses simple conventional spatial language.• Orders angles according to size.• Uses familiar representations to explore

unfamiliar tasks.

Key wordsangle, right angle, acute angle, obtuse angle,vertex, arm

Resources 2D shapes, BLM of analogue clocks, cardboardstrips and fasteners, newspapers,magazines, art books, cardboard

Additional work sheetsTargeting Maths Middle Primary Measurement• Angles — Unit 1


Angles


Time revision

Revise all time facts, eg 60 secondsin 1 minute etc.

How many seconds in 3 12 minutes?

14 of a year, how many months? etc.

Answers can be written or oral.

2D shape revision

Have models of 2D shapes — hexagons,pentagons etc. Children name them.

Ask children to write the names on the board.

Practise spelling.

Revise flip, slide, turn using the shapes.

Clockface angles

Give the class BLMs of analogue clocks. Writetimes on the board and ask the children todraw the times on the clocks and write thetype of angles made by the hands.

Challenge: How many right angles willthe hands make in twelve hours?

Write a time when the hands will makean acute/obtuse angle?

Angle tester

Make angle testers using two cardboard armsand a fastener (also geostrips and Meccano).Ask the children to use the testers to measureangles in the room. Children can then tracethe angles onto paper. Label the anglesacute, right angle and obtuse and put themin ascending order.

Drawing angles

Children look for and draw real things whichmake angles, eg the blades of scissors,compass and pencil, paper fans etc. Compilea list of as many different things as possibleand try to allocate one to each child to drawon art paper. Display in the classroom.

Poster

Look in magazines and newspapers forpictures of acute, obtuse and right-angledtriangles. Art books are also a good source.

Children can also draw some on colouredpaper. Cut out all the triangles and makea poster collage for each type of triangle.


Activity Bank


Activity Card 67

Activity Card 68

Triangles in a DodecagonChoose your favourite colour. Colour all the right-angled triangles.

Choose another colour. Colourall the acute-angled triangles.Choose one other colour. Colourall the obtuse-angled triangles.How many:right-angled triangles? ______acute-angled triangles? ______obtuse-angled triangles? ______

✎


✎Angles in 2D Shapes

Completethe table

Total numberof angles

Number ofright angles

Number ofacute angles

Number ofobtuse angles


Assessment Name __________________________________________

Date _____________________________

From where you are sitting name:1 three right angles you can see. a ____________________ b ____________________

c ____________________2 three acute angles you can see. a ____________________ b ____________________

c ____________________3 three obtuse angles you can see. a ____________________ b ____________________

c ____________________4 a Colour the right angles red, the acute angles green and the obtuse angles blue.

b Put a black dot on all the vertices.

5 Write R on the right-angled triangles, A on the acute-angled trianglesand O on the obtuse-angled triangles.

6 Draw the times on the clocks and write the type of angles the hands make.

7 Draw a triangle pattern using a right-angled triangle, an acute-angled triangleand an obtuse-angled triangle.

Angles

a b c d e f

a 3 o’clock b 14 past 5 c 25 to 2

149

150

Learning focus• Revise the positions North, South, East, West.

Remind children of the abbreviations N, S, E and W. • Have a compass in the classroom and find N. Have children

point to the other directions.• Revise North-East, North-West, South-East, South-West. Again,

have the children point to all the directions in the classroom.Revise the abbreviations NE, NW, SE and SW.

• Look at the map. Read the names of all the places. Makeup a story and encourage the children to make up storieswhich include directions.

Page 146• Revise the compass points. • Show how to draw a grid and rub out some lines to make a

maze.The bigger the grid the more tricky the maze can be.

Page 147• Draw two interlocking circles on the board.• Use information that is relevant to your class to make a Venn

diagram.• Discuss why some information is shared by each circle and is

therefore written in the interlocking portion.• Have the class create another Venn diagram on the board —

you may have to suggest the information to be used.

Answers for assessment page 1531 a block A b toilets c office/hall d steps

e block B f main gate2 a seats b bubbler3 a seats b tree c main gate4 multiples of 3 and 4 5 a b c d e f Teacher check g east6 Teacher check

VELS: SPACE and DATAOutcomes and StandardsLocation 3.3 Interpret and describe locationand direction using grid references andcardinal compass points.Presenting Data 3.2 Use diagrams and two-way tables to summarise and displaydiscrete data.Interpreting Data 3.1 Extract specificinformation from data summarised indiagrams and tables.• Uses regions on a grid to locate places.• Understands conventional location

language to follow a given path.• Uses Venn diagrams to show frequencies

for different categories.• Extracts specific facts from a Venn

diagram.

Key wordsNorth, South, East, West, North-East, North-West, South-East, South-West, clockwise,anticlockwise, plotting, diagram, Venn

Resources 1 cm grid paper, compasses, A4 paper,sports equipment, boxes

Additional work sheetsTargeting Maths Middle Primary Space• Position — Unit 1



Position

151

Classroom “I spy”

Revise all the compass points from the centreof the classroom.

One child stands in the centre and spiesan object. Children ask Is it to the NE? … W?etc.

Once the direction is established childrenguess the object.

Repeat many times.

Position words

On the board build up a bank of positionwords, eg next to, opposite, beside, adjacent.Proceed to include all the compass points.Have the children use the words in sentences.Record the list and add to it as childrendiscover new words.

Locating objects

Find North in the classroom using a compass.

Children make paper compasses showing thedirections N, NE, E, SE, S, SW, W, NW. Ask thechildren to state the location of objects usingthe compass. eg The globe is between Eastand South-East. The door is facing South. etc.

Repeat this activity in the playground.

Book of mazes

Children look at the maze they made for theChallenge, page 147.

Ask them how they could improve their maze(increase difficulty, enlarge etc.).

Children then choose a maze “topic” of theirown and create a new maze on A4 paper.

Display the mazes and have children solveeach other’s. Collate the mazes into a book(good for rainy lunch times).

Venn diagrams

For homework children complete the Challenge on page 147 of the student book.

Each child tells the class about their diagram.

Make a class poster to display all the Venndiagrams.

Playground maze

Make a class maze in the playground usingPE equipment, school bags, boxes, bins etc.Ask children to walk through the maze andrecord the directions they took, eg 3 stepsahead, 5 steps to the right, 3 steps North,5 steps East etc.

Children then return to the classroom andmake a plan of the maze on paper.


Activity Bank


✎

✎

Activity Card 69

Activity Card 70

Fun for Year FourThe sandpit is in the centre of the park.

Draw an activity, eg swings, slippery slide etc in each direction (NE, E, SE, SW, W, NW) from the sandpit.

Make up 5 questions about your map. Give them to a friend to answer.


N

This is a Venn diagram.What do you think it is about?Write your explanation and read it to the class. _________________________________________________________________________________________________________________________________________________

Mrs Smith

Mr Watt

Mr Black

Mr Jones

Mrs Henny

Mr Swan

Mrs Bent

Mrs Mooney

Mr Graham

Miss Elm

Mr Blew

Miss Grey

VennDiagram

Assessment Name __________________________________________

Date _____________________________

Amelia is sitting on a seat in the middleof the playground.

1 What does she see if she looks:a north? __________________b south-east? __________________c west? __________________d north-west? __________________e south? __________________f east? __________________

3 Looking east from his office the principal can see:

a ___________________ b ___________________ c ___________________

2 A bird flies south-west from the tree. It flies over the a _______________________and b _______________________

4 This Venn diagram shows multiples of 3 and 4. Why are the numbers 12 and 24 in the middle section?

_______________________________________

_______________________________________

_______________________________________

Amelia walks home the long way.She starts at *. Each square is a block.Follow the directions to colour her path.a 4 blocks north b 3 blocks eastc 2 blocks south d 4 blocks easte 2 blocks south f 4 blocks west

g What direction is Amelia’s home from

her starting point? ________________

Create a maze for a cat to finda mouse. (Don’t forget to drawa pencil grid first.)

5 6

Position


*

N

NBlock A

Block B

Multiples of 4 Multiples of 3

Seats

Steps

Gate

Toilets

Offi

ceH

all

Tree

Bubbler

4 9 615 3

2118

2412

16 820

154

Learning focus• Revise the meaning of outcomes. • How many outcomes can there be if we:

throw a dice?choose a day of the week?choose an Australian bank note?toss a coin?

• In which one would you have the best chance of selectinga particular outcome? Why?

• Read the problem on page 148. Discuss. Allow timefor children to explain what they think.

• When page 148 is completed discuss the results as a class.

Page 149• Discuss when you might select something at random,

eg lucky-door prize, bag of oranges at the supermarket etc.• Discuss the meaning of certain and impossible. Have children

give examples of things which are certain and things whichare impossible.

• Ask the class what chances come between certain andimpossible — likely, probable etc.

Answers for assessment page 1571 one in two 2 a one in three b one in three c one in three3 a one in six b one in six c one in six

d the chances are the same4 a one in five b one in four c Teacher check d 55 Teacher check6 Teacher check

VELS: CHANCEOutcomes and StandardsChance 3.1 Identify and record outcomesfrom simple chance experiments. 3.2Compare and order the likelihood ofoutcomes of simple chance experiments andof everyday events, and choose appropriatemethods for random selection. Reasoning 3.1 Make and test simpleconjectures. 3.2 Make judgments about theaccuracy of reasoning and results.• Identifies and records all possible

outcomes.• Makes and tests simple conjectures.• Compares the likelihood of outcomes of

simple chance experiments.• Makes judgements about the accuracy of

reasoning.

Key wordspredicting, outcomes, more likely, chance,selecting, random

Resources coins (real or play), coloured pencils,container, bag, counters, dice

Additional work sheetsTargeting Maths Middle PrimarySpace

• Chance and Data — Unit 2



Chance

155

Place value revision

Ask the children to write four-digit numbers.eg This number has 8 in the tens place,4 in the thousands place, 0 in the hundredsplace and 2 in the ones place.

Children then read back the number theyhave written.

Also revise spelling of difficult words,eg eighty, forty etc.

Money revision

Revise rounding to the nearest dollar/nearestcent. Revise notes and coins.

Ask many money questions. eg What changedo I get from $5 if I spend $4.74? Name thecoins I could receive etc.

Increasing chances

Children in pairs, write numbers 1-10 onpieces of paper and put them in a container.They predict the number of times they willpull out number 6 in ten turns. Keep a tally.Make sure the numbers are put back eachtime.Take the number 10 out and repeat theactivity, again ten times. Repeat activitytaking out 9, then 8, then 7.

Discuss the results as a class.

Line predictions

Make a long cardboard strip into a line. Writechance words ranging from impossible at oneend to certain at the other end. Childrenwrite sentences to pin at appropriate placesalong the line (possible, highly likely etc.).

Keep the predictions on display. Discussat a later date.

Organising outcomes

Work in small groups. Children put 20counters in a bag — red, green, blue andyellow. They choose how many of each colour.

We want red to be the most likely to be pulledout, green the next likely and yellow and blueto have the same chance. When the group issatisfied with their choice ask them to pullthe counters out for 30 turns (returningcounters and shaking the bag each time).They keep a tally.

Did you choose wisely?

Improve your chances

Discuss the expression “to improve yourchances”. Give examples of where it is used.eg Dad improved his chance of winning thelottery by buying more tickets. Louiseimproved her chance of winning her agerace by training every day.

Ask children to write examples. Have a classdiscussion.

This could be the basis of a creative writinglesson.


Activity Bank


Activity Card 71

Activity Card 72


�Counters

There is a red, a green, a blue, a yellow and anorange counter in the box. Sally wants a red one.What are her chances? ______________

First Rod pulled out a green one, then Jo pulledout a yellow one. They did not replace them.

What are Sally’s chances now? ______________

She pulled out orange, then had another go. What are her chances now? ______________

✎PredictionsFor each outcome roll a die 20 times. One person usestally marks to keep score. The other throws the die.Predict the number of times before you start.

How close were your predictions? ___________________Discuss your results with another pair.

✎

Challenge: The teacher put 3 white and 2 black counters in another box. She told Sallyto pull out 2 counters. What chance has Sally to pull out a black and white counter?

all eyesclosed

Outcome Prediction Tally Result

Rolled an odd number.

Rolled an even number.

Rolled a square number.

Rolled a number less than 6.


Assessment Name __________________________________________

Date _____________________________Chance

157

1 Mary has tossed a coin 5 times. The results are 4 heads and 1 tail.

What is her chance of tossing a tail next time? ________________

2 A family chooses a holiday. There are 3 choices; a resort, camping or a city visit.

What are the chances they choose:

a a resort? _____________ b camping? ____________ c the city? _____________

3 Eric throws a die. What is the chance that he throws a:

d What would happen if he threw again with a different die?

4 Bozo, the clown, has 5 balls in his pocket — red, yellow,

blue, green and white. Sam wants a yellow one.

What chance does he have of selecting it first go?

a __________________. He selected blue. Now what

chance of selecting yellow? b __________________.

c On the line draw a black arrow to show the chance

he now has of selecting yellow.

d How many goes does he need to be sure of selecting yellow? _____________

5 a Write something that is impossible to happen this year.

b Write something that probably will happen this year.

c Write something that certainly will happen this year.

6 Circle your prediction.

My chances of passing this assessment are:

a six? _____________ b one? ____________ c three? _____________

a certain b very likely c 50-50 d unlikely e impossible

impossible certain

G2 B3 B, C, A, E, F, D, G4 a $85 b $618 c $1 271

d $2 423 e $9565 a $846 b $508 c $1 097

d $2 313 e $9356 a B b E7 D, E, F, G

Page 31 Teacher check2 a nine hundred and forty-six dollars

b seventy-five dollarsc six hundred and eight dollarsd one thousand two hundred and sixty-one dollarse one thousand and thirty-five dollarsf one thousand one hundred and ninety-seven dollarsg two thousand four hundred and thirteen dollars

3 a 427 b 1 634 c 2 186 d 1 742Draw a diagram: Teacher check

Page 41 a 3 000 b 6 000 c 8 000 d 4 0002 a 9 000 b 4 000 c 8 000 d 1 0003 a 500 b 6 500 c 3 500 d 9 500

e 1 500 f 8 5004 a 1 219, 1 221, 1 222 b 2 642, 2 644, 2 645

c 999, 1 000, 1 001 d 3 509, 3 510, 3 5125 a 248 b 811 c 450 d 709

e 1 365 f 2 197 g 4 518 h 7 620Challenge: 9 751, 2 080

Page 51 a 1 235 b 2 462 c 3 107 d 1 0982 a one thousand two hundred and thirty-five

b two thousand four hundred and sixty-twoc three thousand one hundred and sevend one thousand and ninety-eight

3 a 690 b 937 c 1 002 d 5 147e 8 061 f 2 954

4 1 010 one thousand and ten1 001 one thousand and one1 100 one thousand one hundred1 110 one thousand one hundred and ten

Page 61 a 9 + 13 b 47 + 8 c 6 + 85

d 17 + 8 e 68 + 21 f 85 + 14g 14 + 12 h 47 + 15 i 63 + 15

2 a 9 b 17 c 25 d 12 e 9f 38 g 68 h 47 i 96

3 a 116 b 136 c 253 d 814 a 70 b 20 c 70 d 50 e 40

f 20 g 10 h 100 i 10 j 90

Page 71 a 63 b 101 c 73

d 123 e 82 f 151g 159 h 185 i 185

2 a 72 b 80 + 30 + 2 + 9 = 121c 70 + 40 + 5 + 5 = 120 d 40 + 80 + 6 + 6 = 132e 90 + 70 + 3 + 5 = 168 f 120 + 60 + 7 + 7 = 194g 150 + 30 + 5 + 6 = 191

3 a 81 b 63 + 30 + 2 = 95c 18 + 80 – 2 = 96 d 72 + 50 + 1 = 123e 137 + 40 + 3 = 180 f 315 + 70 – 3 = 382

4 22, 24, 26, 28, 30, 32, 34, 36, 38, 405 a 29 b 31 c 23

d 39 e 33 f 26g 36 h 28

Challenge: a 112 b 449 c 761d 400 e 703 f 1 022

Page 81 a 37 b 54 c 72

d 45 e 292 a 88c b 61c c 35c

d 18c e 3c3 a 171 b 290 c 261 d 392

e 662 f 3864 a 87 b 97 c 99 d 587

e 789 f 678 g 839 h 896i 599 j 888 k 499 l 979

5 4986 389

Page 91 a 41 b 24 + 8 = 32 c 34 + 7 = 41

d 13 + 28 = 41 e 37 + 15 = 522 a 66 b 72 c 41 d 91

e 56 f 42 g 36 h 83i 63 j 62 k 85 l 93m 94

Work backwards: John 9, Ali 14, Tim 17

Page 101 a Teacher check b Jerry 3, Josie 3

c 78 – 23 = 55, 77 – 45 = 32, 59 – 27 = 3272 – 30 = 42, 99 – 63 = 36, 47 – 27 = 20

2 a 5, 50, 500 b 5, 40 = 50, 400 = 500c 5, 80 – 30 = 50, 800 – 300 = 500d 2, 90 – 70 = 20, 900 – 700 = 200e 13, 23, 83 f 3, 13, 23, 63g 4, 14, 24, 54 h 3, 13, 23, 93


Year 4 Student Book Answers


Page 111 a 25 b -30 + 1, 35

c -20 + 1 = 27 d -60 + 3 = 28e -70 + 2 = 29 f -40 + 4 = 37g -70 + 2 = 29 h -40 + 4 = 37

2 a 24 b -50 – 2 = 39 c -20 – 4 = 28d -30 – 1 = 44 e -30 – 3 = 47 f -20 – 4 = 17

3 a

b

4 a

b

5 256 748Challenge: Teacher check

Page 121 a 7 b 7 c 8 d 5

e 6 f 8 g 6 h 7i 9 j 9

2 a 27 b 28 c 48 d 44e 45 f 15 g 53 h 14

3 a 26 b, c, d, e Teacher check

Page 131 a 44, 44 b 77, 77 c 51, 51 d 36, 36

e 89, 89 f 23, 232 a 17c b 68c c 55c

d 32c e 21c3 a 221 b 335 c 126 d 301

e 533 f 125 g 120 h 227i 320 j 401 k 842 l 120m 441 n 407 o 464

Work backwards: 27

Page 141 a 10 b 8 c 4 d 222 a 5 b 4 c 2 d 113 a cats b sheep c dogs4 a 1 b 1 c 1 d 2

e 2 f 2

5 a 12 b

110 c

210 d

1010

Page 151 YOU ARE CLEVER

2 a 34 ,

14 b

25 ,

35 c

48 ,

48

d 58 ,

38 e

610 ,

410 f

24 ,

24

g 710 ,

310 h

78 ,

18 i

15 ,

45

Challenge: a 4 b 6 c 6d 11 e 16

Page 161 a 32, 0.32 b 26, 0.26

c 54, 0.54 d 9, 0.092 Teacher check3 0.09, 0.18, 0.23, 0.35, 0.59, 0.614 Teacher check5 a $0.42 b $0.85 c $0.91

d $0.30 e $2.74 f $1.58g $7.02 h $5.00

Challenge: a 375 cm b 418 cmc 206 cm d 65 cm

Page 171 a $8.93 b $10.68 c $11.04 d $17.922 a $1.10 b $5.13 c $2.11 d $1.463 a 10.59 b 11.01 c 9.96 d 4.90

e 9.77 f 6.91 g 8.62 h 7.91i 6.37 j 9.63

4 a 5.13 b 5.31 c 5.52d 0.05 e 4.52

Page 181

2 a 28, 12, 36, 24, 0, 20, 4, 32, 8, 40, 16b 36, 0, 60, 6, 30, 42, 12, 48, 24, 54, 18c 0, 21, 3, 24, 18, 6, 12, 30, 9, 27, 15d 5, 50, 15, 40, 0, 20, 10, 30, 45, 25, 35

3 a 9 b 3 c 7 d 0e 8 f 42 g 1 h 36i 4 j 3 k 6 l 9

Challenge: 10 months

Page 191 a 24 b 24 c 24 d 24

e 24 f 242 a 14 b 20 + 8 = 28

c 30 + 12 = 42 d 40 + 16 = 56e 50 + 20 = 70 f 60 + 24 = 84g 70 + 28 = 98 h 80 + 32 = 112i 90 + 36 = 126 j 100 + 40 = 140

3 a 18c, 6c, 15c, 9c, 30c b 48c, 16c, 40c, 24c, 80cc 42c, 14c, 35c, 21c, 70c d 54c, 18c, 45c, 27c, 90ce 36c, 12c, 30c, 18c, 60c f 30c, 10c, 25c, 15c, 50cg 60c, 20c, 50c, 30c, $1 h 24c, 8c, 20c, 12c, 40c

Page 201 a 4 b 12 c 20 d 28

e + 8 f add 8 each time g 36, 44, 52

Pages 2– 20

29

18

46

35

37

26

22

11

49

38

35

24

54

43

23

12

29

8

59

38

38

17

30

9

55

34

42

21

58

37

51

30

a 5 b 0 c 3d 2 4 e 1 6

f 4 5 g 2 8h 3 2 i 1 4



2 a 4 b 0 c 12 d 16e + 4 f add 4 each time g 20, 24, 28

3 Teacher check

Page 211 Teacher check2 a 48 b 9 Rule: π 6

c 10 d 28 Rule: ÷ 4e 25 b 50 Rule: + 5

Challenge: Teacher check

Page 221 a 8.14, 12.14, 16.14, 20.14, 24.14

b 15.72, 12.72, 9.72, 6.72, 3.72c 12.51, 18.51, 24.51, 30.51, 36.51d 2.62, 2.77, 2.92, 3.07, 3.22e 9.77, 9.66, 9.55, 9.44, 9.33f 41.04, 39.44, 37.84, 36.24, 34.64g 5.72, 8.22, 10.72, 13.22, 15.72h 61.5, 52.25, 43, 33.75, 24.5

Looking for patterns: Teacher check

Page 231 a 8 b 10 c 6 d 4

e 1 f 5 g 20 h 100i 45 j 30 k 73 l 394m number is unchangedn number remains the same when divided by 1

2 a 7 b 9 c 3 d 10e 5 f 20 g 18 h 75i 15 j 64 k 97 l 569m number is unchangedn number remains the same when multiplied by 1

3 a b

c d

e

4 10tha b c

d e

15tha b c

d e

Page 241 Jack 137 cm, 1.37 m; Josh 1 m 19 cm, 1.19 m;

Suellen 1 m 8 cm, 108 cm; Teri 1 m 24 cm, 1.24 m;Kim 110 cm, 1.10 m; Vito 1 m 42 cm, 142 cm

2 108 cm, 110 cm, 119 cm, 124 cm, 128 cm, 137 cm, 142 cm3 a Sandy b 3 cm c Suellen4 34 cm5 Teacher checkChallenge: Man: a Robert Wadlow 2.72 m

b Gul Mohammed 57 cmWoman: a Sandy Allen 2.35 m

b Valentina Kasimjanous 60 cm

Page 251 Teacher check2 Teacher check3 Teacher check4 millimetres – pin, cherry, cotton reel;

centimetres – baby, radio; metres – hat stand, bed, string, church

Page 261 a 5 cm b 7 cm c 8 cm d 1 cm

e 10 cm f 100 cm g 500 cm h 800 cmi 236 cm j 485 cm

2 a 3 m b 8 m c 7 m d 4 me 2 m f 1 m g 3 m h 9 mi 6 m j 0.5 m k 2.3 m l 8.42 m

3 a 20 cm b 20 cm c 15 m d 18 m4 180 mWork backwards: 18 m

Page 271 a 30 b 312 a Sunday b Monday c Tuesday d Wednesday

e Thursday f Friday g Saturday3 a Thursday b Sunday c Saturday d Thursday

e Tuesday f Wednesday4 a 25th b 3rd c 13th d 19th5 a 4 b 46 a Saturday b Sunday

Page 281 Teacher check2 Teacher check3 a 1 b 2 c 104 a 1 b 3 c 105 a 1 b 2 c 10Using a table: a 86 400, 172 800, 259 200, 345 600

b 3 c 24

U

U UU

U


Page 291 Teacher check2 a 3 weeks b 1 minute

c 5 minutes d 2 months3 a 12:35 b 11:55 c 6:07 d 3:33Challenge: a 720 hours b 2 592 000 seconds

Page 301 a square b triangle c pentagon

d rectangle e hexagon2 triangles3 a square pyramid b triangular pyramid

c pentagonal pyramid d rectangular pyramide hexagonal pyramid

4 a 5 b 4 c 6 d 5 e 75 Teacher check

Page 311 A cube B sphere

C cylinder D triangular prismE pentagonal prism F coneG rectangular prism H octagonal prismI cylinder

2 A square B circleC circle D triangleE pentagon F circleG rectangle H octagonI circle Teacher check drawings

Page 32Teacher check

Page 331 a triangular prism b cylinder

c triangular pyramid d pentagonal prisme cube f cone

2 Teacher check

Page 341 a 282 a 10 b 6 c 3 d 4 e 53 Teacher check4 a Cola b Lemonade5 Drinks sold on Friday (or variations)

Page 351 a 6 b Martha c Theresa

d Teacher check2 a Total – 4, 7, 10, 0, 5, 3 b 29

c 4 d Martha because she saw most taxis3 a Boys 16, Girls 13

b Teacher check (2, table in question 2 gives more information)



Page 371 Teacher check a 20 rolls of a die

b side – Number of rolls; bottom – number on die2 Teacher check3 a one in six b one in six

c one in two ( 36 ) d four in six

4 Teacher check5 Teacher checkChallenge: Teacher check

Page 381 a 295, 592, 925 b Teacher check

c nine hundred and twenty-five2 a 356 b 4 112 c 9073 a 2 962 b 5 048 c 4 5004 a 63 b 995 a 101 b 2136 a 88 b 4547 a 24 b 34 c 468 2419 326

+ 273599

10 a 55 b 33 c 4311 a 33 b 2912 2313 a 28c b 47c

Page 3914 a

14 b

12 c

15

15 a 46100 , 0.46

16 tick 0.41, circle 0.0917 a 6.49 b 7.22

18 a 19, 24, 29

b 1.9, 2.1

19 a 2 cm b 600 cm c 125 cm20 a 4 m b 2 m21 a 22 cm b 28 m22 a Friday b Sunday c Tuesday d 21st23 a pentagonal pyramid b square pyramid24 triangular pryramid25 a Totals – 10, 9, 5, 8 b Teacher check

+ 0.2

+ 5

Pages 21–39

Teacher check2 a 9 975 b 1 024 c Teacher check

d Teacher check e 7 995, 1 997f 4 012, 7 012

3 Teacher check

Page 411 a 7 629 b 9 452 c 4 703

d 1 086 e 6 3502 Teacher check3 a 74 b 63 c 20 d 884 a 163 b 592 c 410 d 9025 a 7 004 b 2 500 c 1 234 d 9 990

Page 421 a 20 + 6 b 3 000 + 700 + 40 + 9

c 5 000 + 600 + 10 + 8 d 7 000 + 200 + 90 + 3e 6 000 + 0 + 50 + 4

2 a 2 817 b 8 461 c 4 972 d 1 385e 3 048 f 7 206

3 a 10 b 80 c 6 000 d 3e 3 000 f 7 000 g 50 h 80i 900 j 600 k 7 000 l 4

4 Teacher check5 a 2 048, 3 915, 8 420 b 983, 7 506, 9 375

c 5 013, 5 130, 5 301Challenge: 18 different numbers

Page 431 342 34th3 12th, 13th, 14th, 15th, 16th4 20th, 21st, 12th, 31st5 25th, 26th, 27th, 28th, 29th, 30th, 31st, 32nd,

33rd, 34th6 a 1st b 100th c 80th7 3rd, 4th, 6th, 8th, 9thDraw a diagram: 9th, 10th, 11th, 12th, 13th

Page 441 a 2 b 4 c 7 d 3

e 10 f 5 g 1 h 8 i 15 j 12 k 20 l 16 m 19 n 8 o 9 p 14

2 a II b VII c XII d V e XX f XIV g XVI h VIII i XI j III k IX l XIII m VI n XV o XIX p IV


Page 451 a (7 π 7) 49, 56, 21, 70, 14, 42, 7, 35, 63, 0, 28

b (8 π 7) 56, 64, 24, 80, 16, 48, 8, 40, 72, 0, 32c (9 π 7) 63, 72, 27, 90, 18, 54, 9, 45, 81, 0, 36

2 49, 28, 7, 56, 35, 70, 21 or 63, 14, 423 16, 24, 32, 40, 48, 56, 64, 72, 804 Circle spade, protractor, dustpan, dog bowl, oil lamp,

table lamp

Page 461 a 10 b 9 c 6 d 4

e 5 f 82

3 a 54 b 15 c 56 d 28e 40 f 81

Page 471 a 24, 48, 48 b 32, 64, 64

c 42, 84, 84 d 30, 60, 60e 50, 100, 100 f 34, 68, 68

2 a 30, 60, 120, 120b 44, 88, 176, 176c 62, 124, 248, 248

3 1124 925 2006 208Challenge: a 560 b 672 c 1 168

Page 481 a 16 b 16 c 162 a 12 b 1, 12, 2, 6, 3, 4

c 1, 2, 3, 4, 6, 123 a 24 b 1, 24, 2, 12, 3, 8, 4, 6

c 1, 2, 3, 4, 6, 8, 12, 244 a 1, 3, 9 b 1, 21, 3, 7

c 1, 36, 2, 18, 3, 12, 4, 9, 6d 1, 18, 2, 9, 3, 6 e 1, 11f 1, 40, 2, 20, 4, 10, 5, 8

5 a f b t c t d fe t f t g f h f



20

32

24

45

72

54

25

40

30

40

64

48

30

48

36

50

80

60


Page 491 a 15, 15 b 18, 18 c 32, 32 d 36, 36

e 7, 35,35 f 4, 20, 202 a 14 b 36

c 8 π 5 = 40 d 7 π 7 = 49e 3 π 9 = 27 f 10 π 2 = 20

3 a 45 b 7 c 12 d 0e 56 f 48 g 30 h 81i 70 j 16 k 25 l 0

Page 501 a 8 b 6 c 12 d 4

e 24 f 9 g 4 h 6i 5 j 16 k 48 l 2m 3 n 1 o 2

2 a 6 b 123 a 16 b 2 c 8

d 3 e 54 Teacher check

Page 511 a 8 b 4 c 6 d 4

e 7 f 6 g 6 h 9i 6 j 8

2 a 9 b 5 c 1 d 8e 8 f 6 g 3 h 7i 10 j 5 k 8 l 6

3 a 54 b 7 c 25 d 7e 1 f 40 g 10 h 100


Page 521 a 12 ÷ 5 = 2r2 b 14 ÷ 3 = 4r2

c 55 ÷ 9 = 6r1 d 29 ÷ 3 = 9r2e 65 ÷ 9 = 7r2 f 40 ÷ 7 = 5r5g 300 ÷ 4 = 75r0 h 42 ÷ 6 = 7r0i 70 ÷ 8 = 8r6 j 70 ÷ 7 = 10r0k 82 ÷ 9 = 9r1 l 18 ÷ 6 = 3r0

2 a 4 b 3, 30, 300c 2, 120, 20, 1 200, 200 d 4, 280, 40, 2 800, 7, 400e 6, 80, 4 800 f 35, 350, 5, 3 500, 700

3 10, 40, 5, 15, 3, 24, 4

Page 531

2 a 2 b 2 c 7 d 3e 3 f 4 g 3 h 2i 1 j 4 k 2 l 7

3 a 4 π 2 = 8 b 2 π 2 = 4 c 3 π 7 = 21d 3 π 3 = 9 e 2 π 3 = 6 f 8 π 4 = 32g 5 π 3 = 15 h 3 π 2 = 6 i 4 π 1 = 4j 4 π 2 = 8 k 5 π 2 = 10 l 6 π 7 = 42

4 a 4 π 7 = 28 b 56 ÷ 7 = 8c 36 ÷ 4 = 9 d 5 π 8 = 40

Page 541 a $5 b $20 c $10 d $5

e $10 f $50 g $20 h $5i $5 j $20 k $20

2 a 70c b $6.45 c $4.303 Answers will vary.

Page 551 a 70c b $4.25 c 0 d $4.302 a frame, hobby horse, wagon, blocks b $3.543 a $1.50 b $36 c $19 d $1.38

e $12.92 f $48 g $30 h $10i $8.58 j $24

4 a $7.50 b $180 c $95 d $6.90e $64.60 f $240 g $150 h $50i $42.90 j $120

5 a $45 b $1.44 c $13.79 d $47e $20.25

6 a $8.50 b $7.71Challenge: $95.69

Page 561 a 65c b 60c c 80c d 15c

e 25c f 35c g 40c h 20ci 75c j 65c

2 a $1 b $5 c $8 d $2e $7 f $6 g $8 h $3i $6 j $9

3 a C b A c Ed B e D

4 a $1 b 20c c 50c d $2e 5c f 10c

5 a 50c, 10c, 5cb $2, $1, 50c, 20c, 10c, 5cc $2, $2, $2, $2, $2, 20cd $2, $2, $2, $1, 20c, 10c, 5c

Page 571 Teacher check estimates

a $7.60 b $1.80 c $1.74 d $26.60e $13.90 f $2.92

2 a 4Y b 4X c 423 a $10.20 b $12.85 c $7.754 a 70c b $1.15 c $2.10Challenge: $50.35

Pages 40–57

a242446

b3 π 9 = 279 π 3 = 2727 ÷ 9 = 327 ÷ 3 = 9

c6 π 8 = 488 π 6 = 4848 ÷ 8 = 648 ÷ 6 = 8

d7 π 10 = 7010 π 7 = 7070 ÷ 10 = 770 ÷ 7 = 10

e7 π 9 = 639 π 7 = 6363 ÷ 9 = 763 ÷ 7 = 9

f5 π 7 = 357 π 5 = 3535 ÷ 7 = 535 ÷ 5 = 7



Page 581 B 3

610 , 3.6 C 2

810 , 2.8 D 4

510 , 4.5

E 1 910 , 1.9 F 5

210 , 5.2 G 4

410 , 4.4

H 3 110 , 3.1 I 1

710 , 1.7

2 A 23 B 36 C 28 D 45E 19 F 52 G 44 H 31I 17

Page 591 a

210 , 0.2 b

410 , 0.4 c

610 , 0.6

2 a 20 b 40 c 603 Teacher check4 Teacher check5 a 1

410 , 1.4 b 2

810 , 2.8 c 9

110 , 9.1

d 4 510 , 4.5 e 3

910 , 3.9 f 8

610 , 8.6

Page 601 a < b = c < d >

e > f =2 a 0.1 b 0.7 c 0.3 d 0.9

e 0.4 f 0.2

3 a 510 ,

50100 b

810 ,

80100 c

610 ,

60100

d 110 ,

10100 e

710 ,

70100 f

410 ,

40100

g 210 ,

20100 h

910 ,

90100 i

310 ,

30100

4 a T b F c T d Fe T f T g T h Fi T

5 a $2.60 b $5.70 c $3.40 d $7.506 a 2.6 b 5.7 c 3.4 d 7.5

e the 0 and $f it is showing tenths of a dollar

Challenge: a $3.40 b $1.80c $2.90 d $14.50

Page 611 A 21.6, 31.6, 41.6, 51.6, 61.6, 71.6

B 81.8, 71.8, 61.8, 51.8, 41.8, 31.8, 21.8C 1, 2, 3, 4, 5, 6, 7, 8D 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8

2 A the number gets larger by 10B the number gets smaller by 10C the number increases 10 timesD the number decreases 10 times

3 Teacher check

Page 621 a add 9 to the number in front

b add 1 more each time, + 1, + 2, + 3 etcc multiply the number in front by 3

d square each counting number in turn, 02, 12, 22 etc2 a 15, 31, 63 b 9, 17, 33 c 39, 120, 363

d 4, 4, 4 e 63, 313, 1 5633 Teacher check4 a

b doubles; double; doubles; double; double; doublesTrial and error: π 3 – 1

Page 631 a 13, 13, 13 b 17, 17, 17 c 16, 16, 16

d 14, 14, 14 e 27, 27, 27 f 28, 28, 28g 28, 28, 28 h 31, 31, 31

2 Order does not matter when adding3 a 24, 24, 24 b 42, 42, 42

c 70, 70, 70 d 180, 180, 180e 240, 240, 240 f 540, 540, 540g 64, 64, 64 h 187, 187, 187

4 Order does not matter when multiplying5 a 2 π 3 π 4 b 2 π 3 π 7 c 2 π 5 π 7

d 4 π 5 π 9 e 5 π 6 π 8 f 10 π 6 π 9g 2 π 4 π 8 h 3 π 7 π 9Answers will vary

6 a 16, 14 b 7, 13 c 11, 9d 15, 5 e 6, 4 f 17, 13g 51, 49 h 22, 18 i 19, 31j Teacher check

7 a 45 b 29 c 37 d 28e 22 f 57 g 168 h 76i 93

Page 641 Teacher check2 circle bath, milk barrel, petrol can, bucket3 a bath, milk barrel

b soup can, flask, oil canc baby’s bottle, cup, glass, thimble

4 tick thimble, cross bath5 Teacher check

Page 651 a 2 L b 7 L c 5 L d 9 L2 a 3 000 mL b 6 000 mL c 8 000 mL

d 10 000 mL e 4 000 mL3 a 2 L 500 mL b 3 L 200 mL c 1 L 700mL

d 5 L 850 mL e 6 L 120 mL f 8 L 225 mL4 a B b E c 50 mL, 200 mL5 a 1 500 mL b 7 500 mL c 2 250 mL

d 4 250 mLActivity: Teacher check

2

4

8

4

8

16

6

12

24

8

16

32

10

20

40

12

24

48

14

28

56

16

32

64

18

36

72

20

40

80

165

Page 661 a mL b L c mL d mL

e L f L2 Teacher check3 Teacher check4 Teacher check5 Teacher check

Page 671 A slide B flip C slide or turn2 Teacher check3 a slide b flip c turn4 Teacher check

Page 681 circle a, c, d, g; tick b, e, f2 a 5 cm π 2 cm; opposite sides equal

b 2 12 cm; all sides equal

c 4 cm π 1 12 cm; opposite sides equal

3 Teacher checkChallenge: Teacher check

Page 691 a triangle b hexagon c circle d trapezium

e square f rectangle g pentagon h ovali parallelogram j octagon

2 a it has 3 sides and 3 anglesb its opposite sides are equal and parallel

3 a tick B, D, E, F, H; circle D, F, GDraw a diagram: Teacher check

Page 701 a Freya b Emma2 a Kevin b Billy3 a John b Sally c Kevin d Ned4 a East b South5 a Emma, Jo, Ned b John, Dave, Emma6 a No-one b No-one

Page 711 a panda b penguin c bird d giraffe

e monkey f puppy g tiger h zebra2 a north b east c south

d north-east e south-west f south-east3 Teacher check

Page 721 a 2D b 4C c 5A d 3E

e 1B f 5D g 2A h 3Ci 1E

2 Teacher check3 1D, 2B, 3D, 4A, 4B, 4E, 5EChallenge: Teacher check

Page 731 Teacher check2 10 are possible

Page 741 Teacher check2 a 1 in 12 b 1 in 2 c 1 in 33 a B, D, F b A

c B, D, F because there are equal chancesChallenge: 1 in 2

Page 751 Teacher check2 a horizontal bars and vertical bars

b yes3 a Samad b Peta and Lila

c No – they could come from opposite directions4 Teacher check

Page 761 a 9 530 b 3 0592 a 700 + 20 + 8 b 8 000 + 500 + 0 + 43 2nd, 3rd, 4th, 5th, 6th, 7th, 8th4 a 5 b 20 c 4 d 13

e 8 f 95 646 a T b F c T d T7 a 21 b 48 c 32 d 638 a 3 b 6 c 10 d 459 a 7 b 9 c 7 d 8

e 4 f 810 a 35c b 40c c 70c11 a $1.25 b $2.10 c $6.6512 Teacher check

Page 7713 a 0.2 b 0.7 c 0.2514 a 31, 63 b 30, 8415 a 27 b 29 c 38 d 4716 a 2 L b 8 L17 a 7 000 mL b 12 000 mL18 a mL b L19 a b c

20 Teacher check21 Teacher check22 H, H; T, T; H, T

Pages 58–77




Page 781 a nine thousand two hundred and fifty-four

b five thousand and sixty-onec one thousand nine hundred and ninety-fived three thousand four hundred and seventye four thousand one hundred and ninef four thousand and ninety-oneg five thousand one hundred and six

2 1 995, 3 470, 4 091, 4 109, 5 061, 5 106, 9 2543 a 4 091 b 5 1064 a 3 470 b 3 470 c 4 109 d 5 061

Page 791 a > b > c < d >

e < f <2 Teacher check3 a 9 000 b 900, 90 c 9 d 904 a 4 b 400 c 4 000 d 4 0005 a 50 + 4 b 1 000 + 900 + 90 + 5

c 3 000 + 400 + 70 d 5 000 + 100 + 6e 5 000 + 60 + 1 f 4 000 + 90 + 1

6 a F b F c T d Te T f F g F h T

Challenge: 7 735, 3 507, 3 045, 5 306, 5 637

Page 801 a 7 000 b 8 000 c 3 000 d 7 000

e 1 000 f 4 000 g 9 000 h 4 000i 9 000 j 6 000

2 a 3 664 b 2 881 c 9 118d 8 245 e 5 106

3 a 8 453 b 2 018 c 9 602d 5 569 e 3 095

4 a 7 498 b 1 527 c 5 106d 2 292 e 9 045

5 a 5 550 b 1 801 c 9 336d 3 098 e 7 972

6 a 5 601 b 6 105 c 6 510 d 5 016Work backwards: 5 632

Page 811 a chess sets b paint palettes2 a 99 b 99 c 783 a 104 b 91 c 964 a clocks + telescopes

b chess sets + telescopes

Page 821 a 86 b 101 c 179 d 1532 a 481 b 797 c 891 d 896

e 882 f 722 g 741 h 569i 933 j 775 k 779 l 809m 709 n 930 o 611

3 a compasses + chess setsb telescopes + scalesc trains + telescopes + paintsd telescopes + clocks + compasses

Challenge: 350

Page 831 a 122 b 136 c 135 d 123

e 256 f 579 g 598 h 6822 a 151 b, c, d, e, f Teacher check3 a 561 b 421 c 384 mL

d Teacher checkChallenge: Teacher check

Page 841 a 1, 2, 3, 6, 9 b 1, 5, 7

c 1, 2, 3, 4, 6, 8, 12 d 1, 2, 4, 7e 1, 2, 5, 10 f 1, 7g 1 h 1, 2, 4, 8i 1, 2, 4, 5, 10 j 1

2 a 18 b 35 c 16, 24, 48d 14, 28 e 25, 50 f 49g 19 h 16 i 20j 31

Page 851 a Teacher check2 a 3, 8, 7 b 8, 8 c 70, 0, 423 a 60 b 120 c 160 d 1004 a 210 b 240 c 240 d 300

e 320Challenge: a 360 b 400 c 550

Page 861 a 12 b 42, 420, 4 200

c 45, 450, 4 500 d 64, 640, 6 4002 a 900 b 800 c 800

d 600 e 8003 a 72 b 215 c 384 d 222

e 364 f 368 g 399 h 846i 345 j 444

Page 871 a 4 b 4 π 4 = 16 c 6 π 6 = 362 Teacher check3 1, 4, 9, 16, 25, 36, 49, 64, 81, 1004 a 2 b 4 c 5 d 7

e 9 f 1Challenge: a 121, 144, 169 or 196

b 324 or 361c 625 or 676d 961


Page 881 a 2 b 6 c 3

d 8 e 52 a 6 b 8 c 3

d 7 e 13 a 7 b 3 c 8

d 4 e 5

Page 891 a 3, Teacher check b 6, Teacher check2 Teacher check estimates

a 20 b 32 c 79 d 41e 21 f 72

3 a Flying Saucer b River Caves c Ghost Train4 a 7 b 7 c 8 d 1

e 7 f 95 a 5r6 b 14 c 5 d 60

e 10r5 f 6, 56 a 10, 40, 5, 30, 10 b 8, 64, 32, 8, 72Trial and error: Mia 6, Manny 3

Page 901 a 2r3 b 4r2 c 4r3 d 9r2

e 9r4 f 9r1 g 7r2 h 7r3i 8r2 j 8r6 k 7r2

2 a 3 b 3 c 4Work backwards: 7

Page 911 a 23 b 12 c 34 d 11

e 41 f 12 g 23 h 32i 11

2 a 14 b 14 c 12 d 13e 13 f 12 g 19 h 15i 12 j 13

3 a 15 b 17 c 14 d 14e 17 f 13 g 14 h 19i 17 j 24 k 19 l 19m 28 n 15

4 a 20 b 30r1 c 12r1 d 10r4

Page 921 A 8 B 4 C 5 D 2

E 5 F 4 G 10

2 A 58 B

14 C

15 D

12

E 35 F

34 G

710

3 A 38 B

34 C

45 D

12

E 25 F

14 G

310

4 A 3 B 3 C 45 D 1, 1

E 35 ,

25 F

34 ,

14 G

710 ,

310

5 Teacher check

Page 931 a

45 b

34 c

38

2 Teacher check3 Teacher checkDraw a diagram: Teacher check, 43

Page 941 Teacher check

f 5, 5; 2, 2; 6, 6; 4, 4; 8, 82 a F b T c F d F

e T f T g F h T3 Teacher checkChallenge: Teacher check

Page 951 Teacher check2 a 1 b 2 c 5 d 1

e 33 a 7 b 10 c 9 d 1

e 9 f 16 g 7 h 21i 5 j 17

4 A $12 B $15 C $10 D $19E $24 F $17

5 a ✔ b 23 c 5 d ✔

e ✔ f 2 g 19 h 136 Teacher check7 Teacher check

Page 961 A $5 B $20 C $50 D $10

E $1002 F $1 G 5c H 10c I 50c

J 20c K $23 A 20 B 5 C 2 D 10

E 14 F 10 G 200 H 100 I 20

J 50 K 55 Teacher check6 Teacher check

Page 971 a $1, $1, 50c, 50c or $1, $1, 50c, 20c, 20c, 10c

b $2, 50c, 20c, 10c or $2, 50c, 10c, 10c, 10c etcc $2, $2, $2, $1, 20c, 10c, 5c etcd 50c, 50c, 50c, 20c, 20c, 5c etc

2 Answers will varya $2, $2, 50c b $2, 50c, 20c, 10c, 5cc $1, 20c, 20c, 5c

3 a 50c b $2, 10c, 5cc $2, $1, 50c, 5c

Pages 78–97



Page 981 a $3 b $10 c $9 d $2

e $3 f $3.40 g $10.20 h $8.75i $1.90 j $2.95

2 a $5 b $20 c $10 d $5e $5 f $20 g $10

3 a $1.60 b $2.05 c $3.104 a $9.80 b $11.255 $21.91Challenge: a $27.18 b $22.82

Page 991 a 10 b 1 c 2 d 5

e 2 f 102 Teacher check

Page 1001 a 1.13, 1.14, 1.15, 1.16, 1.17

b 15 ,

16 ,

17 ,

18 ,

19

c 0.7, 0.9, 1.1, 1.3, 1.5d 0.94, 0.93, 0.92, 0.91, 0.90

e 45 ,

55 (1),

65 (1 1

5 ), 75 (1 2

5 ), 85 (1 3

5 )2 a T b T c F d F

e T f F g F h Fi T j T k T l F

3 a 4 b 17 c 7 d 22e 2 f 13 g 2 h 100i 25 j 81 k 63 l 108m 5 n 20 o 10 p 42

Challenge: a 39 b 10

Page 1011 a = b = c =/ d =

e =/ f =/ g = h ==i =/ j = k =/ l =m =/ n =

2 a 5, 7, 9, 11, 13, 15bc Teacher check

3 a 8, 10, 12, 14, 16 b 11=11=11=11=11=11=c Teacher check

4 Teacher check

Page 1021 pumpkin 2 strawberry3 pumpkin, pineapple, rockmelon, cucumber, potato, apple,

tomato, orange, capsicum, onion, mushroom, strawberry4 tomato + rockmelon5 a 40 g b 400 g c 4 kg d 250 g6 tomato, apple, potato, cucumber7 tomato 8 5

Page 1031 a 3 kg b 9 kg c 1 kg

d 7 kg e 5 kg f 1 kg 500 gg 5 kg 200 g h 8 kg 125 g

2 a 4 000 g b 6 000 g c 2 000 gd 5 000 g e 2 600 g f 9 150 gg 3 475 g h 6 500 g i 2 250 kgj 8 750 g k 1 500 g

3 a 1 kg 329 g b 200 g c 1 kg 600 gd 2 kg 880 g e 755 g

4 a 250 g b 95 g c 390 g d 162 g5 a kg b g c g d kg

e g f kg g g h kgi g j kg

6 a 7 kg b 400 g c 2 kg d 1.5 kgChallenge: a 5 kg 629 g b 1 371 g

Page 1041 Teacher check2 Teacher check3 a A 1 250 g B 1 350 g C 1 500 g D 1 600 g

b A, B, C, D c Teacher checkTrial and error: Teacher check

Page 1051 122 a Feb b Jul c Dec

d Aug e Nov f Mar3 June, September4 April, June, September, November5 a Monday b Tuesday c Teacher check

d Thursday e Saturday f Friday6 a 60 b 24 c 2 d 12

e 3 f 42 g 120 h 4Challenge: a every 4 years b, c Teacher check

Page 1061

2 Teacher check3 C, F, H4 a trapezium b trapezium c no5 B6 Teacher check

A B

D

C

E

F G H

169

Page 1071 Teacher check2 a can be B C D E K L M T V W b H O X I3 Teacher check

Page 1081 Circle a, c, d, f2 Colour a, b3 Teacher check


Page 1101 Teacher check2 a 6

b Yes because there are the same number of bridges3 a 4

b No. There are more bridges from the right bank. You can go 9 ways.



Page 1131 Teacher check2 403 Yes4 a Steak b Chicken5 a 9 b 5 c 86 a Chicken b Fish7 a No b Teacher check8 Teacher checkChallenge: Teacher check

Page 1141 a two thousand seven hundred and four

b nine thousand and thirteen2 a 900 b 9 c 9 000 d 903 a 5 000 b 7 0004 a 148 b 922 c 1 3545 1 0776

7 a 344 b 195 c 4978 a 4 b 79 a 6r2 b 4r2 c 7 d 13

e 12 f 23

10 a 15 b

38

11 a 3 b 712 Teacher check13 a 5, 0.5 b 2, 0.214 a 7 b 14 c 1115 20

Page 11516 Teacher check17 a $4 b $7 c $618 a 1.22, 1.23, 1.24 b 0.80, 0.79, 0.78

c 44 ,

54 ,

64 ,

74

19 a 4 b 12 c 3 d 37e 9

20 a strawberry b apple c appled 300 g e 5 f 5

21 a 2 000 b 9 c 3

d 7 500 e 1 12 (1.5)

22 a 31 b 30 c 30 d 3123 a 24 b 7 c 60 d 12

e 2 f 2 g 24 h 4924 Teacher check25 a number (of pieces), people

b 6 c Helen d 6 e 11 pieces

Page 1161 Teacher check2 a 7 962 b 4 599 c 1 108 d 9 015

e 2 011 f 3 006 g 8 040 h 5 0573 a 4 275 b 9 603 c 1 048 d 7 590

Page 1171 a 507 b 301 c 4 026 d 7 020

e 8 009 f 1 5002 Teacher check3 a 9 520 b 2 059 c 2 095 (etc)

d 9 502 (etc) e 9 205 or 9 250 f 9 052 (etc)g 5 029 (etc) h 2 059 (etc) i 2 905


Page 1181 A 500 B 2 000 C 5 000 D 6 000

E 7 5002 Teacher check3 a 1 820 b 2 180 c 2 050 d 2 230

e 2 1004 Teacher check

Page 1191–5 Teacher check6 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,

59, 61, 67, 71, 73, 79, 83, 89, 91, 97

Pages 98–119


7

7

49

4

9

36

8

7

56

5

7

35

8

8

64



Page 1201 a 21 b each has only two factors

c 2 d prime numbers2 a 1, 2, 4, 8 b 1, 2, 3, 5, 6, 10, 15, 30

c 1, 3, 5, 15 d 1, 41e 1, 11 f 1, 2, 4, 13, 26, 52g 1, 2, 4, 7, 14, 28 h 1, 59i Colour 8, 30, 15, 52, 28

3 a 1 b No – it only has 1 factorc No – it only has one factor

4 a 63, 63 b 32, 32 c 21, 21d 50, 50 e 42, 42

5 a T b T c Fd F e T f T

Trial and error: 101 103 107 109 113

Page 1211 a 21, 90, 600, 711 b 48, 300, 600, 948

c 20, 280, 800, 1 100 d 35, 450, 500, 985e 18, 160, 600, 778 f 28, 240, 400, 668g 64, 240, 800, 1 104 h 27, 30, 900, 957i 56, 490, 700, 1 246 j 0, 270, 600, 870

2 882 cowsTrial and error: a 27 b 38 c 53

Page 1221 a 60 ÷ 3 b 88 ÷ 4 c 40 ÷ 2 d 100 ÷ 5

e 66 ÷ 6 f 60 ÷ 4 g 66 ÷ 3 h 140 ÷ 7i 90 ÷ 9 Teacher check estimates. Other answers possible.

2 a 24 b 22r1 c 19 d 18r3e 23 f 37 g 55 h 19r5i 21r6

3 Teacher check4 a T b T c F d F e F f TChallenge: Strawberry balls; 3

Page 1231 439 2 420 3 26 4 112 km5 518 6 155 7 16 8 3829 147 cm 10 14 11 1 335 12 1 296

Page 1241 a $1 500 b $2 113 c $1 501 d $132 a Ford b Honda c Toyota3 a Jeep and Ford b Pulsar and Ford4 a $3 500 b $2 500

Page 1251 a 16 b 12 c 70 + 15 d 10 + 17

e 40 + 11 f 20 + 14 g 30 + 18 h 80 + 13i 50 + 11 j 20 + 16 k 50 + 19 l 70 + 17m 30 + 15 n 60 + 18

2 a 17 b 27 c 14 d 19e 29 f 49 g 18 h 18i 29 j 25 k 27 l 29m 53 n 44

Page 1261 a 54 b 24 c 16 d 38

e 282 A 34 B 52 C 27 D 463 a C and E b A and B c A and E d C and B4 a D and B b E and B5 a b

c d

6 a 29 b 44

Page 1271 11 2 17 3 75 4 585 23 6 84 7 49 8 369 63 10 35 11 54 12 4613 a 352 b 11514 a 233 b 23415 1 257Trial and error: 857 and 229

Page 1281 a 900 km b 615 km c 881 km d 1 241 km2 a 426 km b 227 km c 275 km d 85 km3 a tiger and dog b cow and elephant4 a tiger, dog and elephant

b elephant, cow and house5 a snowman, house, cow and tiger

b elephant and dog

Page 1291 a 110, 1 100

b 15, 150, 1 500c 12, 120, 500 + 700 = 1 200d 12, 40 + 80 = 120, 400 + 800 = 1 200e 3, 30, 300f 4, 90 – 50 = 40, 900 – 500 = 400g 2, 80 – 60 = 20, 800 – 600 = 200h 7, 80 – 10 = 70, 800 – 100 = 700

2 a 13, 9, 13b 23, 7 + 16 = 23, 23 – 7 = 16, 23 – 16 = 7c 19, 28 – 19 = 9, 9 + 19 = 28, 19 + 9 = 28d 17, 23 – 17 = 6, 6 + 17 = 23, 17 + 6 = 23

62 14 4828 12 1634 2 32

73 35 3825 19 648 16 32

58 23 3519 15 439 8 31

90 35 5559 24 3531 11 20

3 a 35, 85, 45, 95, 75, 65 b 8, 18, 58, 78, 28, 68c 41, 51, 81, 101, 71, 91

4 a 591 (591 – 372) b 922 (922 – 564)c 1 134 (1 134 – 755) d 995 (995 – 609)

Page 1301 a + 6 b + 60 c + 300 d + 1 000

e + 222 a – 4 b – 60 c – 300 d – 6 000

e – 17 f – 2093 a T b T c F d F

e F f T g Th Teacher check i Teacher check

Challenge: a 3 904 b 2 605 c 2 014d 903 e 2 850

Page 1311 A $5.82, $6.32, $16.32, $96.32

B $3.41, $3.91, $13.91, $93.91C $3.78, $4.28, $14.28, $94.28D $4.95, $5.45, $15.45, $95.45E $1.37, $1.87, $11.87, $91.87

2 a $9.40 b $10.64 c $13.85 d $14.223 a $2.04 b $2.41 c $1.54 d $2.414 a $16 b $19 c $17 d $14

e $4 f $2 g $1 h $10(Other answers possible)

5 Teacher checkTrial and error: Lee has $2.15, Lily has $2.25,

Lexie has $2.05

Page 1321 a 2 b 42 a T b T c F d F

3 a #4 b 1 = @2 c @4 = !2 d @4 = !2e #4 f $4 = 1

Page 1331 a !2 b Teacher check2 a 3 b 6 c 9 d 12

e 12

3 a @4 = !2 b #4 c 1#4 d 1!4 = %44 a #4 b !2 c !4 d !4

e !4 f @4 = !2 g 0 h 0

5 a 10 b 5 c 15 d 2d 20

Page 1341 a 7 b 55 c 369 d 1 900

e 8 000 f 476 g 6 004 h 888i 5 023 j 741

2 Teacher check

Page 1351 a They make a square

b 1, 4, 9, 16, 25, 36, 49, 64, 81c 100

2 a They make a triangleb 1, 3, 6, 10, 15, 21, 28, 36, 45c 1, 3, 6, 10d + 5 = 15; 1 + 2 + 3 + 4 + 5 + 6 = 21;

1 + 2 + 3 + 4 + 5 + 6 + 7 = 28;1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36;1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

Page 1361 a Teacher check b 144 c 1442 a Teacher check b 783 a 3 b 6 c 10 d 15

e triangular f 36 g Teacher check4 Teacher check5 a T b F c F d F

e T f T

Page 1371 Teacher check2

3 a π 2 and π 8; π 3 and π 7; π 4 and π 6b a pentagon c a decadon

Pages 120– 138


π3 π4 π5

π7

π2

π6 π8 π9



Page 1381 a 6 b 2 c 3 d 32 a strawberry patch and rose garden

b flower garden and vegetable garden3 a herb garden

b rose garden or strawberry patch4 11 square metres5 42 square metresChallenge: about 5 m2

Page 1391 a 10 m b 6 m c 8 m d 10 m

e 7 m f 9 m2 7 m3 a 6 cm2, 6 cm2, 6 cm2, 6 cm2, 6 cm2, 6 cm2

b 14 cm, 10 cm, 12 cm, 12 cm, 14 cm, 14 cmc Teacher check (Shapes with same area do not

necessarily have the same perimeter.)Challenge: Teacher check

Page 1401 Teacher check2 Teacher check3 a cm2 b m2 c m2 d cm2

e m2 f cm2 g cm2 h m2

i cm2

4 Teacher checkDraw a diagram: Teacher check

Page 1411 a Teacher check

b Teacher check2 a days b seconds c hours d years

e months f weeks


Page 1431 Colour red b, e; colour blue a, d; colour green c, f, g2-5 Teacher check

Page 1441 a Teacher check

b Colour green a, fc Colour blue c, ed Colour yellow b, d

2 R on a, g; A on b, d, i; O on c, e, f, hChallenge: Teacher check times

a right angleb acute anglec obtuse angle

Page 1451 a Quicksand Marsh b Lake Eerie

c Crocodile River d Skull Cavee Darkheart Woods f Cramer Castleg Pirate Cemetery h Jolly Dodger

2 a Quicksand Marsh b Crocodile River3 a East b South-east

c North d North-east4 a South b South-west

c South-east d West

Page 1461 SUL2 Teacher checkChallenge: Teacher check

Page 1471 a Tom, Sue, Bill, Anne, Terry, Jim

b Amber, Murphy, Todd, Ben, Ari, Li c Jan, Amy, Jack d 15

2 a Teacher check b 6 c 4 d 4


Page 1481 a Beth

b Each time a coin is tossed there is a one in two chance of tossing either a head or a tail.

2-4 Teacher check

Page 1491 Yes. He can see to pick the fox.2 No. He has one chance in 7 — he cannot see3 Choosing one from a group x4 One chance in seven5 a One chance in five

b There are fewer to choose from6 Seven7 Teacher check8 Teacher check

Pages 139– 152


Page 1501 a 4 627 b 9 015 c 2 1082 a 7 530 b 3 057 c Teacher check

d Teacher checke 7 035 or 7 053 or 7 305 or 7 350

3 Circle 3, 7, 194 a 951 b 9855 a 29 b 18r2 c 126 a Three out of 1, 2, 3, 4, 6, 12

b Teacher check7 a 8 b 148 a 38 b 25 c 459 a b

10 $2511 a 35, 75, 95, 45, 85, 65 b 8, 48, 18, 58, 38, 6812 a 2 b 3 000 c 20 d 500

Page 15113 a $4.50 b $8.15 c $12.10 d $6.2514 315 1516 a @2 = 1 b #4 c !4 d #4

e 1!4 = %4 f &4 = 1#417 10 spots18 25, 36, 49, 64, 81, 10019 a m2 b cm2 c cm2 d m2

20 a 12 cm2 b 14 cm c 10 cm2 d 18 cm21 Colour blue c, d; colour red b, e; colour yellow a, f

Page 15222 Sue Jones23 a 4 b 5 c Paul, Stacey, Vee

d 7 e 924

25 a R, G or B; 3b RR, GG, BB, RG, RB, GB; 6c 5 d 3

64 16 4830 14 1634 2 32

53 27 2634 8 2619 19 0

*

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