Primary Maths TG4.pdf - Winmat Publishers

44TEACHER’S GUIDE

Daniel O. Apronti Juliet C. Donkor Godwin T. Nomo

Mathematicsfor Primary SchoolsMathematicsfor Primary Schools

NEW

EDITION

Mathematicsfor Primary Schools

Teacher’s Guide 4

Daniel O. AprontiJuliet C. DonkorGodwin T. Nomo

AdvisorCharles Duedu

winmatPUBLISHERS LIMITED

Published in 2016 by

WINMAT PUBLISHERS LTD

PO Box AN 8077,

Accra-North, Ghana

ISBN 978-9988-0-4604-0

Text © Daniel O. Apronti, Juliet C. Donkor, Godwin T. Nomo, 2016

All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publishers.

Designed by Kwabena Agyepong

Illustrated by Elkanah Kwadwo Mpesum

The publishers have made every effort to trace all copyright holders but if they have inadvertently overlooked any, they will be pleased to make the necessary arrangements at the first opportunity.

Contents

Introduction 5

Unit 1 Shape and space I 7

Unit 2 Numbers and numerals 0-100,000 11

Unit 3 Investigation with numbers I 17

Unit 4 Addition and subtraction (sum up to 100,000) 24

Unit 5 Measurement of mass/weight and time 29

Unit 6 Fractions I 40

Unit 7 Multiplication 47

Unit 8 Division 54

Unit 9 Fractions II 58

Unit 10 Measurement of length and area 64

Unit 11 Shape and space II 71

Unit 12 Collecting and handling data 75

Unit 13 Investigation with numbers II 79

Unit 14 Measurement of capacity and volume 84

5

Introduction

Basic school mathematicsThe curriculum covers the following five overlapping areas of content:• Numberandnumerals;• Numberoperations;• Measurement,shapeandspace;• Collectingandhandlingdata;• Problemsolvingandapplication.

Pupil materialsSix Pupil’s Books cover the content of the mathematics curriculum. In general the Pupil’s Book provides a presentation of curriculum content and some examples.

Pupil’s Book 4The topics presented in Pupil’s Book 4 are arranged in fourteen units:1 Shape and space I2 Numbers and numerals 0-100,0003 Investigation with numbers I4 Addition and subtraction (sums up to 100,000)5. Measurement of mass / weight and time6 Fractions I7 Multiplication8 Division9 Fractions II10 Measurement of length and area11 Shape and space II12 Collecting and handling data13 Investigation with numbers II14 Measurement of capacity and volumeThe pupils will need some assistance in order to understand the instructions in the Pupil’s Book.

Teacher’s GuidesThe units of the six complementary Teacher’s Guides have sections which provide:• objectives;• backgroundnotes;• teachingmethodsoutliningtheuseofteachingandlearningmaterialsandequipment;• keywords;• alistofmaterials;

6

• alistofactivitieswhichintegratePupil’sBookpagesandpracticalwork;• someassessmenttechniqueswhichgiveanindicationofmasteryandreadiness;• adiagnosticassessmenttestaftereveryunitsothattheteachercanevaluatethesuccessoftheir

teaching methodology.

Teacher’s Guide 4The ideas and suggestions in this book should help teachers and their pupils to:• interactpurposefullywitheachother;• usetheclassroomenvironmentandresources;• developapositiveattitudetowardslearningmathematics.

The teacher should:• firststudythesyllabusandnotethetopicsthataretobetaughtinYear4;• scantheTeacher’sGuideandbeawareofhowitreferstoandfitstogetherwiththePupil’sBook;• becomefamiliarwiththewholeprogrammefortheyearandthedetailsoftheinitialparts;• decidewhichteachingandlearningmaterialsareneededgenerallyandthespecificresourcestobegin

the programme;• recognisethepartsoftheprogrammewhichrequirediscussionswithotherteachersandsupervisors;• makedetailedplansforpresentingeachunit.

Helping the pupils to learnChildren learn best by ‘doing’, ‘thinking’ and ‘talking’. For these reasons the activities that are presented should be both interesting and worthwhile. Teachers should guide, encourage and compliment their pupils and try to anticipate their learning needs. In order to use the resources and materials efficiently it will be necessary to have the pupils organised in small groups.Each unit uses some ideas based on a previous topic. For this reason it is important that the pupils are given sufficient time to ‘think things out’ for themselves. Questioning and guiding will assist them to think for themselves and relate the ideas that are presented to everyday life.

Evaluation and assessmentAssessmentshouldbecomepartofthelearningprocessandwillhelptheteacherdecideiftheobjectivesare being met. The teacher should observe the pupils closely and listen to what they talk about. This will help the teacher to assess if they are ready to move to a new activity or whether a learning situation should be modified. Tests based on the pupil materials can provide a measure of mastery and an indication of readiness for the next topic. A diagnostic assessment test is provided after every unit so that teachers can assess pupils’ progress, see if there are areas they need to go over again and also review their methodology. Teachers should take these tests in to mark so they can see how individual pupils are progressing.

7

UNIT 1 Shape and space IPupil’s Book pages 1 to 6

ObjectivesThe pupils should be able to:• discoverthatapointiswheretwoormorelinesmeet;• identifyandmarkpointswherelinesintersect;• identifycornersofshapesaspoints;• drawtwoormorelinesthroughapoint;• appreciatethatonlyonestraightlinecanbedrawnthroughapairofpoints;• identifyplaneshapesbytheirnumberofsides.

NotesIdentifying points, lines, and the space between them is important later on, when pupils study angles and the properties of polygons.

Teaching methodsThe idea of points of intersection should come from pupils’ observations of what is around them. For example, they should appreciate that where roads and paths meet there is a point of intersection. Once this has been established pupils can consider more abstract examples.

Key wordsPoint, intersection, corner, vertex, side.

MaterialsCollectionoftemplatesforthefollowingshapes:square,isoscelesright-angledtriangle,parallelogram,trapezium, rectangle, pentagon, hexagon (the shapes do not have to be regular).

Activity 1: Points of intersectionPupil’s Book pages 1 and 2.• Askpupilstoidentifyplaceslocallywhereroadsand/ortrackscross.Explainthatthepointwheretwo

roads or tracks meet is called the ‘point of intersection’.

AnswersPupil’s Book page 21 a i) 2 lines ii) 6 intersections

8 UNIT 1 Shape and space I

b i) 2 lines ii) 2 intersectionsc i) 3 lines ii) 3 interactionsd i) 3 lines ii) 5 intersectionse i) 3 lines ii) 2 intersections

2 If two straight lines cross, they have one intersection.

Activity 2: Corners, points and linesPupil’s Book pages 3 and 4.• Usingarectangle,explainthatthepointswheresidesorlinesmeetinashapearealsopointsof

intersection.• Getpupilstodrawatriangleandasquareandmarkthecornersoneach.• Showpupilsasolidshapesuchasacuboid.Remindthemthat,indrawings,notallofthecorners

will be visible.• Remindthepupilsthatsolidshapeshavecorners,facesorsurfacesandedges.Flatsurfacesarecalled

planes. Using the cuboid, show how flat surfaces with straight edges meet to form a straight line.• Usingacylinder,showhowflatsurfaceswithcurvededgesmeettoformacurvedlineoranarc.The

pupils should then look carefully at a variety of everyday solid shapes and identify the meeting of planes (flat surfaces) and note which make straight lines and which make curved lines.

AnswersPupil’s Book pages 3 and 4A triangle has 3 corners; 2 lines meet at each corner.Asquarehasfourcorners;2linesmeetateachcorner.There are 10 corners on the house (2 are hidden); 3 lines meet at each corner.

Activity 3: Lines and cornersPupil’s Book page 5• Showpupilsthatonelinewithachangeofdirectioncouldbedescribedastwolineswithacorner.• Askthepupilshowmanylinescanbedrawnthroughapoint.• Showthepupilshowthreelinescanpassthroughapoint.‘Canyoudrawfourlinesthroughapoint?’• Getthepupilstodrawfourlinesthroughapoint.Emphasisethatanynumberoflinesmaypass

through a point.• Askthepupilstojointhemselvestogetherinpairswithapieceofstringorcloth.Withoutmoving

andkeepingthestringtight,askthemhowmanywaystheycanjointogether.(one)• Showthepupilsthatonlyonestraightlinecanbedrawnthroughapairofpoints.Thepupilsshould

then copy the diagrams into their exercise books, ensuring that the lines are straight and pass through thepoints,andanswerthequestions.

9UNIT 1 Shape and space I

AnswersPupil’s Book page 51 a 3 points and 3 lines b 1 point and 3 lines c 2 points and 3 lines2 Many straight lines can be drawn through a single point.3 Only one straight line can pass through two points.4 a 6 points and 6 lines b 6 points and 6 lines c 6 points and 6 lines(The pupils may recognise that these are all hexagons. If not, refer back to this during the next activity.)

Activity 4: Sides and verticesPupil’s Book page 6.• Showthepupilsthatatrianglehasthreesidesandthreevertices;andthatasquarehasfoursidesand

four vertices.• Getthepupilstocountthenumberofsidesandverticesofothershapes.• Askthemwhatpatterntheyhavefoundbetweenthenumberofsidesandthenumberofvertices.

(They are the same).

AnswersPupil’s Book page 6A pentagon has 5 vertices.A hexagon has 6 sides.

Shape No. of sides No. of vertices

trianglesquarerectanglepentagonhexagon

34456

34456

The number of sides is the same as the number of corners.

A heptagon has 7 corners.A shape with 12 corners has 12 sides.

Rectangles always have four sides and four corners.

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.

10 UNIT 1 Shape and space I

The evaluation exercises should enable the class teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.

To assess pupils’ progress, form a test paper, which has:• 2questionswherethepupilsidentifyandmarkpointswherelinesintersect;• 1questiontoshowthatmanylinescanbedrawnthroughonepointbutonlyonestraightlinecanbe

drawn through a pair of points;• 3questionswherethepupilsidentifycornersofshapesaspointsandthenumberoflinesintersecting

at them;• 2questionswherethepupilsdrawshapesandcountthesidesandcornersofeach;• 2questionsthatusethefactthatforanystraight-sidedshapethenumberofsidesisequaltonumber

of corners.Multiply the score by 10 to get a percentage mark.

Diagnostic assessment test1 Howwerepupilsabletorelateobjectsaroundthemtotheconceptsof:

a points;b intersections;c corners;d vertices;e sides of plane shapes.

2 What skills and strategies did pupils use to identify and mark points; points and intersections; verticesofshapesaspoints;andplaneshapes?

3 What challenges did pupils encounter to discover that ‘for any straight-sided shape, the number of sidesisequaltothenumberofvertices?

11UNIT 2 Numbers and numerals 0-100,000

UNIT 2 Numbers and numerals 0-100,000

Pupil’s Book pages 7 to 15

ObjectivesThe pupils should be able to:• countinten-thousands;• statetheplace-valuesofdigitsinnumbers0-100,000;• writethemultiplesofthousandsandten-thousandsupto100,000;• writethenumeralsforanumberstatedinwordsupto10,000;• writethenumbernamefornumeralsupto1,000;• usethesymbols=,>,<tocomparetwonumbersupto100,000(onehundredthousand).

NotesMost pupils will have heard of numbers in the tens of thousands range and will have used the idea especially with reference to money. Here we are concerned with formally developing the concept of a ‘thousand’ and ‘ten-thousand’ as numbers and place values.

Teaching methodsThe use of teaching and learning materials such as the abacus, the number strip and the number line is highly desirable. The pupils can be assessed by the scores achieved in the exercises. Tests based on these could be developed by the teacher.

Key wordsHundred-thousands, Ten-thousands, Thousands, Hundreds, Tens, Ones, the numbers from 0 to 100,000, greater than, less than, order. The names of all the teaching and learning materials.

MaterialsAbacus, number strips and the number line. Base ten materials.

Activity 1: Tens of thousandsRevise the relationship between Ones, Tens, Hundreds and Thousands using the structured base ten materials and the abacus. Establish the relationship as:

10Ones=1Ten10Tens=1Hundred

10Hundreds=1Thousand

12 UNIT 2 Numbers and numerals 0-100,000

Using a five-spike abacus show 9 counters on each of the Ones, Tens, Hundreds and Thousands spikes. Ask the pupils to say which number is represented. Demonstrate that adding one more counter to the Ones effectively causes all the four spikes to be ‘too full’ and pass on one counter to the empty, fifth, Ten-thousand spike. Explain that’ Adding one more counter to the Ones’ moves:• 10OnestotheTensspikeas1Ten,whichmoves• 10TenstotheHundredsspikeas1Hundred,whichmoves• 10HundredstotheThousandsspikeas1Thousand,whichmoves• 10Thousandstoanewfifthspike-theTen-thousandsspikeas1Ten-thousand.

This number is 10,000.’Ask some pupils to repeat the demonstration.Ask the pupils to describe the representation of 9,999 using the base ten materials. (The Thousands group will be 90 cm high, etc. Adding ‘one more’ will make the ten ‘blocks’ showing Ten-thousand 1 m high.)

Pupil’s Book page 7. Use the two diagrams at the top of the page to explain how four full spikes (9,999) and one extra counter produces a number represented by one counter on the fifth (Ten-thousand) spike. Use the two diagrams at the bottom of the page to Similarly explain how five full spikes (99,999) and one extra counter produces a number represented by one counter on the sixth (Hundred-thousand) spike. The pupils should draw abacus diagrams to represent 1, 10, 100, 1,000, 10,000 and 100,000.

Activity 2: Counting onPupil’s Book page 8. Use the diagrams of the abacuses and the numbers under them to lead the class to count:• inten-thousandsfrom10,000to90,000;• inthousandsfrom91,000to99,000;• inhundredsfrom99,100to99,900;• intensfrom99,910to99,990;• inonesfrom99,991to99,999.

Activity 3: Place valuePupil’s Book page 9. ‘The distance from east to west through the centre of the Earth is 12,754 km.’ Arrange the abacus to show 12,754. Arrange a number strip which shows place values and, when folded, shows how we say the number. Ask some pupils to repeat the demonstrations.

AnswersPupil’s Book page 91 The abacus should show:

• 6 counters on the Ones spike;


• 7 counters on the Tens spike;• 0 counters on the Hundreds spike;• 0 counters on the Thousands spike;• 4 counters on the Ten-thousands spike.

2 Youwillneedtofindoutthepopulationofyourdistrict,forthepupilstoshowitonanabacus.Keep the number lower than 100,000.

Activity 4: Place valuePupil’s Book page 10. Use the example to identify each place value. The class should respond orally for questions1to18beforeproceedingtowritetheseanswersintheirexercisebooks.Theyshouldthenanswerquestion19.

AnswersPupil’s Book page 10

1 2 Hundreds 2 6 Tens 3 9 Thousands4 6 Ones 5 4 Hundreds 6 7 Ones7 5 Tens 8 4 Thousands 9 2 Ten-Thousands

10 7 Ten-Thousands 11 9 Thousands 12 0 Thousands13 5 Hundreds 14 0 Tens 15 0 Hundreds16 0 Hundreds 17 7 Thousands 18 8 Ten-Thousands19 For example:

a 57,432 b 2,493 c 237 d 47,235 e 37,035 e 94,235

Activity 5: OrderPupil’s Bookpage11.Discussthenumberlineinquestion1andassistthepupilstoidentifythemissingnumbers.


1 700, 800, 900, 1,000, 1,1002 1,150, 1,250, 1,350, 1,450, 1,5503 650, 750, 850, 950, 1,0504 13,000, 14,000, 15,000, 16,000, 17,0005 8,500, 9,500, 10,500, 11,500, 12,5006 9,900, 10,000, 10,100, 10,200, 10,3007 30,000, 31,000, 32,000, 33,000, 34,000


8 25,800, 25,900, 26,000, 26,100, 26,2009 99,100 ,99,300, 95,000, 99,600, 99,800

10 91,000 , 93,000, 95,000, 98,000, 100,000

Activity 6: Saying and writing numbersPupil’s Book page 12. Use the three examples to demonstrate how to say and write the numbers.


1 753=7hundredand53 2 540=5hundredand403 826=8hundredand26 4 730=7hundredand305 401=4hundredand1 6 168=1hundredand687 534=5hundredand34 8 811=8hundredand119 553=5hundredand53 10 480=4hundredand80

11 497=4hundredand97 12 843=8hundredand4313 379=3hundredand79 14 630=6hundredand3015 6,328=6thousand,3hundredand2816 3,211=3thousand,2hundredand1117 5,904=5thousand,9hundredand418 8,473=8thousand,4hundredand7319 7,084=7thousandand8420 9,843=9thousand,8hundredand4321 1,256=1thousand,2hundredand5622 5,534=5thousand,5hundredand3423 4,738=4thousand,7hundredand3824 2,029=2thousandand2925 6,209=6thousand,2hundredand926 9,999=9thousand,9hundredand9927 39,287=39thousand,2hundredand8728 48,147=48thousand,1hundredand4729 38,073=38thousandand7330 90,153=90thousand,1hundredand5331 57,630=57thousand,6hundredand3032 75,486=75thousand,4hundredand8633 64,753=64thousand,7hundredand53


34 73,056=73thousandand5635 60,345=60thousand,3hundredand4536 79,999=79thousand,9hundredand9937 80,207=80thousand,2hundredand738 53,538=53thousand,5hundredand38

Activity 7: Writing numbersPupil’s Book page 13. Use the three examples to demonstrate how to write the numbers.

AnswersPupil’s Book page 131 545 2 723 3 907 4 3895 1,168 6 1,645 7 1,639 8 1,6529 15,565 10 25,390 11 80,043 12 76,900

Activity 8: Comparing numbersPupil’s Book page 14. Discuss the steps used to order the numbers. Discuss the meanings of the symbols and practise with a few examples before setting the pupils the exercise.

AnswersPupil’s Book page 14/15(Suggestion: The pupils should correct each other’s work when the correct order is read out.)1 a 65,463, 54,321, 8,895, 4,731, 892, 567

b 82,397, 76,092, 7,671, 1,674,498,489c 13,459, 12,567, 5,782, 2,453, 538, 250d 79,045, 70,843, 3,670, 3,067, 267, 265e 62,456, 62,267, 7,890, 7,390, 876, 785

2 a.>b.<c.<d.<e.<f.>

Pupil’s Book page 15Writing number names1 Five Hundred and forty-five2 Seven hundred and twenty-three3 Nine Hundred and seven


4 Three hundred and eighty-nine5 One thousand6 Nine

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.Theevaluationexercisesshouldenabletheclass teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help pupils overcome their problems.To assess a pupil’s progress, form a test paper which has:• 10placevaluequestionssimilartoquestions1to19onpage10inthe

Pupil’s Book;• 10orderand>/<questionssimilartothoseonpage14inthePupil’sBook;• 5expandingandwritingnumberquestionssimilartothoseonpages12and13inthePupil’sBook.

Multiply the score by 4 to get a percentage mark.

Diagnostic assessment test1 Howrelevantwerethediagramsthatwereusedtoleadpupilstocountfrom0-99,999?2 Howdidyouassesspupils’understandingoftheplacevalueindigits0-99,999?Iftherewere

weaknesses plan strategies to assist pupils to overcome their difficulties.3 List some of the challenges that pupils faced: (a) when they were writing numerals for numbers up to 10,000.(b) and when they were writing number names for numerals up to 1,000.4 Were pupils comfortable with the use of the symbols: (i)=(ii)>(iii)<,tocomparenumbersupto100,000?

17

UNIT 3 Investigation with numbers IPupil’s Book pages 16 to 24

ObjectivesThe pupils should be able to:• discoversomepropertiesofbasicoperations;• usethesepropertiesofbasicoperations;• usetwoormoreofthebasicoperationstowritenumbersentences;• findpossiblecombinationsofthreenumbersfromthedigits1,2,3...9whichhavethesamesum;• writenumbersthatcanbedividedby2andthosethatcannot;• findtheenddigitsofevenandoddnumbers.

NotesLead the pupils to find missing numbers and operation in number statement. We also investigate the associative and the distributive laws. The associative law, as it affects addition, shows that numbers may be added in any order (a + b) +c=a + (b + c).The distributive law shows that, for multiplication and addition, multiplication distributes over addition: a(b +c)=ab + ac. A section investigates the use of the four operations (+, -, × and 7), brackets and the first nine digits (1, 2, 3 ... 9) to produce new numbers. The unit ends with the identification of odd and even numbers.

Teaching methodsThe pupils are led to identify:• thepatternsofusingtheassociativeanddistributivelaws;• additionpatternsinthemakeupofanumber;• oddandevennumbers.The terms ‘associative’ and ‘distributive’ should not be used in lessons but the pupils should be encouraged to identify and use their representative patterns.

Key wordsBrackets, operation, add, subtract, multiply, divide, digit, even, odd.

MaterialsFive copies of cards of each of the first nine digits. Five copies of cards of each of the four operations. Bottle tops or other counters.

18 UNIT 3 Investigation with numbers I

Activity 1: Properties of basic operations Pupil’s Book page 16. Use the example to introduce the properties of basic operations to find numbers and missing operations.

1 3×3=7+2 5 8-2=5+12 4x4=16÷ 2 6 5x3=3x53 12-5=14 ÷ 2 7 12-6=24÷ 44 24 ÷6=2x2 8 5x5=15+10

Activity 2: AddingPupil’s Book page 16. Use the example to introduce the pattern of the associative law for addition.Establish that:• addinginanyordergivesthesametotal;• itisofteneasiertofirstaddtogetherthosenumberswhichmaketenoramultipleof10.WorkthroughthePupil’sBookquestionsorallytohelpthepupilschoosepairsthatmaketen,oramultiple of ten, when bracketed.


1 (6+4)+3=10+3=13 2 (7+3)+6=10+6=163 (8+2)+5=10+5=15 4 (4+6)+8=10+8=185 (3+7)+9=10+9=19 6 (2+8)+7=10+7=177 (12+8)+3=20+3=23 8 (13+7)+6=20+6=269 (6+14)+5=20+5=25 10 (15+5)+7=20+7=27

11 (16+4)+8=20+8=28 12 (3+17)+9=20+9=2913 (26+4)+9=30+9=39 14 (6+34)+7=40+7=4715 (15+15)+8=30+8=38 16 (6+44)+2=50+2=5217 (46+4)+5=50+5=55 18 (36+14)+23=50+23=73

Activity 3: Using × Pupil’s Bookpage18.Usetheexamples3×2=2×3and3×4=4×3tointroducethecommutativelawformultiplication.Otherexamplesonthegridare:2×4=4×2,2×5=5×2,2×6=6×2,3×6=6×3,4×5=5×4,4×6=6×4,5×6=6×5.

AnswersPupil’s Book page 181 3×12=12×3 2 2×9=9×2 3 6×5=5×6 4 7×4=4×7

19UNIT 3 Investigation with numbers I

1 20 2 18 3 16 4 14 5 10 6 21 7 36 8 27 9 18 10 35

Activity 4: Using + and ×Pupil’s Book page 19.Use the example to introduce the pattern of the distributive law for multiplication over addition. The pupils should:• lookatthepatternofsquares,trianglesandcirclesinthepanelundertheexample;• usethepatterntocompletequestions1to3asaclass;activity• completethewholeexerciseintheirexercisebooks.


1 4×(2+5)=(4×2)+(4×5)=8+20=282 5×(3+6)=(5×3)+(5×6)=15+30=453 3×(7+8)=(3×7)+(3×8)=21+24=454 3×(2+5)=(3×2)+(3×5)=6+15=215 4×(5+2)=(4×5)+(4×2)=20+8=286 6×(4+3)=(6×4)+(6×3)=24+18=427 4×(3+4)=(4×3)+(4×4)=12+16=288 3×(7+4)=(3×7)+(3×4)=21+12=339 7×(2+3)=(7×2)+(7×3)=14+21=35

10 5×(4+6)=(5×4)+(5×6)=20+30=5011 6×(4+6)=(6×4)+(6×6)=24+36=6012 8×(2+3)=(8×2)+(8×3)=16+24=4013 3×(7+9)=(3×7)+(3×9)=21+27=4814 9×(3+4)=(9×3)+(9×4)=27+36=6315 10×(3+2)=(10×3)+(10×2)=30+20=5016 7×(4+5)=(7×4)+(7×5)=28+35=6317 4×(6+8)=(4×6)+(4×8)=24+32=5618 5×(4+7)=(5×4)+(5×7)=20+35=55

Activity 5: Missing numbersPupil’s Book page 20. Use the example to show how using the commutative pattern helps us to find the value of the letter.

5 3×6=6×3 6 4×9=9×4 7 5×7=7×5 8 6×4=4×6



1 n =6 2 b =7 3 d =54 p =8 5 r =7 6 t= 67 s=3 8 u =6 9 v =5

10 w=15 11 g= 9 12 y =5

Activity 6: True or false?Pupil’s Book page 20. Use the distributive law pattern to investigate orally:• ifthestatementsinquestions1to6are‘true’or‘false’;• ifthevaluesoneithersideofthe=signinquestions7to12are‘equal’or‘notequal’;• ifthestatementsinquestions7to12are‘true’or‘false’.The pupils should then write their answers.

AnswersPupil’s Book page 201 true 2 false 3 false 4 true 5 false 6 true

Forquestion6thepupilsmayexpecttosee(6×4)+(6×5).Remind them that the order of addition does not matter, so this is the same as (6 × 5) + (6 × 4).7 true 8 false 9 false 10 true 11 true 12 true

Activity 7: Making a totalPupil’s Bookpage21.Usethemeasuringjarsexampletoshowhowatotalcanbemadeupfromdifferent sets of numbers. Use the next example to show how any three digits in the range 1 to 9 are used,onceonly,tomakeaparticulartotal.Encouragethepupilstousealogicalsequencetofindtheresults for the second exercise.

AnswersPupil’s Book page 2130 can be made in the following 14 ways.9 + 9 + 9 + 39 + 9 + 6 + 69 + 9 + 6 + 3 + 39 + 9 + 3 + 3 + 3 + 39 + 6 + 6 + 6 + 3


9 + 6 + 6 + 3 + 3 + 39 + 6 + 3 + 3 + 3 + 3 + 39 + 3 + 3 + 3 + 3 + 3 + 3 + 36 + 6 + 6 + 6 + 66 + 6 + 6 + 6 + 3 + 36 + 6 + 6 + 3 + 3 + 3 + 36 + 6 + 3 + 3 + 3 + 3 + 3 + 36 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 33 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 31 3+5+7+5+3=232 4+7+9+7+4=31

6 can be made in 1 way: 1 + 2 + 37 can be made in 1 way: 1 + 2 + 48 can be made in 2 ways: 1 + 2 + 5

1 + 3 + 4

1 13=9+3+1 2 17=9+7+1 3 12=9+2+1 4 16=9+6+113=8+4+1 17=9+6+2 12=8+3+1 16=9+5+213=8+3+2 17=9+5+3 12=7+4+1 16=9+4+313=7+5+1 17=8+7+2 12=7+3+2 16=8+7+113=7+4+2 17=8+6+3 12=6+5+1 16=8+6+213=6+5+2 17=8+5+4 12=6+4+2 16=8+5+313=6+4+3 17=7+6+4 12=5+4+3 16=7+6+3

16=7+5+4

Activity 8: Using operationsUse the digit cards and the operation cards to build up a positive number.Negative numbers may be produced by inappropriate use of the negative sign, for example (2 - 3) × 4 instead of (3 - 2) × 4.Ask some pupils to select some digit and operation cards and lead the class to find the outcome.Pupil’s Book page 22. Use the four examples to indicate how the digits 1 to 9 and two or more operation signs are used to produce 15.

AnswersPupil’s Book page 22These answers are examples, and not the only answers.1 18=(2×7)+42 17=3×(8-4)+5


3 16=(8+4)×(6+3)-24 21=(6+3)×(8+2)+15 25=(3+2)×(8-4)+5

Activity 9: True or false?Pupil’sBookpage22.Remindtheclassaboutthemeaningof=,>and<beforetheyproceedtoanswerthequestions.

AnswersPupil’s Book page 221 true 2 true 3 true 4 false 5 true6 false 7 false 8 true 9 false 10 false

Activity 10: Even and oddPupil’s Book page 23. Use the example to present the idea that:• evennumberscanbearrangedintwos;• oddnumberscannotbearrangedinexactgroupsoftwos.The pupils should use counters to find all the even and all the odd numbers up to at least 20.

Pupil’s Book page 23. Use the example to show that:• evenandoddnumbersmakeastripedpatternonthehundredboard;• evennumberscanbedividedexactlyby2;• oddnumberscannotbedividedexactlyby2.

AnswersPupil’s Book page 231 2, 4, 6 .... 2 1, 3, 5 .....3 Even numbers end in 2, 4, 6, 8 or 0. They can be divided exactly by 2.4 Odd numbers end in 1, 3, 5, 7 or 9. They cannot be divided exactly by 2.

Pupil’s Book page 24The even and odd numbers make a striped pattern on the hundred board.1 The numbers in the first column of even numbers all end with a ‘2’. The even numbers in each column end with the same digit.2 Even numbers end in 2, 4, 6, 8 or 0.3 Odd numbers end in 1, 3, 5, 7 or 9.


EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.The evaluation exercises should enable the class teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 5associativelawquestionssimilartothequestionsonpage15inthePupil’sBook;• 5distributivelawquestionssimilartoquestions1to18onpage17inthePupil’sBook;• 5‘true’or‘false’questionssimilartothoseonpage20inthePupil’sBook;• 3questionsrequiringtheuseofamixtureofoperations,similartothe‘true’or‘false’questionson

page 22 of the Pupil’s Book;• 2questionsinvolvingtherecognitionordefinitionofoddandevennumberssimilartothoseonpage

23 of the Pupil’s Book.Multiply the score by 5 to get a percentage mark.

Diagnostic assessment test1 Identify some of the difficulties that pupils faced when they were discovering the: (a) associative property of addition; (b) associative property of multiplication; (c) distributive law for multiplication over addition.2 What skills, competencies and strategies did pupils employ to write number sentences using basic

operations?3 How are these skills, competencies and strategies going to help to develop number patterns from

digits1,2,3,...9?4 What attitudes did you discover among the pupils when they were finding the end digits of even and

oddnumbers?Howdidtheyappreciatetheirdiscoveries?

24

UNIT 4 Addition and subtraction (sums up to 100,000)


ObjectivesThe pupils should be able to:• addnumbersuptoasumof999;• addnumberswithsumslessthan100,000;• subtractnumbersinthe0to99,999range;• solvewordproblemsinvolvingadditionandsubtraction.

NotesA sum is the result of addition. Numbers added to form a sum or total are called addends.

The difference between two numbers is found by subtracting a smaller number (subtrahend) from a larger number (minuend).Foraddition:Sum=addend+addend+addend+addend…….Forsubtraction:Difference=minuend–subtrahend.

The use of these terms is not appropriate with pupils unless they make explanations clearer. For teachers and curriculum developers the terms are useful in defining addition and subtraction in particular ranges. For example:• theadditionof5two-digitaddends;• subtractionfromminuends<100,000,etc.

Teaching methodsMethods of considering addition and subtraction have been presented:• usingrealobjectstoshowtheprocess;• usingpicturesinbooks,postersandontheboardtoshowtheprocess;• usingnumbersandsymbolsinbooks,postersandontheboardasanefficientsymbolicprocess.Care should be taken to ensure that the explanations are not more difficult than ‘the rules’ themselves.Atthisstagewehavetorelyonsymbolicrepresentationstoagreaterextentastheuseofobjects,suchascounters and base ten materials, is cumbersome for large numbers.

Key wordsThe numbers from 0 to 100,000, add, sum, total, group, carry, subtract, difference, take-away, ‘change’ (e.g. change Ten-thousands, Thousands, Hundreds or Tens to regroup). The names of all the teaching and learning materials

25UNIT 4 Addition and subtraction (sums up to 100,000)

MaterialsBase ten materials for remedial work.

Activity 1: Addition and subtraction bondsPupil’s Book page 25. Write the addition bonds of 10 on the board. Ask the pupils to describe the patterns in the columns of addends. Point out that as one column decreases by 1 the other column increases by 1. Write the subtraction bonds of 10 on the board. Ask the pupils to describe the patterns in the columns of minuends and subtrahends. Point out that the minuend column is always the same while the subtrahend column decreases by 1. Encourage the pupils to learn the addition and subtraction bonds of 10. Tell the pupils to complete the addition and subtraction bonds of 9 to 4 using the same pattern.

Answers Pupil's Book page 251 a 2+4+5=11 b 3+6+7=162 a 13+7=20 b 15+20=35

Pupil’s Book page 269+0=9 9–9=0 8+0=8 8–8=08+1=9 9–8=1 7+1=8 8–7=17+2=9 9–7=2 6+2=8 8–6=26+3=9 9–6=3 5+3=8 8–5=35+4=9 9–5=4 4+4=8 8–4=44+5=9 9–4=5 3+5=8 8–3=53+6=9 9–3=6 2+6=8 8–2=62+7=9 9–2=7 1+7=8 8–1=71+8=9 9–1=8 0+8=8 8–0=80+9=9 9–0=9

7+0=7 7–7=0 6+0=6 6–6=06+1=7 7–6=1 5+1=6 6–5=15+2=7 7–5=2 4+2=6 6–4=24+3=7 7–4=3 3+3=6 6–3=33+4=7 7–3=4 2+4=6 6–2=42+5=7 7–2=5 1+5=6 6–1=51+6=7 7–1=6 0+6=6 6–0=60+7=7 7–0=7

26 UNIT 4 Addition and subtraction (sums up to 100,000)

5+0=5 5–5=0 4+0=4 4–4=04+1=5 5–4=1 3+1=4 4–3=13+2=5 5–3=2 2+2=4 4–2=22+3=5 5–2=3 1+3=4 4–1=31+4=5 5–1=4 0+4=4 4–0=40+5=5 5–0=5

Activity 2: Addition of two- and three-digit numbersPupil’s Book page 26. Use the examples and the patter to revise the addition of two- and three-digit numbers.


1 57 2 71 3 82 4 93 5 73 6 657 796 8 641 9 464 10 744 11 699 12 565

13 603 14 438 15 480 16 680 17 872 18 853

Activity 3: Addition of four-digit numbersPupil’s Book page 28. Use the example and the patter to revise the addition of four-digit numbers.


1 9,837 2 6,872 3 5,733 4 8,0035 3,649 6 7,984 7 6,754 8 7,4759 6,377 10 7,500 11 9,396 12 8,682

13 5,962 14 7,794 15 8,199 16 9,414

Activity 4: Addition of five-digit numbersPupil’s Book page 29. Demonstrate the example using the patter. Repeat the demonstration and ask somepupilstoleadtheclassthroughthepatterforquestions1,2and3.

27UNIT 4 Addition and subtraction (sums up to 100,000)


1 40138 2 66,041 3 86,422 4 63,8785 67,233 6 56,406 7 61,093 8 78,7149 90,402 10 53,286 11 98,960 12 88,018

Activity 5: Subtraction of two- and three-digit numbersPupil’s Book page 30. Use the two examples and the patter to revise the subtraction of two- and three-digit numbers.


1 42 2 50 3 15 4 17 5 39 6 627 14 8 16 9 22 10 33 11 231 12 292

13 217 14 391 15 235 16 272 17 475 18 548

Activity 6: Subtraction of four-digit numbersPupil’s Book page 31. Use the example and the patter to revise the subtraction of four-digit numbers.


1 3,211 2 3,586 3 5,470 4 4,3775 2,509 6 6,676 7 6,959 8 3,4989 4,269 10 2,170 11 3,966 12 5,534

13 5,359 14 3,905 15 1,469 16 2,64717 5,469 18 4,478 19 3,646 20 3,060

Activity 7: Subtraction of five-digit numbersPupil’s Book page 33. Demonstrate the examples using the patter. Repeat the demonstrations and ask somepupilstoleadtheclassthroughthepatterforquestions1and4.

AnswersPupil’s Book page 33 and 341 47,813 2 61,555 3 67,189 4 37,794 5 37,044 6 45,726

28 UNIT 4 Addition and subtraction (sums up to 100,000)

Activity 8: Word problemsPupil’s Book pages 35 and 36. Discuss each problem to:• definethesituation;• establishthedataorinformation;• decidewhichprocess(additionorsubtraction)willprovideasolution;• performtheprocesscorrectly.Having found the ‘answer’ it is wise to ask whether it makes sense. If it does not the problem should be reconsidered.

AnswersPupil’s Book pages 35 and 361 340 kg 2 l, 715 litres3 a 43,570 loaves b 48,852 loaves

c Second week; 5,282 loaves d Monday and Friday; 48,092 loaves4 a 11,698 people b 620 people5 a Sunday, no visitors

b 7,701 peoplec 7,138 peopled 1st week, 563 peoplee Saturday, 5,412 people

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.The evaluation exercises should enable the class teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 10additionquestionssimilartothoseonpages26to28inthePupil’sBook;• 10subtractionquestionssimilartothoseonpages29to32inthePupil’sBook;• 5wordproblemquestionssimilartothoseonpages34and35inthePupil’sBook.Multiply the score by 4 to get a percentage mark.

Diagnostic assessment test1 Whatskillsdidpupilsusetoaddnumbersupto100,000?2 Whatdifficultiesdidpupilsfaceinsubtractingnumbersintherangeof0to100,000?3 Were the word problems you used probing enough to challenge pupils’ understanding and did they

reflectreallifesituations?

29

UNIT 5 Measurement of mass/weight and time


Measurement of mass (weight)

ObjectivesThe pupils should be able to:• statethatmass/weight,ismeasuredinkilogramsandgrams;• comparethemasses/weightsofobjectstoa1-kilogramsandbagusingasimplebalance;• measuremass/weightaccuratelyusing100,200,250and500gramsandbags;• recallthatthesymbolskgandgareusedtorepresentkilogramandgramandtousethemtoexpress

masses /weights)• calculatethesumoftwoorthreemasses/weightsinkilogramsandgrams,includingexampleswhere

the number of grams will involve ‘carrying’ to kilograms.

NotesThere is often confusion between ‘mass’ and ‘weight’. Technically ‘weight’ includes the effect of gravity and is measured in ‘grams weight’ rather than ‘grams’. However the word ‘weight’ is more usual in speech, and correct usage of the word ‘mass’ should not be insisted upon if it causes confusion. In this book the words are used interchangeably.

Teaching methodsItisexpectedthatonlyrelativelylightobjectswillbeweighed.Teachersshouldappreciatethathome-made balances are unlikely to be strong enough to hold more than 3 or 4 kg on each side. In using smallersandbagstofindthemassesofsmallobjects,teachersshouldemphasisethattheyarebeingusedto find values between whole numbers of kilograms. Reading scales is not mentioned in the syllabus forYear4butashortexerciseisincludedinpreparationforYears5and6,andtoprovideacontextforexercises that follow.

Key wordsKilogram, gram.

MaterialsSandbagsofmass1kilogram,500,250,200and100grams,otherobjectsofmassbetween1and3kilograms, 1-metre lengths of wood and pivots to make simple balances.

30 UNIT 5 Measurement of mass/weight and time

Activity 1: Kilograms and gramsPupil’s Book pages 37 and 38.• Askpupilstoguessthemass(weight)ofsomeobjectsandtocomparethemtoa1-kilogramsandbag

using a balance.• Introducepupilstosmallersandbagscontaining100g,200g,250gand500gandexplainthat

these can be used to find mass more accurately.• Askpupilstofindouthowmany100g,200gand250gsandbagsareequivalenttoa1-kilogram

sandbag.• Remindpupilsthatthesymbolskgandg,areusedtostandfor‘kilograms’and‘grams’.• Getpupilstoguessthemassesofsomeobjectsandthentofindthemassofeachaccuratelyusing

1-kilogram sandbags and 500, 250, 200 and 100 gram sandbags.

AnswersPupil’s Book pages 37 and 381 and 2 Watch the pupils to ensure they use the balances correctly. Check their results.3 4 4 2 5 5 6 10 7 1000Checkthepupils’resultsforquestion8.Discusswhethertheirestimationsweregoodorbad.

Activity 2: Reading scalesPupil’s Book pages 39 and 40.• Remindpupilstowritethemassesusingthesymbolskgandg.• Explainhowtoreadscalestothenearest100g.

AnswersPupil’s Book pages 39 and 40The meat weighs 400 g. The box weighs 900 g. The tin weighs 200 g.The box is heaviest. The tin is lightest. Tin, meat, packet, box

Mr Forson’s meat weighs 700 g. Mrs Owusu’s meat weighs 1 kg 700 g.

1 Mrs Owusu’s meat is heaviest.2 Mr Forson’s meat is 100 g heavier.3 Mrs Owusu’s meat is 1 kg heavier.

Activity 3: Adding weightsPupil’s Book pages 41 and 42.

31UNIT 5 Measurement of mass/weight and time

• RemindpupilsoftheworkonaddingmassesthattheycarriedoutinYear3.Whenaddingmassesthey should take care to add the grams together and add the kilograms together. Examples given at this level involve carry over.

• Getthepupilstodosomeexamplesofaddingmasses.

AnswersPupil’s Book pages 41 and 42The total mass of the two pieces of meat is 1300 g or 1 kg 300 g.

1 2 kg 500 g 2 1000 g or 1 kg 3 800 g4 11 kg 5 10 kg 700 g

The total weight of the two bags of rice is 1kg 450 g.Whenyouaddthegramsyouhave650g+800g=1450g.This is 1 kg 450 g. The 1 kg is carried to the kg column.The two pieces of meat weigh 3 kg 100 g.

1 6 kg 250 g 2 6 kg 200 g3 11 kg 200 g 4 10 kg 200 g5 1 kg 6 7 kg 100 g

Activity 4: Subtracting weightsPupil’s Book page 43. Remind the pupils how to subtract weights. Get them to do the exercise.


1 5 kg 2 1 kg 500 g 3 2 kg 250 g 4 4 kg 900 g 5 500 g

Activity 5: Word problemsPupil’s Book page 43. Discuss the problems to assess the situation and discover which process (addition orsubtraction)needstobecarriedout.Thereisnoneedtousemultiplicationordivisioninquestions3and 5, repeated addition and subtraction are sufficient.



1 1 kg 800 g 2 3 kg 950 g; 1 kg 50 g 3 1 kg 200 g4 700 g 5 300 g 6 1 kg 950 g

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.The evaluation exercises should enable the class teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.

To assess pupils’ progress, form a test paper which has:• 3questionscomparingthemassof1kilogramtomultiplesof100,200,250and500grams;• 6questionsinvolvingadditionofweights(withandwithoutcarrying);• 6questionsinvolvingsubtractionofweights(withandwithoutexchange);• 5wordproblemsinvolvingamixtureofadditionandsubtraction.Multiply the scores by 5 to get a percentage mark.

Diagnostic assessment test1 Howreliablewasthe1kilogramsand-bagthatyouusedtocomparethemassofobjects?2 Howdidpupilsreacttothevariousmeasuresofmass(weight)ofobjectsusing100,200,250and

500gramsand-bags? Howdidyouassesspupils’accuracy?

3 a) What strengths did pupils exhibit in calculating the sum of two or more masses (weights) in kilogramsandgrams?

b) Identify some of their difficulties and give remedies where possible.


Measuring time

ObjectivesThe pupils should be able to:• readaclocktothenearesthour,halfhour,quarterhourandfiveminutes;• showhowananalogueclockwouldappearatanyhour,halfhour,quarterhour,andatanyminute

interval between them;• writethetime,includingtheappropriateuseofa.m.andp.m.;• estimatethetimeitwouldtaketocarryoutcertainactivities,andthentimetheactivitiesinminutes,

using both analogue and digital clocks;• inter-relatehours,days,weeks,monthsandyears;• readacalendar;• writedatesinfullandshortenedforms.

NotesEmphasise that the numbers written on a clock refer to the hours.Minutes have to be deduced from the small markings around the edge of the clock. Use phrases such as ‘It is half past when the minute hand points to the 6,’ as this combines the hour number with the minute hand.

Teaching methodsPupils may find it difficult to convert the time on a traditional analogue clock to the time on a digital clock and vice versa. One aspect of particular difficulty is the interpretation of times ‘to the hour’. In order to avoid confusion between 12 a.m. and 12 p.m., these times should be referred to as 12 noon and 12 midnight respectively. Pupils need to be aware of the many different ways in which the date is written. However the American way of writing the month first (10.4.03 means October 4th 2003) should not be mentioned at this time.

Key wordsHalfpast,quarterpast,quarterto,...minutespast,...minutesto,a.m.,p.m.,approximate,analogueclock, digital clock, minute, hour, day, week, month, year.

MaterialsAnalogue and digital clocks, demonstration clocks, calendars.

Activity 1: Telling the timePupil’s Book page 44.


• Remindpupilsthattheminutehandtakes60minutestomovecompletelyaroundtheclockfaceandoftheterms‘quarterpast’,‘halfpast’and‘quarterto’todescribethetimewhentheminutehandhasmovedonequarter,onehalfandthreequartersofthewayaroundfromthetop

• Getthepupilstoreadthetimeonaclockwhenitisaquarterpastthehour,andaquartertothehour.

• Pointoutthattimesinvolving‘fifteenminutespast’,‘thirtyminutespast’,and‘fifteenminutesto’areoftengivenintheshorterformas‘quarterpast’,‘halfpast’and‘quarterto’.

AnswersPupil’s Book page 44Since we do not know if the clocks in the first exercise are showing a.m. or p.m. times the answers are open to interpretation. Accept any reasonable answers. This exercise enables the class to discuss the need for the terms a.m. and p.m.1 10 o’clock 2 12 o’clock 3 1 o’clock4 3 o’clock 5 8 o’clock 6 6 o’clock7 9 o’clock 8 5 o’clock

Activity 2: Past and toPupil’s Bookpages45to46.Explainthatreadingthetimetothenearestquarterhourisnotveryaccurate, and that the time is accurately given in one minute intervals over an hour. Introduce the terms’ ... minutes past ‘and ‘ ... minutes to’, as a way of indicating the number of minutes after anhour or the number of minutes before the next hour.


1 quarterpast6 2 half past 6 3 quarterto74 7 o’clock 5 quarterpast7 6 half past 77 quarterto8 8 8 o’clock 9 quarterpast8

10 half past 8

Pupil’s Book page 45Ittakes15minutesfortheminutehandtotravelonequarterofthewayaroundaclockface,soif15minuteshavepassed,onequarterofanhourhaspassed.Pupil’s Book page 491 Half past 10, 15 minutes past 10

2 Half past 9, 30 minutes past 9


3 Half to 10, 15 minutes to 10

4 Half to 9, 15 minutes to 9

1 5 past 11 2 10 past 10 3 20 past 11 4 25 past 115 25 to 12 6 20 to 12 7 10 to 12 8 5 to 12

Activity 3: How much time?Pupil’s Book pages 50 to 51. This section enables pupils to gain a feel for how long certain time periods are. Relating the elapse of time to activities the pupils do in an ordinary day helps to reinforce this knowledge.

AnswersPupil’s Book pages 50 to 511 B 2 C 3 A4 These are both morning times: 3 hours5 This is morning to afternoon: 4 hours6 This is morning to afternoon: 7 hours7 E 8 F9 D (Accept any reasonable order. Assume these are all early morning activities.)

10 5 minutes 11 25 minutes 12 30 minutes13 10 to 2, 10 past 2, 20 past 2 14 20 minutes 15 30 minutes

Activity 4: Approximate timePupil’s Book page 51. We often do not need to know the time exactly. This exercise allows the pupils to read clocks and give an approximate time.

AnswersPupil’s Book page 521 F 2 D 3 H 4 E 5 B6 A,halfpast10;C,25past8:G,quarterto4

Activity 5: Digital clocksPupil’s Book pages 53 and 54.• Showthepupilsthatdigitalclocksdonothavehands.


• Explainthatdigitalclocksalwaysshowthehourandtheminutespastthehour.

AnswersPupil’s Book pages 53 and 54A 20 past 12, 12:20B 1/2 past 12, 12:30C 12 o’clock, 12:00

Time Time shown on a digital clock

Time shown on a digital clock

Time

2 o’clock 2:00 3:35 25 to 4

5 past 4 4:05 9:50 10 to 10

quarterpast8 8:15 6:55 5 to 7

20 past 11 11:20 10:45 quarterto11

25 past 1 1:25 9:40 20 to 10

1 b 2 c 3 d 4 a 5 e 6 c

Clock Time Digital clock

1 2 3 4 5 6 7 8

fifteenminutes(orquarter)pastonehalf (or thirty minutes) past sixfive to sixfive past ninetwenty-one minutes to threetwenty-two minutes past sevennine minutes to ninefourteen minutes to ten

01:1506:3005:5509:0502:3907:2208:5109:46

Activity 6: Writing the timePupil’s Book page 55. Get the pupils to read analogue and digital clocks and to write down the times shown in words.



Time Written

123456789

101112

twenty-five minutes past twotwenty-five to fivenineteen minutes past sevenfive past eightquarter(orfifteenminutes)totwelvetwenty-two minutes past onefive minutes to fourfive minutes past sixtwenty minutes past twelvetwelve minutes to eightquartertoeleventwenty-one minutes past nine

2:254:357:198:0511:451:223:556:0512:207:4810:459:21

Activity 7: Before and after middayPupil’s Book pages 56 and 57.• Pointouttopupilsthattimesarerepeatedtwiceduringaday;once'beforemidday'andonce'after

midday.'• Explainthata.m.andp.m.areusedtodifferentiatebetween'beforemidday'and'aftermidday.'• Askpupilstodescribewhattheymightbedoingatcertaintimes,botha.m.andp.m.onaschool

day.

AnswersPupil’s Book page 571 6.55 a.m. e.g. waking up2 5.00 p.m. e.g. eating the evening meal3 12.30 p.m. e.g. eating lunch4 2.30 a.m. e.g. sleeping5 7.45 p.m. e.g. getting ready for bed6 7.45 a.m. e.g. walking to school


Activity 8: How long does it take?Pupil’s Book pages 57 and 58.• Discusshowactivitiesmaybegroupedintothosethattakeashorttimeandthosethattakealong

time. Ask pupils to give examples of short and long activities.• Explainhowthetimetakentocarryoutanactivitymaybemeasuredinminutesbycountingthe

divisions on an analogue clock or using a digital clock.• Getthepupilstonotedownthetimeatthestartofaclassactivity,suchasreadingtheregister,and

the time at the end of it.• Showthepupilshowthenumberofminutestakenfortheactivitycanbefoundbytakingthetimeat

the beginning away from the time at the end.• Getthepupilstocarryoutsomeshortactivities.Foreachactivity,askpupilstoestimatehowmany

minutes it will take and then to measure the time taken.• Getthepupilstotimesomelongeractivitiesinhoursandminutes.Thesemightbeactivitieswhich

goonwhilepupilsaredoingotherwork–suchasthetimebetweenbusesortrainspassingtheschool, or the time for the sun to move from one position to another.

AnswersPupil’s Book page 58Akutey took 8 minutes to run the race. Discuss the lists of activities that the pupils make.

Activity 9: The date and timePupil’s Book page 59.• Reviewtherelationshipbetweenhours,days,weeks,monthsandyears.• Pupilsshouldknowthatthereare24hoursinaday,7daysinaweek,52weeksinayear,and12

months in a year.

Activity 10: Writing the datePupil’s Book pages 59 and 60.• Letthepupilsexaminethefrontpagesofsomeoldnewspapersandmagazinestoidentifythedate

and see how it is written.• Showthepupilshowthedateiswrittenoutinfull.• Getthepupilstowriteouttoday’sdateinfull.• Showthepupilsthedifferentwaysinwhichdatesmaybewrittenshortenedtoasequenceof

numbers separated by ‘/’, or ‘.’.• Getthepupilstowritedatesoutbothinfullandshortenedways.



Date in full Short date

1 22nd May 2009 22/5/09

2 12th September 2010 12-9-10

3 5th May 2008 5.5.08

4 October 21, 2011 21/10/11

5 14 February 2013 14.2.13

Allow any acceptable notation.Check the pupils’ personal tables.

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.The evaluation exercises should enable the class teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 5questionsonreadingthetimeonaclockface;• 5questionsputtingthehandsonaclockface,givenatime;• 5questionscomparinganalogueanddigitalclocks;• 5questionswritingthetimeinwordsgivenanalogueanddigitalclocks;• 5questionswritingdatesindifferentways.Multiply the scores by 4 to get a percentage mark.

Diagnostic assessment test1 Howdidpupilsrelatetheanalogueclocktothedigitalclock?2 What challenges did pupils encounter in the interpretation of:

(a) hours; (b) half-hours; (c)quarterhours;(d)fiveminutes?3 Howdifficultwasitforpupilstoappreciatetheuseofa.m.andp.m.instatingtime?4 Identify some of the challenges and strengths that pupils exhibited in reading the calendar and in

finding the inter-relationships between hours, days, weeks, months and years.

40

UNIT 6 Fractions IPupil’s Book pages 61 to 70

ObjectivesThe pupils should be able to:• recogniseafractionasanumberonthenumberline;• saythedifferentnamesforfractions;• recognisefractionswhichareequalbuthavedifferentnames;• compareunitfractionsandorderthem;• relateafractiontothedivisionofawholenumberbyacountingnumber;• addandsubtractfractionswiththesamedenominators;• addandsubtractfractionswithdifferentdenominators.

NotesThesymbolsforfractionshavetwoparts–thenumeratoristheupperpartandthedenominatoristhelowerpart.Thedenominatorindicatesthetotalnumberofequalpartsthatawholeisdividedinto.Thenumeratorindicatesthenumberofequalpartswearereferringtoataparticulartime.Thenumeratorand denominator of a fraction can be:• multipliedbythesamenumbertocreateequivalentfractions;• dividedbythesamenumbertobringittoitssimplestterms.

Teaching methodsCuttingsuitableobjectsintoequalpartsandfoldingpaperintoequalsectionswillprovidethepupilswith a practical understanding of fractions.Using fraction charts to provide a view of the comparative size of fractions.

Key wordsFraction,half,halves,fourth,fourths,quarter,quarters,eighth,eighths,third,thirds,sixth,sixths,ninth,ninths, fifth, fifths, tenth, tenths, twelfth, twelfths, whole, whole denominator.

MaterialsSuitableobjectsforcutting.Sheetsofpaperforfolding.Fraction charts for:• whole,halves,quartersandeighths;• whole,thirds,sixthsandninths;• whole,halves,thirds,quarters,fifths,sixths,eighths,ninths,tenthsandtwelfths.

41UNIT 6 Fractions I

Activity 1: All kinds of fractionsUsingpre-preparedandmarked-upsuitablematerialsandobjectsdemonstratehowto:• cutobjectsintohalves,thirds,quarters,fifths,sixths,eighths,ninths,tenthsandtwelfths;• nameandwritethefractionsontheboard;• identifythenumeratoranddenominatorforeachfraction;• foldsheetsofpaperintohalves,thirds,quarters,fifths,sixths,eighths,ninths,tenthsandtwelfths;• nameandwritethefractionsonthepiecesofpaper;• identifythenumeratoranddenominatorforeachfractiononthepiecesofpaper.Insmallgroups,usingpre-preparedandmarked-upmaterialsandsuitableobjects,thepupilsshouldrepeat the demonstrations. They should colour the pieces of paper which represent the fractions.

Activity 2: Making fractionsPupil’s Book page 61. Use the examples to identify the numerator and denominator positions.

AnswersPupil’s Book page 611 Check the pupils’ folding and colouring.2 8: eighths3 a 1

6 , 36 , 5

6 b 14 , 2

4 , 34

4 Check the pupils’ drawings.

Activity 3: Paper foldingPupil’s Book page 62. This activity is designed to give pupils practical experience in creating fractions, andalsotoemphasisetheequivalenceoffractions.Thisactivitymayalsobeusedtogivethepupilspractice in following instructions carefully without adult support .• Givepupilsaplainsheetofpaperandaskthemtolookatpage62.• Tellthepupilsthattheymustfollowtheinstructionscarefullyandinorder,emphasisingthatthisis

their task and that they are responsible for the finished product. It will need to be accurate for them toanswerthequestionsatthebottomofthepage.

• Readthroughtheinstructionswiththepupilsandthenaskthemtocompletethepaperfolding,checking that the finished product has 12 sections.

The pupils should then complete the exercise at the bottom of the page.


1 312 2 6

123 9

124 4

125 8

12

42 UNIT 6 Fractions I

Activity 4: Comparing fractionsPupil’s Bookpages63and64.Explainthefeaturesofthehalves,quartersandeighthschartandthe connections between the whole and the other fractions. Draw attention to the positions of these fractions on the number line. Similarly explain the thirds, sixths and ninths chart, together with attention to the number line positions of the fractions.Pupil’s Bookpage64.Explainthefeaturesofthechart.Workthroughthequestionsorallybeforeaskingthe pupils to complete the exercise. The teacher should emphasise that the larger the denominator, the smallerthefraction(providingthenumeratorsareequal).Thiscanbeseeneasilyonthefractionchartonpage 64 of the Pupil’s Book.

AnswersPupil’s Book page 63.

1 1whole= 22 = 4

4 = 88

2 12 = 2

4 = 48

3 ½> 14 > 1

84 7

8 > 34 > 5

8 > 12 > 3

8 > 14 > 1

8

5 1whole= 33 = 6

6 = 99

6 13 > 1

6 > 19

7 23 > 3

6 > 13 > 1

68 1

2 = 24 = 4

8 = 36

Pupil’s Book page 64.1 > 2 < 3 > 4 > 5 < 6 > 7 > 8 <9 > 10 < 11 > 12 < 13 < 14 < 15 < 16 <

17 112 , 1

10 , 19 , 1

8 , 16 , 1

5 , 14 , 1

3 , 12

18 56 , 3

4 , 23 , 5

8 , 12 , 5

12 , 25 , 3

10 , 29

Activity 5: Equivalent fractionsPupil’s Book page65.Usetheexampletodemonstratehowequivalentfractionsareproduced.


1 13 = 2

6 = 39

2 13 = 1×2

3×2 = 26

3 13 = 1×3

3×3 = 39

4 23 = 2×2

3×2 = 46

5 23 = 2×3

3×3 = 69


6 33 = 3×2

3×2 = 66

7 12 = 1×5

2×5 = 510

8 13 = 1×2

3×2 = 1×3 3×3 = 1×4

3×4=

= 1×5 3×5

Activity 6: Fractions of wholesPupil’s Book page 66. Use the examples to explain how to work out and write fractions of wholes.

AnswersPupil’s Book page 661 2÷4= 2

42 2÷5= 2

53 3÷4= 3

4

4 3÷5= 35 5 3÷7= 3

76 5÷8= 5

8

7 4÷5= 45 8 4÷7= 4

7 9 5÷9= 59

Activity 7: Adding like fractionsPupil’s Book page 67. Use the examples to demonstrate the addition of fractions with the same denominator.

AnswersPupil’s Book page 671 2

32 3

63 5

64 3

55 4

86 7

107 6

98 10

129 5

7

Activity 8: Subtracting like fractionsPupil’s Book page 67. Use the examples to demonstrate the subtraction of fractions with the same denominator.


82 2

93 3

74 7

125 3

56 3

15


Activity 9: Renaming fractionsPupil’s Book page 68. Give the pupils a plain sheet of paper and ask them how they could fold it into 12 equalparts.(Folditinhalf,theninhalfagain,givingfourths;thenopenitoutandfoldintothirds.Orfold it into thirds, open it out, then fold in half and half again, giving fourths.) Remind the pupils of the need to fold the paper accurately.Askthepupilstodrawsimilardiagramsintotheirexercisebooks,asrequiredinquestions1and2.Askthepupilstodrawsimilardiagramsintotheirexercisebooks,asrequiredinquestions1and2.Askthepupilstolookatquestion3.Emphasisethattheequalssignisusedagainandagainbecause,ineachpartofthequestion,thefractionsareallequal.Usingthesediagramstohelpthem,thepupilsshouldthencompletequestion3.

AnswersPupils book 681 a. 2

3 = 46

b. 23 = 6

9

c. 23 = 10

15

2 a. 14 = 2

8 b 1

4 = 312

c 14 = 4

16

3 a 23 = 4

6 = 69 = 8

12 = 1015 = 12

18 = 1421

b 14 = 2

8 = 312 = 4

16 = 520 = 6

24 = 728

Activity 10: Addition - using fraction cut-outsPupil’s Book page 69 (top). Ask the pupils to work in small groups to copy the fraction families on page 64, colour them and cut out the fraction parts. (Explain to the pupils that the halves, thirds, fourths, fifths, sixths, eighths, ninths, tenths and twelfths should be kept in separate bags or envelopes.) In pairs, and using the cut-out fractions, the pupils should follow the teacher’s instruction to:• place3-fourthsand1-halfonthedesktop;• place2-fourthsnexttothe1-halftoshowtheyareequivalentfractions;• placethe3-fourthsand2-fourthsendtoend;• statethat3-fourthsaddedto1-halfis5-fourths.Askthepupilstousethecut-outfractionstofindthetotaloffiveotherpairsoffractionsfromquestions1 to 24.


Activity 11: AdditionPupil’s Book page 68. Use the text and diagrams to present the addition of fractions with one denominator as a multiple of the other. Stress the stages of:• convertingonefractiontoanequivalentfractionwiththesamedenominator;• addingthenumeratorsoftheequivalentfractions.Usinganexamplefromquestions1-24,discusstheconversionoffractionswithdifferentdenominatorsintofractionswithequaldenominators.


56 2

96 3

512 4

710 5

1310 6

1110

776 8

86 9

36 10

109 11

109 12

89

13710 14

510 15

1110 16

1710 17

912 18

1512

19312 20

2112 21

412 22

1312 23

1112 24

1012

Activity 12: Subtraction - using fraction cut-outsPupil’s Book page 70 (top). In pairs, and using the cut-out fractions fromActivity 10, the pupils should follow the teacher’s instruction to:• place3-fourthsand1-halfonthedesktop;• place2-fourthsnexttothe1-halftoshowtheyareequivalentfractions;• placethe2-fourthsontopofthe3-fourthsandidentifythedifference;• statethatthedifferencebetween3-fourthsand1-half(2-fourths)is1-fourth.Ask the pupils to use the cut-out fractions to find the difference between five other pairs of fractions fromquestions1to24.

Activity 13: SubtractionPupil’s Book page 70. Use the text and diagrams to present the subtraction of fractions with one denominator as a multiple of the other.Stress the stages of:• convertingonefractiontoanequivalentfractionwiththesamedenominator;• subtractingthenumeratorsoftheequivalentfractions.Usinganexamplefromquestions1-24,discusstheconversionoffractionswithdifferentdenominatorsintofractionswithequaldenominators.



1 36

2 38

3 38

4 510

5 412

6 312

7 112

8 110

9 210

10 59

11 49

12 29

13 310

14 510

15 510

16 512

17 210

18 38

19 312

20 112

21 412

22 112

23 310

24 19

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.The evaluation exercises should enable the class teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 5equivalentfractionsquestions;• 10additionoffractionsquestions;• 10subtractionoffractionsquestions.Multiply the score by 4 to get a percentage mark.

Diagnostic assessment test1 Whatdifferentstrategieswereusedbythepupilstocomparethedifferentsizesoffractions?2 How did pupils demonstrate their understanding of: (a)equalfractions; (b)unitfractions?3 How did you assess the pupils’ understanding of adding and subtracting fractions: (a) with the same denominators; (b)withdifferentdenominators?

47

UNIT 7 MultiplicationPupil’s Book pages 71 to 80

ObjectivesThe pupils should be able to:• recallthebasicmultiplicationfactsuptoaproductof36;• buildmultiplicationfactsuptoaproductof100andfactorsupto10;• multiply2-or3-digitnumbersbya1-digitnumber,withregrouping;• multiply2-or3-digitnumbersbymultiplesof10upto100;• multiply2-or3-digitnumbersby2-digitnumbers;• solvewordproblemsinvolvingtheprocessofmultiplication.

NotesThe ability to recall multiplication facts is a good foundation on which tobuild mathematics. Knowing multiplication facts give the pupils confidence and this also helps them to develop mathematically. Helping the pupils to see order and patterns in multiplication tables and how they relate to division facts is very important. As such the effort put into helpingthe pupils to remember multiplication facts is time well spent.

Teaching methodsTheuseofteachingandlearningmaterialssuchasrealobjectsandthehundredsquarearehighlydesirable. The use of drill and the reciting of tables have a valid place. The pupils can be assessed by the scores achieved in the exercises. Also, tests based on these could be developed by the teacher.

Key wordsMultiply, factor, product. The names of any teaching and learning materials used.

MaterialsBottletops,suitableobjectstocount,realobjects,thehundredsquare.

Activity 1: Buzz gamesBuzz games can be spread over a week of lesson time.At the beginning, the ‘buzz’ game can be used to recall and re-establish the multiples up to and including 36. After every ‘buzz’ activity, ask all the pupils that said ‘buzz’ to raise their hands and say the multiples they could have said instead. These should be written on the board. Lead the class in saying the multiples.

48 UNIT 7 Multiplication

Activity 2: RevisionPupil’s Book page 71. Ask the pupils to recite the coloured parts of the tables. The pupils should then closetheirbooksandbepreparedtoanswerquestions1to32orallybeforewritingtheanswersintheirexercise books.


1 15 2 10 3 6 4 30 5 246 18 7 12 8 24 9 35 10 28

11 20 12 33 13 5 14 12 15 3016 15 17 8 18 21 19 8 20 3621 32 22 2 23 9 24 36 25 1426 6 27 16 28 16 29 24 30 1231 25 32 20

Activity 3: The tables of sixes and tensPupil’s Book pages 72 and 73.Usethetext,bottletopsorappropriatecountersandahundredsquaretodemonstratehow:• groupsofsixesarebuiltupandproducemultiplesof6;• themultiplesof6areshownonthehundredsquare;• the‘tableofsixes’iswritten.

The pupils should:• writethe‘tableofsixes’intheirexercisebooks;• writethe‘tableoftens’.When the pupils have studied the ‘table of sixes’, they should go on to similarly study the ‘table of tens’.


4 × 6 = 245 × 6 = 306 × 6 = 367 × 6 = 428 × 6 = 489 × 6 = 54

10 × 6 = 60

49UNIT 7 Multiplication

11 × 6 = 6612 × 6 = 7236, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96

Pupil’s Book page 734 × 10 = 405 × 10 = 506 × 10 = 607 × 10 = 708 × 10 = 809 × 10 = 90

10 × 10 = 10050, 60, 70, 80, 90, 100

Activity 4: Tables to learnPupil’s Book page 74. Discuss the patterns in the products.Point out that:• forthe‘tableoftwos’,thereisarepetitionofthedigits2,4,6,8,0;• forthe‘tableofthrees’,thereisarepetitionof3,6,9• forthe‘tableoffours’,thereisarepetitionofthedigits4,8,2,6,0;• forthe‘tableoffives’,thereisarepetitionofthedigits5,0;• forthe‘tableofsixes’,thereisarepetitionofthedigits6,2,8,4,0;• forthe‘tableoftens’,thereisarepetitionof0.If possible have the tables written on chart paper and displayed on the classroom walls.Over an appropriate period lead the class in reciting the tables:• thewholeclasstogether;• boystogether;• girlstogether;• groupstogetheretc.Twenty repetitions should be sufficient per table. From time to time the tables should be recited and tested to ensure that they are remembered and recalled easily.

Activity 5: Column multiplication (two-digit by one-digit)Pupil’s Book page 75. Use the first example to revise the multiplication of two-digit numbers by one-digit multipliers by:• establishingtheorderofmultiplying-OnesthenTens;• stressingthe‘patter’.Proceed with the second example in the same style. Tell the pupils to do the exercise using the correct ‘patter’.



1 30 2 48 3 96 4 99 5 75 6 2247 216 8 216 9 180 10 112 11 301 12 288

13 504 14 280 15 225 16 372 17 288

Activity 6: Column multiplication (three-digit by one-digit)Pupil’s Book page 76. Use the example to:• establishtheorderofmultiplying-Ones,thenTens,thenHundreds;• establishtheproducts;• addtheproducts.This is known as the ‘partial products’ approach. For the shortened form of the example use and emphasise the ‘patter’. The pupils should complete the exercise using the partial product and shortened forms.

AnswersPupil’s Book page 761 342 2 544 3 620 4 858 5 792 6 875 7 780 8 954

Activity 7: Multiplying by 10Pupil’s Book page 77. Use the text to demonstrate how to multiply by 10. Stress that digits move one place to the left when multiplied by 10. The effect is the same as placing a zero at the right of the digit or digits that are multiplied. The explanation of ‘add a zero’ or ‘add a nought’ is incorrect and misleading.


1 10 2 30 3 70 4 90 5 20 6 407 0 8 50 9 80 10 60 11 120 12 140

13 160 14 180 15 230 16 250 17 270 18 36019 380 20 990 21 2,490 22 3,110 23 2,980 24 3,75025 8,560 26 4,460 27 2,710 28 9,840 29 6,480 30 9,990

Activity 8: Multiplying by multiples of 10Pupil’s Book page 77. Use the text to demonstrate how to multiply by multiples of 10.


AnswersPupil’s Book page 781 32 × 30 = 32 × (3 × 10) 2 46 × 20 = 46 × (2 × 10)

= (32 × 3) × 10 = (46 × 2) × 10= 96 × 10 = 92 × 10= 960 = 920

3 15 × 60 = 15 × (6 × 10) 4 27 × 40 = 27 × (4 × 10)= (15 × 6) × 10 = (27 × 4) × 10= 90 × 10 = 108 × 10= 900 = 1,080

5 58 × 30 = 58 × (3 × 10) 6 234 × 20 = 234 × (2 × 10)= (58 × 3) × 10 = (234 × 2) × 10= 174 × 10 = 468 × 10= 1,740 = 4,680

7 124 × 30 = 124 × (3 × 10) 8 217 × 40 = 217 × (4 × l0)= (124 × 3) × 10 = (217 × 4) × l0= 372 × 10 = 868 × 10= 3,720 = 8,680

9 159 × 50 = 159 × (5 × 10) 10 273 × 60 = 273 × (6 × 10)= (159 × 5) × 10 = (273 × 6) × 10= 795 × 10 = 1,638 × 10= 7,950 = 16,380

Activity 9: Multiplying by two-digit numbersPupil’s Book page 79. Use the three examples to demonstrate how to multiply by two-digit numbers.Stress that:• thetwo-digitnumberissplitintoTensandOnesinthefirstline;• multiplicationbyOnesandTensisarrangedinthesecondline;• theresultofmultiplyingbyOnesandTensappearinthethirdline-partialproducts;• thesumofthepartialproductsappearsinthefourthline.Point out that the same stages as in column multiplication take place.



1 28 × 14 = 28 × (4 + 10) 2 326 × 18 = 326 × (8 + 10)= (28 × 4) + (28 × 10) = (326 × 8) + (326 × 10)= 112 + 280 = 2,608 + 3,260= 392 = 5,868

3 32 × 13 = 32 × (3 + 10) 4 43 × 15 = 43 × (5 + 10)= (32 × 3) + (32 × 10) = (43 × 5) + (43 × 10)= 96 + 320 = 215 + 430= 416 = 645

5 27 × 19 = 27 × (9 + 10) 6 124 × 14 = 124 × (4 + 10)= (27 × 9) + (27 × 10) = (124 × 4) + (124 × 10)= 243 + 270 = 496 + 1,240= 513 = 1,736

7 3,376 8 5,168 9 4,550 10 5,66811 9,522 12 3,825 13 8,968 14 20,102

Activity 10: Word problemsPupil’s Book page 80. Discuss each problem to:• definethesituation;• establishthedataorinformation;• decidewhichprocesswillprovideasolution(multiplication);• performtheprocesscorrectly.Having found the ‘answer’, stress that it is wise to ask whether it makes sense or is realistic. If it does not, the problem should be reconsidered and the calculation should be checked.AnswersPupil’s Book page 801 460 pencils2 3,456 hours3 2,175 buttons4 14,850 km5 160 km

6 3,885= 105 X 37 = 105 X ( 7 + 30)= 105 X 7 + ( 105 X 3 X 10)= 735 + ( 315 X 10)= 735 + 3150 = 3,885


EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.Theevaluationexercisesshouldenabletheclass teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 40multiplicationtablequestionssimilartothoseonpage74inthePupil’sBook;• 30columnmultiplicationbyaone-digitmultiplierquestionssimilartothoseonpages75and76in

the Pupil’s Book;• 5multiplyingby10questionssimilartothoseonpage77inthePupil’sBook;• 10multiplyingbymultiplesof10questionssimilartothoseonpage78inthePupil’sBook;• 10multiplyingbytwo-digitquestionssimilartothoseonpage79inthePupil’sBook;• 5problemsolvingquestionssimilartothoseonpage80inthePupil’sBook.The score will give a percentage mark.

Diagnostic assessment test1 Howconfidentwerepupilsintheirrecallofbasicmultiplicationfacts?2 Identifying order and patterns in multiplication tables is very important. How efficient was the

strategythatwasusedtodevelopthisconcept?3 How did pupils relate order and patterns in multiplication to multiply 2 or 3-digit numbers: (i) by a I-digit number; (ii) by multiples of 10 up to 100; (iii)bya2-digitnumber?4 Translating word problems into the symbols in multiplication can be rather challenging. What

challengeswereidentified?

54

UNIT 8 DivisionPupil’s Book pages 80 to 86

ObjectivesThe pupils should be able to:• recallbasicdivisionfacts(dividendsorquotients)upto36;• builddivisionfacts(dividendsorquotients)upto72;• dividetwo-digitnumbersbydivisorsupto6,andby10;• findmissingfactorsindivisionsentences;• recognisethatallmultiplesof10aredivisibleby10;• usethesymbols=,>or<tocomparetwodivisionstatements;• solvesimplewordproblems.

NotesDivision is the inverse (or opposite) of multiplication, in the same way that subtraction is the inverse of addition. Success with division is very dependent on knowing the multiplication tables and the associated division facts.

In8÷4=2;8isthedividend,4isthedivisorand2isthequotient.Thereisnoneedtousetheseterms with the pupils. Teachers might find them useful when discussing and defining the range of exercises used in assessment.

Teaching methodsDivision is presented here as:• sharing;• continuedreductionorcontinuedsubtraction;• associatedtomultiplicationfacts.Understanding division as sharing and continued subtraction is particularly helpful in getting to grips with everyday problems which the process of division can solve. Associating division sentences with multiplication facts helps the recall of division facts and makes the mechanical process of long division easier. The pupils can be assessed by the scores achieved in the exercises. Tests based on these could be developed by the teacher.

Key wordsMultiply, factor, product, division, divide, group. The names of the teaching and learning materials.

MaterialsCharts of multiplication tables and division facts. Base ten materials.

55UNIT 8 Division

Activity 1: Division factsPupil’s Book page 81. Use the example to illustrate the connection between multiplication and division. Revise the multiplication table of two and lead the class in saying the division table of two from the text. Similarly lead the class in saying the multiplication table of three, four, five and six.Discuss the form of the division facts and point out that:• theleft-handsidenumberis‘thenumbertobedivided’;• thenumberinthecentreis‘thenumberthatwedivideby’-withinatableitisthesamenumber;• thenumberontherightsideis‘theresult’ofdividing-withinatable,theyascendfrom1to12.


1 2 2 7 3 7 4 6 5 4 6 6 7 18 8 9 10 10 4 11 6 12 11 13 9 14 9

15 4 16 12 17 1 18 5 19 9 20 3

Activity 2: DivisionPupil’s Book page 82. Use the example to present division as:• sharing;• continuedsubtractionorreductionbyequalamounts.Using bottle tops demonstrate both views of division and ask some pupils to repeat the demonstration.

AnswersPupil’s Book page 8248÷8=6 50÷10=554÷9=6 55÷11=560÷10=6 60÷12=566÷11=6 10÷1=1072÷12=6 20÷2=1040÷10=4 30÷3=1044÷11=4 40÷4=1048÷12=4 50÷5=1040÷8=5 60÷6=1045÷9=5 70÷7=10

Activity 3: Division factsPupil’s Book page 83 Revise the form of the division facts and point out that:

56 UNIT 8 Division

• theleft-handsidenumberis‘thenumbertobedivided’;• thenumberinthecentreis‘thenumberthatwedivideby’-withinatableitisthesamenumber;• thenumberontherightsideis‘theresult’ofdividing-withinatabletheyascendfrom1to12.Since the division facts are associated to the multiplication tables, it is important that these are known well. The use of effective drill and the purposeful reciting of tables has a valid place. Such methods used to be regarded as boring and unnecessary but a reduction in their use has caused a lowering in the ability of pupils to recall multiplication and division facts.

Activity 4: Column divisionPupil’s Book page 84. Use the first example and base ten materials to show how 72 is shared into 6 equalgroups.Forthesecondexampleemphasisetheprocedureand‘patter’forcolumndivision.Forboth examples ask some pupils to repeat the demonstration. Stress that the pupils should know the multiplication tables as they are essential for division work.

AnswersPupil’s Book page 851 8 2 13 3 12 4 7 5 13 6 9 7 17 8 22 9 14 10 16

Activity 5: Comparing division sentencesPupil’sBookpage86.Revisethemeaningof>,<and=.Thepupilsshouldcalculatetheleft-handsidefirst, and then the right-hand side. They should then compare the results.

AnswersPupil’s Book page 861 > 2 = 3 < 4 > 5 > 6 = 7 > 8 >9 < 10 > 11 T 12 T 13 F 14 T 15 T 16 F

Activity 6: Word problemsPupil’s Book page 87.Discuss each problem to:• definethesituation;• establishthedataorinformation;• decidewhichprocesswillprovideasolution(division);• performtheprocesscorrectly.Having found the ‘answer’, suggest that everyone should consider if it is sensible or realistic.

57UNIT 8 Division

If the answer does not seem to be correct the problem should be reconsidered or the result recalculated.

AnswersPupil’s Book page 871 9 pupils 2 5 cm 3 6 packets 4 16 oranges5 12 teams and 2 players left out 6 12 cm 7 12 cm 8 24 pupils 9 12 pens

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.Theevaluationexercisesshouldenabletheclass teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 25divisionquestionssimilartothoseonpage83inthePupil’sBook;• 15columndivisionquestionssimilartothoseonpage84inthePupil’sBook;• 5numbersentencequestionssimilartothoseonpage86inthePupil’sBook;• 5wordproblemquestionssimilartothoseonpage87inthePupil’sBook.Multiply the score by 2 to get a percentage mark.

Diagnostic assessment test1 List some of the pupils’ difficulties in: (i) recalling basic division facts; (ii) building division facts.2 Plan strategies to give remedies.3 Whatdifficultiesdidpupilsexhibitwhendividingtwo-digitnumbersby10andbydivisorsupto6?4 What was the general level of competency in solving word problems

58

UNIT 9 Fractions IIPupil’s Book pages 88 to 96

ObjectivesThe pupils should be able to:• findfifthsandtenthsofwholeobjects;• relatedecimalnamestotenths;• locatetenthsandtheirdecimalnamesonthenumberline;• relatedecimalnamestohundredths;• relatepercentnamestohundredths;• recognise%asthesymbolforpercent;• changehalves,fifthsandtenthstohundredthsandpercentnames.

NotesDecimals are numbers where the fractional part is written by extending the HTO columns to the right and having Tenths, Hundredths, Thousandths, etc. For example 0.384 where:• thefirstdigitafterthedecimalpoint,3,representsthree-tenths;• theseconddigitafterthedecimalpoint,8,representseight-hundredths;• thethirddigitafterthedecimalpoint,4,representsfour-thousandths.Percentageisanamountperhundred.Forexample,75%is75partsoutofa100parts.Changingtestorexamination data such as 6

10 or 2025 into something out of 100 lets us compare performances easily. In this

case 610 becomes60%and 20

25 becomes80%.

Teaching methodsThe activities and exercises show the connections between:• fifthsandtenths;• tenthsandone-digitdecimals;• fifths,tenthsandone-digitdecimals;• hundredthsandtwo-digitdecimals;• hundredthsandpercentages;• fifths,tenthsandhundredths.

Key wordsFraction, fifth, fifths, tenth, tenths, hundredth, hundredths, decimal, decimals, percentage, percentages.

MaterialsFractionchartsandhundredsquares.Suitableobjectsforcutting.Sheetsofpaperforfolding.

59UNIT 9 Fractions II

Activity 1: Revising fractionsRevisetheideaofafraction,byusingpre-preparedandmarked-upsuitablematerialsandobjects,byshowing how to:• cutobjectsintohalves,thirds,quarters,fifths,sixths,eighths,ninths,tenthsandtwelfths;• nameandwritethefractions,ontheboard;• identifythenumeratoranddenominatorforeachfraction;• foldsheetsofpaperintohalves,thirds,quarters,fifths,sixths,eighths,ninths,tenthsandtwelfths;• nameandwritethefractions,onthepiecesofpaper;• identifythenumeratoranddenominatorforeachfractiononthepiecesofpaper.Insmallgroups,usingpre-preparedandmarked-upmaterialsandsuitableobjects,thepupilsshouldrepeat the demonstrations. They should colour the pieces of paper which represent the fractions.

Activity 2: Fifths and tenthsPupil’s Book page 88. Discuss the fractions which are represented in both sections of the page in terms of:• thedenominator-thetotalnumberofequalparts;• thenumerator-thenumberofcolouredparts;• thenameofthefraction.


52 2

53 4

54 4

55 3

56 2

57 3

5

1 410

2 510

3 810

4 510

5 510

6 810

Activity 3: Fifths and tenthsPupil’s Book page 89. If possible use a large fraction board to present the relationship between a whole, fifthsandtenths.Askthepupilstoidentifytheequivalentfractions.


102 1

53 2

54 6

105 8

106 3

57 4

58 5

5

60 UNIT 9 Fractions II

Activity 4: OrderPupil’s Bookpage89.Usethediagramandquestionstoestablish:• theorderoffifthsalongthelinefrom0to1orlefttoright;• theorderoftenthsalongthelinefrom0to1orlefttoright;• howmanytenthsareequalto1,2,3,4and5fifths;• howtouse>or<or=correctly.

AnswersPupil’s Book page 891 Zero, one-fifth, two-fifths, three-fifths, four-fifths, one.2 Zero, one-tenth, two-tenths, three-tenths, four-tenths, five-tenths, six-tenths, seven-tenths, eight-

tenths, nine-tenths, one.3 a > b = c > d < e = f < g > h =

Activity 5: DecimalsPupil’s Bookpage90.Usethediagramandquestionstoestablishthat:• n-tenthsisthesameas0.n(wheren=0....9),• 0.nisread‘zeropointn’(wheren=0....9).(Use actual numbers - do not use the general case with ‘n’.)

AnswersPupil’s Book page 902 0.4, zero point 4 3 0.6, zero point 6 4 1

10 ‘ zero point 1 5 510 , 0.5

6 810 , 0.8 7 9

10 , 0.9 8 0.3, zero point 3

1 ‘six point nine’ 2 ‘five point four’ 3 ‘three point eight’4 ‘two point three’ 5 ‘seven point five’ 6 ‘eight point zero’7 ‘nine point six’ 8 ‘zero point eight’ 9 ‘five point nine’

10 ‘one point six’ 11 ‘five point one’ 12 ‘nine point seven’13 ‘four point six’ 14 ‘five point seven’ 15 ‘zero point three’16 ‘seven point seven’ 17 ‘six point six’ 18 ‘five point three’19 ‘seven point two’ 20 ‘zero point seven’


Activity 6: Fifths, tenths and decimalsPupil’s Book page 91. If possible use a large fraction board to present the relationship between a whole, fifths,tenthsanddecimals.Askthepupilstoidentifytheequivalentfractionsanddecimals.


10 =0.4 2 610 =0.6 3 8

10 =0.8 4 45 =0.8 5 3

5 =0.6 6 15 =0.2

Activity 7: OrderPupil’sBookpage91.Usethediagramandquestionstoestablish:• theorderoffifthsalongthelinefrom0to1orlefttoright;• theorderoftenthsalongthelinefrom0to1orlefttoright;• theorderofthedecimalsalongthelinefrom0to1orlefttoright;• howmanytenthsareequalto1,2,3,4and5fifths;• howmany0.1sareequalto1,2,3,4and5fifths;• howtouse>or<or=correctly.

AnswersPupil’s Book page 911 > 2 > 3 = 4 < 5 > 6 =7 > 8 = 9 = 10 < 11 = 12 <

Activity 8: HundredthsPupil’sBookpage92.Discussthefractionswhicharerepresentedintheexampleandthesixquestions.Stress that:• thedenominator(100),below,representsthetotalnumberofequalparts;• thenumerator,atthetop,representsthenumberofcolouredparts.


1002 47

1003 63

1004 7

1005 67

1006 49

100

62 UNIT 9 Fractions II

Activity 9: Hundredths and decimalsPupil’s Bookpage93.Usethediagramandquestionstoestablishthat:• n-hundredthsisthesameas0.n(wheren=00,01,02,....99);• 0.nisread‘zeropointn’(wheren=00,01,....99).

AnswersPupil’s Book page 931 0.44 2 0.81 3 0.46 4 0.07 5 0.64 6 0.10

Activity 10 : Expressing pesewas as decimalsUse the examples on page 94 of the pupils book to establish that15Gp is the same as taking 15 Ghana pesewas out of 100 Ghana pesewas (One Ghana Cedis)Alsorelatetheconceptonpage93–Hundredthanddecimals.

AnswersPupils book page 941 35Gp= 35

100 =0.35=GH¢0.35

2 50Gp= 50100 =0.50=GH¢0.50

3 42Gp= 42100 =0.42=GH¢0.42

4 84Gp= 84100 =0.84=GH¢0.84

Activity 11: PercentagesPupil’s Book page 95. Discuss the everyday examples of using percentages. Ask the pupils to find examplesoftheuseof%innewspapersandmagazines.Insmallgroupstheyshouldgluethe‘clippings’to form posters.Stress that:• %standsforthedenominator(100);• thenumerator,atthetop,representsthenumberofpercentageparts.


100 =46% 2 50100 =50% 3 75

100 =75% 4 9100 =9%


5 33100 =33% 6 66

100 =66% 7 75100 =75% 8 60

100 =60%

Activity 11: How many parts?Pupil’s Book page 96. Use the diagram and text to demonstrate:• theidentificationofequivalentfractions;• thatn-hundredthsandn%areequivalent.


1 25 = 4

10 = 40100 =40% 2 3

5 = 610 = 60

100 =60% 3 45 = 8

10 = 80100 =80%

4 15 = 2

10 = 20100 =20% 5 1

10 = 10100 =10% 6 5

10 = 50100 =50%

7 710= 70

100 =70% 8 610 = 60

100 =60% 9 25100 =25%

10 46100 =46% 11 75

100 =75%

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.The evaluation exercises should enable the class teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 10fifthsandtenthsdiagramstocoloursuchasthoseonpage88inthePupil’sBook;• 10equivalentfractionsquestionssuchasthoseonpages89,91and96inthePupil’sBook;• 10orderquestionssuchasthoseonpages89and91

in Pupil’s Book;• 10writingdecimalsquestionssimilartothoseonpage93inthePupil’sBook;• 10decimalandpercentagequestionssuchasthoseonpages95and96inthePupil’sBook.Multiply the score by 2 to get a percentage mark.

Diagnostic assessment test1 Howcomfortablewerepupilsinsolvingproblemsinvolvingdecimalfractionsandpercentages?2 Were pupils able to translate their concepts of common fractions to develop the concepts of decimals

andpercentages?3 Identify the skills and strategies that some of the pupils used to change halves, fifths, tenths and

hundredths to decimals and percentages.4 How will these skills and strategies help to develop more sophisticated concepts of decimals and

percentages?

64

UNIT 10 Measurement of length and area


ObjectivesThe pupils should be able to:• recallthatlengthismeasuredinmetresandcentimetres;• appreciatethatmeasuringtothenearestmetreisnotveryaccurate;• recallthatthereare100centimetresin1metre;• usethesymbolsmandcmtorepresentmetreandcentimetre;• estimatelengthsanddistancesinmetresandcentimetres;• measurelengthsanddistancestothenearestcentimetre;• recordlengthsanddistancesinmandcm;• measuretheperimeterofvariousgeometricshapes;• measurethecircumferenceofacircleindirectlyusingstring;• findthesumoftwolengthsordistanceswithoutandwith‘carry’;• writelengthsindecimalnotationasadecimalpartofametre;• statethatareaismeasuredinsquarecentimetres;• estimatetheareaofarectangularsurfaceinsquarecentimetres;• findtheareaofarectangularsurfacebyplacingitonacentimetregridandcountingthesquares

covered on the grid;• findtheareaofarectangularsurfacebycoveringitwithsquarecentimetres;• findthelengthandbreadthofarectangularsurfacebycountingtherowsandcolumnsofsquare

centimetres which cover it;• findtheareaofarectangularsurfacebymultiplyingthenumberofrowsbythenumberofcolumns

ofcentimetresquares.

Teaching methodsMeasuring length should be explored using a metre stick before the formal use of units is introduced. Theword‘distance’shouldbeusedinrelationtothegapbetweentwoobjectswhile‘length’isusuallyanattributeofanobject.Atthisstageareashouldberelatedtonumbersofsquaresforthemostpart.Thismaybeeitherbylayingonagridofsquaresorbycoveringinsquares.Theteachershoulddiscusstheadvantagesofusingsquaresrather than leaves, in terms of how they fit exactly together.Ashortexerciseinvolvingmultiplyinglengthandheight,andsquarecentimetresisincludedbywayofintroductiontotheworkpupilswillcarryoutinYear5.

65UNIT 10 Measurement of length and area

Key wordsMetre,centimetre,m,cm,perimeter,circumference,squarecentimetre,cm2.

MaterialsMetre stick, metre stick graduated in centimetres, cm × cm grids, cm × cm grids which can be cut up to provide1cm×1cmsquaresorasuitabletemplate,variousrectangularshapessuitableforpupilstofindtheir area.

Activity 1: Distance and lengthPupil’s Book page 97• Askpupilstomeasuresomeobjectsusingmetresticks.Pointoutthatthisisnotanaccuratewayof

recording lengths and heights.• Introducethecentimetreasasmallerunitoflengththatallowsmoreaccuratemeasurementstobe

taken.• Remindpupilsthatthesymbolsmandcmareusedformetreandcentimetre.• Pointoutthatthereare100cmin1m.• Askpupilstoguessthelengthsofsomeobjectsorthedistancebetweentwoobjectstothenearest

centimetre, and then to measure them accurately using metre sticks graduated in centimetres.• Getpupilstowritedowntheirmeasurementsusingthesymbolsmandcm.

Activity 2: MeasuringPupil’s Book page 98• Getthepupilstomeasurethelinesandrecordtheirmeasurementsintheirexercisebooks.• Askthepupilstomeasuredifferentpartsofthebodyandrecordtheirresultsintheirexercisebooks.

AnswersPupil’s Book page 981 10cm 2 7 cm 3 12 cm 4 13cm 5 8 cm

Activity 3: Measuring around objectsPupil’s Book page 99.• Remindpupilsthattheword‘perimeter’meansthedistancearoundtheedgeofashape.Thisword

hasalreadybeenusedinYear3.• Usestringandametresticktomeasurearounddifferentpartsofthebody.

66 UNIT 10 Measurement of length and area

Activity 4: Measuring around a circlePupil’s Book page 100• Usetheword‘circumference’todescribetheperimeterofacircle.• Showhowwecanfindthecircumferenceofacirclebyusingapieceofstring,inasimilarwayto

finding the perimeter of a person’s head.• AskthepupilstofindthecircumferencesofthecirclesinthePupil’sBook.• Findthecircumferencesofanycirclesyoucanfindintheclassroom.

AnswersPupil’s Book page 100It will be difficult to measure these accurately. Accept any reasonable answers.1 12-13 cm 2 15-17 cm 3 21-23 cm 4 18-20 cm 5 24-26 cm

Activity 5: Measuring around a rectanglePupil’s Book pages 101 and 102.• Demonstratehowtheperimeterofashapecanbefoundbymeasuringallofitssidesandaddingthe

lengths together.• Getpupilstomeasuretheperimetersofsomeshapes.Limitthistoshapeswithstraightsides.• Youmayfindclassroomsarenotperfectrectangles!

AnswersPupil’s Book page 102The perimeter of the classroom is 32 m.The perimeter of the garden is 26 m.1 12 2 12 3 20 4 16 5 22 6 18

Activity 6: Adding lengthsPupil’s Book pages 103 and 104• RemindpupilsoftheworkdoneonaddingdistancesinYear3.Whenaddingdistancestheyshould

take care to add the metres and add the centimetres separately. Examples given in this exercise involve ‘carry’.

• Getthepupilstodosomeexamplesofaddingdistances.

AnswersPupil’s Book pages 103 and 104


1 100 cm 2 65 cm 3 25 cm 4 90cm5 1 m 70 cm 6 1 m 80 cm 7 2m 8 2m 20 cm1 4m 90 cm 2 3m 95 cm 3 8m 47 cm 4 8 m 24 cm5 The second ribbon is longer, by 1 m 5 cm. The total length of the ribbons is 3 m 55 cm.6 1 m 90 cm 7 2 m 25 cm 8 18 m 55 cm

Activity 7: Decimal notationPupil’s Book page 104.• Remindpupilsthat0.01meansonehundredthandthatthereare100cminametre.• Thismeans1cmcanbewrittenas0.01m.

AnswersPupil’s Book page 1041 0.60 m 2 0.45 m4 2.06 m 5 2.60 m3 1.50 m 6 12.05 m

5mand50cm=5.50m 70cm=0.7m5mand5cm=5.05m 50cm=0.5m1mand65cm=1.65m 3mand60cm=3.60m(Note that 0.70 and 0.7 mean the same thing, 7 tenths and 0 hundredths of a metre.)

Activity 8: Measuring areaPupil’s Book page 105.• Showpupilsagridofsquares.• Focusonasinglesquareandexplainthatitcoversanareaof1square.• Tellpupilsthattheunitofareaisthesquare.• Getpupilstoestimatetheareasofsomerectangularshapesandthentofindtheareasbyplacingeach

ofthemonagridandcountingthenumberofsquarestheshapecovers.

Pupil’s Book pages 105 and 106.• Thisactivityprovidesaslightlydifferentapproachtomeasuringarea.• RemindpupilsoftheworktheycarriedoutinYear3wheretheycoveredsurfaceswithunits,suchas

leaves.• Providepupilswithsomesquarescutfromagridorusingasuitabletemplate.• Explainthattheareaofasurfacecanbefoundbycoveringitinsquares.• Pointoutthatthisisexactlythesamemethodastheycarriedoutwiththeleavesbutsquaresprovide

a more accurate measure of area because they fit together better.


• Getpupilstoestimatetheareasofsomerectangularshapesandthentofindtheareasbycoveringeachofthemwithsquares.

AnswersPupil’s Book page 105A 13squares B 14squares C 16squaresC has the largest area.A has the smallest area.

Check the pupils’ drawings.Pupil’s Book page 106A 8squares B 1square C 5squares D 12squaresE 9squares F 12squares

Pupil’s Book page 107A 8 B 12 C 15 D 32D has the largest area.A has the smallest area.

Activity 9: Calculating areaPupil’s Book page 108.• WorkthroughtheexampleinthePupil’sBookandthengetthepupilstofindtheareasofrectangles

bycountingsquaresandbycalculation.• Explainthatiftheareaismeasured(orcalculated)byusingsquaresthatarecentimetresquares,then

theareaissomany‘squarecentimetres’.Thisisabbreviatedtosqcmorcm2.

Word problemsPupils Book page 109.Discuss each problem to :-• definethesituation;• establishthedataorinformation,• decidewhichprocesswillprovideasolution(multiplication,addition)• performtheprocesscorrectlyHaving found the ‘answers’ stress that it is wise to ask whether it makes sense or is realistic. if it does not, the problem should be reconsidered and the calculation should be checked. Also stress that Units (cm2, m2, etc) is very important


AnswersPupil’s Book page 1091 Area of living room = 7m×4m=28m2

Area of dining room = 4m×4m=16m2

Totalarea=Areaoflivingroom+Areaofdiningroom= 28m2 + 16m2

= 44 m2

2 Area of vegetable garden = 8m × 6m= 48 m2

3 Area of the football field = 24m × 20m= 24m × (10m + 10m)= 24 × 10 + 24 + 10= 240m2 + 240m2

= 480m2

4 Area of classroom = 12m × 11m= 132 m2

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.The evaluation exercises should enable the class teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 10questionsonmeasuringincentimetres;• 10questionsonconvertingcentimetrestometresandcentimetres;• 10questionsondecimalnotationasonpage104inthePupil’sBook;• 5questionsonmeasuringperimeters;• 10questionsonaddinglengthsinmetresandcentimetres;• 5questionsoncalculatingtheareaofshapes(basedonsquaresandrectangles).Multiply the score by 2 to find a percentage mark.

Diagnostic assessment test1 How appropriate and reliable were the various materials and activities used to develop the concept of: (a) length; (b) area.2 What were pupils’ level of accuracy in their estimation of lengths and distances as compared to the

actualmeasurements?3 What were the challenges pupils encountered in relating the term ‘perimeter’ to the term

‘circumference’?


4 ‘Perimeter’ and ‘area’ are two separate concepts and difficult to visualise by children. How were you abletoovercomethisproblem?

5 How did the various activities involving finding the area of rectangles probe the understanding, skills andattitudesofpupils?

71

UNIT 11 Shape and space IIPupil’s Book pages 110 to 117

ObjectivesThe pupils should be able to:• identifyanglesastheamountofturningabutapoint• identifyanangleasbeingatapointwheretwolinesmeet;• identifyanangleasthespacebetweentwolineswhichmeet;• identifyarightangleastheangleformedatasquarecorner;• identifyrightanglesinashape;• makeanglesusingtwosticks;• turnthroughrightanglestofaceaparticulardirection;• makeidenticaltrianglesbydividingarectangleandasquarealongdiagonals;• recognisethatthesetrianglescontainarightangle;• appreciatethatasquarecanbefoldedalongadiagonalexactlyontoitself;• recallthattrianglesmadefromasquarehavetwoidenticalsides.

Teaching methodsTheideaofsquarecornersshouldbeexploredbeforeaformaltreatmentofrightangles.Makingright-angledtrianglesbycuttingacrossthediagonalofasquareandarectangleprovidesaninterestingopportunity for pupils to compare and contrast outcomes.

Key wordsAngle, right angle, turn, clockwise, anti-clockwise, diagonal.

MaterialsStickstomakeangles,templatesforcuttingoutsquares,rectangles,rightangledtriangles,right-angledtrapezia, 2 right-angled kites, 2 right-angled pentagons, right-angled arrow heads.

Activity 1: Right anglePupil’s Book pages 110 and 111.• Explainthatarightangleistheangleformedatasquarecorner.• Askthepupilstolookaroundtheclassroomandfindasmanyrightanglesastheycan-theymay

findtheminthecornersoftheclassroomandonobjectssuchasdoors,windows,tablesandbooks.• Getthepupilstodrawaroundsomeshapes(square,rectangle,right-angledtriangle,right-angled

trapezium, 2 right-angled kites, 2 right-angled pentagons, right-angled arrowhead) and to identify any right angles in these shapes.

• Introducethesymbolformarkingrightangles.

72 UNIT 11 Shape and space II

AnswersPupil’s Book page 110Yes,squaresalwayshave4rightangles.The rectangle has the largest number of right angles (4).The triangle has the smallest number of right angles (1).

Activity 2: AnglesPupil’s Book pages 111 and 112.• Explainthatanangleisformedbetweentwolineswhichmeet.• Usingtwosticks,showpupilsthatanangleisformedwhenalineisturnedaboutapointandthat

the more it turns, the greater the angle.• Getthepupilstomakeanglesusingsticksandbyopeningobjectsfoundintheclassroom.

Activity 3: Turning through right anglesPupil’s Book page 112.• Getgroupsoffivepupilstoplayagameinwhichtheystandinacrossshapeandtheoneinthe

centre makes turns of a number of right angles.• Theobjectofthegameisforthepupiltoguesswhichoftheirfriendstheywillbefacingafterthey

have turned through so many right angles.

AnswersPupil’s Book page 112Oti must turn through 1 (or 5 ) right angles to face Baba.Oti must turn through 2 (or 6 ) right angles to face Charles.Oti must turn through 3 (or 7 ) right angles to face Doe.

Activity 4: Right-angled trianglesPupil’s Book pages 113 and 114.• Remindpupilsthatarectanglehasfourrightanglesandthatoppositesidesareequalinlength.• Getthepupilstocutoutarectangleandtofolditalongoneofthediagonals.• Askthepupilstoinvestigatewhetheronesidecanbefoldedexactlyontotheother.• Getthepupilstocutalongthefoldtomaketwotriangles.Askthemtofindoutifthetrianglesare

identical by seeing if one fits exactly on top of the other. Ask them to identify any right angles which the triangles have.

• Repeatthiswithasquare.Pointouttopupilsthatonesideofasquarecanbefoldedalongthediagonal exactly on top of the other side.

73UNIT 11 Shape and space II

• Discusstheresultsoftherectangleandthesquarewiththepupilsandpointoutthatthetrianglesformedfromthesquarehavetwoequalsides.

AnswersPupil’s Book page 113Yes,triangleswithasquarecornerarecalledright-angledtriangles.Squaresandrectanglescanbothbefolded in half, but the rectangle does not fold exactly onto itself.The triangles fit on top of each other, but one from the rectangle has to be turned over to make them match.Thetrianglesfromthesquarehavetwosidesthesamelength.Thetrianglesfromasquarecanbefoldedexactlyontothemselves.

Activity 5: Making shapesPupil’s Book page 114Use the triangles you have made to make shapes and pictures.

Activity 6: Triangles with two equal sides .Pupils Book page 115Trianglewithtwoequalsides.Letpupilsmeasureorfoldtofindthesidesthatareequal.Usethediagrams on page 113 of the Pupil’s Book.

AnswersPupil’s Book page 1161 a c and e2 b and d3 Yes.Atrianglewithtwosidesequalandhasoneofitsinterioranglesas90°(rightangle)isaRight

–angledIsoscelestriangle

Activity 7: Marking right anglesPupil’s Book page 117. Remind the pupils how to make a paper right angle and ask them to make their own.Askthepupilstouseittoidentifyrightanglesineverydayobjectsintheclassroom.Draw a triangle on the board, marking the angles a, b, c. Demonstrate how to use the paper right angle to see whether any of the angles are right angles. Write your results on the board, using the letter for the angle and yes or no. Thepupilsshouldworkthroughquestion1.Demonstrate how to use the paper right angle to draw right angles. Show them the symbol for a right angle.Thepupilsshouldthencompletequestions2to5.

74 UNIT 11 Shape and space II

Answers. Page 1171 Only angle f is a right angle.

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.Theevaluationexercisesshouldenabletheclass teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 10questionsaboutidentifyingrightanglesindifferentshapes;• 8questionsaboutdeterminingthedirectiontobetakenbyturningthroughdifferentnumbersof

right angles;• 7questionsaboutrecognisingtriangleswhichhavetwoequalsides.Multiplythescoreby4togeta

percentage mark.

Diagnostic assessment test1 Werepupilsabletoestablishanideaofsquarecorners?2 What processes did pupils use to identify: (a)ananglebetweentwolineswhichmeet? (b)squarecornersasrightangles?3 How did pupils use the idea of angles to identify right angles in shapes and also make angles using

sticks?4 What strengths and challenges did pupils exhibit in: (a)identifyingdiagonals? (b)identifyingthattrianglesmadefromasquarehavetwoidenticalsides?5 Weretheactivitiesthatyouemployedappropriateandchallenging?

75

UNIT 12 Collecting and handling data


ObjectivesThe pupils should be able to:• carryoutasimplesurveyrequiringdatacollectionbothbycountingandbymeasuringusing

standard units;• recordtheresultsofasurveyinasuitableformsuchasatable;• representtheresultsofasurveyaseitherapicturegraphorablockgraph.

Teaching methodsInthisunitpupilsarerequiredtofindout:1 Which of a given list of fruits each pupil likes best.2 Class scores from a recent test - preferably out of 10.3 Howfareachpupilcanjumpfromstandingstill.

It would be sensible to collect this information as a class activity rather than for each pupil to collect the data individually.

An example of each investigation is given but the emphasis should be placed on the pupils’ investigation and results. The purpose of this section is to lead to an understanding about collecting and recording data. It is not concerned with probability or the interpretation of data.

Key wordsPicturegraph,blockgraph,data,survey,tally,frequency,

MaterialsMetreruleformeasuringhowfarpupilsareabletojump,graphpaperfordrawingpicturegraphsandblock graphs.

Activity 1: Rolling a dicePupil’s Book page 118.• Askthepupilstorolladice40timesandrecordtheresulteachtime.• Getthepupilstorecordtheirresultsinatable.• Getthepupilstodrawapicturegraphtoshowtheirresults.• Checkthepupils’picturegraphs.Ensurethereisatitle,theaxesarelabelledandmarkedcorrectly,as

well as there being the correct number of pictures for each score.

76 UNIT 12 Collecting and handling data

Activity 2: Which is your favourite fruit?Pupil’s Book page 119.• Askthepupilstofindoutwhichfruiteachpupillikesmostfromagivenlist.Itwouldbesensibleto

limit the number of fruits in the list to five or six so as not to end up with an over complicated graph.• Getthepupilstorecordtheirresultsinatable.• Getthepupilstodrawapicturegraphtoshowtheirresults.• Checkthepupils’picturegraphsasbefore.

AnswersPupil’s Book page 1191 InAdjetey’sclassthemostpopularfruitwasmango.2 InAdjetey’sclasstheleastpopularfruitwaswatermelon.

Activity 3: Standing jumpPupil’s Book page 120.• Askthepupilstomeasurehowfareachpupilintheclasscanjumpfromstandingstill,tothenearest

centimetre. It would be sensible to group the distances together in 10 cm intervals so as not to end up with an overcomplicated graph.

• Getthepupilstorecordtheirresultsinatable.• Getthepupilstodrawablockgraphtoshowtheirresults.• Checkthepupils’blockgraphsasbefore.

Activity 4 : -WeightPupils Book Page 121• Askthepupilstoweighonascale• Getthepupilstorecordtheirresults• Getthepupiltorecordtheirresultsingroupsasindicatedonpage119ofthePupil’sbook.• Getthepupilstoanswerthequestionsonpage119

Answer page 1211 40–45kg2 36–40kgand46-50kg3 56–60kg4 5+8+13+8+4+2=40pupils

77UNIT 12 Collecting and handling data

Activity 5: Mathematics testPupil’s Book pages 122 and 123.• Askthepupilstoconsidertheresultsofarecentclasstest.Itwouldbesensibletochooseatestwitha

small maximum score, such as 10, so as not to end up with an overcomplicated graph.• Getthepupilstorecordtheirresultsinatable.• Getthepupilstodrawablockgraphtoshowtheirresults.• Checkthepupils’blockgraphsasbefore.

AnswersPupil’s Book page 1231 a In Ato’s class the highest score was 9. b One pupil got this.2 a In Ato’s class the lowest score was 2. b One pupil got this.

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.Theevaluationexercisesshouldenabletheclass teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which involves:• makingasurveyinvolvingdatacollectionbycountingorbymeasuring;• recordingtheresultsofthesurveyinasuitableformsuchasatable;• constructingapicturegraphorablockgraphtorepresenttheresults.Ensure each pupil has six items in the survey and score the evaluation as indicated below.Multiply the score by 4 to get a percentage mark.

78 UNIT 12 Collecting and handling data

Items surveyed, correctlynamed (1 mark)

Items counted (i.e. children)correctly named (1 mark)

Tally kept (1 mark)

Title (1 mark)

Fruit Tally Number of childrenabcdef

a b c d e f

5

4

3

2

1

Tallie correctly counted(1 mark each)

Axes correctly named(1 mark each)

Items named (1 mark)

Fruit

Number ofchildren

Blocks or pictures correctly drawn (2 marks for each block)

Diagnostic assessment test1 Identify some of the skills, competencies and processes that pupils used to collect data by: (a) counting; (b) measuring.2 How would you assess pupils’ understanding in the way and manner they recorded their results on a

table?3 Whatskillsdidpupilsemploytoconstructapicturegraphorablockgraph?4 Weretheseattitudesandskillspositive?Ifnot,planstrategiestodirectthempositively.

79

UNIT 13 Investigation with numbers IIPupil’s Book pages 124 to 129

ObjectivesThe pupils should be able to:• findnumbersthatwilladduptoagivensumfromagivenlistofnumbers;• writemultiplesofnumbersupto10;• findtheenddigitsformultiplesof5and10;• recognisenumbersofobjectsthatcanbearrangedinatriangularshapeandcontinuethenumbers;• writearelationshipinvolvingonlyonedigittorepresentagivennumber;• findarelationshipbetweenthenumbersina3×3squareinthecalendar;• continueapatternofnumbers;• solvestoryproblemsthatinvolvetwooperations.

NotesHere the properties of even numbers, odd numbers, triangular numbers and multiples of numbers are identified. For the pupils, these properties then define these types of numbers.A section investigates the use of the four processes (+, -, × and 7) and the nine digits (1, 2, 3 ... 9) to produce new numbers. This leads to the use of a specific number, such as 4, and the four processes to produce a specific group of numbers.

Teaching methodsThe emphasis throughout is on investigation to identify a pattern. Once a pattern is identified the propertiesofthepatternassistindefiningthetypesofnumbersandhowmorenumbersinthesequencecan be created.

Key wordsEven numbers, odd numbers, triangular numbers, multiples.Thefourprocesses–addition(+),subtraction(–),multiplication(×)anddivision(÷).

MaterialsHundredsquare.Numeralcardsforthedigits1,2...9andcardswiththefourprocesssigns.

Activity 1: Magic squaresPupil’s Book page 124.• Explainthepuzzle.Eachdigitcanonlybeusedonce.

80 UNIT 13 Investigation with numbers II

• Askthepupilstospend15minutestryingtosolvethepuzzles.Recordsomeoftheireffortsontheboard.

AnswersPupil’s Book page 1242 9 4 4 9 2 6 7 2 2 7 67 5 3 3 5 7 1 5 9 9 5 16 1 8 8 1 6 8 3 4 4 3 8

Ways of making 3 digits add to 15915 816 726 645924 834 735

Triangular numbersPupil’s Book page 125. Demonstrate how some numbers make a triangular shape, as shown at the bottomofthepage.‘Whatpatterncanyousee?’(A row containing 1 more counter than the bottom row of the previous number is added to the base of the triangle each time.) The pupils should use counters to find triangular numbers from 1 to 30 and record their findings in their exercise books.

AnswersPupil’s Book page 1251, 3, 6, 10, 15, 21, 28

Other patterns page 125

a

1 3 5 7 9 11

b

2 4 6 8 10 12c 2,5,8,11, 14, 17, 20d 3,5,7, 9,11, 13e 45, 41, 37, 33,29,25f 86,80,74, 68,62, 56

81UNIT 13 Investigation with numbers II

Activity 3: Funny fours ( Different operations on a given digit )Pupil’s Book page 126.State the puzzle - ‘Use three or more fours to make the numbers 1 to 20’.Ask a pupil to use cards with the numeral 4 and the signs to attempt to produce the number 1 according to the puzzle’s rule.• Usethefiveexamplestodemonstrate,ontheboard,howtoget12,4,5,9and12.• Ingroups,thepupilsshouldusecardswiththenumeral4andtheoperationsignstoattempttoget

three of the numbers. Their suggestions for getting the numbers should be placed on the board.

Activity 4: MultiplesPupil’s Book page 127.• Askthepupilstoreadthelistofnumbersinthetoprow.Telltheclassthatthemultiplesof2,3,4,5,

6 and 10 are in columns underneath.• Usetheinstructionstoleadthepupilstodescribethepatternsformedbythemultiplesinthe

columns.

AnswersPupil’s Book page 1271 a) The end-digits-2, 4, 6, 8, 0, 2, 4, 6, 8, 0, 2, 4 show a repeated pattern. b) All the numbers are even.2 a) The multiples are odd, even, odd ...... b) The added digit pattern is 3, 6, 9, 3, 6, 9 .....3 a) The multiples are even. b) The multiples of 4 are twice the multiples of 2.4 The end-digit pattern is 5, 0, 5, 0, 5 ....5 a) The multiples of 6 are twice the multiples of 3. b) The added digit pattern is 6, 3, 9, 6, 3, 9, 6, 3 (12 ⇒1+2=3)9,6,

3(12=1+2=3),9.6 The end-digit pattern is 0, 0, 0 ....

Activity 5: Calendar squaresPupil’s Book page 128.• Usetheexampletoleadthepupilstoidentifypatternsofthreenumbersinthesquarewhichaddup

to 36. Use the board to check the suggestions.

82 UNIT 13 Investigation with numbers II

AnswersPupil’s Book page 128Answersdependontheselectedsquares.For example:

Sun Mon Tue Wed Thur Fri Sat

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 22

21 22 23 24 25 26 27

28 29 30 31

22 + 23 + 24 = 69

11 + 19 + 27 = 57 12 + 18 + 27 = 57 13 + 19 + 25 = 57

15 + 24 + 30 = 69 16 + 23 + 30 = 69

15 16 17

22 23 24

29 30 31

11 12 13

18 19 20

25 26 27

11 12 13

18 19 20

25 26 27

11 12 13

18 19 20

25 26 27

15 16 17

22 23 24

29 30 31

15 16 17

22 23 24

29 30 31

Activity 6: Word problemsPupil’s Book page 129.These story problems are intended to promote the use of more than one process. Discuss each problem to:• definethesituation;• establishthedataorinformation;• decidewhichprocesseswillprovideasolution;• performtheprocessescorrectly.Having found the’ answer’ suggest that everyone should consider if it is sensible or realistic. If the answer does not seem to be correct the problem should be reconsidered or the result recalculated.Encourage the pupils to make up other similar story problems for the class to solve.

83UNIT 13 Investigation with numbers II

AnswersPupil’s Book page 129138-16=22people2 24 + (2 × 24 + 1

2 ×24)=24+48+12=84bags

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.The evaluation exercises should enable the class teacher to identify the difficult areas for the pupils. The teacher should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 5questionsaboutmultiples;• 5‘tower-topproducts’questions.Multiply the score by 10 to get a percentage mark.

Diagnostic assessment test1 Investigations to identify patterns can be interesting and challenging. What challenges did your

pupilsencounter?2 Howconfidentwerethepupilsinarrangingobjectsintriangularshapes?3 Whatstrategiesdidpupilsusetocontinuegivenpatternsofnumbers?4 Whatchallengesdidpupilsfaceintranslatingstoryproblemsinvolvingtwooperationsintosymbols?5 Whatskillsdidpupilsemploytosolvethesepatterns?

84

UNIT 14 Measurement of capacity and volume


ObjectivesThe pupils should be able to:• statethatcapacityismeasuredinlitres;• comparethecapacitiesofcontainerstoa1-litrebottle;• appreciatethatmeasuringtothenearestlitreisnotveryaccurate;• recallthatthesymbolslandmlareusedtorepresentlitreandmillilitreandusethesesymbolsto

express capacities;• filla1-litrebottleusingmultiplesof100,200,250,400and500millilitrebottles;• estimateandmeasurethecapacitiesofcontainersaccuratelyusing100,200, 250, 400 and 500 millilitre bottles;• findthetotalcapacityoftwocontainers;• findthedifferenceincapacityoftwocontainers;• calculatethesumoftwocapacitiesinlitresandmillilitreswithoutandwith‘carry’.

NotesThe words ‘capacity’ and ‘volume’ are used in this unit. In order to avoid confusion, if the teacher thinks it is appropriate, an explanation of capacity as the amount of water or sand which a container can hold and volume as the amount of water or sand actually in a container should be given.

Teaching methodThe exercise to find the capacities of various containers should not be perceived as a play activity, as might have been the case for pupils in earlier years. Emphasis should be placed on the use of standard units, then addition of standard units and then multiplicative ratios between them.Where water is not readily available sand can be used but the emphasis should remain on volume and not on mass.

The difference between capacity and volume should be explained in terms of capacity being the amount of space available in a container and volume being the amount of water (or sand) it contains. Volumesofregularsolidsshouldnotbeexploredatthisstage;theyarestudiedinYear5.

Key wordsCapacity, litre, millilitre, volume.

85UNIT 14 Measurement of capacity and volume

MaterialsBottles of capacity 1 litre, 500, 400, 250, 200 and 100 millilitres, other containers to a capacity of several litres, water or sand.

Activity 1: Measuring capacity and volumePupil’s Book pages 130 and 131.• Askpupilstoguessthecapacitiesofsomecontainersandtomeasurethemusinga1-litrebottle.• Introducethepupilstosmallerbottleswhichwillhold100ml,200ml,250 ml, 400 ml and 500 ml

and explain that these can be used to find capacity more accurately.• Askthepupilstofindouthowmany100ml,200mland250mlbottlesareneededtofilla1-litre

bottle.• Remindthepupilsthatthesymbolslandmlareoftenusedwhenwritingdownthecapacityofa

container.• Getthepupilstoguessthecapacitiesofsomecontainersandthentofindthecapacityofeach

accurately using a 1-litre bottle and 500, 400, 250, 200 and 100 millilitre bottles.• Remindthepupilstowritethecapacitiesusingthesymbolslandml.

AnswersPupil’s Book page 1311 2 2 4 3 5 4 10 5a 500 ml b 250 ml

Activity 2: Sum and differencePupil’s Book page 132.• Explaintopupilsthatthetotalcapacityoftwocontainerscanbefoundbyaddingtheircapacities

together; and the difference in their capacities can be found by subtracting one capacity from the other.

• Advisepupilsthatwhenfindingthedifference,thesmallercapacityshouldbesubtractedfromthelarger.

• Getthepupilstofindthesumanddifferenceoftwocontainerseitherasapracticalactivityorasawritten exercise.

Pupil’s Book page 1321 750 ml 2 450 ml 3 600 ml 4 350 ml 5 1,250 ml6 400 ml 7 750 ml 8 300 ml 9 200 ml 10 1,000 ml

Ama has 1,000 ml oforangejuice.Salimhas1,500ml of lemonade.1 Salim has most drink. 2 They have 1,500 ml.3 Ama, 500 ml more. 4 They have 2,500 mI.

86 UNIT 14 Measurement of capacity and volume

5 Ama, 500 ml less.

Activity 3: Adding volumesPupil’s Book pages 133 and 134.• Remindpupilsthatwhenaddingcapacities,theyshouldtakecaretoaddthemillilitrestogetherand

add the litres together. Some of the examples given in this level involve carryover.• Getthepupilstodosomeexamplesofaddingcapacities.

AnswersPupil’s Book page 133Total volume is 750 ml1 900 ml 2 700 ml 3 1,500 ml 4 1,700 ml

750 ml + 500 ml =1,250ml =1l 250 ml 2 l + 1 l =3l Total=4l 250 ml

Pupil’s Book page 1331a 2 l 500 ml b 3 l 700 ml c 7 l 500 ml d 11 l 100 ml2 2 l 900 ml 3 4 l 200 ml 4 400 ml 5 2l 250 ml6 350 ml 7 18 l

EvaluationIn setting evaluation exercises, consider the different abilities (mixed abilities) of the pupils in the class. Setquestionstocaterforthesedifferentcategoriesofpupils.Theevaluationexercisesshouldenabletheclass teacher to identify the difficult areas for the pupils. The teachers should then carry out remedial work to help the pupils overcome their problems.To assess pupils’ progress, form a test paper which has:• 5questionswhichcomparethecapacityofa1-litrebottletomultiplesof100,200and250millilitre

bottles,2 questionstomeasurethecapacitiesofcontainersaccuratelyusing100,200,250,400and500

millilitre bottles,• 3questionstocarryoutcalculationstofindthesumoftwocapacitiesinlitresandmillilitreswithout

and with carry.Multiply the score by 10 to find a percentage mark.

Diagnostic assessment test1 Howdidpupilsappreciatemeasuringandcomparingcapacitiesofcontainerstoa1-litrebottle?2 Howdidpupilsreacttomeasuringorfillinga1-litrebottleusingmultiplesof100-millilitrebottles?3 Whatwasthelevelofaccuracywhenpupilsestimatedcapacityandlatermeasuredasacheck?4 What strategies did pupils employ to:

87UNIT 14 Measurement of capacity and volume

(i) find the total capacity of two containers; (ii)findthesumoftwocapacitiesinlitresandmillilitres,withandwithout‘carrying’?

Primary M

athematics

Mathematics for Primary Schools is a six-level course written by leading educationists and practising teachers specifically for the latest Ghanaian syllabus for Primary Mathematics. There is an Activity-based Pupil’s Book and a comprehensive Teacher’s Guide for each level.

The Activity-based Pupil’s Books:

present mathematics in a lively and interesting way

use examples from the immediate environment and in everyday contexts

contain a good balance of content, activities and exercises

develop mathematical understanding and skills gradually and logically

are well illustrated with useful and colourful artwork

have carefully controlled and graded language levels

Mathematicsfor Primary Schools

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