Mathematics Mathematics Teacher's Gu… · presentation of curriculum content, some examples, skill development and practice. Pupil’s Book 1 The topics presented in Pupil’s Book

11TEACHER’S GUIDE

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

Mathematicsfor Primary SchoolsMathematicsfor Primary Schools

NEW

EDITION

Mathematicsfor Primary Schools

Teacher’s Guide 1

Daniel O. Apronti Juliet C. DonkorGodwin T. Nomo

AdvisorCharles Duedu

winmatPUBLISHERS LIMITED

Published in 2016 byWINMAT PUBLISHERS LTDPO Box AN 8077,Accra-North, Ghana

ISBN 978-9988-0-4601-9

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

1 Counting Objects 8

2 Number and Numerals 1 13

3 Addition Sum ( Up to 9) 23

4 Number and Numerals II 32

5 Subtraction 0 -9 37

6 Solid shapes 44

7 Tens and Ones 45

8 Addition and Subtraction 56

9 Measurement of Length, Area, Capacity and Mass 62

10 Measurement of Time and Money 69

11 Collecting and Handling of Data 74

12 Addition and Subtraction of Numbers (0-99) 77

5 Introduction

Introduction

Basic School MathematicsThe curriculum covers the following five overlapping areas of content:• Numbers and numerals;• Number operations;• Measurement, shape and space;• Collecting and handling data;• Problem solving and application

Pupil materialsSix Pupil’s Books cover the content of the mathematics curriculum. Each Pupil’s Book provides a presentation of curriculum content, some examples, skill development and practice.

Pupil’s Book 1The topics presented in Pupil’s Book 1 are arranged in twelve units:1. Counting Objects2. Numbers and Numerals I3. Addition (up to 9)4. Numbers and Numerals II5. Subtraction 0-96. Solid shapes7. Tens and Ones8. Addition and Subtraction 9. Measurement of Length, Area, Capacity and Mass10. Measurement of Time and Money11. Collecting and Handling Data12. Addition and Subtraction of Numbers (0-99)

The instructions in the Pupil’s Book are, initially, for the teacher to interpret as the pupils are only beginning to learn to read.

Teacher’s GuidesThe units of the six complementary Teacher’s Guides have sections which provide:• objectives;• background notes;• teaching methods outlining the use of teaching/learning materials and equipment;• key word;• a list of materials;

6 Introduction

• activities which integrate the Pupil’s Books with practical work;• some checks which give an indication of pupils’ progress;• a diagnostic assessment test after every unit so that the teacher can evaluate the success of their

teaching methodology.

In line with the structure and organisation of the syllabus, no attempt has been made to break the year’s work into terms. This is left for the teacher. However, no topic should be glossed over.

Teacher’s Guide 1The ideas and suggestions in this book should help teachers and their pupils to:• interact purposefully with each other;• use the classroom environment and resources;• develop a positive attitude towards learning mathematics.

The teacher should:• first study the syllabus and note the topics that are to be taught in Year 1;• Scan the Teacher’s Guide and be aware of how it refers to and fits together with the Pupil’s Book;• become familiar with the whole programme for the year and the detail of the initial parts;• decide which teaching aids are needed generally and the specific resources to begin the programme;• recognise the parts of the programme which require discussions with other teachers and supervisors;• make detailed plans for presenting each unit.

Teaching plan for the yearThe following units of work should be covered each term.Term 1 Unit 1, Unit 2, Unit 3, Unit 4, Term 2 Unit 5, Unit 6, Unit 7, Unit 8, Term 3 Unit 9, Unit 10, Unit 11, Unit 12

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.

Additional review questions are provided in some of the units. These may be used as extra teaching materials, or additional assessment exercises.

7 Introduction

Evaluation and assessmentAssessment should become part of the learning process and will help the teacher decide if the objectives are 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 further assess pupils’ progress, see if there are areas they need to go over again and also review their methodology. Teachers should mark these tests so they can see how individual pupils are progressing.

It is also important that pupils start to learn to assess their own progress. For this reason, assessment exercises have been included at the end of each unit. Teachers should set these for pupils to do when indicated in the Teacher’s Guide. (Answers are provided in the Teacher’s Guide.) Pupils can look back at their books when trying to answer these questions. Teachers should write the answers on the board when pupils have finished, and pupils should mark their own work. Teachers should not record the marks for these exercises, but should tell pupils to come and ask them if they couldn’t answer a question. In this way, pupils can check for themselves whether they have understood what they have been taught, or if they need more help.

8 UNIT 1 Counting objects

UNIT 1 Counting objectsPupil’s Book pages 1 - 35

ObjectivesThe pupils should be able to:• recite number names one, two, three, four, five in the correct order;• use one-to-one matching to find which group has as many objects as in a given group.• use one-to-one matching to find which group has one more object than a given group;• count by matching number names to objects in a group, up to 20• match number names with objects in a group• match number names with given groups of objects up to 50.

NotesEarly stages of learning was about groups, objects in a group and matching them. This led to establishing order and this unit is about counting , matching , making groups with one up to fifty objects, recognising and reciting number names of groups of objects up to 50

Teaching methodThrough teacher-led activities and book exercises the pupils will have sufficient opportunities to:• see pictures of groups with up to fifty objects;• identify groups with one to fifty objects;• make groups with one to fifty objects.• recite number names up to 50.

The assessment of the pupils will depend on teacher observation. Pupils’ responses to questions and exercises will indicate their progress.

Key wordscount, matching, group,order , compare , read , number , write, numerals, recite , number name, as many as, more than, less than, one, two, three, four, five, ......fifty

MaterialsCounters , pens , pencils and everyday objects.

Activity 1: One− to−onematching Pupil’s Book 1 (Page 1)Place a group of exercise books and a group of pens on the teacher’s table.Ask the class:• ‘Is there a pen to write in each book?’

9UNIT 1 Counting objects

Demonstrate how to match the pens with the books by placing a pen on each book. If there are no pens ‘left over’, then state that there are ‘as many pens as books’ or ‘as many books as pens’Tell the pupils that the pens and books are matched by drawing a line from each pen to each book. Let them make two groups of objects with one−to−one matching.

Activity 2: One more thanPupil’s Book pages 1-8. Demonstrate how to match the pens with the pencils by drawing lines from one pen to one pencil. If there are pencils left over , state that ‘there are more pencils than pens’.Ask the class ,”Are there more pencils than pens?” Ask the pupils to match the objects in each group under the numeral 1, 2, 3...9 etc and the group with the number of objects. They should identify which of the groups has 1 object. Similarly for the groups under the numerals 2, 3, 4, 5,6, 7, 8 and 9.

Activity 3: Counting objects up to 20Pupil’s Book pages 2 - 17. For each group of objects for the numerals 1 to 20:-• match the number, name and numeral with group of objects ;• say the ‘number name’ e.g. ‘one’, each time and ask the class to repeat it up to 20• match each group of objects with a name and ask class to repeat the number, up to 20• say the counting number and then count the objects. Ask the class to repeat it. Lead the class in

counting and reciting the natural order of numbers 1 to 20

Activity 4: OrderPupil’s Book 18 Ask the class to:• name the balls in the smallest group (green); say the number of balls in the group • name the balls in the largest group (yellow); say the number of balls in the group • name the colour of the group which has one more than the group of red balls (yellow);• name the colour of the group which has one more than the group of blue balls (red);• name the colour of the group which has one more than the group of green balls (blue);• count the green, blue, red and yellow balls. and say the number Assist the class to decide which group of oranges is ‘next’ by counting the oranges in the group with one, then two, then three, then four, five oranges etc.

Activity 5: matching group of objects (1-20) with numbers, names and numerals Pupil’s Book 19 - 30Matching number names with groups of objects up to 20: Match number names with group of objects; match number names with numerals; match group of objects with number names, for numbers up to 20. Let pupils go through the Games on page 20 and go through the exercises on pages 21 - 28. Lead pupils to match group of object, number names and numerals in ascending and descending order as on page 30.



Activity 6: Counting objects from 21-50Pupil’s Book 31 - 35Match number names, numerals with objects up to 50.Pupils go through the Game to consolidate their mastery in counting up to 50. Employ different methods to lead pupils to count objects to 50.

Activity 7: Number rhymesLead the pupils in reciting rhymes such as ‘Fingers and thumbs’ showing the actions.Fingers and thumbsOne finger, one thumb, keep movingOne finger, one thumb, keep movingOne finger, one thumb) keep movingHurrah, hurrah, hurrah.

Two fingers, one thumb, keep movingTwo fingers, one thumb, keep movingTwo fingers, one thumb, keep movingHurrah, hurrah, hurrah.

Three fingers, one thumb, keep movingThree fingers, one thumb, keep movingThree fingers, one thumb, keep movingHurrah, hurrah, hurrah.

Fourth verse:Four fingers, one thumb, keep moving etc.

For specific numbers, rhymes such as ‘Two little black birds’ can be used:

Two little black birdsTwo little black birds sitting on the wall.One named Peter, one named Paul.Flyaway Peter! Flyaway Paul!Come back Peter! Come back Paul!

For ‘counting back’ number rhymes such as ‘Bottles on the wall’ and ‘Cat and rats’ can be used:Bottles on the wall

Five green bottles standing on the wallFive green bottles standing on the wallIf one green bottle should accidentally fall


There’d be four green bottles standing on the wall.(and so on until there are no bottles left.)

Cat and ratsFive little rats go out to playLooking for breakfast on the wayHere comes Mrs Cat, ginger and thinOnly four rats go running in(and so on until no rats are left.)

Activity 7: Numbers and actionsAsk some pupils to demonstrate:• 1, 2, 3, 4,....10.....15 , etc hops ;• 1, 2, 3, 4, ....18.....25, etc steps;• 1, 2, 3, 4, .....20......31. etc jumps In small groups the pupils should copy the actions and count the hops , steps , jumps etc up to 50

EvaluationBy the end of the unit the pupils should be able to:• count objects up to 50;• match number names to group of objects up to 50;• match groups of objects with the numerals 1, 2, 3, 4 , 5 up to 50

Additional review questionCopy the unit assessment on to the board and discuss pupils’ answers.Which is the next group? Include numbers up to 50.


Unit assessment test

1. Which is the next group?

Which has one more oranges?

Unit assessment testCopy this on to the board.

2.

Diagnostic assessment test1. What strengths and challenges did the pupils exhibit when counting and matching number names

up to fifty ?2. What strategies did pupils use to match groups of objects with their corresponding number names?3. How appropriate were the strategies used?

14 UNIT 2 Numbers and numerals 1

UNIT 2 Numbers and numerals 1Pupil’s Book pages 36 to 67

ObjectivesThe pupils should be able to:• read and write the numerals I, 2, 3, 4 ......20 in correct order or natural order• match the number zero (0) with a group with no objects in it;• read and write the numeral zero (0);• read and write the numerals 21-50 in ascending order, descending order and mixed up.

NotesThrough teacher-led activities and book exercises the pupils will have opportunities to:• read and write numerals up to 50

Teaching methodsHere ideas and experiences are gathered together to form an understanding of number from zero to fifty. The assessment of the pupils should be based on their ability to:• recite the numbers in an appropriate order;• write numerals correctly; from 0 up to 50• read numerals in ascending and descending order as well as mixed -up.• remember the counting sequence from 1 to 50.

Key wordsnumber, numeral, zero, one, two, three, four, five, ......fifty,

Materialssuitable objects and dot cards, numeral cards 0 to 50, sandpaper numerals 0 to 50, Cuisenaire rods if possible, playing cards, domino set, spinners, dice, number name cards, from zero to fifty

Activity 1: Reading and Writing ‘ I ’Ask the pupils to match one finger with a single part of the head. They may point to the head, nose, mouth, chin or neck. Point out that one sun shines during the day and one moon at night. Ask the class to provide other examples of a group with one object in school and at home.

15UNIT 2 Numbers and numerals 1

Pupil’s Book page 29. Talk about the single object groups on the page. Demonstrate how to write ‘I’ on the board ten times. Standing facing the board with your back to the class demonstrates the writing of a large ‘I’ in the air five times. The pupils should copy this action, in the air, each time. Left-handed children should perform the action with their left hands.

Recite the rhyme ‘Fingers and thumbs’ showing the actions.Fingers and thumbsOne finger, one thumb, keep movingOne finger, one thumb, keep movingOne finger, one thumb, keep movingHurrah, hurrah, hurrah.If-possible, provide sand trays and slates for the pupils to write ‘I’ many times. Provide sheet of paper on which the pupils should draw a group with one object and write a large ‘I’ beside it. Let pupils practise writing ‘1’

Activity 2: Reading and Writing ‘2’Ask the pupils how many eyes and ears they have. ‘Which other parts of the body do we have two of?’ They may say hands, feet, knees, arms, elbows, shoulders, etc. Ask the class to provide other examples of groups with two objects in school and at home.

Pupil’s Book page 37. Proceed as in Activity 1.Recite the rhymes ‘Fingers and thumbs’ and ‘Two little black birds’. Show the actions.Fingers and thumbsOne finger, one thumb, keep movingOne finger, one thumb, keep movingOne finger, one thumb, keep movingHurrah, hurrah, hurrah.


Two little black birdsTwo little black birds sitting on the wall.One named Peter, one named Paul.Flyaway Peter! Flyaway Paul!Come back Peter! Come back Paul!Provide a sheet of paper on which the pupils should draw a group with two objects and write a large ‘2’ beside it. Lets pupils practice writing ‘2’


Activity 3: Reading and Writing ‘3 ‘Pupil’s Book page 31 Talk about the three coloured balls and the three bananas. Ask the class if they can think of objects which show ‘three’. They may say a three-legged stool, the three sides of a triangle, a bicycle frame etc. Proceed as outlined in Activities 1 and 3.

Recite the rhyme ‘Fingers and thumbs’ showing the actions.Fingers and thumbsOne finger, one thumb, keep movingOne finger, one thumb, keep movingOne finger, one thumb, keep movingHurrah, hurrah, hurrah.

Three fingers, one thumb, keep movingThree fingers, one thumb, keep movingThree fingers, one thumb, keep movingHurrah, hurrah, hurrah.


Provide a sheet of paper on which the pupils should draw a group with three objects and write a large ‘3’ beside it. Let pupils practise the writing of ‘3’

Activity 4: Reading and Writing ‘4‘Pupil’s Book page 39. Talk about the four plates and the four monkeys. Ask the class if they can think of objects which show ‘four’. They may say the four legs of a chair, the four wheels of a car, the four walls of a room etc. Proceed as previously outlined.Recite the rhyme ‘Fingers and thumbs’ and show the actions.Fingers and thumbs (4th verse)Four fingers, one thumb, keep movingFour fingers, one thumb, keep movingFour fingers, one thumb, keep movingHurrah, hurrah, hurrah.Provide a sheet of paper on which the pupils should draw a group with four objects and write a large ‘4’ beside it. Let pupils practice the writing of ‘4’


Activity 5: Reading and Writing ‘5’Pupil’s Book page 40. Talk about the five buttons and the five mangoes. Ask the class if they can think of objects which show ‘five’. They may say the five fingers and five toes. Ask if they know of flowers with five petals. Proceed as previously outlined.Recite the rhymes ‘Fingers and thumbs’, ‘Bottles on the wall’ and ‘Cat and rats’.Show the actions.Fingers and thumbs (5th verse)Five fingers, one thumb, keep movingFive fingers, one thumb, keep movingFive fingers, one thumb, keep movingHurrah, hurrah, hurrah.Bottles on the wall

Five green bottles standing on the wallFive green bottles standing on the wallIf one green bottle should accidentally fallThere’d be four green bottles standing on the wall.(And so on until there are no bottles left.)

Cat and ratsFive little rats go out to playLooking for breakfast on the wayHere comes Mrs Cat, ginger and thinOnly four rats go running in(and so on.)Provide a sheet of paper on which the pupils should draw a group with five objects and write a large ‘5’ beside it. Let pupils practise writing ‘5’

Activity 6 Lead pupil’s to practise writing numerals 6 up to 9 on pages 41 - 44 of the textbook. Continue with similar activities to identify number of objects in a group , read and practise writing the numerals uto 9. Proceed as Activities 1,2,3, 4 and 5 to introduce objects in a group , read , and practise writing numerals up to 9.

Activity 7 Discuss the picture on page 45 with pupils, Place some sand-paper numerals 1 to 20 on the teacher’s table.


Pupil’s Book page 45. Ask:• ‘How many lions are there?’ (2)• ‘How many elephants are there?’ (1)• ‘How many giraffes are there?’ (3)• ‘How many monkeys are there?’ (5)• ‘How many crocodiles are there?’ (4)• ‘How many birds are there?’ (3)• ‘How many fish are there?’ (5)Lead the pupils in pointing to and counting the animals in each group. Ask some pupils to:• identify the appropriate numeral from the teacher’s table and hold it in the air;• identify the appropriate sand-paper numeral from the teacher’s table, hold it in the air and take it to

those who want to touch it;• write these numerals in the air and ask the rest of the class to repeat the action;• write the numerals on the board and say e.g. 5 fish.Recite all the verses of ‘Fingers and thumbs’.

Activity 8: The Numeral ZeroPupil’s Book page 47. Discuss the picture, the position of the fish and the numbers of fishes on the left and right side of the trap. Discuss the question. The answer is zero or 0. Ask the class questions for which you know that the answer is zero, for instance: ‘How many of you have been to the moon?’ and ‘How many children drive cars to school?’ Ask individuals to write ‘0’ in the air and the rest of the class to repeat the action. Ask some pupils to write ‘0’ on the board. Let the pupils practise writing ‘0’.

Activity 9: Ten as a Unit Arrange nine objects on the teacher’s table. ‘How many objects does the set have?’ Ask a pupil to make another group with one more object. ‘Does anyone know how many objects this group has? This group has ‘one more than nine objects. It has ten objects.’ Tell the class to repeat the word ten a number of times. Write the two-digit number, 10, on the board. Ask the pupils to describe it and write it several times on the board.

Pupil’s Book page 49-50 ‘Look at the group at the top of the page – how many objects does it have? Does the group below it have nine objects? How many more than nine objects does it have? “one more than” nine.’ i.e ‘Ten’. Using the groups in the lower half of the page lead the class in counting up to ten several times. Lead the class to practise writing “10” as on page 51.

Activity 10: The story of tenAsk the class to provide stories, incidents or situations where ten is an important number, for example:• 10 fingers;


• 10 toes;• currency notes;• a football/hockey team has 10 players and a goalkeeper

Activity 11: Number rhymesPerform, sing or recite some rhymes which have numbers up to ten.One, two, three, I like tea;Four, five, six, pickup sticks;Seven, eight, must not be late;Nine, ten, a big fat hen.

One, two,Buckle my shoe;Three, four,Shut the door;Five, six,Pickup sticks;Seven, eight,Lay them straightNine, ten,A good fat hen.

One, two, three, four,John is standing at the door;Five, six, seven, eight,Eating mangoes off a plate.Two, four, six, eight,Who do we appreciate:G, H, A, N, A: Ghana.One, two, three, four, five,Once I caught a fish alive;Six, seven, eight, nine, ten;Then I let him go again.

Activity 12: Writing numerals; 1-20Pupil’s Book pages 51 . Lead pupils to practice writing the numerals 1 to 20 as on page 51.

Activity 13: Counting up and down ; numbers 1-20 Pupil’s Book pages 52Using up to twenty bottle tops , pupils should form towers of 1-20 bottle tops next to each other. Let pupils walk up the staircases on page 52 and 53 , saying “one, two, three, four.......twenty” Walking down the staircase they should say ‘“twenty , nineteen, eighteen......three , two one”

Activity 14: Writing numerals; 21-50Pupil’s Book pages 45Repeat activity ‘11’ to lend pupils practise writing numerals 21-50 as on page 45.

Activity 15: Counting 21 to 50 ; (up and down)Pupil’s Book pages 46-48


Repeat Activity ‘12’ here to lead pupil count in ascending and descending order, the number 21-50

Activity 16: Match number names with groups of objects and numerals up to 50.Pupil’s Book pages 67.Lead pupils to match numerals with groups of objects, number names with groups of objects, as well as numerals with number names and with groups of objects, up to 50 using the text on pages 49-51.

Activity 17: Writing missing numbersPupil’s Book page 67. Pupils identify the missing numbers by counting either in ascending or descending order. Write the missing numbers in their notebooks.

AnswersPupil’s Book page 671. 22, 46, 49, 502. 1, 5, 93 10, 6, 3, 2, 04. 1, 5, 9, 13, 17, 5. 17, 13, 5, 1

EvaluationLet pupils:• provide examples of groups with no objects and associate the number of objects with the numeral 0

and the number name zero;• order numbers from zero to fifty;• write the numerals 0 to 50;• count the objects in a group and say the number name;• count the objects in a group and write the numeral for the number;• count in ascending and descending order.

Additional review questions1. Ask pupils to write as many ones as possible.2. Ask pupils to write as many twos as possible.3. Ask pupils to write as many threes as possible.4. Ask pupils to write as many fours as possible.5. Ask pupils to write as many fives as possible. Ask them to recite the five verses of ‘Fingers and

thumbs’ and the five verses of ‘Bottles on the wall’.6. Ask pupils to write as many zeros as possible.


7. Continue to order and write numerals up to 50.

Unit assessment test1. Ask the pupils to look at the picture on below.

Ask the pupils questions. Ask individuals to write the answers in the air and the rest of the class to repeat the action. Ask some pupils to write the numerals on the board.

How many lions are there?How many elephants are there?How many giraffes are there?How many monkeys are there?How many crocodiles are there?How many birds are there?How many fish are there?

Recite all the verses of ‘Fingers and thumbs’ and other numbers rhymes

2. Copy the number sequences on to the board and ask pupils to copy them and write in the missing numbers.

0 1 2 4 5


0 2 3 4 5

0 11 13 14 15

21 22 23 24 25

0 1 2 3 5

31 34

41 42 43 44

32 34 35

20 30 503. How many are there?


Unit assessment test answers2. 3 1 12 20 4 30 32 33 35 40 45 30 31 33 0 10 403. 4 2 2 3 5 1 3 0 3

Diagnostic assessment test1. What were the different activities that helped pupils develop the concept of zero?2. How effective were these activities?3. What were the strengths and challenges the pupils exhibited when (a) ordering groups with zero to

fifty objects? (b) matching number names, numerals and objects?4. Identify numerals that pupils found difficult to write, Identify activities to help pupils overcome

these difficulties.

24 UNIT 3 Addition (sums up to 9)

UNIT 3 Addition (sums up to 9)Pupil’s Book pages 68 - 80

ObjectivesThe pupils should be able to:• Count and tell how many objects are in two groups of objects put together . • identify the plus (+) and equal to (=) symbols;• write an addition sentence for two groups of objects and put them together using the ‘plus’ and ‘equal

to’ symbols.• find the sum of two numbers up to a total of 9;• find missing numbers (addend) in addition sentences whose sum is not greater than 9;• solve simple story problems involving addition of two numbers with sums up to 9.

NotesIn 5 + 4 = 9, 5 and 4 are addends and 9 is the sum.The pupils have:• made up groups with up to 9 objects;• compared groups of objects in the range 0 to 9;• ordered groups in the range 0 to 9.The next stage is addition.

The next stage is the ‘addition of ’ or the ‘bringing together of groups whose sum is nine or less.In 3 + 2 = 5, the 3 and the 2 are addends and 5 is the sum.In 3 +? = 5, an addend is missing. The number sentence can be said,‘Three and what makes five?’ The answer is, of course, 2. This prompts another statement, ‘Five, take away two is three.’. This is a subtraction statement which can be written as 5 – 2 = 3. Finding missing addends or ‘addition with a gap’ leads to subtraction in Unit 8

Teaching methodAddition is presented as putting objects together and finding the total number.Missing addends are calculated by finding “how much more” is required to make a total sumThe assessment of the pupils should be based on their ability to:• match the number of objects in a group with the appropriate numeral;• write numerals correctly;• understand ascending and descending order in the 0 to 9 range;• remember the counting sequences from 1 to 9;• recall 70% of the number bonds of 9.

25UNIT 3 Addition (sums up to 9)

If available, the use of Cuisenaire rods will help the pupils understand and remember the addition bonds. Using the rods, dot-pattern cards and a number line marked on the floor of the classroom will provide other views of addition which may be appreciated by many pupils.

Key wordsPut together, join, add, addition, plus, same as, equal to, sum , estimate, total

MaterialsBottle tops, suitable objects, dot-pattern cards. If available, the white, red, green, pink and yellow Cuisenaire rods. A number line marked on the classroom floor.

Activity 1: Putting groups togetherPupil’s Book page 68. Demonstrate on the teacher’s table the bringing together of two groups of objects whose total is nine or less. Ask the pupils to:• count the objects in each group;• say how many objects each group has;• count one group of objects and then ‘count on’ the objects in the next group;• count the objects brought together;• say the final counting number as the sum of the objects in the two groups;• say a number sentence using ‘and’ (or plus) and ‘makes’ or ‘equals’ which describes the addition.

Pupil’s Book page 68. Ask the pupils to:• state the number of objects in each group by counting;• state the number of objects brought together;• say a number sentence using ‘and’ (or plus) and ‘makes’ or ‘equals’ which describes the addition..

AnswersPupil’s Book page 68.5+4 =9

Activity 2: Using + and =Pupil’s Book page 69. Lead the pupils to:• say ‘plus’ for ‘and’ or ‘+’;• say ‘equals’ for ‘makes’ or ‘=’;• writing + and = to complete addition statements


AnswersPupil’s Book page 55.4+1=53+2=5

1+3=42+2=4

Activity 3: SumsPupil’s Book page 70Arrange two beans and a pencil on the teacher’s table. Form the arrangement of 2 beans and a pencil ,write 2 + 0 = 2 on the board. Use the pencil (/) to separate the groups of beans. Demonstrate the other arrangements with 2 beans and write a number sentences on the board each time.Pupil’s Book page 70 - 71. Discuss the arrangements of beans in each section and the number statements for sums of 1 to 5 which they represent. Use more beans to help pupils add up to 5, as on pages 70-71.

AnswersPupil’s Book page 552+0=21+1=20+2=2

1+0=10+1=1

3+0=32+1=31+2=30+3=3

4+0=43+1=42+2=41+3=40+4=4

5+0=54+1=53+2=52+3=51+4=50+5=5

Activity 4: Making 6, 7, 8, 9 Pupil’s Book page 72. Ask pupils to repeat activity to make 6, 7, 8, and 9. Lead pupils to find which numbers fill the boxes.

AnswersMaking 6. Page 72 6+0=65+1=64+2=63+3=62+4=61+5=60+6=6


AnswersMaking 7, Page 73 7+0=76+1=75+2=74+3=73+4=72+5=71+6=70+7=7

AnswersMaking 8, Page 74

8+0=87+1=86+2=85+3=84+4=83+5=82+6=81+7=80+8=8

AnswersPage 75. Making 9 9+0=98+1=97+2=96+3=95+4=94+5=93+6=92+7=91+8=90+9=9


Activity 5: Missing numbersPupil’s Book pages 77. Direct the pupils to copy and complete the statements by writing the missing numbers.

AnswersPupil’s Book page 77.1.4.

1+2=31+4=5

2.5.

3+2=5 1+3=4

3.6.

4+1=53+2=5

Activity 6: Missing NumbersPupil’s Book page 78. Demonstrate how to complete the examples by:• counting the objects in the first group and ‘counting on’ the objects in the second and third groups;• establish that the last number is the same as the total in the groups on the right side of the = sign;• count the objects in the second group and write the ‘missing number’.

AnswersPupil’s Book page 78 1.2.3.

1 + 2 = 33 + 2 = 54 + 1 = 5

4.5.6.

1 + 4 = 51 + 3 = 43 + 2 = 5

AnswersPupil’s Book page 631.2.3.4.

4422

5.6.7.8.

2 6 3 1

9.10.11.12.

5 1 8 3

13.14.

33

Activity 8: AdditionTest whether the pupils can recall the number bonds of 1 to 9.


Activity 9: Number storiesPupil’s Book page 79. Discuss each picture in terms of:• the situation or scene;• the action: what is happening;• the data: groups and the numbers in them;• the total objects in the groups.

Ask the class to think of stories to describe the pictures.Provide a simple example for the first picture. Ask the class to make up addition stories about any situation and tell them. They should write a number sentence for each story and complete them.

EvaluationBy the end of the unit the pupils should be able to:• count and tell how many objects there are in two groups together up to a total of nine,• recall 70% of the sums of two addends making 1 to 9.

Additional review questions1. Copy the following questions on to the board. Use counters to demonstrate. In demonstrating 4 + 3 = 7:

• place 4 counters on the desk and say ‘four’;• place 3 counters next to the 4 and say ‘and three’;• put the 4 and the 3 together and say’ is seven’.

In small groups the pupils should follow the procedure to complete the number sentences.

1 + 1 = 3 + 2 = 2 + 5 = 4 + 4 =

1 + 2 = 4 + 1 = 3 + 4 = 5 + 3 =

2 + 1 = 1 + 5 = 4 + 3 = 6 + 2 =

1 + 3 = 2 + 4 = 5 + 2 = 7 + 1 =

2 + 2 = 3 + 3 = 6 + 1 = 1 + 8 =

3 + 1 = 4 + 2 = 1 + 7 = 2 + 7 =

1 + 4 = 5 + 1 = 2 + 6 = 3 + 6 =

2 + 3 = 1 + 6 = 3 + 5 = 4 + 5 =


5 + 4 = 8 + 1 = 6 + 3 = 7 + 2 = 2 Copy the questions below on to the board. Ask pupils to copy and complete the sums.

6 + = 7 2 + = 7 1 + = 7

+ 2 = 5 + 4 = 5 + 4 = 8

3 + = 8 + 4 = 7 3 + = 4

1 + = 6 5 + = 8 5 + = 7

+ 3 = 7 + 5 = 9 + 1 = 8

2 + = 6 1 + = 8 1 + = 9

+ 2 = 3 + 2 = 4 +1 = 2

4 + = 6 + 1 = 5 2 + = 9

+ 1 = 6 + 3 = 9 + 3 = 5

7 + = 9 3 + = 6 3 + = 9

6 + = 8 2 + = 3 2 + = 8

+1 = 9 + 3 = 4 + 4 = 9

Answers to additional review questions1. 2 5 7 8 3 5 7 8 3 6 7 8 4 6 7 8 4 6 7 9 4 6 8 9 5 6 8 9 5 7 8 9 9 9 9 9


2. 1 5 6 3 1 4 5 3 1 5 3 2 4 4 7 4 7 8 1 2 1 2 4 7 5 6 2 2 3 6 2 1 6 8 1 5

Unit assessment test1. Copy the questions on to the board. Ask pupils to copy and complete.

1 + 4 =

4 + 2 =

3 + 5 =

6 + 1 =

4 + 5 =

3 + 3 =

1 + 5 =

5 + 3 =

8 + 1 =

9 + 0 =

0 + 9 =

1 + 7 =

2 + 5 =

4 + 3 =

1 + 3 =

4 + 4 =

3 + 6 =

5 + 2 =

0 + 7 =

2 + 7 =

5 + 4 =

5 + 1 =

6 + 2 =

2 + 3 =

4 + 1 =

2 + 2 =

1 + 8 =

3 + 4 =

2 + 6 =

0 + 6 =

7 + 1 =

2 + 4 =

7 + 2 =

8 + 1 =

3 + 1 =

5 + 4 =

8 + 0 =

3 + 3 =

1 + 6 =

4 + 5 =


Unit assessment test answers

5 9 9 8 6 8 6 6 8 7 8 9 7 7 5 9 9 4 5 4 6 8 4 9 6 9 9 8 8 7 7 6 9 7 8 7 9 9 6 9

33UNIT 4 Numbers and Numerals II

UNIT 4 Numbers and Numerals IIPupil’s Book pages 81 to 83

ObjectivesThe pupils should be able to:• use ordinal numbers to describe the positions of objects in a row;• recite simple rhythmic number patterns, e.g. (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1, 4) ... and (1, 1), (1,

2), (1, 3), (1, 4) ... ;• say or sing rhymes involving numbers up to 9.

NotesThe pupils should be familiar with the numbers 0 to 9

Teaching methodHere, ordinals from 1st to 9th are introduced .

Key Words Ordinals , first , second, third, fourth , fifth, sixth, seventh, eighth, ninth, 1st,2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th.

Materials : Number cards , countable objects, bottle tops , unifix cubes

Activity 1: Ordinals Ask nine pupils to stand in a line at the front of the class. Say, ‘Let’s count the number of people in the bus queue. Who will be the first person to get on the bus? Who will be the last person to get on?’ Lead the pupils to say:• person number 1 will be the first to get on the bus;• person number 2 will be the second to get on the bus;• person number 3 will be the third to get on the bus;• person number 4 will be the fourth to get on the bus;• person number 5 will be the fifth to get on the bus;• person number 6 will be the sixth to get on the bus;• person number 7 will be the seventh to get on the bus;• person number 8 will be the eighth to get on the bus;

34 UNIT 4 Numbers and Numerals II

• person number 9 will be the ninth to get on the bus.

Ask nine different pupils to stand in front of the class. Lead the pupils to refer to the order again. The pupils in the queue should be able to refer to their position in the queue by saying, ‘I am __ in the queue.’

Pupil’s Book page 81. Discuss the queue. Ask the pupils to identify people in the queue by referring to the order, the name (if labelled), male or female, girl or boy, colour of clothing, etc.

Activity 2: Number patterns with one-digit numbersPupil’s Book page 82. Use the text to identify a number pattern and show how it can be continued. Lead the pupils to say the next three terms in each question. Tell them to write the answers in their exercise books.

Activity 3: Number rhymes and song Pupil’s Book page 83.Lead the pupils to say or sing number rhymes involving 1- digit numbers as in the text . • Perform, sing and recite some rhymes which have numbers up to nine in the same styles as to those

in Unit 2 and 3

Answers to Number Patterns Pupil’s Book page 822, 1 2, 2 2, 3 2, 4 2, 5 2, 6 2, 7 2, 83, 1 3, 2 3, 3 3, 4 3, 5 3, 6 3, 7 3, 81, 0 1, 1 1, 2 1,3 1,4 1, 5 1, 6 1, 71, 1, 1 1, 1, 2 1, 1, 3 1, 1, 4 1, 1, 5 1, 1, 6 1, 1, 71, 2, 1 1, 2, 2 1, 2, 3 1 ,2, 4 1, 2, 5 1, 2, 6 1, 2, 73, 2, 1 3, 2, 2 3, 2, 3 3, 2, 4 3, 2, 5 3, 2, 6 3, 2, 71, 2, 1 2, 2, 2 3, 2, 3 4, 2, 4 5, 2, 5 6, 2, 6 7, 2, 71, 2, 1 2, 3, 2 3, 4, 3 4, 5, 4 5, 6, 5 6, 7, 6 7, 8, 7


EvaluationBy the end of the unit the pupils should be able to:

• state the position of an object among others in a sequence;• continue simple number patterns;• say number rhymes.

Additional review questions1. Find position of objects in daily life.2. Ask pupils to continue number patterns.3. Ask pupils to recite number rhymes.

Unit assessment test1 Copy the patterns onto the board. Ask pupils to copy them and write the next three parts.

1, 1 1, 2 1 , 3 1,4 , , ,

2, 0 2, 1 2, 2 2, 3 , , ,

3, 2 3, 3 3, 4 3, 5 , , ,

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

8, 1 7, 2 6, 3 5, 4 , , ,

2. Copy the table and ask pupils to write the positions of the people in the queue.

36 UNIT 4 Numbers and Numerals II

Kofi first 1stMary seœond ___ndOfei _______ ___rdJane _______ 4___Daniel _______ _____Juliet _______ _____Godwin _______ _____Akosua _______ _____Ben _______ _____

KofiMary

OfeiJane

Daniel

Juliet

Godwin

Akosua

Ben

2 Unit assessment test answers

1. 1,5 1,6 , 1, 7 2. Mary Ofei Jane

DanielJuliet

GodwinAkosua

Ben

secondthirdforth fifth sixth

seventheighthninth

2nd3rd 4th5th6th7th8th9th

2,4 2, 5 2,63, 6 3,7 3,86,5 7,6 8,74,5 3,6 2,7

Diagnostic assessment tests1. What were the strengths and challenges the pupils exhibited when describing positions of objects in

a row.2. Identify ordinals that pupils found difficult to write. Identify activities that will help pupils

overcome these difficulties.3. How enthusiastic were the pupils when performing the different activities which develop the

concept of ordinal numbers and the number patterns?4. List the challenges the pupils faced in reciting the simple rhythmic number patterns. Plan activities

to help pupils overcome these challenges.


38 UNIT 5 Subtraction 0 - 9

UNIT 5 Subtraction 0 - 9Pupil’s Book pages 84 to 91

ObjectivesThe pupils should be able to:• separate a given collection of objects into two groups and find how many objects are in each group;• find how many objects are left if a number of objects are separated (removed) from a given group;• write subtraction sentences to represent the separation of objects from a given group, using the ‘–’ and

‘=’ symbols;• find how many more or less objects are in one group than another;• find the difference between two numbers;• solve simple story problems involving the subtraction of two one-digit numbers.

NotesIn 5 – 3 = 2, 5 is the minuend and 3 is the subtrahend, 2 is the difference.

This is a ‘take away’ view of subtraction. Terms like addends, minuend and subtrahend are not used to explain subtraction to pupils at this level. They should be used by teachers and other education professionals to define the range of number activities at a particular stage in the curriculum.

Terms like add, sum, difference and take away can be used to explain the process of subtraction to pupils. When these terms are used the aim is to ‘get at’ the central ideas in subtraction which are:• how much more/less: the difference;• taking away or reducing.

Teaching methodSimilar teaching approaches are used to present the process of addition and subtraction: picture groups, the number line, story problems and Cuisenaire rods, where available.The assessment of the pupils should be based on their ability to:• find addends where the sum is up to 9;• find differences where the minuends and subtrahends are 9 or less;• write 70% of the differences, where the minuends and subtrahends are 9 or less, correctly.

Key wordsSubtract, minus, take away, difference, subtraction, separate.

MaterialsBottle tops, beans, suitable objects, number line, Cuisenaire rods when available, number cards

39UNIT 5 Subtraction 0 - 9

Activity 1: Idea of subtractionPupil’s Book page 84. Demonstrate the example by:• placing 8 beans in a row on the teacher’s desk;• putting 5 beans aside;• asking the class how many beans are left (of the 8) when 5 beans are taken away (3);• writing 8 – 5 = 3 on the board to represent the process.Demonstrate the next example (8 – 3 = 5) in a similar way. Using real objects such as beans or bottle tops the pupils should complete the exercise.

AnswersPupil’s Book page 84.7, take away 4 leaves 3 9, take away 5 leaves 47 – 4 = 3 9 – 5 = 46, take away 4 leaves 2 9, take away 6 leaves 36 – 4 = 2 9 – 6 = 3

Activity 2: Taking awayPlace 4 mangoes or any other objects on the teacher’s desk. Show that you take away 1 mango. ‘How many mangoes are left on the table?’(3)Pupil’s Book page 85. Ask the pupils to describe what is happening in the first three pictures.Demonstrate the next example with real bananas.Pupil’s Book page 85 - 86. Ask the pupils to describe what is happening in the picture. Write on the board: 5 – 2 = 3. Explain that (–) means ‘take away’. Say the number sentence as: ‘Five take away two is three.’ and ‘Five minus two is three.’Ask the pupils to repeat the number sentence.Lead the pupils to find the missing numbers and then write the complete number sentences in their exercise books.

AnswersPupil’s Book page 865–3=2 7–3=48–4=4 9–5=46–3=3 9–6=37–2=5 6–5=19–7=2 5–1=4


Activity 3: DifferencePupil’s Book page 87. Demonstrate the 9 – 4 = 5 example on the board.Discuss each subtraction before asking the pupils to write complete subtraction sentences in their exercise books.

AnswersPupil’s Book page 87.8 – 4 = 4 8 – 3 = 5 9 – 3 = 67 – 4 = 3 9 – 6 = 3 6 – 4 = 25 – 4 = 1 9 – 7 = 2 7 – 3 = 49 – 1 = 8 8 – 2 = 6 6 – 6 = 07 – 3 = 4 5 – 3 = 2 9 – 8 = 1

Activity 4: SubtractingPupil’s Book page 88. and 89. Demonstrate the 7 – 6 = 1 and 4 – 4 = 0 examples using coloured bottle tops or counters. The pupils should write complete subtraction sentences in their exercise books.

AnswersPupil’s Book pages 88. and 89.7 – 6 = 1 4 – 4 = 07 – 5 = 2 4 – 3 = 1

7 – 4 = 3 4 – 2 = 27 – 3 = 4 4 – 1 = 37 – 2 = 5 4 – 0 = 4

7 – 1 = 6 2 – 0 = 27 – 0 = 7 2 – 1 = 17 – 7 = 0 2 – 2 = 0

8 – 8 = 0 6 – 5 = 18 – 7 = 1 6 – 4 = 2

8 – 6 = 2 6 – 3 = 38 – 5 = 3 6 – 2 = 4


8 – 4 = 48 – 3 = 58 – 2 = 6

8 – 1 = 78 – 0 = 8

9 – 8 = 19 – 7 = 29 – 6 = 3

9 – 5 = 49 – 4 = 59 – 3 = 6

9 – 2 = 79 – 1 = 8

9 – 0 = 99 – 9 = 0

6 – 1 = 56 – 0 = 66 – 6 = 0

1 – 0 = 11 – 1 = 0

5 – 4 = 15 – 3 = 25 – 2 = 3

5 – 1 = 45 – 0 = 55 – 5 = 0

3 – 2 = 13 – 1 = 2

3 – 0 = 33 – 3 = 0

Activity 5: Subtraction storiesPupil Book page 90. Ask the pupils to describe the pictures.In groups the pupils should:• discuss the pictures;• make up subtraction stories;• write a subtraction sentence for each story.

Ask the class to tell other subtraction stories and record each one on the board using a number sentence. Provide sheets of paper for the pupils to draw a subtraction story and write a number sentence to describe it.

AnswersPupil’s Book page 90Suggested interpretations:5 – 2 = 3 There will be 3 bananas left.9 – 3 = 6 The boy will have 6 mangoes left.8 – 5 = 3 3 birds will be left on the branch.


Pupil’s Book page 911.

2.

3.

4.

7 - 4 = 3

4 + 5 = 9

3 + 4 = 7

5 + 4 =9

5.

6.

7.

8.

7 - 4 = 3

3 + 4 = 7

9 - 3 = 6

7 - 5 = 2

EvaluationBy the end of the unit the pupils should be able to:• find differences where the minuends and subtrahends are 9 or less;• write 70% of the differences, where the minuends and subtrahends are 9 or less, correctly.• find the missing addends in a given number sentence • solve simple story problems involving subtraction 0-9

Additional review questionsCopy the questions onto the board. Ask pupils to copy and complete them.

–7 2 = –9 2 =

–7 3 = –7 5 =–9 6 = –9 7 =–8 5 = –5 3 =–8 4 = –8 2 =

Answers to additional review questions7 – 2 = 5 9 – 2 = 7


7 – 3 = 4 7 – 5 = 29 – 6 = 3 9 – 7 = 28 – 5 = 3 5 – 3 = 2 8 – 4 = 4 8 – 2 = 6

Unit assessment testCopy the questions on to the board. Ask pupils to subtract and find the difference.

5 – 3 =

4 – 1 =

3 – 2 =

6 – 5 =

7 – 4 =

5 – 2 =

4 – 2 =

3 – 1 =

7 – 5 =

6 – 4 =

9 – 7 =

8 – 4 =

7 – 2 =

6 – 1 =

4 – 3 =

5 – 4 =

9 – 6 =

8 – 2 =

7 – 3 =

6 – 3 =

9 – 3 =

8 – 6 =

7 – 6 =

6 – 2 =

5 – 4 =

5 – 1 =

2 – 1 =

9 – 4 =

8 – 3 =

7 – 1 =

6 – 6 =

9 – 8 =

1 – 1 =

8 – 1 =

8 – 7 =

4 – 0 =

9 – 2 =

5 – 5 =

9 – 1 =

9 – 5 =


Unit assessment test answers2 2 6 03 4 2 11 5 1 01 5 4 73 1 1 13 1 4 42 3 1 72 6 5 02 4 5 82 3 6 4

Diagnostic assessment test1. What were the pupils’ reactions to each of the different materials they used in developing the

concepts of addition sums up to 9?2. How appropriate were each of the activities?3. What challenges did the pupils face in identifying the subtraction (–) sign?4. What challenges did pupils face in translating story problems into numbers and symbols?5. Was there sufficient probing of pupils’ knowledge, understanding, skills, attitudes and processes?

45UNIT 6 Solid shapes

UNIT 6 Solid shapesPupil’s Book pages 76 - 80

ObjectivesThe pupils should be able to:• sort objects according to their shape;• identify the faces, edges and corners of objects;• identify the edges of objects that are straight or round;• identify solid objects with straight or round edges;• sort objects according to the shape of their edges;• draw around the faces of solid objects.

NotesThe pupils have had some modelling experience with solid shapes in Unit 1.

Solid shapes are also called three-dimensional shapes. The three dimensions are length, width and height. The faces of solids are two-dimensional shapes. The two dimensions are length and width. When two faces of a solid meet, an edge is formed. When three faces or edges of a solid meet, a corner is formed.

face

edge

corner

Teaching methodThis unit investigates aspects of solid shapes: their faces, edges and corners. Particular faces of solids are used to make new flat shapes. Investigations into whether a shape will roll or slide indicate if its faces are curved or flat.

Key wordsObject, solid shape, faces, edge, roll, round, straight ,

MaterialsAll kinds of everyday objects including empty boxes, milk tin, milo tin, match boxes, chalk box, cubes of sugar, bottles, pencils. books, cones

46 UNIT 6 Solid shapes

Activity 1: Sorting objectsArrange many different solid shapes on the teacher’s table. These should include boxes, bottles, cans, pipes, balls, cones and everyday objects such as fruit and bread. Ask the pupils to describe the objects in terms of their shape, material, purpose, etc.

Pupil’s Book page 92. Ask pupils to name the objects in the picture and allow them to identify similar shapes on the teacher’s table. Lead the pupils to describe the objects in terms of:• material: wood, cardboard, metal, glass, rope, etc.,• purpose: holding liquid or food, building, etc.,• shape: flat, curved, spiral, will roll or slide or rock etc.

The pupils should make up groups of shapes which have particular qualities.

Activity 2: Faces, edges and cornersPupil’s Book page 93. Use the pictures to name objects that have:• faces: flat and curved;• edges: straight and curved;• corners where three surfaces meet;• points such as at the top of a cone or pencil or nail.

Layout a set of objects with similar edges, for example cylinders, and include one object that is different, for example a cuboid. Ask pupils which object is the ‘odd one out’, and ask them to explain why. Repeat with a different set of objects, for example a set of cuboids and one cube. Does the cube belong to the group? Encourage pupils to express their reasons carefully.

Activity 3: Testing for flat and curved surfaces shapesPupil’s Book page 94. Discuss the type of tests that the pictures show. Ask some pupils to demonstrate the tests. The pupils should make groups of objects which have:• flat surfaces;• curved surfaces;• curved surfaces which allow rolling;• surfaces which allow sliding;• surfaces which allow rocking movements;• sharp points so that they can be used to hold things together;• edges that are similar shapes.

Activity 4: Faces of solidsPupil’s Book page 95. Arrange on the teacher’s table as many as possible of the shapes shown in the picture. Discuss the features of the shapes. Hold up a box and ask a pupil to draw the type of faces it has

47UNIT 6 Solid shapes

on the hoard. Similarly ask pupils to draw the types of faces that other solids have. Demonstrate how to use the faces of solid shapes to draw such shapes as rectangles, triangles and circles.

Activity 5: The odd one outPupil’s Book page 96. Ask pupils to describe the shape of each object. Which is the odd object, in terms of its shape? Why?

Answers1. the book (because it has straight surfaces and it slides rather than rolls)2. the bowl (because it has curved surfaces which are not sharp like the other objects)

EvaluationBy the end of the unit the pupils should be able to:• identify the faces, edges and corners of solids;• make pictures using the faces of solids.

Additional review questionsCopy the diagrams on to the board.

Discuss how shapes produced from the faces of solid shapes are used to make new shapes such as the girl and the lorry. The pupils should produce shapes and glue them on to paper to make new shapes.

48 UNIT 6 Solid shapes

Unit assessment testHave the following solid objects available: cuboid, cylinder, triangular prism, cube, pyramid and cone.

Which objects can be used to draw :• straight lines? • curved lines?• this shape? • this shape?

• this shape? • this shape?

Unit assessment test answers• cuboid, cube, prism, pyramid • cone, cylinder• cuboid • cube• cone, cylinder • triangular prism

Diagnostic assessment test1. Were pupils able to sort solid objects into groups according to their own criteria, criteria given by

peers and criteria given by the teacher?2. What challenges did pupils face in identifying the faces, edges and corners of solid objects?3. Was the number of pictures drawn using the faces of solids diverse enough to exhibit different

talents and skills of pupils?

49UNIT 7 Tens and ones

UNIT 7 Tens and onesPupil’s Book pages 97 to 106

ObjectivesThe pupils should be able to:• make a group of ten objects;• a group of ten objects and some more as 11, 12, 13 ... 19 objects;• make two or more groups of ten objects as 20, 30 ... 90;• read and write the numbers 10, 20, 30 ... 90;• read and write the numbers 0 to 99;• break two-digit numbers into tens and ones.

NotesThe pupils should be familiar with:• the numbers 0 to 50• addition and subtraction in this range 0-9.

Here 10, the two-digit number, is introduced. The first digit is 1: the number of ‘tens’; and the second digit is 0: the number of ‘ones’.

Teaching methodThe pupils are introduced to:• ten as one more than nine;• multiples of ten: the ‘ty’ numbers, up to ninety or nine tens (90);• numbers in tens and ones in the ‘teen’ (11 to 19) range;• numbers in multiples of tens and ones in the 20 to 99 range.

It is important to exemplify this range of numbers in different ways which can include:• bundles of tens and single sticks;• the ‘longs’ and ‘cubes’ of base ten materials;• abacus;• Cuisenaire rods;• hundred square.

Key wordsTens, ones, loose sticks, bundle sticks, multi base blocks

MaterialsBottle tops, suitable objects, Bundles of sticks in tens , single sticks, number cards , unifix cubes,

50 UNIT 7 Tens and ones

Hundred square. Where possible: an abacus, base ten material and Cuisenaire rods, scissors.

Activity 1: Counting to tenPupil’s Book page 97. ‘Look at the staircase – count the steps. How many bricks are in the first (second etc, tenth) step?’ Lead the pupils in counting up to ten and from ten to one.

Arrange ten bottle tops on the teacher’s desk. Ask a pupil to arrange them into two groups. Write the arrangement on the board as an addition sentence, e.g. 9 + 1 = 10. Continue to ask for rearrangements of the bottle tops or blocks until all the addition bonds of ten are recorded on the board.

Pupil’s Book page 97 (bottom). The pupils should copy and complete the addition sentences in their exercise books.Ask the class to provide stories, incidents or situations where ten is an important number, for example:• 10 fingers;• 10 toes;• currency notes;• a football/hockey team has 10 players and a goalkeeper

AnswersPupil’s Book page 8110 + 0 = 109 + 1 = 108 + 2 = 107 + 3 = 106 + 4 = 10 5 + 5 = 10

4 + 6 = 103 + 7 = 102 + 8 = 101 + 9 = 100+10 = 10

Activity 2: Cuisenaire staircaseWorking with small groups and using the white, red, green, pink, yellow, dark green, black, brown, blue and orange Cuisenaire rods, demonstrate how to form a staircase and name the colours from shortest to longest. The pupils should say the colours in order ten times. Ask the pupils to say which colour stands for ten (orange). Using the rods they should discover all the addition bonds of 10 and write them in their exercise books.

AnswersAs in Activity 1


Activity 3: Making tensShow the class a large number of sticks cut from reeds to the same length as match-sticks. Demonstrate the counting of ten by counting ten of these sticks and then tying them into a bundle called ‘1 ten’. If appropriate, the pupils can, in small groups, make more bundles of tens.

Activity 4: Tens and onesDemonstrate the representation of eleven (11) using 1 bundle of ten and 1 single stick. Write the numbers 11,12, 13, 14, 15, ..., 20 on the board. Tell the pupils that the first digit shows how many tens and the second digit shows how many ones. Ask the groups to use their bundles and single sticks to represent the numbers on the board.Pupil’s Book page 98. Discuss the arrangements of tens and ones. Emphasise how the ‘teen’ numbers are made up of a ten and from one up to 9 ones. Ask the class to provide examples of ‘teen’ numbers, for example:• eleven players in a football/hockey team;• twelve months in a year;• thirteen players in a rugby league team;• fourteen days in a fortnight;• fifteen players in a rugby union team;• sixteen, seventeen, eighteen and nineteen: the ages of older brothers and sisters etc.

Activity 5: Counting and reading in tens Pupil’s Book pages 99. Discuss the arrangements of tens: emphasise how many tens, the number name and write the two-digit numbers on the board. Lead the class in reciting, a number of times, the ‘ty’ numbers: ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety. Lead them also to recite these ‘ty’ numbers, a number of times, in a similar way to reciting multiplication tables:• one ten: ten;• two tens: twenty;• three tens: thirty;• four tens: forty;• five tens: fifty;• six tens: sixty;• seven tens: seventy;• eight tens: eighty;• nine tens: ninety.

Activity 6: More tensPupil’s Book page 100. Ask the class to provide stories, incidents or situations where ‘ty’ numbers are important, for example:


• my grandfather/grandmother is 70 years old;• my mother/father is 30/40 etc years old;• the number of my house is 10, 20 etc.

Activity 7: More tens and onesPupil’s Book page 101. Explain that:• the ten-strips can be used instead of the bundle of ten to represent ten;• the squares can be used instead of single sticks to represent one.Discuss the representation of the father’s and daughter’s ages. The pupils should name the numbers represented by the arrangements of strips and squares.

AnswersPupil’s Book page 101a. 37 b. 46 c. 58d. 19 e. 88 f. 97

Activity 8: Tens and onesDemonstrate the representation of five numbers in the 11 to 99 range using the orange Cuisenaire rods for Tens and the white to blue rods for Ones. Ask the pupils to represent, say and write ten further numbers.

Activity 9: Numbers to 99:-Pupil’s Book page 86. Discuss the features of the hundred square.‘Count the rows (across) – how many are there?’ (10)‘Count the columns (up) – how many are there?’ (10)‘How many is in the second row?’ (ten, there are two in 11)‘How many 2s in the third row?’ (ten, there are two in 22) etc to the tenth row.‘Which number always appears in the first column?’ (1) ‘How many times?’ (11)‘What do you notice about the other numbers down the first column?’ (They increase; 1, 2 etc. to 9)‘Which number always appears in the second column?’ (2) ‘How many times?’ (11)‘What do you notice about the other numbers down the second column?’ (They increase; 1, 2 etc. to 9)‘Which number always appears in the tenth column?’ (0) ‘How many times?’ (9, or 11 if 100 was there)‘What do you notice about the other numbers down the tenth column?’ (They increase; 1, 2, 3 etc. to 9)‘Go to the first number in the second row – what is it?’ (11) ‘From there move your finger diagonally. What do you notice?’ (The pattern 11, 22, 33, 44 etc. to 99.)


Lead the class, fingers on each number, in reading/reciting the numbers from 1 to 99 several times.Ask a pupil to read a number in the table, another to write it on the board and another to point out its position in the hundred square. Working in groups, ask pupils to find the missing numbers to complete the two tables. Pupils to complete or continue the rows on the page by writing the answers in their notebooks.

Answers1 2 4 6 8 10 12 14 18 20

21 23 25 27 29 31 35 37 3941 42 43 44 45 47 48 49 5053 56 59 61 63 66 71 73 7476 77 79 80 82 83 86 89 9294 96 98

2 1 2 3 4 5 6 8 9 1011 12 13 14 15 16 18 19 2021 22 23 24 25 26 28 29 3041 42 43 44 45 46 48 49 5051 52 53 54 55 56 58 59 6061 62 63 64 65 76 76 79 8071 72 73 74 75 86 88 89 9081 82 83 84 85 86 98 99

Activity 10: Tens and ones – decomposingPupil’s Book page 103. Demonstrate the decomposition of 36 using:• bundles of tens and single sticks;or• the longs and cubes of the base ten material;

Ask some pupils to demonstrate other examples before telling the pupils to write the expansions in their exercise books.Use the example of 8 + 6 = 14. Demonstrate exchanging cubes for one long exchange ten sticks for 1 bundle . i.e. 8 + 6 = 1 ten + 4 ones = 14


AnswersPupil’s Book page 103.2. 21 = 2 tens + l one = 20 + 13. 73 = 7 tens + 3 ones = 70 + 34. 49 = 4 tens + 9 ones = 40 + 95. 65 = 6 tens + 5 ones = 60 + 56. 46 = 4 tens + 6 ones = 40 + 67. 57 = 5 tens + 7 ones = 50 + 7

EvaluationBy the end of the unit the pupils should be able to:• group objects in tens;• say the number of tens in ‘ty’ numbers;• say how many tens and ones in numbers between 11 and 99;• use numbers in this range to describe real life situations.• break two digit number into tens and singles (ones).

Answersa. 92 b. 56 c. 60

Unit assessment testCopy these on to the board and ask pupils to copy and complete them.

24 = 2 tens + ones = 20 +

36 = tens + 6 ones = + 6

57 = tens + ones = +





5 tens + 9 ones = + = 59


8 tens + 4 ones = + =

7 tens + 0 ones = + =

1 ten + 1 one – + =

3 tens + 9 ones = + =

1 ten + 9 ones = + =

5 tens + 6 ones = + =

4 tens + 3 ones = 40 + 3 =

Unit assessment test answers24 = 2 tens + 4 ones = 20 + 436 = 3 tens + 6 ones = 30 + 657 = 5 tens + 7 ones = 50 + 748 = 4 tens + 8 ones = 40 + 860 = 6 tens + 0 ones = 60 + 076 = 7 tens + 6 ones = 70 + 693 = 9 tens + 3 ones = 90 + 35 tens + 9 ones = 50 + 9 = 59

8 tens + 4 ones = 80 + 4 = 847 tens + 0 ones = 70 + 0 = 701 ten + 1 one = 10 + 1 = 113 tens + 9 ones = 30 + 9 = 391 ten + 9 ones = 10 + 9 = 195 tens + 6 ones = 50 + 6 = 564 tens + 3 ones = 40 + 3 = 43

Diagnostic assessment test1. What strategies did pupils use in grouping objects into tens and ones?2. Were the various strategies appropriate?3. Identify the various processes/skills pupils used in reading and writing numbers 0 to 99.4 Identify the various processes/skills pupils used in saying how many tens and ones in numbers between 0 and 99.

56 UNIT 8 Addition and subtraction

UNIT 8 Addition and subtractionPupil’s Book pages 107 to 109

ObjectivesThe pupils should be able to:• add any two one-digit numbers up to a sum of 18;• develop the basic addition facts up to a sum of 18;• subtract a one-digit number from numbers in the range 0 to 18;• develop basic subtraction facts for numbers 0 to 9 only.

NotesThe pupils should be familiar with:• the numbers 0 to 99;• addition and subtraction in the 0 to 9 range.

Teaching methodAddition is demonstrated by:• bringing groups together;• steps forwards (or to the right) on the number line

Subtraction is demonstrated by:

• establishing the difference between two groups;• steps back (or to the left) on the number line.

Key wordsThe numbers from zero to eighteen. Add, subtract.

MaterialsBottle tops, suitable objects.

Activity 1: AdditionPupil’s Book page 91. Use the 8 + 6 = 14 example to show how the objects of two groups are brought together and the total number is determined by counting. If necessary, provide the pupils with counters to find the totals.

57UNIT 8 Addition and subtraction

AnswersPupil’s Book page 91.13 13 1214 18 1117 11 1615 11 12

11 13 1314 15 12

Activity 2: SubtractionPupil’s Book page 108. Demonstrate the 15 – 9 = 6, Subtraction by asking the pupils to:• place 15 green beans or appropriate counters in the 1 to 15 spaces;• change the colour of the 9 of the beans• count the number of green beans;• state that 15 – 9 = 6.Similarly demonstrate 14 – 8 = 6. The pupils should use real beans or counters or the ‘bean spaces’ to complete the subtractions.

AnswersPupil’s Book page 1087 8 95 7 9

Activity 3: More on subtractionPupil’s Book page 109. Tell pupils to use counters to complete the subtractions.

Answers4 4 10 59 4 6 2 8-

Tell pupils that in subtraction another word for answer is differenceAsk pupils to find the differences between the pairs of numbers.


Answers9–7=28–6=27–5=26–4=25–3=24–2=23–1=22–0=2

9–5=48–4=47–3=46–2=45–1=44–0=4

9–2=78–1=77–0=7

Now ask pupils to find all the pairs of numbers (between 0 and 9) whose difference is 3.

Answersa. 9–6=3 b. 6+0=6 8–5=3 5+1=6 7–4=3 4+2=6 6–3=3 3+3=6 5–2=3 2+4=6 4–1=3 1=5=6 3–0=0 0+6=6

EvaluationBy the end of the unit the pupils should be able to:• add and subtract numbers in the 0 to 18 range using counters;• achieve 70% in subtraction tests based on the range 0 to 9 without using counters.

Additional review questionsCopy these questions on to the board. Ask pupils to copy and complete them.


9 – 9 = 9 – 8 = 9 – 7 = 9 – 6 = 9 – 5 = 9 – 4 = 9 – 3 = 9 – 2 = 9 – 1 = 9 – 0 = 3 – 3 = 3 – 2 = 3 – 1 = 3 – 0 =

7 – 7 = 7 – 6 = 7 – 5 = 7 – 4 = 7 – 3 = 7 – 2 = 7 – 1 = 7 – 0 = 2 – 2 = 2 – 1 = 2 – 0 = 1 – 1 = 1 – 0 =

6 – 6 = 6 – 5 = 6 – 4 = 6 – 3 = 6 – 2 = 6 – 1 = 6 – 0 = 5 – 5 = 5 – 4 = 5 – 3 = 5 – 2 = 5 – 1 = 5 – 0 =

8 – 8 = 8 – 7 = 8 – 6 = 8 – 5 = 8 – 4 = 8 – 3 = 8 – 2 = 8 – 1 = 8 – 0 = 4 – 4 = 4 – 3 = 4 – 2 = 4 – 1 = 4 – 0 =

Answers to additional review questions0 0 0 01 1 1 12 2 2 23 3 3 34 4 4 45 5 5 56 6 6 67 78 7 0 89 0 1 1 2 00 2 3 11 4 22 0 5 33 1 4

Unit assessment testCopy the questions on to the board. Ask pupils to copy and complete them.


1. 9 + 2 = 8 + 4 = 7 + 6 = 8 + 3 = 7 + 5 = 6 + 7 = 9 + 6 = 7 + 4 = 6 + 6 = 5 + 8 = 5 + 6 = 9 + 1 = 5 + 7 = 4 + 9 =

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

5 + 5 = 4 + 7 = 3 + 9 = 4 + 6 = 3 + 8 = 4 + 8 = 3 + 7 = 2 + 9 = 9 + 4 = 5 + 9 = 9 + 3 = 8 + 5 = 1 + 9 = 8 + 2 =

2. 14 – 5 = 15 – 7 = 16 – 9 = 15 – 6 = 17 – 9 = 14 – 6 = 15 – 8 = 14 – 7 = 15 – 9 = 10 – 4 = 18 – 9 = 14 – 8 = 10 – 8 = 17 – 8 =

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

10 – 5 = 11 – 7 = 12 – 9 = 10 – 6 = 11 – 8 = 12 – 8 = 10 – 7 = 11 – 9 = 13 – 4 = 10 – 2 = 14 – 9 = 12 – 3 = 13 – 5 = 10 – 9 =


Unit assessment test answers1. 11 14 10 2. 9 9 5 12 15 11 8 8 4 13 16 12 7 7 3 11 11 10 9 8 4 12 17 11 8 7 3 13 14 12 8 6 4 15 15 10 7 9 3 11 14 11 7 7 2 12 15 13 6 6 9 13 10 14 6 5 8 11 18 12 9 5 5 10 14 13 6 9 9 12 10 10 2 5 8 13 17 10 9 4 1

Diagnostic assessment test1. What competencies did pupils exhibit in adding and subtracting numbers in the 0 to 18 range?2. How will these competencies enhance pupils’ development of concepts of addition and subtraction

of larger numbers?3. Identify any challenges pupils faced. Plan strategies to overcome these challenges.

62 UNIT 9 Measurement of length, area, capacity and mass

UNIT 9 Measurement of length, area, capacity and mass

Pupil’s Book pages 94 to 105

ObjectivesThe pupils should be able to:• compare the lengths/heights of two objects and tell which is taller/longer/shorter • use arbitrary units to compare the lengths and heights of various objects; • compare the capacities of two containers and tell which holds more or less or equal amounts of water

or sand;• use arbitrary units to compare the capacities of various containers;• compare the size of two surfaces (areas) and tell which one is bigger /smaller• compare the mass of objects by observing and feeling the differences in mass and using a simple

balance.

NotesMost pupils will be familiar with different-sized containers and boxes or surfaces, but they may not know the terms area, capacity or mass. The mass and weight of an object are different although there is no need to explain the difference between the two term to pupils at this level. The region covered by an object/surface is the area.

The mass of an object is the amount of material it contains. It never changes wherever the object is, for example the North Pole, the equator, in space or on the moon. An astronaut is weightless in space but has the same mass because he or she is made of the same material.

The weight of an object depends on its location. A person is a little heavier at the poles than at the equator because the earth is not a perfect sphere. The weight of a person on the moon is about a sixth of their weight on earth because the moon’s force of gravity is less than the earth’s.

Weight is measured in newtons (N) while mass is measured in kilograms (kg). On earth a mass of 1 kg weighs 10 N. Weight and mass are connected by W = mg, where g is the force due to earth’s gravity. For everyday use we say that an object’s weight is n kg because we know that the same value applies (within limits) on earth. We also use the words mass and weight to mean the same thing in everyday language. Area is measured in square unit (e.g. cm2 , m2 ....)

63UNIT 9 Measurement of length, area, capacity and mass

Teaching methodWhenever possible the activities outlined in the Pupil’s Book should be supplemented with practical activities in comparing lengths/heights, area, capacities and masses.

Key wordsLonger than, shorter than, as short as, as long as, as tall as, tallest of all, longest of all, shortest of all, capacity, holds more than, holds less than, holds the same as, holds the most, holds the least, mass, is heavier than, is lighter than, is as heavy as, lightest, heaviest, bigger/smaller than, as big/small as smallest, biggest, small , big.

MaterialsA variety of containers of different capacities, a larger bowl of water or dry sand, wooden strips, surface of books, empty cans and wire suitable to make simple beam balances, a variety of small objects suitable for weighing on a simple balance such as coins, bolts, marbles etc, a supply of small nails or bottle tops as arbitrary units of mass.

Activity 1: Length and heightAsk the pupils to compare the lengths or heights of pairs of objects in the classroom. Choose objects which are significantly different in length/height so that the pupils are able to easily see which is the longer/taller. Introduce the phrases ‘taller than’, ‘longer than’ and ‘shorter than’ for expressing the differences in length and height. Extend this idea to groups of objects where an object might be described as the longest, tallest or shortest of all. Explain that where the objects being considered are equal in length the phrases ‘as short as’, ‘as long as’ and ‘as tall as’ are used.

Pupil’s Book pages 110 - 112. Discuss the pictures and encourage the pupils to use the appropriate vocabulary.

Activity 2: Comparing lengthsExplain to the pupils that when objects are very different in length or height there is no need to measure them to find out which is the longer or taller because the difference is easy to see. Ask the pupils how they might find which is the longer or taller when objects are similar in size. Introduce the idea that the size of objects could be compared to another object such as the length of a pencil or a book. A pencil or book length is then referred to as an arbitrary unit.

Pupil’s Book page 113. Ask the pupils to estimate (guess) the length of, and then measure, some objects in the classroom using a pencil length or a book length as arbitrary units.Ask the pupils to order the objects according to their lengths


Activity 3: idea of areaPupil’s Book pages 114 - 116. Lead pupil to estimate the number of times a small notebook can cover an exercise book. Place one flat object on top of another to find out which one is bigger or smaller. Find how many times the smaller object can cover the bigger object. Ask pupils to repeat this activity for surfaces such as the top of teachers table, pupils table, and the blackboard (if possible). Use arbitrary units to measure surface (area) of the objects . Ask pupils to order the areas of objects selected from smaller to the biggest and vice versa.

Activity 4: Comparing Capacities Show the pupils a range of familiar containers such as a cup, a jug, a pan and a bucket. Pour water (or sand) from one to another to show that they each hold different amounts. Ask some pupils to repeat the tests. Use arbitrary units to measure the capacities: ‘How many cups does the jug, pan or bucket hold?’ Introduce the word capacity as the amount that a container will hold.

Demonstrate that a tall thin container may hold less than a short wide one even though the tall container looks as if it could hold more.

Pupil’s Book pages 117 - 119. Ask the pupils to compare the capacities of the containers using words such as ‘holds more than’ and ‘holds less than’. Ask the pupils to arrange the containers in order from ‘holds most’ to ‘holds least’.

AnswersPupil’s Book pages 118 and 119.The jar holds less than the vase.The vase holds more than the tin.The tin holds the same as the jar.The bowl holds the most.The tin is next.The jar is next.The cup holds the least.

Activity 4: Comparing massesIntroduce the word mass as a measure of how heavy an object is. Treat the words mass and weight as meaning the same thing at this stage.

Pupil’s Book pages 120-122. Explain that when objects are very different in mass there is no need to measure their masses in order to find which is the heavier because this can be easily done by holding them. Ask the pupils to compare the masses of objects using the terms ‘heavier than’ ‘lighter than’ and ‘the same mass as’.


Explain that when objects are similar in mass, comparing their masses by feel is not sufficiently accurate. Introduce the idea of using simple balance for comparing the masses of objects. A suitable balance can be made by suspending a wooden beam, 40 to 50 cm long, from its mid-point on a wire or piece of string. An empty tin should be attached, by wire, to each end of the beam. Ask the pupils to compare and order the masses of objects of similar masses using a simple balance and some nails. Explain that, in the same way that a pencil and book edge were used as arbitrary units when measuring length, the masses of objects can be compared using nails, of the same weight, as arbitrary units. They should record the mass of each object as being the same as so many nails and then order them.

AnswersPupil’s Book page 120The pineapple is heavier than the orange.The lemon is lighter than the orange.The orange has the same mass as the mango.

Pupil’s Book pages 121•The stone is heavier than the sponge •The sponge is lighter than the stone

EvaluationBy the end of the unit the pupils should be able to compare the lengths or heights of objects, which are obviously of different sizes, by sight and say which is the longer, taller or shorter. They should have used objects such as a pencil or the edge of a book as arbitrary units, to make rough measurements of objects in the classroom and express the results in such terms as ‘longer than’, ‘shorter than’ and ‘the same length as’. The pupils should be able to order objects according to their length or height. The pupils should understand the term - area and have awareness of areas, different surfaces of objects . They should be able to compare the areas of different surfaces and use the terms as big as, bigger than, small, smaller than.

The pupils should understand the term ‘capacity’ and have some awareness of the relative capacities of different containers. They should be able to compare the capacity of different containers and express the results in such terms as ‘holds more than’, ‘holds less than’ and ‘holds the same as’. They should be able to order objects according to their capacities.

The pupils should understand the term ‘mass’ and appreciate that objects have different masses. They should have compared the masses of objects by feel and by using a simple balance. They should have used an arbitrary unit to measure the masses of objects and express the results in such terms as ‘heavier than’, ‘lighter than’ and ‘as heavy as’. They should be able to order objects according to their mass.

Unit assessment test1. Draw the trees on the board. Ask pupils to write which is the tallest and which the shortest.


AB

C

2. Draw the pencils on the board. Ask pupils to write which is the longest and which is the shortest.

A

B

C

D

AB

CD

E

3. Copy the diagram and sentences on to the board. Ask pupils to copy and complete the sentences.

A

B

C

D

AB

CD

E

C holds more than…………… and …………….. ……………..holds more than B. …….……….holds as much as E. D holds ……………… than E. A holds ……………… than D B holds more than __ , __ and __ . D holds more than __ , __ , __ and __ .


4. Copy the exercise on the board and ask pupils to complete

A. Notebook B. Maths Textbook C. Teachers Notebook

1. A is ...................than B2. C is .......... .......than A3. B is .................. than C

5. Copy the diagram onto the board. Ask pupils to copy the diagram and mark the heavier bag of flour with H and the lighter bag of flour with L.

FLOUR

FLOUR

Unit Assessment Answers 3. A , E 4. smaller D bigger A smaller more less A , C, E A, B , C , E


Diagnostic assessment test1. What information did you gather from the pupils’ responses to the activities? Was the information

sufficient to ensure pupils’ understanding of the concepts involving length, area, capacity and mass?2. Relating the correct terms to activities involving comparison of lengths, area, capacities and masses

can be very challenging. What strategies did you use in overcoming these challenges?3. How appropriate were the arbitrary units the pupils used for length, area, capacity and mass?

69UNIT 10 Measurement of time and money

UNIT 10 Measurement of time and money

Pupil’s Book pages123 to 1281

ObjectivesThe pupils should be able to:• identify some events and tell when they take place;• identify events which take a short time and those which take a long time;• recognise currency notes and coins up to GH¢10.00;• name items that each note or coin can buy;• use token coins up to GH¢1.00 to buy everyday items in a play shop.

NotesThe 1 Gp , 5 Gp,10 Gp, 20 Gp, 50 Gp and GH¢1.00 coins have been included since they are in use. The GH¢1.00, GH¢ 2.00, GH¢5.00 , and GH¢10.00 bank notes are to be introduced now. The GH¢20.00 and GH¢50.00 will be introduced later in the course.

The prices and the denominations of notes and coins used in the book must be changed as necessary to suit prevailing conditions.

Teaching methodThe pupils are led to look at how money is used to buy everyday items. Through book exercises and ‘class market stall’ play, they will get the opportunity to identify and use the coins and notes necessary to buy price labelled items.

Key wordsmoney, time, currency, note, coin, sunrise, sunset, token money, playshop, buy , change, balance , morning, afternoon, evening

MaterialsThe 1 Gp , 5 Gp,10 Gp, 20 Gp, 50 Gp and GH¢1.00 coins and GH¢1.00, GH¢2.00, GH¢5.00 , and GH¢10.00 bank notes, token coins, token notes, water timer or sand timer, bottle tops, card, scissors, colouring pencils, empty packets and real shop or market items for making a ‘classroom market stall’.

Activity 1: Idea of timePupil’s Book page 123. Discuss how the day may be divided into parts, such as morning, afternoon and evening. Ask the pupils to:

70 UNIT 10 Measurement of time and money

• describe what they do during the different parts of the day;• compare a typical school day with a day at the weekend.

Explain that talking about activities in terms of parts of the day is acceptable for many purposes but not sufficiently accurate for other purposes. For example, if school started ‘after breakfast’ pupils would turn up at different times because they would have their breakfasts at different times and take different amounts of time to get to school.

Point out that clocks and watches allow time to be measured more accurately. When events occur at a particular time on the clock everyone can be sure when that is and come at the same time. Discuss some examples where the need to know time accurately is important. The start and end of a school day is one example. Other examples could include a timetable for catching buses and trains, and a programme schedule for television.

Activity 2: Measuring timePupil’s Book pages 124 - 125. – Point out that doing different things takes different amounts of time. Ask the pupils to describe some of the things they do which take only a short time, and others which take a long time. Show the pupils how to use a simple water timer or sand timer to compare the time taken to carry out different events. A simple water timer can be made by making a small hole in the bottom of a milk tin and standing this over a clear plastic bottle. When water is placed in the milk tin, it will drip into the bottle. Pupils can determine the relative amount of time taken for different events by counting drips, if the events are short, or looking at the depth of water which accumulates in the bottle.

Ask the pupils to compare the times taken for some different activities. Encourage them to use phrases like longer, shorter, quicker and slower when comparing the times taken to do these activities.

AnswersPupil’s Book pages 125. cleaning the blackboard took most time. Reading a page of a book took less time. Counting up to 99 took even less time. Touching the walls of the classroom took least time.

Activity 3: MoneyDiscuss how people work to earn money which is used to buy food and other things. Ask the pupils if they buy food and other items at the market each day.

Pupil’s Book page 109. Show the pupils the coins and currency notes up to GH¢10.00, Ask the pupils which coins and which bank notes they recognize. Show the pupils that each coin and each note is worth a certain amount in cedis, and point out the number on each coin and note. Pass the coins around and ask the pupils to examine them carefully. Discuss the designs on each coin and point out that the shapes and colours of the coins give people an easy way of identifying the coins.

Ask the pupils to write down the values of the coins and describe the designs on them.


Pass the notes around and ask the pupils to examine them carefully. Discuss the main colours used in printing the notes and the designs on them. Point out that the different colours of the notes , give people a quick and easy way of identying them.

Get the pupils to play a game called ‘What am I?’ in pairs. One pupil should describe a coin or note and the other has to guess its value from the description.

AnswersPupil’s Book page 126GH¢ 1.00 note is predominantly red. On one side is the picutre of the big six made up of Kwame Nkrumah, Ako Adjei, J.B Danquah, Edward Akuffo-Addo, Emmanuel Obetsebi-Lamptey and William Ofori-Atta .)GH¢ 2.00 is predominantly yellowish, brown. On one side is the picture of the 1st president of the Republic of Ghana, Osagefo Dr. Kwame Nkrumah.GH¢ 5.00 is predominately blue. It has a picture of the University of Ghana on one side and a picture of the Big Six on the other side. GH¢ 10.00 is predominately green. It has a picture of the Headquarters of Bank of Ghana on one side and and picture of the Big Six on the other side.GH¢ 20.00 is predominately purple. It has a picture of the Supreme Court Building for Ghana at one side a picture of the Big Six at the other side GH¢ 50.00 is predominantly brown . It has a picture of the Christianborg Castle on one side and a picture of the Big Six on the other side

AnswersPupil’s Book page 129 The GH¢ 1.00 note is predominately red . On one side is a picture of the Akosombo Dam at the other side is the picture of the Big Six on the front. .The GH¢5.00 note is predominantly blue. It has a picture of the University of Ghana on one side and a picture of the Big Six on the other side . The GH¢10.00 note is predominantly green. It has a picture of the Headquarters of Bank of Ghana on one side and picture of the Big Six on the other side

Activity 4: ShoppingPupil’s Book page 129 Explain to the pupils that when they buy an item they must look at the price and find the coin or note which has the same value as the price of the item. Point out that sometimes they may not have a coin or note of the correct value. Ask the pupils what they should do then? Introduce the idea that two or more of one coin have the same value as (are equal to) another coin or note.

72 UNIT 10 Measurement of time and money

Lead the pupils to work out how many of one coin is or are equal in value to another coin or note.

AnswersPupil’s Book page 110

Ofeibea, GH¢ 1.00A coconut, orange, mango, banana, pawpaw or sugar cane

Mensah, GH¢ 1.00,A sugar cane stick or a coconut, orange, mango,pawpaw or banana.Some pupils might point out that Mensah could buy several pieces of fruit which cost a total of GH¢ 1.00,.

Activity 5: Make your own market stallThe pupils enjoy buying and selling things amongst themselves.Pupil’s Book page 128. Ask the pupils to collect materials: empty packets and real shop or market items for making a ‘classroom market stall’. They should make labels to show the cost of each item. They will also need to make some ‘play money’ from any suitable material. When they have made their shop and money they can trade with each other: selling their goods and buying the goods of other pupils.

EvaluationThe pupils should:• be aware that we often divide a day on the basis of what we are doing at different times;• have some appreciation of the relative times taken to do different activities;• should appreciate that it is adequate to describe some events as happening during different parts of

the day for many purposes but is not sufficiently accurate for others;• know that a clock has a long minute hand and a shorter hour hand;• be able to tell the time to the nearest hour.

The pupils should:• know that the monetary unit of Ghana is the cedi, and be able to write the symbol, GH¢,• be able to recognise the 1 Gp , 5 Gp,10 Gp, 20 Gp, 50 Gp and GH¢1.00 coins,• be able to recognise the GH¢1.00, GH¢2.00, GH¢5.00 and GH¢10.00 notes,• select the appropriate coin or note to pay for familiar items,• find the total cost of two or three items.

Additional review questionsCopy the diagram and questions onto the board for pupils to answer.


What coins does Kwame have?

How many are equal to

?

How many

are equal to

?

Answers to additional review questions2. 5 3. 5

Diagnostic assessment test1. Was the range of information collected from pupils sufficient to indicate that pupils have developed

the concepts of time and money?2. How realistic were the materials in relation to the pricing system?

74 UNIT 11 Collecting and handling data

UNIT 11 Collecting and handling data

Pupil’s Book pages129 to134

ObjectivesThe pupils should be able to:• collect or identify different kinds of similar items and find how many of each kind there is;• record the data collected;• arrange the collected items/data to form rows/columns.

NotesData are facts or figures from which conclusions can be drawn

Teaching methodThe pupils are shown how:• to collect information;• numerical information can be represented graphically;• simple graphs can be interpreted.

Key wordsInformation, data, collect, record, class, rows, columns

MaterialsBoxes or cans, bottle tops, counters or coins, countable objects,

Activity 1: Collecting and recordingPupil’s Book page 129.Discuss this page with pupils and explain the recording of the data in the table.

Pupil’s Book page 130 and 131. Explain to pupils how Boama and Stella represented the data in their table as a graph. Tell them to complete the graph by drawing in the number of stones Boama and Stella recorded (7). Encourage pupils to go out into the playground and make their own collection of leaves, twigs and stones. They should group these objects into types and count the objects in each group. Then they should record the numbers in a table. Finally, pupils should represent their data in a graph.

75UNIT 11 Collecting and handling data

Activity 2: On what day were you born?In advance, the pupils should find out from their parents on which day of the week they were born.

Pupil’s Book page 131. Explain to the class that it is often useful to collect information and show it in a special way. Write a list of the days of the week on the board. Ask each pupil to name the day of week on which they were born and make a mark next to the day on the blackboard. Tell the pupils to write down the days of the week and, from the information on the board, find by counting, how many pupils were born on each day. Explain to the class that gathering information in this way is called a survey.

Pupil’s Book page 132. Ask the pupils to build a graph using boxes or cans to represent the results of the survey.

Activity 3: Rows and ColumnsLead pupils to collect data on sitting arrangements in the classroom. Ask pupils to wrtie the number of pupils who sit in each row and each column as on top of page 133 of the Pupil’s book. Pupils represent the data in rows and columns, in rows as at the bottom of the page 133.

Activity 4: What letter does your name begin with?Write the letters of the alphabet vertically on the chalkboard. Ask each pupil what letter of the alphabet his or her name starts with and make a mark next to the appropriate letter on the chalkboard.

Pupil’s Book page 134. Ask the pupils to write down the letters of the English alphabet and count to find how many pupils’ names start with each letter from the information on the chalkboard. The pupils should build a graph using counters or coins to represent the results of the survey.

EvaluationBy the end of the unit the pupils should be able to collect data, represent data in rows and columns -(represent the information as a block graph).

76 UNIT 11 Collecting and handling data

Unit assessment testCopy this diagram and questions on to the board.

Sun Mon Tues Wed Thurs Fri Sat

89

Graph showing days on whiœh pupils inSt Miœhael’s Grade 1, were born

7654321

1. How many pupils were born on: Sunday? Monday? Tuesday Wednesday? Thursday? Friday? Saturday?2. On which day were most pupils born? On which day was the smallest number of pupils born?

Unit Assessment test answers1. 7, 3, 8, 5, 7, 4, 6 2. Tuesday , Monday

Diagnostic assessment test1. Identify the processes, skills and strategies that pupils used to collect, organise and present the

information.2. Were the range of activities varied enough for the pupils to identify various sources of

77UNIT 12 Addition and subtraction of numbers , (0 to 99)

UNIT 12 Addition and subtraction of numbers , (0 to 99)

Pupil’s Book pages 135 to 140

ObjectivesThe pupils should be able to:• add two numbers expressed as tens and ones without renaming/ regrouping;• add two two-digit numbers without renaming/regrouping;• subtract two two-digit numbers expressed as tens and ones without regrouping/borrowing;• subtract two two-digit numbers without regrouping/borrowing;• solve simple story problems involving the use of the basic addition and subtraction facts.

NotesThe pupils should be familiar with:• the numbers 0 to 99,• addition and subtraction in the 0 to 18 range with no renaming.

Teaching methodIt is important to exemplify addition using:• bundles of tens and single sticks;• ten-strips and squares;• the ‘longs’ and ‘cubes’ of base ten materials;• the white and orange Cuisenaire rods.At this stage renaming or decomposition is not required for addition and subtraction.

Key wordsThe numbers from zero to ninety-nine, tens, ones, sum, difference, renaming, regrouping, bundles, Dienes blocks.

MaterialsBundles of sticks in tens and single sticks. Where possible, base ten material or Cuisenaire rods.

Activity 1: Adding tens and onesWrite 23 + 34 on the board. Ask some pupils to:• show the expansion of 23 as 2 bundles of ten and 3 single sticks;• show the expansion of 34 as 3 bundles of ten and 4 single sticks;

78 UNIT 12 Addition and subtraction of numbers , (0 to 99)

• add the ones by collecting the single sticks and placing them together making 7 sticks;• add the tens by collecting the bundles of tens and placing them together making 5 bundles;• placing the 5 bundles and 7 sticks together to show the sum of 57.

Note:Ten-strips and squares or longs and cubes or orange and white Cuisenaire rods can be used instead of bundles of ten and single sticks.

Pupil’s Book page 135. Lead the pupils through the expansions and addition of tens and ones.The pupils should set out their work in a similar fashion in their exercise books.

AnswersPupil’s Book page 118.1. 46 7. 35 13. 362. 36 8. 39 14. 373. 56 9. 59 15. 684. 79 10. 68 16. 595. 59 11. 88 17. 696. 79 12. 79 18. 79

Activity 2: AdditionPupil’s Book page 136. Demonstrate:• the representation of 34: 3 tens and 4 ones using the available material;• the representation of 25: 2 tens and 5 ones in the same style;• the collection of the ones (Also say: 4 ones and 5 ones equal 9 ones);• the collection of the tens (Also say: 3 tens and 2 tens equal 5 tens, The answer is fifty-nine’.)

The sentences in the brackets are known as the addition pattern. They are what is said by the teacher in demonstrating addition. They should also be used by the pupils, initially, when doing addition. Getting the pattern correct is very important.

Ask some pupils to demonstrate the other examples using the appropriate materials and the correct pattern. They should write the sums in their exercise books.

AnswersPupil’s Book page 136.1. 73 2. 87 3. 78 4. 985. 96 6. 59 7. 88 8. 68


Activity 3: Subtraction using expansionsWrite 48 – 23 on the board. Ask some pupils to:• show the expansion of 48 as 4 bundles of ten and 8 single sticks;• show the expansion of 23 as 2 bundles of ten and 3 single sticks;• remove 3 sticks from the 8 sticks leaving 5 sticks;• remove 2 bundles from the 4 bundles leaving 2 bundles;• placing the 2 bundles and 5 sticks together to show the sum of 25.

Note:Ten-strips and squares or longs and cubes or orange and white Cuisenaire rods can be used instead of bundles of ten and single sticks.

Pupil’s Book page 137. Lead the pupils through the expansions and subtraction of tens and ones. The pupils should set out their work in a similar fashion in their exercise books.

AnswersPupil’s Book page 137.1. 22 6. 13 11. 14 16. 192. 31 7. 34 12. 14 17. 233. 32 8. 37 13. 55 18. 324. 22 9. 33 14. 25 19. 635. 29 10. 23 15. 21 20. 21

Activity 4: Subtracting tens and onesPupil’s Book page 138. Demonstrate 38 – 12 by:• representing 38 using the available material;• the taking away of 2 ones (Also say: ‘8 ones, take away 2 ones equals 6 ones’);• the taking away of 1 ten (Also say: ‘3 tens, take away 1 ten equals 2 tens.

The answer is twenty-six’.)The sentences in the brackets are known as the subtraction pattern. They are what is said by the teacher in demonstrating subtraction. They should also be used by the pupils, initially, when doing subtraction. Getting the pattern correct is very important.

Ask some pupils to demonstrate the other examples using the appropriate materials and the correct pattern. They should write the differences in their exercise books.

AnswersPupil’s Book page 138 -139. 1. 22 2. 21 3. 22 4. 35 5. 52 6. 31 7. 22


8. 25 9. 53 10. 11 11. 63 12. 51 13. 34 14. 2215. 14 16. 53 17. 21 18. 32 19. 24 20. 21

Activity 5: Story problemsPupil’s Book page 122. Discuss:• the situations;• the numerical information;• the process (addition or subtraction) that will be required to solve the problem.

Demonstrate the addition or subtraction using the correct patter. Tell the pupils to write the answers in their exercise books.

AnswersPupil’s Book page 1221. 25 2. 59 3. 29 4. 44 5. 62 6 a. 15 b. 22 c. 68

EvaluationBy the end of the unit the pupils should be able to:• expand two-digit numbers into tens and ones;• complete addition sentences with no re-naming for sums up to 99;• complete subtraction sentences with no re-naming for minuends up to 99;• do vertical addition and subtraction;• solve simple story problems involving addition and subtraction.

Additional review questions1. Write the questions on to the board. Ask pupils to copy and complete them, writing the sums in the

spaces. Collect the ones, then the tens.

T 0 4 3

+ 2 4

T 03 5

+ 5 1

T 02 7

+ 3 2

T 05 4

+ 3 5

4 5+ 3 3

6 2+ 1 7

3 0+ 4 6

4 3+ 5 0


T 0 7 6

+ 2 3

T 05 9

+ 2 0

T 06 4

+ 3 3

T 01 7

+ 7 2

2. Write the questions on to the board. Ask pupils to copy and complete them, writing the differences in the spaces.

Take the ones away, then the tens.

T 0 9 7

– 3 5

T 08 6

– 5 3

T 05 4

– 3 1

T 07 9

– 2 7

6 9– 3 4

5 8– 2 4

7 9– 6 1

4 9– 2 0

T 0 7 6

– 4 1

T 09 7

– 3 6

T 06 6

– 3 0

T 08 6

– 6 3

Answers to additional review questions1. 67 86 59 89 78 79 76 93 99 79 97 89

2. 62 33 23 52 35 34 18 29 35 61 36 23

Unit assessment testWrite questions on the board. Ask pupils to copy and complete them, writing sums or differences in the spaces.


T 0 2 6

+ 3 1

T 04 2

+ 2 4

T 03 4

+ 4 3

T 0 5 3

+ 1 5

T 02 7

+ 5 2

T 03 9

+ 3 0

T 0 2 1

+ 7 8

T 01 0

+ 8 7

T 08 5

+ 1 2

T 0 7 0

+ 1 9

T 06 6

+ 2 2

T 05 4

+ 2 3

T 0 3 8

– 2 4

T 04 6

– 3 3

T 05 7

– 2 5

T 04 9

– 1 6

T 0 6 5

– 3 2

T 08 7

– 4 4

T 09 6

– 6 0

T 04 7

– 1 7


T 0 1 2

+ 8 3

T 06 4

+ 3 5

T 08 9

– 5 2

T 09 9

– 6 8

Unit assessment test answers1. 57 66 77 68 79 69 99 97 97 89 88 772. 14 13 32 33 33 43 36 30 95 99 37 31

Diagnostic assessment test1. What competencies did pupils exhibit in adding and subtracting two digit numbers with and

without renaming and regrouping?2. How will these competencies enhance pupils’ development of concepts of addition and subtraction

of larger numbers?

3. Identify any challenges pupils faced. Plan strategies to overcome these challenges.


11Mathematics 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

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Mathematics Mathematics Teacher's Gu… · presentation of curriculum content, some examples, skill development and practice. Pupil’s Book 1 The topics presented in Pupil’s Book