smart mathematics primary 2 tg - cambridge.org

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2PR

IMARY

TEACHE R ’S GUI DE

NEW

Mathematics

Contributors/Reviewers

D. A. AfariogunF. C. Onabanjo

SmartSmartSmartSmartSmartSmartSmartSmartSmart

2PR

IMARY

TEACHE R ’ S G

UIDE

NEW

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Introduction � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � v

The purpose of the curriculum� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � v

The role of the teacher � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � v

How to use the scheme of work � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � vi

Scheme of work � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � vii

Term 1Revision of last year’s work � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Theme: Numbers and numeration � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 2

Topic 1 Whole numbers 1 to 200 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 2

Topic 2 Fractions � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 11

Theme: Basic operations � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 14

Topic 3 Addition � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 14

Topic 4 Subtraction� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 19

Revision of work for Term 1 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 22

Term 2Revision of the first term’s work � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 23

Theme: Basic operations � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 24

Topic 5 Multiplication� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 24

Theme: Algebraic processes � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 27

Topic 6 Open sentences � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 27


Term 3Revision of the second term’s work� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 29

Theme: Mensuration and geometry � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 30

Topic 7 Primary measures – money � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 30

Topic 8 Primary measures – length � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 31

Contents

Topic 9 Primary measures – time � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 33

Topic 10 Primary measures – mass (weight) � � � � � � � � � � � � � � � � � � � � � � � � � � 36

Topic 11 Secondary measures – capacity � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 37

Topic 12 Primary measures – area � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 38

Topic 13 Three-dimensional shapes� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 40

Topic 14 Two-dimensional shapes � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 42

Theme: Everyday statistics � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 44

Topic 15 Data collection � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 44


vIntroduction

Introduction

The purpose of the curriculumThe main objectives of the curriculum are to prepare the pupils to:• acquire the mathematical literacy necessary to function in an information age• cultivate the understanding and application of mathematical concepts and skills

necessary to thrive in the ever-changing technological world• develop the essential elements of problem solving, communication, reasoning and

connection within the study of Mathematics• take advantage of the numerous career opportunities provided by Mathematics• further their studies in Mathematics and other related fields.

The role of the teacherOne of the principal duties of a Mathematics teacher is to prepare and present good lessons to his or her pupils. It is your role to:• be as well informed as possible on the scheme of work• know the aims and objectives of each topic• select appropriate content material• decide on the best methods of presentation such as group work, worksheets,

question-and-answer sessions, debates, etc.• keep informed about social and environmental issues, and other current news in

Nigeria and the rest of the world• encourage learning that will promote creativity and critical thinking in pupils

through innovative teaching approaches.

To be effective in presentation, you, the teacher, must do a written/typed plan for each lesson. This must include aims, objectives, resources, time frames, content for the lesson, activities, homework, assessment, and ideas/additional worksheets to cater for pupils requiring extension or learning support (remedial).

Prepare each topic in advance. Many teachers go into the classroom inadequately prepared. It is your responsibility as a Mathematics teacher to actively involve your pupils in the learning process. It is a proven fact that pupils learn far more by doing than by listening.

Mathematics involves being curious and asking questions. Wherever possible, ask questions to engage the pupils and to encourage independent thought processes and to develop problem-solving skills. Start your lessons by asking the pupils to write down answers to questions related to your lesson (approximately five). This will settle them into the lesson. You can use different types of questions in your lessons:

Introductionvi

• diagnostic, enabling you to determine prior knowledge on the topic• for consolidation of challenging concepts during the lesson• for stimulation of interest in the subject• for concluding the lesson.

This will assist you to find out whether pupils have understood the concepts/terminology in the lesson. It will also highlight any areas that they need to revise at home or for you to revisit in the next lesson.

Teachers must ensure that they do not appear to have favourites in the class, so devise a system to ensure that you ask questions fairly, but be careful not to embarrass weaker pupils if they cannot answer questions.

How to use the scheme of workA scheme of work is defined as the part of the curriculum that you, the teacher, will be required to teach in any particular subject. Its primary function is to provide an outline of the subject matter and its content, and to indicate how much work a pupil should cover. The scheme of work allows you to clarify your thinking and plan and develop particular curriculum experiences that you believe may require more time and attention when preparing lessons. The criteria all teachers should bear in mind when planning a scheme of work are continuity in learning and progression of experience. You can add your own notes to the scheme of work provided on pages vii to xii.

The scheme of work is sequential. The sequence is aligned with the Pupil’s Book and Workbook. Do not be tempted to jump around. Rather spend time carefully planning the term to ensure that you adhere to the sequence of teaching laid out in the scheme of work.

The year is divided into three terms. Each term is divided into 13 weeks. The end of term allows time for revision and an examination. This time frame may vary depending on the planning of your particular school.

Your management of the class will have an enormous influence on your ability to adhere to the time frames. Focus on effective discipline strategies. You will have fewer discipline issues if you are punctual, well prepared, follow a plan (write this on the board at the start of the lesson), keep your word (don’t make empty threats) and consistently adhere to rules.

A teacher of Mathematics is a professional instructor who facilitates, promotes and influences pupils to achieve the outcomes of the scheme of work. It is the wish of the authors that the pupils will, at the end of each course in the series, attain a level of mathematical proficiency that will equip them for future studies in this field.

viiScheme of work

Scheme of work

Term 1

Lesson objectives PB page

WB page

Revision of counting and writing numerals up to 99

Pupils should be able to:• Count up to 99• Write numerals up to 99• Recognise the place value of numbers up

to 99

p. 1 p. 1

NUMBERS AND NUMERATION

Topic 1 Whole numbers 1 to 200

Identification and counting of numbers

Pupils should be able to:• Identify numbers from 1–200• Count numbers up to 200• Identify order and write numbers up to 100

p. 6 p. 4

Reading and writing numbers from 1 to 200

Pupils should be able to:• Recognise the numerals up to 200• Read and write numerals from 100–200

p. 12 p. 7

Odd and even numbers up to 50

Pupils should be able to:• Identify a number that is even by using

these methodsa) Building numbers in two equal rowsb) Showing numbers with the same number

of figures on each hand to indicate that the numbers are even

• Show that the sum of two even numbers as well as the sum of two odd numbers give an even number

• Identify even and odd numbers from 1 to 50

Place value of numbers up to 200

Pupils should be able to:• Identify the place value of numbers up

to 200• Write the place value of numbers up to 200

p. 16 p. 10

Ordering numbers up to 200

Pupils should be able to:• Order numbers up to 200

p. 23 p. 14

Scheme of workviii


WB page

Using the symbols >, < and = to order numbers

Pupils should be able to:• Express inequalities of 1- or 2-digit numbers

using the terms greater than or less than• Use inequalities of 1- or 2-digit numbers

using the symbols <, > and = (the curved left arm and right arm can be used to symbolise < and > respectively)

p. 25 p. 17

Topic 2 Fractions

Fractions 1 _ 2 and 1 _ 4 of a given collection

Pupils should be able to:• Divide a collection of concrete objects into

two equals parts ( 1 _ 2 ) and quarter parts ( 1 _ 4 ) e.g.c) 1 _ 2 of 10 balls = o

d) 1 _ 2 of 24 apples = o

e) 1 _ 4 of 8 pens = o

f) 1 _ 4 of 12 apples = o

p. 43 p. 20

Fraction 3 _ 4 of a given collection

Pupils should be able to:• Obtain 3 _ 4 of concrete objects e.g. 3 _ 4 of

8 balls = o

p. 51 p. 22

BASIC OPERATIONS

Topic 3 Addition

Addition and subtrac-tion on a number line

Pupils should be able to:• Add up numbers from 0–20 on a number

line• Subtract numbers from 0–20 using a number

line

p. 35 p. 26

Addition of 2-digit numbers without re-naming or exchanging

Pupils should be able to:• Add 2-digit numbers without exchanging

or remaining e.g. 52 = 50 + 2 + 21 = 20 + 1 73 = 70 + 3

p. 57 p. 28

ixScheme of work


WB page

Addition of 2-digit numbers with renaming or exchanging

Pupils should be able to:• Add 2-digit numbers with remaining

or exchanging e.g. 38 = 30 + 8 + 25 = 20 + 5 63 = 50 + 13

p. 69 p. 32

Topic 4 Subtraction

Subtraction of 2-digit numbers with renaming or exchanging

Pupils should be able to:• Subtract 2-digit numbers with remaining

or exchanging e.g. 62 = 60 + 2 = 50 + 12 – 47 = 40 + 7 = 40 + 7 15 = = 10 + 5

p. 82 p. 38

Subtraction of 2-digit numbers without re-naming or exchanging

Pupils should be able to:• Subtract 2-digit numbers without renaming

or exchanging e.g. 78 = 70 + 8 – 25 = 20 + 5 53 = 50 + 3

p. 94, 98, 99

p. 41

Revision of term’s work Pupils should be able to:• Recall what they have learnt for the term

p. 100 p. 49

Examination Examination

Term 2


WB page

Revision of the first term’s work

Pupils should be able to:• Review the first term’s lessons• Perfect the knowledge of counting and

grouping of numbers• Acquire more skills on the use of symbols,

fractions, addition and subtraction of numbers

p. 107 p. 55

Scheme of workx


WB page

BASIC OPERATIONS

Topic 5 Multiplication

Multiplication using repeated addition

Pupils should be able to:• Multiply numbers using repeated addition

e.g. 2 + 2 + 2 = 6 and 4 + 4 = 8

• Introduce the multiplication sign “×” e.g.2 + 2 + 2 = 2 × 3 = 6

+ + =

× = 6

4 + 4 = 4 × 2 = 8

+ =

× = 8

p. 114 p. 61

Multiplication of 2-digit numbers by 2 and 3 without renaming or exchanging

Pupils should be able to:• Arrange and multiply 2-digit numbers by a

1-digit number e.g. 13 × 3 = 39 OR 13

× 3 39

p. 127 p. 64

ALGEBRAIC OPERATIONS

Topic 6 Open sentences

Open sentences involving addition and subtraction

Pupils should be able to:• Find the missing number o + 30 = 50 15 + o = 30 o – 10 = 15 40 – o = 35

p. 132 p. 68


p. 152 p. 77

Examination Examination

Term 3


WB page

Revision of the second term’s work

Pupils should be able to:• Recapitulate the first and second term’s lessons• Recap every detail in addition, subtraction

and multiplication of numbers

p. 157 p. 82

xiScheme of work


WB page

MENSURATION AND GEOMETRY

Topic 7 Primary measures – money

Pupils should be able to:• Recognise all types of Nigerian currencies

(coins and bank notes)• Change money up to ₦10 into small units

(coins)• Go for shopping with money greater than

₦10.00

p. 162 p. 89

Topic 8 Primary measures – length

Pupils should be able to:• Compare standard units of measurement e.g.

group of children using their arm lengths, foot lengths, hand spans, etc.

• Measurement in metres and centimetres e.g. measuring their desks and boards

p. 175 p. 92

Topic 9 Primary measures – time

Pupils should be able to:• Tell time on hour and half hour e.g.

3 o’clock, half past 2• Reading clock, telling time on hour and

half hour• Name and arrange days of the week• List certain activities performed on certain

days of the week (e.g. the song – Monday we go to school …)

p. 182 p. 94

Topic 10 Primary measures – mass (weight)

Pupils should be able to:• Make comparisons of objects by weight e.g.

stick, ruler, book, stone, chalk• Order objects by weight

p. 191 p. 99

Topic 11 Primary measures – capacity

Pupils should be able to:• Identify and name objects that could be

used for measuring capacity e.g. cups, empty containers, spoons, buckets, etc.

• Order containers based on their capacities e.g. spoon, bottle, cup

p. 199 p. 102

Scheme of workxii


WB page

Topic 12 Primary measures – area

Pupils should be able to:• Compare the area of different concrete

objects e.g. rectangles, squares, triangles, circles and other plane shapes

p. 207 p. 104

Topic 13 Primary measures – Three-dimensional shapes

Cubes and cuboids Pupils should be able to:• Identify and count the flat faces of a cube

and a cuboid • Identify and count the corners of a cube and

a cuboid• Identify and count the edges of a cube and

a cuboid

p. 212 p. 106

Spheres and cylinders Pupils should be able to:• Identify spheres and cylinders• Solve problems involving spheres and

cylinders

p. 216 p. 107

Topic 14 Primary measures – Two-dimensional shapes

Pupils should be able to:• Identify square, rectangle, circle and

triangular shapes of objects in their environment e.g. surface of a table, orange, tampico juice pack

• Indicate (or identify) which corner of a 2-dimensional shape is a square corner

p. 220 p. 109

EVERYDAY STATISTICS

Topic 15 Data collection

Pupils should be able to:• Sort and record data• Read and interpret data

p. 225 p. 111


p. 230 p. 114

1Revision of last year’s work

Revision of last year’s workTerm

1

Revision of counting and writing numerals up to 99

Skills: counting, reading, matching, writing, recognisingResources: number chart, number line, counters, concrete objects (such as stones, beads, sticks, buttons), pencils, crayons, exercise books, paper Concepts: counting, numbers, number names

Learning experiencesRegard these first revision exercises as a baseline to determine where the pupils are at in terms of: their counting skills, writing of the numerals and number names, their understanding of numbers and place value of numbers up to 99. This will enable you, the teacher, to see their level of understanding or shortcomings and this could guide you with regards to the future planning and interventions required.

Lesson focus• Do counting exercises daily. • Let the pupils count using concrete objects first, such as

stones, buttons, sticks, beads, and so on.• Next, let them identify the numbers on a number chart by

counting from the number chart. They can use a counter whilst counting on their number charts. Also make use of a number line.

• Have the pupils work on their own so you’ll have a clear baseline to monitor their level of understanding before even starting to teach the new concepts for this year.

The exercises are set out for the week. Explain the instructions and examples to the pupils so that they understand what to do in each exercise. Give the pupils enough practice by doing:Pupil’s Book: Revision: Revision exercises 1–6, pages 1–5Workbook: Exercises 1−3, pages 1–3.

Term 12

THEMETerm

1Numbers and numeration

Topic 1 Whole numbers 1 to 200

Identification and counting of numbers

Skills: counting, reading, matching, writing, recognisingResources: number chart, number line, counters, concrete objects (such as stones, beads, sticks, buttons), number name cards, number cards, exercise books, paper, pencils, crayons Concept: countingVocabulary: number names 0–200, forwards, backwards, biggest, smallest, more, less, before, after, between

Learning experiencesThe lessons and exercises in this topic will reinforce and build on what the pupils have learnt in Primary 1. Counting backwards and forwards in ones, twos, fives and tens will assist the pupils to automatically recognise numbers and groups of numbers.

Lesson focusCountingDo counting daily with the pupils as a whole class or with small groups. Use a variety of concrete objects and counters, such as buttons, sticks, stones, and so on. Vary the counting:• Count concrete objects, for example beads.• Count objects in a picture.• Count from counting charts and number lines, identifying

the numbers.• Count forwards and backwards in ones.• Count forwards and backwards in tens.• Count forwards and backwards from a given number to a

given number.• Count in multiples – skip counting.• Draw twelve balls and eight bats.• Heap up counters and count them in groups, for example in

twos, fives, tens, threes, fours.

3Theme: Numbers and numeration

The important thing is that the pupils need to get as much practice in counting as they can.

Identifying numbers• Use number cards, number charts and number lines for the

pupils to identify specific numbers by pointing to them.• Let the pupils identify numbers by matching numbers to

quantities of objects.

20

• Also use number cards and number name cards for the pupils to match one with the other.

• Use a pack of cards up to 99. Let the pupils play, “Who has?”

46 forty-six

• Give the pupils a card. Each gets a turn to ask for example, “Who has number 46?” They hold up the card and the pupil who has it says, “I have forty-six.” and holds up the card. They continue in this way to match the numbers and number names.

The exercises are set out for the week. Explain the instructions and examples to the pupils so that they understand what to do in each exercise. Give the pupils enough practice by doing:Pupil’s Book: Topic 1: Exercises 1–5, pages 6–11Workbook: Exercises 1−3, pages 4–6.

Reading and writing numbers from 1 to 200

Skills: counting, reading, writing, matching, identifyingResources: number chart, number lines, counters, concrete objects (such as sticks, bottle tops or buttons), envelopes or small packets or small boxes or containers with number name cards and number cards ranging from 0–200, crayons, pencils, paper, exercise books Concept: numbersVocabulary: number names – 200, odd, even, more, less, before, after, between

4 Term 1

Learning experiencesThe number charts will help the pupils to recognise numbers over 100. These number charts will also help the pupils to recognise odd and even numbers. The number name cards help the pupils to read and write numbers over 100.

Lesson focus• The focus in this lesson is on larger numbers and their names.

The pupils would have learnt the numbers and names up to 99 in the previous grade. The reading and writing of the larger numbers and names from 100–200 would be new to the pupils.

• First revise the numbers and number names from 0–99 and revise the concepts of more and less. Ask: Which number is more than/less than/bigger than/smaller than …? Also ask: Which number comes before/after/between …? Let the pupils read the numbers from the chart each time.

• Pair work: Give each pair of pupils an envelope with number cards and number name cards in it. The numbers should be in groups of ten and range from 0–10, 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90, 90–100 and card groups in the same way from 100–200. The pairs read the numbers and number names on their cards and match them. They must put the cards in sequence and then write the numbers and number names in the correct order.


Odd and even numbers up to 50

Skills: counting, reading, writing, matching, identifyingResources: number chart, counters, concrete objects (such as sticks, bottle tops, buttons), crayons, pencils, paper, exercise booksConcept: odd and even Vocabulary: numbers 0–200, odd, even


Learning experiencesThe pupils practise identifying odd and even numbers using the objects provided. They use the number charts to identify odd and even numbers up to 200, and the number lines to copy and fill in the odd numbers up to 50.

Lesson focus• Draw a pattern on the board showing the odd and even

numbers. Point out the even numbers and the odd numbers in the pattern. Explain that odd numbers have an odd one.

1 2 3 4 5 6 7 8 9 10

• Point out that even numbers can be divided equally. Even numbers end with the digits 0, 2, 4, 6, 8, for example 38 or 50.

• Odd numbers always have a remainder when it is divided.• Let the pupils find odd numbers on a number chart.• Let them find even numbers on a number chart.

Place value of numbers up to 200

Skills: counting, recognising, explaining, identifyingResources: number chart, number lines, counters, concrete objects, place value cards for 100, 10 and 1, dienes blocks, 100–200 sticks, rubber bands, interlocking cubes, blocks, abacus, crayons, pencils, paper, exercise books Concept: place valueVocabulary: hundreds, tens, units

Learning experiencesThe pupils first build up piles in tens and units to demonstrate place value. They then expand on these piles to include one hundred. This helps them to visually understand the concept of hundreds, tens and units.

Lesson focus• Group work: Ask the pupils to each take ten sticks. Explain

that they are going to exchange their ten loose sticks for

6 Term 1

one whole ten. Show them how to tie a rubber band for one whole ten. Explain that they now have one ten. Show the number card 10 and point to the 1 (meaning one ten) and to the zero (meaning no or zero ones/units). Ask the pupils to place the number card next to the bundle.

• Pair work: Ask each pair of pupils how many tens they have. Explain that two tens equal 20, meaning two tens and zero units. Show the number card 20.

• Let the pupils repeat the activity by having one learner join each pair until the group has nine tens. Put down the number card each time.

• Individual work: Ask the pupils to choose any number between 10 and 99. Encourage them to think carefully about how many tens and how many units there are in the number they have chosen. Give them time to do this before asking individual pupils to explain their numbers.

• Tell the pupils to use the place-value cards to help them. For example: 62 = six tens and 2 units or 60 + 2. Show the number cards 60 and 2 and put the 2 over the 0. Let them practise more with other numbers up to 99 in this activity.

60

+

2 602

10 2 units sixty-two

10

10

10

10

10

• Explain that the value of six tens equals 60 and the value of 2 units equals 2.

• Introduce the 100.• Put the number card 99 on the board. Point to 99 on the

number chart or number line and ask the pupils: What number is one more than 99? 100 is one more than 99. Let them count from 90 to 100. Show them the 100 squares (if you don’t have the dienes blocks, make 100 squares on card or paper and cut them out). Let the pupils count the blocks. Ask: How many units make up 100? One hundred


units equal 100. Put out two hundred squares. Let them count from the 100 to the next number.

• Show them the tens bars and the loose unit blocks (these can also be made with card if there are no dienes blocks) or use the bundles of sticks. Let them count the ten bars/bundles in tens first to 100 then up to 200. Ask: How many tens in 100? How many tens in 200?

• Ask the pupils to choose any number between 99 and 200 and to place it in front of them. Ask them to read their numbers out aloud. Encourage them to think carefully about how many hundreds, how many tens and how many units there are in the number they have chosen. Give them time to do this before asking individual pupils to explain their numbers.

• Tell the pupils to use the place-value cards to help them. For example: 159 = one hundred and five tens and nine units or 100 + 50 + 9. Show the number cards 100 with 50 and place over the zero of 100 and the 9 over the 0 of 50. Let them practise with other numbers up to 200 in this activity.

100

+

50

+

9 1 5 9

100 10 9 units one hundred and fifty-nine

10

10

10

10

• Explain that the value of one hundred equals 100 and the value of five tens equals 50 and the value of nine units equals 9.

• Small group work: Pupils sit in a small circle and each pupil has a turn to pull out a number using the place value cards, the sticks or dienes blocks. The pupil next to him/her must say the number and write out the number name. They continue in this way until everyone has had a turn or two.


8 Term 1

Ordering numbers up to 200

Skills: ordering, recognising, sequencing, identifying, readingResources: number chart and number lines for referencing, number cards for the number ranges required for the work area, number name cards, greater than and less than symbol cards, before and after cards, more and less cards, crayons, pencils, sheet of paper, exercise books Concepts: ordering, sequence, greater than, less than, more than, bigger, smaller, highest, lowestVocabulary: ordering, sequence, greater than, less than, more than, bigger, smaller, highest, lowest, ordinals, descending, ascending

Learning experiencesThe pupils learn the more than, less than symbols. The number lines assist pupils to order and sequence numbers from smallest to biggest and from biggest to smallest. Exercise 22 visually demonstrates ordering and introduces the concept and vocabulary for ordinals – first, second, third, fourth.

Lesson focusIn order for the pupils to place numbers in any sequence, they must understand the concepts: more than/greater than, less than, before, after and between.

Make four groups of four pupils to work in work areas.

Work area 1• Prepare a set of greater than and less than symbol cards, a

set of number cards and a set of number name cards for this work area.

• Place each set of cards face down in this order: number cards and number name cards.

• The pupils take turns to choose a card from each set, read it aloud and state if it is true or false.

For example: (false).145 < eighty


Work area 2• Prepare a set of before and after cards, a set of number

cards (with order range of, for example, 320 to 340), a set of number cards and sheets of paper with before, after and between written on them.

• Place the cards face down in their sets.• The pupils take turns to choose a card from each set and place

them in the correct column on the before and after sheets.• Let the pupils move the cards around until they have the

correct answer.

Work area 3• Prepare a set of number cards and each of the following

instruction cards: – Arrange from the biggest to the smallest. – Arrange from the highest to the lowest/in descending

order. – Arrange from the smallest to the biggest. – Arrange from the lowest to the highest/in ascending order.

• The group chooses one instruction card at a time and arranges the numbers accordingly.

• They repeat the activity for all the instruction cards.

Work area 4• Prepare a set of more or less cards (i.e. 10 more, 20 more,

50 more, 100 less, 40 less, 30 less); a set of number cards and a sheet of paper to write on.

• The pupils choose a number card and a more and less card. They write their answers on the sheet of paper provided.

• The group discusses the answer and passes the sheet to the next pupil to write their answer.

• The pupils continue until all the number cards have been collected and answered.

Organisation• Allow each group about 15 minutes to work at each

work area. • Give each group a turn at all the work areas. • Move around the groups to give guidance, support and

encouragement where necessary.

10 Term 1

• The remainder of the class do the exercises from the Pupil’s Book and Workbook until it is their turn.

• Make sure that each pupil has a turn at each work area.


Using symbols >, < and = to order numbers

Skills: counting, recognising, explaining, identifyingResources: number chart, number lines, counters, concrete objects, flash cards, crayons, pencils, paper, exercise books Concepts: ordering, sequence, greater than, less than, more than, bigger, smaller, highest, lowestVocabulary: ordering, sequence, greater than, less than, more than, bigger, smaller, highest, lowest, ordinals, descending, ascending

Learning experiencesThe pupils use the more than, less than and equals symbols in their sums. This reinforces their understanding of ordering numbers, and the concepts of greater than and less than.

Lesson focus• Have flash cards with the following symbols on them:

> < =

• Explain the name and meaning of each symbol using examples. For example: 99 < 100.

• Have the pupils work in small groups of six and give each group a set of cards with equations on them.

• Each pupil gets a turn to take a card and give the answer true or false. For example:

25 > 30 73 < 6 + 6 61 > 60

fifty-one > 40 + 40 5 + 4 = 8 + 1


The exercises are set out for the week. Explain the instructions and examples to the pupils so that they understand what to do in each exercise. Give the pupils enough practice by doing:Pupil’s Book: Topic 1: Exercises 19–25, pages 25–34Workbook: Exercises 14–16, pages 17–19.

Note that addition and subtraction on a number line is introduced later on, in Topic 3 (see page 14 of this Teacher’s Guide).

Topic 2 Fractions

Fractions 1 _ 2 and 1 _ 4 of a given collection

Skills: identifying, recognising, problem solving, explaining, drawing, writing, communicatingResources: concrete objects (such as bottle tops, sticks, buttons, beads, seeds), counters, number lines, fraction flash cards, pencils, crayons, a sheet of paper, exercise booksConcepts: fraction, half, one-quarter, three-quartersVocabulary: whole, half, quarter, share, divide, fraction

Learning experiencesThe pupils revise how to divide objects into two equal parts (halves) and four equal parts (quarters). They also practise writing their sums in fraction form. They verbally explain to their peers how they got their answer. This reinforces their understanding of the use of fractions.

Lesson focus• First, quickly revise their understanding of a whole, a half

and quarters using concrete objects. This was taught in the previous grade.

• Have the pupils work in pairs. Each pair will use a number of concrete objects or counters. Give each pair a number card and ask them to count out the number of counters or objects as is indicated on their number card. For example:

24

12 Term 1

• Ask the pairs to divide their objects of counters into halves or quarters respectively.

• Let them explain to each other how/what they did and what their answer is.

• Then show them how to write their number sentence and their answer.

1 _ 2 of 24 = 12 1 _ 4 of 24 = 6

• Next, give them a new number or let them swop numbers and they find halves and/or quarters respectively of those numbers. They again communicate to their peers how they got their answers.

• Ask them to draw the pictures and write out their sums as shown in the examples above.

• Ask a few pupils to read their sums out aloud.


Fractions 3 _ 4 of a given collection

Skills: identifying, recognising, problem solving, explaining, drawing, writing, communicatingResources: concrete objects (bottle tops, sticks, buttons, beads, seeds), counters, number lines, fraction flash cards, pencils, crayons, a sheet of paper, exercise books Concepts: fraction, half, one-quarter, three-quartersVocabulary: whole, half, quarter, three-quarters, share, divide, fraction

Learning experiencesThe pupils expand on their previous knowledge of fractions, and use objects to divide into quarters. They explain how they got their answers. This will show their understanding of the concept of fractions. The pupils practise their reading and writing skills by answering the word sums in Exercises 13 and 14.

Lesson focus• First, revise halves and quarters of collections using concrete

objects as was taught in the previous lesson.


• Ask the pupils to count out 12 counters or objects and to divide the group into quarters. Ask: How many are in each quarter? We will have 3 counters in each quarter. 3 is one equal part out of 4 equal parts of the whole.

• Now explain that 1 _ 4 of 12 = 3, and if we add another 1 _ 4 it will be 6, and if we add another 1 _ 4 it will be 9 therefore, 3 _ 4 of 12 = 9. It means that 1 _ 4 + 1 _ 4 + 1 _ 4 = 3 _ 4 meaning 3 + 3 + 3 = 9.

• Have the pupils work in pairs. Each pair will use a number of concrete objects or counters. Give each pair a number card and ask them to count out the number of counters or objects as is indicated on their number card. For example:

24

• Ask the pairs to divide their objects of counters into three-quarters.

• Let them explain to each other how/what they did and what their answer is.

• Then show them how to write their number sentence and their answer.

3 _ 4 of 24 = 18

• Next, give them a new number or let them swop numbers and they find three-quarters of those numbers. They again communicate to their peers how they got their answers.

• Ask them to draw the pictures and write out their sums as shown in the examples above.

• Ask a few pupils to read their sums out aloud.


Term 114

Term 1THEME Basic operations

Topic 3 Addition

Addition and subtraction on a number line

Skills: adding, adding on, counting on, counting forwards, counting backwards, taking awayResources: number chart and number lines, pencils, crayons, exercise books Concepts: addition, subtractionVocabulary: add, subtract, count on, forward, backward, take away, left, right, smaller, bigger

Learning experiencesThe number lines assist the pupils’ understanding of addition and subtraction, reinforcing the concept of more than and less than. The pupils must be able to say and write the numbers in the expanded form – hundreds, tens and units.

Learning focus• Demonstrate an example on the board. Draw a number line

on the board and write the number sentence 16 + 7 on the board.

• Explain to the pupils that you’ll start at 16 and count on 7 more/add 7 more. Let the pupils count out aloud with you. Ask: Where do we stop?

• Draw in the jump from 16 to 23.• Point out that when we add on the number line we move

to the right and the answer becomes more as the number becomes bigger.

15Theme: Basic operations

16 + 7 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

• Demonstrate subtraction on the number line on the board. Write the number sentence 25 − 9 on the board.

• Explain that, when we subtract on a number line, we move to the left, so we’ll start at 25 and count backwards for 9 counts because we are taking away 9. Let the pupils count out aloud with you. Ask: Where do we stop?

• Draw in the jump from 25 to 16.• Point out that, when we subtract, the answer becomes less as

the numbers become smaller.

25 – 9 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25


Addition of 2-digit numbers without renaming or exchanging

Skills: adding, counting on, problem solving, reading, explaining, calculatingResources: concrete objects like bottle tops, sticks, buttons, beads, seeds and so on, counters, number lines, number chart, pencils, crayons, a sheet of paper, exercise books Concept: additionVocabulary: add, addition, more, plus, sum, tens, units, break down, break up, altogether, total, vertical, horizontal

Learning experiencesThe pupils revise the addition of 2-digit numbers without renaming or exchanging. They practise breaking numbers down into tens and units, and learn how to add vertically, horizontally and by expanding numbers using place value.

16 Term 1

Lesson focus• First, do a variety of counting exercises as was described in

the lesson focusing on counting. • Next, do a quick mental activity to revise bonds using flash

cards. Quickly show the flash card, the pupil silently reads the sum on the card and gives the answer aloud.

• The pupils need to understand that we can add numbers in different ways. They need to be able to break down numbers into tens and units, for example: 52 is 50 and 2, and 21 is 20 and 1. Show how to write it out on the board as you say it.

52 + 21 5 2 = 50 + 2

2 1 = 20 + 1 if we add it together it will be:

= 70 + 3 = 73

• They also need to understand that we can add numbers in a vertical way or in a horizontal way. Explain that vertical means down – from top to bottom and that horizontal means across – from left to right.

Vertical addition (in columns)

Horizontal addition (breaking down the numbers)

T U

3 4

+ 2 5

= 5 9

34 + 25

30 + 20 = 50

4 + 5 = 9

50 + 9 = 59

• We can also add by expanding numbers and by using place value.

3 tens + 4 units

+ 4 tens + 5 units

= 7 tens + 9 units = 79

30 + 4

40 + 5

70 + 9 = 79

The exercises are set out for the week. Explain the instructions and examples to the pupils so that they understand what to do in each activity. Give the pupils enough practice by doing:Pupil’s Book: Topic 3: Exercises 1–12, pages 57–68Workbook: Exercises 3–5, pages 28–30.


Addition of 2-digit numbers with renaming or exchanging

Skills: counting, adding, counting on, problem solving, reading, explaining, calculatingResources: concrete objects (such as bottle tops, sticks, buttons, beads, seeds), counters, number lines, number chart, flash cards, pencils, crayons, a sheet of paper, exercise booksConcept: additionVocabulary: add, adding, addition, plus more, plus, sum, tens, units, break down, break up, altogether, total, vertical, horizontal

Learning experiencesThis topic covers addition of 2-digit numbers with renaming or exchanging. The pupils need to understand that we can add numbers in different ways. They need to understand that we have to be able to break down numbers into tens and units. Revise place value and addition without renaming to make sure the pupils understand the concepts. They learnt this in the first term.

Lesson focus• First do a variety of counting exercises. • Next do a quick mental activity to revise bonds using flash

cards. • The pupils need to understand that we can add numbers in

different ways. • Explain vertical – down, from top to bottom.• Explain horizontal – across, from left to right.

Add with renaming by breaking down the numbers• Write the number sentence on the board. For example: 56 + 39

(56 is 50 and 6) 50 + 30 = 80

(39 is 30 and 9) 6 + 9 = 15

80 +10 + 5 = 95• We can also break it down by keeping one number whole.

56 + 30 + 9

86 + 9 = 95

18 Term 1

Add by using place value• They need to understand that they break down the number

into tens and units, then add.47 + 38 4 tens + 7 units

+ 3 tens + 8 units

= 7 tens + 15 units = 70 + 10 + 5 = 85

Add vertically Add horizontally

29 + 43 47 + 25 or 47 + 25

29 40 + 7 + 20 + 5 40 + 20 = 60

+ 43 60 + 10 + 2 7 + 5 = 12

= 72 = 72 = 72

• Let the pupils practise a few sums in pairs and compare their answers.

• Next let them practise a few individually and compare answers. If needed, they will then be able to see and understand where they’ve gone wrong and be able to fix it. Discussion with their peers and comparing answers will help their understanding.

Solving addition problems/word sums• The pupils need to read the sums carefully and make sense of

them. They then choose the method they prefer to work out the sums.

• Guide the pupils to make sense of the mathematical vocabulary in the story sums which helps them to know what calculation has to be made.

• Explain ‘sum’– find the sum of numbers – we add.



Topic 4 Subtraction

Subtraction of 2-digit numbers without renaming or exchanging

Skills: subtracting, problem solving, reading, explaining, calculatingResources: concrete objects (such as bottle tops, sticks, buttons, beads, seeds), counters, number lines, number chart, pencils, crayons, a sheet of paper, exercise books Concept: subtractionVocabulary: subtract, subtraction, less, minus, difference, tens, units, break down, left, vertical, horizontal, difference

Learning experiencesThe pupils revise subtraction of 2-digit numbers without renaming or exchanging. They practise breaking numbers down into tens and units, and learn how to subtract vertically, horizontally and by expanding numbers using place value.

Lesson focus• First do a variety of counting exercises as was described in

the lesson focusing on counting. • Do a quick mental activity to revise bonds using flash cards.

Quickly show the flash card, the pupil silently reads the sum on the card and gives the answer aloud.

• Explain that to subtract is to take away. We take away a smaller number from a bigger number.

• The pupils need to understand that we can subtract numbers in different ways. They need to be able to break down numbers into tens and units just like they did with addition. Show them how to do it on the board. For example:

87 – 52 8 7 = 80 + 7

5 2 = 50 + 2

30 + 5 = 35

• They need to understand that we can subtract numbers in a vertical way or in a horizontal way.

20 Term 1

Vertical subtraction (in columns)

Horizontal subtraction (breaking down the numbers)

T U

9 6

− 2 5

= 7 1

96 − 25

90 – 20 = 70

6 – 5 = 1

70 + 1 = 71

• We can also subtract by expanding numbers and by using place value.

8 tens + 5 units

– 4 tens + 5 units

= 4 tens + 0 units = 40

80 + 5

40 + 5

40 + 0 = 40


Subtraction of 2-digit numbers with renaming or exchanging

Skills: counting, subtracting, taking away, problem solving, reading, explaining, calculatingResources: concrete objects (such as bottle tops, sticks, buttons, beads, seeds), counters, number lines, number chart, flash cards, pencils, crayons, a sheet of paper, exercise booksConcept: subtractionVocabulary: minus, take away, subtract, subtracting, subtraction, difference, tens, units, break down, break up, left, vertical, horizontal

Learning experiencesThis topic covers subtraction of 2-digit numbers with renaming or exchanging. The pupils need to understand that we can subtract numbers in different ways. They need to understand that we have to be able to break down numbers into tens and


units. Revise place value and subtraction without renaming to make sure the pupils understand the concepts.

Lesson focus• Remind the pupils that subtraction can be done in different

ways by using renaming, breaking down the number, vertically, horizontally and by using place value.

• First, do a variety of counting exercises. • Next, do a quick mental activity to revise subtraction bonds

using flash cards. • The pupils need to understand that we can subtract numbers

in different ways. • Demonstrate each example on the board.

Subtract by renaming and by breaking down the numbers• Write the example on the board and explain it.

For example: 53 − 375 3

– 3 7

1 6

50 + 3

30 + 7

40 + 13

30 + 7

10 + 6

Break down the number using place valueThe pupils need to understand that they can break down their numbers into tens and units.• Write the example on the board and explain it.

For example: 82 – 568 tens + 2 units

5 tens + 6 units

7 tens + 12 units

– 5 tens + 6 units

2 tens + 6 units

• Using the place value helps the pupils to understand how numbers can be exchanged, like a ten for units.

Subtract horizontally by using the breaking down method• Write the example on the board and explain it.

22 Term 1

75 − 38

60 − 30 = 30

15 − 8 = 7

30 + 7 = 37

• Explain ‘difference’. To find the difference between two numbers means to subtract.

Solving subtraction problems/word sums• The pupils need to read the sums carefully to make sense of

them. They then choose the method they prefer to work out the sums.

• Guide the pupils to make sense of the mathematical vocabulary in the story sums which helps them to know what calculation has to be made.

The exercises are set out for the week. Explain the instructions and examples to the pupils so that they understand what to do in each exercise. Give the pupils enough practice by doing:Pupil’s Book: Topic 4: Exercises 12 and 16–17, pages 94 and 98–99

Revision of work for Term 1

• The pupils work on their own to complete the exercises.• Explain the instructions so the pupils understand what to do.• The exercises will revise and consolidate the work done

through the term.

Pupil’s Book: Revision: Revision exercises 1–7, pages 100–106Workbook: Exercises 1–3, pages 49–54

23Revision of the first term’s work

Term 2Revision of the first term’s work

Skills: counting, reading, matching, writing, recognising, grouping, symbols, fractions, addition and subtractionResources: number chart, number line, counters, concrete objects (such as stones, beads, sticks, buttons), pencils, crayons, exercise books, paper Concepts: counting, symbols, addition, subtraction, fractions

Learning experiencesRegard these revision exercises as a baseline to determine where the pupils are at in terms of their understanding of what they learnt in Term 1. This will enable you, the teacher, to see their level of understanding or shortcomings and this could guide you with regards to the future planning and interventions required.

Lesson focus• These exercises are to evaluate the pupils’ understanding

of the various skills and concepts that were taught in the previous term.

• The pupils work on their own to complete the exercises. Ensure that they understand the instructions beforehand.

The exercises are set out for the week so the pupils can do a different exercise each day. Explain the instructions and examples to the pupils so that they understand what to do in each exercise. Give the pupils enough practice by doing:Pupil’s Book: Revision exercises 1–6, pages 107–113Workbook: Exercises 1–3, pages 55–60.

Term 224

Term 2THEME Basic operations

Topic 5 Multiplication

Multiplication using repeated addition

Skills: counting, adding, counting on, grouping, problem solving, reading, explaining, calculatingResources: concrete objects (such as bottle tops, sticks, buttons, beads, seeds), counters, number lines, number charts, flash cards, pencils, crayons, a sheet of paper, exercise booksConcepts: multiplication, additionVocabulary: repeated addition, times, multiply, more, product, same amount, hundreds, tens, units, vertical, horizontal

Learning experiencesCounting: The pupils count in 2s, 3s, 4s, 5s and 10s, using counters or concrete objects like stones or beads, and they can do counting exercises on number charts and/or a worksheet.

Grouping: The pupils make groups of 2, 3, 4, 5 and count their number of groups. They work out how many the groups make altogether, for example, if they have 7 groups of 2, they have 14 altogether. They should know how to count in twos. These exercises are to be done before doing calculations with bigger numbers.

Lesson focusRepeated addition leading to multiplication• The pupils must understand that multiplication is repeated

addition – adding the same amount over and over again. Repeated addition: 5 + 5 + 5 + 5 + 5 + 5 = 30 becomes multiplication and we can say 6 × 5 = 30.

• Let the pupils solve a problem by making groups. They write out the repeated addition.


• Explain the multiplication by asking them how many groups there are and how many are in each group.

• Write the multiplication sum and the answer. Explain that, when we repeatedly have to add the same amount over again and again, we can multiply.

• Let them do a few more examples together.

Multiplication on the number line• Show the pupils how to do the jumps for multiplication on

the number line by doing a few examples.• Explain the jumps on the number line according to the

number in the groups and the number of groups. • Let the pupils do a few multiplication sums on the number

line and let them write out their sums.

Multiplication by decomposing the number• The pupils solve problems by doing multiplication with two-

digit numbers and by breaking down the numbers. • Demonstrate and explain the breaking down of the numbers

into tens and units and the calculation of multiplication.• Let the pupils do a few calculations together.

Solving multiplication problems/word sums• The pupils need to read the sums carefully and make sense of

them. • They need to be aware of key words, the question being

asked and what to look for. • Guide the pupils to make sense of the mathematical

vocabulary in the story sums which helps them to know what calculation has to be made.

• They should be able to identify the kind of sum they need to do and write out a number sentence.

• They then choose the method they prefer to work out the sums.


26 Term 2

Horizontal and vertical multiplication

Skills: counting, adding, counting on, grouping, problem solving, reading, explaining, calculatingResources: concrete objects (such as bottle tops, sticks, buttons, beads, seeds), counters, number lines, number chart, flash cards, pencils, crayons, a sheet of paper, exercise booksConcepts: multiplication, additionVocabulary: repeated addition, times, multiply, more, product, same amount, hundreds, tens, units, vertical, horizontal

Learning experiencesEmphasise the importance of correct multiplication in everyday activities and ask the pupils to give examples of this, for example trading. The pupils also practise vertical and horizontal multiplication, and story sums.

Lesson focusMultiply tens and units by 2Multiply vertically, for example: 13 × 2

T U

1 3

× 2

2 6

(10 twos + 3 twos)

20 + 6 = 26

Multiply horizontally24 × 2

20 × 2 = 40

4 × 2 = 8

40 + 8 = 48


27Theme: Algebraic processes

Term 2THEME Algebraic processes

Topic 6 Open sentences

Skills: counting, adding, subtracting, counting on, taking away, problem solving, reading, explaining, calculatingResources: concrete objects (such as bottle tops, sticks, buttons, beads, seeds), counters, number lines, number chart, flash cards, dice, pencils, crayons, a sheet of paper, exercise booksConcepts: addition, subtractionVocabulary: add, addition, sum of, minus, take away, subtract, more, less, subtraction, difference, tens, units, break down, left, horizontal, vertical

Learning experiencesThese exercises are designed to get the pupils to calculate quickly as well as mentally. These calculations involve addition and subtraction in various ways, such as open sentences, true and false statements, using the symbols +, − , =, using diagrams and number lines. The pupils should understand they can use a variety of techniques to calculate.

Mental calculations can also be done in various ways, such as a game (for example a game using dice), question-and-answer method, pencil-and-paper method, flash cards, quick short exercises, or simple quick tests.

Lesson focus • Do a quick mental activity to revise subtraction bonds using

flash cards.• Ensure the pupils know that we can subtract numbers in

different ways.• Do a quick mental activity to revise addition bonds using

flash cards.• Ensure the pupils know that we can add numbers in different

ways.

28 Term 2

The exercises are set out for the week. Explain the instructions and examples to the pupils so that they understand what to do in each exercise. Exercises 7 to 20 are quantitative reasoning exercises. Let the pupils work individually at their desks. They can use counters and a counting chart. Read and explain each instruction to ensure the pupils understand what they need to do. Give the pupils enough practice by doing:Pupil’s Book: Topic 6: Exercises 1–6, pages 132–137

Exercises 7–20, pages 138–151Workbook: Exercises 1–9, pages 68–76.

Revision of work for Term 2


through the term.

Pupil’s Book: Revision: Revision exercises 1–5, pages 152–156Workbook: Exercises 1–5, pages 77–81

29Revision of the second term’s work

Term 3Revision of the second term’s work

Revision of addition, subtraction and multiplication

Skills: counting, reading, adding, subtracting, multiplyingResources: concrete objects (such as bottle tops, sticks, buttons, beads, seeds), counters, number lines, number chart, flash cards, pencils, crayons, a sheet of paper, exercise booksConcepts: addition, subtraction, multiplication

Learning experiencesRegard these revision exercises as a base line to determine where the pupils are at in terms of their counting skills, reading and writing numbers, addition, subtraction and multiplication, and their understanding of word problems and story sums. This will enable you, the teacher, to see their level of understanding or shortcomings and this could guide you with regards to the future planning and interventions required.

Lesson focus• These exercises are to evaluate the pupils’ understanding

of the various skills and concepts that were taught in the previous term.

• The pupils work on their own to complete the exercises. Ensure that they understand the instructions beforehand.

The exercises are set out for the week. Explain the instructions and examples to the pupils so that they understand what to do in each exercise. Give the pupils enough practice by doing:Pupil’s Book: Revision: Revision exercises 1–5, pages 157–161Workbook: Exercises 1–7, pages 82–88.

Term 330

Term 3THEME Mensuration and geometry

Topic 7 Primary measures – money

Skills: counting, adding, counting on, subtracting, problem solving, reading, explaining, calculating change, calculating total costResources: chart about Nigerian money, real naira and kobo, novelty money, shopping items in the class for the shopping activity, pencils, crayons, a sheet of paper, exercise booksConcept: moneyVocabulary: total, total cost, change, cheap, expensive, money, naira, kobo, value, cost more, and cost less

Learning experiencesThe pupils learn about the importance of currency in Nigeria. They become familiar with the terms ‘naira’ and ‘kobo’ and the value of each. They learn how to break larger currencies into smaller amounts, and how much change they should receive when making a purchase.

Lesson focus• Let the pupils discuss the currency in terms of the notes and

coins used in Nigeria.• Let the pupils discuss why we need money, what we use it

for and how people get money.• They need to discuss what the different notes and coins look

like, the symbols on them, the colours and values of the coins and the notes.

• Let the pupils feel, touch and identify the notes and coins.• Let them say what they can buy for various values of money.• Make use of pictures of money as well as the real coins and

notes. Let the pupils handle the real money, and use plastic/novelty/play money for the pupils to play with in class and for discussion.

• Do simple shopping activities whereby they calculate totals and change is given. Have change up to 10.00 and shopping money greater than 10.00.

31Theme: Mensuration and geometry

• The pupils must also be able to exchange coins or notes for smaller amounts. Let the pupils do these exchanges in the class using the novelty money or real money. They could also be allowed to make their own paper money.


Topic 8 Primary measures – length

Skills: sequencing, ordering, identifying, measuring, comparing, estimatingResources: objects like a box, a book, a desk, a table, a door, a cupboard, the board, ruler, pencils, crayons, a sheet of paper, exercise booksConcept: lengthVocabulary: long, short, longest, shortest, longer, shorter, hand-spans, cubits, metres (m), centimetres (cm), tape measure, ruler, metre stick

Learning experiencesThe pupils learn how to measure length with their hands, their feet, their arms, a ruler and a tape measure, and how to measure curved edges with string. By doing these activities, the pupils will be able to realise that accurate measurements are important, and that standard measurements are necessary.

Lesson focusHand spans• Explain to the pupils that, in the old days, there were no

rulers and tape measures, so people had to work out other ways to measure objects.

• Ask the pupils to suggest ways in which we can measure without instruments.

• Show the pupils how to measure using hand spans. (A hand span is from the tip of the little finger to the tip of the thumb when the fingers are extended.)

32 Term 3

• Then ask the pupils to estimate the height of their desks in hand spans. Then let them measure the height in hand-spans and compare the number of hand spans to their estimate to see the difference.

• Divide the pupils into pairs and let them measure different objects in the classroom using hand spans.

Foot lengths• Show the pupils how to measure using their feet.

Demonstrate by placing one foot in front of the other, heel to toe, and counting as you take each step.

• Let the pupils work with their peers to practise measuring using their feet. They could measure the length of their classroom or the distance from their desks to the classroom door.

• Introduce the pupils to paces or steps as another informal form of measurement. Paces are the normal-sized steps people take when they walk. Demonstrate by pacing from one end of the classroom to the other, counting as you take each step. Let the pupils practise this outside the classroom.

Arm lengths/cubits• Show the pupils how to measure in cubits/arm lengths.

Explain that a cubit is the length of the arm from the elbow to the tip of the middle finger.

• Demonstrate by measuring the length of a table by using arm lengths – cubits. Place your elbow on the edge of the table and stretch it out so the hand is flat on the table. Let the pupils count the cubits. They can measure bigger objects like a cupboard.

Formal standard measuring units• Introduce the standard units – metres and centimetres.

Explain again that, in the old days, there were no rulers and tape measures, so people had to work out other ways to measure objects. These measures are not accurate. Ask the pupils why they think that is. Further explain that accuracy is important when we measure anything. Standard measurements are necessary.

• Today, we measure length in metres and centimetres. Write the words on the board or use flashcards. The pupils should read the words aloud, repeat them and write them. Also show the abbreviated forms (m; cm).


• Use a ruler to demonstrate how to measure; explain that we start from zero. Use a tape measure. Let the pupils work with their peers and measure a number of objects using standard formal measuring instruments – tape measures, rulers, metre sticks.

• Demonstrate how to measure curved edges using string and thereafter measuring the length of the string in metres or centimetres. Let the pupils practise this.

• Let the pupils record their measurements and draw the pictures. • Draw lines on the board and demonstrate how to measure

lines. Let the pupils practise this.

The exercises are set out for the week. Explain the instructions and examples to the pupils so that they understand what to do in each exercise. Give the pupils enough practice by doing:Pupil’s Book: Topic 8: Exercises 1–7, pages 175–181Workbook: Exercises 1–2, pages: 92–93.

Topic 9 Primary measures – time

Skills: reading the time, writing the time, calculating time in hours and minutesResources: clocks, clock templates for the pupils to make their own clocks, scissors, split pins, board, flashcards, pencils, crayons, a sheet of paper, exercise booksConcept: timeVocabulary: time, hours, minutes, seconds, o’clock, half past, half hours, analogue, digital

Learning experiencesThe pupils learn about analogue and digital time. They practise reading and writing different times for each.

Lesson focus• Use a big clock to show the pupils the clock face and the

time. The pupils should be able to identify a clock face and understand it – the numbers, the long hand (hour hand) and the short hand (minute hand).

• Explain the hours on a clock, the hour hand and how it

34 Term 3

moves. Show one o’clock on the clock face and explain and demonstrate how the hands move to the next hour. Explain and demonstrate the hours in a day.

• Discuss analogue time and how we say, read and write analogue time. Write the time on the board and/or use flashcards.

• Make use of a digital clock and explain and discuss digital time in terms of how we say, read and write digital time. Again write the time on the board and/or use flashcards.

• Let the pupils show the time in hours on the big clock. Let them read the time in hours as it is written in analogue form as well as in digital form.

• Explain the minutes in the same way. Demonstrate how to count the minutes in fives on the clock. Discuss the minutes in an hour, half hour, one and a half hours. Let them show the times on a clock, read and write their time.

• It is important for the pupils to make their own clocks so they can practise writing the time.


Days of the week

Skills: reading and writing the days of the weekResources: calendar, board, flashcards, pencils, crayons, a sheet of paper, exercise booksConcept: days of the weekVocabulary: time, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday

Learning experiencesThe pupils learn to read, write and spell the days of the week. They learn a poem to help them remember the days of the week and the order in which they fall. The pupils revise the ordinal numbers to help them place the days in the correct order.


Lesson focus• Teach the days of the week by using flashcards. Let the

pupils read the names and repeat them. Point out that the days are written with capital letters (they are proper nouns).

• Teach them which day is the first day of the week, second, third, fourth, fifth, sixth and seventh day of the week.

• Let the pupils cut out letters from newspapers or magazines to build the names of the days of the week. Let them paste the names on paper in the correct order. Display their work in the classroom.

• Let the pupils read the names aloud as they paste them and then they can write the names into their exercise books.

• Let the pupils say what they do on each day. They can draw a picture.

• Ask them on what day their birthday falls. Let them look at a calendar.

• Let the pupils discuss what they do on the weekends.• Let the pupils keep a picture diary for a week. They need to

write the name of the day on each page and draw a picture about what they experience on that day.

• Also discuss special days or events on the calendar and let them find those days on the calendar.

• Let the pupils read and recite the poem, Days of the week in the Pupil’s Book.


36 Term 3

Topic 10 Primary measures – mass (weight)

Skills: sequencing, ordering, identifying, measuring, comparing, estimatingResources: possible objects like rice, flour, sugar, feather, wool, book, soap, potato, pumpkin, shoe, bag, brick, stone, a balancing scale, board, flashcards, pencils, crayons, a sheet of paper, exercise booksConcept: massVocabulary: heavy, light, more, less, most, least, compare, balance scale

Learning experiencesThe pupils learn about mass – a measure of how much matter is in an object. Mass is commonly measured by how much something weighs. The pupils practise holding objects to determine how light or heavy they are. The pupils assess the mass of various objects so that they can arrange them in order from the lightest to the heaviest.

Lesson focus• Expose the pupils to a variety of objects of different sizes.• Let them discover the mass of the various items by using

their hands to feel the mass of each item.• Let them feel the mass of a variety of objects such as a book,

a schoolbag, a shoe, a lunchbox, a stone, a feather, a packet of rice, a loaf of bread, a box of tissues, a matchbox, a ruler, a cap and so on. They will then actually be estimating the mass of the various items.

• Let them draw and label their measurements.• Let them compare the quantities and solve some problems.• It is important for the pupils to be able to order the objects in

the correct sequence from heavy to light or from the lightest to the heaviest.

• Explain that, when we measure using informal measures like our hands, we will not get accurate measures. Ask them why they think that is.

• Next, introduce a balance scale for the pupils to see how the one side would go down if the object is heavy and how it will


go up if the object is light. Let the pupils practise weighing a variety of objects and compare the different masses.

• Let them record their measurements by drawing the pictures.


Topic 11 Secondary measures – capacity

Skills: sequencing, ordering, identifying, measuring, comparingResources: jug, jar, spoon, bottle, glass, teaspoon, pot, can, tank board, flashcards, pencils, crayons, a sheet of paper, exercise booksConcept: capacityVocabulary: full, empty, half full, cup, bucket, jug, jar, spoon, bottle, glass, teaspoon, pot, can, tank, more, less, most, least, compare

Learning experiencesThe pupils learn about capacity – the maximum amount that something can hold. The pupils identify and name objects that could be used for measuring capacity, for example cups, empty containers, buckets, etc. They also learn how to order these containers based on their capacities.

Lesson focus• Expose the pupils to different sizes and shapes of containers.• Let them discover the capacity of the various containers by

using everyday objects like cups, teaspoons, spoons, mugs, jugs, bottles and so on.

• Let them use water to measure the capacity of the containers, for example they use a cup to fill a litre jug with water to measure the capacity of the jug or a bottle. They could discover that the bottle holds 4 cups of water or the cup holds 50 teaspoons of water.

• Let them draw and label their measurements.• Let them compare the quantities and solve some problems.• It is important for the pupils to be able to order the quantities

or capacities in the correct sequence from least to most or

38 Term 3

from the smallest to the biggest, or most to least and biggest to smallest.

• The pupils should then also be able to estimate. Let them practise this.


Topic 12 Secondary measures – area

Skills: comparing, measuring, calculating areaResources: squared paper, ruler, board, pencils, exercise booksConcept: areaVocabulary: area, squares, length times breadth, bigger, smaller, squared paper, inside a space, circle, diameter, tessellate

Learning experiencesThe pupils learn how to use squares to measure the area in a flat space. They need to be able to compare areas of different surfaces, so that they understand the idea of larger than, smaller than, largest, smallest, and the same. They also tessellate squares to make new shapes, whereby a pattern is made of identical shapes, where the shapes must fit together without any gaps and the shapes should not overlap.

Lesson focus• Ask the pupils what we could do to find out how many tiles

we would need to tile the classroom floor. Let the pupils speculate and offer suggestions about what they think should be done. Then say, “Let’s find out what we can do.”

• Give the pupils a sheet of squared paper and tell them that squared paper will be used to measure the area of a space.

• Ask the pupils to put their non-writing hand with their fingers together flat on the sheet of squared paper. Tell them to trace around their hand.

• Instruct them to count all the squares inside the outline of their traced area. Explain that we measure area in squares.


We have to count each square inside the border/outline. Explain to the pupils that a hand takes up a certain space. That space is the area that we measure.

• They can compare the number of squares of their hand with that of a peer.

• They can practise by doing the same exercise with their feet and squared paper.

• Do another exercise to measure the area of their desk top. • Give the pupils two books and ask them to use the books to

measure the area of the desk top. Let the pupils give their views. • Guide the pupils to do this. If necessary, demonstrate how to

use two books to measure area.• Follow these steps:

– Place one book in a corner of the desk. Count one. – Place the second book next to the first book. Add one to

your count. – Then remove the first book and place it on the other side

of the second book. Increase the count by one. You should now have three.

– Do this, until you reach the end of the desk. Then place one book above the other and continue across the desk again until the whole area of the desk has been covered.

– The pupils should remember to keep count of the areas of their books as they measure.

– Then explain that area is the number of squares or square units that cover a flat space/area.

– Next draw a shape on the board. Explain that we can write the numbers in the squares as we count the squares.

1 2 3

4 5 6

The area of the rectangle is six squares.


40 Term 3

Topic 13 Three-dimensional shapes

Cubes and cuboids

Skills: identifying, describing, comparing, drawing, recognisingResources: solid shapes of cubes and cuboids, board, pencil, crayon, paper, exercise booksConcepts: three-dimensional (3-D) shapes, cubesVocabulary: 3-D, cubes, cuboids, corners, edges, faces, solid shapes, dimensions, length, width, height

Learning experiencesThe pupils are introduced to cubes and cuboids which are 3-D shapes. They have three dimensions – length, width and height. The pupils identify and count the faces, corners and edges of a cuboid and a cube. They also identify objects at home that are cuboids and cubes. The pupils make their own cubes and cuboids.

Lesson focus• Have a number of cubes and cuboids in the class for the

pupils to describe.• Hold up one of the objects and explain the three dimensions

of height, width, and length.• Point out the corners, the edges and the faces. Let the pupils

count the corners, the edges and the faces. Let them describe the faces.

• Let them investigate whether the shapes can roll or slide, and why and why not.

• Let them open a box. Refer to the open box as a net. • Let them see the nets of the cube and the nets of the cuboid.

Let them refold it.• Let them trace the nets and make new cubes and cuboids.• Let them identify more cubes and cuboids in the classroom, at

home, in their environment and in newspapers and magazines.

The exercises are set out for the week. Explain the instructions and examples to the pupils so that they understand what to do in each exercise. Give the pupils enough practice by doing:Pupil’s Book: Topic 13: Exercise 1–4, pages 212–215Workbook: Exercise 1, page 106.


Spheres and cylinders

Skills: identifying, describing, comparing, drawing, recognisingResources: solid shapes of spheres and cylinders, board, pencil, crayon, paper, exercise bookConcepts: 3-D spheres, cylindersVocabulary: 3-D, spheres, cylinders, curved faces, circular edges, solid shapes, dimensions, length, width, height

Learning experiencesThe pupils identify the flat faces and curved surfaces of a cylinder and a sphere. They need to know the difference between the flat faces and the curved surfaces. Spheres and cylinders are 3-D objects and so have the three dimensions of length, width and height. The pupils must be able to name objects at home that are spheres and cylinders.

Lesson focus• Have a number of spheres and cylinders in the class for the

pupils to describe.• Hold up one of the objects and explain the three dimensions

of length, width, and height.• Ask them to describe the shapes. • Then point out the curved surfaces, the circular edges and the

fact that there are no corners and straight edges nor flat surfaces. • Let them investigate whether these shapes slide or roll and

explain why and why not.• Let them identify more spheres and cylinders in the

classroom or at home in their environment.• They can identify and cut out pictures from magazines and

newspapers of spheres and cylinders to paste in their exercise books and arrange them according to size, for example from the smallest to the biggest.

• In Exercises 8 and 9, they will make their own balls and spheres.

42 Term 3

The exercises are set out for the week. Explain the instructions and examples to the pupils so that they understand what to do in each exercise. Give the pupils enough practice by doing:Pupil’s Book: Topic 13: Exercises 5–9, pages 216–219Workbook: Exercise 3, page 108.

Topic 14 Two-dimensional shapes

Skills: identifying, describing, comparing, drawingResources: objects like small boxes, oranges, cylinders, cut out 2-D shapes, ruler, pencils, crayons, scissors, a sheet of paper, exercise booksConcept: two-dimensional (2-D) shapesVocabulary: square, circle, rectangle, triangle, straight sides, circular, flat faces, square corner, dimensions

Learning experiencesThe pupils identify the different shapes of a square, a rectangle, a triangle and a circle. They learn that 2-D shapes have two dimensions – length and width. The pupils use these 2-D shapes to create patterns and pictures.

Lesson focus• Have a number of cylinders, prisms (boxes) and spheres in

the classroom.• Let the pupils work in small groups.• Each group has each of the different 3-D objects to work

with and a sheet of paper.• Ask the pupils to trace around the open edge of the cylinder

and to trace around a variety of prisms.• Explain to the pupils that the shapes on their sheet of paper

are 2-dimensional shapes – 2-D. Ask them to identify the 2-D shapes – square, rectangle, triangle and circle. Write the names on the board and use flashcards. Let the pupils read and say the words.

• Ask them to describe the 2-D shapes.• Explain and show the flat faces, straight sides and the number

of straight sides, the corners and the number of corners, the circular flat face, no corners and no sides.

• Explain and show the square corners and let the pupils count the number of square corners.


• Let them compare the different 2-D shapes in terms of their descriptions, for example the differences between the square and the triangle, and the square and the rectangle.

• Let the pupils identify 2-D shapes in magazines or newspapers.

• Let the pupils use 2-D shapes to make patterns and they could add colour to their patterns.

• Let the pupils build pictures with 2-D shapes and make new shapes with 2-D shapes.

• They need to open a 3-D prism (box) to see the net of the boxes which will then be a 2-D shape.


Term 344

Term 3THEME Everyday statistics

Topic 15 Data collection

Skills: observing, sorting, classifying, answering questions, interpreting, reasoning, recordingConcepts: sorting, data, recordingResources: books, pencils, crayons, scissors, glueVocabulary: sorting, data, recording

Learning experiencesThe pupils learn about sorting, grouping, recording, reading and interpreting data.

Lesson focusSorting• The pupils work in small groups on a mat. • Give them a variety of objects. Explain that the objects are

mixed up. • Ask the pupils to sort the objects into groups that belong

together. • Explain that after they have finished sorting or grouping the

objects, they can name the groups. • Let them name the groups and explain why they chose a

particular name.

Data• Explain to the pupils that all the information they have in

front of them (the sorted groups) is called data and that data is another word for information. We collect data when we gather information.

• Explain to the pupils that they have sorted the data into specific groups and named the groups according to specific characteristics.

45Theme: Everyday statistics

• Tell them that we can collect data by asking questions, looking in books, magazines, newspapers and by looking around us.

Recording• Explain that when we write down data we say that we are

recording the data. • Show the pupils how we can record data in different ways.

We can use pictures, ticks, strokes, crosses, dots or colours to represent data.

• Show the pupils that each symbol that we record represents one item, for example: we can write a to represent 1 child.

Reading and interpreting data• Explain to the pupils that it is important to read all the data

they have in front of them. When they look at data and read the information, they need to understand what it is and what it says. The data will inspire them to think of questions as they will want to know more about the data. They will ask ‘why?’ and ‘why not?’ questions. Pupils must be able to read and interpret the data to answer questions about the data or to make decisions about it.

The exercises are set out for the week. Give the pupils enough practice by doing:Pupil’s Book: Exercises 1–5, pages 225–229 Workbook: Exercises 1–3 pages 111–113.

Revision of the third term’s work


through the term.

Pupil’s Book: Revision: Revision exercises 1–6, pages 230–236Workbook: Exercises 1–6, pages: 114–123

46

Notes

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