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Chapter 1 Numbers and numeration

Whole numbers

Objectives

At the end of this chapter, pupils should be able to:

1 count numbers up to millions,

2 count up to billions,

3 identify the place value of numbers up to billions,

4 write numerals up to billions in word form and figures,

5 apply counting large numbers to population,

6 compare and order large numbers.

Unit 1 Counting up to millions

Guide pupils to use the abacus to form numbers and read given

numbers. Lead pupils to understand the importance of numbers and

their application in real life activities. e.g. daily business transactions in

the markets, banks, airports, sea ports, etc.

Exercise 1-5, pages 2-4

Select some questions from each exercise and give pupils as classwork.

Give the workbook exercises as homework. Ensure that you mark both

class work and workbook exercises. This will give you the true

understanding of how far pupils understand the topic.

Unit 2 Counting up to one billion

Lead pupils to understand that billion is greater number than million

and how the two are related. (how many millions make one billion, etc).

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Guide the pupils through the topic by using the table on page 4 to

explain.

Exercise 1 – 3, page 4 – 5

Select some questions from the above exercises and give as classwork

or you can use the workbook exercises as classwork and that of the

textbook as homework.

Unit 3 Place-value

The pupils are already familiar with place value of numbers less than

billion, lead them to the table on page 5 and explain.

e.g. Billions Millions Thousands Hundreds

H T U H T U H T U H T U

1 5 6 4 3 1 2 6

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

3 6 8 4 9 7

1 5643126 2 21683547328 3 68497

The table will enable pupils to see the difference and place value of

each digit. Ensure that the pupils should use the above table to guide

themselves to master how to determine the value of each digit.

Exercise 1 – 3, pages 6 – 7

Select some of the questions and give the pupils as classwork, and

exercises in the workbook can be given as home work.

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Unit 4 Writing numbers in words and figures

Lead pupils to follow the following steps when writing numbers in

words.

1 Put a space in the number, three digits from the right.

2 Treat each 3-digit part like separate number. e.g. 4 612 352

Four million, six hundred and twelve thousand, three hundred and

fifty-two.

Note that the first digit is mentioned before the rest.

Exercise 1 – 2, page 8

Select some of the questions in the above exercises and give as

classwork. The workbook exercise can be given as homework.

Unit 5 Application of counting large numbers to population

Lead pupils to examples of activities where large numbers are applied.

e.g. populations of cities, countries, continent, distances covered by

ship, airplane, space ships, money, etc.


Give the exercise as classwork and that of workbook as homework.

Unit 6 Comparing and ordering numbers

Lead pupils to be able to identify large and small numbers and how to

arrange numbers in ascending and descending order. Explain how to

use the inequalities signs.


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Select some of the questions and give as class work and that of

workbook as home work.

Chapter 2 Numbers

Objectives


1 find the factors and multiples of numbers,

2 identify prime numbers and composite numbers,

3 express numbers as the product of prime numbers,

4 find the highest common factor of two or more 2-digit numbers,

5 find the lowest common multiple of two or more 2-digit numbers.

Unit 1 Factors and multiples

Lead pupils to examples and explain

e.g. 12 = 2 × 2 × 3, 36 = 2 × 2 × 3 × 3

1, 2, 3, 4, 6, 18 are factors of 18 (divide without remainder)

1, 2, 3, 4, 6, 9, 12, 18, 36 are factors of 36 (divide without

remainder)

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Factors or divisors of a number are all whole numbers which divide

exactly into that number. Guide the pupils through Activity 1 on page

13 and Activity 2 on page 2 with explanation. Revise the multiplication

table for numbers greater than 12 with the pupils, and guide them to

use the tables to find the multiples of given numbers.

Exercise on page 14

Guide pupils to this exercise in the class.

Unit 2 Prime numbers and composite numbers

Lead pupils to examples of prime and composite numbers.

example of prime numbers 3, 5, 7, 11, 13, 17, 19, etc. They are

numbers that can be expressed as the product of two different

numbers.

1 × 5, 1 × 7, 1 × 11, etc.

Note: 1 is not a prime number because it does not have two different

factors.

Introduce the pupils to Activity on page 15, guide them through and

explain. Introduce them to examples of composite numbers.

e.g. 8 = 1 × 8 = 2 × 4, 12 = 1 × 12 = 2 × 6 = 2 × 2 × 3, etc.


You can treat Exercise 1 questions No. 1, 2, 6 can be given orally and

the rest as written class work.

Exercises in workbook can be given as homework.

Unit 3 Prime factorisation

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Lead the pupils through the explanation and examples on page 16 and

17.

Exercise 1 and 2

Give this exercises as classwork by selecting some questions from the

above exercise.

Introduce the two methods of factorising numbers on page 18 by

giving the pupils examples.

Exercise 3 on page 19

Give the exercise as classwork by selecting some questions from A and

allow them to complete the factor three method.

Workbook exercises can be given as homework.

Unit 4 Highest Common Factor (HCF)

Lead pupils through example on page 20 introduce one or two

examples in addition to the textbook. Example

e.g. The HCF of 16 and 20

16 = 2 × 2 × 2 × 2

20 = 2 × 2 × 5

HCF = 2 × 2 = 4

or use the venn diagram.

HCF of 24 and 36

24 = 2 × 2 × 2 × 3 Illus.

36 = 2 × 2 × 3 × 3

HCF = 2 × 2 × 3 = 13

Exercise on page 20

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Guide pupils through this exercise as a class work. Workbook exercise

as home work.

Unit 5 Lowest Common Multiple (LCM)

Lead pupils through examples on pages 21– 22 and guide them

through the exercise on page 22.

Workbook exercises can be given as homework.

Chapter 3 Fractions (Decimals)

Objectives


1 recognise the meaning of decimals,

2 identify the place value of decimals,

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3 write decimals in words and figures,

4 compare and order decimals,

5 convert decimals to fractions and vice versa,

6 find the fraction of quantities.

Unit 1 Meaning of decimals

Lead pupils through examples on pages 25 – 26 and guide them

through.

Exercise 1 – 3

Select some questions from the exercises and give as class work.

Exercises in the workbook can be given as home work.

Unit 2 Place value of decimals

Lead pupils through the table on page 26, this table will enable pupils

to understand the position and place value of each digit.

e.g. Ten thousand Thousand Hundred Tens Units Decimal Tenths Hundredth

Thousandths

T.Th Th H (T) (U) points (t) (h) (th)

1 2 • 3 4 2

2 5 6 • 1 4 6

0 • 3 7 8

12.342, 256.146, 0.378

The table shows the place value of each digit. This should be well

explained using examples.

Exercise 1 – 2, page 26 – 27

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These exercise can be given as class work. Workbook exercise can be

given as homework.

Unit 3 Reading and writing decimals in words and in figures

Guide the pupils through examples on page 28, if possible give them

more examples.

e.g. 3.006 = three point zero zero six

0.894 = zero point eight nine four, etc.

Exercise 1 and 2, page 28

Guide pupils through these exercise in the class (can be given as

classowrk). Workbook exercise can be given as homework.

Unit 4 Comparing and ordering decimals

Lead pupils through examples on page 29. Pupils should be able to

identify the size of numbers by comparing two or more numbers and

arrange numbers in order of ascending or descending.

e.g. 94.608 < 105.469 → 105.469 is larger or greater than 94.608

Guide the pupils on how to use or apply the symbols > < =

Exercise 1, 2 and 3 page 29

This exercises can be given as classwork. Workbook exercises can be

given as homework.

Unit 5 Conversion from fractions to decimals and vice versa

Changing fractions to decimals

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Lead pupils through the exercises

Exercises 1 – 3, pages 30 – 31

Exercise 1, should be completed in the class as class work.

Select some questions from Exercise 2 and 3 and give pupils as

classwork.

Changing decimals to fractions

Lead the pupils through examples on pages 31 – 32. Guide them

through exercises by selecting some questions from Exercises 4 – 5,

page 32 as classwork.

Mixed exercises on decimals and fractions

Exercise 6, page 33

This exercise can be treated as a revision in the class. Allow pupils to

work some selected questions and revise the rest with them in the

class.

Application of decimals to money and other measures

Lead pupils through examples which are more applicable in daily

activities.

e.g. If I have $100 and spend $45 in buying snacks, what fraction of

the money did I spent?

Solution

=

A 4 metre plank was bought in timber market, if 1.25 metre was cut

from the plank what fraction was cut?

= = =

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Guide the pupils through this as a class work. Workbook exercises can

be given as homework.

Unit 6 Fractions of quantities

Lead the pupils through examples

e.g. Find of $2 500 = × $2 500 = $1 875

Express of 60 kg in grams

× 60 × 1 000 g = × 60 000 g = 24 000 g

or × 60 kg = 2 × 12 kg = 24 kg = 24 × 1 000 g = 24

000 g

Exercise on page 36

Give this exercise as classwork.

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Chapter 4 Percentages

Objectives


1 recognise what ‘percentage’ means,

2 convert percentages to fractions and vice versa,

3 convert percentages to decimals and vice versa,

4 express part of a whole in different ways,

5 find percentage of quantities.

Unit 1 The idea of a percentage

Explain this topic using graph board, the graph board has small squares

which can be use as examples.

e.g. 50% = → fifty parts out of hundred parts

25% = → twenty five parts out of hundred parts

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The graph can easily be used to demonstrate the above for better

illustration.

Exercise 1 – 2 page 38

Give this exercise as class work.

Unit 2 Conversion from percentages to fractions and vice versa

Lead pupils through examples

e.g. 45% = = =

= × 100 = 60%

Exercise 1 – 2 on pages 39 – 40


Unit 3 Conversion from percentages to decimals and vice versa

Converting percentages to decimals

Lead the pupils through examples

e.g. 75% = = 0.75, 12 % = × = = = 0.125

or 12.5% = = = 0.125


This exercise can be given as class work.

Converting decimals to percentages


e.g. 0.25 = 0.25 × 100% 12.45 = 12.45 × 100%

= × 100 = 12 × 100%

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= 25% = × 100 = 1 245%

Guide the pupils through

Exercise 2 on page 41 can be given as class work.

Unit 4 Expressing parts of a whole in different ways

Guide pupils to the exercise on page 41. The exercise can be given as

class work. Remember that this exercise will enable teacher to

understand and know pupils weakness, after marking.

Unit 5 Percentages of quantities


e.g. 60% of 180 kg 45% of 12.5 m

× 180 kg = 108 kg × 12.5 m = = 5 m

= 5.625

m


Guide pupils through this exercise by selecting some question A, B, C,

D and E and give as class work.


The questions here are word problems, guide pupils through the

exercises. Workbook exercise can be given as classwork.

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Chapter 5 Ratio

Objectives


1 recognise the idea of ratio,

2 simplify ratio in its lowest term,

3 solve problems involving ratio.

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Unit 1 Idea of ratio, the relationship between ratio and fractions and

equivalent ratio

Introduce objects to be used in the class for demonstration among the

pupils.

e.g. share oranges to two pupils

1st pupil 2nd pupil

↓ ↓ ⇒ Ratio 2 : 3 =

2 oranges 3 oranges

What is the total oranges shared = 2 + 3 = 5

Other objects can be use as well.

Exercise 1 on page 46, this can be done orally in the class.

Exercise 2 and 3 on pages 47 – 48

Guide pupils through examples

e.g. 3 : 5 = 18 : x ⇒ = ⇒ 3x = 18 × 5

x =

x = 30

Select 6 or 8 questions from Exercise 2 and give it as classwork.

Exercise 3 can be done orally in the class

Workbook exercises can be given as home work.

Unit 2 Simplifying a ratio in its lowest form


e.g. 10 : 30 = 1: c ⇒ : = 1 : c ⇒ 1:3

10 : 30 = 1:3, etc.

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Exercises 1 – 2 on page 48

Select some questions from these exercises as a class work.

Exercise 3 on page 49 can be done orally in the class

Workbook exercise as homework.

Unit 3 More problems involving ratio

Guide the pupils through examples, since Exercise 1 on page 49 is

revising it can be done orally in the class.


Introduce examples on this exercise

e.g. Increase $60 in the ratio of 5:3

× $60 = = $100

Decrease $60 in the ratio of 3:5

× $60 = = $36

Guide pupils through this exercise as classwork.


Guide pupils through this exercise (since is word problems) as

classwork. Workbook exercise can be given as homework.

Chapter 6 Basic operations

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Addition and subtraction (Whole numbers)

Objectives


1 add numbers,

2 subtract numbers,

3 solve mixed operation problems involving addition and

subtraction.

Unit 1 Addition of three 3- and 4-digit whole numbers

Pupils are familiar with addition and subtraction of 2 and 3 digit

numbers. Introduce examples on addition and subtraction of 3 and 4

digit numbers.

e.g. Th H T U Th H T U

2 4 3 6 6 7 4 3

+ 4 5 7 and - 3 8 4 5

9 8 2 1 2 8 9 8

12 7 1 4

Guide pupil to follow the steps below when adding whole numbers.

1 Write the numbers one on top of other with the units line up.

Vertical arrangement.

2 Start with the units column first, then the tens, then the

hundreds, then the thousands, etc.

3 Follow the way you have been taught to add.

e.g. Add the following 2054 + 562 + 7081

2 0 5 4

+ 5 6 2

7 0 8 1

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9 6 9 7


Select 6 questions from No. 1 – 12

and 6 questions from No. 13 – 20

Remind and guide the pupils to follow the 3 steps for solving questions

No. 13– 20 previously mentioned.


Guide the pupils through Exercise 2 and 3. Select 8 questions in

Exercise 2 and 7 in Exercise 3 after picking 2 questions as examples.

Workbook exercise can be given as homework.

Unit 2 Subtraction of 3-digit and 4-digit whole numbers

Guide the pupils through examples.


Give questions in Exercise 1 and select 8 questions from Exercise 2 as

classwork.

Subtraction of 3 whole numbers taking two at a time

Introduce examples and follow the steps below.

Step 1: First subtract the second number from the first number.

Step 2: Then subtract the third number from the answer you obtain

in step 1.

e.g. 8769 – 6512 – 1235 8 7 6 9

– 6 5 1 2

2 2 5 7

– 1 2 3 5

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1 0 2 2

Exercise 3

Select 8 questions from the exercise and give as classwork.

Workbook exercise can be given as home work.

Unit 3 Mixed operations of addition and subtraction

Lead pupils through examples by explaining the steps to take.

e.g. 7506 – 3412 – 2168

In the above question rearrange the numbers so that the positive

numbers will come first followed by the negative (subtraction)

numbers.

7506 + 2168 – 3412 7 5 0 6

+ 2 1 6 8

9 6 7 4

– 3 4 1 2

6 2 6 2


Select questions No. 1, 3, 5, 7, 9 and 10 as classwork.


Guide the pupils through examples and give the questions as

classwork.


Give this exercise as classwork. Workbook exercise can be given as

homework.

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Unit 4 Word problems involving addition and subtraction

Exercise on page 60

Lead pupils to practical examples in the class.

e.g. Using scale to take the weight of pupils ad adding them in kg.

Measuring the size of objects in mm by pupils and adding or

subtracting the results.

Select two questions from the exercise and use it as examples in

addition to the practical examples.

Give the rest as classwork and the workbook exercise may be given as

homework.

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Chapter 7 Addition and subtraction of fractions

Objectives


1 add fractions and mixed numbers,

2 subtract fractions and mixed numbers,

3 carry out mixed operations involving addition and subtraction of

fractions,

4 solve word problems involving addition and subtraction of

fractions.

Unit 1 Addition of fractions and mixed numbers

Lead the pupils to examples of cases of fractions with same

denominators and cases of different denominators.

e.g. 1 + = = =

2 + = = = 1

3 2 + 4 = 2 + 4 + = 6 + = 6

The case of (3) is addition of mixed numbers

(Note: the whole numbers are added separately before adding it to the

fraction)

Exercises 1 and 2 pages 64

Select questions No. 1, 3, 5, 7 and 9 from Exercise 1

Select questions No. 1, 3, 5, 7 and 9 from Exercise 2 to be given as

class work.

Workbook exercises to be given as home work.

Unit 2 Subtraction of fractions and mixed numbers

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Lead pupils through examples and explaining

e.g. 1 5 – 2 = 5 – 2 + – = 3 + = 3

2 2 – = 1+1+ – = 1+ + – = 1+ – = 1+

= 1

3 6 – = 5+1– = 5+ – = 5+ = 5+ = 5

Be very careful when explaining (2) and (3) and give them more

examples on similar fractions.

Exercise on page 65

Select questions No. 1, 3, 5, 7, 9, 11, 13, 15, 17 and 19 to be given

as class work.


Unit 3 Mixed operations of addition and subtraction of fractions

Use examples to explain to the pupils.

e.g. 1 5 +1 – 3 = 5+1–3+ + – = 3+ = 3

2 4 –2 +1 this can be re-arrange as 4 +1 –2 before

solving or simplifying.

Exercise on page 66

This exercise can be given as class work. Workbook exercise can be

given as homework.

Unit 4 Word problems

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Lead the pupils through the examples on page 66 and select two

questions from exercise on page 66 and give as examples.

Exercise on page 66

Give the remaining exercise (8 questions) as class work. Workbook

exercise can be given as homework.

Chapter 8 Addition and subtraction of decimals

Objectives


1 add decimals,

2 subtract decimals,

3 carry out mixed operations involving addition and subtraction of

decimals.

4 solve word problems involving addition and subtraction of

decimals.

Unit 1 Addition of decimals

Guide pupils on how to arrange decimal numbers under the heading.

Th, H, T, U, t, h and th by giving examples

e.g. Add the following 48.35 + 0.92 + 2.305 + 1.4

4 8 • 3 5 Th H T U • t h th

1 • 4 4 8 • 3 5

+ 0 • 9 2 ⇒ 1 • 4

2 • 3 0 5 0 • 9 2

5 2 • 9 7 5 2 • 3 0 5

5 2 • 9 7 5

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The decimal points should be in vertical line position such that to the

left side are whole number greater than 0 (zero) and to the right side

are numbers less than 0 (zero)


Guide the pupils through the above exercises.

Select Exercise 1 No. 1, 3, 5, 8, 9

Select Exercise 2 No. 1, 2, 3, 6, 7, 10 as class work.


Unit 2 Subtracting of decimals

Lead pupils to follow the steps for addition (arrangement where the

decimal sign is arranged vertically)

Exercise on page 70

Give this exercise as class work and workbook exercise as homework.

Unit 3 Mixed operations of addition and subtraction of decimals

Lead pupils through examples under Unit 3 on pages 70 – 71.

Exercise on page 71

Select questions No. 1, 3, 5, 7, 10, 14 and 15 as class work and

workbook exercise can be given as homework.


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Select 2 questions and use as examples and give the rest as class

work. Workbook exercise can be given as homework.

Chapter 9 Multiplication (Whole numbers)

Objectives


1 multiply numbers by 1, 0 and multiples of 10,

2 multiply 2-digit numbers by 2-digit numbers,

3 multiply 3-digit numbers by 3-digit numbers,

4 solve word problems involving multiplication.

Unit 1 Multiplication by 0, 1 and multiples of 10

Lead pupils to understand that any number multiplied by 0 will give an

answer (zero) 0.

e.g. 3 × 0 = 0, 100 × 0 = 0, 78 × 0 = 0, etc.

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Lead pupils to understand that any number multiplied by 1 will give an

answer of the same number.

e.g. 3 × 1 = 3, 100 × 1 = 100, 78 × 1 = 78, etc

Lead the pupils to understand that when multiplying two or more

numbers which end with zero by another number which ends in zero,

multiply the digits and then write the number of zeros to the right of

the answer (check page 73 of textbook)

e.g. 1 5 0 2 4 8 0 3 2 1 0 0

× 1 0 × 2 0 × 3 0 0

5 0 0 9 6 0 0 6 3 0 0 0 0

4 20 × 6 × 300

= 2 × 6 × 3 × 1 000

= 36 × 1 000 = 36 000

Exercise on page 73

Guide pupils to this exercise as class work.

Unit 2 Multiplying a 2-digit number by another 2-digit number

Lead pupils through example on page 74 and if possible give more

examples (if pupils are finding it difficult to understand).


Select questions No. 1, 3, 5, 7, 9, 11, 13, 17 and 19 as class work.


Guide the pupils through this exercise. Give workbook exercise as home

work.

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Unit 3 Multiplying 3-digit numbers by 3-digit numbers

Lead pupils through example on page 75. Select 1 or 2 questions from

Exercise 1 on page 75 and use as more examples.


Select questions No. 3, 5, 7, 11, 13, 17 and 19 as class work.

Lead pupils through example on page 76.

Exercise 2 and 3 on page 76

Guide pupils through this exercise

Select questions from the exercises

Exercise 2, questions no. 1, 3, 5, 7

Exercise 3, questions no. 1, 3, 5, 7 can be given as class work.

Workbook exercise can be given as home work.

Unit 4 Word problems involving multiplication

Select two questions from the exercise and give it as examples, then

guide the pupils through exercise on page 76 and give as classwork.

Give workbook exercise as homework.

Chapter 10 Multiplication (Fractions and decimals)

Objectives


1 multiply a fraction by another fraction,

2 multiply two mixed fractions,

3 apply ‘of’ as multiplication,

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4 multiply decimals by 1- and 2-digit numbers,

5 solve word problems involving multiplication of fractions and

decimals.

Unit 1 Multiplication of a fraction by another fraction

Lead pupils through the examples on page 79 and give one or two

examples.

e.g. × × = × × = Explain to pupils that fractions

× × = × × = should be reduce to simplest form

before simplifying

Exercise on page 79

Select questions No. 1-7 and 9-15 as class work.

Unit 2 Multiplication of two mixed numbers

Explain mixed numbers to pupils with examples

e.g. 2 , 10 , 12 is mixed fraction

, , is improper fractions.

Lead pupils to understand that when multiplying mixed fractions, they

should change them to improper fractions first.

e.g. 2 × 1 = × = = 4, 4 × 1 × 2 = × ×

= = 20

Unit 3 Applying ‘of’ as multiplication

Explain the use of ‘of’ in multiplication to the pupils by using examples.

e.g. of 18 = × 18 = = 6

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of 2 = × 2 = × = = 1

Guide the pupils through the examples on page 80


Select questions No. 1, 3, 5, 7, 9, 11, 13 and 17 as class work.

Introduce pupils to examples on page 81, explain the examples if

possible select 1 or 2 questions from Exercise 2 and 3 to be given as

examples.

e.g. 1 Find the difference between the two

of 8 km 364 m and of 3 km 636 m

× (8 km 364 m) and × (3 km 636 m)

× (8 000 + 364) m and × (3 000 + 636) m

× 8364 m – × 3 636 = 5 × 1 394 – 5 × 606

= 5(1 394 – 606) = 5 × 788

= 3 940 m = 3.94 km

2 One-quarter of a man’s monthly salary is spent on food for

his family. He earns $46 400 in one month. How much does

he spend on food?

Monthly salary = $46 400

One-quarter spent on food =

of $46 400 = × $46 400 = $11 600

Exercise 2 and 3 on pages 81 and 82

Give questions No. 1 – 11 of Exercise 2

Give questions No. 3 – 11 of Exercise 3 can be given as a class work.

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Unit 4 Multiplication of decimals by 1- and 2-digit whole numbers

Lead the pupils through the examples on pages 82 – 83 and introduce

exercises as class work.


Questions No. 1, 3, 5, 7, 9, 11, 13 of Exercise 1

Questions No. 1(a, c, e, g, i, k) of Exercise 2 can be given as class

work.

Exercise 2, questions No. 2 and workbook exercise can be given as

home work.


Introduce 2 or more questions as examples. It will be better if a

practical examples in the class is introduced to the pupils.

e.g. Ask pupils to measure the length and breadth of the class.

L = ___________ B = ___________

Ask the pupils to find of the length + of the breadth and multiply

the result by 2.

Ask pupils to find the perimeter of class.

Ask them to compare the two answers.

Exercise on page 84

Give this exercise as a classwork. Workbook exercise can be given as

homework.

29

Chapter 11 Squares and square roots

Objectives


1 find the squares of whole numbers greater than 50,

2 solve problems involving squares of numbers greater than 50,

3 find the square roots of perfect squares greater than 400.

Unit 1 Squares of whole numbers greater than 50

Lead the pupils on how to find the squares of whole numbers.

Introduce this topic by revising on how to find the square of single

digit numbers.

e.g. find the squares of the following numbers

1 2 2 4 3 5 4 7 5 9

Solution

1 22 = 2 × 2 = 4 2 42 = 4 × 4 = 16 3 52 = 5 × 5 = 25

4 72 = 7 × 7 = 49 5 92 = 9 × 9 = 81

Introduce examples on squares of 2-digit numbers less than 50 by

guiding the pupils through Exercise 1 on page 86

e.g. 192 = 19 × 19 → 1 9

× 1 9

1 7 1

1 9

3 6 1, etc.

30


Select some question from this exercise (No. 1, 3, 5, 7, 9) as a class

work.

Lead the pupils through example on page 87


Give these exercises as class work. Workbook exercise can be given as

homework.

Unit 2 Solving problems involving squares of numbers

Lead the pupils through the examples on page 87 – 88 and guide them

through Exercises 1 – 3, on page 88

e.g. Find the values of the following:

1 412 + 402 = 41 × 41 + 40 × 40 = 1 681 + 1 600 = 3 281

2 542 – 272 = 2 916 – 729 = 2 189

3 82 – 42 = 64 ÷ 16 = = 2 × 2 = 4, etc.

Exercise 1 – 2

Select questions No. 1, 2, 4, 6, 7, 9, 11 of Exercise 1

Select questions No. 1 – 8 of Exercise 2 as a class work.

Exercise 3 No. 1 – 5 should be included as a class work.

Exercises in the workbook can be given as homework.

Unit 3 Square roots of perfect squares greater than 400

Introduce the square root symbol and use it as an example.

e.g. = = = 4, = = = 5

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Lead pupils to examples on square root of perfect numbers greater

than 400.

e.g. Find the square root of the following numbers

1 441 2 729 3 1 600

Solution

1 441 = = 3 441

3 147

7 49

7 7

1

= = 3 × 7 = 21

2 729 = = 3 729

3 243

3 81

3 27

3 9

3 3

1

= = =

= 3 × 3 × 3

3 1 600 = = = 2 1 600 or

2 800 = 4 × 10

2 400 = 40

2 200

32

2 100

2 50

5 25

5 5

1

= = = 2 × 2 × 2 ×

5

= 40

Explain to pupils that when factorising they should use prime numbers

to divide the number into prime factors. Guide pupils on how to use

the square and square root tables.

Exercise on page 90


Revision Exercise 11 on page 11

Select some questions which are challenging in this exercise as

examples.

e.g. Find the values of the following:

1 + 2 3 –

+ –

2 × 7 6 – 5

8 1

4 – 5 –

–

10 – 6

= 4

33

Explain the examples and let them compare No. 2 and 5 and

understand that they are not the same. Guide the pupils through the

exercise in the class.

Give work book exercise as homework.

Chapter 12 Division (Whole numbers)

Objectives


1 divide whole numbers without remainders,

2 divide whole numbers with remainders,

3 divide whole numbers by multiples of 100 up to 900,

4 solve word problems.

Unit 1 Division of 4-digit whole numbers by 1-digit numbers without

and with remainder

34

Lead the pupils to understand that, there is a relationship between

multiplication and division.

e.g. 5 × 8 = 40 and = 8 or = 5

= 8 8 × 5 = 40

5 × 8 = 40

Introduce examples using long division method.

e.g. 1 3 228 ÷ 6 2 3228 ÷ 8

538 403

6 8

30 - 32

22 2

18 - 0

48 28

48 24

… 4

3 228 ÷ 6 = 538 3228 ÷ 8 = 403 Remainder 4

Exercise 1 – 2 on page 95

Select some questions in both exercises and treat it as a class work.


Unit 2 Division of 4- and 5-digit whole numbers by 2-digit numbers,

without and with remainder

Lead the pupils through examples on page 96 and guide them through

the Exercises 1 and 2.

Exercises 1 and 2 on pages 96 – 97

Select questions No. 3, 5, 7, 9, 11, 13, 17 of Exercise 1

Select questions No. 1 – 10 can be given as class work.

35


Unit 3 Division of whole numbers by multiples of 10 up to 90

Lead pupils to the examples on page 97 and guide pupils through

exercise on page 98.

Exercise on page 98

Guide the pupils through (A) questions No. 3, 5, 7, 9, 11, 13, 17 and

table under (B) No. 1 – 9 as a class work.

Unit 4 Division of whole numbers by multiples of 100 up to 900

Lead the pupils through the examples on pages 98 – 99.

Exercise on page 99

Guide pupils through this exercise as a class work. Give workbook

exercise as homework.

34

Chapter 13 Division (Fractions)

Objectives


1 divide whole numbers by fractions,

2 divide fractions by whole numbers,

3 divide fractions by fractions,

4 divide a mixed number by another mixed number.

Unit 1 Division of whole numbers by fractions

Lead the pupils through examples on page 102, ensure that you

explain this using aids (pebbles, counters, etc) to demonstrate in the

classroom.

Give more examples before guiding the pupils through the exercise.

e.g. 1 42 ÷ = 42 × = 252

2 36 ÷ = 36 × = 9 × 9 = 81, etc.

Exercise on page 103

Give this exercise as a class work. Workbook exercise can be given as

homework.

Unit 2 Division of fractions by whole numbers

Use diagrams to explain to pupils. After explaining the diagrams of

examples on pages 103–104, introduce more examples using

diagrams.

Lead the pupils to understand that any whole number divided by 1 is

the same as the whole number.

35

e.g. = 5, 7 =

and also when dividing any fraction by a whole, the whole number

becomes the denominator and 1 becomes the numerator. The division

sign also changes to multiplication sign.

e.g. ÷ 4 = ÷ = × = =

÷ 5 = ÷ = × = =


Guide pupils through this exercise as a classwork. Workbook exercise

can be given as a homework.

Unit 3 Division of fractions by fractions

Lead pupils through examples on pages 104 – 105 and give more

examples.

e.g. ÷ = × = , ÷ = × =


Guide pupils through this exercise to be given as a classwork.


Unit 4 Division of mixed numbers by mixed numbers

Introduce examples to the pupils.

e.g. 1 3 ÷ 1 = ÷ = × = = 2

2 10 ÷ 1 = ÷ = × = × = 3 × 2 = = 6

36

3 3 ÷ 2 = ÷ = × = = 1


Guide pupils through this exercise as classwork. Workbook exercise can

be given as homework. Revision Exercise 13 on page 107 can be given

as homework or weekend exercise.

Chapter 14 Division (Decimals)

Objectives


1 divide decimals by whole numbers,

2 divide decimals by multiples of 10 up to 90,

3 divide decimals by multiples of 100 up to 900.

Unit 1 Division of decimals by whole numbers

Lead pupils through the examples on page 108. Remember that this

examples will enable pupils to learn the techniques of dividing decimal

numbers by whole numbers taking the position of the decimal point to

be very important.

e.g. 1 12.15 ÷ 15 2 0.36 ÷ 8

2.43 0.045

5 12.15 8 0.36

10 0.32

2.1 0.040

2.1 0.040

0.15

0.15

…..

37


Guide the pupils through this exercise as class work. Workbook

exercise can be given as home work.

Unit 2 Division of decimals by multiples of 10 up to 90

Lead the pupils to determine how many group of 10, 20 … 90 are in a

given number.

e.g. 50 ÷ 10 = 5, 70 ÷ 10 = 7, 60 ÷ 20 = 3, 60 ÷ 30 = 2, etc.

From the above examples the answers are exact whole numbers. Lead

the pupils to more examples.

e.g. 45 ÷ 10, 145 ÷ 20, 92.5 ÷ 50, 284.8 ÷ 80

4.5 7.25 1.85 3.56

10 20 50 80

40 140 50 240

50 50 425 448

50 40 400 400

100 250 480

100 250 480

Guide pupils through exercise on page 109.

Give questions No. 1 – 15 as a class work.

Give questions No. 16 – 25 and workbook exercise as homework.

Unit 3 Division of decimals by multiples of 100 up to 900

Guide pupils to divide decimals by multiples of 100 to 900 by

introducing examples:

e.g. 1 308.6 ÷ 100 2 750.5 ÷ 500 3 ÷ 900

38

3.086 1.501 7.107

100 308.6 500 750.8 900 6396.3

300 500 6300

86 505 963

00 500 900

860 50 630

800 00 000

600 500 6300

600 500 6300

…..

Lead the pupils through the examples on page 110 after explaining the

previous examples.


Give this exercise as classwork and guide them through where they

have challenges.

Revision Exercise 14 on page 111 and work book exercise can be given

as home work.

Quantitative reasoning 12 can also be done orally in class or as home

assignment.

39

Chapter 15 Estimation

Objectives


1 round numbers to the nearest 10, 100 and whole numbers,

2 round numbers to the nearest tenth, hundredth and thousandth,

3 estimate sums, differences and products.

Unit 1 Rounding to the nearest 10, 100 and whole numbers

Lead the pupils to understand that rounding of numbers does not give

the exact value of the number but something nearer to the correct

number. Introduce examples and guide pupils on how to follow the

rules. Reference textbook page 112.

40

e.g. Round off the following numbers to the nearest ten.

1 46 2 43

1 Illus. Note that 46 is between 45 and 50.

Since it is more than halfway of the range

(40 – 50) 46 can be rounded up to 50

43 is between 40 and 45 and it is not up to halfway so it can be

rounded down to 40.

– Round off the following numbers to the nearest 100

1 365 Note that 365 is between 350 and 400,

it is more than halfway of the range (300

– 400). 365 can be rounded up to 400

Guide the pupils through the examples on page 112.


This exercise can be treated orally in the class. Exercise 2 on page 113

can be treated as class work after.

Exercise 1 has been treated orally. Workbook exercise can be given as

homework.

Unit 2 Rounding to the nearest tenth

Guide pupils to follow the rules below when rounding numbers to the

nearest tenth.

1 Identify the digit in the decimal place you have to round to.

2 Look at the digit to the right of the decimal place you have

identified. This digit is called the decider.

3 If the decider is 5 or more than 5, then round up the digit in the

decimal place you have to round to. If the decider is 4 or less than

4, then round down. (Reference to textbook page 113)

e.g. 36.65 and 38.63

41

Solution

38 . 6 7 = 38.7

decider

digit to be

rounded

Note that the decider is more than 5 and the digit 6 is rounded up to 7

(that is one decimal place).

Remember that ‘to the nearest tenth’ is the same as 1 decimal place.

In the case of 38.6 3 = 38.6

decider

digit to be

rounded

The decider is less than 5 and the digit 6 is left as it is, since 3 is less

than 5.


This exercise can be treated orally in the class.

Unit 3 Rounding to the nearest hundredth

Lead the pupils through the examples on page 114. Remind pupils the

difference between tenth and hundredth and thousandth.

e.g. 48 . 6 9 4

tenth thousandth

42

hundredth

Guide the pupils to understand that the number to the right of the

hundredth number is the decider. If the decider is 5 or greater than 5,

then the hundredth number increases by 1 but if it is less than 5 the

hundredth number remains as it is.

e.g. 48.674 to the nearest hundredth is 48.6

48.678 to the nearest hundredth is 48.68

48.698 to the nearest hundredth is 48.70

In the last case the hundredth digit is 9, when 1 is added to it, it

becomes 10.

48.698 → 48 . 6 9 8

[6+1] 0

48.70


This exercise can be treated as oral exercise in the class.

Unit 4 Rounding to the nearest thousandth

Lead pupils by introducing examples as treated under Unit 3.

e.g. 1 8.2144 rounded to the nearest thousandth is 8.214

2 100.1246 rounded to the nearest thousandth is 100.125

Exercise on page 115 can be given as oral exercise in the class.

Unit 5 Estimating sums and difference (decimals)

Explain the word estimate to the pupils. To estimate means to give an

approximate rather than an exact answer.

Let them also understand that rounding each number first makes it

easy to estimate an answer.

e.g. Actual Estimate Actual Estimate

115.85 → 116 115.85 116

43

+ 25.62 → + 26 –25.62 –26

141.47 142 90.23 90

Difference = 142 – 141.47 Difference = 90.23 – 90 = 0.23

= 0.53

Guide the pupils to always round off decimal numbers to whole

numbers before estimating and also the difference between the

estimate and actual numbers will never be one or more.


Guide the pupils through this exercise as a classwork.

Unit 6 Estimating products (decimals)

Introduce example to the pupils, remember that, there is no difference

in the steps to follow when evaluating product of numbers.

e.g. 8.61 × 2.2

Actual Estimate

8.61 — 9

× 2.2 — × 2

1722 18

1722

18.942

Difference = 18.942 – 18 = 0.942


Treat this exercise as a classwork

Workbook exercise and Revision Exercise 15 on page 116 can be given

as homework.

Chapter 16 Number line (Integers)

44

Objectives


1 add and subtract whole numbers, using a number line,

2 draw number lines extended beyond zero and identify positive and

negative numbers,

3 add positive numbers, using a number line,

4 subtract positive numbers, using a number line.

Unit 1 Addition and subtraction of whole numbers using number

lines

Guide the pupils to recall that in Primary 1 – 3, whole numbers were

added and subtracted on a number lines.

Select two questions from exercise on page 117–119 as an exercise

(revision).


Guide the pupils through this exercise as a classwork. Ensure that you

go round to check them if they have any challenges (may be some

may have forgotten)

Unit 2 Extending the number line

Draw the number line on the board to show the difference between the

previous number lines treated and the present one.

Illus.

45

Explain the difference between the two and guide the pupils to

understand that the present one extends with negative numbers to

the direction left of zero and positive numbers extend to the right of

zero.

Explain to the pupils that numbers to the left of zero are negative and

as the numbers move further to the left they come smaller.

e.g. 0 is greater than -1, -2, -3, etc.

-3 is greater than -6

Numbers to the right of 0 are greater than 0 and as they move further

to the right they become bigger.

Illus.

From the number line we can deduce that

-5 < -2, -2 < 0, 3 >1, 0 < 4, etc.

Symbol of inequalities > or < are the same

Position of bigger Position of smaller number

number (open side — > — (pointed side of the symbol)

of the symbol)


Guide pupils through this exercise as a classwork. Guide them on how

to recognize when a number is negative or positive, and finding the

assigned values of letters on the number line.


Guide pupils through this exercise by making them to put the correct

symbol in the box as a class work.

46

Unit 3 Addition of positive integers, using a number line

Guide the pupils to follow the steps below when adding a positive

integers together.

1 start at the first number.

2 move by counting the second number further to the right.

e.g. 1 2 + 3 2 -2 + 6 3 2 + 3 = 5

An integer is a positive and negative whole numbers. Lead the pupils

through examples on pages 122–123


Guide the pupils through this exercise as a classwork. Give workbook

exercise as homework.

Unit 4 Subtraction of positive integers, using a number line

Lead the pupils through the Activity on page 124. Guide the pupils

through the examples on pages 124 – 125. Explain the examples using

the same principles used under Unit 3.


Guide the pupils through this exercise as a classwork. Workbook

exercise and Revision exercise 16 can be given as home work.

47

Chapter 17 Algebraic processes

Introduction to simple algebra

Objectives


1 solve simple equations,

2 solve equations, using the balance method,

3 solve word problems involving equations,

4 simplify expressions involving like and unlike terms,

5 find the value of algebraic expression by substitution.

Unit 1 Solving simple equations

This topic was discussed in Book 4 so is more of revision exercise.

Guide pupils to recall by introducing some examples.

e.g. 1 Solve the following:

1 x + 6 = 20 2 y – 4 =16 3 = 3 4 = 6

48

x = 20 – 6 y = 16 + 4 × 5 = 3 × 5 × z = 6 ×

z

x = 14 y = 20 9 = 15 6z = 12

=

z = 2


Treat this exercise as a classwork.

Unit 2 Solving equations, using the balance method

Introduce the balance scale and use it to demonstrate (illustrate) in

the class, on how to measure the weight of objects.

Lead the pupils to examples and compare the similarity between the

two.

e.g. 1 x + 3 = 6 2 y – 6 = 2 3 = 2

x + 3 – 3 = 6 – 3 y – 6 + 6 = 2 + 6 × = 2 ×

x = 3 y = 8 x = 6

Note that 3 is subtracted Note that 6 is added Note that 3 is

from both sides to both sides multiplied to

both

sides

Explain why numbers are added, subtracted and multiplied to both

sides of the equations, this is called the balance method.

Another example is a case involving combination of all the 3 steps in

one equation.

e.g. 4x – 6 = 10 y + 2 = 4

49

4x – 6 + 6 = 10 + 6 and y + 2 – 2 = 4 – 2

4x = 16 y = 2

= y × = 2 ×

x = 4 2y = 6

=

y = 3

Guide the pupils through examples on pages 129 – 131 after

explaining the examples above. Encourage pupils to use the number

line method of addition and subtraction in eliminating some numbers.


Select questions (A) No. 1 – 4

Select questions (B) No. 1, 3, 5, 7, 10, 12, 17, 23, 29, 31, 33 and 35

To be given as classwork. Workbook exercise can be given as

homework.

Unit 3 Word problems involving simple equations

Give examples of word problems in simple form and ask pupils if they

can put the statement into equations.

e.g. 1 If I add four to a number the answer will be 10. What is the

number?

2 A number is subtracted from 15 and the result is 8. What is

the number.

Solution

50

1 Let the number be x 2 Let the number be y

4 + x = 10 15 – y = 8

x + 4 = 10 15 – y + y = 8 + y

x + 4 – 4 = 10 – 4 15 = 8 + y

x = 6 15 – 8 = 8 – 8 + y

y = 7

The number is 7

Guide pupils to follow the steps below when solving word problems.

1 Choose a letter to represent the unknown.

2 Form the equation.

3 Solve to find the unknown (value of letter).

Lead the pupils through the examples on page 133.


Guide the pupils through this exercise as a classwork in the class.

Unit 4 Like and unlike terms

Use examples to explain to the pupils.

e.g. If you add 3 oranges to 8 oranges the result will be 11 oranges.

Represent oranges by 0

30 + 80 = 110

If you subtract 5 apples from 12 apples the result will be 7 apples

Let apples be represented by A

12A – 5A = 7A

Explain what co-efficient means

e.g. 5A = A + A + A + A + A

Coefficient is the number of objects

51

Guide the pupils through the examples on pages 135 – 136. Like terms

are of the same objects or type. When they are added or subtracted

the result will always be the same coefficient as illustrated above.


Questions (A) No. 1 – 10 and (B) No. 1 – 14 can be treated orally in

the class.

Question (C) No. 1 – 8 can be treated in the class as class work.

Unlike term

Guide the pupils through Activity on page 137, allow them to list like

objects and unlike objects. Introduce some examples,

John has 10 apples and Yakubu has 12 banana (B)

This can be written in mathematical (algebraic expression) form as.

10A + 12B

A and B are not the same type

e.g. 8x + 2x + 10y – 3x – 5y

To simplify the above, we group like terms

8x + 2x – 3x + 10y – 5y = 7x + 5y

and simplify as shown above


Guide the pupils through this exercise as a classwork.

Unit 5 Substitution

Pupils are already familiar with algebraic expression.

e.g. 6x + 2y, 4m – 2n, etc.

If each letter is assigned a number, the expression can be calculated

e.g. a = 4, b = 2, c = 1

52

1 3c + 2a – B 2 a + 3c + B 3 = =

3(1) + 2(4) – (2) (4) + 3(1) + (2) = = 8

3 + 8 – 2 4 + 3 + 2

11 – 2 9

9

The above calculation is called substitution.

Lead the pupils through the examples on page 140 – 141



Revision exercise 17 on page 142 and workbook exercise can be given

as homework.

53

Chapter 18 Mensuration and geometry

Money

Objectives


1 recognise currencies used in Nigeria and other countries,

2 convert from one currency to another, using the rate exchange,

3 solve problems involving profit and loss,

4 solve problems involving simple interest,

5 solve problems involving discount and commission,

6 solve problems involving money transactions.

Unit 1 Recognising the Naira and the currencies of other countries

Lead the pupils to the table of currency of Nigeria and other countries

on page 145. Revise conversion of money with pupils. Guide them

through examples on page 145.

Exercise on page 145 can be treated as class exercise.

Unit 2 Rates of exchange

Lead pupils to understand that when traveling from one country to

another the rate exchange is used to convert money into other

currency. The table on page 146 shows the value of Nigeria $ to other

country currency.

Examples

Find the value of the following in $

1 £60 2 $250 3 €80

54

1 £1 = $260 2 $1 = $160 3 €1 =

$210

£60 = $260 × 60 = $160 × 250 €80 = $210

× 80

= $15 600 = $40 000 = $16 800

Convert $80 000 in a) £ b) $

a) $80 000 = × £1 = £307.70

b) $80 000 = × $1 = $500


Treat as a classwork

Unit 3 Profit and loss

Lead the pupils through the examples on page 147 – 148

Recall the following from Book 4

Gain/Profit → when selling is greater than or more than cost

Profit = SP – CP

Loss → selling is less than cost price

L = CP – SP

This terms should be explained and applied.


Can be treated as classwork

Profit and loss percent

Explain the following

55

Profit percent (P%) = × 100%

Loss percent (L%) = × 100%


Can be treated as classwork


Unit 4 Simple interest

Recall that:

Simple Interest (I) =

P = Principal

R = Rate

T = Time

I = Interest

A = Amount

e.g. find I when P = $8 000 R = 5% T = 2 years

I = = = $800

Amount (A) = I + P = $800 + $80 000 = $8 800


Treat as classwork

Calculating the principal, rate and time

I = ⇒ P = ⇒ R = ⇒ T =

56

Guide the pupils to substitute the values given to get what is required.

e.g. P = $150 000 I = $20 000 T = 4 years R = ?

R = = = 3 % = 3 %, etc.


Can be treated as class work.

Unit 5 Discount and commission

Explain discount and commission and where is commonly applied in

everyday life activities.

Discount → it is the amount of money that is removed or taken off the

actual cost of an article.

e.g. A price of an article marked $12 000 and the percentage

discount is 15%. Find the discount if sales price is $10 000

If sales price is $10 000

Marked price = $12 000

Sales price = $10 000

Discount = $20 000

Percentage discount = × 100%

= × 100%

= 16.7%


Treat as class work

Commission

An amount of money that is paid to an agent.

Yinka sold $130 000 worth of goods from a distributor and received

8% as commission. Find the commission.

57

Value of good = $130 000

Commission % = 8%

= × $130 000

= $10 400


Treat as a classwork.

Unit 6 Transactions involving money

Guide the pupils through the examples on page 160. Explain the

examples and guide the pupils through.


Treat as a class work


55

Chapter 19 Length

Objectives


1 find the perimeter of polygons and composite shapes,

2 establish the relationship between and π,

3 find the circumference of a circle given its radius or diameter,

4 solve word problems.

Unit 1 Perimeter of polygons and composite shapes

Explain the terms perimeter and circumference. Perimeter is the

distance round an object. Circumference is the distance round a

circular objects.

Engage pupils in practical activities.

Group the pupils and ask them to use ruler or tape to measure

perimeter of objects (Perimeter of board, top of table, classroom, etc.)


Give this as classwork. Introduce the pupils to formulii which will make

their work easier.

Perimeter of rectangle = L + B + L + B = 2L + 2B = 2(L + B)

Square = L + L + L + L = 4L


Treat this exercise as a classwork. Guide them through if they face

some challenges in some of the questions. Workbook exercise can be

given as homework.

56

Unit 2 Establishing the relationship between c/d and π

Introduce the pupils to the Activities under this topic on page 165.

Allow them to discover the radius, diameter and circumference using

sticks and string or rope.

2 radii = diameter

Plural of radius is radii

Observation of pupils after completing the table on page 166

Relation of diamater and circumference from the table.

Unit 3 Circumference (Perimeter of circles)

From Unit 2, the result of table shows that the circumference of a

circle is a little more than three times the diameter. Lead the pupils to

understand that the result of the table if measured accurately shows

that the circumference will be close to 3.14 times the diameter.

Circumference = 3.14 × diameter.

Introduce π and let them understand that the

Value of π = d 3.14

∴ Circumference (C) = 3.14d d = diameter

and π = =


Treat this exercise as classwork.

Unit 4 Drawings circles

Guide pupils to master different methods of drawing circles (using

strings, round object, compasses, etc).


Treat this as classwork activity.

57


Lead the pupils through the examples, remind them of the following:

C = 3.14d or C = 2πr

π = or 3.14 (approximated)

Perimeter of rectangle = 2(L + B)

Perimeter of square = 4L

Perimeter of other shapes = the length of sides are added

together

= sum of all sides.


Treat this as classwork exercise and guide them where there are

challenges. Workbook exercises and Revision exercise 19 can be given

as homework.

58

Chapter 20 Weight

Objectives

At the end of this chapter, pupils should be to:

1 convert from one unit of weight to another,

2 solve problems involving weight, using the basic operations.

Unit 1 Conversion of the units of weight

Guide pupils to weight objects using scales on their own. Guide them

on how to read the scales. Introduce them to the units of weight.

1 kilogram (kg) = 1 000 grams (g)

1 metric tonne = 1 000 k

To change g to kg – divide g by 1 000

To change kg to g – multiply by 1 000

To change tonne to kg – multiply by 1 000

Use examples to illustrate the above

59

e.g. 1 2.5 kg = 2.5 × 1 000 g = 2 500 g

2 16 480 tonnes = 5.6 × 1 000 kg = 5 600 kg

3 5.6 tonnes = 5.6 × 1 000 kg = 5 600 kg

4 1 480 kg = tonnes = 1.48 tonnes

Exercise 1 – 2 on page 172 – 173

Guide the pupils to study the diagrams and graph and lead them

through the exercises.

Unit 2 Basic operations on weight

Use examples to explain by selecting two questions from Exercise 1 on

page 173.

e.g. Kg g Kg g

46 854 161 136 (1 136 – 478)

+ (33 629) – (129 478) = 658 g

80 483 — 1 483 31 658

↓ ↓ 79+1 1+483

kg g


Treat this exercise as class work (excluding No. 4 and 10)

K g 3 934

4 237 kg g

× 5 4 15 736

21 185 – 12

237g × 5 = 1 185g 3 from kg to g

= 1 kg 185 g ×

4 kg × 5 = 20 kg 1 000

20 kg + 1 kg + 185 g +736

60

21 kg 185 g 3 736

– 3 736

Explain the above if possible give more examples


Select questions No. 1, 3, 5, 7, 9, 11, 13, 15, 17 and 19 to be given

as class work.

Workbook can be given as homework.

Unit 3 Word problems involving weight

Select two questions and treat as examples and give the rest as class

work. workbook exercise and Revision exercise 20 can be given as

home work.

Chapter 21 Time

Objectives


1 find the duration between one time and another,

2 find distance covered within a length of time,

3 find the average speed of a moving object given the total

distance travelled and the time taken.

Unit 1 Average speed

61

Lead pupils through the information time on page 178. Ensure that

pupils learn the tables, you can even make them recite the table

everyday.

Guide the pupils through the examples on page 179. Lead pupils to

understand that

Average speed =

In most the speed is expressed as km/hr or m/s


Treat this exercise as classwork.


Guide pupils to complete the table as classwork.


Guide pupils through this exercise as classwork.


Guide pupils through this exercise (average speed = m/s)


Select one or two questions as an example and guide pupils through

the rest as class work. Workbook exercise should be given as

homework.

Chapter 22 Temperature

Objectives


1 recognise the idea of temperature,

62

2 identify the mercury thermometer and read the thermometer,

3 identify the clinical thermometer and interpret the reading of

human temperature,

4 identify the maximum and minimum thermometer and interpret

the temperature of our environment,

5 establish the relationship between degrees Celsius (ºc) and

Fahrenheit (ºF)

Unit 1 Idea of temperature

Introduce items like water heater or boiler, ice block, cold water, warm

water, thermometer, etc. Once the pupils see this items, they will be

thinking of hot and cold.

Ask them questions about the items (what they are used for). Guide

them to discover the concept of temperature by practical

demonstration using some of the mentioned items.

Unit 2 Mercury thermometer

Introduce the mercury thermometer to the pupils. Ask questions (or

commonly seen where they can be found, hospitals, lab, etc). Guide

pupils on how to use the mercury thermometer inside the classroom.

Group the pupils and allow them to take their friends temperature.


Treat this exercise orally in the class.

Unit 3 Clinical thermometer

63

Explain how the clinical thermometer works and for accurate reading it

is divided into ten divisions. Allow the pupils to take their own

temperature by placing the thermometer under their armpit and guide

them on how to take average temperatures.


You can treat this exercise orally in the class. Workbook exercise can

be treated as classwork.

Unit 4 Maximum and minimum thermometer

Explain to the pupils where this type of thermometer is used and how

it works.


Guide pupils through this exercise in the class.


Guide pupils through this exercise. Explain questions (A) since it

involves graph (can be treated orally).

Questions (B) and (C) can also be treated orally. Workbook exercise

can be treated as classwork or homework.

Unit 5 Relationship between degrees Celsius and degrees Fahrenheit

Guide the pupils through the relationship between degree Celsius and

degrees Fahrenheit.

1 Celsius unit = Fahrenheit unit

= 1.8 Fahrenheit unit

= Fahrenheit unit

Introduce examples

64

1 40ºC to be converted to degrees Fahrenheit

F = × C + 32

F = × 40 + 32 = 72 + 32 = 104

40ºC = 104ºF

2 85ºF is converted to degrees Celsius

C = (85 – 32)

C = (53)

C = × 53

C = = 29.4º

C = 29.4º


Treat this exercise as classwork. Workbook exercise can be given as

homework.

65

Chapter 23 Area

Objectives


1 find the area of squares and rectangles,

2 find the area of compound shapes,

3 find the area of a right-angled triangle,

4 solve word problems involving area.

Unit 1 Area of squares and rectangles

The area of a plane shape is the amount of flat space that it occupies.

Area of rectangles = length × breadth

A = L × b

Area of square = length × length

A = L × L = L2

Unit of Area are square centimeter (cm2)

Square metre (m2), square kilometer (km2)


Guide the pupils through this exercise by selecting some questions

Questions (A) No. 1 – 8

(B) No. 1 – 5

(C) No. 3, 5, 7, 11 Can be treated as classwork

(D) No. 3, 5, 7, 11

66

(E) No. 3, 5, 7, 11

Unit 2 Area of compound shapes and shaded parts

A compound shape consists of more than one plane shape. Guide the

pupils to divide a compound shape into easily be calculated.

e.g. Find the area of this shape

Illus.

Area of A = 50 cm × 16 cm = 800 cm3

Area of B = 16 cm × 10 cm = 160 cm3

Area of C = 50 cm × 16 cm = 800 cm3

Total area = 1 760 cm3



Unit 3 Area of a right-angled triangle

Introduce the shape to the pupils and ask them to list shapes which

are right-angle triangle. Lead the pupils through page 199 for more

explanation.

Illus.

Area = × b × h

Lead the pupils to examples on page 200


Select questions (A) No. 1 – 6 and 18 – 20

can be treated as classwork

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(B) No. 1 – 5

Unit 4 Word problems involving area

Guide the pupils through the examples on page 201.

Exercise on page 202 can be treated as a classwork.

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Chapter 24 Volume

Objectives


1 measure the volume of cuboids and cubes using unit cubes,

2 measure the volume of cuboids and cube, using formula,

3 compare the volume of spheres and cuboids.

Unit 1 Volume of cuboids and cubes, using the unit cube

The amount of space a solid takes up is called its volume. Lead pupils

through example on page 205, the small cube is 1 cm3, the bar A has

8 small cubes.

Guide the pupils through the Activity on 205

1 Cuboid

2 8 cm3 Explain the solution

3 8 cm3

4 a) 1 cm × 8 = 8 cm b) 1 cm c) 1 cm


Guide the pupils through this as classwork.


Guide the pupils through this as classwork.

Unit 2 Volume of cuboid and cubes, using the unit formula

Lead pupils to understand that using small cube to determine or find

the volume of cube or cuboid takes time, therefore calculation method

can be used to calculate the volume cubes and cuboids.

Volume = length × breadth × height


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Guide pupil through this exercise, allow the pupils to do the

measurements on their own and find the volume by completing the

table questions No. 1 – 3.

Questions No. 4 – 15 can be found by the pupils using the formula

V = L × B × H

Questions No. 16 – 19 can be given as homework.


This exercise can be treated as classwork.

Guide pupils on how to use the formula

V = L × B × H

to find any L, B, H when any two and volume is given.

e.g. Find the height of a cuboid with volume = 210 cm3,

Length = 6 cm and breadth = 5

L = 6 cm B = 5 cm V = 210 cm3

V = LBH → H = = = 7 cm

Height (H) = 7 cm


Treat this exercise as classwork

Unit 3 Volume of a sphere

Introduce a solid sphere (football, globe, orange, etc) to the pupils.

The earth is spherical in shape.

Volume of sphere = πr3

Volume of hemisphere = × πr3 = πr3

e.g. find the volume of a sphere with radius 14 cm

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Volume = × × 14 cm × 14 cm × 14 cm =

= 11 498 cm3

Remind pupils that diameter = d = 2r (r = radius)

r =


Select questions No. 1, 2, 7, 12, 14, 23, 27, 29, 32 to be treated as

classwork.

Unit 4 Structure of the earth and volume of a sphere

Guide the pupils through the following exercises to treat as class work.


Revision exercise 24 and workbook exercises as homework.

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Chapter 25 Capacity

Objectives


1 discover the relationship between the litre (l) and the cubic

centimeter (cm3).

Unit 1 Relationship between litre and cubic centimeter

Remind pupils on definition of volume. The amount of space that a

solid occupies is called volume.

1 litre = 1 000 cm3 (10 cm × 10 cm × 10 cm)

Litre is the metric unit of liquid measure

Capacity of a container is the ability to hold or receive.

Lead pupils to examples on conversions.

e.g. Convert the following to cubic centimetres.

1 5 litres 2 3.4 litres

1 5 litres = 5 × 1 000 cm3 = 5 000 cm3

2 3.4 litres = 3.4 × 1 000 cm3 = 3 400 cm3

Note: 1 litre = 1 000 millilitres (ml)

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1 litre = 100 centilitres (cl)



Treat the exercises as a classwork. Guide pupils to have idea of

quantity or volume of containers, spoon, bucket, bottles, etc.


Chapter 26 Lines, angles and bearing

Objectives


1 identify parallel and perpendicular lines,

2 measure and draw angles, using the protractor,

3 identify complementary and supplementary angles,

4 tell direction accurately, using angles.

Unit 1 Parallel and perpendicular lines

Revise the following from book 4

1 A line that is in the same position with the flat surface is said to

be horizontal.

2 A line that stands upright to a flat surface is said to be vertical.

3 A line that is neither horizontal nor vertical is oblique.


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Treat these exercises orally in the class with the pupils.

Parallel lines

Lead pupils to observe the classroom, then tell them to list parallel

lines (shapes).

Illus.

Two straight lines that are always the same distance apart are called

parallel lines.

e.g. rail lines, electric cable on a pole, etc.

Perpendicular lines

Lead pupils to name (list) perpendicular lines in the classroom.

Illus.

Two lines that are at right angles to each other are said to be

perpendicular.

Guide pupils to the practical exercise on page 218 to be treated orally.

Unit 2 Measuring and drawing angles

Introduce a protractor to the pupils and explain how is used in

measuring angles. Ensure that you go round to assist each pupils on

how to use it.

The unit of measuring angles is the degree. Lead them through the

example on page 219.


Guide the pupils through this exercise, make sure that you take your

time putting the pupils through when they have some challenges.

Drawing angles

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Guide the pupils on how to draw angles using the protractor. Lead

them to the steps under the example on page 220.

Ensure that all the pupils have protractors. Allow each of them the

opportunity to identify the scales on the protractor and also measure

and draw given angles accurately.


Treat this exercise as a classwork in the class. Workbook exercise can

be treated as homework.

Unit 3 Complementary and supplementary angles

Guide the pupils through Activity 1 and 2 on page 221. Explain

complementary angles (angles that sum up to 90º) e.g. 34º + 56º =

90º and supplementary angles (angles that sum up to 180º) e.g. 95º +

85º = 180º.

Oral exercise on page 221

Treat this exercise in the class. Guide pupils to use addition process to

find the complementary and supplementary angles.


Encourage pupils to use the process mentioned (addition process) to

find the values of the letter.

e.g. Illus. y + 62º = 180º

y = 180º – 62º = 118º

Unit 4 Compass bearing

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Revise the cardinal points of a compass with the pupils (treated in

book 4)


Treat this as a classwork (may be orally). Workbook exercise can be

given as homework.

Chapter 27 Plane shapes

Objectives

74

At the end of the chapter, pupils should be able to:

1 identify types and state basic properties of triangles,

2 identify quadrilateral and state basic properties of quadrilaterals,

3 identify component parts of a circle and draw circles.

Unit 1 Triangles

A two-dimensional shapes that has three sides and three angles is a

triangle. Introduce an example and explain.

The three sides are AB, BC and CA

The angles are or < A, or < B Illus.

and or < C

Remind the pupils that the sum of angle in any triangle is 180º

<A + <B + <C = 180º or + + = 180º

Guide pupils to be able to identify the sides of a triangle.

Lead pupils to types of triangles. (Reference to textbook page 226)

with their properties. Guide pupils to Activity on page 226.

Assist the pupils if they have challenges under this activity.

Guide them to understand that

1 the sum of angles in a triangle is 180º

2 Triangles have three sides

3 The sum of two sides in triangle is greater than the third side.


Treat questions (B) No. 1 – 10 as oral exercises

Treat questions (A) No. 1 – 19 as classwork


Use examples to explain

75

Illus. Illus.

+ + = 180º A + B + C = 180º

40º + + 65º = 180º 20º + 18º + = 180º

= 180º – 40º – 65º = 180º – 20º – 18º

B = 75º C = 142º


Guide the pupils through this exercise as a classwork. Workbook

exercise can be homework.

A two-dimentional shape that has four sides is called a quadrilateral.

e.g. are square, rectangle, parallelogram, kite, rhombus, trapezium,

etc.

Special quadrilaterals

All the sides are equal

The four angles are equal (90º)

The diagonal bisect each other at right-angles

It has 4 lines of symmetry

Rectangle

Opposite sides are equal

The four angles are equal (90º)

The diagonal bisect each other at right-angles

It has 2 lines of symmetry

Parallelogram

Opposite sides are equal and parallel

The angles opposite each other are equal

It has no line of symmetry

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The diagonal bisect each other

Trapezium

It has one pair of parallel sides

The sides are not equal

The angles are not equal

It has no line of symmetry

Rhombus

All the sides are equal

Opposite sides are parallel

It has two line of symmetry

The lines of symmetry meet at right angle

Lead the pupils to discover some of the properties of quadrilaterals.

Explain each of them with their properties.

The sum of angles in quadrilateral is 360º


This exercise can be given as oral exercise in the class.

Guide pupils through examples on page 231


This exercise should be treated as classwork. Workbook exercise can

be given as home work.

Unit 3 Circles

Draw the circle on the board and label the important parts.

77

Illus.

Allow the pupils to draw it in their note.


Treat this exercise as a classwork

Drawing circles

This topic as been treated in one of the chapters but guide the pupils

through the example and the Activity.


Treat this exercise as a classwork. Revision exercise 27 can be given as

home work.

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Chapter 29 Three-dimensional shapes

Objectives


1 identify prisms and pyramids

2 draw nets of 3-D shapes

Unit 1 Prisms and pyramids

Introduce solid shapes (different types of prisms and pyramids). A

prism is solid with uniform cross section (top and bottom faces are the

same).

e.g. triangular prism, rectangular prism, square or cube prism, circular

prism, etc.

A pyramid is a solid with a non-uniform cross-section. The top has

only one vertex.

Allow the pupils to identify prism and pyramid from the solid models in

the class.

e.g. of pyramids are triangular-based pyramid, square based

pyramid, circular-based pyramid, etc.

79

Explain the following vertex, face, edge using the shapes. Lead the

pupils through the table of properties of the shapes on page 239.


Treat this as oral exercise in the class.

Unit 2 Drawing nets of 3-D shapes

Lead pupils through Activities on pages 240 – 243. Guide them in

drawing of the nets of the shapes, then cut the drawings and fold to

shape. Teacher should ensure that all pupils participate in these

activities. Assist them in the drawing and cutting to shape.

Give workbook exercise as classwork. Exercise 1 – 2 on pages 241 –

242 can be given as homework.

Revision exercise 28 can be treated orally using the nets of the

shapes.

Chapter 29 Everyday statistics

Data presentation

Objectives


1 read and interpret

– bar graph

– pictograms

2 write tallies and draw frequency tables

Unit 1 Pictograms and bar graphs

Guide pupils to select data after grouping them e.g. Height of pupils,

weight in kg, those who like a particular fruits, etc.

80

Guide pupils on how to use tally to represent data on frequency

table (tabular form and easy to read)

Pictogram diagrams are ways of giving information through pictorial

figures on designs. Guide the pupils on how to represent data using

pictogram and how to answer pictogram questions.

Bar graphs is a way of representing information pictorially.

Rectangular bars of equal widths are used to represent bar graphs.

Guide the pupils on how to draw bar graphs and how to answer

questions using bar graph.

Guide the pupils through examples on page 246 – 247


Treat this orally in the class.

Unit 2 Tally marks and frequency tables

Explain what is meant by tally. It is fast way of recording information

or data.

e.g. 1 = I

2 = II

3 = III

4 = IIII

5 = IIII

6 = IIII I

7 = IIII II


Exercise 1, 2 and 3 on pages 249 – 251

Guide pupils through these exercises as a classwork. Workbook

exercise can be given as homework.

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Chapter 30 Measures of central tendency

Objectives


1 find the mean of given data,

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2 find the mode of given data,

3 find the median of any given data.

Unit 1 Mode

Mode is the item or number that occurs most frequently in a given

data. Lead pupils to collect data themselves.

e.g. Days on which pupils were born

Monday, Tuesday, … Saturday

Guide them to draw table of frequency table and prepare a tally of the

data.

e.g. Days of the week Tally Frequency

Monday

Tuesday

Sunday

Allow the pupils to identify the mode from their table.


Give this exercise as a classwork.

Unit 2 Mean

Mean is the average of a given set of numbers.

Mean =

Lead the pupils to collect data from their environment e.g.

Measurement of height of pupils, age of pupils, etc.

Divide pupils into group of 10 or 15 first and ask them to find the

mean of their data by guiding them.

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e.g. find the mean of the weight given

10 kg, 15 kg, 20 kg, 25 kg, 30 kg, 28 kg

Mean =

Mean = = 21 kg


Select some question and treat it as classwork.

Unit 3 Median

The median of a set of numbers is that number that is exactly at the

middle of the set of numbers when they are arranged in order of size.

Lead the pupils through example. Find the median of the following set

of numbers:

20, 30, 10, 90, 80, 100, 70

1 Arrange the numbers in ascending order (from the least to the

largest)

10, 20, 30, 70, 80, 90, 100

↓

middle

number is the median

Median = 70

2 5, 2, 5, 6, 8, 6, 2, 2

2, 2, 2, 5, 5, 6, 6, 8

5 = = → the two numbers in the middle are added and

divided by two.

Median = 5


84

Treat this exercise as a classwork. Workbook exercise and Revision

exercise 30 can be given as homework.

Chapter 31 Chance

Objectives


1 discover the meaning of chance,

2 prepare frequency tables, using coins and dice.

Unit 1 Chance

Guide pupils to toss a coin or dice for (allow them to predict the

results first before tossing).

Guide the pupils to discover likely and unlikely events when throwing

dice or coins.

Guide them to throw the examples given on page 260

Discuss what can happen, using real-life activities of thing that are

certain to happen.

Guide pupils to realise that chance is the possibility of something

happening.


Treat this exercise orally

Unit 2 Experiment

Lead pupils to toss a coin or dice for at least 20 times and record the

result.

e.g. Tally f Tally Frequency

H 1 III 3

T 2 II 2

85

3 IIII 4

4

5

6

Ask questions from their results.


Involve them in Activity 1 and 2 (Group the pupils for the activity). Let

them compare their results.

Guide them to use their result (frequency table) to draw bar graph.


Treat this exercise orally with the pupils. Workbook exercise and

Revision exercise 31 can be treated as homework.