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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.

Exercise 1 2, page 9

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.

Exercise 1 4, page 11

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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

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

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.

Exercise 1 2, page 16

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

6

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

7

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

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

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

10

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