Longhorn

Mathematics

Revision

Grade 5

Philip Obwoge

Leonard King’oo

Isaac Ochoo

Tonnia Masai

Published by

Longhorn Publishers PLC

Funzi Road, Industrial Area

P.O. Box 18033-00500 Nairobi, Kenya

Tel: +254 02 6532579/81, +254 02 558551,

+254 708 282 260, +254 722 204 608

enquiries@longhornpublishers.com

www.longhornpublishers.com

Longhorn Publishers (Uganda) Ltd

Plot 4 Vubyabirenge Road, Ntinda Stretcher

P. O. Box 24745 Kampala, Uganda

Tel: +256 414 286 093

Email: ug@longhornpublishers.com

www.longhornpublishers.com

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Kinondoni District, Light Industry

Mikocheni Plot No. 92

P.O. Box 1237 Dar es Salaam,Tanzania

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Email: longhorntz@longhornpublishers.com

www.longhornpublishers.com

Longhorn Publishers (Rwanda) Ltd

Remera opposite COGE Bank

P.O. Box 5910 Kigali, Rwanda

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Email: rwanda@longhornpublishers.com

www.longhornpublishers.com

transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise

without the prior written permission of the publisher.

First published 2022

ISBN 978-9966-64-359-9

Printed by Autolitho Ltd., Enterprise Road, Industrial Area,

P. O. Box 73476-00200, Nairobi, Kenya.

iii

Table of Contents

Term 1 Opener assessment .................................................................................................... 1

1 Numbers .................................................................................................. 3

Whole numbers....................................................................................................................................... 3

Addition..................................................................................................................................................... 17

Term 1 Mid term assessment ................................................................................................. 23

Subtraction............................................................................................................................................... 25

Multiplication ........................................................................................................................................... 30

Division...................................................................................................................................................... 35

Term 1 End term assessment ................................................................................................. 40

Term 2 Opener assessment .................................................................................................... 41

Fractions ................................................................................................................................................... 43

Decimals ................................................................................................................................................... 52

Term 2 Mid term assessment ................................................................................................. 58

2 Measurement........................................................................................... 60

Length........................................................................................................................................................ 60

Area ........................................................................................................................................................... 67

Volume....................................................................................................................................................... 73

Capacity.................................................................................................................................................... 77

Term 2 End term assessment ................................................................................................. 84

Term 3 Opener assessment .................................................................................................... 86

Mass ........................................................................................................................................................... 88

Time ........................................................................................................................................................... 96

Money........................................................................................................................................................ 102

3 Geometry................................................................................................. 105

Lines ........................................................................................................................................................... 105

Term 3 Mid term assessment ................................................................................................. 108

Angles........................................................................................................................................................ 110

3-D objects............................................................................................................................................... 116

4 Data handling .......................................................................................... 118

Data representation .............................................................................................................................. 118

5 Algebra .................................................................................................... 125

Simple equation ...................................................................................................................................... 125

Term 3 End term assessment ................................................................................................. 128

Answers..................................................................................................................................... 130

TERM 1

OPENER ASSESSMENT

1. Write eight hundred and thirty-ﬁve in symbols.

2. What is the place value of digit 6 in the number 6 032?

3. Work out the total value of digit 4 in the number 3 462.

4. Arrange the following numbers in ascending order: 666, 606, 626, 662, 660

5. Kirwa planted 567 tea bushes on his farm. How many tea bushes did he plant to the

nearest ten?

6. Write the ﬁrst four multiples of 7.

7. Circle the odd numbers in the following set.

12, 19, 34, 47, 90, 53

8. Write the next number in the pattern

45, 48, 53, 60, ______

9. A school has 456 boys and 327 girls.Determine the number of learners in this school.

10. The government gave a sub-county 4 566 books in the ﬁrst term and 3 258 in the

second term. Find the total number of books given to the school.

11. Find the value of 43 x 12.

12. A hall has 46 benches. Each bench can sit 16 people. Calculate the total number of

people who can sit in the hall at one time.

13. A teacher bought 27 sweets. The teacher shared the sweets equally among 8 learners

and took the sweets that remained. Find the number of sweets that remained.

14. Change 7

into an improper fraction.

15. Write 43 hundredths as a decimal.

16. What is the place value of digit 6 in the number 3.56?

17. The length of a wire is 234 cm.Write the length of the wire in metre and centimetres.

18. Calculate the perimeter of the shape below.

3 cm

7 cm

19. Calculate the area of the shape below.

20. How many quarter kilogramme masses can balance 3 kg?

21. Calculate the volume of the cube below.

22. Work out the number of 1-litre bottles that can be ﬁlled by 24-quarter litre bottles.

23. Salome woke up at 5.30 to go to school. State whether this time is a.m. or p.m.

24. How many hours and minutes are there in 166 minutes?

25. Salim attended school for 14 weeks in a term. How many days did he attend school?

26. How many notes of sh. 200 can be obtained as change from sh. 1 000 note?

27. Draw a reﬂex angle.

28. Name two objects that have the shape of a circle.

29. Draw the next two shapes in the pattern.

_____, _____

30. Simplify:

15r – 4r – 2r

Place value of digits up to hundreds of thousands

Activity 1

1. Draw a place value chart.

2. Write the number 462 395 in the place value chart you have drawn.

3. Identify is the place value of digit 2?

4. Write the place value of the other digits.

Using a place value chart, identify the place value of digit 3 in the number 370 162.

Working

Write the number 370 162 in the place value chart as shown below.

Hundreds of

thousands

Tens of thousands Thousands Hundreds Tens Ones

3 7 0

6 2

The place value of digit 3 is hundreds of thousands.

Example 1

Assessment Task 1

1. Complete the place value chart below.

Number Hundreds of

thousands

Tens of

thousands

Thousands Hundreds Tens ones

(a)

674 439

(b)

57 420

(d)

142 983

2. What is the place value of digit 7 in each of the following numbers?

(a) 327 682 (b) 743 002 (c) 473 921

(d) 74 326 (e) 341 473 (f) 67 321

3. Write the place value of the underlined digits.

(a) 643 651 (b) 745 903 (c) 453 261

(d) 86 902 (e) 10 283 (f) 360 471

Numbers

Whole Numbers

Further Assessment 1

1. Identify the digit in the place value of tens of thousands in each of the following

numbers?

(a) 653 294

(d) 473 219

(b) 45 732

(e) 89 326

(f) 321 798

2. Represent 654 329 in a place value chart.

3. A constituency has 456 279 registered voters. Find the place value of digit 6 in the

number representing the voters.

Total value of digits up to hundreds of thousands

Activity 2

1. Write 4 568 in expanded form.

2. Use the expanded form of the number 4 568 to write the total value of each digit.

3. Write down other numbers of your choice.

4. Write the total value of each digit in the numbers you have written.

Determine the total value of digit 8 in the number 863 721.

Working

The total value of each digit is given as follows:

1 x 1 = 1

2 x 10 = 20

7 x 100 = 700

3 x 1000 = 3000

6 x 10000 = 60 000

8 x 100 000 = 800 000

The total value of digit 8 is 800 000.

Example 2

Assessment Task 2

1. What is the total value of digit 2 in the following numbers?

(a) 429 513 (b) 245 671 (c) 9 729

(d) 3 452 (e) 32 136 (f) 892 451

2. Write the total value of the coloured digits in each of the following numbers.

(a) 543 761 (b) 87 219 (c) 34 761

(d) 213 907 (e) 432 670 (f) 421 683

3. The number of Grade ﬁve learners in a certain county is 45 782. Find the total value of

digit 4 in the number representing the total learners.

Further Assessment 2

1. How many hundreds are in the total value of digit 2 in the number 567 283?

2. Work out the difference between the total value of digit 3 and the total value of

digit 9 in the number 3 901.

3. Form a 4-digit number with:

(a) 7 in the hundreds place value.

(b) 5 in the tens place value.

Using numbers in symbols

Activity 3

1. Think about the numbers you use every day.

2. Write down where the numbers are used and give examples of the numbers used.

Assessment Task 3

Complete the following table to show where numbers are used in real life.

Place used Number

(a) In which year are we?

(b) Which year were you born?

Reading and writing numbers in symbols

Activity

1. Make number cards like the ones shown below.

2. Rearrange the number cards to make different ﬁve-digit numbers.

(a) Write down the numbers that you have formed in symbols.

(b) Read aloud the number that you formed.

Read the number: 42 958.

Working

Begin from the right and separate this number into two parts. Begin at the left and read

each part individually as shown.

Forty-two thousand

Thousand part

nine hundred ﬁfty-eight

Hundreds part

42 958 is read as forty-two thousand nine hundred and ﬁfty-eight.

Example 3

Assessment Task

1. Write then read the largest four-digit number that can be formed using the digits 7,

5, 8, and 2.

2. Complete the following table by writing the missing numbers.

(a) 8 950 8 951 8 952

8 954

8 955 8 957

(b) 703 705 708 801

(d) 87 708 87 713

3. Write 3 - four-digit numbers using the following digits: 3, 6, 9 and 1.

4. Find the number that comes immediately after 9 999.

5. Write the number that comes just before 37 429.

6. Use the digits 3, 5, 6, 9, and 2 to form the smallest ﬁve-digit number that can be

formed from the numbers.

Reading and writing numbers in words

Activity 5

1. Write 43 561 in expanded form.

(a) 43 561 = 40 000 + _______+ 500 +_______+ 1

(b) Write the number in words

2. Read the number you have written in words.

Write 52 326 in words.

Working

Number 5 2 3 2 6

Expanded form 50 000 2 000 300 20 6

Number in words Fifty thousand Two thousand Three hundred Twenty Six

52 326 in words is ﬁfty-two thousand three hundred and twenty-six.

Example

Assessment Task 5

1. Write the following numbers in words.

(a) 43 002 (b) 9 026 (c) 2 003

(d) 45 679 (e) 55 555 (f) 70707

2. There are 3 456 learners in Mare Primary School.Write the number of learners in

Mare Primary School in words.

3. James planted 43 210 trees on his farm. How many trees did he plant in words?

4. Which one of the following numbers is ﬁve thousand seven hundred and ﬁfty-nine.

(a) 559 (b) 759 (c) 5 759 (d) 579

Further Assessment 3

1. Match the numbers in words with their correct form in symbols.

Number in words Number in symbols

(a) Eighty thousand ﬁve hundred

and sixty-one

39 001

(b) Sixty-one thousand seven

hundred and eight

39 100

hundred

80 561

(d) Thirty-nine thousand and one 61 708

2. During the school elections, the winner got one thousand two hundred twenty-

ﬁve votes while the learner

who came second, got three

hundred and three votes.

Write in symbols, the

number of votes that the

ﬁrst and second learners

got.

3. Eight hundred and twenty-

ﬁve people were vaccinated

at a vaccination station

against COVID-19. During

the 9 p.m. television news,

it was reported that

825 people had been

vaccinated at that station.

Was the reporting

correct?

Ordering numbers

Arranging numbers from the smallest to the largest

Activity 6

1. Make number cards like the ones shown below.

56 231

65 324

50 234

56 702

2. Arrange the numbers on the cards from the smallest to the largest.

Use a place value chart to arrange the following numbers from the smallest to the

largest. 56 432, 54 632, 46 523, 53 264

Working

Write the numbers in a place value chart.

Tens of thousands Thousands Hundreds Tens Ones

5 6

3 2

6 3 2

6 5 2 3

5 3 2 6

Compare the values of the numbers starting with the tens of thousands column. Arranging

the numbers in an increasing order, we get:

46 523, 53 264, 54 632, 56 432

Example 5

Assessment Task 6

1. Arrange the following numbers from the smallest to the largest.

(a) 56 736, 57 736, 55 736, 54 736

(b) 4 024, 4 034, 4 135, 4 563

(d) 99 332, 98 433, 99 443, 99 544

2. The number of bags of maize sold to the National Cereals Board in 5 months was

as follows: 43 567, 67 302, 57 821, 60 734 and 34 543.Arrange the number of bags

sold in an ascending order.

Further Assessment

1. Write the numbers; 40 057, 40 061, 50 034 and 45 305 in ascending order.

2. The following receipt shows the items that Megan bought from a wholesale shop

to go and sell in her shop.

(a) What is the cost of the least

expensive items that she

bought?

(b) Assuming she only had

sh.15 000 with her and had

to return the most expensive

item, what should she return?

from the least expensive to

the most expensive.

Receipt

Pamoja Supermarket

PO Box 12 Pamoja

Date: 02/ 10/ 2021

Description Quantity Amount (ksh)

Rice 20 kg

4 887

Sugar 20 kg

2 844

Pens 1 carton 2 662

Sweets 10 packets 500

Cooking oil 20 l

3 499

Exercise books 1 carton

4 608

Total 19 000

Arranging numbers from the largest to the smallest

Activity 7

Andrew wants to ﬁnd the difference between the largest and smallest 4 - digit number

that can be formed using the digits 9, 2, 8, and 0.

1. Form the different 4- digit numbers that can be formed by these digits.

2. Arrange the numbers from the largest to the smallest.

3. Find the difference between the largest and the smallest number you formed.

Arrange the following numbers from the largest to the smallest.

87 953, 86 359, 87 359, 86 459

Working

87 953, 87 359, 86 459, 86 359

Example 6

Assessment Task 7

1. Arrange the following numbers from the largest to the smallest.

(a) 7 554, 8 564, 4 765, 4 856

(b) 30 045, 30 054, 45400, 34500

(d) 76 523, 75 412, 76 301, 75 534

2. The population of 4 sub-counties are 56 703, 57 894, 62 458 and 93 021. Arrange

the populations in a decreasing order.

3. Write 65 733, 56 845, 54 376 and 65 465 in descending order.

Further Assessment 5

1. John did a research and recorded in the following table the distance of ﬂights from

Nairobi to other cities.

Nairobi – Kisumu Nairobi – Entebbe Nairobi – Eldoret Nairobi – Mombasa

279 km 521 km 268 km

422 km

Put the ﬂight distances in order from farthest to the nearest.

2. Leila and Eveline placed some numbers in descending order.

Who wrote the numbers correctly in descending order?

Leila

400 450

500

550 600 650

Eveline

650 600 550 500

450 400

Rounding off numbers

Rounding off numbers to the nearest hundred

Activity 8

1. Make a number line like the one shown below.

790 800

810

820 830

840

850 860 870 880 890 900

2. Mark the position of the following numbers using dots on the number line.

(a) 804 (b) 859 (c) 892 (d) 847

3. Using the marked positions on the number line, round off the numbers to the nearest

hundred.

Learning point

If a number is below the midpoint it is rounded down to the nearest hundred. If a

number is at the midpoint or above, it is rounded up to the next hundred.

What is 3 567 rounded off to the nearest 100?

Working

Write multiples of 100 that are near the number.

3 500, 3600

Identify the midpoint of the numbers.

3 500, 3 550, 3 600

3 567 is above the mid-point. It is therefore nearer to 3 600.

3 567 rounded off to the nearest hundred is 3 600.

Example 7

Round off 712 to the nearest hundred.

Working

Draw a number line as shown.

700650 750 800 850

Mark on the number line, the position where 712 would be if it was put on the number

line.

700650 750

712

800 850

712 is closer to 700 than to 800.

712 rounded off to the nearest hundred is 700.

Example 8

Assessment Task 8

1. Round off the following numbers to the nearest 100.

(a) 567 (b) 64 327 (c) 4 578

(d) 45 (e) 38 092 (f) 8 054

2. The learners who reported to school for third term in Maisha primary school were

3 621. How many learners are these to the nearest hundred?

3. The number of passengers transported by the standard gauge railway train in ten days is

8 734. Write the number of passengers transported by the train to the nearest hundred.

Further Assessment 6

1. A book publishing company sold 45 379 copies of a book. On the newspaper

report, the ﬁgure was rounded to the nearest 100.What was the ﬁgure published

in the newspaper?

2. What is the smallest number that rounds off to 300 when rounded off to the

nearest hundred?

3. Round off the following numbers to the nearest hundred. Use the answers to

complete the cross-number puzzle given.

f. g.

Across: Down:

(a) 2 264 = (e) 3 709 =

(b) 4 973 = (f) 672 =

(d) 545 = (h) 8 816 =

Rounding off numbers to the nearest thousand

Activity

Round off 1 340 and 3 700 to the nearest thousand.

1. Write numbers in multiples of 1 000 starting from 1 000 to 5 000.

2 0001 000 3 000

4 000

5 000

2. Identify the midpoints between these numbers.

1 5001 000 2 000 2 500 3 5003 000

4 000 4 500

(a) Is 1 340 near 1 000 or near 2 000?

(b) Is 3 700 near 3 000 or near 4 000?

3. (a) 1 340 rounded off to the nearest thousand becomes ________.

(b) 3 700 rounded off to the nearest thousand becomes ________.

Learning point

If a number is below the midpoint, it is rounded down to the nearest thousand. If a

number is at the midpoint or above, it is rounded up to the next thousand.

What is 5 734 rounded off to the nearest thousand?

Working

Write multiples of 1 000 that are near the numbers to be rounded off.

5 000, 6 000

Identify the midpoint

5 500, 5 500, 6000

5 734 is above the midpoint. It is, therefore, nearer to 6 000.

5 734 rounded off to the nearest 1 000 is 6 000.

Example

Assessment Task

1. Round off the following numbers to the nearest thousand.

(a) 5 476 (b) 39 127 (c) 432 (d) 999

(e) 9 999 (f) 34 (g) 56 799 (h) 32 108

2. There were 4 568 elephants inTsavo National Park.What is the number of elephants

to the nearest thousands?

Further Assessment 7

1. The schools in a certain sub-county were supplied with 45 673 Mathematics books.

Rewrite the number of books supplied to the sub-county to the nearest thousand.

2. What is the biggest number that rounds off to 10 000 when rounded off to the

nearest thousand?

3. Round off 4 567 and 6 708 to the nearest thousand and ﬁnd the sum of the rouded off

numbers.

Divisibility of numbers

Divisibility test of 2

Activity

1. Divide each of the following numbers by 2:

10, 12, 14, 16, 18

2. What do you notice?

Do they leave a remainder?

3. Look at the last digit in each of the numbers.

What do you notice?

Learning point

A number is divisible by 2 if the digit in the ones place value is 0, 2, 4, 6 or 8.

Using the divisibility test of 2, ﬁnd out whether the following numbers are divisible by 2

or not.

(a) 26 (b) 53 (c) 40

Working

Check the digit in the ones place in each of the numbers.

(a) The digit in the one’s place value is 6.Therefore, 26 is divisible by 2.

(b) The digit in the one’s place value is 3.Therefore, 53 is not divisible by 2.

Example

Assessment Task

1. Use divisibility test of 2 to ﬁnd out whether the following numbers are divisible by 2

(a) 94 (b) 41 (c) 100 (d) 28

(e) 154 (f) 77 (g) 28 (h) 444

(i) 200 (j) 223

Divisibility test of 5

Activity

1. Divide each of the following numbers by 5: 10, 15, 100, and 35.

What do you notice?

2. Look at the last digit in each of the numbers. What do you notice

Learning point

A number is divisible by 5 if the digit in the ones place value is 0 or 5.

Using the divisibility test of 5, find out whether the following numbers are divisible by 5

or not.

(a) 75 (b) 30 (c) 54

Working

Check the last digit in each of the numbers.

(a) The digit in the ones place value in 75 is 5.Therefore, 75 is divisible by 5.

(b) The digit in the ones place value in 30 is 0.Therefore, 30 is divisible by 5.

Example

Assessment Task

Use divisibility test of 5 to ﬁnd out whether the following numbers are divisible by 5

(a) 60 (b) 45 (c) 125 (d) 56

(e) 28 (f) 90 (g) 85 (h) 235

(i) 450 (j) 551

Divisibility test of 10

Activity

1. Divide the following numbers by 10: 20, 50, and 200.

What do you notice?

2. Look at the last digit in each of the numbers.What do you notice?

Learning point

A number is divisible by 10 if the digit in the ones place value is 0.

Using the divisibility test of 10, ﬁnd out whether the following numbers are divisible by 10.

(a) 80 (b) 35 (c) 130

Working

Check the last digit in each of the numbers.

(a) The digit in the ones place value in 80 is 0.Therefore, 80 is divisible by 10.

(b) The digit in the ones place value in 35 is 5.Therefore, 35 is not divisible by 10.

Example

Assessment Task

1. Use the divisibility test of 10 to determine whether the following numbers are divisible

by 10 or not.

(a) 70 (b) 500 (c) 230 (d) 27 (e) 101

(f) 252 (g) 260 (h) 130 (i) 456 (j) 55

2. The following numbers are divisible by 10 except?

(a) 2 015 (b) 3 000 (c) 4 170 (d) 8 990

Further Assessment 8

1. Which of the following numbers are divisible by both 5 and 10?

(a) 45 (b) 80 (c) 35 (d) 50

2. James harvested 540 bags of maize from his farm. Was the number of bags

harvested divisible by 10?

3. Show that 40 and 35 are both divisible by 5.

4. What is the least number that can be added to 276 to make it divisible by 10?

Highest common factor (HCF)

Activity

1. List down all numbers that you can multiply to get 6. What are the factors of 6?

2. List down numbers that you can multiply to get 18. What are the factors of 18?

3. Write the factors of 6 and 18 then identify the common factors.

Learning point

Factors are numbers that we multiply to get another number.

What is the highest common factor of 15 and 20?

Working

1 x 15 = 15

3 x 5 = 15

The factors of 15 are 1, 3, 5 and 15.

1 x 20 = 20

2 x 10 = 20

4 x 5 = 20

The factors of 20 are 1, 2, 4, 5, 10 and 20.

The common factors of 15 and 20 are: 1 and 5.

The highest common factor (HCF) is 5.

Example 13

Find the greatest common divisor of 12 and 36?

Working

The divisors of 12 are; 1, 2, 3, 4, 6 and 12.

The divisors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18 and 36.

The common divisors are 1, 2, 3, 4, 6 and 12.

The greatest common divisor (GCD) of 12 and 36 is 12.

Example 14

Assessment Task

1. List the factors of the following numbers:

(a) 16 (b) 36 (c) 60 (d) 72

2. Write the divisors of the following numbers.

(a) 36 (b) 81 (c) 40 (d) 26

3. List the common divisors of 21 and 42.

4. Work out the HCF of the following numbers.

(a) 9 and 36 (b) 18 and 54

5. What is the GCD of the following numbers?

(a) 42 and 63 (b) 12, 15 and 30

Further Assessment

1. Find out the greatest number that can divide 48 and 72 without a remainder.

2. 48 bananas and 84 oranges were to be shared equally among some learners.Calculate

to show the greatest number of learners that can share the fruits without a remainder.

3. Katana had 12 oranges and 18 pears. He shared them equally among his children.

Calculate the largest possible number of his children.

4. Calculate the biggest number that can divide 12 and 36 without a remainder.

5. List the common divisors of 36, 48 and 72.

Least Common Multiple (LCM)

Activity

1. Write down the numbers that you will get after multiplying 4 by:

(a) 1 (b) 2 (c) 3

2. Write down the numbers that you will get after multiplying 5 by the numbers:

(a) 1 (b) 2 (c) 3

3. What do we call the numbers that we get after multiplying numbers by other counting

numbers?

4. Are there some common answers?

What is the LCM of 6 and 9?

Working

The multiples of 6 are 1, 6, 12, 18, 24, 30, 36, 42…

The multiples of 9 are 1, 9, 18, 27, 36, 45…

The common multiples of 6 and 9 are 18 and 36.

The least common multiple is 18.

The LCM of 6 and 9 is 18.

Example 15

Assessment Task

1. Write the ﬁrst 5 multiples of the following numbers.

(a) 5 (b) 7 (c) 11 (d) 2

(e) 14

2. Work out the LCM of the following numbers?

(a) 18 and 27 (b) 7 and 14 (c) 20 and 30 (d) 15 and 20

(e) 6, 8 and 12 (f) 9, 15 and 45

Addition

Addition without regrouping

Adding up to 2 six-digit numbers

Activity

Read the following number story and answer the questions that follow.

In the Fuzu Society Library, there are 338 454 books.An NGO that is championing for

growth in education donated 61 325 new books to the library.

(a) Write an addition sentence for the number of books that will be in the library.

(b) How many books will be there in the library?

Find the sum of: 519 010 and 480 736

Working

Example 1

H TH T TH T H T O

0 7 3 6

9 9

Place the numbers in a place value chart

then add the digits in the same place value

starting from the ones.

519 010 + 480 736 = 999 746

Assessment Task

1. Evaluate each of the following:

(a) 343 111 + 406 622 = (b) 331 045 + 300 704 = (c) 717 231 + 242 737 =

2. Find the sum of each of the following:

285 335

+ 102 623

331 147

+ 166 551

520 654

+ 211 131

413 432

+ 503 243

(a) (b) (c) (d)

A company manufactured 523 500 shirts on Monday and 324 300 shirts on Tuesday.

Find the total number of shirts manufactured in those two days.

Example 2

Working

We add 523 500 to 324 300 to ﬁnd the number of shirts manufactured in the two days.

Place the numbers in a place value chart then add the digits in the same place value

H TH T TH T H T O

5 2 3 5 0 0

3 2

3 0 0

7 8 0 0

starting from the ones place value.

Therefore, 847 800 shirts were

manufactured in the two days.

Further Assessment

1. Michawl bought a vehicle for 580 325 shillings. He spent 18 652 shillings on repairs.

How much did the vehicle cost him?

2. There were 302 089 wild beasts in an animal sanctuary. During the rainy season,

404 310 more wild beasts migrated into

the sanctuary. Find the number of wild

beasts in the sanctuary during the rainy

season.

3. A call centre of a telecommunications

company received 319 262 calls in one

week and 380 535 calls in the next

week. Determine the number of calls

they received in the two weeks.

. Adam bought an acoustic guitars worth

100 460 shillings and keyboards worth

299 520 shillings for his band. Work out the amount that Adam spent on the items.

Adding up to 3-six digit numbers

Activity 2

Read the following number story

and answer the questions that

follow.

In the census that was carried out in

2019, there were 405 633 men,

302 212 women and 312 141 children

in a town.

(a) Write the addition sentence to show

the total population of the town.

(b) Find the total population of the town.

Evaluate:

133 810 + 206 125 + 630 053

Working

Place the numbers in a place value chart then add the digits in the same place value.

H TH T TH T H T O

3 3 8

2 0 6

2 5

6 3 0 0 5 3

9 9

8 8

Example 3

Maya withdrew 360 000 shillings from her bank account to pay for the land she had

recently bought. She also withdrew 102 065 shillings to buy goods to sell in her shop.

On checking her account balance, she found a balance of 26 532 shillings in her account.

What amount did Maya have in her account before the two withdrawals?

Example 4

H TH T TH T H T O

3 6 0 0 0 0

0 2 0 6 5

2 6 5 3 2

8 8 5

Working

To get the total number amount Maya had

in her account, we add the amount she

withdrew and the balance in her account.

Put the numbers in a place value chart

and add.

Therefore, Maya had 488 597 shillings in her account.

Assessment Task 2

1. Evaluate each of the following:

132 320

+ 125 220

432 459

111 600

+ 461 004

100 214

406 250

+ 482 445

11 100

(a) (b) (c)

2. A shopping mall received 105 962 shoppers on the ﬁrst week that it opened, 123 011

shoppers on the second week and 272 032 on the third week.Find the number of shoppers

who visited the shopping mall for the three weeks.

3. During a football match, 110 200 people watched the match live at the stadium,

34 389 people watched the match from the screens erected across towns while 433

000 watched the match on their television. Determine the total number of people who

watched the match.

. A farmer harvested mangoes from his three farms. From one farm, he harvested 435 111

mangoes. From the second farm, he harvested 230 450 mangoes and 333 420 mangoes

from the third farm. Find the total number of mangoes harvested from the three farms.

5. There are 307 530 bags of maize, 384 120 bags of rice and 205 240 bags of wheat in a

store. Find the total number of bags in the store.

Addition with regrouping

Working

202 837

+ 794 077

996 914

1 1

Example 5

• Add ones: (7 + 7 = 14) ones.

• Regroup 14 tens into 1 tens and 4 ones.

• Add tens: (1 + 3 + 7 = 11) tens.

• Regroup 11 tens into 1 hundreds and 1 tens.

• Add hundreds: (1 + 8 + 0 = 9) hundreds.

• Add thousands: (2 + 4 = 6) thousands.

• Add ten thousands: (0 + 9 = 9) ten thousands.

• Add hundred thousands: (2 + 7= 9) hundred thousands.

Work out 202 837 + 794 077

Assessment Task 3

1. Work out each of the following:

218 870

+ 317 818

837 277

+ 29 491

532 634

+ 119 830

(a) (b)

(c)

2. Gregory played a car game and scored 460 453 points in the ﬁrst round and

526 173 points in the second round. The game was over after the second round.

Work out the total number of points he had at the end of the second game.

Further Assessment 2

1. Evaluate each of the following:

(a) 207 234 + 195 201 = (b) 191 191 + 607 475 =

2. In a grand musical show, 101 201 men and 101 389 women participated. What is the

total number of participants in the musical show?

3. Five hundred and eighty-two people watched the ﬁnals of a football match live at a

stadium. Thirty-one thousand four hundred and seven more people watched the match

on their televisions. Find the total number of people who watched the football match.

Estimating sum by rounding off the addends to the nearest hundred

Activity 3

Estimate the sum of 362 and 159 by rounding off the numbers to the nearest hundred and

compare the answer to the actual sum.

Estimating addition through rounding off to the nearest hundred

Activity

1. What is 362 rounded off to the nearest hundred?

2. What is 159 rounded off to the nearest hundred?

3. Evaluate 400 + 200.

4. Evaluate 362 + 159.

5. Compare the answers you get.

Find the estimate sum and the actual sum of 43 389 and 606 535 by rounding off the

numbers to the nearest hundred.

Working

When rounded off to the nearest hundred:

43 389 becomes 43 400

606 535 becomes 606 500

Estimated sum 43 400 + 606 500 = 649 900

Actual sum 43 389 + 606 535 = 649 924

Example 6

Assessment Task 4

1. Estimate the sum of each of the following pair of numbers, by rounding off each numbers

to the nearest hundred:

(a) 546 and 342 (b) 4 280 and 50 295 (c) 254 230 and 2 410

2. Estimate the sum 1 472 + 722 + 105 164 by rounding off each number to the nearest

hundred.

3. Complete the following table by rounding off the given numbers to the nearest hundred.

Find the estimated and the actual sum.

Numbers Estimate Sum Actual Sum

(a) 276 582 and 157

(b)

245 and 90 163

(d)

746 812 and 99 111

Further Assessment 3

1. Limberia rounds off some sums to the nearest hundred.Does she round off correctly?

Choose Yes or No for each of the following.

(a) 103 273 + 365 is about 103 700. Yes or No

(b) 154 + 152 is about 300.Yes or No

(d) 535 + 112 294 is about 112 800.Yes or No

2. Jasmin had 20 236 shillings. Her dad added her 10 289 shillings. Does Jasmin have

more than 30 600 in all? Estimate the answer to the nearest hundred.

3. Mwadime cycled 3 247 m to church, then 582 m to the market. He then cycled

1 634 m back to his house.Estimate the total distance he travelled by ﬁrst rounding

off each distance to the nearest hundred.

Estimating sum by rounding off the addends to the nearest thousand

Activity 5

Read the following number story and answer the questions that follow.

In one month, a graphic designer earned sh. 123 590 for designing storybooks, sh. 26 099

for designing logos and sh. 49 175 for designing websites.

1. What is the actual amount he earned in that month?

2. Use a number line to round off each of the amounts the designer earned to the

nearest thousand.

3. Find the sum of the rounded-off amounts.

Evaluate 42 505 + 127 807 + 21 397 by rounding off each number to the nearest thousand.

Working

42 505 rounded off to the nearest thousand becomes 43 000.

127 807 rounded off to the nearest thousand becomes 128 000.

21 397 rounded off to the nearest thousand becomes 21 000.

The sum of the rounded off numbers is 43 000 + 128 000 + 21 000 = 192 000.

Example 7

Assessment Task

1. Estimate the sum of each of the following by rounding off to the nearest thousand.

(a) 342 125 + 35 637 (b) 504 837 + 141 354 (c) 33 231 + 200 097

2. Estimate the sum by rounding off to the nearest thousand. Compare the result to the

actual sum for each of the following.

(a) There are 123 465 red roses, 110 250 white roses and 96 752 pink roses in a

garden. Estimate the total number of roses in the garden.

(b) The population of Maendeleo village is 53 628 and that of Salama village is

78 426. Estimate the total population of the two villages.

Patterns involving addition

Activity 6

1. Make different addition patterns.

2. State the rule that you used to make the pattern.

3. Use the rule to ﬁnd the next number in the pattern.

Find the missing numbers marked A, B and C in the following pattern.

__A___, 501 301, 502 401, __B___, __C___, 505 701

Working

From the given numbers:

502 401−501 301=1100

So, the rule is to add 1100 to get the next number to the right.

To ﬁnd the missing number B, 502 401+1100 = 503 501

To ﬁnd the missing number C, 503 501+ 1100 = 504 601

To get the number A, 501 301−1100 = 500 201.

The pattern is 500 201, 501 301, 502 401, 503 501, 504 601, 505 701

+ 1 100 + 1 100 + 1 100 + 1 100 + 1 100

Example 7

Assessment Task

1. Write the next number in each of the following patterns.

(a) 76 524, 77 666, 78 808, _______

(b) 4 556, 5 556, 6 556 ______

2. A ﬂower shop sells different number of roses every month. It sold 466 roses in

October,566 roses in November and 666 roses in December. If this pattern continues,

how many roses will the ﬂower shop sell in January of the following year?

3. Rehema applied for a job. She got the job with a starting monthly salary of

sh. 80 000, with an annual increment of sh. 5 000 in her salary. Write an addition

pattern to show the salary she will be earning for the ﬁrst 4 years.

Term 1

Mid Term Assesment

1. Write 45 300 in words.

2. Use a place value chart to show the place value of digit 7 in the number 37 231.

3. Work out the total value of digit 5 in the number 53 451.

4. Calculate the difference between the largest and the smallest numbers formed from

the following digits: 4, 0, 1, 2, 5.

5. Arrange the following numbers from the smallest to the largest:

32 021, 31 021, 33 132, 32 132.

6. Kirimi harvested 2 045 avocados from his farm. Write the number of avocados he

harvested to the nearest hundred.

7. Simplify: b + 2b + 5b.

8. Use divisibility tests of 5 and 10 to ﬁnd out whether 90 is divisible by both 5 and 10.

9. Work out the volume of the following cube.

10. List all the divisors of 30.

11. Which is the smallest number of fruits that can be shared by 6 boys and 15 girls

without a remainder?

12. List the ﬁrst 5 multiples of 13.

13. Write 6

as an improper fraction.

14. Calculate the perimeter of the shape below.

17 cm

8 cm

20 cm

6 cm

15. In a certain county, there are 164 546 women, 123 609 men and 204 128 children.

Calculate the total number of people in that county.

16. Write

100

as a decimal.

17. Round off 45 634 and 32 621 to the nearest hundred and ﬁnd their sum.

18. Arrange the following decimals in descending order: 8.02, 8.03, 8.92, 8.82, 8.98.

19. Convert 678 cm into metres and centimetres.

20. How many hours and minutes are in 324 minutes?

21. What is the next number in the pattern? 34 500, 35 500, 36 500.

22. Michael fell sick and stayed at home for 34 days. Calculate the number of weeks and

days he stayed home.

23. The price of a packet of unga is sh. 94. Write the cost in cents.

24. List two properties of a rectangle.

25. Draw a reﬂex angle.

26. Complete the table below

Fruits Tally marks Number

Mangoes

Oranges

27. Find the number of half kilogrammes in 8 kg.

28. Kimani divided 12 m 90 cm piece of rope into 3 equal pieces.What is the length of

each of the pieces?

29. Write 19 in roman numbers.

30. Sharon bought 6y books in the ﬁrst term. She bought 5y more books in term three.

How many books did she buy altogether?

Subtraction

Subtraction of numbers without regrouping

Activity

Write any two three-digit numbers and subtract the smaller number from the greater

number.

What answer do you get?

Compare your answers.

The registered voters in a certain county are 456 234. During the national election,

334 113 voted, how many voters did not vote?

Working

Start by subtracting the ones, tens, hundreds, thousands, tens of thousands and lastly

hundreds of thousands.

Hundreds of thousands Tens of thousands Thousands Hundreds Tens Ones

5 6 2 3

– 3 3

1 1

1 2 2

456 234 – 334 113 = 122 121

Example 1

Assessment Task 1

1. Evaluate each of the following.

(a) 353 789

– 230 561

– 2 531

(b) 75 693

– 43 272

(d) 56 823

– 4 822

2. Lamek’s ranch had 34 234 cattle in the year 2011. After a severe drought in 2012,

the number of cattle reduced by 213. How many cattle did he have at the end of 2012?

3. The number of books bought by the government for Grade 4 and 5 learners in a

certain county was 978 546. If Grade 4 learners received 432 134 books, how many

books were received by Grade 5 learners?

Further Assessment 1

1. Work out each of the following:

(a) 887 499

– 140 288

(b) 943 976

– 211 664

– 260 162

(d) 758 799

– 232 682

2. Saﬁ town recycled 385 345 kilograms of waste in January of 2019. It recycled 597

598 kilogrammes of waste in March

of 2019. How much more waste was

recycled in March than in January?

3. A website had 595 760 visitors in

January of 2021 and 615 355 visitors

in February of 2021. How many

more visitors visited the website in

February than January?

4. A shopping mall received 105 962

shoppers on the ﬁrst week that it

opened, 123 011 and on the second

week. How many more shoppers

came into the mall in the second week than the ﬁrst week?

Subtraction of numbers with double regrouping

Example 2

9 5 3 6 2 9

– 3 4 5 2 1 6

6 0 8 4 1 3

953 629 – 345 216 = 608 413

Mungai planted orange and mango trees on his farm. The number of orange trees was 345 216.

How many mango trees did he plant if the total fruit trees on the farm were 953 629?

Working

1. Subtract ones: 9 – 6 = 3 ones.

2. Subtract tens: 2 – 1 = 1 tens.

3. Subtract hundreds: 6 – 2 = 4 hundreds.

4. To subtract thousands, regroup 1 ten thousands

and add it to 3 thousands then subtract.

13 – 5 = 8 thousands

5. Subtract tens of thousands:4 – 4 = 0 tens of thousands

6. Subtract hundreds of thousands:9 – 3 = 6 hundreds

of thousands.

Assessment Task 2

1. Work out each of the following:

(a) 359 245

– 238 154

(b) 647 859

– 475 629

– 4 543

2. A contractor bought 9 603 iron sheets to construct classrooms in two schools.

School A used 4 262 iron sheets and the rest were used to construct classrooms in

school B. How many iron sheets were used to build classrooms in school B?

3. During the county athletics competition, 5 459 learners participated. If 3 285 of the

participants were boys, how many girls took part in the competition?

Further Assessment 2

1. Evaluate each of the following:

(a) 68 731 – 2 831 (b) 89 732 – 67 821 (c) 46 845 – 37 632

2. Selina worked out the difference between two numbers and got 1 307. If the larger

number was 9 577, ﬁnd the smaller number.

3. Samuel made a journey of 8 473 km. Out of this, he covered 4 253 km by train and the rest

of the journey by car. How many km did he cover by car?

4. A company that sells cement had 8 436 bags of cement in their store.They sold

3 565 bags of cement. How many bags were left in the store?

Estimating differences by rounding off numbers to the nearest hundred

Activity 2

1. Make number cards like the ones shown below.

56 735

2 543 3 456 72 547

2. Pick any two number cards from the ones you have made.

3. Round off the numbers to the nearest hundred.

4. Get the difference between the two rounded off numbers.

A sub-county has 54 674 learners.If 23 457 are boys,what is the estimated number of girls

in the sub-county if the numbers are rounded off to the nearest hundred.

Working

54 674 rounded off to the nearest hundred becomes 54 700

23 457 rounded off to the nearest hundred becomes 23 500

Estimated number of girls: 54 700 – 23 500 = 31 200.

Example 3

Assessment Task 3

1. Estimate the differences between the following numbers by ﬁrst rounding off to the nearest

hundred.

(a) 5 645 and 353 (b) 47 915 and 25 561 (c) 54 783 and 31 640

2. Samson delivered 34 561 litres of milk to a dairy in the month of July. He delivered 22

476 the following month of August. Use rounding off to the nearest hundred to estimate

the difference in the milk delivered in the two months.

Estimating difference by rounding off to the nearest thousand

Activity 3

Round off 54 320 and 21 432 to the nearest thousand.

What is the difference between the two numbers after rounding off?

A coffee factory processed 45 672 bags in 2019 and a further 98 756 bags the following

year. What is the estimated increase in the number of bags processed by rounding off to

the nearest thousand?

Working

45 672 rounded off to the nearest thousand becomes 46 000.

98 756 rounded off to the nearest thousand becomes 99 000.

Estimated difference in processed bags: 99 000 – 46 000 = 53 000.

Example

Assessment Task

1. Estimate the difference between the following numbers by ﬁrst rounding them off to

the nearest thousand.

(a) 54 671 and 564 (b) 65 472 and 99 420

2. Wanyama planted 66 734 cabbages in January and another 56 832 in the month of

March. Round off the number of cabbages planted in the two months to the nearest

thousand, then ﬁnd the difference.

Combined operations involving addition and subtraction

Work out:

435 781 + 456 780 – 203 452

Working

Add: 435 781 + 456 780 = 892 561

Subtract: 892 561 – 203 452 = 689 109

Example 5

Learning point

When an operation involves addition and subtraction, always start with addition then

subtraction.

Assessment Task 5

1. Evaluate each of the following.

(a) 56 803 + 40 322 – 22 001 (b) 98 812 + 10 034 – 34 512

2. Kantet had 4 556 goats.He sold 3 240 of the goats to raise money for his children’s school

fees. Later, he bought an additional 2 400 goats. How many goats did he have ﬁnally?

Further Assessment 3

1. For each of the following ﬁnd the value of the missing numbers marked with letters.

(a) 59 k 83k

– 456 728

140 10k

(b) 46m 994

– 222 83m

247 155

– 269 147

516 018

2. A mango processing factory received 45 3216 mangoes on day one. 2 345 mangoes

were rejected and thrown away.On the second day,64 9317 mangoes were delivered

with no rejections. How many good mangoes were received in the two days?

Number patterns involving subtraction

Activity

1. Make number cards like the ones shown below.

350 002

340 002

360 002

2. Arrange the numbers from the biggest to the smallest.

3. What criteria have you used to arrange the numbers?

What is the next number in the pattern below?

56 700, 54 700, 52 700, 50 700, _____

Working

Find what is being subtracted to get the next number in the pattern.

56 700 – 54 700 = 2 000

54 700 – 52 700 = 2 000

2 000 is the number being subtracted from the previous number in each instance.

Th next number will be: 50 700 – 2 000 = 48 700

Example 6

Assessment Task

1. What is the next number in the patterns below?

(a) 30 234, 29 234, 28 234, 27 234, _______

(b) 7 692, 6 692, 5 692, 4 692, ________

(d) 67 834, 67 714, 67 594, 67 474, ___________

(e) 5 832, 5 682, 5 532, 5 382, _________

2. A boarding school had 35 647 litres of water in their storage tank. 24 56 litres were

used every day. How many litres of water was in the tank after four days?

3. Kimani had 450 000 shillings in his bank account. He started withdrawing 20 000

shillings every day to pay workers at a construction site. How much did he have in his

account at end of the third day?

Multiplication

Multiplication of up to 3-digit number by 2-digit number

Activity

1. Make practice cards like the ones shown below.

126 x 15 332 x 20 188 x 18

2. Pick one practice card at a time and work out the product of the numbers on the number card.

3. Repeat this for all the cards.

Work out 2 7 4 x 1 5

Working

1 5

7 0

+ 2 7 4 0

4 1 1 0

Example 1

Add the products to get the ﬁnal answer.

Multiply 274 by 10.

Multiply 274 by 5.

A lorry can carry 245 bags of cement in one trip. Determine the number of bags of

cement the lorry can carry in 26 trips.

Working

2 4 5

x 2 6

1 4 7 0 (6 x 245)

+ 4 9 0 0 (20 x 245)

6 3 7 0 The lorry can carry 6 370 bags of cement in 26 trips.

Example 2

Assessment Task

1. Evaluate each of the following.

(a) 215 x 14 (b) 111 x 25 (c) 222 x 46 (d) 444 x 34 (e) 413 x 21

2. Work out each of the following.

(a) 2 5 6

x 1 2

(b) 3 3 2

x 1 2

x 2 2

(d) 6 1 9

x 1 1

(e) 5 1 2

x 3 0

3. A movie theatre has a daily sitting capacity of 545 people. One time, a play ran for 14

days.Determine the maximum number of people that watched the play in the 14 days.

4. Brian is a boda boda rider and he saves sh. 350 per day in a Sacco. How much money

will he save in 18 days if he works every day?

Further Assessment 1

1. Hassan, a maize farmer, harvested 523 bags of maize in one season. If one bag has

a mass of 90 kg, how many kilograms of maize did Hassan harvest that season?

2. A chair costs 452 shillings and a table costs 750 shillings. An organisation bought

30 chairs and 15 tables.Which item cost more and by how much?

3. A biscuit factory makes 718 boxes of biscuits daily. Each box carries a total of

15 biscuits. Determine the number of biscuits the factory makes in a day.

4. A warehouse restocked 25 cartons each of mass 725 kg. Determine the total mass

of the cartons that the warehouse restocked.

Estimation of products

Rounding off factors

Activity 2

1. Make number cards like the ones shown below.

725 x 14 = 812 x 38 = 592 x 56 =

2. Pick one number card at a time. Find the product of the numbers on the number card.

3. Round off the factors on the number card to the nearest ten.

4. Find the estimated product of the rounded-off numbers.

5. Compare the estimate product and the actual product.What do you notice?

Work out the estimate product of 715 × 21 by ﬁrst rounding off the factors to the nearest ten.

Working

Rounding off 715 to nearest ten = 720

Rounding off 21 to the nearest ten = 20

Therefore,

7 2 0

x 2 0

0 0 0 (0 x 720)

+ 1 4 4 0 0 (20 x 720)

1 4 4 0 0

Multiply tens by 720.

Multiply ones by 720.

Example 3

The estimate product is 14 400.

A county has 385 primary schools. On average, each school has 46 Grade 5 learners. By

rounding off the factors to the nearest ten, determine the estimate number of Grade 5

learners in the county.

Working

385 rounded off to nearest ten = 390

46 rounded off to nearest ten = 50

Therefore,

Example

Multiply tens by 390.

Multiply ones by 390.

There are 19 500 Grade 5 learners in the county.

3 9 0

x 5 0

0 0 0 (0 x 390)

+1 9 5 0 0 (50 x 390)

1 9 5 0 0

Assessment Task 2

1. Estimate the product of each of the following by rounding off the factors to the

nearest ten.

(a) 772 x 12 (b) 455 x 29 (c) 314 x 74 (d) 916 x 22 (e) 867 x 33

2. Estimate the product by rounding off the factors to the nearest ten

(a) 3 1 9

x 2 4

(b) 7 7 5

x 4 6

x 3 3

(d) 9 0 6

x 1 8

(e) 5 1 4

x 6 1

Further Assessment 2

1. Grade 5 learners in Utu Bora Primary School use 415 litres of water every week.

If the learners stay in school for 14 weeks in a term, estimate by rounding off the

factors to the nearest ten, the amount of water in litres they use in one term.

2. During a community-based programme in Mwangemi Primary School, Grade 5

learners planted tree seedlings in 415 rows and 58 columns. Estimate by rounding

off the factors to the nearest ten, the total number of seedlings they planted.

3. During a read-aloud competition in Hekima Primary School, each Grade 5 learner

read 137 words. If there are 48 learners in Grade 5, estimate by rounding off the

factors to the nearest ten, the total number of words read by the Grade 5 learners

during the competition.

4. A farmer transported tomatoes in 45 crates. Each crate carried 618 tomatoes. By

rounding off the factors to the nearest ten, estimate the total number of tomatoes

the farmer transported.

Other methods of multiplication

Activity 3

1. Write down some numbers to multiply.

2. Use any method such as multiplication charts to work out the multiplication of the numbers.

3. Do the methods give the same answer?

4. Which method is easier to work with?

Work out 746 x 22 by using compatible numbers.

Working

746 is approximately 745 and 22 is approximately 20

Therefore, 746 x 22 is approximately 745 x 20

7 4 5

x 2 0

0 0 0

+1 4 9 0 0

1 4 9 0 0

Example 5

Multiply 745 by tens.

Multiply 745 by ones.

Work out the product of 789 x 49 by using the expanding method of addition

Working

789 = 700 + 80 + 9

49 = 40 + 9

Therefore,

(700 x 40) + (80 x 40) + (9 x 40) + (700 x 9) + (80 x 9) + (9 x 9)

28 000 + 3 200 + 360 = 31 560

6 300 + 720 + 81 = 7 101

38 661

Therefore, 789 x 49 = 38 661.

Example 6

Assessment Task 3

1. Estimate the product of the following using the compatible numbers method.

(a) 719 x 24 (b) 216 x 72 (c) 344 x 17 (d) 418 x 34

2. Work out the product of the following by expanding method.

(a) 3 1 4

x 5 2

(b) 9 1 2

x 4 6

x 1 9

(d) 9 4 7

x 2 5

Further Assessment

1. A bookshop sells 164 textbooks every week on average. Estimate the number of

textbooks sold in 14 weeks by using compatible numbers.

2. A farmer bought 24 milking cans for his farm.If each can hold 106 litres of milk,what amount

of milk in litres does the farmer produce if all the can full? Use the expansion method.

3. Heshima Primary School received 36 cartons of textbooks from the national

government.Each carton contained 24 textbooks. Using the expansion method,work

out the number of textbooks Heshima Primary received.

Patterns involving multiplication

Activity

1. Alvin made and arranged number cards as shown below.

5 25 125

2. What pattern do the cards form?

3. What is the next number on the cards?

4. Predict the next three numbers on the cards.

What are the missing numbers in the number pattern below?

8 32 ________ 512

Working

The multiplication rule is multiplying the previous number by 4.

The missing number is 32 x 4 = 128.

Example 8

A librarian arranged textbooks on shelves such that the ﬁrst shelf carried 25 textbooks,

the second shelf had 50 textbooks and the third shelf had 100 textbooks. If this pattern

continued, how many textbooks were arranged on the ﬁfth shelf?

Working

25 50 100 ________ ________

Fourth shelf = 100 x 2 = 200

Fifth shelf = 200 x 2 =

400 textbooks

Example

Assessment Task 4

Complete the following number patterns.

240

2. 25 75 675

3. 8

1000

10 30 810

22 88

Further Assessment 4

1. Mr Waswa gives his daughter different amounts for pocket money each term as

follows, sh. 150 in term one and sh. 300 in term two. If this pattern continues, how

much money does he give his daughter in term three?

2. Grade 3 learners in Sunshine Primary School went out to a shopping centre to

collect bottle tops.They collected 20 bottle tops on day one, 80 bottle tops on day

two and 320 bottle tops on day three. If this pattern continued, how many bottle

tops did they collect on day four and ﬁve?

3. Abel, a Grade 5 learner typed 30 words on his tablet on day one, 90 words on day

two and 270 words on day three. If this pattern continued, how many words did he

type on days four and ﬁve?

4. In a street light decoration, lamps were placed at 12 m interval, 48 m internal then

192 m interval. If this pattern is retained, work out the next interval.

Division

Division of up to a 3-digit number by up to a two-digit number

Activity

Read the following number story and use it to answer the questions that follow.

Tom had a birthday party. His mother bought him a packet of sweets that had 216 sweets

inside. He wanted to share the sweets equally among his 24 friends who attended the

birthday party.

(a) How can he share an equal number of sweets with his friends?

(b) Find the number of sweets each friend will receive.

Divide 198 by 33.

Working

Using the relationship between multiplication and division:

33 x = 198

33 x 6 = 198

Therefore, 198 ÷ 33 = 6.

Example 1

Divide 124 by 13.

Working

Using multiples,

1. Which number can you multiply by 13 to get 124 or a number close to it?

2. Pick the multiple that is closest to 124 but is less.

3. Take away the multiple from 124.

124 ÷ 13 = 9 remainder 7.

Example 2

Assessment Task

1. Work out each of the following.

(a) 360 ÷ 45 = (b) 120 ÷ 60 = (c) 420 ÷ 28 = (d) 100 ÷ 18 =

2. Akinyi sells sukuma wiki in her estate. One time, she bought 500 leaves of Sukuma

wiki. If she tied them in bunches of 10 leaves, how many bunches did she make?

3. Tom shared his 200 mango seedlings equally with his 20 friends. How many mango

seedlings did each of them get?

4. Uncle Jerry picked 117 apple fruits from the tree. He shared them equally among 14

children in his plot. How many apples did each child get?

5. A farmer planted 420 seedlings in 35 rows. How many seedlings were planted in

each row if each row had an equal number of seedlings?

Further Assessment

1. A teacher shared 789 pencils equally among her 48 learners.

(a) How many pencils did each learner get?

(b) How many pencils remained?

2. The government bought books from a publishing company and asked them to

distribute the books to schools.The publishing company packed nine hundred and

ninety-eight cartons of books in one of the distributing vehicles.The books were to

be distributed equally to 33 schools.

(a) Determine the number of cartons of books each school got.

(b) The remaining books were to be delivered to the county education ofﬁce. How

many cartons were delivered to the county ofﬁce?

3. At a party, there were four hundred and sixty-six men and ﬁve hundred and ﬁfty-

four women. If there were twenty minibuses to ferry them home and each bus was

to carry an equal number of people, how many people did each bus carry?

4. 13 vans were used to transport learners on a trip to the Nairobi trade fair. If each

van carried 21 pupils and the total number of learners was 819, how many trips did

each van make?

5. What is 684 divided by 12?

Long division

Learners from Excel Primary School were requested to help in arranging chairs and

tables in the community hall.There are 809 chairs to

be arranged around tables. They were supposed to

arrange 12 chairs around each regular table and the

rest on theVIP.

(a) Determine the number of regular tables needed.

(b) How many chairs were arranged on theVIP table?

Working

(a) To get the number of regular tables needed,

divide the total number of chairs by the number

of chairs needed around each table.

12 809

– 72 (12 x 6)

84 (12 x 7)

67 regular tables are needed.

(b) The number of VIP chairs, are the

remaining chairs

There were 5VIP chairs.

Steps

1. Divide 80 by 12 = 6 remainder 8

2. Write 6 above 0

3. Subtract 72 from 80 to get 8

4. Bring down 9 to get 89

5. Divide 89 by 12 = 7 remainder 5.

6. Write 7 above 9.

7. Multiply 12 by 7 = 84.

8. Subtract 89 from 84 to get 5.

Example 3

Assessment Task 2

1. Use the long method to work out the following.

(a) 192 ÷ 15 (b) 331 ÷ 31 (c) 280 ÷ 50 (d) 462 ÷ 22 (e) 242 ÷ 13

2. Divide 525 by 35.

3. Kate had sh. 600. She bought loaves of bread each at sh.55. How many loaves of bread

did she buy if she spent all the money she had?

4. Otieno made 10 baskets. If he wanted to get sh. 900 from them, how much did he sell

each basket?

Further Assessment 2

1. Mrs Okeyo shared 321 counters equally to 32 learners in her class that they would

use for counting. How many counters did each learner get?

2. You are to share 624 books equally among your 52 classmates. How many books

will each one of you get.

3. In a game reserve, there are 210 elephants.The rangers vaccinated 14 elephants

every day. How many days did they take to vaccinate all the elephants?

4. If packets of milk were shared among, 45 learners in a class where each learner

got 6 packets and 18 packets remained, how many packets of milk were there?

5. A shopkeeper has seven packs of 12 pencils and two packs of 54 pencils. The

shopkeeper redistributes all these pencils into a pack of 8 pencils for sale. How

many pencils will be in each pack?

Relationship between multiplication and division

Activity 2

Play the game ‘THINK OF A NUMBER’.

1. Think of a number and write it down.

2. Multiply the number by 10.

3. The answer is _____.

4. What is the number?

Learning point

Numbers in multiplication and division are related.We can say,

Multiplication is the reverse of division, or

Multiplication is the opposite of division.

x 10 = 120. x 10 = 330

12 = 120 ÷ 10 33 = 330 ÷ 10

120 ÷ 10 = 12 330 ÷ 10 = 33

The number is 12. The number is 33.

Example 4 Example 5

Assessment Task 3

1. I think of a number, I multiply it by 17 the answer is 153.What is the number?

2. I think of a number, if I divide it by 225, the answer is 25.What is the number?

3. Some sweets were shared among Grade 5 learners at Kari Primary School. If the

learners were 40 and each got 15 sweets, how many sweets were they in total?

4. Atieno bought 5 shirts for 600 shillings. How much money did each shirt cost.

Further Assessment 3

1. Workout 12 x 15 and show its division sentence.

2. Workout 200 ÷ 25 and show its multiplication sentence.

3. Tom thought of a number, He multiplied the number by 16 and the result was 480.

(a) What was the number?

(b) Write the reverse of the question above using a division sentence. Let 16 be the

quotient.

4. Antonio makes 15 queen cakes in 1 hour. If she made a total of 165 queen cakes,

how long did she take?

5. One umbrella is straightened up with 20 strings of wire. If 400 wires are used, how

many umbrellas are made? Fill in with the information given.

(a) _ ×_ = _ (b) _ ÷_ = _

6. Fill in the blanks and come up with your questions from the following information.

(a) How many desks are in your class?____

(b) How many learners are on each desk? _____

Estimate quotients

Activity 3

1. Write down a division sentence.

2. Round off the dividend to the nearest 10.

3. Round off the divisor to the nearest 10.

4. Work out the quotient of the rounded-off numbers.

5. Divide the remaining numbers by simplifying.

Work out each of the following by rounding off the numbers to the nearest ten.

(a) 122 ÷ 14 = (b) 265 ÷ 33 =

Working

122 ÷ 14 becomes 120 ÷ 10 = 12

265 ÷ 33 becomes 270 ÷ 30 = 9

Example 6

Assessment Task

1. Estimate the quotient of each of the following by rounding off the dividend and the

divisor to the nearest ten.

(a) 276 ÷ 12 = (b) 396 ÷ 45 (c) 22 ÷ 78 (d) 644 ÷ 21

2. Mary drove her car for 478 km. She made a stop after every 43 km. Estimate how

many stops she made by rounding off the dividend and the divisor to the nearest 10.

3. Use your method of estimation to work out the following.

(a) A teacher asks the learners to arrange 36 chairs into rows of nine chairs. How

many rows will be there?

(b) There are 425 boys and 387 girls in a school. During the thanksgiving service,

14 learners were required to sit on each bench. How many benches would be

enough for all the learners to be seated?

Combined operations involving addition,subtraction,multiplication and division

Activity

1. Work out: 2 + 3 x 5 – 10

2. How did you work out the question?

3. What answer do you get?

Learning point

When dealing with problems that involve the four operations, we start by working out

division, followed by multiplication, addition and lastly subtraction.

5 – 3 + 4 = 6 + 12 ÷ (10 – 7) = 38 – 5 x 15 ÷ 3 =

5 + 4 = 9 – 3 = 6 10 – 7 = 3 15 ÷ 3 = 5 x 5 = 25

Answer = 6 12 ÷ 3 = 4 38 – 25

6 + 4 = 10 Answer = 13.

Answer = 10.

Example 7 Example 8 Example 9

Assessment Task 5

1. Work out each of the following.

(a) 89 x 32 ÷ 16 = (b) 369 + 142 – 198 =

2. A primary school had 989 learners in the year 2012, two hundred and thirteen

transitioned to junior secondary.At the beginning of 2013, four hundred and thirty-

two more learners joined the school, how many learners were in the school in the

year 2013?

Further Assessment

1. A safari rally car covered 476 km on the ﬁrst leg of the journey then 534 km on the

second leg, if it covered 2 024 km by the end of the competition, how long was the

fourth leg if it was half of the remaining distance?

2. Talia had 20 sausages, she ate 3 and gave 2 to her mother. She shared the remaining

with her three siblings. How many sausages did each sibling get?

3. A mother bought 3 packets of sweets for Maria’s birthday party, each packet had 40

sweets, the sweets were all shared among the 30 children who attended the party, how

many sweets did each child get?

4. Mumo has 34 pencils and Oki has 23 pencils, they put them together and shared

them equally among their 3 friends, how many pencils did each friend get?

Term

End Term Assesment

1. Write seventy-ﬁve thousand two hundred and thirty in symbols.

2. Use a place value chart to show the place value of 6 in the number 46 789.

3. Calculate the total value of digit 5 in the number 450 321.

4. Write the place value of digit 4 in the number 32.74.

5. Calculate the number of hours in 6 days.

6. Round off 56 745 to the nearest thousand.

7. Arrange the following numbers from the smallest to the largest:

52 781, 51 671, 50 782, 53 761

8. Write 7.41 in decimal notation.

9. Find the LCM of 24 and 36.

10. In a certain meeting, there are 453 136 adults. If 20 1012 are women, how many men

were there in that meeting?

11. Wanjala harvested 5 673 bags of maize.Write the number of bags harvested to the

nearest hundreds.

12. Work out: 24 034 – 34 042 + 34 571.

13. Write 7 in roman numbers.

14. Find the next number in the pattern: 34 502, 33 502, 32 502, 31 502, _______.

15. List all the divisors of 24.

16. Calculate the value of 232 x 6.

17. A train has 15 coaches.There are 102 seats in each coach.Calculate the total number

of passengers the train can carry when full.

18. Use the divisibility test to choose the numbers that are divisible by both 2 and 5 from

the following numbers. (44, 50, 75, 120, 76)

19. Omondi planted 920 trees in 46 rows. Find the number of trees he planted in one row.

20. Simplify 43z + 5z + z.

21. Estimate the value of 323 ÷ 18 by ﬁrst rounding of the dividend and the divisor to the

nearest ten.

22. Which is the greatest number that can divide by 15 and 20 without a remainder?

23. Work out the value of 48 ÷ 12 + 6 – 4.

24. 45 681 patients were treated in a certain hospital in the month of March. In the

month of April, 42 509 patients were treated. Calculate the total number of patients

treated in the two months.

25. Calculate the perimeter of the square below.

100 m

26. List the ﬁrst three multiples of 15.

27. How many half-kilogram packets can be obtained from 38 kilogrammes?

28. The length of a building is 23 m 45 cm. Express its length in centimetres.

29. Draw an acute angle.

30. Name two objects in the classroom that have a shape similar to the one shown below.

Term 2

Opener Assesment

1. Write 94 562 in words.

2. Musa travelled to Nairobi and stayed there for 4 days. Calculate the number of

hours he spent in Nairobi.

3. Write the place value of digit 7 in 37.54.

4. What is the total value of digit 3 in the number 356 702?

5. Arrange the following numbers in descending order: 56 805, 54 805, 57 805, 53 805

6. Find the GCD of 36 and 48.

7. Kirwa harvested 34 567 bags of maize.Write the number of bags harvested to the

nearest thousand.

8. Write

345

100

as a decimal.

9. Write 9 in roman numbers.

10. Work out 456 + 56 – 455.

11. A certain sub-county has 54 684 learners in Grade 5. If there are 32 452 girls, how

many boys are there?

12. List the ﬁrst 5 multiples of 9.

13. Find the next number in the pattern: 72 432, 73 432, 74 432, 75 432, ______

14. A school has 456 learners. Each learner was given 6 exercise books. Calculate the

total number of books given to the learners.

15. What is the least number that can be divided by 18 and 24 without leaving a remainder?

16. Select the numbers that are divisible by both 5 and 10 from the given numbers in

brackets (55, 70, 45, 600).

17. Name the type of angle shown below.

18. The length of a rope is 5 m 12 cm.Write the length of the rope in centimetres only.

19. How many quarter kilogramme packets can be obtained from 3 kilogrammes?

20. List all the divisors of 18.

21. Calculate the perimeter of the ﬁgure below.

9 cm

12 cm

22. Simplify: 5w − w − 2w.

23. Work out the value of 45 − 6 ÷ 3 + 5.

24. Estimate the value of 456 ÷ 23 by ﬁrst rounding off the dividend and divisor to the

nearest 10.

25. Change 6

into an improper fraction.

26. Waswa has a piece of timber measuring 2 m 56 cm. He joined it with another piece

measuring 3 m 14 cm.Work out the length of the new piece of timber.

27. Calculate the volume of the cube below.

28. How many quarter litres are in 3 litres?

29. Write a.m. or p.m. ; Mercy took supper at 8.30______

30. The cost of a pencil is sh. 43.Write its cost in cents.

Fractions

Equivalent fractions

Activity

1. Make a table of 6 rows.

2. Divide the ﬁrst row into two equal parts.

3. Divide the second row into four equal parts.

4. Divide the third row into 6 equal parts.

5. Divide the fourth row into 8 equal parts.

6. Divide the ﬁfth row into 10 equal parts.

7. Divide the sixth row into 12 equal parts.

8. Shade one half of each row and write down the fraction it makes.

What can you say about the fractions you have written?

Learning point

Fractions that have the same value, even though they may look different are called

equivalent fractions.When all equivalent fractions are expressed in their simplest form,

they reduce to the same fraction.

The following shows an example of equivalent fractions.

Shade and complete the following to show equivalent fractions.

Example 1

Working

Activity 2

1. Write any fraction down.

2. Multiply both the numerator and denominator by the same number.

3. Write down the answer.

4. Repeat the same with different numbers to make different fractions. What do you

note about the fractions formed?

Learning point

Multiplication can be used to make equivalent fractions. The numerator and the

denominator must both be multiplied by the same number.

Division can also be used to make equivalent fractions. The numerator and the denominator

must both be divided by the same number.

Find the ﬁrst four equivalent fractions of

Working

2 × 2 = 4 2 × 3 = 6 2 × 4 = 8 2 × 5 = 10

3 × 2 = 6 3 × 3 = 9 3 × 4 = 12 3 × 5 = 15

Therefore, the ﬁrst four equivalent fractions of

are

and

Example 2

Example 3

Write three equivalent fractions of

Working

18 ÷ 3 6 6 ÷ 3 2 2 ÷ 2 1

36 ÷ 3 12 12 ÷ 3 4 4 ÷ 2 2

Therefore, the equivalent fractions of

are

and

Assessment Task

1. Using circular cut-outs, show the ﬁrst two equivalent fractions of

2. Use rectangular cutouts to show two equivalent fractions of

3. Write true or false for each of the following.

(a)

is equal to

(b)

is equal to

(c)

is same as

4. Make the ﬁrst four equivalent fractions of each of the following.

(a)

(b)

(c)

5. Identify two fractions that are equivalent:

Further Assessment

1. The two fractions

and

are equivalent. Determine the value of x.

2. Omar drew the following shape and said that one-third of this shape is shaded.

Is he correct? Why?

3. Martha plans to bake a cake. How many pieces can she cut it into, for four children

to share the cake equally and eat two slices each?

4. Mary expected 12 guests at her party. She cut the watermelon into 12 pieces. If

only 4 guests came, how many pieces of the whole watermelon did one guest eat

if they still ate equal number of pieces?

Simplifying fractions

Activity 3

1. Write down different fractions like

2. Divide both the numerator and denominator with a number that can completely

divide both.

3. What do you notice about the fraction formed?

Simplify the fraction

Working

÷ 2

÷ 3

Example

To get the simplest form, divide the denominator and

numerator with the same whole number until the numbers

cannot be divided any further.

Express

in their simplest form.

Working

÷ 4

expressed in its simplest form is

Example 5

Look for the largest number that divides 8 and 12 exactly.

That is the Greatest Common Factor of 8 and 12.

Greatest Common Factor of 8 and 12 is 4.

Divide both numerator and denominator by 4.

Mary has two children. She cut an orange into 4 pieces and gave each an equal number of

pieces.What fraction of the whole did each child eat? What is its simplest form?

Working

Now each child ate

of the whole orange.

÷ 2

Therefore,

in its simplest form is

Example 6

There are 4 pieces of an orange, there are 2 children who ate an

equal number of pieces.

Assessment Task 2

1. Simplify each of the fractions.

(a)

(b)

(c)

(d)

2. Use division to simplify the fractions.

(a)

(b)

(c)

(d)

Further Assessment 2

1. Mama Mboga had 14 pineapples. She sold 7 of the pineapples. Write the fraction

that remained in its simplest form.

2. A whole pizza was cut into 16 equal parts. If each person present ate four pieces of pizza:

(a) How many people were present?

(b) What fraction did each person eat?

3. Akinyi had a thermos of tea. She poured all the tea into 10 cups. She then drank 2

cups of tea; what fraction of the tea did she drink?

4. A farmer had 25 trees in his plot of land. He cut down 5 trees.What fraction of the

trees remained?

Comparing fractions

Activity

1. Cut two rectangular strips of paper of equal length and width.

2. On one strip, draw lines to divide it into 3 equal parts.

3. On the other, draw lines to divide it into 5 equal parts.

4. Shade or colour 1 part of each one of them. Cut out the coloured parts and compare

them.

(a) Which part of the fraction is big?

(b) Which part is small?

5. Use the answers you give to compare

and

Learning point

When the numeric fractions are the same, the smaller the denominator, the bigger the

fraction and vice-versa.

Compare the following fractions.

and

Working

is greater than

Example 7

Assessment Task 3

1. Using different shapes cut-outs, show which fraction is bigger or greater.

(a)

(b)

(c)

(d)

2. Use real objects to show which fraction is smaller or less.

(a)

(b)

(c)

(d)

Ordering fractions

Activity 5

1. Using paper cut outs, make four strips of equal sizes.

2. Shade each strip to represent the following fractions

3. Compare the shaded fractions.

4. Use the shaded strips to arrange the fractions from the greatest to the smallest.

Use real objects to arrange from the greatest to the smallest.

Working

Example 8

Assessment Task

1. Arrange from the largest to the smallest.

(a)

(b)

(c)

. (d)

2. A farmer gave napier grass to his cows. He gave

of a sack to the ﬁrst,

of a sack

to the second and to the third he gave a

of the sack. Find out which cow ate the

greatest amount of nappier grass down to the one that ate the least.

3. The following types of cake require different quantities of sugar as follows:

Lemon green,

Black forest ,

Strawberry,

Vanilla,

White forest cake

kg.

(a) Which cake requires the least amount of sugar?

(b) Which two cakes require the same amount of sugar?

to the one that requires the highest amount of sugar.

Addition of fractions

Addition of fractions with the same denominator

Activity 6

Find the sum of

and

by following the steps below:

1. Identify the numerators and add them together.

2. Copy the denominator as it is. A denominator is never added.

3. Simplify and write the answer in the simplest form.

4. Try working out sums of other fractions with the same denominator.

Work out the sum of each of the following.

(a)

= (b)

= (c)

Working

(a)

(b)

(c)

Example 9

Assessment Task 5

1. Work out each of the following:

(a)

= (b)

(c)

= (d)

2. A car used

of fuel in the fuel tank from Nairobi to Machakos. It remained with

in the

fuel tank.The driver then added

of fuel at a fuel station. How much fuel did the car had?

Further Assessment 3

1. A cup holds

litres of tea. If Magdalene takes 3 such cups of tea, how many litres

will she have taken?

2. Mumo fetched

litres of water on Monday,

litres on Tuesday and

litres on

Wednesday. How many litres of water did she fetch in the 3 days?

3. A ﬁfth and two-ﬁfths makes?

4. Put together 3 eighths and 4 eighths.What answer do you get?

5. A cow gives

of milk in the morning and

in the evening. How much milk does

the cow give daily?

Addition of fractions with one renaming

Activity 7

Follow the steps given to work out

1. Check the fractions.

2. Identify the fraction to be renamed.

3. Rename the fraction by multiplying both its numerator and denominator by the

same whole number.

4. Add the fractions that you have renamed.

5. Write and add more fractions of your choice.

Work out:

Working

1 x 2

3 x 2

= =

Example 10

Rename one fraction so that both fractions have

the same denominator.

Add the fractions with same denominator after

renaming.

Work out:

Working

2 x 3

5 x 3

+ += =

Example 11

Rename one fraction so that both fractions have

the same denominator.

Add the fractions with same denominator after

renaming.

Simply the answer.

Assessment Task 6

1. Evaluate the following.

(a)

= (b)

= (c)

(d)

= (e)

= (f)

2. Tony put a half-litre of milk for his cat.The cat only drank an eighth of the milk. How

much milk remained?

3. A shopkeeper had a

of rice remaining. He added a

of rice. What fraction of

rice did he have?

4. Put

and

together. What fraction do you get?

Subtraction of fractions

Subtraction of fractions with the same denominator

Activity 8

Follow the following steps to evaluate

–

1. Identify the numerators and subtract.

2. Copy the denominator as it is.

Work out each of the following.

(a)

–

(b)

–

Working

(a)

–

(b)

–

Example 12

Assessment Task 7

1. Evaluate each of the following.

(a)

–

= (b)

–

= (c)

–

2. Take away

from

3. Maryann had a

kg of meat, she gave her brother

kg of meat, how many kg did

she remain with?

Further Assessment

1. Subtract three tenths from eight tenths.

2. A tailor cut half a piece of cloth from a whole cloth. What fraction of the cloth

remained?

3. Tabby cooked 2 chapatis and ate 1 and a quarter chapati. What fraction of the

chapati remained?

4. A loaf of bread has 21 slices. Okello’s mother ate 4 slices while Okello’s father ate

6 slices. Okello ate 4 slices while the ate baby 2 slices.

(a) Show the fraction of bread eaten by:

(i) Okello’s father (ii) Okello (iii) the baby (iv) Okello’s mother

(b) Who ate the biggest portion?

Subtracting fractions with one re-naming

Activity

Follow the following steps to work out

–

1. Check the fractions.

2. Identify the fraction to be renamed.

3. Multiply it by a whole fraction that equals the denominator of the other fraction.

4. Carry out the subtraction of the fractions with the same denominator.

Work out

–

Working

1 x 2

3 x 2

–

Example 13

Rename one fraction so that both fractions have

the same denominator.

Subtract the fractions with same denominator

after renaming.

Evaluate

–

in its simplest form.

Working

2 x 3

4 x 3

–

Example 14

Rename one fraction so that both fractions have the

same denominator.

Subtract the fractions with same denominator after renaming.

Simply the answer.

Assessment Task 8

1. Evaluate each of the following.

(a)

–

= (b)

–

= (c)

–

= (d) 1 –

2. To m received a

advance payment of his May salary. He spent

of the amount on

food.What fraction of the money remained?

Further Assessment 5

1. During the class trip to the game park, learners were given water to drink. By

lunch, Peter had drunk

of his bottle of water while Mary had taken

of her

bottle of water.

(a) Who had taken more water by lunch?

(b) By what fraction was it more?

2. A school bought

P.E uniforms for the learners.

of the uniforms were small and

needed to be returned.What fraction of the uniforms was ﬁtting?

3. A packet of biscuits has

biscuits, if

is removed.What fraction is left?

Decimals

Identifying a thousandth

Activity

1. Make a place value chart up to three decimal places.

2. Place various numbers on the place value chart.

3. Identify the number in the thousandths place value.

Write the correct decimal form of the following fractions.

(a)

1000

(b)

1000

(c)

1000

Working

(a)

1000

= 0.065

(b)

1000

= 0.028

(c)

1000

= 0.013

Example 1

Write the following decimals and identify the number in the thousandths place value.

(a) Three thousandths (b) Forty-four thousandths

Working

(a) Three thousandths: 0.003, the value in the thousandths is 3.

(b) Forty-four thousandths: 0.044, the value in the thousandths is 4.

Example 2

Assessment Task

1. Identify the digit in the place value indicated for each of the following.

(a) 0.004 (thousandths) (b) 0.034 (hundredths) (c) 7.086 (thousandths)

(d) 6.807 (tenths) (e) 0.405 ( hundredths) (f) 0.008 (tenths)

2. Write the following decimals and identify the digit in the thousandths place value.

(a) Fourteen thousandths (b) Fifty-nine thousandths (c) Sixty four thousandths

(d) Two thousandths (e) Seventy-two thousandths (f) Six thousandths

Identifying place value of decimals up to thousandths

Activity 2

You will need bottle tops, nails and a piece of timber.

1. Make an abacus that has decimal places up to thousandths as shown below.

Thousands OnesHundreds Tenths

•

Tens

Hundredths

Thousandths

2. Write down different decimal numbers.

3. Choose one decimal number at a time.

4. Place bottle tops on the abacus to represent the decimal that you have chosen.

5. Identify the number in each decimal place.

6. Write down the number in the thousandths place each time.

Identify the place value of each digit of the number 10.046.

Working

Tens Ones Decimal point Tenths Hundredths Thousandths

0 . 0

Example 3

What is the place value of digit 8 in each of the following numbers?

(a) 12.348 (b) 34.286 (c) 105.865

Working

(a) Thousandths (b) Hundredths (c) Tenths

Example

Assessment Task 2

1. Place the following decimals in a place value chart.

(a) 112.456

(e) 34.847

(b) 92.659

(f) 518.235

(g) 556.124

(d) 1.564

(h) 0.034

2. Identify the place value of digit 5 in the following numbers.

(a) 13.005

(d) 146.025

(g) 46.564

(b) 12.645

(e) 17.115

(h) 42.751

(f) 32.765

3. Complete the following number puzzle. A decimal point takes its own square. The

ﬁrst one has been done for you.

2 . 5 2

B E

Across: Down:

A. 2 ones and 52 hundredths A. 2 tens and 76 thousandths

B. 42 thousandths

B. 7 thousandths

C. 8 and 1tenth C. 87and 56 thousandths

D. 5 and 5 tenths E. 7 and 51 hundredths

Ordering decimals up to thousandths

Activity 3

1. Make number cards like the ones shown below.

5.325

5.235

5.532

5.352

2. Arrange the number cards to show the decimals arranged in:

(a) Ascending order (b) Descending order

3. Repeat this for various cards.

Order the following decimals from the smallest to the largest.

61.087, 61.807, 56.666, 56.606.

Working

1. Write the decimals below each other.

2. Compare the decimals, two at a time.

3. Write the decimals starting with the smallest.

56.606, 56.666, 61.087, 61.807

Example 5

Arrange the following decimals in descending order. 1.402, 1.42, 1.375, 2.2, 1.85.

Working

Put the decimals on a table like the one shown below. You can make the decimals the same by

adding zeros.

Ones Decimal Point Tenths Hundredths Thousandths

0 2

2 0

. 3 7 5

2 . 2 0 0

. 8 5 0

Compare the decimals starting from the ones column.

The decimals in descending order are: 2.2, 1.85, 1.42, 1.402, 1.375.

Example 6

Assessment Task 3

1. Order the following decimals in ascending order.

(a) 0.99, 0.909, 0.099,9.009

(b) 345.459, 345.549, 45.989, 45.909

(d) 20.004, 22.004,20.404,20.044

2. Arrange the following decimals in descending order.

(a) 48.672, 48.9, 48.671, 48.721 (b) 0.793, 0.321, 0.980, 0.979

3. Five friends measured their heights as 1.566 cm, 1.656 cm, 1.567 cm, 1.6057 cm and

1.067 cm.Arrange this heights from the smallest to the largest.

Further Assessment

1. During the school swimming competition, ﬁve swimmers took part in the ﬁnals.

Their ﬁnishing time were 9.8 s, 9.75 s, 9.79 s, 9.81 s and 9.72 s.

(a) Arrange the time from the one who came ﬁrst to the one who came last in the ﬁnals.

(b) What time did the winner take?

2. Water containers were found to hold water in litres as follows: 3.343 l, 3.434l,

3.324 l, 3.324 l and 3.423 l.Arrange this amounts in litres from the largest to the

smallest.

3. Grade ﬁve learners shared sugarcane as follows: 5.545 cm, 5.455 cm, 5.504 cm,

5.045 cm,5.645 and 5.654 cm.Order these lengths from the largest to the smallest.

4. Four packets of maize ﬂour were found to measure 2.756 kg, 2.567 kg, 2.657 kg

and 2.576 kg respectively. Order these masses in descending order.

Adding decimals up to thousandths

Activity

1. Make number cards like the ones shown.

7.345 5.034

6.263

2. Choose any two number cards from the ones you have made.

3. Add the decimals on the number cards.

Work out 32.41 + 0.295.

Working

Line up the decimal points with respect to their place value.

3 2 . 4 1 0

+ 0 . 2 9 5

3 2 . 7 0 5

32.41 + 0.295 = 32.705

Add starting from thousandths, regrouping

where necessary.

Example 7

Assessment Task 3

1. Work out each of the following:

(a) 10.9 + 21.009 (b) 345.662 + 112.096 (c) 449.281 + 27.134

2. Evaluate each of the following.

3 . 4 5 6

+ 2 . 7 4 1

(a)

3 . 3 5 6

+ 8 . 9 7 2

(b)

1 8 . 7 7 4

+ 7 . 6 3 1

(c)

2 5 . 6 5 4

+ 4 5 . 2 2 1

(d)

Three friends shared a piece of sugarcane as: 6.562 cm, 6.653 cm and 6. 546 cm.What is

the total length of sugarcane they shared?

Working

Add the length that each one got.

6.562 + 6.653 + 6. 546 = 19.761

Example 8

Further Assessment 2

1. A butcher sold 46.584 kg of meat on Saturday and 54.355 kg of meat on Sunday.

Determine the total mass of meat the butcher sold for the two days.

2. Massai donated cooking oil to the

ﬂood victims. On the ﬁrst day, his

team distributed 525.575 litres and on

the second day, 834.576 litres were

distributed. Find the number of litres

they distributed in the two days.

3. Grade ﬁve learners used 32.674 litres

of water on day one and 43.775 litres

on day two during their camping tour.

How much water was used by the

learners for the two days?

4. A carton of mass 123.456 kg has ten items. Six items of total mass 48.945 kg were

added to the carton.Work out the new mass of the carton.

Subtracting decimals up to thousandths

Activity 5

1. Make decimal number cards like the ones shown.

7.345 5.034

6.263

4.786

2. Pick any two number cards at a time.

3. Work out the difference between the decimals numbers in the two number cards.

Evaluate each of the following.

(a) 0.784 – 0.02 (b) 41.559 – 20.415

Working

Subtract starting from the thousandths, regrouping where necessary.

(a) 0.784 – 0.02 = 0.764 (b) 41.559 – 20.415 = 21.144

Example 9

Assessment Task 4

1. Work out each of the following.

(a) 345.94 – 121.319 (b) 264.87 – 64.028

2. Evaluate each of the following.

342.567

– 122.713

(a)

26.543

– 17.61

(b)

77.705

– 18.234

(c)

61.235

– 30.221

(d)

Halima had 7.456 cm of a piece of sugarcane. She gave a 2.435 cm piece to Joshua and

3.125 cm to Judith.What length of sugarcane did she remain with?

Working

Length she gave out = 3.125 + 2.435

= 5.560 cm

Length she remained with = 7.456 – 5.560

= 1.896 cm

Example 10

Further Assessment 3

1. A tank has 884.572 litres of water. After being used for one week, the water

reduced to 132.225 litres. How much water was used for the one week?

2. A supermarket ordered 745.775 kg of meat then they sold 48.251kg on that day.

Determine the amount of meat that remained.

3. A farmer harvested 458.612 kg of tomatoes. 38.672 kg got spoilt before being sold

at the market. How many kilogrammes of tomatoes were sold?

4. A loaded vehicle had a mass of 2455.098 kg. The vehicle ofﬂoaded two cartons of

total mass 125.954 kg to a customer and then later ofﬂoaded ﬁve cartons of total

mass 375.672 kg to another customer.Work out the new mass of the vehicle.

Term 2

Mid Term Assesment

1. Write the place value of digit 7 in the number 78 452.

2. Complete the chart below to show the total value of each digit in 68 054.

Number 6 8 0 5

Total value 60 000

3. Form the largest number from the following digits: 4, 5, 7, 0, 9.

4. Arrange the following numbers from the largest to the smallest.

34 560, 34 460, 34 960, 34 760

5. Round off 47 070 to the nearest thousand.

6. Identify the two numbers that are divisible by 2 from: (25, 68, 223, 346).

7. Find the HCF of 48 and 36.

8. Write twenty-three thousandths as a decimal.

9. What is the perimeter of the shape alongside?

10. Find the least number of fruits that can be equally shared

by 12 boys and 18 girls without a remainder.

15 cm

11. Work out: 526 056 + 333 830.

12. What is the place value of digit 5 in the number 347.758?

13. In a certain county, there are 232 537 learners in Grade 4 and 203 380 learners in

Grade 5. Calculate the number of learners in the two grades.

14. Work out:

15. Estimate the sum of 44 836 and 65 367 by ﬁrst rounding off the numbers to the

nearest hundred.

16. What is the next number in the pattern 67 320, 66 320, 65 320, 64 320, _________?

17. Samuel had 356 340 shillings. He used 230 110 shillings to buy two dairy cows. He

used the rest of the money to pay his workers on the farm. How much was used to

pay his workers?

18. A tank contained 8 645.6 litres of water. A family used 125.32 litres in one day.

Calculate the amount of water in litres that remained.

19. A family uses 12 litres of milk every day. Find the number of litres the family uses in

the month of April.

20. Use the long division method to work out 854 ÷ 13.

21. Arrange the following numbers from the smallest to the largest.

367.896, 436.289, 367.98, 436.9.

22. Calculate the value of 14 ÷ 2 − 3 + 2.

23. Write the ﬁrst two equivalent fractions of

24. Arrange the following fractions in an increasing order.

25. Sarah bought

kg of sugar and

kg of salt. She wanted to send them home

using a courier that uses mass to calculate the cost of sending items. Calculate the

total mass the courier found when they weighed Sarah’s items.

26. Work out 53.113 + 945.5.

27. Simplify 3 m + 5 m + 6 m.

28. Complete the table below.

Sport Number of learners Tally marks

Football 16

Hockey

Basketball 12

29. How many quarter kilograms are there in 8 kg?

30. Draw a cuboid.

Kilometre as a unit of measuring length

Activity

Look at the following picture and use it to answer the questions that follow.

(d) How far is the school from the swimming pool?

(e) Ochanda moved from the house to the supermarket and then to the swimming

pool. Determine the distance he covered.

Learning point

A kilometre is a unit of measuring length that is longer than a metre.It is written in short

as km and it is often used when measuring the distance between places.

Estimating and measuring length in kilometres

Activity 2

1. Mention destinations you have travelled to before.

2. How far do you think was the distance covered in kilometres?

Assessment Task

1. Name three places near your school which are about 1 kilometre away.

2. What is the estimate distance from your home to school?

3. Identify and write the most reasonable unit to measure the distance from Nairobi

city to Kisumu city.

4. What is the estimate distance from your school to the nearest shopping centre?

Measurement

Length

Relationship between kilometre and metre

Activity 3

Imagine that you and your friends have been on a nature walk in the forest for the whole

day. On your way back to town, you are all

very tired and you want to get home using the

shortest route.You come across a road sign on

the road, that shows two possible routes. One

is 1000 metres.The other is 1 kilometre long.

1. How can you know the shortest route to

take?

2. Which one of the routes would you take?

3. What is the relationship in distance

between the two routes?

Converting kilometres to metres

Activity

1. Make ﬂashcards like the ones shown below.

5 km

10 km

6.6 km

8.1 km

2. Pick one ﬂashcard at a time.

3. Convert the distance written on the ﬂashcard to metres.

The distance from Mali Primary School to Mali shopping centre is 2 km 230 m. Express

this distance in metres.

Working

1 km = 1 000 m

Convert the km to m; 2 x 1 000 = 2 000 m

Add 230 m to 2 000 m: 2 000 + 230 = 2 230 m

Example 1

Assessment Task 2

1. Convert the following measurements to metres.

(a) 12 km (b) 8 km 3 m (c) 5 km (d) 18 km 36 m

(e) 5 km 200 m

(f) 56 km 740 m (g) 34 km 780 m (h) 43 km 999 m

2. Express 42.88 kilometres in metres.

Further Assessment 1

1. The distance between a church and a school is 5 km. Convert this distance to

metres.

2. Karanja walked for 5 km 21 m to cast his vote during a general election. What

distance did he cover in metres only?

3. Wambui’s family moved to a new house. Their old house is 3 km from the new

house. How many metres is the old house from the new house?

4. Benard ran a 42 km race during the Tokyo Olympics in a time of 2 hours. How

many metres did he cover in the whole race?

Converting metres to kilometres

Activity 5

1. Make ﬂashcards like the ones shown below.

1000 m 6600 m 8100 m

5000 m

2. Pick one ﬂashcard at a time.

3. Convert the distance written on the ﬂashcard to kilometres.

Convert 5 000 m into kilometres.

Working

1 000 m = 1 km

5 000 m = 5 000 ÷ 1 000 = 5 km

Example 2

Express 4 210 m in kilometres and metres.

Working

Divide 4210 by 1000.

4 km

1000 4 210 m.

4 000

210 m.

4 210 m = 4 km 210 m

Example 3

Assessment Task 3

1. Convert the following measurements into km.

(a) 3 000 m (b) 34 000 m (c) 25 000 m (d) 90 000 m

2. Convert the following measurements into km and metres.

(a) 4 530 m (b) 2 370 m (c) 2 300 m (d) 76 780 m

3. Match the distance in metres to the correct distance in kilometres.

Distance in metres Distance in kilometres

55 000 m

34.06 km

5 005 m 34.006 km

34 006 m

5.005 km

34 060 m

55 km

Further Assessment 2

1. The distance from Thika to Nairobi is 5 100 m.What is this distance in km?

2. Madaraka express train covered 60 000 m in one hour. Express this distance in

kilometres?

3. The fence around Bokono’s garden is 760 m long. How long is the fence in

kilometres?

4. Stanley walks 2 000 metres a day. Determine the number of kilometres he walks

in two days.

Addition involving metres and kilometres

Activity 6

1. Write measurements on the cards as shown below.

32 km 210 m

41 km 342 m

2. Add the measurements on the cards.

Workout: 3 km 210 m + 5 km 873 m.

Working

Example 4

Add the metres; 210 m + 873 m = 1 083 m

Since 1 km = 1 000 m.

Regroup 1 083 m to 1 km 83 m.

Write 83 m on the column of metres.

Add the 1 km to the km column and write 9 km.

km m

3 210

+ 5 873

9 083

Assessment Task 4

1. Work out each of the following.

km m

6 424

+ 2 302

(a)

km m

7 457

+ 19 426

(b)

km m

78 886

+ 57 60

(c)

2. Find the sum of each of the following.

(a) 5 km 670 m + 3 km 213 m (b) 6 km 430 m + 4 km 400 m

Sabrina went on a journey to visit her grandmother. She used a train and travelled for a

distance of 65 km 146 m and then used the bus for the rest of the 29 km 950 m journey.

Determine the distance she covered on her journey.

Working

Add the two distances.

km m

6 5

1 4 6

+ 2 9 9 5 0

9 5 0 9 6

Example 5

The total distance she travelled was 95 km 96 m.

Add the metres: 146 m + 950 m = 1 096 m.

Regroup the 1096 m = 1 km and 96 m.

Add the kilometres: 65 + 29 + 1 = 95 km.

Further Assessment 3

1. Sarah walked for 5 km 400 m to the market and a further 2 km 875 m to the

nearest hospital to visit a patient.What is the total distance that she covered?

2. A county government contracted two companies to build two roads in the county.

One contractor constructed a road that was 47 km 172 m while the other

constructed a road that was 20 km 502 m long. Determine the total length of roads

constructed by the two companies.

CONSTRUCTION BY

COUNTY GOVERNMENT

3. Tourists arrived at Mombasa Airport on a plane after travelling for 300 km 567

metres. They then took a tour bus to National Park covering a distance of 152

km 42 metres.Work out the total distance they covered.

Subtraction involving metres and kilometres

Work out 5 km 230 m – 2 km 115 m.

Working

Subtract the two distances.

km m

5 230

– 2 115

3 115

(a)

Example 6

Subtract the metres: 230 – 115 = 115 m

Subtract the km: 5 – 2 = 3 km

Assessment Task 5

1. Subtract 75 km 345 m from 200 km 20 m.

2. Becky and Kate were exercising using a treadmill.They each ran for exactly

20 minutes on the treadmill. Kate’s

treadmill recorded that she had

run for 1 km 500 metres. Becky’s

treadmill recorded that she had

run 2 kilometres.Who ran a longer

distance, and by how much?

3. The distance between Saﬁ town and

Unity town is 64 km 185 m. Peter

travelled from Saﬁ town to Unity

town. He travelled 49 km 365 m by

bus and the rest by car.Determine the

distance peter travelled by car.

Multiplication of metres and kilometres by a whole number

Work out: 21 km 206 m x 6.

Working

Multiply the two distances.

km m

21 206

x 6

127 236

Example 7

Multiply the metres: 206 x 6 = 1 236 m

Regroup 1 236 m to get 1 km and 236 m.

Write 236 in the metres column.

Multiply km: 21 x 6 = 126 km

Add the 1 km you regrouped: 126 + 1= 127 km.

Assessment Task 6

1. Work out each of the following.

(a) 6 km 200 m x 4 (b) 23 km 342 m x 6

2. Evaluate each of the following.

km m

61 30

x 12

(a)

km m

213 431

x 4

(b)

km m

5 299

x 3

(c)

3. The distance around a circular athletics track is 3 km 450 m. Limo ran around the

track 4 times.What distance did he cover?

4. What is 34 km 345 m multiplied by 3?

Division of metres and kilometres by a whole number

Work out: 7 km 200 m ÷ 3.

Working

Example 8

Divide the km: 7 ÷ 3 = 2 km remainder 1 km

Convert the remaining 1 km to metres.

1 x 1000 m = 1 000 m

Add 1000 + 200 = 1 200 m

Divide 1 200 m by 3 = 400 m.

2 400

3 7 km 200 m

- 6 +

1 x 1000 = 1000

1200

–12

000

– 000

Assessment Task 7

1. Work out each of the following.

(a) 9 km 600 m ÷ 3 (b) 67 km 200 ÷ 12 (c) 44 km 400 m ÷ 4

(d) 45 km 900 m ÷ 3 (e) 69 km 160 m ÷ 13

2. Evaluate each of the following.

(a) 4 14 km 400 m (b) 6 13 km 242 m

Further Assessment 4

1. A road 54 km 600 m was divided into 6 equal sections for different contractors.

What is the length of each section?

2. A cyclist covered a distance of 53 km 400 m after going round a circular route

3 times.What was the distance covered in each round?

Area

Using a square centimetre (cm

) as a unit of measurement

Activity 1

1. Use a ruler to measure and draw a square of sides 1 cm on a manila paper.

1 cm

2. Cut out the square using a pair of scissors.

3. What is the area of the square that you have cut out?

Learning point

Area is measured in square centimetres (cm

). A square of sides 1 cm has an area of

1 square centimetre, written in short as 1 cm

Find the area of the shaded part.

1 cm

Working

The shaded part of the ﬁgure is made up of seven 1cm by 1 cm small squares.

The area of each of the small 1-cm squares is 1 cm

Therefore, the area of the shaded ﬁgure is 7 cm

Example 1

Assessment Task 1

1. Evaluate the area of each of the shaded regions in each of the following shapes.

1 cm

(a)

1 cm

(b)

1 cm

(c)

1 cm

(d)

Working out the area of squares and rectangles in square centimetres by

counting the squares

Activity 2

1. Draw 1 cm

grid on a manila paper.

2. Carefully cut out the 1 cm

grid from the Manila paper.

3. Draw different rectangular and squared shapes.

4. Place the square centimetre grids to ﬁt the shapes that you have drawn.

4. Count the number of squares that ﬁt each shape.

5. What is the area of each shape?

The following shape is made up of 1 cm

squares. Find its area by counting the squares.

Working

There are 30 squares.

Each square is made up of 1 cm

The area of the shape is 30 x 1 cm

= 30 cm

Example 2

Assessment Task 2

1. The following shapes are made up of 1 cm

squares.Find their area by counting the squares.

Area =

(a)

Area =

(b)

Area =

(c)

Area =

(d)

2. Eveline and Sonia are measuring the area of a rectangle. Eveline used circles and

Sonia used squares as shown to ﬁnd the area.

Eveline Sonia

(a) Identify the one who used the correct method. Explain why.

(b) What is the actual area of the rectangle?

3. Festus drew the following shapes in his squared book that is made up of a 1 cm

grid.

Work out the area of each shape.

(a) (b) (c) (d)

Working out area in square centimetres by multiplying length times width

Activity 3

1. Use a ruler to draw a 3 cm by 6 cm rectangle on manilla paper.

Length = 6 cm

Width = 3 cm

2. Multiply the size of the length by the size of the width and write down your answer.

3. Draw grid lines that are 1 cm on the rectangle.

1 cm

4. Count and write the number of squares along the length.

5. Count and write the number of squares along the width.

6. Find the area of the rectangle by multiplying the number of squares along the length

by the number of squares along the width.

7. Compare the two areas that you got.What do you notice?

Learning point

Area of a rectangle = Length (l) × width (w).That is, A = l x w where l is the length

and w is the width of the rectangle.

A square is a special type of rectangle because its sides are equal.

So for squares, the area is given by multiplying side by side.

The formula we use is Area = side × side.

Find the area of each of the following if each of the squares has an area of 1 square

centimetre.

(a) (b)

Working

(a) Area of a rectangle = length × width

= 8 × 6

= 48

Each of the squares has an area of 1 square centimetre.

Therefore, the area is 48 cm

(b) Area of a square =side × side

= 8 × 8

= 64

Each of the squares has an area of 1 square centimetre.

Therefore, the area is 64 cm

Example 3

Work out the area of the following ﬁgures.

7 cm

3 cm

18 cm

(a) (b)

Working

(a) Area of a square = side × side

= 7 cm × 7 cm

= 49 cm

(b) Area of a rectangle = length × width

= 3 cm × 18 cm

= 54 cm

Example 4

Assessment Task 3

1. Work out the area of each of the following shapes.

25 cm

(d)

10 cm

8 cm

(e)

40 cm

(f)

12 cm

7 cm

(a)

8 cm

(b)

34 cm

28 cm

(c)

2. A sheet of paper measures 29.7 cm by 21 cm. Determine the area of the paper.

3. Find the area of a rectangle if its length is 25 cm and width is 10 cm.

The cost of repairing a tiled ﬂoor is 10 shillings per square centimetre. Paloma repaired

a rectangular section of her tiled ﬂoor of length 80 cm and width 30 cm. How much did

Paloma spend to repair her ﬂoor?

Working

To ﬁnd the total cost of repairing the ﬂoor, we multiply the area of the section of the

ﬂoor to be repaired by the cost of repairing one square centimetre (1 cm

Area = l x w

= 80 cm x 30 cm = 2 400 cm

Cost of cementing = area x cost of cementing

= 2 400 cm

x 10 shillings per cm

= 2 4 000 shillings.

Example 5

A tailor cut a 25 cm by 6 cm cloth into 5 equal pieces to use in making pockets of

trousers that he was making.

25 cm

6 cm

Determine the area of each piece.

Working

The ﬁrst step is to ﬁnd the area of the whole cloth.

Area of the cloth = l x w

= 25 × 6

= 150 cm

To ﬁnd the area of each piece:

= 150 ÷ 5

= 30 cm

The area of each piece is 30 cm

Example 6

Further Assessment 1

1. A rectangular picture measures 75 cm by 32 cm.Find the cost of printing the picture

if the rate of printing is 2 shillings per 5 square centimetre.

2. To keep the pedestrians safe as they walk along the road, the government tiled

footpaths using squared tiles. In one of the

parts, 100 tiles of length 24 cm and width

15 cm were used.What is the area of the

path the tiles covered?

3. Determine the number of tiles of length

5 cm and width 2 cm that are required

to tile the ﬂoor of a room that measures

400 cm by 400 cm.

4. Lilian loves collecting stamps. One day, she collected 9 square stamps of sides 3 cm

each. She glued them onto a card to form a bigger square as shown.

What area do the stamps

cover on the card?

What we have learnt

Area is measured in square centimetres (cm

). A square of sides 1 cm has an area of 1

square centimetre, written in short as 1 cm

Area of a rectangle = length × width that is,A = l x w where l is the length and w is the

width of the rectangle.

Area of a square = side × side.

Volume

Volume of cubes and cuboids

Cubic centimetre as a unit of measuring volume

Activity 1

Observe the following cube and use it to answer the questions that follow.

1. Measure the side of the cube using a ruler.

2. Work out the volume of the cube shown.

3. What are the units of the cube that you have worked out?

Learning point

To ﬁnd the volume of the cube, we multiply side by side by side. The units are also

multiplied the same way that is, cm x cm x cm = cm

Cubic centimetre (cm

) is the unit of measuring volume.

Finding the volume of cubes and cuboids in cubic centimetres

Activity 2

1. Use a ruler to draw a cube and a cuboid made of 1 cm cubes.

1 cm

2. Work out the volume of the cube and the cuboid you have drawn.

3. What are the units for the volumes you have worked out?

The following shapes are made from 1 cm cubes. Find the volume of each shape:

(a) (b)

Working

(a) Volume = columns × rows × layers

= 3 × 3 × 3 = 27

Each smaller cube making the shape is a 1 cm

Therefore, the volume of the cube is 27 cm

(b) Volume = columns × rows × layers

= 2 × 5 × 2 = 20

Each cube making the bigger cube is a 1 cm

Therefore, the volume of the cube is 20 cm

Example 1

Assessment Task 1

Each of the following is made from 1 cm cubes. Calculate the volume of each of them.

(a)

(c)

(b)

(d)

Formula for ﬁnding volume of cubes and cuboids

Activity 2

1. Use a manila paper to make 36 cubes of the size 1 cm by 1 cm by 1 cm.

2. Arrange the cubes in different ways to form different cubes and cuboids.

3. Use the cubes and cuboids you form to complete a table like the one shown.

Cube or cuboid Number of 1 cm

cube in the rows

Number of 1 cm

cube in the columns

Number of 1 cm

cube in the layers

Volume

4. What observation do you make about the volume of the cube or cuboid you make?

Learning point

The volume of each cuboid is equal to the product of its length, width and height.

Length

Width

Height

Volume of cuboid = l × w × h.

Volume of a cube = side × side × side.

Work out the volume of the following cuboid.

Working

Volume = l x w x h

= 12 cm x 5 cm x 3 cm

= 180 cm

Example 2

Find the volume of a cube of side 9 cm.

Working

Volume = side × side × side

= 9 cm x 9 cm x 9 cm

= 729 cm

Example 3

Assessment Task 2

1. Copy and complete the following table.

l w h Volume

(a) 6 cm 18 cm

4 cm

(b) 6 cm 6 cm 6 cm

(d) 1 cm 17 cm 3 cm

(e) 7 cm 7 cm

343 cm

(f)

24 cm

3 cm

144 cm

2. Work out the volume of each of the following shapes.

14 cm

12 cm

8 cm

(a)

8 cm

6 cm

(b)

13 cm

(c)

3. The following measurements show the measurement of different containers. Find the

volume of each of the container.

(a) Length = 16 cm, width = 60 cm and height = 20 cm

(b) Length = 22 cm, width = 22 cm and height = 1.5 m

Further Assessment 1

1. A container is 45 cm long, 15 cm wide and 10 cm high.What is its volume?

2. A brick has a length of 20 cm, a width of 9 cm and a height of 5 cm. Determine the

volume of the brick.

3. Gatweri’s cat food is sold in cubical tins of side 5 cm.What is the maximum volume

of food the tin can carry?

4. Calculate the volume of a cuboid-shaped crate that measures 30 cm by 20 m by 17 cm.

5. The following picture shows the sizes of two boxes that a manufacturing company

wants to make.

40 cm

50 cm

60 cm

50 cm

Identify and explain the box that will require a lesser amount of material to make?

What we have learnt

The volume of a cuboid is calculated using the formula V= length × width × height.

The volume of a cube is calculated using the formula:V= side × side × side.

Capacity

Millilitre as a unit of measuring capacity

Activity 1

1. Collect different containers from your environment.

500 ml

100ml

250ml

300ml

2. Check the units of measurement written on the containers.

2. Identify the containers that have millimetres as a unit of measurement.

Learning point

Millilitre (ml) is a unit of measuring capacity.

Measuring capacity in millilitres

Activity 2

1. Take a 10 ml bottle cap and use it to ﬁll a bottle with water.

2. How many 10 ml bottle caps ﬁll the bottle?

3. What is the capacity of the bottle in ml?

Fatuma used two-5 ml bottles to ﬁll a container.What is the capacity of the container

in millilitres?

Working

The bottle is ﬁlled with two small bottles of capacity 5 ml. Its capacity is 10 ml.

Example 1

Assessment Task 1

1. Three bottles of 10 ml each are used to ﬁll a bigger bottle.What is the capacity of

the bigger bottle in millilitres?

2. One bottle of a certain drug can hold thirteen 1 ml doses.What is the capacity of

the bottle in ml?

3. A patient received 6 drops of 1 ml medicine into the eye. What capacity of the

medicine did the patient receive?

Measuring capacity in multiples of 5 millilitres

Activity 3

1. Use a 5 ml container to ﬁll a bigger container.

2. How many of the 5 ml containers did you use to ﬁll the bigger container?

3. What is the capacity of the bigger container that you ﬁlled?

Angela used four 5 ml containers to ﬁll a bottle.What is the capacity of the bottle?

Working

One small container = 5 ml

4 small containers = 5 + 5 + 5 + 5 = 20 ml or 5 x 4 = 20 ml

Example 2

Assessment Task 2

1. How many 5 ml bottles can ﬁll containers of the following capacities?

(a) 10 ml (b) 50 ml (c) 100 ml (d) 75 ml (e) 200 ml

2. How many 5 ml spoons can be obtained from a 40 ml bottle of honey?

3. What is the capacity of a container that can be ﬁlled with twelve 5 ml bottles?

4. What is the capacity of a container that can be ﬁlled with ten 5 ml bottles?

Relationship between litres and millilitres

Activity 4

1. Use a 1-litre jug to ﬁll 100 ml cups.

(a) How many containers have you ﬁlled?

(b) How many millilitres are those?

2. Use the same1-litre bottle to ﬁll 250 ml cups.

(a) How many containers have you ﬁlled?

(b) How many millilitres are those?

3. What do you note about the number of millilitres ﬁlling the cups from the 1-litre

bottle in each case?

Learning point

1 000 millilitres is equal to 1 litre.

Conversion of litres into millilitres

Convert 6 litres into millilitres.

Working

1 l = 1 000 ml

6 l = 6 x 1 000 ml

= 6 000 ml

Example 3

Convert 5 l 230 ml to millilitres.

Working

Convert the litres: 5 x 1 000 = 5 000 ml

Add: 5 000 + 230 = 5 230ml

Example 4

Assessment Task 3

1. Convert the following to millilitres.

(a) 6 litres (b) 34 litres (c) 9 litrres

(d) 4 litres 340 ml (e) 12 litres 23 ml (f) 5 litres 450 ml.

2. Kimani milked 30 litres from his cows in the evening. How many millilitres was the milk?

3. A well produced 23 litres 367 ml every minute .Express the water produced in millilitres.

Conversion of millilitres to litres

Convert 9 000 ml into litres.

Working

1 000 ml = 1 litre

9 000 ml = 9 000 ÷ 1 000

= 9 litres

Example 5

Express 3 456 ml in litres and ml.

Working

1000 ml = 1 litre

3456 ml = 3456 ÷ 1000

= 3 remainder 456

= 3 litres 456 ml

Example 6

Assessment Task 4

1. Convert into litres.

(a) 5 000 ml (b) 4 000 ml (c) 23 000 ml (d) 54 000 ml (e) 1 000 ml

2. Convert to litres and millilitres.

(a) 7 600 ml (b) 5 468 ml (c) 3 240 ml (d) 2300 ml (e) 4 500 ml

3. A farmer bought 9 600 ml of pesticide.How many litres and millilitres was the pesticide?

Addition involving litres and millilitres

Workout:

23 l 673 ml + 40 l 465 ml

L ml

23 673

+ 40 465

64 138

23 l 673 ml + 40 l 465 ml = 64 l 138 ml

Example 7

Add ml: 673 + 456 = 1138 ml

Regroup 1138 ml = 1l and 138 ml.

Add L: 1 + 23 + 40 = 64 l

Assessment Task 5

1. Evaluate each of the following:

(a) 53 l 456 ml + 23 l 340 ml (b) 32 l 568 ml + 45 l 876 ml

2. Work out each of the following.

L ml

78 600

+ 37 357

(a)

L ml

47 900

+ 21 211

(b)

L ml

60 301

+ 25 70

(c)

Further Assessment 1

1. Karisa used 45 l 567 ml to wash clothes. He also used 345 l 785 ml to water her

animals. How much water did he use for the two activities?

2. A community tank has 785 l 200 ml. 555 l 150 ml more water is pumped into the

tank. How much water is there in the tank?

3. A school uses 46 l 320 ml of milk to prepare 10 o’clock tea and 20 l 830ml to

prepare 4 o’clock tea in a day. How much milk does the school use in a day?

4. Selina bought oil for three consecutive days measuring 6 l 500 ml, 3 l 200 ml, and

9 l 600 ml. How much oil was bought by Selina for the three days?

5. After learning that it is healthy to drink enough water each day, Alexia drunk

15 l 240 ml of water in 2 days and 27 l 23 ml litres of water in the rest of the days

of the week. Determine the amount of water Alexia drunk that week.

Subtraction involving litres and millilitres

Working

Subtract 235 l 133 ml from 515 l 225 ml.

Working

L ml

515 225

− 235 133

280 92

Therefore, 515 l 225 ml − 235 l 133 ml = 280 l 92 ml.

Example 8

Arrange the numbers vertically.

Write the capacities to be subtracted in l and ml

as shown.

First, subtract millilitres from right and then

subtract the litres.

Assessment Task 6

1. Work out:

L ml

45 548

− 8 745

(b)

L ml

74 754

− 38 458

(c)

L ml

57 435

− 21 123

(a)

2. Work out:

(a) 54 l 456 ml – 28 l 332 l (b) 67 l 444 ml – 32 l 76 ml

Maingi practises irrigation farming. One day, he had 456 l 386 ml of water in one

storage tank. He used 120 l 765 ml of water from the tank to irrigate his crops. How

much water remained in the tank?

Working

To get the amount of water that remained, we subtract the amount of water that was

used from the initial amount of water.

Example 9

The amount of water that remained was 335 l 621 ml.

L ml

456 386

– 120 765

335 621

Arrange the numbers vertically.

Write the capacities to be subtracted in l

and ml as shown.

First subtract millilitres from right and

then subtract the litres.

Further Assessment 2

1. A baby swimming pool had 540 litres 200 ml of water. During cleaning, 120 l 100

ml was drained out. How much water remained in the swimming pool?

2. A tank had 5 063 l 457 ml in the morning.At the end of the day, 89 l 598 ml had

been used. How much water was remaining in the tank at the end of that day?

3. The full capacity of one of the fuel storage tanks at a petrol station is 626 l 134 ml.

One morning before reﬁlling the tank, they measured its capacity and found that

there was 167 l 380 ml of fuel in the tank. Determine the maximum amount of fuel

that can be added to the tank.

4. A dairy factory processed 56 l 678 ml on the ﬁrst day of its operation. On the

second day, it processed 49 l 601 ml. What was the drop in the amount of milk

processed in the two days?

Multiplication of litres and millilitres by a whole number

Workout: 210 l 34 ml x 6

Working

L ml

2 2

210 34

x 6

1 262 04

Arrange the numbers vertically as shown.

Multiply 34 ml by 6.

Multiply 210 by 6.

210 l 34 ml x 6 = 1 262 l 4 ml

Example 10

Assessment Task 7

1. Work out each of the following.

L ml

75 324

x 7

(c)

L ml

34 00

x 2

(b)

L ml

34 400

x 2

(a)

2. Evaluate each of the following.

(a) 70 l 400 ml x 5 (b) 45 l 234 ml x 7

A bus uses 45 l 456 ml of fuel in a day. How much fuel does the bus use in 5 days?

Working

L ml

45 456

x 5

227 280

Arrange the numbers vertically as shown.

Multiply 456 ml by 5

Multiply 45 by 5

The bus uses 227 litres 280 ml of fuel in ﬁve days.

Example 11

Further Assessment 3

1. Sururu uses 120 l 400 ml of water for his animals every day. How much water does

he require for his animals for 7 days?

2. A school uses 45 l 200 ml of water every day for cooking. How much water does

it need in one week?

3. Gerry, the milkman delivers 10 l 250 ml of milk every day to Wasaﬁ hotel.What

quantity of milk does he deliver to the hotel in a week?

Division of litres and millilitres by a whole number

Activity 5

1. Fill a container with 20 l 400 ml.

2. If you want to draw all the water in 5 equal amounts, how will you determine how

much water to draw at a time?

A certain bus uses 79 l 560 ml of fuel in 5 days. If the bus uses an equal amount of fuel

everyday, how many litres of fuel does the bus use in a day?

15 l 912 ml

5 79 l 560 ml

− 5

− 25

4 x 1000 = 4000

4560

−45

−5

–10

79 l 560 ml ÷ 5 = 15 l 912 ml

Example 12

Divide the litres: 79 ÷ 5 = 15 remainder 4 litres

Convert the 4 l to ml = 4 x 1 000 = 4 000 ml

Add 4 000 ml to 560 ml = 4 560 ml

Divide millilitres: 4 560 ÷ 5 = 912 ml

Assessment Task 8

1. Work out the following.

(a) 50 l 65 ml ÷ 5 (b) 105 l 490 ml ÷ 7 (c) 41 l 200 ml ÷ 8

(d) 76 l 560 ml ÷ 3 (e) 96 l 480 ml ÷ 4

2. Evaluate each of the following.

9 108 l 810 ml

(a)

4 488 l 560 ml

(c)

8 65 l 200 ml

(b)

7 65 l 100 ml

(d)

3. Samson had 21 litres 420 millilitres of mango juice. He packed it into 7 equal bottles.

What was the capacity of each bottle?

4. A tank holds 765 litres 200 millilitres of water.The water was transferred to 5 smaller

containers with equal capacity. Determine the capacity of each container.

5. Shelly has 2 l 50 ml of oil. She wants to pack it equally into 50 ml bottles.Work out

the number of bottles she can be able to ﬁll with the oil.

Term 2

End Term Assesment

1. Calculate the total value of digit 5 in the number 567 032.

2. Write ﬁfty-six thousand three hundred and thirty-ﬁve in symbols.

3. Use a place value chart to write the place value of digit 6 in the number 67 843.

4. Calculate the GCD of 45 and 60.

5. Hassan sold 261 chicken each day in the month of September.Write the number of

chickens he sold that month to the nearest hundred.

6. A laptop has a length of 15 cm and a width of 6 cm. Calculate the area of the laptop

in square centimetres.

7. Choose the numbers that are divisible by 5 from (346, 430, 455, 557)

8. Write

100

as a decimal.

9. Arrange the following numbers in ascending order.

56 087, 55 087, 54 087, 53 807

10. Samson had 56 798 eggs on her farm.He sold 32 459 eggs.How many eggs remained?

11. The distance from Maua’s home to the river is 5 km 200 m.What is the distance in metres?

12. Work out:

13. What is the value of 4 569 + 3 402 – 2 022?

14. Calculate the perimetre of a rectangle with width 8 cm and length 10 cm.

15. Identify the digit in the place value of hundredths in the number 45.892

16. Which is the next number in the pattern 45 601, 46 601, 47 601, 48 601,__________

17. Find the LCM of 18 and 27.

18. Write the number of 5-millilitre bottles that can ﬁll a 30-millilitre bottle.

19. Calculate the value of 568 ÷ 14.

20. Estimate the difference between 4 567 and 3 245 by ﬁrst rounding off the numbers

to the nearest hundred.

21. What is the volume of the cube below?

22. Sanare’s cow produced 33 litres of milk every day. Write the amount of milk produced

by the cow in millilitres.

23. Convert

into an improper fraction.

24. Calculate the number of

kg packets that can be obtained from 16 kg.

25. Work out the value of 45.61 + 23. 56.

26. What is the name of the angle shown below?

27. Kyla had b bananas. He bought 3b more bananas. How many bananas does he have

altogether?

28. The length of a building is 765 cm.Write its length in metres and centimetres.

29. Find the volume of the ﬁgure below.

5 cm

4 cm

3 cm

30. Ndatho bought 34.783 kg of sugar for sale in week one of March. He bought 12.12 kg

more sugar in week two.What was the total amount of sugar he had brought to his

shop for sale in the two weeks?

Term 3

Opener Assesment

1. Identify the place value of each digit in 946.73 using a place value chart.

2. Five learners in Grade 5 made the following number cards.

Tom 36 674

Mueni 35 674

Mary 23 764

Wambui 9 999

Akinyi 23 674

(a) Whose card had the number with the least value?

(b) If the children stood in a line from the one with the greatest number to the one

with the least, how would they follow each other?

3. Mary had ﬁve hundred and two thousand and twenty-ﬁve goats.Write this number

of goats in symbols.

4. What is

in words?

5. A farmer sold 54 944 litres of milk in the month of September. Round off the number

of litres of milk sold to the nearest hundred.

6. After adding 57 843 to 2 349, Tom placed the answer on a place value chart.What

was the total value of the ﬁrst digit from the left?

7. Complete the pattern below.

8. A shopkeeper sold milk as follows in a week. Monday 678 l,Tuesday 1201 l,Wednesay

999 l,Thursday 689 l. Arrange the litres sold in ascending order.

9. Identify the numbers that are divisible by 5 and ﬁnd their sum. (3 452, 5 675, 2 020, 5 551)

10. Karuri is in Grade 5. He wanted to know how many bundles of ten could be made from

the number 2 340. How many bundles did he get?

11. Akili sold 120 kg of sugar every day in the month of May. How many kilograms had

he sold by the 15

day of that month?

12. List the ﬁrst ﬁve multiples of 8.

13. A children’s home received the sum of sh. 334 542, sh. 62 310 and sh. 5 784 as

donations in their account. How much money did they receive altogether?

14. Tamara shared 351 pencils among 15 learners. How many pencils remained?

15. Akinyi had 1111 books to share among her 12 cousins.What is the estimated number

of books that each cousin would receive?

16. Work out: 22 579 × 26 =

17. Machuki and Mathu each had a full chapati. Machuki cut his in the middle to make

two pieces. Mathu cut his twice to make 4 equal pieces. If Mathu ate two of his pieces

and Machuki ate 1 of his, who ate a bigger piece?

18. Find the area of the following ﬁgure if each small square has an area of 1 cm square.

19. Work out. 6 l 25 ml × 5 =

20. Sonnia earned sh.15 000 at the end of the month,after which she made the following budget.

Saving 1 000

Rent 4 000

Food, 5 000

Clothes 1 000

Fee 3 000

Is the money she earned enough for her budget?

21. Find the value of two hundred and ﬁve multiplied by seven.

22. Draw a cuboid with the measurements 8 cm by 6 cm by 4 cm and ﬁnd its volume.

23. Patricia gave Salim her son

of a cake. His aunt also gave him a

of her cake.

What fraction of cake did Salim have?

24. Dr Joygrace paid sh. 1 200 after buying two packets of facemasks for her patients.

Each pack costs sh. 575. How much balance was she given?

25. Name the angle shown in the ﬁgure below.

26. The following data represents the ages of learners in Grade 5 at Raha Primary School.

11, 13, 15, 11 , 11 10, 14, 12, 11, 13, 12, 11, 11, 11, 15, 10, 12, 14, 15, 11, 12, 11, 11, 13,

14, 11,12, 10,11, 13,11,12,12,13,11,11,15,14,12,14,14,11,14,11, 13.

(a) Represent the data on a table.

(b) How many learners are in the class?

27. Measure the angle formed at point k.

28. Elsie saves sh. 15 every day from the pocket money given to her by her parents. How

much can she save in the month of April?

29. How many containers of B can be used to ﬁll container A?

250 ml.

50 litres

30. Estimate the weight of your Mathematics textbook.

Mass

Mass in grammes

Activity 1

1. Collect different items majorly found at home and school.

Medicine

50g

500g

250g

Chalk

2. List the items that can be measured in grammes.

3. Group the items with more mass in grammes.

4. Group those items with less mass in grammes.

Learning point

Gramme is a unit of measuring mass that is smaller than a kilogramme.

Assessment Task 1

1. List ﬁve items found at school whose mass can be measured in grammes.

2. List ﬁve items found at home whose mass can be measured in grammes.

3. List ﬁve items found at a marketplace whose mass can be measured in grammes.

Estimation and measurement of mass in grammes

Activity 2

1. Collect items such as a packet of chalk, duster, pen, pencil or exercise book.

2. Estimate the mass of each item you have collected.

3. Using a weighing balance, measure the actual mass of the items and complete a

table like the one shown.

Item Estimated mass Actual mass

State the approximate mass of the following from the list provided.

(a) Butterﬂy (b) Leaf (c) Toothbrush

Working

(a) 6 g (b) 12 g (c) 8 g

Example 1

List items found at school whose mass is approximately 50 g.

Working

Piece of chalk, pencil, pen and duster.

Example 2

Assessment Task 2

1. Estimate the mass of each of the following.

(a) (b)

(c)

(d)

2. List items at home whose mass is measured in grammes.

3. List items at school that can be measured in grammes.

Relationship between gramme and kilogramme

Activity 3

1. Make number cards showing different masses in grammes and kilogrammes as shown.

2. Group the cards with same masses in grammes and kilogrammes.

1 kg 500 g 0.5 kg 1000 g

3. Use this to show the relationship between gramme and kilogramme.

Learning point

1 kilogramme = 1000 grammes or 1 kg = 1000 g

Conversion of kilogrammes to grammes

Convert the following mass in kilogrammes into grammes.

(a) 3.5 kg (b) 8 kg

Working

1 kg = 1000 g

8 kg = ?

= (8 kg x 1000 g)

(1 kg)

= 8 000 g

(b)

1 kg = 1000 g

3.5 kg = ?

= (3.5 kg x 1000 g)

(1 kg)

= 3 500 g

(a)

Example 2

Conversion of kilogrammes to grammes

Convert the following masses in grammes into kilogrammes.

(a) 2 800 g (b) 7 500 g

Working

(a) 1 kg = 1 000 g

? = 2 800 g

= (2800 g x 1 kg)

(1000 g)

= 2.8 kg

(b) 1 kg = 1 000 g

? = 7 500 g

= (7500 g x 1 kg)

(1000 g)

= 7.5 kg

Example 3

Assessment Task 3

1. Convert the following mass in kilogrammes into grammes.

(a) 23 kg (b) 17 kg (c) 111 kg (d) 25.2 kg (e) 11.3 kg

(f) 156 kg

(g) 24.8 kg (h) 48.1 kg (i) 311.4 kg (j) 144.8 kg

2. Express the following masses in kilogrammes.

(a) 120 g

(b) 2450 g

(f) 817 g

(g) 445 g (h) 3418 g

(i) 1355 g

(j) 4680 g

Addition of grammes and kilogrammes

Activity 4

1. Make number cards like the ones shown below.

405 kg 127 g + 106 kg 203 g

294 kg 116 g + 180 kg 126 g

235 kg 502 g + 142 kg 326 g

2. Pick one practice card at a time.

3. Work out the sum of the mass written on the number card.

Work out 32 kg 751 g + 8 kg 213 g

Working

Kg g

3 2 7 5 1

+ 8 2 1 3

4 0 9 6 4

32 kg 751 g + 8 kg 213 g = 40 kg 964 g

Example 4

Add grammes: 751 + 213 = 964 g

Kilogrammes: 32 + 8 = 40 kg

Assessment Task 4

1. Work out the following.

(a) 123 kg 776 g + 413 kg 312 g (b) 718 kg 218 g + 216 kg 514 g

2. Evaluate each of the following.

Kg g

5 5 8 1 2

3 9 2 1 3

+ 1 6 3 1 7

(a)

Kg g

1 2 7 1 6

3 7 7 0 9

+ 4 5 5 4 2

(c)

Kg g

9 1 2 1 6

8 3 4 5

+ 6 2 4 1 1

(b)

Kg g

6 1 9 1 2

2 1 2 2 1

+ 1 1 6 5 9

(d)

Three Grade 5 learners in Elimu Bora primary school recorded their masses as

42 kg 811 g, 37 kg 119 g and 56 kg 215 g.What is their total mass?

Working

Kg g

42 811

37 119

+ 56 215

136 kg 145 g

The total mass of the learners is 136 kg 145 g.

Example 5

1 1

Further Assessment 1

1. A fruit dealer recorded masses of fruits sold as Tomatoes: 234 kg 554 g, oranges:

112 kg 314 g and passion:113 kg 406 g. Determine the total mass of the fruits sold.

2. Jenifer bought 7 kg 200 g of sugar and 9 kg 395 g of rice. Calculate the total mass

Jenifer bought.

3. A farmer loaded his truck with 352 kg 100 g of pumpkins and 207 kg 432 g of

watermelons to take to the market for sale.Find the total mass that the truck carried.

4. A farmer recorded the mass of eggs produced in his farm in week one as

48 kg 613 g, week two as 98 kg 445 g and week three as 106 kg 496 g.What is

the total mass of eggs produced?

5. Four Grade 5 learners recorded their masses as 45 kg 715 g, 50 kg 886 g 45 kg 992 g

and 51 kg 211 g. Calculate the total mass of the learners.

Subtraction of grammes and kilogrammes

Activity 5

1. Make practice cards like the ones shown.

445 kg 125 g – 126 kg 205

194 kg 16 g – 160 kg 46 g

230 kg 512 g – 132 kg 306 g

2. Pick one practice card at a time and work out the difference in mass.

Work out 17 kg 812 g – 10 kg 601 g.

Working

Kg g

1 7 8 1 2

− 1 0 6 0 1

0 7 2 1 1

The answer is 7 kg 211 g.

Example 6

Assessment Task 5

1. Work out:

(a) 530 kg 344 g – 114 kg 456 g (b) 126 kg 640 g – 76 kg 718 g

2. Evaluate each of the following:

Kg g

3 4 7 6 7 5

− 1 3 3 46 2

(a)

Kg g

8 2 5 5 1 3

− 3 1 1 2 7 5

(d)

Kg g

5 4 8 2 6 6

− 1 2 7 1 0 8

(b)

Kg g

9 1 2 7 1 7

− 6 0 9 4 1 9

(c)

Halima, James, Bahati and Barasa measured their mass and found that when they all

stand on the electronic balance,their total mass is 127 kg 675 g.When Bahati and Barasa

stepped out of the electronic balance, the machine indicated 75 kg 845 g. Determine the

mass of Bahati and Barasa.

Working

Kg g

1 2 7 6 7 5

− 7 5 8 4 5

5 1 8 3 0

The mass of Bahati and Barasa is 51 kg 830 g.

Example 7

Further Assessment 2

1. Abel’s mass is 49 kg 357 g while Ronny’s mass is 32 kg 458 g.Whose mass is less

and by how much?

2. In one season, Kiuna harvested 347 kg 918 g of tomatoes while Kipruto harvested

4115 kg 313 g of tomatoes.Work out the difference in mass in their harvests.

3. Grade ﬁve learners in Shikao Primary School recorded their masses as Haron:36 kg

918 g,Hesborn:42 kg 516 g, Andrew:38 kg 246 g and Beatrice:36 kg 204 g.Calculate;

(a) The difference between the mass of Andrew and Beatrice.

(b) The difference in mass between Haron and Hesborn.

4. During a bullﬁghting community event, two farmers measured the mass of their

bulls as 718 kg 405 g and 696 kg 918 g. Determine which bull has more mass and by

how much?

Multiplication of grammes and kilogrammes by a whole number

Activity 6

1. Make number cards like the ones shown.

125 kg 15 g x 5

190 kg 45 g x 6

155 kg 56 g x 7

2. Pick one practice card at a time.

3. Work out the product of the mass and the whole number on the number card.

Work out: 123 kg 615 g x 8.

Working

Kg g

1 2 3 6 1 5

x 8

9 8 8 9 2 0

The answer is 988 kg 920 g.

Example 8

1 2

4 4

Multiply15 g by 8 = 4920 g.

Regroup 4 920 as 4 kg 920 g.

Multiply 123 kg by 8 = 984 kg.

Add regrouped 4 kg to 984.

984 kg + 4 Kg = 988 kg.

Assessment Task 6

1. Work out the following.

(a) 123 kg 211 g x 4 (b) 56 kg 345 g x 9 (c) 443 kg 312 g x 6

(d) 416 kg 206 g x 3 (e) 719 kg 216 g x 2 (f) 304 kg 411 g x 5

2. Work out:

Kg g

1 0 5 2 1 1

x 5

(a)

Kg g

1 7 2 3 0 1

x 4

(c)

Kg g

4 1 1 2 0 6

x 3

(b)

Kg g

7 1 4 2 0 6

x 2

(d)

A transportation lorry carried textbooks in 9 cartons. If each carton has a mass of 582 kg

311 g, calculate the mass of the textbooks in the lorry?

Working

Kg g

7 2 2

5 8 2 3 1 1

x 9

5 2 4 0 7 9 9

The mass of the textbooks is 5240 kg 799 g.

Example

Further Assessment 3

1. Five Grade 5 learners measured their mass and found it to be equal. If each had a

mass of 45 kg 346 g, work out their total mass.

2. One reference textbook has a mass of 3 kg 103 g. Determine the total mass of 12

such books.

3. One sack of beans has a mass of 114 kg 788 g.A farmer harvested 9 such sacks.

Find the total mass of beans the farmer harvested.

Division of grammes and kilogrammes by a whole number

Activity 7

1. Make practice cards like the ones shown.

25 kg 5 g ÷ 5

96 kg 48 g ÷ 16

125 kg 50 g ÷ 5

2. Pick one practice card at a time.

3. Work out the quotient on the practice card you pick.

Work out: 38 kg 520 g ÷ 5

Working

7 704

3 8 kg 520 g

− 3 5 +

3 x 1000 = 3000

3520

–35

− 0

The answer is 7 kg 704 g.

Example 10

Divide 38 kg by 5 to get 7 kg reminder 3.

Converts 3 kg to grammes.

3 x 1 000 = 3 000g

Add 3 000 g to 520 g + 3 520 g.

Divide 3 520 g by 5 to get 704.

Assessment Task 7

Work out the following:

(a) 12 kg 48 g ÷ 4 (b) 145 kg 150 g ÷ 5

(d) 408 kg 396 g ÷ 6 (e) 315 kg 16 g ÷ 4 (f) 444 kg 312 g ÷ 2

(g) 264 kg 416 g ÷ 8

(h) 81 kg 819 g ÷ 9

2. Work out:

4 212 kg 36 g

(a)

5 625 kg 175 g

(b)

9 918 kg 72 g

(c)

Grade 5 learners from Uzima primary school measured the mass of 9 watermelon and

found it to be 31 kg 815 g. If all the watermelons had the same mass, work out the mass

of one watermelon.

Working

3 535

31 kg 815 g

− 27 +

4 x 1000 = 4 000

4 815

− 27

− 45

The mass of one watermelon was 3 kg 535 g.

Example 11

Further Assessment 4

1. The School librarian at Utumishi Primary School recorded a total mass of 9 cartons

of Mathematics textbooks as 981 kg 441 g. Determine the mass of one carton of

Mathematics textbooks.

2. Victims of ﬂoods received rice from donors. If a total of 1 618 kg 335 g of rice was

delivered by 3 vans each carring equal mass, calculate the mass each van was

carrying.

3. Grade 5 learners at Heshima Primary School measured the mass of 5 sacks of rice

as 520 kg 320 g. If the sack had equal mass, what was the mass of one sack of rice?

What we have learnt

1 kilogramme = 1000 grammes or 1 kg = 1000 g.

To convert kilogrammes into grammes, we multiply the number of kilogrammes by 1 000.

To convert grammes into kilogrammes, we divide the number of grammes by 1000.

Time

Second as a unit of measuring time

Activity 1

1. Go out of the class with a stopwatch or a digital watch. Get some space outside the

classroom.

2. Start the stopwatch and jump 5 times.

How long did it take you to jump ﬁve times?

Learning point

The second is the basic or standard unit of measuring time.

Relationship between minutes and seconds

Activity 2

1. Get a digital clock.

2. Observe the digits showing minutes and seconds.

3. How many seconds does it take before the minute number changes to the next number?

4. Use your observation to write the relationship between seconds and minutes.

Learning point

1 minute is equal to 60 seconds.

Converting minutes to seconds

Convert 4 minutes to seconds.

Working

1 minute = 60 seconds

4 minutes = 4 x 60 seconds

= 240 seconds.

Example 1

Learning point

When converting minutes to seconds, multiply the number of minutes by 60 seconds.

Assessment Task 1

1. Convert the following to seconds.

(a) 6 minutes (b) 2 minutes (c) 11 minutes

(d) 7 minutes (e) 9 minutes (d) 50 minutes

2. Saruni took 30 minutes to walk from school to his home. How long did he take in

seconds?

Further Assessment 1

1. Waswa took 42 minutes to complete his mathematics assignment. How long did

he take in seconds?

2. Isabella was practising for a swimming competition. Her target is to complete

one swimming cycle in under 5 minutes. After making an attempt, it took her 319

seconds to complete one cycle. Explain if Isabella achieved her target.

3. What is 3 minutes and 14 seconds in seconds?

Converting seconds to minutes

Convert 300 seconds to minutes.

Working

60 seconds = 1 minute

300 seconds = 300 ÷ 60

= 5 minutes.

Example 2

Learning point

To convert seconds to minutes, divide the number of seconds by 60.

Assessment Task 2

1. How many seconds are there in each of the following minutes?

(a) 120 minutes (b) 180 minutes (c) 420 minutes

(d) 540 minutes (e) 240 minutes (f) 360 minutes

2. How many seconds are there in 5 minutes and 37 seconds?

3. Sheena took 840 seconds to ﬁnish a race. Express the time she took in minutes.

Further Assessment 2

1. Rewrite three hundred and eighty-six minutes in minutes and seconds.

2. A clubs session took 1 800 seconds. How long did the session take in minutes?

3. Omondi took 660 seconds feeding the chicken. How long did he take to feed the

chicken in minutes?

4. Jay visited a gaming station with his mother.His mother allowed him to play games

for 120 minutes. Each game lasts 180 seconds. Determine the number of games

that Jay can play.

5. Heston ran in a race during the interclass competitions. He ﬁnished in 420 seconds.

How many minutes did it take him to run the race?

Addition involving minutes and seconds

Work out: 12 minutes 20 seconds + 6 minutes 45 seconds

Working

Minutes Seconds

12 20

+ 6 45

19 05

Example 2

Add the seconds: 20 + 45 = 65 seconds.

Since 1 minute has 60 seconds, regroup 65

to 1 minute 5 seconds.

Add the minutes: 12 + 6 + 1 = 19 minutes.

Assessment Task 3

1. Work out each of the following.

Minutes seconds

23 15

+ 34 40

(a)

Minutes seconds

42 36

+ 8 50

(b)

Minutes seconds

52 46

+ 44 45

(c)

2. Find the total time for each of the following:

(a) 18 minutes 38 seconds and 11 minutes 37 seconds.

(b) 29 minutes 40 seconds and 22 minutes 44 seconds.

(d) 33 minutes 5 seconds and 29 minutes 26 seconds.

3. While going to his village, Romeo travelled for 74 minutes 40 seconds by train and

40 minutes 30 seconds by bus. Determine how long it took him to reach his village.

Subtraction involving minutes and seconds

Work out each of the following:

(a) Minutes Seconds

45 54

− 12 13

Working

Example 3

(a) Minutes Seconds

45 54

− 12 13

33 41

(b) Minutes Seconds

56 27

− 12 38

43 49

Subtract the seconds: 54 – 13 = 41 seconds.

Subtract the minutes: 45 – 12 = 33 minutes.

Since 27 is less than 38, regroup 1 minute to 60 seconds

and add it to 27 seconds: 60 + 27 = 87 seconds.

Subtract 87 seconds – 38 seconds = 49 seconds.

Subtract 55 minutes – 12 minutes = 43 minutes.

(b) Minutes Seconds

56 27

− 12 38

Assessment Task 4

1. Find the difference between:

(a) 38 minutes 50 seconds and 13 minutes 33 seconds.

(b) 24 minutes 45 seconds and 8 minutes 56 seconds.

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(d) 8 minutes 35 seconds and 3 minutes 46 seconds.

2. Mwali took 35 minutes 25 seconds to cycle from town A to town B while Sambu

took 22 minutes 46 seconds to cycle the same distance. How much more time did

Sambu take to complete the journey?

Multiplication involving time in minutes and seconds by a whole number

A farmer takes 12 minutes 10 seconds to fetch one jerrycan of water from a well. How

long will it take to fetch 6 jerrycans of water?

Working

Minutes Seconds

12 10

x 6

73 00

The farmer took 73 minutes to fetch 6 jerrycans of water.

Example 4

Multiply the seconds by 6: 10 x 6 = 60 seconds.

Regroup the 60 seconds to 1 minute.

Multiply the minutes by 6: 12 x 6 = 72 minutes.

Add the 1 minute you regrouped: 72 + 1 = 73 minutes.

Assessment Task 5

1. Evaluate each of the following.

Minutes seconds

11 13

x 6

(a)

Minutes seconds

24 30

x 8

(b)

Minutes seconds

36 23

x 5

(c)

2. A mason takes 26 minutes 40 seconds to ﬁx one window. How long will he take to

ﬁx 7 windows?

3. Kimani takes 32 minutes 24 seconds to load one lorry of potatoes. How long will it

take him to load 10 such lorries?

4. Tiffany takes 13 minutes 23 seconds to harvest avocados from one avocado tree.

How long will it take her to harvest avocados from 20 such avocado trees?

Division of time involving minutes and seconds

Activity 3

Musa took 30 minute 20 seconds to clean 5 rooms in a hotel. How much time did he take

to clean the room?

Discuss your answer with your friends.

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It takes 43 minutes 36 seconds for 6 camels to take water from a dam in turns. If each

camel takes equal time to take water, how much time does one camel take to take water?

Working

7 minutes 16 seconds

6 43 minutes 36 seconds

− 42

1 x 60 = + 60 seconds

− 6

− 36

Time taken by each camel is 7 minutes 16 seconds.

Example 5

Divide minutes by 6: 43 ÷ 6 = 7 minutes remainder 1

minute.

Convert the 1 minute to seconds and add it to 30

seconds.

1 minute = 60 seconds + 36 seconds = 96 seconds.

Divide the seconds by 6: 96 ÷ 6 = 16 seconds.

Assessment Task 6

1. Work out each of the following.

4 24 minutes 36 seconds

(a)

9 19 minutes 12 seconds

(c)

20 63 minutes 20 seconds

(e)

12 60 minutes 48 seconds

(b)

8 49 minutes 4 seconds

(d)

7 9 minutes 6 seconds

(f)

2. Ndunge took 26 minutes 20 seconds to wash 5 jackets. How long did she take to

wash one jacket?

3. A nurse took 36 minutes 48 seconds to vaccinate 12 children against measles. How

long did it take the nurse to vaccinate one child?

4. 12 lorries took 37 minutes 12 seconds to cross a border checkpoint from Tanzania to

Kenya. How long did it take one lorry to cross the checkpoint if each took equal time?

Learning point

1 minute is eqaul to 60 seconds.

When converting minutes to seconds, multiply the number of minutes by 60 seconds.

To convert seconds to minutes, divide the number of seconds by 60.

When adding time in minutes and seconds, we add the seconds ﬁrst then the minutes

regrouping where necessary.

When subtracting time in minutes and seconds, we subtract the seconds ﬁrst then the

minutes regrouping where necessary.

When dividing time in minutes and seconds by a whole number, we divide the minutes

ﬁrst then the seconds regrouping where necessary.

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Money

Budgeting

Activity 1

You have been given 500 shillings by your parent to spend before you go to a boarding school.

1. Prepare a list of the items you can buy.

2. Ask for the prices of the items that you have listed.

3. Pick out the items that you can be able to spend on the 500 shillings that you have.

4. How can you identify the needs and the wants so that you decide on what to spend on?

Learning point

To plan on how you will spend money that you have is called budgeting.A budget is a

plan that shows how one will spend money wisely.

The budget helps us to make a decision on how to spend money on our needs and wants.

Assessment Task 1

1. Explain what a budget is.

2. Your agriculture group has been given 400 shillings to spend on some items that you

will need for your group farm. Prepare a budget including all the items you will need.

3. What would you consider in order to make a good budget?

Importance of a budget

Activity 2

1. Use a digital device to research from the internet on the importance of a budget.

2. Make notes on your ﬁndings.

3. State why it would be important for you to make a budget.

Assessment Task 2

1. Salome owns a small grocery store in the village. One day, she earned 1 000 shillings

from the business. She made the following budget.

Saving 200

Food

400

Travelling 500

Paying debts 200

(a) Is the money she earned enough for her budget?

(b) Give a reason to explain if Salome’s budget is a good or bad budget.

2. You and your friends want to start a small business.You need to make a budget for

the small business.

(a) List what you will consider when making the budget.

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(b) Why is it important for you to make a budget before you start the business?

3. Give three advantages of preparing a budget.

Ta x

Activity 3

1. Look at the following pictures and answer the questions that follow.

What are the people in the picture doing?

2. Use a digital device to search for tax in Kenya.

3. Make notes on your ﬁndings.

4. Talk about what tax is. Share your ﬁndings with other groups.

Learning point

Tax is money that people pay to the government to help support the government

facilitate its services to its citizens.

Everyone is always encouraged to pay his or her taxes faithfully and in time. If they do

not pay tax,the government will lack money to provide important services to the citizens.

Importance of tax to the government

Activity 4

Look at the following pictures and answer the questions that follow.

CONSTRUCTION BY

THE

GOVERNMENT

(a) What is happening in each of the pictures?

(b) Where does the government get the money to provide for the services?

Learning point

In order to provide services, the government collects taxes from the citizens.

It is important for the citizens to pay taxes so that the government can get money to

pay for and provide services.

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Assessment Task 3

1. State why it is important for people to pay tax.

2. How do people in your area pay their tax?

Banking and loan services

Activity 5

Look at the picture below and answer the questions that follow.

(a) What are some of the services the people in the picture are getting at the bank?

(b) Name other services that are offered in the bank.

Assessment Task 4

1. Name the different services offered in banks.

2. List three things of value, which you can keep in safe custody in a bank.

Saving money

Activity 6

1. Talk to a resource person about the following:

(a) Why do you need to save money?

(b) What do you consider when you want to save money?

2. In pairs, ask your friend if he or she has ever saved any money at home in a home

bank.

3. Share your ﬁndings about the savings with the rest of the class.

Assessment Task 5

1. State the importance of saving money.

2. What are some of the ways you can save money?

3. Give reasons why it is important to keep money in the bank and not at home.

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Geometry

Lines

Identifying horizontal and vertical lines

Activity 1

1. Find different objects with straight lines in your environment.

2. Identify horizontal and vertical lines in the objects.

Learning point

Vertical line Horizontal line

Vertical lines are lines that run from top to

bottom as shown.

Horizontal lines are lines that run from

the left to the right as shown.

Assessment Task 1

1. Identify the vertical and thehorizontal line.

(a) (b)

2. How many horizontal lines do we have in a rectangle?

3. Draw the vertical lines on the shape below.

Drawing horizontal and vertical lines

When drawing horizontal and vertical lines, use a ruler or a straight piece of wood.

Use a ruler to draw a shape made up of horizontal and vertical lines.

Working

The horizontal lines are in black while the vertical lines are in green.

Example 1

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Assessment Task 2

1. Draw 3 horizontal lines of any measurement.

2. Draw 3 vertical lines of any measurement.

3. Draw three objects that have a horizontal line and a vertical line and show the lines.

4. Identify horizontal and vertical lines in the ﬁgure below.

Identifying and drawing perpendicular lines

Activity 2

1. Use a ruler to draw two lines intersecting at a right angle.

2. What is the name of the lines you have drawn?

Learning point

Lines that intersect at right angles are called perpendicular lines.

Assessment Task 3

1. Draw 3 sets of perpendicular lines.

2. Identify 3 objects in your environment that have perpendicular lines.

Identifying parallel lines

Activity 3

1. Look around the environment and identify objects with straight lines.

2. Do these straight lines meet?

3. Draw objects with lines like the ones shown below.

What is the name of the lines?

Learning point

Parallel lines are straight lines that do not meet.

Assessment Task 4

Identify pairs of parallel lines.

(a) (b)

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Drawing parallel lines

Activity 4

1. Use a ruler, pencil and a set square.

2. Place a ruler and a set square,on a paper with the set square on the edge of the

ruler.

3. Without moving the ruler or set square, use a pencil to draw a line as shown.

4. Slide the set square along the ruler and draw another line as shown below.

5. Identify the lines you have drawn.

Assessment Task 5

1. Draw lines parallel to the following lines.

(a)

(b)

(c)

2. Draw three pairs of parallel lines using a set square and a ruler.

108

Term 3

Mid Term Assesment

1. A forest has 200 200 baobab trees.Write the number of baobab trees in the forest in words.

2. What is the place value of digit 5 in the product of 32 and 81?

3. Write the number 46.02 in a place value chart.

4. Simplify the fraction

5. A factory produced an average of 120 cotton bales every day. How many bales did

it produce in the month of March?

6. Convert 12 minutes to seconds.

7. Give four equivalent fractions of

8. When a clocks, hour hand points at 12 and the minute hand points at 9 as shown,

what angle do the two hands make?

9. Mary subtracted 82 704 from 783 922. What was her answer?

10. Matete sketched the following simple drawing of a house. He counted the horizontal

and vertical lines.

(a) How many horizontal lines did he get?

(b) How many vertical lines did he count?

11. Machuki had sh. 565 which she wanted to change into 20 shillings coins to reward

her class for performing well in the mid term assessment.

(a) How many sh. 20 coins did he get?

(b) How many shillings remained?

12. Use digits 6, 4, 0, 5 to form 5 numbers that are divisible by 2,5 and 10. (Use each digit

once in a number.)

13. Using factors, ﬁnd the GCD of 12, 18 and 36.

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14. Represent the times below on the clock faces.

(a) 12: 30 (b) 2 : 45

15. Find the volume of the following cuboid.

16. Work out.

Litres ml

15 200

× 8

________________

17. Draw a vertical line C K and draw line M B parallel to it.

18. Write 9 in roman numerals.

19. Circle the wants in the following items.

20. What is the time shown on the clock?

21. Draw a shape that has 2 horizontal lines and two vertical lines.

22. Draw two lines that are perpendicular to each other.

23. Which one is heavier? 2 kg or 2 000 g?

24. Work out.

Minutes Seconds

15 25

+ 7 45

______________

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25. What fraction is unshaded?

26. Find the sum of the vertical lines and the horizontal lines of a square.

27. What is 16 kg 720 g ÷ 8?

28. Measure the following angle using a protractor.

29. Karen had sh. 2 500. She bought a present for her teacher at sh. 2 005 and saved the

rest. How much did she save?

30. Find the perimeter of the isosceles triangle below.

9 cm

7 cm

Angles

Relating turns and angles

Activity 1

1. Use a stick or piece of chalk to mark on the ground letters W, L and O as shown.

111

2. Walk along each of the letters that you have drawn from the beginning of each

letter to the end.

(a) How many turns are there in the model of each letter?

(b) What do we form in the spaces between the turns?

Learning point

An angle is a measure of a turn between two lines.

Assessment Task 1

1. How many turns are there in each of the ﬁgures below?

(b)

(a)

2. Identify the turns in each of the diagrams below.

(a) (b) (c)

3. Count and record turns in the following diagrams.

(a) (b)

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Further Assessment 1

Complete each of the following sentences to show how each animal has moved.

(a) The spider has made a ______ turn and

moved forward _______.

(b) The butterﬂy has moved _____ and made a

quater turn.

clockwise and moved forward _______.

(d) The ladybird has moved ______, made

a ______ turn and then moved forward

________.

Angles in the environment

Activity 2

1. Look at a wall clock in your school.

2. Identify the turns made by the hands of the clock.

3. Reset the clock to read various times.

4. Discuss the angle between the hour hand and minute hand when it indicates 12.30 pm

5. Identify other areas in the environment where angles have been used.

Assessment Task 2

1. Identify, count and record angles in the following structures.

(a)

2. Look at the following picture and answer the question that follows.

Mark the angles formed on the rooftop shown.

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Angles and unit angle

Activity 3

1. Trace the following unit angle.

2. Cut out the unit angle that you have traced.

3. Use the unit angle to measure the different angles formed around you.

Assessment Task 3

1. Use the unit angle to measure the number of unit angles in each of the following ﬁgures.

(a)

(b) (c) (d)

2. Fit and count how many times a unit angle ﬁts into the following angles.

(a)

(b)

(c)

Degree as a unit of measuring angles

Activity 4

1. Trace the following 10˚ angle on plain paper and cut it out.

2. Divide the angle you have drawn into ten equal parts.

3. What is the size of each small part in degrees?

Learning point

Angles are measured using a protractor. The unit for measuring angles is called a

degree.

180

Protractor

180

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Measuring angles in degrees

Activity 5

1. Draw any angle on a plain paper.

2. Place the protractor on the angle to be measured,such that the midpoint of the protractor

lies where two lines forming the angle meet.

3. Align one line forming the angle with the zero line of the protractor.

180

4. Read the degrees where the other side crosses the number scale.

What is the size of the angle that you have measured?

What is the value of the angle formed between the two of the following pair of scissors?

Working

Place the protractor such that the zero-mark line lies along one arm and measure the angle.

Angle formed = 60°

Example 1

Assessment Task 4

1. Measure the following angles using a protractor.

(a)

(i) BAD

(ii) BAC

(iii) DAC

(b)

(i) AFE

(ii) AFC

(iii) BFC

(iv) EFD

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2. Identify the value of each of the following angles being measured.

(a) (b)

(d)(c)

Further Assessment 2

1. Use a protractor to measure each of the following angles.

(a)

(d)

(b)

(e)

(c)

(f)

2. Measure angles ADC and DCB.

3. Measure the angles shown in each of the following objects.

(a)

(d)

(c)

(b)

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3 - D Objects in the environment

Activity 1

1. Collect different objects from your environment.

2. Identify the shape from which each of the objects you collected is made of.

3. Write down the shape and items you identiﬁed for each shape.

Assessment Task 1

1. Identify the 3-D shape of each of the following objects.

(a) (b) (c)

(d) (e) (f)

2. Make models of the following 3-D objects using wires.

(a)

(b)

2-D Shapes in 3-D Objects

Activity 2

1. Join pieces of wire and manila cut out to

make different 3-D shapes.

2. Identify the 2-D shapes in each of the

3-D shapes you have made.

3-D Objects

117

Assessment Task 2

1. Identify the following 2-D shapes.

(a) (b) (c) (d)

2. Identify the 2-D shapes in each of the following 3–D objects.

(a)

(b)

(c)

(d)

Further Assessment 1

1. Juma, a Grade 5 learner walked around his school to identify various objects.

(a) Draw ﬁve 3-D objects that he is likely to ﬁnd in the school.

(b) Name the 2-D shapes in the objects you have drawn.

2. Study the following picture and use it to answer the questions that follows.

(a) Identify 2–D shapes in the picture.

(b) Identify 3–D objects in the picture.

118

Data Handling

Data Representation

Collecting and representing data

Activity 1

1. Make several number cards with numbers 1 to 6.

2. Put the number cards upside down on a ﬂat surface.

3. Pick one number card at a time and use it to complete a tally table like the one

shown below.

Number Number of times picked

4. Construct a frequency table to show the data you have collected.

(a) Which is the most picked number?

(b) How many times was the most picked number picked?

119

Learning point

We can follow the following steps when constructing a frequency table:

1. Draw a table with three columns.Write down the data items that will be collected

in the ﬁrst column.

2. Complete the second column by placing one tally mark at the appropriate place

for every data value collected. When the ﬁfth tally is reached for a mark, draw a

horizontal line through the ﬁrst four tally marks. We continue this process until all

data values in the list are tallied.

3. Count the number of tally marks for each data value and write it in the third column.

Example 1

The teacher awarded marks for a project that he had given to Grade ﬁve learners as follows:

6 7 5 7 7 8 7 6 9 7 4 10 6 8 8 9 5 6 4 8

(a) Represent this information in a frequency table.

(b) How many learners scored the highest mark?

(d) What is the mark with the lowest number of learners?

(e) How many learners worked on the project?

Working

(a)

Mark Tally Frequency

(b) 1 learner

(d) 10 marks

(e) 2 + 2 + 4 + 5 + 4 + 2 + 1 = 20

Assessment Task 1

1. Learners in Grade four have the following items; 20 pens, 30 pencils, 15 rubbers,

10 sharpeners and 20 rulers. Represent this information using a frequency table.

2. Juanita maintains the record of the number of customers who take items on credit

from her shop each day. One week, she had the following record: Monday-18,

Tuesday-13,Wednesday-20,Thursday-14, Friday-21, Saturday-27 and Sunday-26.

(a) Represent the data using a frequency table.

(b) How many people took items on credit on Tuesday?

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3. Learners visited the computer room to practise making spreadsheets that they had

learnt during the science lesson.The computer room assistant recorded the number

of times different groups of learners had visited the computer room for practice as

shown below.

Group number

2 3

Number of visits 7 5 5 6

(a) Represent the data using a table.

(b) How many more times did group 1 visit the lab than group 3?

Representing data through piling

Activity 2

Read the following story and answer the questions that follow.

In April 2020, the COVID-19 infections increased leading to schools getting closed and

children were advised to stay indoors all day. A local school conducted a survey on Grade 5

learners to asses how they spent their time during the week.They recorded the data they

got in the following table.

Activity Online

classes

Sleeping Self studies Digital

games

Other

things

Time

spent

4 hours

10 hours 2 hours 3 hours 5 hours

(a) Represent this data by pilling items vertically.

(b) How long did learners spend on digital games?

(d) Write the numbers of hours the learners spent on other activities.

121

Sudi is a wholesale fruit vendor. One day one of his customer bought the following fruits.

10 kg lemons, 6 kg bananas, 8 kg apples and 13 kg oranges.

(a) Pile matchboxes vertically to represent

this information.

(b) Which fruits does the tallest pile

represent?

Working

(a)

Lemons Banana Apples Oranges

(b) Oranges

Example 2

Assessment Task 2

1. The following table shows the number of laptops sold by a laptop shop in the ﬁrst 5

days of the month of February 2021.

Day 1

Day 2 Day 3

Day

Day 5

13 10 8

(a) Arrange boxes or match boxes vertically to represent the data.

(b) Which day forms the tallest pile?

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2. During the blood donation exercise, a survey was conducted on the different blood

groups of people who donated blood.

Blood group A B AB O

Number of donors

10 6 10

(a) Draw cubes arranged vertically to represent the data.

(b) Which blood group forms the tallest pile?

3. A Grade 4 teacher researched on the different colours that the learners in class

liked. 15 learners liked red, 7 liked colour yellow, 8 liked colour blue and 10 liked

colour pink.

(a) Represent this data by pilling objects vertically.

(b) Which colour is the most liked?

Interpreting data represented by piles

Activity 3

Read the following story and answer the questions that follow.

A mobile phone selling company’s computer is programmed to pile cubes vertically for a

carton of each type of phone that is sold.At the end of one day, the computer showed the

following data for the different types of phones sold that day.

P20

P40

X2 X7

(a) Which phone made the most sales for the day?

(b) Which phone made the least sales for the day?

(d) If each carton had 24 phones inside, calculate the number of phones sold that day.

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Assessment Task 3

1. Wakine has four shop outlets that sell milk.The following piles show the number of

cartons of milk sold by the four outlets in a day. Use the piles to answer the questions

that follow.

Shop A Shop B Shop C

(a) Which shop sold the highest number of cartons of milk?

(b) Which shop sold the least number of cartons of milk?

were sold by shop B.

(d) What is the difference between the number of cartons of milk sold by shop B

and the number of cartons sold by shop C?

2. Observe the following piles that show the pets kept by learners of Grade 3 in Shujaa

Primary School.

Cats

Dogs Ducks Rabbits

(a) Which pet is kept by most learners?

(b) How many learners keep cats as their pet?

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3. Lola asked her classmates the best mode of transport they have ever used. She

collected data and piled bottle tops to represent the data as shown below.

(a) How many learners have train as their best mode of transport?

(b) How many more learners have aeroplane as their best mode of transport than

a bus?

125

Forming simple equations

Activity 1

Jamal created a game of converting information into a simple equation. Read some of

the information he wrote for the game. Convert each of the information into a simple

equation.

Information Simple equation

When 5 is added to a number, the answer is 9.

When 14 is taken away from 8 times a number b the answer is 30.

2 multiplied by the sum of the number y and 7 is 13.

Twice a number less 22 is 48.

Jane spent 420 shillings on a pair of shoes. This was 140 shillings less than twice what

she spent for a dress. Form a simple equation to represent the amount Jane spent on

the dress.

Working

The price of the dress is unknown. You can let x represent the unknown amount.

The price of the pair of shoes is 420 shillings.

The price of the dress was 140 less twice the price of the pair of shoes.

Therefore, the equation for the price of the dress is: 2x – 140 = 420.

Example 1

Assessment Task 1

1. Kibori and Jane were coming home from school.They walked for some seconds

and then ran for 6 minutes.They walked

again for half the time they had walked

at the beginning.Their journey took

900 seconds. Write an expression to

represent this information.

2. Peter’s mother is four times as old as Peter.

In four years, their combined ages will

be 54 years. Write a simple equation to

represent this information.

3. Hadima added two numbers and got their

sum as 84. One of the numbers was 12 more than the other. Express this information

as a simple equation.

Algebra

Simple Equation

126

Solving simple equations

Activity 2

Read and talk about the following story then answer the questions that follows.

The government received COVID–19 vaccines from Europe at the airport. They then

distributed the vaccines to different sub-

counties in the country. In one of the

sub-county, 8 000 vaccines were divided

among the 3 vaccination centres such

that the second centre had twice as

much as the ﬁrst and the third had 500

less than the second.

(a) Write an expression to show the

total number of vaccines that the 3

vaccination centres received.

(b) Work out the number of vaccines

that each vaccination centre received.

Mwende spent 3 500 shillings at the market. This was seven hundred shillings less than

three times what she had spent at the shop.

(a) Express this information as a simple equation.

(b) How much did she spend at the market?

Working

(a) Let the amount she spent at the shop be p.

This was 700 less than 3 times what she spent at the market.

She spent 3 500 shillings at the market.

Therefore, the simple equation is, 3 p − 700 = 3 500

(b) To get how much she spent at the shop, solve the expression for the value of p:

3 p − 700 = 3 500

3 p – 700 + 700 = 3 500 + 700

3p = 4 200

4200

p = 1400

She spent 1 400 shillings at the shop.

Example 2

127

Assessment Task 2

Find the value of x for each of the following:

1. x + 5 = 9 2. x − 3 = 12

3. 5 x - 2 = 4 4. 2 (x + 2) = 14

Salim added two consecutive numbers and found their sum to be 37. Find the two

numbers that she added.

Working

Let the ﬁrst number be n.

Because the numbers she added are consecutive, then the other number is n + 1.

The sum of the two numbers is 37

Therefore,

n + n + 1 = 37

2n + 1− 1 = 37−1

n = 18

The other number is 18 + 1 = 19

The two numbers are 18 and 19.

Example 3

Further Assessment 1

1. Abuga keeps goats and sheep on his farm.The total number of goats and sheep is

99.There are 17 more goats than sheep. Find the number of:

(a) Sheep that Abuga has.

(b) Goats that Abuga has.

2. Mwajuma used a barbed wire that was 300 m long to fence her rectangular piece

of land. The length of the piece of land was twice its width. Find the length and

width of the piece of land.

3. A shopkeeper who owns two shops bought 50 books to sell in the two shops. He

divided the books for two shops such that one shop had eight fewer books than the

other. Calculate the number of books in each shop.

4. Job found the sum of 3 consecutive numbers to be 90. Find the 3 numbers that Job

added.

128

Term 3

End Term Assesment

1. Write the following numbers in symbols.

(a) 777 707 (c) 707 707

(b) 700 777 (d) 777 700

2. Joy had

of a piece of cake. Give 2 equivalent fractions of Joy’s piece of cake.

3. Work out: Q ÷ 4 = 5.

4. Evaluate 12 x d = 48.

5. Draw a cuboid and show the corners, lines and faces.

6. Round off 6 999 to the nearest thousand.

7. A candidate in a parliamentary election received 4 567 votes from a certain ward and

8 670 from another ward. How many votes did the candidate get from the two wards?

8. Work out:

km m

4 324

× 6

9. In a class of 25 learners, each was given 12 exercise books. How many books did all

the learners receive?

10. Convert 7 km 320 m into metres.

11. Kingatwa Primary School learners were identifying 3-D shapes.Which of these were

not 3-D shapes?

12. Fill in the table below.

3-D object Number of sides Number of lines Number of corners

Sphere

13. The ________________ of a cube or cuboid are same whether closed or open.

(sides, corners , lines. )

14. Work out: 456 − ___ = 210.

15. Fifty people attended a school parents meeting. 15 were men and the rest were

women. If w represents the number of women, form an equation that can be used to

ﬁnd the value of w.

129

16. Children from Pendo School gave their fruit preferences as follows:

Apple, orange, orange, mango, apple, apple, mango, pawpaw, grapes, pawpaw, mango,

apple, mango, orange, apple, mango, mango, apple pawpaw, grapes, apple, grapes, pawpaw,

mango, orange.

Represent the data on a frequency table.

17. Tom had 20 pencils and Maria had y pencils. If the total number of pencils they had

was 43, form a simple equation that can be used to ﬁnd the value of y.

18. Salura took 234 litres of milk to the local dairy. How much milk in mililitres did he

deliver to the dairy.

19. Draw and name three types of fruits that have a spherical shape.

(a) _________________

(b) __________________

20. Name the 2-D shapes that make each of the 3-D shapes below.

(a) pyramid

(b) sphere

21. I am a four-sided 3–D shaped object with one sharp corner above the other three.

What am I?

22. A biscuit company needs to pack 63 packets of biscuits in 9 cartons. If b represents

the number of packets in one carton, form an equation one can use to ﬁnd the value

of b.

23. A company party was attended by 120 of its employees, where 78 were female. How

many males were there?

24. The product of p and 15 is equal to 210. Find out the value of p and round it off to

the nearest 10.

25. Solve for h in the equation 81 – h = 75.

26. How many 200 millilitres can ﬁll a container of 6 litres?

27. Prepare a simple budget of the personal items you will need in class for the ﬁrst term

for an amount not exceeding sh. 2 500.

28. What is the smallest number of bananas that can be shared equally among 16 girls

and 24 boys without any banana remaining?

29. Arrange the following numbers in a descending order: 45678, 46567, 44765, 45876.

30. A school bus carried 66 learners. On a certain day, the girls were 39 and boys were

z. How many boys were on the bus that day?

130

Term 1 opener

1. 835

2. Thousands

3. 400

4. 606, 626, 660, 662, 666

5. 570 6. 7, 14, 21, 28

7. 12,

, 34,

, 90,

9. 783 10. 7 824

11. 516 12. 736 13. 3

14.

15. 0.43

16. Hundredths

17. 2 m 34 cm 18. 34 cm

19. 25 square units

20. 12

21. 8 22. 6 23. a.m.

24. 2 hours 46 minutess

25. 98 days

26. 5

27.

28. Bottle top, basin, sufuria or bowel.

29.

30. 9r

1. Numbers1. Numbers

Whole Numbers

Assessment Task 1

Number Hundreds of

thousands

Tens of

thousands

Thousands Hundreds Tens Ones

(e)674 439

6 7

4 4

(f) 57 420

5 7

2 0

(g)702 853 7 0 2 8 5 3

(h)142 983 1 4

8 3

2. (a) thousands (b) hundred thousands (c) ten thousands (d) ten thousands (e) tens

(f) thousands

3. (a) tens (b) ten thousands (c) ones (d) ten thousands (e) hundreds (f) hundreds

Further Assessment 1

1. (a) 5 (b) 4 (c) 0 (d) 7 (e) 8 (f) 2

Number Hundreds of

thousands

Tens of

thousands

Thousands Hundreds Tens Ones

654 329

6 5

3 2

Answers

131

3. Thousands

Assessment Task 2

1. (a) 20 000 (b) 200 000 (c) 20

(d) 2 (e) 2 000 (f) 2 000

2. (a) 60 (b) 7 000 (c) 1

(d) 200 000 (e) 600 (f) 400 000

3. 40 000

Further Assessment 2

1. Two 2. 2100

3. (a) Varied answers

(b) Varied answers

Assessment Task 3

Varied answers

Assessment Task 4

1. 1.8752

(a)

8 950 8 951 8 952 8953 8 954 8 955 8956 8 957 8 958

(b) 703

704

705 706 707 708

709 710 711

7(c) 56 000

56 001

56 002 56 003

56 004

56 005 56 006 56 007 56 008

(d) 87 705 87 706 87 707 87 708

87 709 87 710 87 711 87 712 87 713

3. 9 613, 6 931, 1 396, 3 169, 1 963, ..

4. 10 000

5. 37 428

6. 23 569

Assessment Task 5

1. (a) forty three thousand and two

(b) nine thousand and twenty six

(d) forty ﬁve thousand six hundred

and seventy nine

(e) ﬁfty ﬁve thousand ﬁve hundred

and ﬁfty ﬁve

(f) seventy thousand seven hundred

and seven

2. three thousand four hundred and

fifty six

3. forty three thousand two hundred

and ten.

4. (c)

Further Assessment 3

Number in

words

Number in

symbols

Eighty thousand

five hundred and

sixty-one

39 001

Sixty-one

thousand seven

hundred and

eight

39 100

Thirty-nine

thousand one

hundred

80 561

Thirty-nine

thousand and

one

61 708

2. The first got 1 225 votes and the

second got 303 votes

3. Eight hundred and twenty-five in

symbols is written as 825. So what

was reported in the news was

correct.

132

Assessment Task 6

1. (a) 54 736, 55 736, 56 736, 57 736

(b) 4 024, 4 034, 4 135, 4 563

(d) 98 433, 99 332, 99 443, 99 544

2. 34 543, 43 567, 57 821, 60 734, 67 302

Further assessment 4

1. 40 057, 40 061, 45 305, 50 034

2. (a) 500

(b) rice

4 887

Assessment Task 7

1. (a) 8 564, 7 554, 4 856, 4 765

(b) 45 400, 34 500, 30 054, 30 045

(d) 76 523, 76 301, 75 534, 75 412

2. 93 021, 62 458, 57 894, 56 703

3. 65 733, 65 456, 56 845, 54 376

Further assessment 5

1. 521 km, 422 km, 279 km, 268 km

2. Eveline

Assessment Task 8

1. (a) 600 (b) 64 300 (c) 4 600

(d) 0 (e) 38 100 (f) 8 100

2. 3 600 3. 8 700

Further assessment 6

1. 45 400 2. 300

3. (a) 2 300 (b) 5 000 (c) 4 200

(d) 500 (e) 3 700 (f) 700

(g) 5 400 (h) 8 800

Assessment Task 9

1. (a) 5 000 (b) 39 000 (c) 0

(d) 1 000 (e) 10 000 (f) 0

(g) 57 000 (h) 32 000

2. 5 000

Further assessment 7

1. 46 000 2. 10 499 3. 12 000

Assessment Task 10

1. (a) divisible (b) not divisible

(e) divisible (f) not divisible

(g) divisible (h) divisible

(i) divisible (j) not divisible

Assessment Task 11

(a) Divisible (b) Divisible (c) Divisible

(d) not divisible (e) not divisible

(f) divisible (g) divisible (h) divisible

(i) divisible (j) not divisible

Assessment Task 12

1. (a) Divisible (b) divisible

(e) not divisible (f) not divisible

(g) divisible (h) divisible

(i) not divisible (j) not divisible

2. 2015

Further assessment 8

1. 80, 50

2. Yes

3. A number is divisible by 5 if the last

digit is 5 or 0. Since the last digit in

40 is 0 and the last digit in 35 is 5,

then they are both divisible by 5.

4. 4

Assessment Task 13

1. (a) 1, 2, 4, 8, 16

(b) 1, 2, 3, 4, 6 , 9, 12, 18, 36

(d) 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

2. (a) 1, 2, 3, 4, 6 , 9, 12, 18, 36

133

(b) 1, 3, 9, 27, 81

(d) 1, 2, 13, 26

3. 1, 3, 7, 21

4. (a) 9 (b) 18 (c) 27 (d) 12

5. (a) 21 (b) 3 (c) 2 (d) 26

Further Assessment 9

1. 24 2. 12 3. 6

4. 12 5. 12

Assessment Task 14

1. (a) 5, 10, 15, 20, 25

(b) 7, 14, 21, 28, 35

(d) 2, 4, 6, 8, 10, 12

(e) 14, 28, 42, 56, 70

2. (a) 54 (b) 14 (c) 60

(d) 60 (e) 24 (f) 45

Addition

Assessment Task 1

1. (a) 749 733 (b) 631 749

2. (a) 387 958 (b) 497 698

Further assessment 1

1. 598 977 2. 706 399

3. 699 797 4. 399 980

Assessment Task 2

1. (a) 68 999 (b) 672 818 (c) 899 795

2. 501 005 3. 577 589 4. 998 981

5. 896 890

Assessment Task 3

1. (a) 536 688 (b) 866 768 (c) 652 464

2. 986 626

Further assessment 2

1. (a) 402 435 (b) 798 666

2. 202 590 3. 31 9 89

Assessment Task 4

1. (a) 800 (b) 54 600 (c) 256 600

2. 107 400

3. (a) 276 800, 276 739

(b) 90 400, 90 408

(d) 845 900, 845 923

Further assessment 3

1. (a) No (b) No (c) No (d) Yes

2. No, 30 500

3. 5 400 m

Assessment Task 4

1. (a) 378 000 (b) 646 000 (c) 233 000

2. (a) Estimate = 330 000,

Actual = 330 467

(b) Estimate =132 000,

Actual = 132 054

Assessment Task 5

1. (a) 79 950 (b) 7 556

2. 766

3. 80 000, 85 000, 90 000, 95 000

134

Term 1, Mid Term Assessment

1. Forty five thousand three hundred.

Hundred

thousands

Ten

thousands

Thousands Hundreds Tens Ones

3 7 2 3

Place value of 7 is thousands

Subtraction

Assessment Task 1

1. (a) 123 228 (b) 32 421 (c) 46 926

(d) 52 001

2. 34 021 3. 546 412

Further assessment 1

1. (a) 747 211 (b) 732 312 (c) 134 832

(d) 526 117

2. 212 253 3. 19 595 4. 17 049

Assessment Task 2

1. (a) 121 091 (b) 172 230 (c) 51 803

2. 5 341 3. 2 174

Further assessment 2

1. (a) 65 900 (b) 21 911 (c) 9 213

2. 8 270 3. 4 220 4. 4 871

Assessment Task 3

1. (a) 5 200 (b) 22 300 (c) 23 200

2. 12100

Assessment Task 4

1. (a) 54 000 (b) 34 000 (c) 4 000

(d) 23 000

2. 10 000

Assessment Task 5

1. (a) 75 124 (b) 74 334 (c) 433

(d) 234 188

2. 3 716

Further assessment 3

1. (a) k=6 (b) m =9 (c) n = 5

3. 50 000 4. 43 965

5. 31 021, 32 021, 32 132, 33 132

6. 2 000 7. 8b

8. A number is divisible by 5 if the last

digit is 0 or 5. A number is divisible by

10 if the last digit is 0. 90 is divisible

by 5 and 10

9. 4 × 4 × 4 = 64 square units.

10. 1, 2, 3, 5, 6, 10, 15, 30

11. 30

12. 13, 26, 39, 52, 65

13.

14. 51 15. 492 283

16. 0.74 17. 78 200

18. 8.98, 8.92, 8.82, 8.03, 8.02

19. 6 m 78 cm 20. 5 hours 24 mins

21. 37 500 22. 4 weeks 6 days

23. 9 400 cts

24. All angles are equal = 900, it has 4

sides

25.

26.

Fruits Tally marks Number

Mangoes

Oranges

27. 16

28. 4 m 30 cm

29. Xix

30. 11y

135

2. 1 100 188

Assessment Task 4

1. (a) 26 234 (b) 3 692 (c) 230 001

(d) 67 374 (e) 5 232

2. 25 823

3. 390 000

Multiplication

Assessment Task 1

1. (a) 3 010 (b) 2 775 (c) 10 212

(d) 15 096 (e) 8 673

2. (a) 3 072 (b) 3 984 (c) 8 536

(d) 6 809 (e) 15 360

3. 7 630

4. 6 300

Further assessment 1

1. 47 070 2. 2 310

3. 10 770 4. 18 125

Assessment Task 2

1. (a) 7 700 (b) 13 800 (c) 21 700

(d) 18 400 (e) 26 100

2. (a) 6 400 (b) 39 000 (c) 6 900

(d) 18 200 (e) 30 600

Further assessment 2

1. 4 200 2. 25 200

3. 7 000 4. 31 000

Assessment Task 3

1. (a) 18 000 (b) 15 050 (c) 6 900

(d) 14 700

2. (a) 16 328 (b) 41 9 52 (c) 14 288

(d) 23 675

Further assessment 3

1. 1 650 2. 2 544 3. 8 64

Assessment Task 3

120 240 480 960

2. 25 75 225 675 2 025

3. 8

200

1 000

5 000

4. 10

270

810

176

Further assessment 4

1. Sh. 600 2. 1 280, 5 120

3. 810, 2 430 4. 768

Division

Assessment Task 1

1. (a) 8 (b) 2 (c) 15

(d) 5 remainder 10

2. 50 3. 10 4. 8 reminder 5

5. 12

Further assessment 1

1. (a) 16 (b) 21

2. (a) 30 (b) 8

3. 51 4. 39 5. 57

Assessment Task 2

1. (a) 12 remainder 12

(b) 10 remainder 20

(d) 21 (e) 18

2. 15 3. 10 reminder 50

4. 90

Further assessment 2

1. 10 reminder 1 2. 12

3. 15 4. 288 5. 24

Assessment Task 3

1. 9 2. 9 3. 600 4. 120

136

Further assessment 3

1. 12 × 15 = 180

Division sentence = 180 ÷ 15 = 12 or

180 ÷ 12 = 15

2. 200 ÷ 25 = 8

Multiplication sentence = 25 × 8

= 200

3. (a) 30 (b) 480 ÷ 30 = 16

4. 11 hours

5. (a) 20 x 20 = 400 (b) 400 ÷ 20 = 20

6. Varied answers

Assessment Task 4

1. (a) 28 (b) 8 (c)

(d) 32

2. 12

3. (a) 4 (b) 58

Assessment Task 5

1. (a) 178 (b) 313 (c) 95 (d) 30

2. 1 208

Further assessment 4

1. 507 km 2. 5 3. 4

4. 19

Term 1, End Term Assessment

1. 75 230

Hundred

thousands

Ten

thousands

Thousands Hundreds Tens Ones

6 7 8

The place value of 6 is thousands.

3. 50 000 4. Hundredths

5. 144 hours 6. 57 000

7. 50 782, 51 671, 52 781, 53 761

741

1 00

9. 72 10. 252 124

11. 5 700 12. 24 563 13. Vii

14. 30 502

15. 1,2,3,4,6,8,12,24

16. 1 416 17. 1 530 18. 50, 120

19. 20 20. 49z 21. 16 22. 5

23. 6 24. 88 190 25. 400m

26. 15, 30, 45 27. 76

28. 2 345 cm

29. accept any angle less than a

right angle

30. Teachers table, exercise book,

mathematics learners book,

geometrical set.

Term 2 Opener Assessment

1. Ninety four thousand five hundred

and sixty two.

2. 96 hours 3. Ones

4. 300 000

5. 57 805, 56 805, 54 805, 53 805

6. 12 7. 35 000

8. 3.45 9. ix 10. 57

11. 22 232 12. 9, 18, 27, 36

13. 76 432 14. 2 736 15. 72

16. 70, 600 17. Reflex angle

18. 512 cm 19. 12

20. 1, 2, 3, 6, 9, 18 21. 42 cm

22. 2w 23. 48 24. 23

25.

26. 5 m 70 cm

27. 8 cubic units

28. 12 29. P.m. 30. 4 300 cts

137

Fractions

Assessment Task 1

3. (a) false (b) true (c) false

4. (a)

(b)

(c)

and

Further assessment

1. x = 15

2. Because

is equivalent to

3. 8 4. 3

Assessment Task 2

1. (a)

(b)

(c)

(d)

2. (a)

(b)

(c)

(d)

Further assessment 2

2. (a) 4 (b)

(c)

Assessment Task 3

1. (a)

is bigger

(b)

is bigger

(c)

is bigger

2. Different objects like pieces of wood

or fruits can be used.

Further assessment 4

1. (a)

(b)

(c)

(d)

138

3. (a) Black forest

(b) strawberry and vanilla

and strawberry.

Assessment Task 5

1. (a) 1

(b)

(c)

(d)

Further assessment 3

litres

2. 1

litres

= three fifths

Assessment Task 6

1.(a)

(b)

(d)

(e)

(f)

or 1

Assessment Task 7

1. (a)

(b)

(c)

Further assessment 4

4. (a) (i)

(ii)

(iii)

(iv)

correction

(b)Okello’s father (c)

Assessment Task 8

1. (a)

(b)

(c)

(d)

Further assessment 5

1. (a) Mary (b)

Decimals

Assessment Task 1

1. (a) 4 (b) 3 (c) 6 (d) 8 (e) 0 (f) 0

2. (a) 0.014, 4 (b) 0.059, 9 (c) 0.064, 4 (d) 0.002, 2 (e) 0.072, 2 (f) 0.006, 6

Assessment Task 2

Hundreds Tens Ones . Tenths Hundredths Thousandths

1 1

2 .

5 6

2 . 6 5

c 3 5 6 .

4 4

. 5 6

e 3

. 8

f 5

8 . 2 3 5

g 5 5 6 .

h 0 . 0 3

139

2. (a) thousandths (b) thousandths

(e) thousandths (f) thousandths

(g) tenths (h) hundredths

2 . 5 2

8 .

0 7

0 . 0

2 .

. 0 0 .

0 7

5 5

0 6 6

Assessment Task 3

1. (a) 0.099, 0.909, 0.99, 9.009

(b) 45.909, 45.989, 345.459, 345.549

(d) 20.004, 20.044, 20.404, 22.004

2. (a) 48.9, 48.721, 48.672, 48.671

(b) 0.980, 0.979, 0.793, 0.321

(d) 5.54, 5.505, 5.445, 5.04

3. 1.067, 1.566, 1.567, 1.6057, 1.656

Further assessment 1

1. (a) 9.72 s, 9.75 s, 9.79 s, 9.8 s, 9.81 s

(b) 9.72 s

2. 3.434 l, 3.423 l, 3.343 l, 3.324 l, 3.324

3. 5.654 cm, 5.645 cm, 5.545 cm,

5.504 cm, 5.455 cm, 5.045 cm.

4. 2.756 kg, 2.657 kg, 2.576 kg, 2.567 kg

Assessment Task 3

1. (a) 31.909 (b) 457.758 (c) 476.415

2. (a) 6.197 (b) 12.328 (c) 26.405

(d) 70.875

Further assessment 2

1. 100.939 kg 2. 1360.151 kg

3. 76.449 kg 4. 172.401 kg

Assessment Task 4

1. (a) 224.621 (b) 200.842

2. (a) 219.854 (b) 8.933

Further assessment 3

1. 752.347 litres 2. 697.524 kg

3. 419.94 4. 1953.472 kg

Term 2 Midterm Assessment

1. Ten thousands

Number 6 8 0 5

Total value 60 000 8 000 0 50

3. 97 540

4. 34 960, 34 760, 34 560, 34 460

5. 47 000 6. 68, 346 7. 12

8. 0.023 9. 60cm 10. 36

11. 859 886 12. Hundredths

13. 435 917

14.

15. 110 200

16. 63 320 17. 126 230

18. 8 520.28 litres 19. 360

20. 65 remainder 9

21. 367.896, 367.98, 436.289, 436.9

22. 6

23.

24.

25. Spelling of courier –

26. 998.613

27. 14 m

28. Football = 16

Hockey =9

Basketball = 12

29. 32

30.

140

Length

Assessment Task 1

Varied answers

Assessment Task 2

1. (a) 12 000 m (b) 8 003 m

(e) 5 200 m (f) 56 740 m

(g) 34 780 m (h) 43 999 m

2. 42 880 m

Further assessment 1

1. 5 000 m 2. 502 1m

3. 3 000 m 4. 42 000 m

Assessment Task 3

1. (a) 3 km (b) 34 km (c) 25 km

(d) 90 km

2. (a) 4 km 530 m (b) 2 km 370 m

Distance in

metres

Distance in

kilometres

55 000 m

34.06 km

5 005 m

34.006 km

34 006 m

5.005 km

34 060 m

55 km

Further assessment 2

1. 5.1 km 2. 60 km

3. 0.76 km 4. 4 km

Assessment Task 4

1. (a) 8 km 726 m (b) 26 km 883 m

2. (a) 8 km 883 m (b) 10 km 830 m

Further assessment 3

1. 8 km 275 m

2. 67 km 674 m

3. 452 km 609 m

Assessment Task 5

1. 124 km 675 m

2. Becky, by 500 m

3. 14 km 820 m

Assessment Task 6

1. (a) 24 km 800 m (b) 140 km 52 m

2. (a) 732 km 360 m (b) 853 km 724

3. 13 km 800 m

4. 103 km 35 m

Assessment Task 7

1. (a) 3 km 200 m (b) 5 km 600 m

(e) 5 km 320 m

2. (a)3 km 600 m (b) 2 km 207 m

Further assessment 4

1. 9 km 100 m

2. 17 km 800 m

Area

Assessment Task 1

1. (a) 8 cm

(b) 12 cm

(d) 16cm

Assessment Task 2

1. (a) 24 cm

(b) 15 cm

(d) 36 cm

2 Measurement2 Measurement

141

2. (a) Sonia; the squares completely fit

in the rectangle while the circles

leave some spaces.

3. (b) 6 square units

4. (a) 28 cm

(b) 16 cm

(d) 16 cm

Assessment Task 3

1. (a) 84 cm

(b) 64 cm

(d) 625 cm

(e) 80 cm

(f) 1600 cm

2. 623.7 cm

3. 250 cm

Further assessment 1

1. Sh 960 2. 36 000 cm

3. 16 000 4. 81 cm

Volume

Assessment Task 1

1. (a) 64 cm

(b) 48 cm

(d) 125 cm

Assessment Task 2

1. (a) 432 cm

(b) 216 cm

(e) 7 cm (f) 2 cm

2. (a) 1 344 cm

(b) 288 cm

3. (a) 19 200 cm

(b) 726 cm

Further assessment 1

1. 6 750 cm

2. 900 cm

3. 125 cm

4. 10 200 cm

5. Box A of volume 12 000 cm

Capacity

Assessment Task 1

1. 30 ml 2. 13 ml 3. 6 ml

Assessment Task 2

1. (a) 2 (b) 10 (c) 20 (d) 15

(e) 40

2. 8 3. 60 ml 4. 50 ml

Assessment Task 3

1. (a) 6 000 ml (b) 34 000 ml

(e) 12 023 ml (f) 5 450 ml

2. 30 000 ml 3. 23 367 ml

Assessment Task 4

1. (a) 5 l (b) 4 (c) 23

(d) 54 (e) 1

2. (a) 7 l 600ml (b) 5l 468 ml

(e) 4 l 500ml

3. 9 l 600 ml

Assessment Task 5

1. (a) 76 l 796 ml (b) 78 l 444 ml

(d) 357 l 730 ml

2. (a) 115 l 957 ml (b) 69 l 111 ml

Further assessment 1

1. 391 l 352 ml

2. 1 340 l 350 ml

3. 67 l 150 ml

4. 19 l 300 ml

5. 42 l 263 ml

Assessment Task 6

1. (a) 36 l 312 ml (b) 36 l 803 ml

142

2. (a) 26 l 124 ml (b) 35 l 368 ml

Further assessment 2

1. 420 l 100 ml

2. 4 973 l 859 ml

3. 458 l 754 ml

4. 7 l 77 ml

Assessment Task 7

1. (a) 68 l 800 ml (b) 68 l 00 ml

2. (a) 352 l 00 ml (b) 316 l 638 ml

Further assessment 3

1. 842 l 800 ml 2. 316 l 400 ml

3. 71 l 750 ml

Assessment Task 8

1. (a) 10 l 13 ml (b) 15 l 70 ml

(e) 24 l 120 ml

2. (a) 12 l 90 ml (b) 8 l 150 ml

3. 3 l 60 ml 4. 153 l 40 ml

5. 41

Term 2 : End Term Assessment

1. 500 000

2. 56 335

3. Place value of digit 6 is tens of thousands

Number Hundreds of

thousands

Tens of

thousands

Thousands Hundreds Tens Ones

67 843

6 7 8

4. 15 5. 7 800 6. 90 cm

7. 430, 455

8. 0.46 9. 53 807, 54 087, 55 087, 56 087

10. 24 339 11. 5 200 m

12.

13. 5 949

14. 36 cm 15. 9 16. 49 601 17. 54

18. 6

19. 40

or 40

20. 27

21. 33 000 ml

22.

23. 32

24. 69.17 25. Acute angle

26. 4b 27. 7 m 65 cm 28. 60cm

29. 46.903kg

Term 3 Opener Assessment

Number Hundreds Tens Ones . Tenths hundredths

946.73 9 4

6 . 7 3

2. (a) wambui (b) Tom, Mueni, Mary, Akinyi, Wambui

143

3. 502 025

4. Three quarters

5. 54 9 00 6. 60 000 7. 25, 36

8. 6 781, 6 891, 9 991, 12 011

9. (5 675, 2 020), 7 695

10. 234 11. 1 800 kg

12. 8, 16, 24, 32, 40

13. 402 636 14. 6 15. 92

16. 587 054 17. None

18. 18 cm

19. 30 l 125 ml

20. Yes 21. 1 435 22. 192 cm

23.

24. Sh 50

25. Obtuse angle

26. (a)

Age of

learners

Number of

learners

11 17

15 4

(b) 45

27. 90 28. sh 450 29. 200

30. 300 g

Mass

Assessment Task 1

Answers may vary

1. Pencils, pens, books and rulers.

Answers may vary

2. Spoon and plate. Answers may vary

3. Kales, spinach and fruits. Answers

may vary

Assessment Task 2

1. (a) 1 kg (b) 300 g (c) 60 kg (d) 4 kg.

Answers may vary

2. Varied answers

3. Varied answers

Assessment Task 3

1. (a) 23 000 g (b) 17 000 g

(e) 11 300 g (f) 156 000 g

(g) 24 800 g (h) 48 100 g

(i) 311 400 g (j) 144 800 g

2. (a) 0.12 kg (b) 2.45 kg

(e) 1.23 kg (f) 0.817 kg

(g) 0.445 kg (h) 3.418 kg

(i) 1.355 kg (j) 4.68 kg

Assessment Task 4

1. (a) 537 kg 88 g (b) 934 kg 732 g

2. (a) 111 kg 342 g (b) 161 kg 972 g

Further assessment 1

1. 460 kg 274 g

2. 16 kg 595 g

3. 559 kg 532 g

4. 253 kg 554 g

5. 193 kg 804 g

Assessment Task 5

1. (a) 415 kg 888 g (b) 49 kg 922 g

2. (a) 214 kg 213 g (b) 421 kg 158 g

Further assessment 2

1. 16 kg 899 g

144

2. 3 767 kg 39 5g

3. (a) 2 kg 42 g (b) 5 kg 598 g

4. The bull that measures 718 kg 405 g

by 21 kg 487 g

Assessment Task 6

1. (a) 492 kg 844 g (b) 507 kg 105g

(e) 1 438 kg 432 g (f) 1 522 kg 55 g

2. (a) 526 kg 55 g (b) 1 233 kg 618 g

Further assessment 3

1. 226 kg 730 g

2. 37 kg 236 g

3. 1 033 kg 92 g

Assessment Task 7

1. (a) 3 kg 12 g (b) 29 kg 30 g

(e) 78 kg 754 g (f) 222 kg 156 g

(g) 33 kg 52 g (h) 9 kg 91 g

2. (a) 53 kg 9 g (b) 125 kg 35 g

Further assessment 4

1. 109 kg 49 g

2. 539 kg 445 g

3. 104 kg 64 g

Time

Assessment Task 1

1. (a) 360 seconds (b) 120 seconds (c) 660 seconds (d) 420 seconds

(e) 540 seconds (f) 3 000 seconds

2. 1 800 seconds

Further assessment 1

1. 2 520 seconds

2. She did not achieve her target because she took 300 seconds, which was 11

seconds more than her intended time.

3. 194 second

Assessment Task 2

1. (a) 7 200 seconds (b) 10 800 seconds (c) 25 200 seconds (d) 32 400 seconds

(e) 14 400 seconds (f) 21 600 seconds

2. 337 seconds 3. 14 minutes

Further assessment 2

1. 6 minutes 26 seconds 2. 30 minutes 3. 11 minutes

4. 40 games 5. 7 minutes

Assessment Task 3

1. (a) 57 minutes 55 seconds (b) 51 minutes 26 seconds

145

2. (a) 30 minutes 15 seconds (b) 52 minutes 24 seconds

3. 115 minutes 10 seconds = 1 hour 55 minutes 10 seconds

Assessment Task 4

1. (a) 25 minutes 17 seconds (b) 15 minutes 49 seconds

2. 12 minutes 39 seconds

Assessment Task 5

1. (a) 67 minutes 18 seconds (b) 196 minutes (c) 181 minutes 55 seconds

2. 186 minutes 40 seconds 3. 324 minutes 4. 267 minutes 40 seconds

Assessment Task 6

1. (a) 6 minutes 9 seconds (b) 5 minutes 4 seconds (c) 2 minutes 8 seconds

(d) 6 minutes 8 seconds (e) 3 minutes 10 seconds (f) 1 minute 18 seconds

2. 5 minutes 16 seconds 3. 3 minutes 4 seconds 4. 3 minutes 6 seconds

Money

Assessment Task 1

1. A budget is a plan that shows how one will spend money wisely.

2. Varied answers

3. Varied answers

Assessment Task 2

4. (a) The money is not enough because the budget amounts to sh 1 300 but she only

has sh 1 000 to spend.

(b) Her budget is a bad one because it is much more than the money she earned.

3. Geometry3. Geometry

Lines

Assessment Task1

1. (a) horizontal (b) vertical

2. 2

146

Assessment Task 2

Horizontal lines

Vertical lines

Horizontal lines

Vertical lines

Assessment Task 3

1. (a)

(b)

(c)

2. Doors, Windows, Desks, Tables

Assessment Task 4

Parallel lines (b), (c)

Assessment Task 5

1. (a)

(b)

(c)

2. Check drawing and the use of the set

square and ruler.

Midterm 3 assessment

1. Two hundred thousand two hundred.

2. Hundreds

Tens Ones . Tenths Hundredths

6 . 0 2

5. 3 720 6. 720 sec

8. Right angle

9. 701 218

10. (a) 8 (b) 8

11. (a) 28 (b) sh. 5

12. 40, 50, 60, 450, 640

13. 6

147

14. (a)

(b)

15. 144

16. 121 l 600ml 17.

18. ix

19. Wants : house, cake

20. 9.45

21.

22.

23. None 24. 23 mins 10 sec

25.

26. 4

27. 2 kg 90 g

28. 118° 29. Sh 495 30. 23

ANGLES

Assessment Task 1

1. (a) 3 (b) 2

2. (a) 3 (b) 4 (c) 5

3. (a) 7 (b) 12

Further Assessment 1

(a) U, 2 steps

(b) 3 steps backward

(d) 2 steps forward, 90° anticlockwise, 1

step

Assessment Task 4

1. (a) (i) BAD 23° (ii) BAC 25°

(iii) DAC 48°

(b) (i) AFE 95° (ii) AFC 42°

(iii) BFC 17° (iv) EFD 185°

Further Assessment 2

(a) 70° (b) 43° (c) 129°

(d) 111° (e) 16° (f) 92°

3D Objects

Assessment Task 1

1. (a) Cylinder (b)circle

(e) cylinder (f) ube

2. Varied shapes

Assessment Task 2

1. (a) rectangle (b) circle

2. (a) rectangle, triangle

3. (b) Triangle (c) rectangle, triangle

(d) Rectangle

Further assessment

1. (a) Varied 3-D objects: dustbin, desks,

school bus, cylindrical jerrycans,

bricks, ball

(b) Varied answers

2. (a) wall clock, table top, plate,

window

(b) cupboard, ball, television, milk

packet, fruit

148

Data representation

Assessment Task 1

Items Tally marks Number of items

Pens //// //// //// //// 20

Pencils //// //// //// //// //// //// 30

Rubbers //// //// ////

Sharpeners //// ////

Rulers //// //// //// //// 20

2. (a).

Days Tally marks Number of items

Monday //// //// //// ///

Tuesday //// //// ///

Wednesday //// //// //// //// 20

Thursday //// //// ////

Friday //// //// //// //// /

Saturday //// //// //// //// //// // 27

Sunday //// //// //// //// //// / 26

(b) 13 (c) Saturday

3. (a).

Group number Tally marks Number of items

//// // 7

2 //// 5

3 //// 5

//// / 6

5 ////

(b)2 (c) 1

Assessment Task 2

1. (b) day 5 (c) day 4

2. (b) A (c) B and O

3. (b) red (c) 40

Assessment Task 3

1. (a) shop B (b) shop C (c) 408

(d) 5

2. (a) Dog (b) 7

3. (a) 8 (b) 4

149

Algebra

Assessment Task 1

1. x + 240 +

= 900

2. 5x + 8 = 54

3. 2x + 12 = 84

Assessment Task 2

1. 4 2. 15

or 1

4. x = 5

Further assessment 1

1. (a) 41 (b) 58

2. Length = 100 m, width = 50 m

3. 21, 29

4. 29,30,31

End term 3 assessment

1. (a)seven hundred and seventy seven

thousand seven hundred and

seven.

(b) seven hundred and seven thousand

seven hundred and seven.

hundred and seventy seven.

(d) seven hundred and seventy seven

thousand seven hundred.

3. Q= 20 4. d = 4

Vartices

Edges

Faces

6. 7 000 7. 13 237

8. 25 km 944 m 9. 300

10. 7 320 m 11. B and D

12.

3-D object Number

of sides

Number

of lines

Number

of corners

Sphere 0 0 0

13. Corners and edges 14. 246 15. w + 15 = 50

16.

Type of fruit Tally marks Number of fruits

Apple |||| || 7

Orange ||||

Mango |||| || 7

pawpaw ||||

Grapes ||| 3

17. y + 20 = 43

18. 234 000 ml

19. varied answers

20. (a) triangles, squares, rectangles (b) circles

150

21. triangular pyramid

22. 9b = 63

23. 42

24. 10

25. 6

26. 30

27. answers will vary: sample; exercise

books = 500

Ink pen = 100

Ink bottle = 200

Pencil = 40

Rubber = 20

Geometrical set = 250

Story books = 400

28. 48

29. 46 567, 45 876, 45 678, 44 765.

27(d) 5

30. (a) Dog (b) 27 boys

31. (a) 8 (b) 4