Maths Gr7 Teachers Book

Written by: Ali Naseer, Wood Land, Male’

Edited by: Ali Naseer

Typesetting: Ali Naseer

Layout by: Ali Naseer

Graphics by: Ali Naseer

Proofread by: Hassan Nizam

Ahmed Riyaz Jauhary

Cover design by: Mohamed Tholal

Abdullah Zaki

Cover photos by: Ali Adam

Second Edition: 2003

ISBN 99915-0-491-5

A-145/2002/DPE

EDUCATIONAL DEVELOPMENT CENTREMinistry of Education, Republic of Maldives

© 2003

Printed by: Book Production Unit (2003)

iii

c

This is the Teacher’s Resource Book for Mathematics for MaldivianSchools 7 which is the prescribed teacher’s book for Grade 7.

The right to modify the contents of this book lies exclusively with theEducational Development Centre of the Ministry of Education.

Ministry of Education

v

Mathematics for Maldivian Schools Seven is written specificallyto meet the requirements of the Grade 7 Mathematics syllabusrevised in 2000.

The grade 7 course consists of a textbook, a workbook and ateacher’s resource book.

This teacher’s resource book contains Suggested Time Frame,Syllabus, Unit Notes, Activities, Unit Tests, Answers ofExercises, Answers of Revision Exercises, Answers ofAssignments, Answers of Self Tests, Answers of Brain Teasers,Answers of Activities and Answers of Unit Tests.

Introduction

Acknowledgements

The publisher wish to acknowledge the contributions of manyfriends, colleagues and advisors who have helped in the productionof Mathematics for Maldivian Schools Seven.

In particular, we wish to thank Mr. Ali Adam, Mr. Ahmed RiyazJauhary (EDC), and Ms. Nahid Shakir (EDC),

We would also like to thank Madhrasathul Ahmadhiyya for theircontribution to the production of this book.

vi

Contents

1 NumbersSyllabus Content 20Unit Notes 21Activities 22Unit Test 1 24Answers of Exercises 25

2 FractionsSyllabus Content 27Unit Notes 28Activities 29Unit Test 2 31Answers of Exercises 32

About the Textbook 1About the Workbook 3About the Teacher’s Guide 5Suggested Time Frame 6Assessment 7Syllabus 8

3 DecimalsSyllabus Content 34Unit Notes 35Activities 36Unit Test 3 38Answers of Exercises 39

vii

5 Indices and AlgebraSyllabus Content 47Unit Notes 48Activities 49Unit Test 5 52Answers of Exercises 53

6 EquationsSyllabus Content 55Unit Notes 56Activities 57Unit Test 6 59Answers of Exercises 60

4 Directed NumbersSyllabus Content 41Unit Notes 42Activities 43Unit Test 4 45Answers of Exercises 46

7 GeometrySyllabus Content 61Unit Notes 62Activities 63Unit Test 7 65Answers of Exercises 67

viii

10 VolumeSyllabus Content 83Unit Notes 84Activities 85Unit Test 10 87Answers of Exercises 88

11 Rate, Ratio & ProportionSyllabus Content 89Unit Notes 90Activities 91Unit Test 11 93Answers of Exercises 94

9 Perimeter and AreaSyllabus Content 74Unit Notes 75Activities 76Unit Test 9 78Answers of Exercises 80

8 MeasuresSyllabus Content 68Unit Notes 69Activities 70Unit Test 8 72Answers of Exercises 73

ix

Answers of Revision Exercises 115

Answers of Assignments 122

Answers of Self Tests 126

Answers of Brain Teasers 129

Answers of Activities 131

Answers of Unit Tests 135

14 Straight line graphsSyllabus Content 109Unit Notes 110Activities 111Unit Test 14 113Answers of Exercises 114

12 PercentageSyllabus Content 95Unit Notes 96Activities 97Unit Test 12 99Answers of Exercises 100

13 StatisticsSyllabus Content 102Unit Notes 103Activities 104Unit Test 13 106Answers of Exercises 107

1

About the Textbook Grade 7

Brain Teaser

Brain Teasers are given to develop students’ thinking abilityand to stimulate interest in the further study of Mathematics.When students come across a Brain Teaser ask them to solve itin the class after completing the class work. If not solve it intheir free time. Students should not be tested on this.

Message of the Week

Message of the week is given to develop students morally andto teach religious and moral values. When you come acrossthese messages, talk to students about them. Students shouldnot be tested on this.

Examples

The examples in the textbook are carefully worked out tofacilitate self-learning and mastery through review. In theexamples all the steps are shown and on the right of the stepsthe explanation on how the steps are being carried out isgiven. Teachers should not demand the students to copy theexamples to their note books, as this is absolutely useless.

Teachers should also encourage the students to refer theexamples when they forget or do not know how to proceedwith a certain problem.

2

Dhivehi words used for measuring

Words used for measuring in the past are given in alphabeticalorder. This is because people rarely refer the conversionfactor for these units in purposes like building boats, makingfood for old recipes etc. Students should not be tested on this.

Useful Information

This is included to give more information on Mathematics andits history. Students should not be tested on this.

Encourage the students to make full use of the textbook in all themathematics periods.

Key words used in units

At the end of each unit, the dhivehi words for the key wordsused in the unit are given. This is because we do not want toobsolete old dhivehi used by our ancestors. Students shouldnot be tested on this.

3

About the Workbook Grade 7

Assignments

Assignments cover almost all the work done up to the givenassignment. The same Revision Exercise book can be used todo these assignments. In marking and discussing the mistakesof the assignments, follow the same procedure as the RevisionExercises.

Revision Exercises

A revision exercise is given at the end of each unit. Thiswould help the students to revisit the unit once again. At theend of the unit give the students a deadline to complete theRevision Exercise. Ask them to use a separate exercise bookfor this. The Revision Exercises should not be marked in theclassroom. When marking, identify the common mistakes anddiscuss these mistakes with students as soon as possible andgive the unit test in the following mathematics period.

Exercises

There are two types of exercises. Some of the exercises aregiven for students to do in their exercise books, theseexercises would indicate so. The other exercises (which arenot stated to do in the exercise book) need to be done in theworkbook itself.

4

Self Tests

There are three Self Tests in the workbook. Self tests wouldhelp students to evaluate themselves before their exams. Ifpossible try to hold these tests in exam condition. If not, testscan also be done at home in the given duration.

The format of these tests are similar to the IGCSEmathematics papers which they have to sit at the end of Grade10. Teachers should follow this format in their term testpapers as well.

It is very important to work-out each and every question in all theExercises, Revision Exercises, Assignments and Self Tests. Theseexercises are carefully designed to drill students in particular skills.

5

About the Teacher’s Resource Book Grade 7

Unit Tests

Unit Tests which are included in the Teacher’s Guide givesyou an idea of the format and the types of questions that youcould give in the unit test. If you are sure that this Teacher’sGuide does not reach the students you are allowed to give thesame tests for the Unit Tests.

Activities

There are at least two activities included in each unit of thisTeacher’s Guide. These activities are designed to reduce themonotony in doing the numbers repeatedly. These activitiesare made so that students can enjoy and have a positiveattitude towards mathematics. Each activity will give studentsconfidence as they solve problems, since they will knowwhether they are right or wrong.

Most of the activities can be carried out as revision whileothers can be done at the end of a particular exercise. Pre-activities are also included. These activities will recall whatthey have learned in the previous grades on the unit.

6

Suggested Time Frame

In Grade 7 the students should study mathematics for at least 7 periods of35 minutes per week.

Grade 7

TOPICS Suggested Time(approximate)

Unit 1 Numbers 18 periods of 35 minutes

Unit 2 Fractions 20 periods of 35 minutes

Unit 3 Decimals 18 periods of 35 minutes

Unit 4 Directed Numbers 7 periods of 35 minutes

Unit 5 Indices and Algebra 17 periods of 35 minutes

Unit 6 Equations 9 periods of 35 minutes

Unit 7 Geometry 9 periods of 35 minutes

Unit 8 Measures 7 periods of 35 minutes

Unit 9 Perimeter and Area 23 periods of 35 minutes

Unit 10 Volume 9 periods of 35 minutes

Unit 11 Rate, Ratio & Proportion 14 periods of 35 minutes

Unit 12 Percentage 15 periods of 35 minutes

Unit 13 Statistics 13 periods of 35 minutes

Unit 14 Straight line graphs 10 periods of 35 minutes

7

Assessment Grade 7

In Grade 7 a term test should be given at the end of each term. Theseterm tests should include about 35% of the previous term/terms work,about 50% on current term work and the remaining 15% should be marksobtained from the unit tests given at the end of each unit completed inthat term.

8

Syllabus

Arithmetical operations.1

1.1 Add, subtract, multiply and divide whole numbers.1.2 Solve operations involving combined addition,

subtraction, multiplication and division of whole numbers.1.3 Solve word problems involving addition, subtraction,

multiplication and division of whole numbers.

Divisibility, prime factorization, L.C.M. and H.C.F.2

2.1 Use the divisibility rules of 2, 3, 4, 5, 6, 9 and 10.2.2 Find the prime factorization of whole numbers.2.3 Find the lowest common multiples of two to three 1-2

digit numbers.2.4 Find the highest common factors of two to three 1-2 digit

numbers.

NUMBERS

Grade 7

Binary numerals3

3.1 Convert decimal numerals to binary numerals.3.2 Convert binary numerals to decimal numerals.

9

FRACTIONS

Comprehension of fractions.1

1.1 Form fractions from given information.1.2 Form equivalent fractions to a given fraction.1.3 Reduce fractions to their lowest term.1.4 Compare fractions with different denominators.1.5 Convert improper fractions to mixed numbers and vice versa.

Operations of fractions.2

2.1 Carry out addition of 2-3 fractions (where the denominatoris a 1-2 digit number) with different denominators.

2.2 Carry out subtraction of 2-3 fractions (where thedenominator is a 1-2 digit number) with differentdenominators.

2.3 Carry out multiplication of 2-3 fractions.2.4 Carry out division of 2-3 fractions.2.5 Carry out combined operations involving the four

operations and the use of brackets.

Application of fractions.3

3.1 Solve word problems involving fractions.

10

DECIMALS

Comprehension of decimal numbers.1

1.1 Read and interpret decimal numbers.1.2 Compare decimal numbers using > or <.1.3 Round off whole numbers to the nearest tens, hundreds,

thousands etc.1.4 Round off decimals to the nearest whole number and to the

specified number of decimal places.1.5 Convert fractions to decimals and vice-versa.

Operation of decimal numbers.2

2.1 Addition of decimal numbers.2.2 Subtraction of decimal numbers.2.3 Solve operations involving addition and subtraction of

decimal numbers.2.4 Multiplication of decimal number by a decimal number.2.5 Multiplication and division of decimals by 10, 100, 1000 etc.2.6 Division of decimal numbers by a decimal number.

Application of decimal numbers.3

3.1 Solve word problems involving decimal numbers.

11

DIRECTED NUMBERS

Comprehension of directed numbers.1

1.1 Compare positive and negative numbers using > or <.1.2 Use addition rule to solve addition and subtraction of

directed numbers.1.3 Use multiplication rule to solve multiplication and

division of directed numbers.

INDICES

Comprehension of indices.1

1.1 Introduce the index form.1.2 Find the values of numbers written in the index form.1.3 Use the multiplication law of indices in simplifying.1.4 Use the division law of indices in simplifying.

12

Comprehension of algebra.1

1.1 Use letters to represent unknowns and write simple

algebraic expressions (e.g. 6c + d).

1.2 Add and subtract algebraic terms (e.g. 4m2n + 8mn2 – 7m2n).

1.3 Multiply algebraic terms (e.g. – x3 (2xy3)(–5y5z)).

1.4 Divide algebraic terms (e.g. 2

3

5

15–

a

ba ).

1.5 Evaluate algebraic expressions by substitution.

1.6 Simplify expressions with parenthesis (e.g. (3x + 2)(4x – 1)).

1.7 Factorize algebraic expressions (exclude group factorization).

Comprehension of equations.2

2.1 Solve linear equations (include cases involving fractional

coefficients, exclude: 15

122

3=

−+

− xx ).

ALGEBRA AND EQUATIONS

13

GEOMETRY

Comprehension of angles.1

1.1 Find unknown angles involving angles on a straight lineand angles at a point.

Angle properties of quadrilaterals.2

2.1 Use the angle sum of the quadrilateral in finding theunknown angles of the quadrilaterals.

Angle properties of triangles.3

3.1 Use the angle sum of the triangle in finding the unknownangles of the triangles.

3.2 Identify the base angles of an isosceles triangle.3.3 Find the size of angles of an equilateral triangle.3.4 Use the relationship between exterior angle of a triangle

and the sum of the far interior angles of the triangle to findthe unknown angles.

14

RATE, RATIO AND PROPORTION

Comprehension of rate.1

1.1 Introduce rate.1.2 Solve problems involving rate.

Comprehension of ratio.2

2.1 Find the ratio of two or more quantities.2.2 Simplify ratios with whole numbers.2.3 Simplify ratios with units. (e.g. 20 hr : 1 day)2.4 Simplify fractional ratios.

Comprehension of proportion.3

3.1 Solve word problems involving direct proportions.3.2 Solve word problems involving proportional parts (sharing).3.3 Solve word problems involving alms (zakaaiy).

15

Comprehension of percentage.1

1.1 Recognize the equivalent between percentage and fraction.1.2 Change fraction to percentage, and vice versa.1.3 Change decimal to percentage, and vice versa.1.4 Calculate the percentage of a quantity.

Application of percentage.2

2.1 Solve word problems involving percentages.2.2 Solve word problems involving percentage of a quantity.2.3 Solve word problems involving percentage increase and

decrease.2.4 Solve word problems involving discount.2.5 Solve word problems involving profit and loss percentage.

PERCENTAGE

STATISTICS

Measure of central tendency.1

1.1 Find mean, median and mode from a given data.

Comprehension of graph.2

2.1 Read and interpret data presented in pie charts.2.2 Construct pie charts.

16

PERIMETER

Comprehension of perimeter.1

1.1 Find the perimeter of different shapes when the sides aregiven.

1.2 Find the circumference of circles, where the radius ordiameter is given.

1.3 Find the perimeter of semi circles and quarter circles.1.4 Find the perimeter of compound figures.1.5 Find the dimensions of rectangles, squares and circles

given its perimeter and other dimensions.

Application of perimeter.2

2.1 Solve word problems involving perimeter.

17

Comprehension of area.1

1.1 Use formula to calculate the area of rectangles, squares,triangles, parallelograms, trapeziums and circles.

1.2 Find the area of semi circles and quarter circles.1.3 Find the dimensions of rectangles, parallelograms, triangles

and trapeziums given its area and other dimensions.1.4 Find the area of compound figures.1.5 Find the area of shaded regions.

Application of area.2

2.2 Solve word problems involving area.

AREA

18

Comprehension of volume.1

1.1 Find the volume of cubes and cuboids.1.2 Find the dimension of a cuboid given its volume and

other dimensions.1.3 Find the volume of prisms.1.4 Find the length of a prism given its volume and area of the

cross-section.

Application of volume.2

2.1 Solve word problems involving volume of cuboids, cubesand prisms.

VOLUME

19

MEASURES

Metric units.1

1.1 Express the units of length (km, m, cm, mm) in terms oflarger or smaller quantities.

1.2 Express the units of mass (t, kg, g) in terms of larger orsmaller quantities.

1.3 Express the units of capacity (l, ml or cm3) in terms oflarger or smaller quantities.

Imperial units.2

2.1 Express other units of length (miles, feet, inches) in termsof larger or smaller quantities.

2.2 Express the units of time (s, min, hr) in terms of larger orsmaller quantities.

STRAIGHT LINE GRAPH

Comprehension of straight line graphs.1

1.1 Use Cartesian coordinates in two dimensions.1.2 Draw straight line graphs for the equations in the form

y = mx + c.

20

Unit 1 Numbers

Syllabus Content

Arithmetical operations.1

1.1 Add, subtract, multiply and divide whole numbers.1.2 Solve operations involving combined addition,

subtraction, multiplication and division of whole numbers.1.3 Solve word problems involving addition, subtraction,

multiplication and division of whole numbers.

Divisibility, prime factorization, L.C.M. and H.C.F.2

2.1 Use the divisibility rules of 2, 3, 4, 5, 6, 9 and 10.2.2 Find the prime factorization of whole numbers.2.3 Find the lowest common multiples of two to three 1-2

digit numbers.2.4 Find the highest common factors of two to three 1-2 digit

numbers.

Binary numerals3

3.1 Convert decimal numerals to binary numerals.3.2 Convert binary numerals to decimal numerals.

21

The Exercises from 1.1 to 1.4 are concepts of four basic operations.These exercises are intended to help you find out which of yourstudents do not have concepts of basic operations needed to succeedin Grade 7, and to provide some help in developing those skills.

Teachers could use the discovery method when introducingBODMAS rule. Write an expression, for e.g. 8 – 3 × 4 ÷ 2, of thistype and ask the students to simplify. Get the answers from thestudents. Tell them the fact that students getting different answers isa proof of the need for a rule. Then introduce the above rule.

When doing the numbers in Exercise 1.5 they do not have to use theDirected Number’s addition and multiplication rule. In doingnumbers like 5 – 6 + 9, they first have to add and then subtract.These type of numbers have been introduced since Grade 5.

In doing prime factorization we recommend to use the divisionmethod rather than the factor tree method. Recall the first few primenumbers, short division and divisibility rules before explaining theexamples of prime factorization.

Highest Common Factor, conversion of decimal numerals tobinary numerals and vice versa are introduced in this grade.Teachers need to spend more time on these topics than others.

Unit Notes Numbers

22

Activity 1

Fill in each with the correct number.

Activities Numbers

1190 + 14 – 2970

× 3 × 26

– 97 ÷ 18

÷ 5 + 2177

23

Activity 2

Do the following sums. Then join the dot for Answer 1 to the dot forAnswer 2 and so on. What picture do you get?

Activities Numbers

1. 15 – 8 + 12 9. LCM of 18 and 8

2. 197 – 93 – 20 10. LCM of 9, 12 and 16

3. 8 – 2 × 3 11. HCF of 27 and 9

4. 12 × 6 ÷ 3 12. HCF of 30 and 42

5. 24 ÷ 6 + 6 ÷ 6 13. HCF of 48, 36 and 60

6. 48 – 7 × 3 + 16 ÷ 4 14. 1101002 as a decimal numeral.

7. (16 × 3) ÷ 2 + 9 – 3 15. The sum of 29 and 128.

8. LCM of 10 and 4 16. The product of 11 and 24.

19

84

2

264

245

31

30

20

72144

96 12

52157

99

159

65 120

104256

404

3 18

8

4834

24

1. Find the sum of 210 and 3089. [1]

2. Calculate the value of 17 – 500 + 498. [1]

3. Calculate the value of 2041 × 72. [1]

4. Use short division to divide 720 by 4. [2]

5. Use long division to find the value of 10253 ÷ 51. [2]

6. Find the prime factorization of 252. [2]

7. Find the lowest common multiple of 20, 18 and 32. [2]

8. Find the highest common factor of 12, 42 and 36. [2]

9. Express 37 in base two. [2]

10. Express 1001102 as a decimal numeral. [2]

11. Find the value of 15 × (34 – 22) ÷ 3. [3]

12. Inadh bought a mobile phone. He paid the cashier Rf. 3000

and received Rf. 285 change. How much did the mobile

phone cost? [3]

13. A motorist used 168 litres of petrol in 4 weeks. If he used the

same amount of petrol every week, how much petrol did he

use each week?. [3]

14. Husna bought 2 bags of mangoes and 3 boxes of oranges.

There were 6 mangoes in each bag and 12 oranges in each box.

How many fruits did she buy altogether? [4]

Unit Test 1 Numbers

Answer all the questions on a separate paper.Show all the working.Do not write on this paper.

TIME 30 minutes

Total marks [30]

25

1. 1381 6. 1662. 372 7. 46733. 14 642 8. 10904. 158 9. 68195. 27 369 10. 3072

1. 852 6. 257 8382. 51 160 7. 13 9923. 27 420 8. 3 323 7354. 40 380 9. 4 963 0505. 223 184

1. 235 R 1 7. 2692. 72 8. 64 R 303. 26 R 5 9. 20 R 374. 10 R 7 10. 996 R 35. 206 R 17 11. 908 R 516. 350 R 12 12. 610

Page 1Exercise 1.1

Page 1Exercise 1.2

Page 1Exercise 1.3

1. 116 9. 367 R 82. 168 R 1 10. 185 R 83. 170 R 3 11. 281 R 14. 180 R 1 12. 587 R 85. 1 054 R 3 13. 4306. 714 R 5 14. 428 R 37. 1 066 R 3 15. 4908. 236 R 6

Page 2Exercise 1.4

1. 41 7. 162. 26 8. 93. 8 9. 424. 9 10. 615. 67 11. 176. 13 12. 31

Page 2Exercise 1.5

1. 408 6. Rf. 1082. 21 164 7. 64343. 32 8. 11 packs, Rf. 54. Rf. 20 9. 45335. Rf. 4045 10. Rf. 5600

Pages 2-5Exercise 1.6

Page 6Exercise 1.7

1. 3×7 5. 2×5×5×3×72. 3×3×3×3 6. 2×2×3×7×113. 2×2×3×3×5 7. 2×5×414. 2×5×7×7 8. 7×11×13

Page 6Exercise 1.8

Answers of Exercises Numbers

45051631506 94388 52447 14550 000187 920410 9689 000 367

by 2 by 3 by 4 by 5 by 6 by 9 by 10

26

Page 7Exercise 1.9

Answers of Exercises Numbers

1. 18 7. 722. 60 8. 903. 36 9. 604. 154 10. 965. 36 11. 2706. 60 12. 182

1. 3 7. 52. 8 8. 153. 6 9. 144. 8 10. 95. 2 11. 36. 9 12. 72

1. 10012 7. 111100022. 100002 8. 1000010023. 110002 9. 100011114. 10000012 10. 1001011025. 11000002 11. 1010010026. 11001002 12. 110001102

1. 6 7. 612. 7 8. 383. 11 9. 544. 10 10. 465. 25 11. 636. 30 12. 65

Page 7Exercise 1.10

Page 8Exercise 1.11


27

Unit 2 Fractions

Syllabus Content

Comprehension of fractions.1

1.1 Form fractions from given information.1.2 Form equivalent fractions to a given fraction.1.3 Reduce fractions to their lowest term.1.4 Compare fractions with different denominators.1.5 Convert improper fractions to mixed numbers and vice versa.

Operations of fractions.2

2.1 Carry out addition of 2-3 fractions (where the denominatoris a 1-2 digit number) with different denominators.

2.2 Carry out subtraction of 2-3 fractions (where thedenominator is a 1-2 digit number) with differentdenominators.

2.3 Carry out multiplication of 2-3 fractions.2.4 Carry out division of 2-3 fractions.2.5 Carry out combined operations involving the four

operations and the use of brackets.

Application of fractions.3

3.1 Solve word problems involving fractions.

28

Fractions have been introduced from Grade 1 onwards.However, many students are still weak in fraction conceptsand make a lot of mistakes in doing fractions. So it isnecessary to revise the basic concepts of fractions in thisstage as well.

Part-whole methodIt is obvious that the part-whole method is very useful. Thestudents should be encouraged to draw the (part-whole)diagrams to help them to analyse and solve word problems.Especially word problems involving fractions. For example:

Muhammad spent 35 of his money and had Rf. 36 left. How much

money did he have at first?

Unit Notes Fractions

Try this. This will improve their problem solving skills.

Does not understand word problems.Read through the problems with poorer readers. Have thempick out the key words that tell what operation to use to solvethe problem.

Rf. 18 Rf. 18

Money spent

Money Muhammad had at first

Money left (Rf. 36)

Money Muhammad had at first = 18 × 5 = Rf. 90

29

Activity 1

What is the name given to the Battles in which Prophet Muhammad ‘himself led the Muslims?

To find the answer:1. Circle the greater fraction.2. Write the letter that goes with the greater fraction in the box.

Activities Fractions

1.57

, 67

GH

2.56

, 14

AH

3.12

, 25

NA

4.38

, 59

ZD

5.712

, 815

AW

6.1120

, 6

11

GA

30

Activity 2

Activities Fractions

Fill in the ’s to get the answer.

2 4 7 7= 67

+1.

1 3 5 9= 89

+2.

2 3 4 5= 2

15–3.

4 9 12 18= 23

×4.

4 7 8 21= 16

÷5.

31

Unit Test 2 Fractions


TIME 30 minutes

Total marks [25]

1. Change 677

into a mixed number.. [1]

2. Change 32

13 into an improper fraction. [1]

3. Reduce 30

120to its lowest term. [2]

4. Complete 2 85 35= = . [2]

5. Compare 38

, 12

. [2]

6. Find the value of 57

of 49. [2]

7. Simplify the following fractions.

(a)38

+ 18

[1] (c)23

÷ 47

⎛⎜⎝

× 12⎞⎟⎠

[3]

(b) 412

÷ 34

[2] (d) 317

+ 3

14 – 2 [3]

8. A fruit basket contains 18 bananas and 6 papayas. What fraction ofthe fruits in the basket are bananas? [3]

9. Thirty students did a test, and 13

of them failed. How many students

passed? [3]

32

1. (a) 12 (b)

23 (c)

15

(d) 7

10 (e) 49 (f)

1316

2. 1237 4.

31126 6.

18226

3. 8

13 5. 218355


Answers of Exercises Fractions

1. 239 3.

22318

2. 9310 4.

3169105

Page 13Exercise 2.2

1. 315 3. 11

2431

2. 31920 4. 23

2239

Page 13Exercise 2.3

1. 27 3.

45 5. 2

23

2. 23 4.

101152 6. 5

15

Page 13Exercise 2.4

1. (a) 4 (b) 68 (c) 13(d) 7 (e) 40 (f) 80

2. (a) 6, 21 (b) 8, 33, 12(c) 15, 48, 10, 96 (d) 6, 72, 24


1. < 4. < 7. <2. > 5. > 8. <3. < 6. > 9. <

Page 14Exercise 2.6

1. 34 3. 1

13 5.

13

2. 12 4.

211 6.

47

Page 14Exercise 2.7

1. 1324 3. 1

89 5.

18

2. 1150 4. 2

718 6. 5

320

Page 15Exercise 2.8

1. 1056 3. 10

34 5. 7

34

2. 5

12 4. 115

18 6. 1247490

Page 15Exercise 2.9

33

Answers of Exercises Fractions

1. 1056 3. 10

34 5. 7

34

2. 5

12 4. 115

18 6. 1247490

Page 15Exercise 2.9

1. 4256 l 2. 60

34 in 3. 3

34

Pages 15 -16Exercise 2.10

1. 12 bananas 4. 25 cm

2. 105 muslims 5. 77 muh

3. 972 seconds 6. 3759 in

Page 16Exercise 2.11

1. 3

10 4. 2 7. 5

2. 1 5. 6

11 8. 1245

3. 6 6. 140 9. 20


1. 20 girls 2. 817 pupils 3. 45 l


1. 179 3. 1

17175 5. 1

827

2. 3

16 4. 634 6.

34


1. 3

16 m 2. 24 pieces 3. 14 packets


1. 11

18 4. 3

10 7. 278

2. 138 5. 3 8.

65108

3. 736 6. 1

12 9. 6

116


1. 112 kg 4. 6

2. 150 eggs 5. Rf. 4100

3. 614 litres 6.

718


34

Unit 3 Decimals

Syllabus Content

Comprehension of decimal numbers.1

1.1 Read and interpret decimal numbers.1.2 Compare decimal numbers using > or <.1.3 Round off whole numbers to the nearest tens, hundreds,

thousands etc.1.4 Round off decimals to the nearest whole number and to the

specified number of decimal places.1.5 Convert fractions to decimals and vice-versa.

Operation of decimal numbers.2

2.1 Addition of decimal numbers.2.2 Subtraction of decimal numbers.2.3 Solve operations involving addition and subtraction of

decimal numbers.2.4 Multiplication of decimal number by a decimal number.2.5 Multiplication and division of decimals by 10, 100, 1000 etc.2.6 Division of decimal numbers by a decimal number.

Application of decimal numbers.3

3.1 Solve word problems involving decimal numbers.

35

Unit Notes Decimals

To locate decimal numbers on the number lineDraw a number line on the board and ask the following questions.“What number is midway between 3 and 4?” (3.5, write it on thenumber line). “Give another number between 3 and 4?” (Label thenew points on the number line). Repeat the above question and yournumber line may look something like this:

Draw this number line on the board and ask the following questions.

“What number is between 0.2 and 0.3?” Ask questions and label asmany points on the number line as shown above.

Rounding off numbers is a skill needed when we do estimation. Thenumber line approach is used to help the students understand“rounding off” concept. To round off a number to the nearesthundred means to find the multiple of hundred which is nearest tothe number.

If a student knows how to add and subtract whole numbers, no newproblems arise in addition and subtraction of decimals. Inmultiplication of decimals always remind the students that afterfinding the product, place the decimal point in the correct place.

Also remind the students that any zero which does not change theplace value of the digits are useless zeroes.

0 1 2 3 4

3.1 3.5 3.8

0 0.1 0.2 0.3 0.4

0.21 0.24 0.28

36

Activity 1

Complete the grids by writing a number or a mathematical symbol(+, –, ×, ÷) in the empty squares.

Activities Decimals

8

×

56

55

÷

5

63

35

45

1.7.6

×

2.8

–

–

7

9

5.6

0.4

2.

0.03

÷

0.003

×

×

+

÷

4

33.

0.4

6

–

÷

÷

0.02

×

0.2

0.56

4.

37

Activity 2

Fractions and Decimals Game.

Activities Decimals

1. Two players take it in turn to select two numbers from table 2.

2. Divide the larger number by the smaller number.

3. If the answer is in the table 1 and if the number is not yet crossed out,the player crosses out that square and write his/her initials.

4. The winner is the first player to cross out three squares in a line, eitherin a column or a row or a diagonal.

Note that some answers are corrected to 4 decimal places.

Table 1 Table 2

1

4

2

5

8

3

6

0.4 0.375 0.8 0.6667 0.8333

0.625 0.75 0.3333 0.25 0.6

0.125 0.875 0.2 0.5 0.1667

38

1. Give the place value of 3 in each of the following.

(a) 34078.12 (b) 152.739 [2]

2. Write > or < in the blanks.

(a) 8.6 __ 8.5819 (b) 127.09 __ 128.0009 [2]

3. Express 0.016 as a fraction in its lowest term [2]

4. Express 134

as a decimal [2]

5. Round off each number to the nearest place given in the bracket.

(a) 584.605 (2 d.p.) (c) 40750.1769 (thousands)

(b) 706.149 (tenths) (d) 4539.817 (whole number) [4]

6. Calculate the values of:

(a) 34 + 9.1 – 0.471 (c) 0.68 × 10 000

(b) 204.52 × 0.012 (d) 7 ÷ 1000 [8]

7. Evaluate and give your answer correct to 2 decimal places.

54.29 ÷ 25 [3]

8. A tank of a motor cycle holds 5 litres of petrol. On a journey

1.527 litres were burned. How much petrol is left. [3]

9. At a sale, bulbs were sold at 6 for Rf. 15. Umar bought 30 bulbs.

How much did he pay for the bulbs? [4]

Unit Test 3 Decimals


TIME 30 minutes

Total marks [30]

39

Page 26Exercise 3.1

Page 26Exercise 3.2

Page 27Exercise 3.3

Page 27Exercise 3.4

Answers of Exercises Decimals

1. hundredths2. tens3. hundreds4. tenths5. ten-thousandths6. ones7. thousandths8. hundred-thousandths

1. 105.5, 107.1, 108.82. 10.09, 10.26, 10.43. 4.773, 4.787, 4.804. 0.010, 0.011, 0.0122

1. > 4. > 7. <2. < 5. > 8. <3. < 6. > 9. >

1. (a) 920 (b) 7 0402. (a) 2 600 (b) 6 1003. (a) 40 000 (b) 54 000

1. 550 5. 34 0002. 2 730 6. 16 0003. 3 100 7. 8 0004. 9 900 8. 200 000

Page 28Exercise 3.5

Page 28Exercise 3.6

1. 0.64 5. 0.5142. 18.8 6. 1.53. 5.342 7. 57.304. 47 8. 110

1. (a) 1.413 (b) 956.3582(c) 13.53 (d) 2.9(e) 64.2668 (f) 0.9212(g) 974.9826 (h) 6.4223

2. 539.6843. 60.928

1. 846.4 4. 6 0002. 990 5. 15.0003. 3.14 6. 100

Page 28Exercise 3.7

Page 29Exercise 3.8

1. 6 6. 1.64162. 4.014 7. 0.655693. 426.76 8. 28.765534. 63 9. 0.1751235. 25.812

1. 38.3°2. 59.13 litres3. Rf. 168.75

Page 29 -30Exercise 3.9


40


Answers of Exercises Decimals


1. 50.9 7. 600002. 0.3 8. 284003. 4.54 9. 0.000594. 0.00428 10. 0.0025. 1.9 11. 8490006. 701 12. 0.17

1. 3.25 4. 6.42. 2.37 5. 2.553. 1.05 6. 1.204

1. Rf 8.75 3. 63 km2. Rf 115.83

1. 2.14 4. 6.132. 1.71 5. 0.223. 0.02 6. 0.49

1. 1.6 6. 0.612. 4.7 7. 0.433. 372 8. 64. 0.2 9. 0.1205. 1.05



1. (a) 0.5 (b) 0.75(c) 1.8 (d) 2.95

2. (a) 0.3 (b) 0.2(c) 1.9 (d) 2.3



1. 35 4.

21200 7. 30

8125

2. 925 5. 3

125 8. 94

58

3. 9

200 6. 11720


1. 78 m 5. Rf. 108.252. 2.2° C 6. 8 kg3. Rf. 1118.85 7. 2.18 kg4. Rf. 27.05


41

Unit 4 Directed Numbers

Syllabus Content

Comprehension of directed numbers.1

1.1 Compare positive and negative numbers using > or <.1.2 Use addition rule to solve addition and subtraction of

directed numbers.1.3 Use multiplication rule to solve multiplication and

division of directed numbers.

42

Introduction of directed numbersThe following method can be used to introduce directed numbers.“What is the answer of: 5 – 3 = ?This is easy. The answer is 2.What is the answer to the sum 3 – 5 = ?.You may think that there is no answerbecause 3 is less than 5. However, there isan answer.” Now explain the diagram onthe right. The diagram shows a yachtanchored in a harbour. Note that the top ofthe mast is 6 m above the sea level. Toreach the top of the mast you have to climb6 m up from the sea level. The anchor is4 m below the sea level. To touch theanchor you have to dive down 4 m. In thediagram to show that the anchor is 4 mbelow the sea level we have written –4 .

It is desirable that both directions of measurement should belabelled, rather than only the “below zero” direction, for they are ofequal importance. If 4ºC below zero is described as (–4)ºC, then 4ºCabove zero should be written as (+4)ºC. Thus the signs “+” and “–”are used to show two directions of measurement. Although thesesigns are the same as the signs for the arithmetical operations ofaddition and subtraction, students should realize that the signs areused in different sense.

Unit Notes Directed Numbers

+6

+5

+4

+3

+2

+1

0

–1

–2

–3

–4

43

Activity 1

What is the world’s smallest ocean?Use a ruler to join each question with its answer. The letters withoutlines through them spell out the answer.

Activities Directed Numbers

(+11) + (–13)

(–26) + (–24)

– 7 + 13

(+2) × (–9)

(+12) ÷ (+6)

(+13) – (–7)

(–25) × (–10)

+ (–250)

(+64) – (+75)

(–300) ÷ (–6)

– 19 – 23 – 7

– 11

+ 20

– 49

– 50

– 2

+ 250

+ 50

– 18

+ 2

– 250

+ 6

A

B

C

D

E

F

G

I

K

L

M

R

T

O

C

C

N

P

W

A

N

44

Activity 2

Complete the following puzzle.

Activities

ACROSS2. base ten number system4. total result5. the result of multiplying numbers6. thousand million7. symbol that stands for a numberDOWN1. has only two factors3. the number on the top of the fraction

2

5

7

4

1

6

3

45

1. Compare the following pairs of directed numbers.

(a) (–7) __ (+11) [1]

(b) (–2) __ (–99) [1]

(c) (0) __ (–105) [1]

2. Simplify the following.

(a) (+3) + (+5) [1]

(b) (+2) × (+1) [1]

(c) (+6) ÷ (+3) [1]

(d) – (+41) [1]

(e) (+12) + (–6) [2]

(f) (–8) × (–12) [2]

(g) (–78) ÷ (+13) [2]

(h) 7 – 8 [2]

(i) – 7 – 10 [2]

(j) – 3 × 5 [2]

(k) – 3 ÷ (–3) [2]

(l) – 5 – 6 + 14 [3]

(m) (–10) – (–3) [3]

(n) (–21) – (+9) [3]

Unit Test 4 Directed Numbers


TIME 20 minutes

Total marks [30]

46

Page 37Exercise 4.1 Page 38Exercise 4.5

Answers of Exercises Directed Numbers

1. +11 4. +200 7. +2502. + 5 5. +424 8. +114233. + 81 6. –1 037 9. 0

1. +14 4. +21 7. –3562. –17 5. –120 8. –14843. –2 6. +130 9. 0

1. + 3 3. –15 5. +1102. + 8 4. –42 6. + 900

1. +9 4. +11 7. –2122. –12 5. –70 8. 03. + 4 6. –31 9. –525

1. –6 3. –7 5. +12

2. + 5 4. + 10 6. –51

16

1. +9 6. +30 11. –322. –18 7. –54 12. –13. +49 8. –7 13. –844. –11 9. +9 14. –135. –13 10. 0 15. –26

1. > 4. > 7. <2. < 5. < 8. >3. < 6. > 9. >

Page 37Exercise 4.2

1. +172. –63. –4

Page 38Exercise 4.3

Page 38Exercise 4.4

Page 39Exercise 4.6

Page 39Exercise 4.7

Page 39Exercise 4.8

47

Unit 5 Indices and Algebra

Syllabus Content

Comprehension of algebra.2

2.1 Use letters to represent unknowns and write simple

algebraic expressions (e.g. 6c + d).

2.2 Add and subtract algebraic terms (e.g. 4m2n + 8mn2 – 7m2n).

2.3 Multiply algebraic terms (e.g. – x3 (2xy3)(–5y5z)).

2.4 Divide algebraic terms (e.g. 2

3

5

15–

a

ba ).

2.5 Evaluate algebraic expressions by substitution.

2.6 Simplify expressions with parenthesis (e.g. (3x + 2)(4x – 1)).

2.7 Factorize algebraic expressions (exclude group factorization).

Comprehension of indices.1

1.1 Introduce the index form.1.2 Find the values of numbers written in the index form.1.3 Use the multiplication law of indices in simplifying.1.4 Use the division law of indices in simplifying.

48

Unit Notes Indices and Algebra

Indices are introduced at this stage. Teacher’s should explain to thestudents that indices is a shorter way to write long expressions thatinvolve the multiplication of the same factor repeatedly. Alsoemphasize them on how to read numbers in index form. For example:52 is read as “5 to the power 2” or “5 squared”,53 is read as “5 to the power 3” or “5 cubed”,54 is read as “5 to the power 4” and so on.

Multiplication law and division law of indices are also introduced inthis grade. Students have to apply these laws not only inExercises 5.2 and 5.3, but they also have to apply these laws whenthey do Exercises from 5.7 to 5.11.

Writing algebraic expressions is a difficult concept for the students.Activity 2 of this unit should be done prior to Exercise 5.4 so thatstudents will be familiar with writing algebraic expressions for wordphrases.

Group workMake four groups and name them +, –, × and ÷. Have students makea list of different words or expressions to the particular operationassigned for the group. Each group should try to get about 10expressions. Then display the charts on the wall. As newexpressions are found or thought of, add them to the list.

While doing the “simplifying topics” of algebra it is important torevise the directed numbers addition rule and the multiplication ruleif the need arises.

49

Activity 1

Complete the cross-number puzzle.

Activities Indices and Algebra

ACROSSA. 42

C. 83

E. 42 × 43

G. 84

I. –112

J. 325 ÷ 320

L. 44

DOWNB. 54

D. –104

F. 1211 ÷ 129

H. 63

J. 7 × 73

K. 25

M. –94

A B J K

L M

C D

F I H

E

G

50


Activity 2

PRE-ACTIVITY

Match

Five times x. 2 + x

Divide x by y. x + y

Two greater than a number x. x – 2

The sum of any number x andany number y. 5 + x

The product of two numbers xand y. x – 5

Subtract 2 from x. 5x

A number x decreased by 5. xy

Five times a number x plus asecond number y.

xy

Your age after x years if youare 5 years old now. 5x + y

51

Activity 3

What is the slowest moving fish?

To find the answer:1. Substitute and simplify.2. Write the letter under its matching number in the DECODER.


29

A

v = 1 w = 2 x = – 3 y = – 1 z = 5

5 w

H

y z 2

E

– 2 x y

O

2 x – 5 y

S

2 y 2 – x 3

R

2 x 2 – 4 v 2 0

DECODER

– 6 10 – 25 – 1 14 29 – 6

52

1. Find the values of the following.

(a) (52) (b) (–73) [2]

2. Work out the following in index form.

(a) 63 × 6 × 64 (b)318

18 [2]


(a) x15 × x2 (b)21

6

aa [2]

4. Write an algebraic expression for each of the following.

(a) Six less than a number m. [1]

(b) Three times a number w plus a second number s. [2]


(a) 20x + 13x [2] (c) (– 3p2) (– 4p2q) [3]

(b)3

2

42–6

vv [3] (d) – 4u2 + 2u – 3u2 – 5u [3]

6. Remove the brackets and simplify.

(a) 3c – 2(7a + 5c) [2] (b) (7z + 1) (z – 3) [3]

7. Factorize.

(a) bc – 2c [2] (b) 6x – 12xy + 3x2 [3]

8. Evaluate.

(a) 4a3 when a = 1 [2] (b) xy – 2x when x =1, y = –2 [3]

Unit Test 5 Indices and Algebra


TIME 30 minutes

Total marks [35]

53

Page 49Exercise 5.1 Page 51Exercise 5.5

Answers of Exercises Indices and Algebra

1. 26 4. 812 7. 1224

2. 53 5. 98 8. 1419

3. 617 6. 76

1. 9 4. 32 7. 24012. 8 5. –125 8. –2433. 16 6. 3125 9. 1000000

1. a8 4. m11 7. u49

2. b17 5. n14 8. y15

3. c3 6. s6

1. 10u 7. 8p – q

2. w – 13 8. g +15

3.4n 9. r + s kg

4. x + y 10. 13 + y years

5. z – 5 11. 30z students

6. ab 12. 800 – x + y people

Page 49Exercise 5.2

Page 49Exercise 5.3

Page 50Exercise 5.4

1. 2a 7. 02. 3d 8. 3p2

3. – 4xy 9. 14a4. 6x5 10. 11g3

5. – 3y2 11. – 15x3y6. – 17ac3 12. 13t7

1. 7x – 5 6. – 3m2. 10x2 + 6xy2 7. 12u + 14y2

3. – 4a2 8. 3y – 2xy4. 13x3 + 3x2 9. p7q8

5. 12x2 – 18

Page 51Exercise 5.6

Page 51Exercise 5.7

1. 5cd 7. 6d3

2. – 14pq 8. 12a10

3. u15 9. 20x6

4. s7 10. – 15m11n10

5. 12p5 11. 20w6 x8

6. – 30a2 b 12. – 30x6 y7 z3

54

Page 52Exercise 5.8

Answers of Exercises Indices and Algebra

1. p2 5. 4c 9. 6y2. 6 6. 9k2 10. – 9ab3. 3e 7. 11t 11. 4m4. 5a2 8. – 6u 12. 5x3 y3 z

1. 2a + 14 4. 6m2

2. – 20 + 4b 5. – 16n3 + 2n5

3. – 12c + 15d 6. x6 y + 9x3

1. – 2a – 3 6. – 2x – 2y2. 4x – y 7. 5x + 113. 6a + 6 8. 2x2 + 5x + 64. x – 10 9. x2 – 45. 4a

1. x2 + 3x + 22. a2 + 5a + 63. 2a2 + 13a + 204. s2 + 3s – 185. n2 – 96. 6u2 – 7u + 27. 2w2 + 3w – 208. 6x2 – 11xy + 4y2

9. y2 – 2510. a2 + 2ab + b2

11. 4z2 – 12z + 912. x2 – 2xy + y2

1. x (y + z)2. m (p – n)3. q (p + 3)4. 2 (a – b)5. 4 (m – 2n)6. 5 (u + 2)7. u (u – v)8. x (x + 1)9. b2 (1 – b)

10. 3a (1 – 3a)11. 9c (2c2 – d2)12. x2y2 (3x4y + 5)13. x (a + b + c)14. p (q – r – 1)15. z (z2 – z + 1)16. 3a (b – 3c – 2d)17. 3x (4y2 + 3xy – x2)18. 2c2d2 (3cd3 + 1 + 4c3d)

Page 52Exercise 5.9




1. (a) 6 (b) –28(c) –12 (d) 36(e) 0 (f) 18(g) –20 (h) 40(i) –600 (j) 14(k) –1 (l) 18(m) 7 (n) 8(o) 17

2. –3 4. –883. 11 5. 43


55

Unit 6 Equations

Syllabus Content

Comprehension of equations.1

1.1 Solve linear equations (include cases involving fractional

coefficients, exclude: 15

122

3=

−+

− xx ).

56

Unit Notes Equations

Students have already done simple linear equations (e.g: x + 5 = 9,

8e

= 10, 6x – 4 = 13) in grade 6. But at this stage also, when

explaining examples, show them the two methods of solving

the equations. The students can choose any of the methods.

The “balancing equation” method (add, subtract, multiply or dividethe same value by both sides of the equation) must be used to buildthe concept.

In the explanation of the type, –2x = 14 show them why the minussign of 2 does not change when you move the 2 to the other side.This can be done by using the “balancing method”.

When the equations get more difficult you should break them downinto stages and deal with each operation (+, –, ÷, ×) in turn. Anything added or subtracted from the unknown (letter term) quantity isdealt with first. Next you deal with any values which divide ormultiply the unknown.

Sometimes the unknown appears on both sides of an equation. Tosolve this type of equation you first need to get all the unknowns onone side and the numbers to the other side. Preferably theunknowns to the left of the equal sign.

Note that the students can always check their answers bysubstituting their answer back into the equation.

57

Activity 1

MYSTERY WORD

1. Start from the top left box.2. Solve the equation in the box.3. Look for the solution in the corner of another box.4. Write down the letter in the box and then solve the equation in the box.5. Look for the solution as before and continue until you arrive back at

top left box.6. Read the word and draw it.

Activities Equations

x – 5 = 10

x = 10

O

x = – 2

25x

= 1610

N

x = – 8

25x

= 9 – 2x

G

x = 4

L

x = – 4

B

x = 7

O

x = 15

x – 3 = 11 – x

–11 = 2x – 3

3(x + 4) = 6(x + 3)

– 6 = 34x

58

Activity 2

Join each equation to its solution with a straight line. If you do itcorrectly you will get 3 triangles.

Activities Equations

710

x =

52x

+ 9

7x + 5 = 26

–2(3x – 1) = 3(x + 4)

– 12 = 25x

12 = x + 7

5

3

– 30

–119

– 5

59

Solve the following equations.

1. a + 4 = 9 [1]

2. – 17 = – 3 + b [2]

3. – 10c = 50 [2]

4. 8e

= 6 [2]

5.7

2u = –511 [3]

6. 5h + 9 = 39 [3]

7. 12 – 2m = 14 [3]

8. 2n + 12 = – 21 – 5n [4]

9. 4 (1 + 3s) = 5(4s – 2) [5]

10.56x

– 13 = 2

x[5]

Unit Test 6 Equations


TIME 25 minutes

Total marks [30]

60

Page 56Exercise 6.1

Answers of Exercises Equations

1. 5 4. –7 7. 812

2. 12 5. –56 8. –30

3. –40 6. 108

1. 8 4. –2 7. –132. 1 5. –7 8. –403. 0 6. 19

1. 2 4. –16 7. 0

2. 4 5. –123 8. 1

23

3.12 6. –7 9. 2

67

1. 9 3. 5 5. 6

2. 6 4. 334 6. 3

12

Page 56Exercise 6.2

Page 56Exercise 6.3

Page 57Exercise 6.4

1. 5 4. 8 7. –2

2. 1 5. 213 8. 2

3. 218 6. 1

12 9. – 2

12

Page 57Exercise 6.5

1. 2 4. 123 7. –1

15

2. 9 5.14 8. –

528

3. 415 6.

310 9.

322

Page 57Exercise 6.6

1.13 4. –10 7. 2

15

2. 623 5. 0 8. –70

3. 12 6. 1012 9.

114

Page 58Exercise 6.7

61

Unit 7 Geometry

Syllabus Content

Comprehension of angles.1

1.1 Find unknown angles involving angles on a straight lineand angles at a point.

Angle properties of quadrilaterals.2

2.1 Use the angle sum of the quadrilateral in finding theunknown angles of the quadrilaterals.

Angle properties of triangles.3

3.1 Use the angle sum of the triangle in finding the unknownangles of the triangles.

3.2 Identify the base angles of an isosceles triangle.3.3 Find the size of angles of an equilateral triangle.3.4 Use the relationship between exterior angle of a triangle

and the sum of the far interior angles of the triangle to findthe unknown angles.

62

Unit Notes Geometry

It is essential to do the first question of Activity 1 before doing theexercises in the workbook. Spend about 5 to 10 minutes measuringthe angles. Second question of Activity 1 should be done prior toExercise 7.5.

Naming angles using three letters have been introduced in Grade 5.However, students confuse this concept very often. To name usingthree letters we write, “one from a point on one side of the angle, onefrom the vertex, and one from a point on the other side”.

Students should explore that:Sum of the angles on a straight line is 180º, angles at a point add upto 360º, angles in a quadrilateral add up to 360º, angles in a triangleadd up to 180º and exterior angle of a triangle is equal to the sum ofthe opposite interior angles.

Teachers should introduce the above angle properties one at a time.For example if you are introducing sum of the angles on a straightline is 180º, ask the students to draw 3 different diagrams of Type 1.Ask them to measure the angles in each diagram and add them.Students may come with answers of range +3º. Explain to them thatthe errors are due to the mistakes that they have made in measuringthe angles.

Type 1 Type 2 Type 3 Type 4

63

Activity 1

PRE-ACTIVITY

Activities Geometry

2. Name the following angles in three different ways.

(a) (b)

c

de

n

P

Q

RS

T

a

b

A B

C

D

1. Measure the following angles with a protractor.

(a) (b)

(c) (d)

64

Activity 2

Each of these figures can be cut into two parts by one straight line andthen arrange to form a square.

Activities Geometry

65

1. Find the equal angles in the following isosceles triangles.

Unit Test 7 Geometry


TIME 30 minutes

(a)

A

[1]

C

B

X

Y Z

(b)

2. Calculate the size of each of the unknown angles marked with lettersin the diagrams.

e108º

26º 87º

(b)

2c

51º

(c)

c

(a)

a48º72º [2] [2]

[4] 62ºm2m

4m

46º

(d)

[4]

[1]

66

(e)

[3] s

(f)

[4]76º

n

(g)

x

107ºz

(h)

[4][4]

Total marks [29]

68º

135º

67


Answers of Exercises Geometry

1. 60º 5. 67º 9. 45º2. 16º 6. 56º 10. 34º3. 44º 7. 70º 11. 60º4. 177º 8. m = 107º 12. 60º

n = 61º

1. 95º 3. 55º 5. 90º2. 91º 4. 45º 6. 198º

1. 70º 3. 59º2. 75º 4. 50º

1. ∠ CAB = ∠ CBA2. ∠ FEG = ∠ EGF3. ∠ IJH = ∠ IHJ4. ∠ LKM = ∠ LMK5. ∠ ONP = ∠ OPN6. ∠ QRS = ∠ RSQ

1. 50º 3. 32º 5. 78º2. 62.5º 4. 36º 6. 45º

1. 115º 4. 65º 7. 135º2. 96º 5. 30º 8. 120º3. 63º 6. 145º



Page 66Exercise 7.4



68

Unit 8 Measures

Syllabus Content

Metric units.1

1.1 Express the units of length (km, m, cm, mm) in terms oflarger or smaller quantities.

1.2 Express the units of mass (t, kg, g) in terms of larger orsmaller quantities.

1.3 Express the units of capacity (l, ml or cm3) in terms oflarger or smaller quantities.

Imperial units.2

2.1 Express other units of length (miles, feet, inches) in termsof larger or smaller quantities.

2.2 Express the units of time (s, min, hr) in terms of larger orsmaller quantities.

69

Unit Notes Measures

Students have already measured in centimetres, metres, kilometres(from a scaled drawing), inches, feet, grams, kilograms, millilitres,litres, seconds, minutes and hours in grades 2, 3 and 4.

In grade 4 they have done conversions without the knowledge ofdecimal numbers. Questions of the type 1050 g = ? kg ? g are doneat that level.

In grade 5 and 6 conversions have not been carried out (refer to thescope and sequence chart of measures in the syllabus) sincemultiplication and division of decimals by 10,100, 1000 ... areintroduced in grade 6.

Tonnes, miles, cm3, conversion of metric units and imperial units areintroduced in this grade. Teachers should recall all the metric andimperial units that they have learned before. Also explain to themthe differences of metric and imperial systems. If possible, try tomeasure some of the lengths of objects and distances. Measuring thestudents height and weight also can be done during these lessons.

Explain that, since the metric system is based on the number 10, youcan change from one unit to another by multiplying or dividing by10, 100 or 1000. Students usually remember which number to use,but they forget whether to multiply or divide. Half the time theychoose the wrong operation. This could be solved by using thediagrams repeatedly. These diagrams could be displayed on thewalls of the classroom.

70

Activity 1

Complete the cross-number puzzle.

Activities Measures

ACROSS

1. 2.85 m =__ cm

3. 50 min = __ s

5. 3 508 000 g = __ kg

7. 790 000 kg = __ t

8. 1620 in = __ ft

9. 3 miles = __ ft

10. 5.129 km = __ cm

DOWN

2. 0.5 m = __ mm

4. 0.23 l = __ ml

6. 81.05 km = __ m

11. 3 hours = __ s

12. 0.19 l = __ cm3

1

3

2

9

4

5

7

6

8

10

12

11

71

Activity 2

MATHEMATICAL WORDSEARCH

Find as many mathematical words as possible and make a list.

Activities

Your rating: 7-9 Average 15-19 Very good10-14 Good 20-22 Excellent

R C A P E Q U A L S E A T

A A G B S U M S E L I M U

T P A I D A B O V X R I N

N A L S E D E G R E E S S

E C L E N R L O V T W O D

I I O C O I A W A R O S N

C T N T M L S N R E P C O

I Y C E I A Z C I V I E C

F A N N N T R I A N G L E

F E R S A E O R B L S E S

E A E I T R S C L U E S G

O T A T O A E L E K T N B

C O D E R L A E F B A S E

72

Convert the following.

1. 8 cm into mm [1]

2. 12 l into ml [1]

3. 5000 m into km [1]

4. 0.8 kg into g [1]

5. 21.8 mm into cm [1]

6. 208 kg into t [1]

7. 75 cm3 into l [1]

8. 11 feet into inches [2]

9. 13200 feet into miles [2]

10. 30 minutes into seconds [2]

11. 225 minutes into hours [2]

12. 3 km into cm [3]

13. 91 mm into m [3]

14. 2 hours into seconds [3]

15. 16200 seconds into hours [3]

Unit Test 8 Measures


TIME 35 minutes

Total marks [27]

73

Page 76Exercise 8.1

Answers of Exercises Measures

Page 76Exercise 8.2

Page 76Exercise 8.3

1. 60 mm 5. 7 180 m2. 3 km 6. 10.2 cm3. 957 mm 7. 9.39 m4. 1 406 cm 8. 0.013 km

1. 5 000g 4. 3 250 kg2. 8 t 5. 0.0135 kg3. 0.6 kg 6. 0.5169 t

1. 7 000 ml 3. 1 l2. 3 800 cm3 4. 4.8 l

1. 400 000 cm2. 1 800 mm3. 0.43221 km4. 0.063 m5. 0.006 km6. 75 mm7. 5 000 000 mm8. 0.017 km

1. 120 seconds

2. 3 minutes

3. 300 minutes

4. 5 hours

5. 612 hours

6. 814 hours

7. 10 800 seconds

8. 18 000 seconds

9. 6 hours

10. 812 hours

1. 84 in 4. 237

12 ft

2. 6 miles 5. 1513 ft

3. 15 840 ft 6. 214 miles

Page 77Exercise 8.4

Page 77Exercise 8.5

Page 77Exercise 8.6

74

Unit 9 Perimeter and Area

Syllabus Content

Comprehension of perimeter.1

1.1 Find the perimeter of different shapes when the sides aregiven.

1.2 Find the circumference of circles, where the radius ordiameter is given.

1.3 Find the perimeter of semi circles and quarter circles.1.4 Find the perimeter of compound figures.1.5 Find the dimensions of rectangles, squares and circles

given its perimeter and other dimensions.

Application of area and perimeter.3

2.1 Solve word problems involving perimeter and area.

Comprehension of area.2

1.1 Use formula to calculate the area of rectangles, squares,triangles, parallelograms, trapeziums and circles.

1.2 Find the area of semi circles and quarter circles.1.3 Find the dimensions of rectangles, parallelograms, triangles

and trapeziums given its area and other dimensions.1.4 Find the area of compound figures.1.5 Find the area of shaded regions.

75

Unit Notes Perimeter and Area

At the beginning of this unit, the concepts of perimeter and area arerevised. The perimeter of a figure is the distance around it. The areaof the figure is the amount of space in it. Perimeter and area are twoindependent attributes of a figure. A figure which has a greaterperimeter than another may not have a greater area.

After introducing the perimeter ask the students to do the firstactivity of this unit.

In the previous grades, the students have learnt to find perimeter andarea of compound figures (excluding semi circles and quartercircles). At this level, they will learn to find the perimeter and areaof semi circles, quarter circles and compound figures (including semicircles and quarter circles).

Lead the students to see that we need to indicate only one side of asquare and two sides of a rectangle. Similarly, not all the sides of acompound figure need to be indicated. So the students have to findthe missing dimensions before the perimeter of the figure.

They have already used the formulae to calculate the areas ofrectangles, squares, triangles and circles . At this stage you have tointroduce the formulae for finding the areas of parallelograms andtrapeziums.

It is important that the students have an idea of how big 1 cm2, 1 m2

and 1 km2 are.

76

Activity 1

Match the shapes which has the same perimeter.

Activities Perimeter and Area

Activity 2

Dhunya has a piece of squared paper of sides4 cm. Help her to divide it into four equalparts. Each part must have a perimeter of10 cm and must not be a rectangle.

77

Activity 3

Measure to the nearest centimetre. Calculate the area of these figures.

Activities Perimeter and Area

1. Figure CDEM = _____ cm2

2. Figure ABJ = _____ cm2

3. Figure AJKI = _____ cm2

4. Figure IKH = _____ cm2

5. Figure KLGH = _____ cm2

6. Figure BCLKJ = _____ cm2

7. Figure EFGLM = _____ cm2

8. Check yourself. Add up the area of all seven figures. _______ cm2

9. Is your total same as the area of rectangle ADFH? _______ cm2

A DB

J

KI

H G F

E

L

M

C

78

Unit Test 9 Perimeter and Area


TIME 50 minutes

1. Find the perimeters of the following figures.

[2]

(a)

9 m

(b)

7 m

7 m

6 m

2 m 2 m

20 mm

[3]

(c) (d)

21 cm [4] [4]7 km 8 km

10 km

2. Find the unknown measurement of the following figures.

9 m P = 44 m

?

(a)

7 ft

?

A = 5212 ft2

(b)

[3] [3]

3. Find the area of the following figures.

(a)

14 km

7 km

10 km (b)13 cm

[2] [3]

79

Total marks [42]

4. Find the area of each shape. If an area is shaded, find the shaded area.

(b)(a)

[4][4]

7 m12 m

12 m

7 mm

11 mm

2 mm

10 mm

5. The perimeter of a football field is 250 m. Hussain ran round 12

times. How far did he run? [2]

6. The area of a rectangle is 42 cm2. If its breadth is 6 cm, find its

perimeter? [4]

7. A carpet, 9 m long and 7 m wide, is laid in a square room of side

10 m. Find the area of the floor left uncovered? [4]

80

Page 79Exercise 9.1

Answers of Exercises Perimeter and Area

1. 130 mm 4. 48 cm2. 24 m 5. 32 ft3. 37 km 6. 108 m

1. 20 km 4. 82.4 mm2. 28 m 5. 33.8 ft3. 19 cm 6. 70 in

1. 264 mm

2. 34.54 km or 3447 km

3. 176 cm or 175.84 cm

4. 100.48 m or 10027 m

1. 162 cm

2. 75 mm

3. 180 m

4. 10.71 km or 1057 km

Page 80Exercise 9.2

Page 81Exercise 9.3

Page 82Exercise 9.4

1. 128 mm

2. 1657 km or 16.71 km

3. 6757 cm or 67.71 cm

4. 195 m

Pages 83 - 84Exercise 9.5

1. 19 km 4. 3 cm

2. 15 cm 5. 21 mm

3. 63 m 6. 512 m


1. 40 cm 4. 10 m2. 1 560 m 5. Rf. 5 7603. 28 cm 6. 220 m


1. 5 cm2

2. 8 cm2

3. 11 cm2

Page 89Exercise 9.8

81



1. 64 cm2 4. 255.15 m2

2. 25.46 m2 5. 120 cm2

3. 98 km2 6. 360 mm2

1. 108cm2 4. 57775 mm2

2. 96 m2 5. 22 km2

3. 88 m2 6. 39.6 km2

1. (a) 616 mm2 or 615.44 mm2

(b) 1386 cm2 or 1384.74 cm2

(c) 639

14 cm2 or 63.585 cm2

(d) 11317 m2 or 113.04 m2

2. (a) 53117 km2 or 530.66 km2

(b) 70717 m2 or 706.5 m2

(c) 5721114 cm2 or 572.265 cm2

(d) 7546 mm2 or 7539.14 mm2



1. 3812 cm2 3. 346

12 m2

2. 77 km2 4. 48114 mm2

1. 25 m2

2. 1 000 mm2

3. 1 736 cm2

4. 10047 cm2 or 100.34 cm2 or

100.48 cm2

5. 21.5 m2

6. 55 km2

7. 21 cm2

8. 2 187.5 m2

9. 1576.9075 mm2 or 157634 mm2




1. 9 cm 4. 314 m

2. 12 m 5. 27911 km

3. 8 mm 6. 13 cm

82



1. P = 9 cm

A = 78 cm2

2. P = 51.9 cm

A = 55 cm2

3. P = 47.4 cm

A = 72 cm2

4. triangle

5. rectangle

1. 77.6 or 7735 m

2. 1 200 m

3. 50.24 or 5027 m2

4. 26 cm

5. 81 cm2

6. 24 m2

7. 15 m2, Rf. 6000

8. 13313 tiles

9. 72.22 or 7229 tiles


83

Unit 10 Volume

Syllabus Content

Comprehension of volume.1

1.1 Find the volume of cubes and cuboids.1.2 Find the dimension of a cuboid given its volume and

other dimensions.1.3 Find the volume of prisms.1.4 Find the length of a prism given its volume and area of the

cross-section.

Application of volume.2

2.1 Solve word problems involving volume of cuboids, cubesand prisms.

84

Unit Notes Volume

In the previous grades, the students have learnt to find the volume ofcubes and cuboids. At this level, they will learn to find the volumeof prisms.

The concept of the cubic centimetre (cm3) should be revised andrelated to centimetre (cm) as a unit of the length and square centime-tre (cm2) as a unit of area.

It is important that the students have an idea of how big 1 cm3 and 1 m3

are. Students should become aware that it is more appropriate tomeasure the volume of large objects and containers in cubic metres.

Use suitable one centimetre cubes to construct models shown inExercise 10.1. Determine the volume of each model by counting thenumber of cubes.

Before introducing the formula to find the volume of prisms, showthem 3 dimensional objects similar to the solids shown below.

Show them one at a time. Ask the students which of them areprisms. Each time when you show a prism also ask them which faceis the cross-sectional face.

A prism is a 3 dimensional shape which has a uniform cross-section.A uniform cross-section means that if you slice the shape withparallel slices you get slices of the same shape and size.

85

Activity 1

Draw the cross-section of each of the following prisms.

Activities Volume

1. 2.

3.

4. 5.

6.

86

Activity 2

Fill in the missing letters.

Activities Volume

A B

F

AB

E

F

D

B C

F

B

C D

F

D AF

E

F

B B

C

C C

D

D D

EE E

F

F FAB

87

1. Find the volumes of the following.

Unit Test 10 Volume


TIME 25 minutes

Total marks [25]

(b)

18 m7 m

10 m(a)

2. Find the volume of a cube with an edge of 2.1 cm. [2]

3. The volume of a rectangular room is 75 m3. The area of its floor is

15 m2. Find its height. [2]

4. The length of a prism is 12 mm and the volume is 294 mm3. Find the

area of cross-section of the prism. [3]

5. The box of a packet of juice is a cuboid of length 5 cm, breadth 3 cm

and height 6 cm.

(a) Calculate the volume of the box. [2]

(b) Calculate the number juice packets which can be placed in a

rectangular tray of length 50 cm, breadth 9 cm and height 12 cm. [4]

46 mm2

13 mm[2][2]

(c) (d)

[4] [4]20 cm

35 cm

8 km

12 km

7 km

6 km

5 km

88


Answers of Exercises Volume

1. (a) 24 cm3 (b) 32 cm3

2. (a) 5670 mm3 (b) 636.056 m3

3. 1120 cm3

4. 0.729 m3

5. 1 365 000 mm3

6. 240 m3

1. 32 m3 5. 1 564 cm3

2. 243 cm3 6. 5 250 mm3

3. 1050 mm3 7. 1 302 m3

4. 702 m3 8. 1 404 cm3

1. 112 m3 6. 217 m3

2. 2772 cm3 7. 6859 m3

3. 4480 mm3 8. 2 600.1 cm3

4. 162 cm3 9. 1413 mm3 or

5. 7168 mm3 141427 mm3

1. 3080 cm3 6. 36 m3

2. 20 mm2 7. 900 m3

3. 4 m 8. 650 kg

4. 16 cm 9. 66623 bricks

5. 50 cm2




89

Unit 11 Rate, Ratio & Proportion

Syllabus Content

Comprehension of rate.1

1.1 Introduce rate.1.2 Solve problems involving rate.

Comprehension of ratio.2

2.1 Find the ratio of two or more quantities.2.2 Simplify ratios with whole numbers.2.3 Simplify ratios with units. (e.g. 20 hr : 1 day)2.4 Simplify fractional ratios.

Comprehension of proportion.3

3.1 Solve word problems involving direct proportions.3.2 Solve word problems involving proportional parts (sharing).3.3 Solve word problems involving alms (zakaaiy).

90

Unit Notes Rate, Ratio & Proportion

Ratio and proportions were introduced in grade 6. In this grade weteach the students to write the ratio of two or more quantities,simplify ratios with units, simplify fractional ratios and solveproblems involving proportional parts (sharing). Also in this gradewe teach rate and calculations on zakaath.

Rate is another way of expressing the relationship betweenquantities. For example: Rf. 5 per litre, 20 km per hour, etc. Theconcept of rate is quite different from the concept of ratio. Forexample: A dhoani travels 3 km every 10 min. “3 km every 10 min”is a rate. It expresses the relationship between two quantities,namely distance travelled and time taken. It is not a ratioexpression. To express the relationship as a ratio we must think interms of pure numbers.

Additional information on zakaathFrom the money that is saved, if the nisaab is due, and if one hijriyear has passed since the money was saved, each person has to givezakaath.

Zakaath is an obligatory form of charity on savings. It is not anincome tax, but a savings tax. Its major recipients are the workingpoor, who cannot meet all of their needs without some additionalhelp, and the destitute, who cannoteven meet their basic needs.

The amount due is 2.5% of savingswhen it reaches the equivalentvalue of 595 grams of silver. Thisminimum amount on whichzakaath is due is called the nisaab.The graph shows how nisaab haschanged from 2000 to 2002 in theMaldives. 2

000

Jan-

Jun

200

0 Ju

l-Dec

200

1 Ja

n-Ju

n

200

1 Ju

l-Dec

200

2 Ja

n-Ju

n

200

2 Ju

l-Dec

1300

1200

1100

1000

900

Am

ount

in R

ufiy

aa

Rf.

976

Rf.

1065

.05 Rf.

1214

Rf.

1047

Rf.

1119

Rf.

1184

91

Activity 1

Study the three price charts carefully and find the cheaper drink from each.

Activities Rate, Ratio & Proportion

300 ml

apple

Rf. 6 only

250 ml

orange

Rf. 6 only

1

300 ml

milo

Rf. 6 only

300 ml

milk

Rf. 5.50 only

2

300 ml

vanilla

330 ml

chocolate

Rf. 7.26 only

3

Rf. 6.75 only

92

Activity 2

When do we mark the day Maldives embraced Islam?Use a ruler to join each question with its answer. The letters withoutlines through them spell out the answer.

Activities Rate, Ratio & Proportion

10 : 4 4 : 5S

7 : 16

15

: 14

5 : 2

412

: 12 1 : 8

116

: 223

25 : 3

25 : 1

9 : 24

5 : 1

16 : 128

8 cm : 16 mm

6 t : 720 kg

Rf. 5 : 20 L

E

R

A

A

A

A

B

JY

C

O

B

E

K

H

C

D

L

S

T

N

D

E

U

I

R

F

LM

N

U

P

W

X

93

1. Express the following ratios in their simplest forms.

(a) 6 : 10 (b) 3000 : 560 [2]

(c)14

: 23

(d) 117

: 312

[4]

(e) 2 kg : 700 g (f) 3 hr : 45 min [4]

Unit Test 11 Rate, Ratio & Proportion


TIME 30 minutes

Total marks [27]

2. A bowl of fruit contains 5 apples, 3 bananas and 7 oranges. What is

the ratio of

(a) oranges to apples [1]

(b) apples to the total number of fruits. [2]

3. A machine fills 900 bottles of drinks in 20 minutes. How many

bottles of drinks can it fill per minute? [2]

4. A car travels 60 miles on 2 gallons of petrol. How far will it travel

on 5 gallons of petrol ? [3]

5. Rashidha saved Rf. 34 000 over a Hijri year. If the Nisaab is Rf.1270,

find the amount due on Zakaath on her savings? [3]

6. A piece of wood 88 feet long is divided into two parts in the ratio

5 : 3. How long is each part? [3]

7. Mortar is made by mixing sand and cement in the ratio 5 : 2. How

much sand would be needed to mix with 25 kg cement? [3]

94

Answers of Exercises Rate, Ratio & Proportion


1. 20 pages per hour2. Rf. 3 per student3. Rf. 250 per students4. 2 people per day5. 20 cans per minute6. 400 calls per telephone7. Rf. 2150 per month8. 30 km per hour

1. 1 : 4 4. 1 : 42. 3 : 2 5. 1 : 43. 5 : 3 6. 6 : 5

1. (a) 2 : 3 (b) 4 : 12. (a) 3 : 8 (b) 8 : 113. (a) 3 : 2 (b) 6 : 2 : 3

(c) 6 : 114. (a) 5 : 3 (b) 1 : 5

(c) 5 : 3 : 15. (a) 13 (b) 13 : 22

(c) 13 : 356. (a) 7 : 13 (b) 13 : 40

(c) 7 : 40

1. 1 : 4 6. 32 : 12. 1 : 5 7. 63 : 16003. 2 : 5 8. 1 : 74. 4 : 1 9. 9 : 565. 2 : 1 10. 1 : 6

1. Rf. 275 4. 39 m2. 296 guavas 5. 16 cm3. 7 l 6. 312 studentsPages 130 - 131Exercise 11.2




1. 2 : 3 6. 7 : 102. 2 : 7 7. 26 : 333. 2 : 3 8. 8 : 1034. 11 : 2 9. 3 : 45. 8 : 1 10. 48 : 19


1. Rf. 50 4. Rf. 236.252. Rf. 29.75 5. Rf. 11253. Rf. 30.63 6. Nil


1. Rf. 60, Rf. 302. 135 mm, 45 mm, 90 mm3. Rf. 432, Rf. 6484. 20 girls, 15 boys5. 180 men, 135 women, 225 children6. 9 g zinc, 36 g tin, 855 g copper

1. Rf 105, Rf 1502. 7 cm3. 30 m4. 206 kg cement, 412 kg sand,

618 kg gravel5. 9 cm, 12 cm, 15 cm6. Rf 1450



95

Unit 12 Percentage

Syllabus Content

Comprehension of percentage.1

1.1 Recognize the equivalent between percentage and fraction.1.2 Change fraction to percentage, and vice versa.1.3 Change decimal to percentage, and vice versa.1.4 Calculate the percentage of a quantity.

Application of percentage.2

2.1 Solve word problems involving percentages.2.2 Solve word problems involving percentage of a quantity.2.3 Solve word problems involving percentage increase and

decrease.2.4 Solve word problems involving discount.2.5 Solve word problems involving profit and loss percentage.

96

Unit Notes Percentage

Percentage was introduced in grade 6. This unit consolidates thestudents’ understanding of percentage calculations first introduced ingrade 6. That is changing proper fraction to percentage and viceversa, calculating the percentage of a quantity and solving wordproblems. For more information refer to the scope and sequencechart of percentages in the syllabus.

Before doing the exercises, remind them the

meaning of percent. Draw the diagram on the

board. Ask the students what part of the square is

shaded. Write the answer on the board in two

ways, 35

100 and 0.35. The third way is to use percents and write

35%. Summarise the above as 35

100 = 0.35 = 35%.

When giving examples of the percentages which are greater than100%, teachers should explain them lots of everyday situations inwhich we use percentages greater than 100%. For example: theimport duty of some vehicles is 200%, profit of 300% etc. Elaborateon these types of examples.

After explaining the examples and assigning the exercises, observethe students work as they begin the exercise to be sure that they getoff to a good start.

We recommend the teachers to use the proportion method asexplained in the text book in calculating percentage profit/loss andpercentage increase/decrease.

97

Activities Percentage

Activity 1

Each of the diagrams shown has 100 squares. Count the number ofshaded squares. Express this number as a fraction of the total number ofsquares. Then convert it into a decimal and a percentage.

PercentageDecimalFraction

1.


3.


2.

98

Activity 2

Circle the correct answer. Write the letter for each circled answer abovethe related question number at the bottom of the page. Now you can seethe secret message.

Activities Percentage

1.12 = S 10% P 50%

2.1250 = T 6% R 24%

3.825 = A 32% U 16%

4.85 = C 160% D 80%

5. 714 = T 725% Y 25%

6. 0.425 = E 4.25% I 42.5%

7. 0.06 = S 6% V 60%

8. 2.25 = A 22.5% E 225%

9. 0.015 = R 15% M 1.5%

10. 84.9% = Y 8.49 A 0.849

11. 49% = K 0.49 D 4.9

12. 8.7% = E 0.087 A 0.87

13. 5% = Y 5

10 S 120

14. 30% = U 3010 P

310

15. 220% = N 1022 E 2

15

16.72 % = R

7200 T 3.5

17. 415 % = I 4.2 F

21500

18. 10 % of 230 = E 23 L 2.3

19. 15% of 1000 = C 150 O 15

20. 3 % of 150 = T 4.5 N 45

9 10 11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8

99

1. Convert the following into percentages.

(a) 1120

(b) 318

(c) 0.65 (d) 3.2 [4]

2. Convert the following percentages into decimals.

(a) 8.2% (b) 785% [2]

3. Express these percentages as fractions in their simplest form.

(a) 76% (b) 35

% (c) 256

% [1+2+2]

4. Find the values of each of the following.

(a) 35% of Rf. 50 (b) 120% of 65 kg [4]

5. Naufal scores 56 marks out of 80 in an examination. Calculate

Naufal’s percentage score. [3]

6. Eeman collected Rf. 720 for a party. She spent 90% of the money on

food and the rest on gifts. How much money did she spend on gifts? [4]

7. In 2000, the population of an island was 1600. In 2003, the population

has risen to 1680. Find the percentage increase of the population. [4]

8. A house cost Rf. 400 000 and was sold for Rf. 680 000. Calculate the

percentage profit. [4]

9. If I paid Rf. 120 for a book after a discount of 20%, what was the

marked price of the book? [4]

Unit Test 12 Percentage


TIME 35 minutes

Total marks [34]

100

Answers of Exercises Percentage

Pages 142Exercise 12.1 Page 143Exercise 12.4

1. 20% 7. 513 %

2. 95% 8. 329

13 %

3. 40% 9. 130%

4. 80% 10. 440%

5. 3557 % 11. 242

67 %

6. 1558 % 12. 241

23 %

1. 12% 5. 84%2. 66% 6. 439.9%3. 20% 7. 80%4. 272% 8. 605.5%

1.35 5. 2

14 9.

7400

2.1120 6.

1200 10.

112

3.2325 7.

1125 11.

73600

4. 1 8.2

225 12.38

1. 0.674 5. 0.2072. 0.98 6. 0.0823. 0.029 7. 0.00054. 0.11 8. 2.67

Pages 142Exercise 12.2

Pages 142Exercise 12.3

1. 25% 3. 45% 5. 6212 %

2. 20% 4. 60% 6. 9313 %


1. 3 6. 441 eggs

2. 26 g 7. 4212 ml

3. 810 8. 143

10

4. 1560 girls 9. 14735 s

5. 1430

1. Rf. 480 4. 1008 pupils

2. 192 books 5. 1912 marks

3. 1275 females



101

Answers of Exercises Percentage


1. Rf. 275 4. 76 members2. 360 km 5. 25 %3. 780 6. Rf. 400

1. Rf. 4500 4. Rf. 7002. Rf. 150 5. Rf. 1983. Rf. 17 6. Rf. 135


1. 50% 4. Rf. 13802. 25% 5. Rf. 403. Rf. 117 6. Rf. 8256.25


1. Rf. 735 4. 16%

2. Rf. 828 5. Rf. 68

3. Rf. 599.50 6. 8313 %


102

Unit 13 Statistics

Syllabus Content

Measure of central tendency.1

1.1 Find mean, median and mode from a given data.

Comprehension of graph.2

2.1 Read and interpret data presented in pie charts.2.2 Construct pie charts.

103

Unit Notes Statistics

The table below gives a brief summary on statistics in the primary.

Grade 3 pictograph, where each symbol represents one unit.

Grade 4 bar graph, where the scale represents 1 unit for one.

Grade 5 line graph

Grade 6 pictograph, bar graph and line graph (revised and elaborated)

Grade 7 pie charts, averages (mean, median and mode)

When introducing mean, median and mode explain the meaning ofthe terms and the calculations used to find the values. Be sure thestudents start by arranging the data in the sequence before they findthe median and mode. Check over the work for the errors to seewhether the mistakes are in the concepts or in the calculations.

Students have already seen different ways to display statistical data.These include pictographs, bar charts and line graphs. In this unit wehave introduced pie charts.

Most of the pie charts given in the exercise are fairly easy to drawbut students may have problems in reading and interpreting the piecharts given in the exercises because the questions in the exercisesdiffer from each other. After giving ample time to answer thequestions and if they have problems in answering, discuss themethods to solve the questions.

Students need a proper instrument box to draw the pie charts. Theteacher should check whether they have the proper instruments at thebeginning of the unit.

104

Activities Statistics

Activity 1

Divide the class into 4 groups and select a group leader for each group.Ask them to find their mass and height.Mass in kilograms to the nearest kilogram and the height incentimetres to the nearest centimetre.Before measuring their mass and height discuss how they can recordtheir data.A sample of how they can record their data is shown below.

Ask them to find their mean, mode and median mass of the group.Also ask them to find their mean, mode and median height of thegroup.Tell the group leaders to find the mean , mode and median (mass andheight) of the whole class and display their findings in the class.

Height (cm)Mass (kg)Name

105

Activity 2

Make copies of the questionnaire below.

Activities Statistics

Get the data from at least 20 students.You may collect the data from other class students during the breaktime.Use your questionnaires to form a database and draw a pie chart forone of the above category.

Questionnaire

Name

Class Age

1. Favourite colour

2. Favourite drink

3. Favourite food

4. Favourite sport

5. Favourite radio programme

6. Favourite TV programme

106

Unit Test 13 Statistics


TIME 35 minutes

Total marks [24]

1. Find the mode of each set of numbers.(a) 4, 3, 5, 3, 4, 3, 3, 5, 6 [1]

(b) 90, 70, 90, 50, 60, 80, 90, 60, 40, 60 [2]

2. Find the median of each set of numbers.(a) 3, 8, 4, 6, 5 [1]

(b) 25, 18, 19, 21, 16, 17, 28 , 23 [2]

3. Find the mean of 32, 30, 37, 33 and 38 [2]

4. The mean of eggs sold in 3 days is 81. Calculate the totalnumber of eggs sold. [2]

5. The pie chart shows the way in which thenationalities represented in a resort.(a) Which country has the greatest number of

people in the resort? [1]

(b) What is the angle of the sector allottedfor others? [2]

(c) What fraction of the tourists are Italian? [2]

(d) What percentage of the tourists are German? [2]

6. Draw a pie chart for the following information.Favourite sport of a group of children.

135º

92º

70ºItalian

Japanese

GermanOthers

[7]

Sport Football Volleyball Swimming Tennis

No. of children 70 60 40 30

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Answers of Exercises Statistics


1. 21 4. 25.8 or 2545 kg

2. 3212 5. Rf. 27

3. 16 6. 141 cm

1. Rf. 29 4. 532 marks

2. 33 students 5. 3036 fish

3. 79.5 or 7912 marks 6. 84

1. 1, 4 6. 21, 252. 6 7. 243. 8 8. 604. 10 9. 20, 21, 225. 10, 18 10. Nil

1. mean = 4, mode = 4, median = 4

2. mean = 23

10 , mode = 2, median = 2

3. mean = 8, mode = 10, median = 8

4. mean = 1214 , mode = 11, median = 111

12

1. 6 6. 50

2. 12 7. 40

3. 512 8. 43

4. 27 9. 70

5. 32 10. 30





1. (a) 2 (b)13

(c) 50% (d) 40º

2. (a)13 (b) Rf. 600

(c) 24º (d) 20%

3. (a)3

20 (b) 5% (c) 1000

(d) 36º (e) 200



Degrees alloted for sectors

1. (a) Kavaabu = 60ºBajiya = 30ºGulha = 180ºFolhi = 90º

(b) Bangladesh = 90ºIndia = 108ºPhilippines = 9ºSri Lanka = 135ºOthers = 18º

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Answers of Exercises Statistics

contd.Exercise 13.7

4. A = 72°B = 180°C = 90°D = 18°

5. Current Affairs = 90°Entertainment = 54°Educational = 20°Sports = 36°Religious = 108°

2. Apple = 54°Grape = 36°Papaya = 72°Mango = 108°Orange = 90°

3. Cat = 40°Fish = 180°Bird = 120°Rabbit = 20°

contd.Exercise 13.7

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Unit 14 Straight line graphs

Syllabus Content

Comprehension of straight line graphs.1

1.1 Use Cartesian coordinates in two dimensions.1.2 Draw straight line graphs for the equations in the form

y = mx + c.

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Unit Notes Straight line graphs

Coordinates and straight line graphs are introduced in this grade.Even though this is the last unit in the book do not rush to finish thesyllabus. This unit needs lot of time and practise because it dealswith drawings as well as calculations.

It is very difficult to use the black board to explain graphs. Ifschools can arrange to use over head projectors to carry out theselessons, it will reduce the monotony, it will help the students tounderstand the concept well and will need less time for the teachersto explain.

If the schools cannot afford an over head projector they should findan alternative method to carry out these lessons.

When teachers introduce the coordinates, discuss the map given onpage 162 of the textbook . Students should be familiar with thewords: x-axis, y-axis, ordered pair, x-coordinate, y-coordinate andorigin before doing the exercises in the workbook.

Teachers should carefully explain the students how to place thex-axis and y-axis when drawing straight line graphs.

Tell the students that it is always better to sketch a diagram of thetwo axis before they start drawing the axis on the graph paper. Atthe beginning, students may find placing the axis difficult but thisconcept will develop gradually when they draw more graphs.

111

Activities Straight line graphs

Activity 1

Mark the points with the given coordinates. To form the picture, join thepoints in order as you plot them.

–1–4 –3 –2 4 51 2

–3

–2

–1

1

2

3

3 x

4

y

A (5, –1)B (4, –2)C (2.6, –2.6)D (0.8, –2.8)E (–0.4, –2.6)F (–1.4, –2.2)G (–2.6, –2.2)

H (–2.2, –1.4)I (–1.7, –1.2)J (–1.2, –1.4)K (–1, –1)L (–2.2, 0.2)M (–2.4, 0.6)N (–4.2, 1.2)

V (2.6, 3.6)W (1.6, 2.4)X (1.8, –0.2)Y (3, –0.9)Z (5, –1)

O (–3.8, 1.6)P (–2, 1)Q (–1.6, 1)R (–0.6, –0.2)S (0, 0)T (–0.4, 1.2)U (2.4, 4.4)

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Activity 2

Complete the following cross-number puzzle by writing the values of y inthe squares.

Activities Straight line graphs

ACROSSy = x + 2

A. x = 8B. x = 10D. x = 9H. x = 25

y = 3x + 4C. x = 7E. x = 8F. x = 2

DOWNy = 2x – 1

A. x = 6B. x = 8C. x = 11F. x = 9

y = x – 5D. x = 21E. x = 27G. x = 35

A123456789123456789123456789123456789123456789123456789123456789123456789123456789

E

1234567812345678123456781234567812345678123456781234567812345678

B1234567812345678123456781234567812345678123456781234567812345678123456789

123456789123456789123456789123456789123456789123456789123456789123456789

C123456781234567812345678123456781234567812345678123456781234567812345678

G

D123456789123456789123456789123456789123456789123456789123456789123456789

F

1234567812345678123456781234567812345678123456781234567812345678

H1234567812345678123456781234567812345678123456781234567812345678

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Unit Test 14 Straight line graphs


TIME 35 minutes

Total marks [25]

1. Write down the coordinates of the following points.

2. Draw graphs for the following equations.(a) y = 2x, take the values of x as 0, 1, 2. [7]

(b) y = –3x + 4, take the values of x from –2 to +2 [9]

(c) y = –1 [5]

[4]

–1–4 –3 –2 4 51 2

–3

–2

y

–1

1

2

3

3 x

A

B

C

D

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Answers of Exercises Straight line graphs


B (1 , 4) G (0 , –7)C (–7 , 2) H (6, 7.2)D (4 , –2) I (–4.3 , 5)E (–3 , –9) J (–3.5 , –3.5)F (1 , 0) K (0 , 8.7)

Ordered pairs are:1. (–2 , –6), (–1 , –3), (0 , 0)

(1 , 3), (2 , 6)2. (–2 , -8), (–1 , -4), (0 , 0)

(1 , 4), (2 , 8)3. (–2 , 6), (–1 , 3), (0 , 0)

(1 , –3), (2 , –6)

Ordered pairs are:1. (a) (–3 , –7), (–2 , –5),

(–1 , –3), (0 , –1), (1 , 1),(2 , 3), (3 , 5)

(b) (–3 , –4), (–2 , –2),(–1 , 0), (0 , 2), (1 , 4),(2 , 6), (3 , 8)

(c) (–3 , –12), (–2 , –9),(–1 , –6), (0 , –3), (1 , 0),(2 , 3), (3 , 6)

(d) (–3 , 7), (–2 , 5), (–1 , 3),(0 , 1), (1 , –1), (2 , –3),(3 , –5)

Page 178 - 180Exercise 14.3

Page 181 - 195Exercise 14.4

2. (a) (–2 , 8), (–1 , 6), (0 , 4),

(1 , 2), (2 , 0), (3 , –2),

(4 , –4)

(b) (–2 , 0), (–1 , 1), (0 , 2),

(1 , 3), (2 , 4), (3 , 5),

(4 , 6)

(c) (–2 , 0), (–1 , –1), (0 , –2),

(1 , –3), (2 , –4), (3 , –5),

(4 , –6)

(d) (–2 , –1), (–1 , –2),

(0 , –3), (1 , –4), (2 , –5),

(3 , –6), (4 , –7)

3. (a) (–2 , 4), (–1 , 2), (0 , 0),

(1 , –2), (2 , –4)

(b) (–2 , 4), (–1 , 1), (0 , –2),

(1 , –5), (2 , –8)

(c) (–2 , –2), (–1 , –1), (0 , 0),

(1 , 1), (2 , 2)

(d) (–2 , 2), (–1 , 2), (0 , 2),

(1 , 2), (2 , 2)

(e) (–2 , –5), (–1 , –5),

(0 , –5), (1 , –5), (2 , –5)

(f) (6 , –2), (6 , –1), (6 , 0),

(6 , 1), (6 , 2)

(g) (–1 , –2), (–1 , –1),

(–1 , 0), (–1 , 1), (–1 , 2)

contd.Exercise 14.4

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Numbers1 Page 10

1. (a) 1353 (b) 7521(c) 3271 (d) 4384(e) 2502 (f) 2 985 192

2. (a) 102 (b) 898 R 123. (a) 106 R 1 (b) 543 R 14. (a) 35 (b) 62

(c) 15 (d) 29(e) 27

5. (a) 2 × 3 × 3(b) 2 × 2 × 3 × 5(c) 3 × 3 × 5 × 7(d) 2 × 3 × 3 × 5 × 7

6. (a) 24 (b) 42(c) 504 (d) 1440

7. (a) 6 (b) 11(c) 15 (d) 21

8. (a) 10002 (b) 101112

(c) 100000102 (d) 110000112

9. (a) 5 (b) 13(c) 16 (d) 58

10. 1904 13. 111. 30 451 14. Rf 74.7512. Rf 7 15. 8 760

Fractions2 Pages 22 - 23

1. (a)318 (b)

27419

2. (a) 317 (b) 9

129

3. (a)23 (b) 1

27 (c) 6

1327

4. (a) 15 (b) 15, 45, 40(c) 6, 11, 18

5. (a) > (b) < (c) >

6. (a) 112 (b)

313 (c) 1

1118

(d)760 (e) 5

4150 (f) 4

1730

(g) 5740 (h) 2

12

7. (a) 100 (b) 81 lemons

8. (a)34 (b) 16

12 (c) 6

916

(d) 5 (e) 14 (f) 213

(g) 513 (h)

18

9. (a)7

12 (b)15 (c)

122

(d) 2730 (e) 9

154

10.25

11. (a)15 (b)

13 (c)

815

12. 161120 16. 9

14 laahi

13. 47212 m 17. Rf. 2750

14. 600 18. 445 kg

15.18

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Decimals3 Page 36

1. (a) tens(b) thousandths(c) hundred thousandths

2. (a) > (b) < (c) >3. (a) 5500 (b) 740 000

(c) 8.63 (d) 20.6(e) 79.850 (f) 41

4. (a) 110.77 (b) 445.61(c) 30.193 (d) 11.289(e) 36.775 (f) 29.4(g) 1.4553 (h) 0.161(i) 9.59 (j) 0.00195(k) 600 (l) 0.0076

5. (a) 2.75 (b) 3.65(c) 63.7

6. (a) 2.1 (b) 0.2(c) 3.7 (d) 11.7(e) 0.2 (f) 3.3

7. (a) 0.25 (b) 2.375

8. (a)1225 (b) 21

140

9. Rf. 16010. Rf. 1.2511. 143.5 cm12. Rf. 28.25

Directed Numbers4 Page 40

1. (a) < (b) > (c) <2. (a) –1 (b) +101 (c) –4443. (a) –15 (b) + 60 (c) –5074. (a) –19 (b) + 122 (c) –405. (a) +20 (b) –136 (c) +2526. (a) –4 (b) +6 (c) +17

7. (a) +19 (b) + 81 (c) +16(d) –19 (e) –14 (f) +28(g) –6 (h) –77 (i) –2(j) +16 (k) –33 (l) –85(m) –10 (n) –1 (o) +37

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Indices and Algebra5 Page 55

1. (a) 16(b) 64(c) –27

2. (a) 37 (b) 47

(c) 917 (d) 713

3. (a) x6 (b) y14

(c) w16 (d) c10

4. (a) 12y (b) x – 17(c) 6t – u (d) p + q

5. (a) 7ab (b) –3m3

(c) 11z4 – 19 (d) 3c – 12bc(e) p5 q2

6. (a) –18abc (b) 20e9

(c) 6n8 (d) –24s8 t4 u8

7. (a) 3c4 (b) 9w(c) –9cd (d) 2s3 t4 u

8. (a) 2a – 18b(b) –12n6 + 14n3

(c) 4c + 2d(d) 7x – 7(e) x2 + x – 6(f) 8z2 – 10z + 3(g) 9x2 + 6x + 1

9. (a) a (b – c)(b) 5 (x – 2y)(c) p (p – q)(d) 6m2n2 (2m2 + 3)(e) x (y – z – 1)(f) 5x2y2 (4y + 3x – 2x2y)

10. (a) 40 (b) 42 (c) –24(d) 21 (e) –28 (f) –5(g) 200

Equations6 Page 59

6. (a) 2 (b) 445 (c) 1

37

(d) 1 (e)5

16

7. (a) 5 (b) 97

17

(c) 6 (d) –60

8. (a) –3 (b) 42

(c) 178 (d) –3

23

(e) – 613 (f) –1

114

(g) 21625

1. (a) 3 (b) 6(c) –114 (d) –18

2. (a) 3 (b) 33

(c) 45 (d) – 417

3. (a) 3 (b) –8

(c) 415 (d) – 8

23

4. (a) 6 (b) 3

(c) 813 (d) 4

14

5. (a) 8 (b) 523

(c) –4 (d) –23

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Geometry7 Pages 71 - 72

1. (a) 63º (b) 138º(c) 75º (d) 35º(e) 105º (f) 55º(g) 105º (h) 52º(i) 30º, 90º (j) 35º, 70º(k) 30º, 60º, 90º

2. (a) ∠ QPR = ∠ PQR(b) ∠ ACB = ∠ ABC

3. (a) 80º (b) 30º(c) 45º (d) 111º(e) 67º (f) 50º(g) 135º

Measures8 Page 78

1. 2000 m2. 0.147 m3. 800 mm4. 1509 cm5. 5 060 000 g6. 9.430 kg7. 0.825 kg8. 5350 kg9. 4000 ml

10. 9000 ml11. 6.5 l12. 5200 cm3

13. 0.008 km14. 2500 mm

15. 0.04558 km16. 60 inches17. 108 inches

18. 195

12 ft

19. 26 400 ft

20. 513 miles

21. 180 seconds

22. 634 minutes

23. 10 hours

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Perimeter and Area9 Pages 104 - 105

1. (a) 27.13 cm (b) 424 mm2. (a) 32.8 m (b) 320 mm3. (a) 220 m (b) 81.64 cm4. (a) 144 mm

(b) 39.27 km or 3927 km

(c) 43.2 m(d) 117 m

5. 70 m6. (a) 121 mm2

(b) 112.2 cm2

(c) 40 m2

(d) 80 km2

(e) 45 m2

7. (a) 314 mm2

(b) 3812 cm2 or 38.46 cm2

8. 1761114 km2 or 176.625 km2

9. (a) 352 m2

(b) 126 km2

(c) 114 cm2

(d) 281914 mm2 or 2817.8325 mm2

(e) 306.96 m2

10. (a) 17 cm(b) 12 mm

11. 44 cm12. 3300 m13. 66 ft14. 42 in15. 402 m2

16. 53.29 m2

17. Rf. 1350

Volume10

1. (a) 6859 mm3

(b) 3465 cm3

2. 945 cm3

3. 0.512 m3

4. (a) 1000 mm3

(b) 504 cm3

(c) 85 m3

(d) 2691 ft3

(e) 3234 cm3

(f) 330 000 mm3

(g) 96 cm3

5. 252 m3

6. 616 m2

7. 64 cm2

8. Rf. 225 0009. 24 tapes

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Rate, Ratio and Proportion11 Page 141

1. (a) 1 : 6 (b) 3 : 11(c) 2 : 5 (d) 100 : 17(e) 4 : 5 (f) 3 : 4(g) 20 : 11 (h) 63 : 22(i) 1 : 4 (j) 9 : 40(k) 1 : 10 (l) 3 : 10

2. 19 : 233. Rf. 40 per hour4. Rf. 5075. Rf. 16, Rf. 566. Rf. 87.50

7. 60 kilometre per hour8. (a) 10 : 1 (b) 13 : 12

(c) 1 : 209. 120 cm, 300 cm

10. Rf. 6011. 48 mm12. 3 : 513. Rf. 325.5014. Rf. 100.75 per candidate15. 50º, 60º, 70º

Percentage12 Page 155

1. (a) 60% (b) 2813 %

(c) 191419 % (d) 212

12 %

2. (a) 30% (b) 80%

(c) 150% (d) 315.9%

3. (a)925 (b)

920

(c)740 (d)

7150

4. (a) 0.563 (b) 0.47

(c) 0.0007 (d) 3.89

5. (a) 60 m (b) Rf. 8

(c) 1.44 or 11125 (d) 20 kg

6. 20%7. 70%8. 45 ml9. 38 oranges

10. Rf. 13011. 127512. Rf. 53013. Rf. 112.5014. 20%15. Rf. 716. 20%

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Statistics13 Page 175

1. (a) 8 (b) 1556 m

2. (a) 1 (b) 38

3. (a) 4 (b) 4912

4. (a) mean = 329

mode = 3median = 3

(b) mean = 1045

mode = 9, 10, 12

median = 1012

5. 16.5 marks6. 285 passengers

7. (a) Rf. 30 (b)3

20(c) 30% (d) 162°

8. (a) 10% (b)9

50(c) 480 books (d) 144º

9. Utheemu Ganduvaru = 60ºNational Museum = 75ºIslamic Centre = 105ºFriday Mosque = 36ºSagaafy Marukazu = 84º

10. News = 144ºEntertainment = 36ºHealth = 72ºSports = 60ºAdvertisements = 48º

Straight line graphs14 Page 196

1. A (1 , 2)B (3 , 4)C (2 , –3)D (–3 , 2)E (–2 , –5)F (–2 , 0)G (0 , –4)H (–1.8 , 4.5)I (2.5, –4.5)

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Units 1 - 21 Pages 24 - 25

1. (a) 1763 (b) 1460(c) 2925 (d) 323 554

2. (a) 104 (b) 12403. (a) 43 R 2 (b) 1024. (a) 10 (b) 39 (c) –205. (a) 2 × 3 × 3 × 5 × 5

(b) 2 × 3 × 5 × 7 × 116. (a) 120 (b) 1 0507. (a) 20 (b) 258. (a) 110012 (b) 111100129. (a) 18 (b) 52

10. (a)377 (b)

34617

11. (a) 619 (b) 8

34

12. (a)38 (b) 8

712

13. (a) 64 (b) 3, 30, 21

14. (a) < (b) >

15. (a)1924 (b)

512 (c) –

1340

16. (a) 30 (b) 25 water melons

17. (a)1

12 (b)25

(c) 19

16 (d) 7119

18. (a) 1 (b) 11320 (c) 3

19. 16 runs20. 680 pages21. Yes

22. 4120

23. 234 cm

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Units 1 - 72 Pages 73 - 75

1. (a) 4 (b) 233 537(c) 2179 R 12

2. 10843. (a) 49 (b) 44. 2 × 3 × 5 × 7 × 75. 1086. 27. 101111128. 30

9.618

10. 929

11.38

12. 5, 10813. <

14. (a)23 (b) 2

720

15. 20

16. (a) 40 (b) 214

17. (a)5

16 (b) 712

18. (a) hundred thoudandths(b) hundred thousands

19. (a) < (b) <20. (a) 7860 (b) 86 000

(c) 43.486 (d) 54.31(e) 99.7 (f) 60

21. (a) 36.737 (b) 375.512(c) 12.25 (d) 3.9(e) 0.0456 (f) 300

22. 6.875

23.29

50024. (a) < (b) >25. (a) –106 (b) 28

(c) –16 (d) –6(e) 2 (f) –21(g) –15 (h) –6

26. (a) 25 (b) –6427. (a) 45 (b) 62

28. (a) m73 (b) n79

29. (a) x + y + z (b) 24ab(c) (l + m) – k

30. (a) 2 z(b) 3a3b – 5a3b2

(c) 42q6

(d) 10u16 v6 w(e) 3x(f) –10p5qr

31. (a) 18a – 6b(b) –16u3 + 24uv(c) 3m + 11n(d) 2y + 13x(e) 2x2 – 3x – 20(f) x2 – 16x + 64

32. (a) u2(12u4 – 1)(b) 7x2y (4 – x2z4)(c) 4a2b3 (a3 + 2 – 3ab)

33. (a) 12 (b) –12(c) –216 (d) 26

34. (a) –9 (b) – 4

(c) – 60 (d) –525

(e) 1 (f) – 6

(g)45 (h) –24

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35. (a) 25º (b) 51º

(c) 75º (d) 1812 º

(e) 5312 º

36. 8750

37. Rf. 938. 3.8 m39. 1240. Rf. 550041. Rf. 135

42.56

Units 1 - 123 Pages 156 - 160

18. (a) > (b) <19. (a) 2400 (b) 700 000

(c) 175.09 (d) 0.2(e) 812.0 (f) 304

20. (a) 634.239 (b) 62.557(c) 8.125 (d) 120(e) 0.0042 (f) 36

21. 0.45

22. 1241

20023. (a) > (b) <24. (a) +34 (b) +35

(c) –5 (d) –126(e) –6 (f) –17(g) –2 (h) +31

25. (a) 343 (b) 1626. (a) 2019 (b) 39

27. (a) c19 (b) a14

28. (a) a – 12 (b)14 b (c)

3xz

29. (a) 0(b) 3x2 y – 6x5 y2

(c) –24n9

(d) –10s6 r10 u(e) 11a(f) 4x8 y5 z2

1. (a) 7794 (b) 233 537(c) 2179 R 12

2. 1006 R 13. (a) 48 (b) 104

4. 3 × 3 × 5 × 5 × 75. LCM = 2100, HCF = 26. 10110017. 43

8.534

9. 1212

10. 337

11. 4, 35, 3612. <

13. (a)3148 (b) 1

124

14. 21 km

15. (a) 2635 (b)

15

16. (a) 82

19 (b) 1745

17. (a) hundredths (b) millions

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30. (a) 12a – 3b(b) –10s2 t + 10t2

(c) –7p + 18q(d) 7a + 9b(e) 3x2 – 11x – 20(f) 4x2 – 12x + 9

31. (a) m3(m2 – 1)(b) 5a2 b(c3 – 5a2)(c) 3xy3 (9x + x4 y2 – 3y5)

32. (a) –36 (b) –12(c) –72 (d) –60

33. (a) 6 (b) 417

(c) –312 (d) – 63

(e) –20 (f) 17

19

(g) –58 (h) –7

117

34. (a) a = 142°, b = 29°(b) 33° (c) 54°

(d) 7612 º (e) 135°

35. (a) 70 mm (b) 8200 mm(c) 509 cm (d) 9.125 kg(e) 3100 kg (f) 8.5 l(g) 55 ft (h) 42 240 ft(i) 360 minutes (j) 18 minutes(k) 2 500 mm (l) 7 hours

36. (a) 28 m2 (b) 63 km2

(c) 56 m2

37. (a) P = 44 m, A = 117 m2

(b) P = 8.4 km, A = 4.41 km2

38. (a) C = 484 m, A = 18 634 m2

(b) C = 94.2 mm, A = 706.5 mm2

39. (a) 26.09 cm or 26111 cm

(b) 21 m

40. (a) P = 200 mm, A = 2464 mm2

(b) P = 55.5 m, A = 372 km2

41. 3612 m2

42. (a) 74 088 mm3

(b) 120 m3

(c) 9551.88 mm3

(d) 1 404 m3

43. (a) 2 : 9 (b) 5 : 1(c) 1 : 2 (d) 29 : 45(e) 1 : 50 (f) 250 : 1(g) 1 : 20

44. (a) 15% (b) 38313 %

45. (a) 61.8% (b) 205%

46. (a)1120 (b)

19200

47. (a) 0.313 (b) 0.0848. (a) 27 (b) 24.6 s49. 6750 passengers

50.3

1151. 0.365 kg52. 169 cm2

53.732 m

54. 4 photos55. 0.015625 m3

56. 1 200 bricks

57. 223 or 2.67 babies

58. Rf. 1859. Rf. 8060. 4 pupils61. Rf. 114062. (a) Rf. 540 (b) Rf. 3540

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Units 1 - 41 Pages 41 - 48

1. (a)8310 (b)

14811

2. (a) 279 (b) 3

2425

3. (a)13 (b) 6

89

4. 75. (a) hundred thousands

(b) ten thousandths6. (a) > (b) <7. (a) 695.4 (b) 8008. (a) 0.01257 (b) 96 0009. 81 981

10. 231 44011. 103612. 406 R 513. 2 × 2 × 2 × 2 × 3 × 514. 10815. 1516. 1001011217. 2118. 27

19.25

20. <

21. 650 hours22. 34.65023. 2.0324. 0.6

25. 156

12526. (a) + 2 (b) –3927. (a) –1 (b) + 15

28. 12077

29.16

30.14

31. 171790

32. 916

33. 4.734. Rf. 2535. 6132 m36. Rf. 190.6337. 120 students38. 24 m

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Units 1 - 92 Pages 106 - 116

1.3

102. 363. 1111

4. 25x

5.13

6. 5 l

7.1

128. (a) –5 (b) +69. (a) –2 (b) –7

10. (a) 96.2 (b) 873.41(c) 50

11.

12. 409 R 113. 1014. 4015. 6

16. 313

17. 7.11218. 51.75

19.21

25020. 3a – 2ab21. –20m6 n2

22. –2uw2

23. 2m(m2 – 3)

24.328

25. 926. 122º27. 20º28. 10800 seconds29. 80 000 cm30. 34 m

31. 312 mm

32. 15 km2

33. 1234. x2 – x – 235. 15 cm

36. 723

37. –2038. z = 111º39. 1092 cm2

40. Rf. 43541. 8 kg

42.14

43. 18.4 kg44. 484 cm45. 124 cm2

9 520 452

by 2 by 3 by 4 by 5 by 6 by 9 by 10

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Units 1 - 143 Pages 197 - 210

1. (a) –10 (b) –3 (c) –2

2. 247

3. 24. 31 7005. 25.496. 7 – a7. 110º8. (a) 0.009 km (b) 7 feet9. 50 km2

10. 6000 mm3

11. 13%12. mode = 5, 7

median = 613. A (3, 1), B (0, –2)15. 2 × 2 × 3 × 5 × 716. 7317. 1018. 0.6319. 2x2 – 5x – 320. 2m(4m + 1 – 3n)21. 1322. 71º23. 67.5 mm2

24. (a)143 (b)

14

25.1

12026. 87.5

27. (a)245 (b) 45º

28. 759

29. 530. 42.5 m2

31. 455 cm3

33. 5 balloons34. 26 cm35. 21 m36. 59.5 cm37. 500 m per min38. Rf. 58.5039. 10%

40. 134

41. Rf. 64.5042. 60, 150, 12043. 216044. Rf. 23.4045. Ordered pairs are: (–2, 7),

(–1, 5), (0, 3), (1, 1), (2, –1)

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1 Page 19

46953 (lots of possibilities)

2 Page 39

(23 + 3) × 7

3 Page 44

7777 –

77

4 Page 48

23

5 Page 55

2, 1, 3

6 Page 74

8 years

7 Page 81

44 triangles

8 Page 84

9 Page 101

3 people

10 Page 111

148296 +

3570 = 1

11 Page 125

4 days

12 Page 131

13

31

2

12 4

8

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14 Page 145

7 books

15 Page 149

“19 kg” barrel

16 Page 152

9 bananas

17 Page 158

Rf. 13

18 Page 163

131

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Numbers Activity 1

1204, 3612, 3515, 703, 2880, 160,4160

Numbers Activity 2

1. 19 9. 722. 84 10. 1443. 2 11. 94. 24 12. 65. 5 13. 126. 31 14. 527. 30 15. 1578. 20 16. 264A cap.

Fractions Activity 1

GHAZWA

Fractions Activity 2

1. 27 +

47 =

67

2. 59 +

13 =

89

3. 45 –

23 =

215

4. 49 ×

1812 =

23

5. 78 ÷

214 =

16

Decimals Activity 1

1. 8

×

56

55

÷

5

63

35

45

+

7 ×

11–

2. 7.6

×

21.28

2

+

7

5.6

0.4

12.28

–

2.8 ÷

9–

3. 0.03

÷

0.003

100

÷

25

3

250

4.003

×

10 ×

4+

4. 0.4

+

6

0.02

×

10

0.38

0.56

30

–

5.6 ÷

0.2÷

Directed Numbers Activity 1

Arctic Ocean

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Directed Numbers Activity 2

D

P

N

E

R

U

N

S

O

M

A

U

D

E

PRI

MENUMBER

Y

C

I

A

T

L

L

L I

NUMERATOR

N

Indices and Algebra Activity 1

625

1

10000

2

2144 0

1

9

216

2401

4 32 5 6

561


2 + x

x + y

x – 2

5 + x

x – 5

5x

xy

x

Your age after x years if youare 5 years old now.

5x + y

Five times x.

Divide x by y.

Two greater than a number x.

Subtract 2 from x.

A number x decreased by 5.

Five times a number x plus a secondnumber y.

The sum of any number x andany number y.

The product of two numbersx and y.

y

SEA HORSE


OBLONG

Equations Activity 1

Equations Activity 2

Geometry Activity 1

1. (a) 53º- 55º (b) 129º - 131º(c) 90º (d) 265º - 267º

2. ∠ a, ∠ ABC, ∠ CBA∠ b, ∠ BCD, ∠ DCB∠ c, ∠ STP, , ∠ PTS∠ d, ∠ SPQ, ∠ QPS∠ e, ∠ PQS, ∠ SQP∠ n, ∠ PSR, ∠ RSP

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Geometry Activity 2

1 2 2 1

1 2 2

1

1 2 1

21 2 2

1

Measures Activity 1

2 8

3

500 0

1

230

5

5

7

8

0

9

4

81050

3

1

5

2190

0

10800

Measures Activity 2

seconds, miles, feet, capacity, gallon,isosceles, scalene, triangle, vertex,degrees, quadrilateral, equal, factor,coefficient, variable, power, base,tens, denominator, bisect, circle, angle

Perimeter and Area Activity 1



1. 15 cm2 6. 18 cm2

2. 5 cm2 7. 15 cm2

3. 9 cm2 8. 88 cm2

4. 6 cm2 9. 88 cm2,5. 20 cm2 Yes

Volume Activity 1

1. 3.2.

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Rate, Ratio & Proportion Activity 2

SECOND RABEEUL AAKHIR

4. 6.5.

Volume Activity 2

A B C

FD

Rate, Ratio & Proportion Activity 1

1. apple 2. milk 3. chocolate

Percentage Activity 1

1.75

100 , 0.75, 75%

2.34

100 , 0.34, 34%

3.46

100 , 0.46, 46%

PRACTISE MAKES PERFECT

Percentage Activity 2

Straight line graphs Activity 1

Straight line graphs Activity 2

10

16

0

21

15

2

22

17

8

30

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Unit Test 1 Numbers

1. 3299 [1]2. 15 [1]3. 1 46 952 [1]4. 180 [2]5. 201 R 2 [2]6. 2 × 2 × 3 × 3 × 7 [2]7. 1440 [2]8. 6 [2]9. 1001012 [2]

10. 38 [2]11. 60 [3]12. Rf. 2715 [3]13. 42 litres [3]14. 48 fruits [4]

Unit Test 2 Fractions

1. 947 [1]

2.4113 [1]

3.14 [2]

4. 20, 14 [2]5. < [2]6. 35 [2]

7. (a)12 [1]

(b) 6 [2]

(c) 213 [3]

(d) 15

14 [3]

8.34 [3]

9. 20 students [3]

Unit Test 3 Decimals

1. (a) ten thousands [1](b) hundredths [1]

2. (a) > [1](b) < [1]

3.2

125 [2]

4. 1.75 [2]5. (a) 584.61 [1]

(b) 706.1 [1](c) 41 000 [1](d) 4540 [1]

6. (a) 42.629 [2](b) 2.45424 [2](c) 6800 [2](d) 0.007 [2]

7. 2.17 [3]8. 3.473 litres [3]9. Rf. 75 [4]

Unit Test 4 Directed Numbers

1. (a) < [1](b) > [1](c) > [1]

2. (a) +8 [1](b) +2 [1](c) +2 [1](d) –41 [1](e) +6 [2](f) +96 [2](g) –6 [2](h) –1 [2](i) –17 [2](j) –15 [2](k) +1 [2](l) +3 [3](m)–7 [3](n) –30 [3]

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Unit Test 5 Indices and Algebra

1. (a) 25 [1](b) –343 [1]

2. (a) 68 [1](b) 182 [1]

3. (a) x17 [1](b) a15 [1]

4. (a) m – 6 [1](b) 3w + s [2]

5. (a) 33x [2](b) –7v [3](c) 12p4q [3](d) –7u2 – 3u [3]

6. (a) –7c – 14a [2](b) 7z2 – 20z – 3 [3]

7. (a) c(b – 2) [2](b) 3x(2 – 4y + x) [3]

8. (a) 4 [2](b) –4 [3]

Unit Test 6 Equations

1. a = 5 [1]2. b = –14 [2]3. c = –5 [2]4. e = 48 [2]

5. u = –77

10 [3]

6. h = 6 [3]7. m = –1 [3]

8. n = –457 [4]

9. s = 134 [5]

10. x = 1 [5]

Unit Test 7 Geometry

1. (a) ∠ ABC = ∠ BCA or the other

correct alternatives. [1]

(b) ∠ XYZ = ∠ XZY or the other

correct alternatives. [1]2. (a) 60º [2]

(b) 139º [2](c) 43º, 86º [4](d) 36º, 72º, 144º [4](e) 28º [3](f) 67º [4]

(g) 3612 º [4]

(h) 135º [4]

Unit Test 8 Measures

1. 80 mm [1]2. 12 000 ml [1]3. 5 km [1]4. 800 g [1]5. 2.18 cm [1]6. 0.208 t [1]7. 0.075 l [1]8. 132 in [2]

9. 212 miles [2]

10. 1800 s [2]

11. 334 hr [2]

12. 300 000 cm [3]13. 0.091 m [3]14. 7200 s [3]

15. 412 hr [3]

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Unit Test 9 Perimeter and Area

1. (a) 94 m [2]

(b) 62.8 or 6267 mm [3]

(c) 108 cm [4](d) 36 km [4]

2. (a) 13 m [3](b) 15 ft [3]

3. (a) 84 km2 [2]

(b) 1321114 or 132.665 cm2 [3]

4. (a) 54 mm2 [4]

(b) 10512 m2 [4]

5. 3000 m [2]6. 26 cm [4]7. 37 m2 [4]

Unit Test 10 Volume

1. (a) 598 mm3 [2](b) 1260 m3 [2](c) 420 km3 [4](d) 19250 cm3 [4]

2. 9.261 cm3 [2]3. 5 m [2]

4. 2412 m2 [3]

5. (a) 90 cm3 [2](b) 60 packets [4]

Unit Test 11 Rate, Ratio & Proportion

1. (a) 3 : 5 [1](b) 75 : 14 [1](c) 3 : 8 [2](d) 16 : 49 [2](e) 20 : 7 [2](f) 4 : 1 [2]

2. (a) 7 : 5 [1](b) 1 : 3 [2]

3. 45 bottles per min [2]4. 150 miles [3]5. Rf. 850 [3]6. 55 ft, 33 ft [3]

7. 6212 kg [3]

Unit Test 12 Percentage

1. (a) 55% [1]

(b) 31212 % [1]

(c) 65% [1](d) 320% [1]

2. (a) 0.082 [1](b) 7.85 [1]

3. (a)1925 [1]

(b)3

500 [2]

(c)17600 [2]

4. (a) Rf. 17.50 [2](b) 78 kg [2]

5. 70% [3]6. Rf. 72 [4]7. 5% [4]8. 70% [4]9. Rf. 150 [4]

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Unit Test 13 Statistics

1. (a) 3 [1](b) 60, 90 [2]

2. (a) 5 [1](b) 20 [2]

3. 34 [2]4. 243 eggs [2]5. (a) Japan [1]

(b) 63º [2]

(c)7

36 [2]

(d) 2559 % [2]

6. Degrees alloted for sectorsFootball = 126ºVolleyball = 108ºSwimming = 72ºTennis = 54º [7]

Unit Test 14 Straight line graphs

1. A (2 , 3) [1]B (5 , –2) [1]C (–1.6 , –1.2) [1]D (–3.1 , 1.5) [1]

2. Ordered pairs are:(a) (0 , 0), (1 , 2), (2 , 4) [7](b) (–2 , 10), (–1 , 7), (0 , 4),

(1 , 1), (2 , –2) [9]

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Maths Gr7 Teachers Book

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Transcript of Maths Gr7 Teachers Book