Maths Quest - 8 TM - SARASWATI HOUSE

[Pages:96]8

Maths

Quest

Teacher's Manual

S Purkayastha

(An imprint of New Saraswati House (India) Pvt. Ltd.) New Delhi-110002 (INDIA)

R

(An imprint of New Saraswati House (India) Pvt. Ltd.)

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First published 2016

ISBN: 978-93-5199-703-0

Published by: New Saraswati House (India) Pvt. Ltd. 19 Ansari Road, Daryaganj, New Delhi-110002 (India)

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?Reserved with the Publishers

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Preface

The Math Quest Teacher's Resource Pack is based on guidelines and aids to support and supplement classroom teaching. The aim of this pack is to empower teachers so that the process of teaching and learning becomes interesting and interactive. The tools and techniques provided will ensure a seamless flow of knowledge so that the students take an inherent interest in the subject. The main purpose of the pack is to allay the fear of Maths from the minds of the students such that they develop an inherent liking for the subject and become curious to know more. A wide array of resources are included in the Teacher's Resource Pack to provide maximum support to teachers.

The main components of the Teacher's Resource Pack are as follows.

Teacher's Manual

Teacher's Manual has been developed to provide teaching guidelines to teachers so that they are prepared to teach a topic in the best possible manner. The manual comprises detailed lesson plans, which are supported by ample practice material in the form of Worksheets and Model Test Papers and their answers. There is a Teacher's CD as a digital support so that students are familiarised with the modern ways of teaching.

Lesson plans

Each lesson plan explains each topic in detail. Its components are as follows.

? Learning objectives list out the measurable aims of each chapter, which should be achieved after teaching the chapter.

? Concept explanation gives a detailed method of explaining the important concepts of the chapter using various teaching aids.

? Reinforce puts emphasis on important points that should not be missed while teaching.

Practice material

Worksheets and Model Test Papers along with their answers form the part of the practice material. These ensure that the students learn to solve the questions based on the concepts taught. This will help students have a good base right from the beginning on tackling tricky questions.

Teacher's CD

Teacher's CD comprises flip book, animated concepts, interactive activities, lesson plans, along with worksheets and Model Test Papers and their answers.

Web Support

The web support consists of worksheets, Model Test Papers, and answers to worksheets and Model Test Papers. These would help teachers in assessing students on the concepts taught in the class.

Contents

1.Rational Numbers

5

2.Exponents and Powers

10

3.Squares and Square Roots

14

4.Cubes and Cube Roots

18

5. Playing with Numbers

22

6.Algebraic Expressions and Identities

26

7.Factorisation

31

8.Linear Equations in One Variable

35

9.Direct and Inverse Variations

39

10. Percentage and its Applications

43

11. Compound Interest

48

Model Test Paper 1

52

12. Understanding Quadrilaterals

54

13. Practical Geometry

59

14. Visualising Solid Shapes

64

15. Area of Polygons

68

16. Surface Area and Volume

72

17. Data Handling

76

18. Introduction to Graphs

80

19. Probability

84

Model Test Paper 2

88

Answer Key

91

1 Rational Numbers

Learning Objectives

Students will be able to recapitulate the concept of natural numbers, whole numbers, integers and rational numbers express rational numbers in standard form and represent them on the number line compare and order rational numbers apply addition, subtraction, multiplication and division on the rational numbers and also state their basic properties nd rational numbers between two given rational numbers solve real life problems based on rational numbers

Concept Explanation ? Students are already familiar with what are natural numbers, whole numbers, integers

and rational numbers. ? Read the Introduction section to recapitulate the concepts. ? Explain to the students that the whole numbers along with the negative of natural numbers

are called integers. us, ..., ?5, ?4, ?3, ?2, ?1, 0, 1, 2, 3, 4, 5, ..., etc. are the integers.

Express rational numbers in standard form their comparison and ordering ? Explain the concept of equality of rational numbers. ? Tell them that rational numbers are in standard from only when the HCF of numerator

and denominator is 1. Also explain to them how to reduce a given rational number to its standard form using various examples. ? Make them understand how to compare and order the rational numbers with same denominators. ? Next explain to them how to compare and order the rational numbers with di erent denominators by nding the equivalent rational numbers using the LCM of their denominators using various examples. ? Explain that the absolute value of a rational number is the quantitative value of that number irrespective of its sign. ? To reinforce the concept, the teacher can use the Maths Lab Activity section from the textbook. ? For practice, ask them to do Check Point 1.1 from the textbook.

5

+% ? 0?

Addition and subtraction of rational numbers and their properties ? Explain to the students how to add and subtract rational numbers with same denominators

and also in case of di erent denominators by nding their LCM. ? Explain the properties satis ed by rational numbers under addition and subtraction. ? Ask the students to keep in mind the additive identity of rational numbers and how to

nd the additive inverse of the given rational number. ? Explain the simpli cation of expressions involving additions and subtractions. ? For practice, ask them to do Check Point 1.2 and Check Point 1.3 from the textbook.

Multiplication and divison of rational numbers and their properties ? Explain that the product of two rational numbers is obtained by multiplying their

respective numerators and denominators. ? Tell the students that the reciprocal of a rational number is obtained by interchanging

the numerator and denominator. ? Specify that reciprocal exists only for non-zero rational numbers. ? Explain how to use the concept of reciprocal of rational numbers while dividing two

rational numbers. ? Make them understand the properties satis ed by rational numbers under multiplication

and division. ? Ask the students to keep in mind the multiplicative identity of rational numbers and how

to nd the multiplicative inverse of the given rational number. ? To recapitulate the concepts learnt in the chapter, ask them to do the Values and Maths

in real life sections from the textbook. ? For practice, ask them to do Check Point 1.4 and Check Point 1.5 from the textbook.

Rational numbers on number line and rational number between two rational numbers ? Revise the presentation of integers on the number line and tell them that representation

of rational numbers on the number line is same as that of representation of fractions. ? Tell them that we can insert countless number of rational numbers in between the two

given rational numbers. is property of rational numbers is called the dense property. ? Guide the students to review the method of inserting rational numbers between two

given rational numbers by nding LCM of denominators using various examples. ? Explain to them the alternate method of inserting rational numbers between two rational

numbers by nding their mean (average) using various examples. ? To recapitulate the concepts learnt in the chapter, ask them to do the Brain Workout

section from the textbook. ? For practice, ask them to do Check Point 1.6 from the text book

6

0? ?

+ % Real life problems based on rational numbers

? Discuss various situations where rational numbers are used in real life. ? Guide them to solve the problems related to real life given in the textbook. To revise the concepts learnt in the chapter, students will do Test Yourself section from the textbook. Use the Multiple Choice Questions and Mental Maths sections to conduct a quiz contest in the class. Use the At a Glance section to revise the key points of the concepts.

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+% ? 0 ?

Worksheet 1

1. Fill in the blanks.

(a)

2 5

=

30

(b)

?

6 9

=

10

(c)

30

=

30 45

2. Arrange the following in ascending order.

(a)

1151,

?

72,

13,

?

1102,

3 4

__________________________________

(b)

1314,

394,

?

1354,

1,

?

25 34

__________________________________

3. Arrange the following in descending order.

(a) 154, ? 151, 53, 457, 5

__________________________________

(b)

114,

37,

?

251,

0,

?

2 49

__________________________________

4. Find the additive inverse and multiplicative inverse of each of the following.

(a)

7 5

__________________________________

(b)

?

10 15

__________________________________

(c)

43 21

__________________________________

(d) 1

__________________________________

(e) ?1

__________________________________

5. Verify the commutative property of addition and multiplication of rational

numbers, i.e.,

(a

+

b)

=

(b

+

a)

and

(a

?

b)

=

(b

?

a)

when

a

=

3 5

and

b

=

9 12

6. Simpilify the following.

(a)

2 15

+

3 4

+

?1 5

=

__________

(c)

21 15

?

?75 84

?

8 10

=

__________

(b)

?3 4

+

3 8

?

?9 16

= __________

(d)

19 78

?

?57 91

=

__________

7.

What

must

be

subtracted

from

22 15

to

get

?1795?

_________________

8.

Find 5 rational numbers

between

3 4

and

1.

_________________

8

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