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Teacher’sManual

Destination Maths

Anju Loomba

Kusum Wadhwa

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

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

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Second Floor, MGM Tower, 19 Ansari Road, Daryaganj, New Delhi-110002 (India) Phone : +91-11-43556600Fax : +91-11-43556688E-mail : delhi@saraswatihouse.comWebsite : www.saraswatihouse.comCIN : U22110DL2013PTC262320Import-Export Licence No. 0513086293

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First published 2017

ISBN: 978-93-86413-88-8

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

The moral rights of the author has been asserted.

©Reserved with the Publishers

All rights reserved under the Copyright Act. No part of this publication may be reproduced, transcribed, transmitted, stored in a retrieval system or translated into any language or computer, in any form or by any means, electronic, mechanical, magnetic, optical, chemical, manual, photocopy or otherwise without the prior permission of the copyright owner. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages.

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This book is meant for educational and learning purposes. The author(s) of the book has/have taken all reasonable care to ensure that the contents of the book do not violate any copyright or other intellectual property rights of any person in any manner whatsoever. In the event the author(s) has/have been unable to track any source and if any copyright has been inadvertently infringed, please notify the publisher in writing for any corrective action.

PrefaceThe Destination Maths 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 building 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 solved worksheets and Model Test Papers.

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.

ContentsContents 1. Knowing Our Numbers 5

2. Whole Numbers 10

3. Playing With Numbers 15

4. HCF and LCM 22

5. Integers 27

6. Fractions 32

7. Decimals 37

8. Introductory Algebra 42

9. Linear Equations 46

10. Ratio, Proportion and Unitary Method 50

Model Test Paper 1 54

11. Basic Geometrical Ideas 56

12. Understanding Elementary Shapes 61

13. Understanding Three-Dimensional Shapes 65

14. Constructions 69

15. Symmetry 73

16. Perimeter and Area of Plane Figures 77

17. Data Handling 81

Model Test Paper 2 85

Answer Key 89

5

Knowing Our Numbers1Learning Objectives

Students will be able to read and write numerals beyond ten lakhs. arrange the digits of the given numerals in the place value chart. read and write numerals according to the Indian and International Systems of

Numeration. compare numerals in Indian as well as the International Systems of Numeration. estimate large numbers, and estimate the sum, di� erence, product and quotient. convert larger units of length and mass to smaller units and vice versa. express Hindu -Arabic numerals as Roman numerals and vice versa.

Concept Building• Students are already familiar with the large numbers.• Read the Introduction section to recapitulate these concepts.• Explain students the diff erence between natural numbers and whole numbers and let

them understand that all natural numbers are whole numbers but all whole numbers are not natural numbers hence focusing on exception of zero.

Extension of Numbers; Indian System of numeration (Place value, face value, expanded form); International System of numeration (Place value, face value, expanded form) • Make the students understand the diff erence between the terms notation and numeration.• Have a quick recap of the Indian and International system of numeration and the common

place values in both that is up to 5 places. Make the students understand that aft er the 5th place the places in both the systems are called by diff erent names. Emphasise the use of commas in both the systems at di� erent places in both the systems and how to read the numbers in both the systems.

• Students have already learnt place value and face value up to 8-digit numbers in their previous class so just a quick recall and then extension of the concept towards bigger number is required.

• To reinforce ask them to do the Exercise 1.1 from the textbook.

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Formation of Numbers With the Given Digits; Comparison of Numbers• Read the related sections from the textbook.• Explain students that largest number using given number of digits is formed by arranging

the given digits in descending order and smallest number using given digits is formed by arranging the digits in ascending order for example if they have to use the digits 9,8,5,1,2,6,7,4,3,0 to make the largest and the smallest number using all digits, then the largest number will be 987653210 and smallest number will be 1023456789 (without repeating any digit).

• Use examples given in the related section to make them understand how to form numbers with the given digits.

• To reinforce ask the students to do the related Try � ese section from the textbook.• Rules of comparing numbers needs to be clarify with respect to bigger numbers.• Aft er making them understand comparison of numbers conduct the an activity with

students where they will reinforce ascending and descending orders.• Bring 10 cm X 10 cm pieces of thick chart paper/cardboard of diff erent colours, one big

chart paper to the class.• Cut out 10 cm X 10 cm pieces of thick chart paper/cardboard of diff erent colours (one

for each student).• Divide the class into fi ve groups and give diff erent coloured chartpaper/cardboard pieces

to each group. For example group A gets green, group B red and so on. • Give a certain range of numbers to each group for example, group A gets 100-1000,

group B gets 1000-10000 and so on.• Each member writes any number of his/her choice that falls within the specifi ed range

on the piece of chart paper in fi gures and in words.• On a big chart paper, draw 10 cm X 10 cm squares (as many squares as the number of

students) in fi ve columns. Students of group A will then go and paste their slips (with the written numbers) in their column in ascending order.

• Students of other groups will also follow the steps taken by group A.• Th is will continue till all squares are fi lled with multicoloured pieces.• Use examples given in the textbook to make them understand the concept in a better

way.• Instruct the students to do the Exercise 1.2 from the textbook.

Operations on Large Numbers; Introducing Brackets • Read the related sections from the textbook.

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• Students have enough understanding of bigger numbers now so make them understand the application of bigger numbers in real life.

• Make students attempt some more real life applications of bigger numbers for example conversion of units of length, weight and capacity, etc. and the word problems based on the same.

• Make them practise the four operations involving bigger numbers. • Defi ne Brackets are symbols used in pairs to group things together. • It is used around the part of an expression that is need to be done fi rst. • To reinforce ask the students to do the related Try � ese section and Exercise 1.3 from

the textbook.

Estimation ; Estimating sum, di� erence, product and quotient; Large Numbers and Small Numbers in practice; Roman numbers• Explain the method of rounding off numbers to their nearest tens, hundreds and

thousands and explain students that we can also estimate the sum, di� erence, products and quotients by fi rst rounding off the numbers involved and then rounding them off .

• Use examples given in the related section to make them understand the concept of estimation in a better way.

• Explain the relation between bigger units and smaller units of measurement.• Use the Remember section to point out the important facts related to topics.• Students have learnt enough about the 7 symbols of the Roman system and the diff erent

rules to form the same. Have a revision of their understanding so far by giving them some numbers and asking them to convert them into Roman numerals and vice versa. Now make them understand the meaning and usage of the bar used in Roman numbers by illustrating a few examples on the board.

• Use examples related to the topics to make them understand the topics in a better way.• To reinforce ask the students to do the Values sections from the textbook.• Ask the students to do Exercise 1.4, Exercise 1.5 and Exercise 1.6 from the textbook.To revise the concepts learnt in the chapter students will do Let’s Revise, Let’s Link, Life Skills and HOTS sections from the textbook.Use Multiple Choice Questions and Testing Zone section to conduct a quiz contest in the class. Use Let’s Recap section to revise the key points of the concepts.

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1. Complete the following statements with suitable words or � gures.

(a) 100 lakh = ________ crore (b) 1 million = ________ thousand

(c) 1 lakh = ________ thousand (d) 10 crore = ________ ten lakh

(e) 1 billion = ________ million (f) 5 crore = ________ million

(g) 6 km = ________ m (h) 3 mm = ________ cm

(i) 4 g = ________ kg (j) 257 L = ________ mL

(k) 67 cm = ________ m

(l) Th ere are only seven symbols in ________ numerals. (Roman/Hindu-Arabic)

(m) MMM = 3 × ________

(n) 600 is represented by ________ in Roman system of numeration.

2. Do as directed. (a) Write: i. 1 lakh in hundreds ___________________________________________________ ii. 1 million in thousands ___________________________________________________ iii. 100 million in crores ___________________________________________________ (b) Write the smallest whole number. Is it a natural number also? ______________________________________________________________ (c) Write the smallest natural number. Is it a whole number? ______________________________________________________________ (d) Write place-value and face value of 7 in 6571489. ______________________________________________________________ (e) Write the number 45 lakhs, 8 thousands, 4 ones in International system of

numeration. ______________________________________________________________

Worksheet 1

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1. From the numeral 25648751, pick out the digits in each of the following place.

(a) Th ousands = ________ (b) Ten lakhs = ________

(c) Hundreds = ________ (d) Crores = ________

2. Write the greatest and smallest 6-digit numbers using the digits.

(a) 0, 2, 6, 7, 3, 8 only once (b) 1, 9, 3, 0, 4, 8 only once

3. Find the di� erence between the greatest and the smallest numbers that are formed using the digits 9, 0, 2, 1, 6, 4 only once.

4. � e population of a city is 6525895. If the number of males is 3256409, � nd the number of females in the city.

5. Find the estimated sum of 60745 and 12547 by estimating the numbers to their nearest (a) hundreds and (b) thousands. Also, � nd the di� erence between the estimated sum and the actual sum.

6. Estimate the following by rounding o� each number to its greatest place.

(a) 236 + 548 + 5025 (b) 3256 + 4785 – 3256

7. Convert the following into Hindu-Arabic numerals:

(a) CDLVIII (b) DCCLXXXIX

(c) MCDXXV (d) DCCCI

8. State whether the following statements are True or False. (a) One million is equal to ten lakh. (b) Th e smallest 6-digit number using the digits 0 and 1 with repetition of digits is

100001. (c) Th e place value and face value of the digit 1 in the number 12548 is same. (d) Th e Roman numeral DXII in Hindu-Arabic numeral is 542. (e) Number of ten thousand in 100 millions is ten thousand.

Worksheet 2

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Whole Numbers2Learning Objectives

Students will be able to di� erentiate between natural and whole numbers. represent natural and whole numbers on a number line. add, subtract, multiply and divide the whole numbers on the number line. understand and verify properties of addition, subtraction, multiplication and

division of whole numbers.

Concept Building• Students are already familiar with the natural numbers and can apply the basic operations

on these.• Read the introduction to recapitulate the concepts like successor, predecessor, etc.• Tell them counting numbers are called Natural Numbers, i.e., 1, 2, 3, 4, 5, 6 .....• Discuss the need for Whole Numbers and also the di� erence between the two, i.e., the

natural numbers and whole numbers.• Also make them understand the fact that every natural number is a whole number but

every whole number is not a natural number, i.e., 0 is not a natural number but 1, 2, 3, 4, .... are natural numbers.

• To point out the important facts about numbers use Remember section.

Representation of Whole Numbers on a Number Line• Plotting whole numbers on the number line will give a better understanding about the

whole number.• Following points can be discussed. – 0 is the smallest whole number is 0. – Th ere is no largest whole number. – Number line is also very useful in discussing order property of whole numbers,

addition of whole numbers, subtraction of whole number, multiplication and division of whole numbers.

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Properties of Whole Numbers• Use the examples of the related section to make them understand the above concepts.• Instruct them to do Exercise 2.1 from the book.

Activity• Bring 3 paper plates and some counters. Call any three students from the class and

instruct them to pack out some counters and put them each of the two trays and also say whether the numbers are whole numbers or not. Now, ask third student to collect all the counters and count in front of the class. Announce the fi nal number. Now ask students whether this number is whole number or not? Now explain that the sum of two whole numbers is always a whole number. Th is property of whole numbers is called the closure property of addition of whole numbers.

4 + 6 = 10

Now again take fi ve paper plates.• Take few counters. Call four students from the class.

+

I II A III IV

+= =

• Ask two of them to place 3 counters in plate I and 4 counters in plate 2. Another two students to place 4 counters in plate III and 3 counters in plate IV. One more student comes and counts the number of counters in plate I and II, i.e., 7 and

puts equal number (7) of counters in plate A. Now counts the total number of counter in plate III and IV, i.e., 7. Check whether counters in plate I and II is same as in plate III and IV is also same as in plate A.

• Now explain to them that during addition if we change the order of whole numbers then also the sum remains the same. Th is properly is called commutative property of addition of whole numbers.

• Students are already familiar with the four basic operations, i.e., addition, subtraction, multiplication and division etc.

• Now to discuss the properties of these operation use examples given in the section using graphs and paper cutting.

• To reinforce commutative property of addition of whole numbers use Maths Lab Activitygiven on page 37.

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• To reinforce addition and subtraction ask them to do the Life skills section to on page 34.

• To reinforce multiplication of whole numbers use Values section given on page 37.• Instruct them to do Exercise 2.2 given on page 34.

Patterns• Students are already familiar with the concept of patterns. Th ey already know that

patterns can be any design.• Patterns follow certain rules like they are symmetrice, repetitive, etc.• Discuss some number patterns.• To reinforce discuss Let’s Link section given on page 38.• Instruct the students to do Exercise 2.3 given on page 34.To revise the concepts learnt in the chapter students will do Let’s Revise and Hots sections from the textbook.Use Multiple Choice Questions and Testing Zone to conduct a quiz contest in the class for a quick revision.Use Let’ Recap section to revise the key points of the concepts.

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1. Fill in the blanks.

(a) (400 + 5) × (400 – 5) = ______ × _________

(b) 666 + 555 +444 = _____ × 120

(c) 215 × 55 = (200 + _____ ) × ( 50 + _______)

(d) 76 × (100 – 3) = 97 × (100 – _____ )

(e) (10 + 6) (10 – 6) = _____ – 36

2. Write the next four natural numbers a� er 21421.

3. Which is the smallest whole number?

4. How many whole numbers are their between 25 and 48?

5. Write the successor of: (a) 428541 (b) 100441 (c) 41017236

6. Write the predecessor of: (a) 78 (b) 6 (c) 3124045

7. Find the sum by suitable arrangement. (a) 837 + 208 + 363 (b) 1692 + 345 + 1358 + 745

8. Find the product by suitable arrangement. (a) 16 × 625 × 297 (b) 4 × 165 × 25 (c) 8 × 125 × 431 (d) 2 × 1695 × 50 (e) 125 × 40 × 8 × 25

9. Simply: 318 × 55 + 318 × 45

10. � e school canteen charges `40 for lunch and `10 for milk for each day. How much money do you spend in 5 days on these things?

11. Find the number which when divided by 24 gives the quotient 14 and remainder 13.

Worksheet 1

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1. Which of the following statements are true (T) and which are false (F)? (a) Zero is the smallest whole number. _______ (b) 499 is the predecessor of 500. _______ (c) Zero is the smallest natural number. _______ (d) 600 is the successor of 601. _______ (e) All the natural numbers are whole numbers. _______ (f) All the whole numbers are natural numbers. _______ (g) Th e predecessor of a 2-digit number is never a 1-digit number. _______ (h) Th e natural number 1 has no predecessor. _______ (i) Th e whole number 1 has no predecessor. _______ (j) Th e whole number 0 has its predecessor. _______ (k) Th e successor of a 2-digit number is always a 2-digit number. _______

2. Study the given pattern and � ll in the blanks. 1 × 8 + 1 = 9 12 × 8 + 2 = 98 123 × 8 + 3 = 987 1234 × 8 + 4 = 9876 12345 × 8 + 5 = 98765 ______ × 8 + 6 = ______ _______ × 8 + 7 = _______

3. Give two examples of each of the following properties of whole numbers.

(a) Closure property of addition and multiplication.

(b) Commutative property of addition and multiplication.

(c) Associative property of addition and multiplication.

(d) Distributive property of multiplication over addition and subtraction.

4. 15 cans can be packed in one carton. How many cartons are required to pack such 450 cans?

Worksheet 2

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Playing with Numbers3Learning Objectives

Students will be able to simplify a given expression involving two or more operations. simplify a given expressions using DMAS, ODMAS and BODMAS rules. recognise and fi nd multiples, divisors, factors of a number. fi nd and state various types of numbers, i.e., prime and composite, even and odd,

etc. test divisibility by numbers 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, etc., using divisibility

rules and not by actual division.

Concept Building• Students are already familiar with the whole numbers, properties of a addition,

subtraction, multiplication and divisor and can apply the basic operations with the whole numbers.

• Read the introduction section to recapitulate those concepts.

Simpli� cation, DMAS• Take diff erent questions, show the students while solving such problems which involve

the four operations can give us di� erent answers. For example write the questions given below on the white/blackboard. Discuss the diff erent ways in which it can be solved 20 ÷ 5 + 30 + 45 – 6 Answer (i). 20 ÷ 35 + 45 – 6 Answer (ii). 20 ÷ 5 + 75 – 6 = 20 ÷ 74 = 4 + 75 – 6

= 2074 = 10

37 = 73

Answer (iii). 20 ÷ 80 – 6

= 2080 – 6 = 14 – 6 = 1 – 24

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• Now stress upon the fact that why we get diff erent answers.

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Th us, we see there is a need for a convention regarding the order of operations so that everyone follows the same order.

Th e convention is DMAS D M A S

↓ ↓ ↓ ↓ Division Multiplication Addition Subtraction• Use examples given in the related section to make them understand the concept in a

better way.• Ask the students to do the Exercise 3.1 from the text book.

Using the Operation ‘of ’; Using Brackets• Th e operation ‘Of ’ means multiplication. If ‘of ’ appears then order of operation is

‘ODMAS’.• Use examples given in the related section to make them understand the concept in a

better way.• Ask students to do the ‘Try � ese’ section and Exercise 3.2. Similarly if a bracket also appears then the rule is B O D M A S

↓ ↓ ↓ ↓ ↓ ↓ Bracket ‘of ’ Division Multiplication Addition Subtraction open Example: (15 ÷ 5 + 3) × 9 – 16 = (3 + 3) × 9 – 16 = 6 × 9 – 16 = 54 – 16 = 38• Th ere are many types of brackets. We need to follow a convention in the order of brackets

as well. {{(–)}} Write an expression involving all the bracket. Ask the students to solve and discuss the

di� erent answers they get. Now discuss the correct order of brackets.• Instruct students to do the Exercise 3.3. Th is will help students to understand the use of rule properly.

Factors and multiples; Common factors and multiples• Students are already familiar with multiples and factors. Pick up a number say 48.

Its factors are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. Some of the factors are prime factors, e.g. 2 and 3 while others are composite numbers, except 1.

• Discuss the facts about factors given on page 44 with examples.

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Discuss multiple of a number and facts about multiples with examples given on page 44 and 45. Examples given on page 45 and 46 will help in the better understanding of the fact.

• Discuss common factors and multiples of a number.• Use examples given in the related section to make them understand the concept in a

better way.• Ask students to do Exercise 3.4 given on page 46.

Activity• Multiples can also be introduced using the 10 × 10 square grid with the fi rst 100 natural

numbers.1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

• Provide such 10 × 10 square grid to each student.• Ask them to colour every 3rd number on the grid. First number to be coloured is 3. For

example, 3, 6, 9, 12, .... .• Now discuss that all the numbers that we have coloured are the multiples of 3.• Now, write another number on the board say 5 and multiply this with each number from

1 to 10 to obtain 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.• Now, explain that all the numbers obtained are the multiples of 5. Th en explain that this

way we can obtain any number of multiples of any number. Also, the product that we obtain aft er multiplying like 5 × 1 =5, 5 × 2 = 10, 5 × 3 = 15, etc. Products, 5, 10, 15, etc., are called the multiples of 5.

• In the above table the students can be asked to make multiples of 2, 3, 4, 5, 6, 7, 8 and 9 in di� erent colours.

• Now point out the fact that some numbers will have two or more colours, e.g., 6 will have 3 colours means it is a multiple of 3 numbers 2, 3 and 6; 12 will have 4 colours, etc. So, there will be many numbers which are multiples of more than one number.

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• Th is exercise will be helpful in making them understand that a number can be a multiple of more than one number.

• Now, discuss the fact that 12 is a multiple of 2, 3, 4, 6 and 12. 2, 4, 3, 6 and 12 are called the factors of 12.

• Stress upon the fact that the number 1 is a factor of every number. Every number is a factor of itself.

• Life skills on page 52 can be used to reinforce the concept of multiples.

Types of Numbers• Explain the concept of even and odd numbers with examples given on page 46.• Remember section can be used to discuss properties of even numbers given on page 46.• To reinforce ask them to do the section Let’s Link given on page 53.

Prime Number• In the square grid activity students have already marked the numbers with one coloured

line. Th is explain that such numbers have only two factors, i.e., 1 and the number itself. Such numbers are called prime numbers.

Perfect Number• To explain the concept of perfect numbers from the same grid ask them to pick numbers

like 6, 7, 8. Now ask them to list all the factors of these numbers and fi nd the sum of these factors.

6: 1, 2, 3, 6 and 1 + 2 + 3 + 6 = 12 = 2 × 6 7: 1, 7 1 + 7 = 8 = 2 × 4 8: 1, 2, 4, 8 1 + 2 + 4 + 8 = 15 ≠ 2 × 8 Th e number with sum of factors equal to twice the number such a number is called a

perfect number. Now as ask them to list all the perfect numbers till 100.• Use examples given in the related section to make the understand the concept in a better

way.

Activity• Th is simple activity linking mathematics with GK can be done. Ask students to get a day

old news paper and pick one news item each of their interest from even pages odd pages composite, prime and perfect number pages.

• Students can be asked to do Exercise 3.5 on page 48.

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Divisibility Tests for Numbers• To introduce general rules of divisibility use pages 48, 49, and 50.

Game• For better retention this game can be played in class.• Cut equilateral 9 triangles of diff erent zones and paste them as shown here.

3

1

57

24

68

9

• Write numbers on fl ags and ask them to pin the fl ag in that triangle with a number with which it is divisible.

General Properties of Divisibility• Discuss the properties given on page 50 and 51 with the class.• Along with these properties following parts can also be discussed. — No perfect number is odd. — What are prime, twin prime and co-prime numbers. — 1 is neither a prime number nor composite. — 2 is the smallest composite number.• For further reinforcement discuss Hots given on page 53.• Use Maths Lab Activity on page 53 for revising diff erent kinds of numbers.To revise the concepts learnt in the chapter students will do Let’s Revise section given on page 52.Multiple Choice Questions on page 51 and Testing Zone on page 54 can be used for conducting oral quiz in the class. Crossword and riddle on page 54 will serve dual purpose of revising the concept, learnt as well as students will have fun in doing these and this with in turn help them to retain the concept better.Use Let’s Recap section to revise the key points of the concepts.

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1. State whether the following statements are True or False.

(a) Th e sum of three odd numbers is even.

(b) Th e sum of two even numbers and one odd number is even.

(c) Th e product of three even numbers is even.

(d) Th e product of two odd numbers and one even number is odd.

(e) When an odd number is divided by 2, the quotient is always even.

(f) All prime numbers are odd.

(g) Prime numbers do not have any factors.

(h) Sum of two prime numbers is always even.

(i) All even numbers are composite numbers.

(j) Number which is divisible by 2 is also divisible by 4.

(k) Number which is divisible by 9 is also divisible by 3.

(l) Number which is divisible by 2 and 3 is also divisible by 12.

(m) Number which is divisible by 15 is also divisible by 3 and 5.

(n) Th e product of two even numbers is always even.

2. Complete the following statements with suitable words or � gures.

(a) 23 is a ............ number.

(b) Th e prime factors of 110 are ............ .

(c) A prime number has only ............ factors.

(d) A composite number has ............ or ............ factors.

(e) ............ is the smallest even composite number.

3. � e numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers upto 100.

Worksheet 1

21

1. Using divisibility tests, determine which of the following numbers are divisible by the given numbers as directed.

Number Divisibility test

2 3 4 5 6 8 9 10 11

128 Yes No Yes No No Yes No No No

990

1586

275

6686

639210

429714

2856

3060

406839

2. Simplify the following and � ll in the blanks.

(a) 8 × 4 – 3 × 5 + 42 ÷ 14 = ............

(b) 80 – 2 of 45 + 36 ÷ 9 – 8 × 6 = ..........

(c) 5 + 5 × 12 – 9 = ............

(d) 16 – 20 ÷ 5 + 5 = ............

(e) 85 – 20 ÷ 4 × 8 = ............

(f) 27 – [6 + 4 – (6 + 3 – 5 – 3)] = ............

(g) 63 – 12 ÷ 3 of 2 + 2(17 – 5) ÷ 4 = ........

Worksheet 2

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HCF and LCM4Learning Objectives

Students will be able to understand prime factorisation or the fundamental theorem of arithmetic. fi nd the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) by

prime factorisation method. fi nd the HCF by listing factors and long division method. understand the relation between HCF and LCM of two numbers. solve word problems involving HCF and LCM of two numbers related to real life

situations.

Concept Building• Before talking about HCF and LCM recall factors and multiples, prime numbers, prime

factors, etc. For better understanding of prime factors you can use a small game of building blocks. Take a building made up of blocks. How ask the students to break it till the time all pieces of the di� erent sizes fall apart.

• Once they have done to ask them to further divide into pieces. Th ey can’t. Now introduce the concept of prime factorisation.

Prime Factorisation• Prime factorisation is performed to break a given number

into factors which cannot be divided any further. In other words we may say that Prime factorisation is the way of expressing a given number as a product of prime numbers.

• Now explain the diff erent methods of prime factorisation.• For this use pages 55 and 56 from the book where these

methods are well explained with examples.• Encircled numbers are prime numbers, which means

that cannot be divided further more.• Instruct students to do Exercise 4.1 given on page 56.

2 122 2

96

4 24

2

2

6

3

23

HCF and LCM• First take up problems from real life situations where LCM and HCF are used. Some

such situations are given at the end of this chapter. Pick up some of these and try and solve them using basic principles of mathematics before even talking about HCF and LCM. Th is will help them in retaining the concept better. Sometimes they don’t even know the di� erence between the two.

• It is very important to give them a clear understanding of the two.• Th ey should know that HCF is a factor and LCM is a multiple.HCF• Discuss the following points that HCF is a factor.• A factor cannot be greater than a number.• A common factor of two or more numbers cannot be bigger than the smallest number.

Let us consider the numbers 5, 10, 15 and their HCF is 5• HCF of two or more numbers is always greater than or equal to 1.• Th ough HCF means the greatest or the highest factor but a greater or a highest factor

cannot be smaller than 1 but it can be 1. For example HCF of 4 and 9 is 1.• Use page 57 and 58 for discussing diff erent methods of fi nding HCF.• To point out some important facts about HCF use remember section given on page 57.• To reinforce ask students to do the related Try � ese section given on page 58.• Exercise 4.2 on page 59 can be discussed partially in class and partially student may be

asked to attempt it.• To reinforce the concepts learnt use the section Maths Lab Activity given on page 64-65

and Hots section given on page 66.

LCM• Again take some real life situations to introduce LCM before this discuss the need. Discuss

that there are a lot of things around us that repeat themselves aft er a defi nite interval. For example train, traffi c lights, ringing of bells in school, etc. Many such problems can be solved using factors and multiples.

• Let us suppose you are decorating your class for Christmas. For this you went to market to buy some decoratives. You notice that balloons are available in a packing of 9 and stars in the packs of 4 each. You are interested in buying both items in equal amounts. How will you calculate this. Have a discussion in class.

• Let everybody speak and when they come up with solutions listen to them and correct them or help them in reaching the corrects solution.

24

• To discuss methods of fi nding LCM use pages 59 and 60. Examples on pages 60 and 61 will further help in better understanding of the book.

• Students can be asked to use Exercise 4.3 given on page 61.• For further reinforcement use the sections Life Skills, Values given on page 64 and the

section Hots given on page 66.Properties of HCF and LCM of given Numbers• Use page 62 for discussing properties of HCF and LCM.• Use examples given in the related section to make them understand the concepts in a

better way.• Instruct them to do Exercise 4.4 from the text book.To revise the concepts learnt in the chapter students should do Let’s Revise and Testing Zone sections from the text book.Use Multiple Choice Questions to conduct a quiz contest in the class.Use Let’s Recap section given on page 64 to revise the key points of the concepts.

25

1. Which of the following express prime factorisation?

(a) 1125 = 3 × 3 × 125

(b) 2600 = 2 × 2 × 2 × 5 × 5 × 13

(c) 578 = 17 × 34

(d) 1236 = 2 × 2 × 2 × 167

2. Find the HCF and LCM of the following numbers by the prime factorisation method.

(a) 8, 12 (b) 20, 35 (c) 40, 52 (d) 88, 96 (e) 12, 18, 20 (f) 30, 35, 40 (g) 33, 36, 39 (h) 15, 20, 25

3. Find the HCF and LCM of the following numbers by the division method. (a) 10, 70 (b) 25, 50, 75 (c) 14, 42, 98 (d) 33, 99, 121 (e) 35, 55, 60 (f) 24, 72, 144 (g) 30, 60, 120, 150 (h) 68, 102, 136, 204

4. Find the HCF of 28, 84, and 98 by the long division method.

5. Find the greatest number which divides 17 and 21 leaving the remainder 1 in each case.

6. Determine two numbers nearest to (greater than or less than) 99999 which are exactly divisible by 2, 3 and 4.

7. � e marbles in a jar can be divided into groups of 2, 4, 6 and 8.What is the least number of marbles in the jar?

8. � e LCM of two numbers is 456 and their product is 912. Find the HCF of the numbers.

9. Can two numbers have 15 as their HCF and 1875 as their LCM? Give reason in support of your answer.

Worksheet 1

26

1. Which of the following express prime factorisation?

(a) 1200 = 2 × 2 × 2 × 2 × 3 × 5 × 5

(b) 2525 = 5 × 5 × 101

(c) 408 = 2 × 2 × 2 × 3 × 17

(d) 1460 = 2 × 2 × 365

2. Find the HCF and LCM of the following numbers by the prime factorisation method.

(a) 5, 10 (b) 21, 35 (c) 42, 56 (d) 80, 90 (e) 30, 45 (f) 169, 52 (g) 100, 75, 40 (h) 150, 200, 225

3. Find the HCF and LCM of the following numbers by the division method. (a) 11, 99 (b) 15, 40, 85 (c) 16, 48, 102 (d) 39, 117, 143 (e) 12, 60 (f) 30, 60, 90 (g) 18, 36, 50, 68 (h) 7, 28, 35, 42, 63

4. Find the HCF of 36, 108, and 162 by the long division method.

5. Find the greatest number which divides 19 and 70 leaving the remainder 2 in each case.

6. Determine two numbers nearest to (greater than or less than) 55000 which are exactly divisible by 3, 5 and 7.

7. A rectangular courtyard is 24 m 72 cm long and 18 m 90 cm broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.

8. Can two numbers have 28 as their HCF and 3976 as their LCM? Give reason in support of your answer.

9. � e HCF of two numbers is 25. If the numbers are 75 and 100, � nd their LCM.

Worksheet 2

27

Integers5Learning Objectives

Students will be able to understand the need and meaning of integers. understand the use of integers in diff erent (opposite) situations. represent integers on the number line. compare integers and order integers. add and subtract integers.

Concept Building• Start with introduction to recapitulate the need of whole numbers and also the fact that

every natural number is a whole number but the whole number 0 is not a natural number. Lead this discussion to the need for the Integers.

Integers• Discuss what are integers. Stress upon the fact that every natural number and every

whole number is also an integer. Th e integer 0 is neither –ve nor +ve.• Use Remember section to point out important facts related to the topic.• While discussing the table given on page 68 make sure to clear the misunderstanding

about the height, depth and profi t or loss etc. As we tend to believe that depth and loss are negative while height and profi t are positive. In mathematics this + and – just denotes the opposite nature of the two. So +`60 and –`60 represent the same quantity or magnitude. Only diff erence of that positive and negative sign. Th ese signs only denote the opposite direction of each other, i.e., if – denotes left

+ denotes right or – denotes right + denotes left Similarly + denotes profi t – denotes loss or – denotes profi t + denotes loss etc.

28

• Use examples given on page 68 to clear the above concept.• Instruct them to do Exercise 5.1 from the textbook.• To recapitulate use the section Life Skills given on page 76 and the section Hots given

on page 79.

Representation of Integers on a Number LineOrdering of integers• Use page 68 to explain this concept. Use graph papers for explaining the representation

of integers on the number line. Th is will help them understand the placement of integers on the number line clearly.

–4 –3 –2 –1 0 1 2 3 4 5 6 7 8

• Do example given on page 69.• Opposite of an integer can be explained with the help of a mirror and a number line as

shown on the page 69.• To point out the important facts about placement of integers on the number line use

Remember sections on page 69.• Discuss example 5 given on page 69.

Absolute value of a integer• Use number line to explain the ordering of integers as shown on the page 69 and 70.• Th e summary points given on this page will be very helpful to explain these.• Use Remember section given on page 70 for pointing out the important facts about the

ordering of integers.• Discuss solved examples given on page 70.• To reinforce use the section Let’s Link given on page 78 and the section Hots question 2

given on page 29.• Explain absolute value of an integer from the related section. Use of number line will give

a clearer idea of oppositeness. Discuss |x| = {x if x >, 0; –x of x < 0} as this is an important point to clear the oppositeness.• Ask the students to do Exercise 5.2 given on page 71.

Operations on integer• Before discussing operations on integers discuss rules to add integers given on page 71

and 72.

29

• Start discussing addition of integers using the number line as explained on the page number 72.

• Solved examples given on page 72 and 73 will help in better understanding.• Discuss additive inverse or negative of an integer.• To reinforce ask them to do Maths Lab Activity given on page 77.• Ask the students to do Exercise 5.3 given on page 73.• Subtraction of integers can be explained using a number line as shown on page 74.• Discuss Common Errors on page 74 for better understand.• Use Remember section to point out the important facts related to the topic.• Ask the students to do Exercise 5.4 given on page 75.• To revise the concepts learnt use the section Let’s Revise given on page 76.• To review the important concepts learnt in the chapter use the section Let’s Recap given

on page 77.To revise the concepts learnt in the chapter students will do Testing Zone section given on page 79.Multiple Choice Questions given on pages 75 and 76 can be used to conduct a quiz contest in the class.

30

1. Represent the following numbers as integers with appropriate signs. (a) An eagle is fl ying at a height of one thousand and two hundred metres above the

sea level. (b) A fi sh is moving at a depth of fi ve hundred twenty metres below the sea level. (c) A deposit of rupees two hundred. (d) A withdrawal of rupees four hundred.

2. Following is the list of temperatures of � ve places in India on a particular day of the year. Write these temperatures with appropriate sign in the blanks given.

Place Temperature (a) Manali 1°C below 0°C __________ (b) Patna 25°C above 0°C __________ (c) Delhi 18°C above 0°C __________ (d) Jammu 4°C below 0°C __________ (e) Nasik 22°C above 0°C __________

3. Write all the integers between the given pairs of integers. (a) 0 and –8 (b) –6 and 6 (c) –15 and –6 (d) 41 and 29 (e) –31 and –35

4. Write the absolute values of the following integers. (a) 14 (b) –12 (c) –201 (d) 654

5. Write the opposite of the following integers. (a) +52 (b) +30 (c) +91 (d) +112

6. Simplify. (a) (–75) + (–25) (b) 600 + (–66) – (–100)

7. Evaluate. (a) |– 32 – 7| – |13 – (–2)| (b) |– 67 – (– 12)| + |– 67 + 38|

8. Subtract the sum of – 33 and 17 from the sum of – 31 and – 70.

9. On a day Rohan earns a pro� t of `1200 on the sale of a refrigerator and loses `400 on the sale of a camera. Find what is Rohan’s actual pro� t or loss?

Worksheet 1

31

1. Write the solution of the following using number line. (a) (+5) + (–13) (b) (–11) + (+10) (c) (–9) + (–8) (d) (+4) + (–10)

2. Find the sum of (a) 123 and –341 (b) –73 and 73 (c) –193, 37 and 219 (d) 29 + (–3) + (–66) + (–6)

3. Subtract. (a) 5 from 7 (b) –10 from 35 (c) –32 from - 63 (d) 13 from –13

4. Fill in the blanks. (a) –5 + ____ = 0 (b) 19 + ____ = 0 (c) 18 + (–18) = ____ (d) (–6) + ____ = 17 (e) ____ – 16 = –10 (f) 26 + ____ = –26

5. Fill in the blanks with >, < or = sign. (a) (–3) + (–5) … (–3) – (–5) (b) (–12) + (–10) … (–13) + (–8) (c) 54 – (–11) … 75 + (–4) (d) (–52) – (–42) … (–42) – (–52)

6. Simplify. (– 2) + 5 + (– 3) + 44 + (– 26) + 21 + (– 26)

7. � e sum of two integers is 80. If one of them is 150, � nd the other. ___________________________________________________________________ ___________________________________________________________________

8. At 3 o’clock in the morning, the temperature was 2°C below zero. At 2 pm, the temperature was 8°C above zero. Find the di� erence between the two temperatures.

___________________________________________________________________ ___________________________________________________________________

Worksheet 2

32

Fractions6Learning Objectives

Students will be able to understand and explain the meaning (concept) of fraction (i) as a part of a whole

(ii) as a part of a group. represent a fraction on the number line. understand types of fractions: (i) like and unlike fractions (ii) mixed and improper

fractions (iii) equivalent fractions and their properties. write a fraction in the simplest form. compare, add and subtract fractions. solve simple problems of daily life involving fractions.

Concept Building• Introduction on Page 80 will help in recalling the literal meaning of fraction and use

basic defi nition of fractions.• Fraction a sa part of a whole; fraction as a part of a group; fraction as a divison;

Types of fractions• While discussing the point that fractions are formed when a whole is divided into equal

parts. Focus on the point that words equal divisions are very important. 49 means that

the whole is divided into 9 equal parts and out of these 9 equal parts 4 are taken into considerations.

• Discuss fraction as a part of a group or collection.• Th e total number of divisions the whole is divided into is called the denominator and

the number of parts considered is called the numerator.• To recapitulate use the section Hots, question 1 on page 95.• Take the example of the number of students in a class as a whole (i.e., a single unit). Now

ask students to fi nd the fraction for the number of boys and strength of the class and number of girles and the stregtn of the class.

• Ask them to write the numerator and denominator of the fractions.• To reinforce ask them to do the related Try � ese section.

33

• Use types of fractions section on page 81 and 82 to explain like, unlike proper, improper, unit and mixed fractions. Activity on page 82 will help in reinforcing these concepts.

• Use Try these sections given on page 83 for better understanding of these concepts.• To recapitulate use question 2 of the Hots section given on page 95.• Explain how to represent a fraction on the numbers line by using the related section

given on page 83.• Discuss examples on page 84.• Examples 3 and 5 on page 84 can be used to explain conversion of mixed numbers to

improper fractions and an Improper fractions to mixed number.

Activity-1• Following activity will help the students understand the concept of converting an

improper fraction into a mixed number.Step 1: Take some cards of semicircular shape. For example, 5 semi circles.

= 52Step 2: Join two semicircles to make one circle

= 212

Th is shows that 52 = 212. Now introduce the formula to convert improper fractions into

mixed numbers.

Activity-2• Now to show the conversion of mixed number into improper fraction. Take full and one

half squares.

Divide full square into halves we get fi ve haves. So, 21

2 = 52• Instruct students to do Exercise 6.1.

Equivalent Fractions; comparison of fractions• Use page 86 to explain the concept of equivalent fractions.

34

• Use the concept of equivalent fraction to introduce how to fi nd lowest (smallest) form of a fraction.

• To recapitulate do questions 3 of the Hots section given on page 95.• Using the concept of equivalent fraction to do conversion of unlike fraction to like

fraction given page 89.• Use examples given in the section comparision of fractions to make them understand

the concept in a better way.• Instruct students to do Exercise 6.2 on page 90.• To reinforce them use Life Skills section question 1 given on page 94.

Operations on fractions• Addition of fractions can be explained well with the activity given on page 90.• Use examples given in the related section to make them understand how to add or

subtract like and unlike fractions.• Instruct students to do Exercise 6.3.• For reinforcement use the section Life Skills question 2, the section Values given on

page 94 and the section Let’s Link given on page 95.• For developing skills of addition of fractions use Maths Lab Activity section given on

page 95.Use Let’s Revise on page 94 for revising the concepts learnt in the chapter.Let’s Recap on page 94 and 95 can be used for revising the important concepts of the chapter. A class quiz can be conducted for quick assessment of concepts in a fun way where Multiple Choice Questions on page 93 and Testing zone on page 96 can be used.

35

1. Draw number lines and represent the following fractions on them.

(a) 12, 14, 34, 44 (b) 1

9, 39, 59, 79

(c) 27, 37, 87, 11

7

2. Express the following as improper fractions.

(a) 347 (b) 17

8 (c) 367

(d) 1123 (e) 75

9

3. Find the equivalent fraction of 25 having

(a) denominator 15 (b) numerator 6 (c) denominator 30 (d) numerator 18 (e) denominator 45

4. Find the equivalent fraction of 3648 with

(a) numerator 9 (b) denominator 4

5. Reduce the following fractions in to its simplest form:

(a) 3560 (b) 120

90 (c) 8498

(d) 1680 (e) 17

68

6. Match the equivalent fractions.

(a) 250400 (b) 180

200 (c) 660990 (d) 180

360 (e) 220550

(i) 910 (ii) 2

5 (iii) 12 (iv) 2

3 (v) 58

7. Compare which is bigger, 45 or 56?

8. Simplify.

(a) 123 + 31

2 (b) 930 + 7

24 + 518 (c) 31

4 + 212 + 11

3

Worksheet 1

36

1. Write Yes or No for each of the following.

(a) Is 59 equal to 45? (b) Is 916 equal to 59?

(c) Is 45 equal to 1620? (d) Is 1

15 equal to 430?

2. Solve.

(a) 126 + 1

26 (b) 77 – 57 (c) 1

33 + 2133

(d) 815 + 3

15 (e) 56 + 46 (f) 1 – 13

(g) 27 + 07 (h) 6 – 13

5

3. Fill in the missing fractions.

(a) 710 – ____ = 3

10 (b) 36 = 36 – ____

(c) ____ – 321 = 5

21 (d) ____ + 527 = 12

27

4. Solve.

(a) 23 + 34 + 12 (b) 11

3 + 323

(c) 423 + 31

4 (d) 34 – 13

5. Shreya’s house is 910 km from her school. She walked some distance and then look

a bus for 12 km to reach the school. How far did she walk?

___________________________________________________________________

6. In a class A of 25 students, 20 passed in � rst class; in another class B of 30 students, 24 passed in � rst class. In which class was a greater fraction of students getting � rst class?

___________________________________________________________________

___________________________________________________________________

Worksheet 2

37

Decimals7Learning Objectives

Students will be able to know what are decimals. use models to represent decimals. write fractions with denominators 10, 100, 1000, etc., as decimals and vice versa. understand the place value chart of a decimal. read and write decimals. understand the di� erence between like and unlike decimals. compare decimals. convert decimals into fractions and fractions into decimals. add and subtract decimals. apply the knowledge of decimals in solving real-life problems.

Concept Building• Recall natural numbers, whole numbers and integers. Recall relationship between them.

Read instroduction section to teach the need for decimal numbers and use of decimals in daily life given on page 97.

• To reinforce ask studens to do the Try � ese sections.• To explain the meaning of tenths and hundredths in detail use square grids given on

page 97 and 98.• Defi ne the meaning of a Integral (whole) part and fractional (decimal) part by giving

diff erent examples. To read decimals use explanation given on page 99.• To reinforce use Life Skills question 1 given on page 110 and Let’s Link given on

page 112.• Relation of decimals to daily life can be explained by telling the students that the most

common use of decimals is in the money matters. We use decimal to separate ` and paise.

Decimals and place value chart• Our number system is an organised system based on multiples of ten.

38

7 8 9 . 1 2 3 4 5 6↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓

7 × 100 + 8 × 10 + 9 × 1 + 110 + 2

100 + 31000 + 4

10000 + 5100000 + 6

1000000

700 + 80 + 9 + .0 + .02 + .003 + .0004 + .00005 + .000006• To explain the place value system given on page 99 and page 100.• Start explaining by using simple numbers and tell them position of a digit in a number

shows its place. Th e digit 3 in 38 is placed at tens plane whereas in 398 it is at hundreds place. Tell them that places to the right of decimal point are called decimal places with tenths, hundredths, thousandths in the fi rst three decimal places. Emphasise the diff erence between ‘tens’ and ‘tenths’, ‘hundreds’ and ‘hundredths’, etc.

• Also make them notice that a zero ‘place holder is needed to in 7.06 to keep the 6 in its correct place.

• To reinforce ask the students to do the related Try � ese section.

Representation of Decimals on the Number Line• Draw a number line and explain how to place decimals on it. Explain the placement at

least till three places of decimals.0.356

0.1 0.2 0.3 0.4

• To reinforce use the section Hots question 3 given on page 113.• Ask them to do the Exercise 7.1 given on page 100.• Conversion of Decimal Numbers into the Fractions; Equivalent Decimals; Comparison

of Decimals• Conversion of fractions into decimals can be explained using example given on page 101

and conversion of decimal number into the fractions.• Use extended place value chart and examples given on page 102.• Explain equivalent decimal with the help of a square grid using page 103.• Discuss diff erence between like and unlike decimal as given on page 103 as well

conversion of one to another.• Explain comparison of decimals using place value chart on the number line given on

page 104.• To reinforce use question 2 of Life Skills section given on page 110, and question of

given the Value section given on page 111 Exercise 7.2 from the textbook.• Explain addition and subtraction of decimals use examples given on page 106 and 107.

39

• Common Error given on page 107 can be used to explain the mistakes of place value. Instruct them to do Exercise 7.3.

• To reinforce ask them to do the section values question 2 given on page 111. Hotsquestion 1 and 2 given on page 112 and Maths Lab Activity on page 112.

Use of Decimals notation in Real Life• Use of decimals in daily life can be explained by using pages 108 and 109.• Ask them to do the Exercise 7.4.• Use Let’s Revise given on page 110 to revise the concepts learnt in the chapter.Lets Recap on page 111 can be used to recapitulate important points learnt in the chapter.Testing Zone on page 113 and Multiples Choice Question on page 109 can be used to conduct a short quiz in class for revision.

40

1. Write the following decimals in the place value table. (a) 17.2 (b) 0.4 (c) 10.9 (d) 203.7

2. Write each of the following as decimals. (a) Six point one (b) Th ree hundred point twenty-three (c) Fourteen point eight (d) One hundred point zero two (e) Five hundred point two

3. Write the following decimals as fractions and reduce to lowest term. (a) 0.4 (b) 2.7 (c) 1.0 (d) 3.2 (e) 12.8 (f) 21.5

4. Write each of the following as a decimal. (a) Four hundred six and fi ve-hundredths (b) Eight and sixty-fi ve thousandths

5. Write each of the following decimals in words. (a) 0.01 (b) 1.30 (c) 107.54 (d) 10.02 (e) 0.012

6. Which is greater? (a) 0.2 or 0.3 (b) 0.079 or 0.18 (c) 1.4 or 1.40 (d) 1.321 or 1.339 (e) 3.3 or 3.300 (f) 0.07 or 0.008

7. Add the following. (a) 0.25, 3.26, 1.258 (b) 5.25, 2.35, 2.058 (c) 23.245, 125.250, 100.024

8. Subtract. (a) 4.25 from 5 (b) 7 from 9.025 (c) 111.45 from 213.5

9. Simplify. (a) 100 – 44.36 + 20.64 (b) 999.99 – 9.9

10. What should be subtracted from 500 to get 249.25?

11. Manish purchased a hockey for `1135.50 and a ball for `167.50. He gave two 1000-rupee notes to the shopkeeper. What amount did he get back?

Worksheet 1

41

1. Convert the following into decimals.

(a) 3100 (b) 7

10 (c) 54210

(d) 761000 (e) 854

1000

2. Convert the following into fractions. (a) 3.4 (b) 0.6 (c) 0.25 (d) 40.12 (e) 2.015

3. Express in rupees using decimals. (a) 6 paise (b) 60 paise (c) 15 paise (d) 615 paise (e) 40 rupees 75 paise

4. Express in metres using decimals. (a) 17 cm (b) 4 cm (c) 2 m 45 cm (d) 941 cm

5. Express in cm using decimals. (a) 4 mm (b) 33 mm (c) 125 mm (d) 6 cm 5 mm

6. Express in km using decimals. (a) 5 m (b) 50 m (c) 6666 m (d) 80 km 8 m

7. Add the following. (a) 15 + 0.632 + 13.6 (b) 25.65 + 8.006 + 8.7 (c) 0.65 + 11.425 + 2 (d) 280.69 + 25.2 + 7 (e) 27.076 + 0.35 + 0.004

8. Find the value of (a) 9.756 – 6.22 (b) 41.06 – 32.28 (c) 18.5 – 3.97 (d) 11.6 – 7.973 (e) 78.009 – 9.088 (f) 14.815 – 12.681

Worksheet 2

42

Introductory Algebra8Learning Objectives

Students will be able to understand and defi ne variables, constants and algebraic expressions. understand how to frame algebraic expressions. defi ne and explain the terms, coeffi cient, monomial, binomial, trinomial and

polynomial evaluate an algebraic expression.

Concept Building• Students are already familiar with the natural numbers, whole numbers, decimal numbers

and can apply operations on numbers and can simplify arithmetic expressions.• Read the related sections to recapitulate these concepts.

Variables; Algebraic Expressions; Algebra as Generalisation• Th is is fi rst time students are being introduced to literal numbers. Use page 115 for this.

Major mistake in this is that they may think that ‘a’ is smaller than its successor ‘b’ and ‘a’ is the smallest while ‘z’ is the greatest number. Just like is the case in whole numbers.

• You need to make them understand this that a literal number, i.e., a, b, c, x, y or z is a variable taking di� erent values depending upon the situation or problem but in a particular problem the literal number has the same value.

• For writing and framing of algebraic expressions use examples given on page 116.• Ask the students to do Exercise 8.1 given on page 117.

Operations on variables and constants• Let the cost of a pencil be ‘a’ rupees. If we buy 8 pencils or 9 pencils, the value of ‘h’ can

be found similarly. Th us 8a and 9a are like terms and can be added to get 17a. If the cost of 1 pen be ‘b’ then the cost of 5 pens is 5b. Cost of 9 pencils and 5 pens is 9a + 5b. Since ‘a’ and ‘b’ have diff erent values so the terms 9a and 5b are di� erent so they are unlike terms and hence cannot be added and their sum remains 9a + 5b. Same is the case in subtraction 4a – 2a = 2a but 4a – 2a cannot be fi nished. Th us, only like terms can be added and subtracted.

• Make sure that they understand the diff erence between like and unlike terms.

43

• Instruct them to do the Exercise 8.2.• For reinforcement use Life Skills question 1 given on page 124 and Hots given on

page 125.

Evaluating an algebraic expression• Use examples given on page 122 for teaching the concept of evaluation of an algebraic

expression.• For reinforcement of the concept learnt use the section Values given on page 124,

the section Let’s Link given on page 175, the section Hots questions 1 and 3 given on page 125 and Maths Lab Activity given on page 124.

• Use the section Let’s Revise given on page 123 for revising the concepts learnt.• For quickly revising the concepts learnt use the topic Let’s Recap given on page 124.• Use Multiple Choice Questions given on page 123 and Testing Time given on page 126

to conduct a quiz contest in the class.

44

1. Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.

(a) A pattern of letter M. (b) A pattern of letter A.

(c) A pattern of letter E. (d) A pattern of letter T.

(e) A pattern of letter B . (f) A pattern of letter N.

(g) A pattern of letter F. (h) A pattern of letter L.

2. If there are 60 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (use ‘y’ for the number of boxes).

3. � e side of a regular hexagon is denoted by ‘s’. Express the perimeter of the hexagon using ‘s’.

4. Which out of the following are expressions with number only?

(a) x + 3 (b) (7 × 15) – 7m

(c) 8 (d) 5y

(e) 6 – 2y (f) 5(35 – 8) + 11 × 2

(f) (5 × 18) – (6 × 10) – 45 + x

5. Write expressions for the following cases. (a) 5 added to x (b) 3 subtracted from y (c) y multiplied by 7 (d) y divided by 6 (e) 4 subtracted from –x (f) –y multiplied by 2 (g) –x divided by –4 (h) –y multiplied by –9

6. Write each of the following in the product form. (a) x3y2 (b) m²n³ (c) 169y4 (d) 36x7y8t9

7. Write down each of the following in the exponential form. (a) 3y² × 5y2x × 4x2 (b) 10a3b3 × 5a³b4 × 2a2b

Worksheet 1

45

1. Change the following statements using expressions into statements in ordinary language.

(a) A notebook cost ` T. A book cost ` 3T. (b) Abhay puts y marble’s on a table. He has 7y marbles in his box. (c) Our class has m students. Th e school has 25m students. (d) Raghu is t years old. His uncle is 4t years old and his aunt is (4t – 3) years old.

2. Given, Aman’s age is x years. (a) Can you guess what (x – 2) may show? (b) Can you guess what (x + 4) may show? (c) Can you guess what (5x + 4) may show?

3. Given, m students in a class like football.

(a) What may 3m show?

(b) What may m2 show?

4. Form expressions using u and 3. Use not more than one number operation. Every expression must have u in it.

5. Write each of the following phrases using numbers, literals, and the basic operations.

(a) x divided by 3 (b) Divide y by 12 (c) Th e product of m and 21 (d) s times 7 (e) Th e sum of a and b (d) subtracting l from 40

6. Change the following statements using expressions into statements in ordinary language.

(a) Our class has ‘a’ boys. Th e school has ‘14a’ girls. (b) Amal eats ‘x’ cookies. He has ‘4x’ cookies in all. (c) Th ere are y rows in a garden. Each row has 3 plants.

7. Write each of the following in the expanded form. (a) x5y3 (b) 4a2 (c) 12m3n4p5 (d) 300a5b5c5

Worksheet 2

46

Linear Equations9Learning Objectives

Students will be able to understand what is an equation. understand what is the solution (root) of the equation. solve an equation by diff erent methods such as:

(a) mentally (b) by trial and error (c) by systematic method (d) by transposition translate statements into algebraic expressions.

Concept Building• What is an equation. Use introduction section given on page 127 with the help of

examples given on this page. As an activity for introducing the concept it will be a good idea if the teacher can use a balance to demonstrate an equation, i.e., balancing. Keep some weights on the left side and ask them to balance this with the right hand side by keeping an equal amount of weight.

• Ask if one big cube is equal to 4 kg and denoted by ‘a’, then how many small cubes of wieght 250 g denoted by ‘b’ are required to balance weight on both the sides?

• Representing this as an equation we can write as a = 16 b. How many small cubes of 500 g (b) are required to balance the weight on both the sides?a = 8 b

Solving an Equation Mentally;• Use examples given on page 127.• Write a simple algebraic equation in one variable on board and ask the students to fi nd

the value of x by trial and error method. Ask them to fi nd the various values and check what value balances the equation 3x + 4 = 10.

x = 0 x = 1 x = 2 x = 3 3 × 0 + 4 = 4 3 × 1 + 4 = 7 3 × 2 + 4 = 10 3 × 3 + 4 = 13

47

Th us, x = 2 is the correct solution.• To reinforce ask the students to do the related Try � ese section from the textbook.• To graph the solution of an equation we can use a number line as given on page 129.• Use related Common Error section to avoid the mistakes while plotting graph of the

solution of an equation.• To translate a statement into an equation use examples given a page 129 and page 130.• Instruct the students to do Exercise 9.1.• To reinforce the concept learnt use Maths Lab Activity given on page 136.

Solving Equations• Before teaching systematic method write a diffi cult equation on the board. By diffi cult it

is meant that a big value so that the understand the need of systematic method to solve an equation.

• As using trial and error method becomes very time consuming. Here explain the use of four operations properly. Explain the rules for a systematic method with the help of examples given on page 131 and 132.

• To reinforce use the sections Life Skills given on page 135, Let’s Link given on page 136 and Hots given on page 137.

• Similarly, use black/whiteboard to explain the students how to solve an equation in one variable by using transposition method.

• Use the related examples from the textbook to explain the concept in a better way.• To reinforce ask them to do the related Try � ese sections given on page 133.• Instruct them to do Exercise 9.2 from the textbook.• To revise use Lets Revise section given on page 135.• For quickly revising the concepts learnt us the topic Let’s Recap given on page 136.• Use Multiple Choice Questions given on page 135 and Testing Zone given on page 137

to conduct a quiz contest in the class.

48

1. Read the given phrase and answer the following:

‘Arti’s present age is t years.’

(a) What will be her age 7 years from now?

(b) What was her age 3 years back?

(c) Arti’s grandfather is 7 times her age. What is the age of her grandfather?

(d) Grandmother is 3 years younger than grandfather. What is the age of grandmother?

(e) Arti’s father age is 8 years more than 2 and half times Arti’s age. What is her father’s age?

2. State which of the following are equations (with one variable). Give reason for your answer. Identify the variable from the equations with a variable.

(a) 13 = x + 7 (b) x – 4 > 8 (c) 82 = 4

(d) (6 × 5) – 21 = 9 (e) 4 × 6 – 18 = 2m (f) 3y2 < 7

(g) 7 = (11 × 2) + t (h) 20 = 4m (i) 13 – (10 – 7) = 2 × 5 (j) x + 14 > 25

3. Solve each of the following equations by the trial and error method.

(a) b + 5 = 21 (b) x + 3 = 17 (c) 5m = 45 (d) 19y = 57

4. Solve each of the following equations by the trial and error method.

(a) m + 9 = 72 (b) 84 – x = 200

(c) 5.5 x = 16.5 (d) 4y7 = 20

5. Ravi’s son is two times as old as his daughter. A� er 10 years, the son will be 32

times as old as his daughter. Find the present age of Ravi’s son and his daughter. ___________________________________________________________________ ___________________________________________________________________

Worksheet 1

49

1. Pick out the solution from the values given in the bracket next to each equation. Show that the other values do not satisfy the equation.

(a) 5m = 75 (5, 10, 15, 20) (b) y + 12 = 25 (9, 10, 11, 13)

(c) s – 5 = 5 (0, 5, 10, 20) (d) y2 = 8 (15, 16, 17, 18)

(e) 6a – 2 = 10 (0, 1, 2, 3) (f) t + 4 = 2 (–2, 0, 2, 4)

2. Complete the table and by inspection of the given table to � nd the solution to the equation x + 10 = 16.

x 1 2 3 4 5 6 7 8 9 10 .....x + 10

3. Solve the following equations.

(a) 2m5 + 12 = 4 (b) y + 1

2 + y – 12 = 6

(c) 23

a5 – 45

3a2 = 17 (d) 2y + 1

4 – 13 5 – y – 12 = 10

4. � e sum of three consecutive even natural numbers is 54. Find the numbers.

___________________________________________________________________

5. � e breadth of a rectangle is 6 cm less than its length. If perimeter of the rectangle is 60 cm, � nd the length and breadth of the rectangle.

___________________________________________________________________

6. Divide 60 into two parts such that one part is two times the other part.

___________________________________________________________________

7. 8 added to 9 times of a number gives 107. Find the number.

___________________________________________________________________

8. Find three consecutive multiples of 8 whose sum is 168.

___________________________________________________________________

Worksheet 2

50

Ratio, Proportion and Unitary Method

10Learning Objectives

Students will be able to compare quantities of the same type by using division. fi nd an equivalent ratio of a given ratio. understand concept of proportion by equating two ratios. apply unitary method to fi nd the value of the required number of units.

Concept Building• Students are already familiar with the concept of fractions and can apply basic operations

in real life problems.• Recapitulate these concepts with some examples.

Ratio; Proportion• To explain what is a ratio use examples given on page 138. Explain what is an equivalent

ratio, comparison of ratios and ratio in the simplest from with the help of examples and Common Error section given on page 140 and page 141.

• Ask students to do Exercise 10.1 given on page 142.• To reinforce use the sections Life Skills given on page 148 and Values questions 1 and

2 given on page 149, HOTS questions 2 and 4, Lets Link on page 150. Highlight the di� erence between a ratio and a proportion. Ratio is a tool to compare two quantities and proportion is an equality of two ratios.

• For given any three quantities, the fourth in a proportion can be easily found out. Students have to know how one element can be found from the four elements of a proportion by a relationship, i.e., product of the extremes = product of the middle terms.

• Th ey must understand that the key factor in solving word problems involving proportion is to read the problem and write the proportion correctly.

• Ask them to do the Exercise 10.2.• To reinforce the concept learnt use Maths Lab Activity given on page 149 and Let’s Link

question 1 on page 150 and question 5 Hots given on page 150.

51

Rate; Unitary method• Use examples given on page 146 and 147 to explains the concept of Rate and Unitary

method.• Instruct students to do the Exercise 10.3 from the textbook.• To revise the main points of the chapter use the section Let’s Recap given on page 149.• Use Testing Zone section given on page 150, 151 and Multiple Choice Questions given

on page 148 to conduct a quiz contest in the class.

52

1. Out of 35 students in a class, 8 like football, 15 like cricket and remaining like tennis. Find the ratio of:

(a) number of students like football to the number of students like tennis. (b) number of students like cricket to the total number of students.

2. Fill in the following blank boxes.

(a) 1020 = 4 = 30 = 2 (b) 21

27 = 36 = 7 = 72 Are these equivalent ratios?

3. Find the ratio of the following.

(a) 72 to 108 (b) 98 to 70 (c) 44 km to 120 km (d) 45 minutes to 72 minutes (e) 48 kg to 200 kg (f) `55 to `121 (g) 150 mL to 350 mL (h) 7.5 to 22.5

4. Compare the following ratios. (a) 2 : 3 and 6 : 5 (b) 1 : 3 and 1 : 4 (c) 4 : 5 and 5 : 4 (d) 12 : 14 and 5 : 6 (e) 3 : 7 and 2 : 8 (f) 4 : 20 and 8 : 24

5. Divide 40 pens between Sony and Reena in the ratio of 3 : 2.

___________________________________________________________________

6. Present age of a father is 42 years and that of his son is 14 years. Find the ratio of (a) present age of father to the age of son. (b) age of the father to the age of son, when son was 12 years old. (c) age of father aft er 10 years to the age of son aft er 10 years. (d) age of father to the age of son when father was 30 years old.

7. Find the third proportional to 8, 12. ___________________________________________________________________

8. Find the mean proportional between 5 and 20. ___________________________________________________________________

Worksheet 1

53

1. Determine if the following are in proportion.

(a) 15, 45, 40, 120 (b) 33, 121, 9, 96 (c) 24, 28, 36, 48

(d) 4, 6, 8, 12 (f) 33, 44, 75, 100 (g) 32, 48, 70, 210

2. Write True (T) or False (F) against each of the following statements:

(a) 12 : 18 : : 28 : 12 ______ (b) 6 : 21 : : 10 : 35 ______

(c) 16 : 20 : : 24 : 30 ______ (d) 8 : 24 : : 9 : 27 ______

(e) 5.2 : 3. 9 : : 3 : 4 ______ (f) 0.9 : 0.36 : : 10 : 4 ______

3. Find the value of x in each of the following proportions.

(a) 6 : 5 : : 48 : x (b) x : 3 : : 4 : 4

4. Find the value of x so that the given four numbers are in proportion.

(a) 8, x, 24 and 15 (b) 18, 6, 27 and x

5. Find the mean proportional between:

(a) 25 and 36 (b) 0.16 and 0.49

6. Find the fourth proportional to:

(a) 5, 15, 25 (b) 3.5, 1.4, 7

7. If the cost of 7 cans of juice is `210, what will be the cost of 4 such cans of juice?

___________________________________________________________________

8. If the cost of a dozen of biscuit packets is `153.60, what will be the cost of 15 such packets?

___________________________________________________________________

9. Manish made 42 runs in 7 overs and Swarup made 63 runs in 9 overs. Who made more runs per over?

___________________________________________________________________

Worksheet 2

54

General Instructions: (i) All questions are compulsory. (ii) Th e question paper consists of 29 questions divided into four sections A, B,C and D. Section A consists of 8 questions of 1 mark each. Section B consists of 6 questions of 2 marks each. Section C consists of 10 questions of 3 marks each. Section D consists of 5 questions of 4 marks each. (iii) Th ere is no overall choice. However an internal choice has been provided in some

questions. Attempt only one options in such questions.

SECTION - A 1. Write opposite of loss of `125.

2. Represent 127 in the form of mixed fraction.

3. If 7a = 28, then fi nd the value of ‘a’. 4. Write the 3.45 in words. 5. Find the ratio of 50 to 150. 6. Using divisibility test, check whether 526592 is divisible by 11 or not. 7. Write 265,302,229 in words. 8. Represent 4 + 3 on the number line.

SECTION - B

9. Write the following as decimal. 5 + 310 + 6

100 10. Convert DCCLXXVI into Hindu-Arabic numeral.

11. Find the equivalent fraction of 3545 having the numerator 7.

12. Solve. 69 – 37 13. Write all integers between –5 and 5. 14. Express in litres using decimals: 3 L 60 mL.

MathematicsModel Test Paper 1

Time: 2½ hoursClass 6

Total Marks: 70

55

SECTION - C 15. Find the greatest number of 5-digits exactly divisible by 6, 12 and 30.16. Find the sum of 4 + 6.205 + 35.2517. Find all possible 3-digit numbers using all the digits 3, 0 and 4. Given, repetition of

digits is that allowed.18. Subtract the sum of 2.35 and 4.15 from the sum of 5.75 and 2.25.19. Check whether 12, 10, 6 and 5 are in proportion or not?

20. Suresh works for 35 of an hour, while Rakesh works for 78 of an hour. Find who works

for a longer time? 21. Find the HCF of 24, 36, 54 and 60 using division method. 22. Using distributive property to simplify the following.

(a) 1545 × 1545 + 1545 × 455 (b) 98 × 49 23. Write the following fractions in ascending and descending order.

35, 4

10, 75, 234, 54

24. Write expressions for the following statements. (a) 15 more than a. (b) 6 subtracted from the product of b and 3. (c) 4 added to the product of 4 and x.

SECTION - D 25. A student multiplied 1278 by 85 instead of multiplying by 58. By how much was his/

her answer greater than the correct answer?26. A bike consumed 12 litres of petrol in going from town P to town Q and another

10 litres of petrol in going from town Q to town R. If the petrol cost `62 per litre, fi nd the total amount spent on petrol.

27. Determine the longest tape which can be used to measure exactly the lengths 4 m, 2 m 20 cm and 8 m 60 cm.

28. Anvar travelled 20 km 250 m by train, 2 km 500 m by bus and 200 m on foot in order to reach his home from the o� ce. Find how far is the o� ce from his house.

29. State whether the following statements are true (T) or false (F). (a) 6 : 15 : : 50 : 125 (b) HCF × LCM = Product of the given numbers (c) –2 is less than –7. (d) 0 is the smallest positive integer.

56

Basic Geometrical Ideas11Learning Objectives

Students will be able to understand what is a point, line, line segment, plane. know the incidence properties in a plane. know about intersecting lines, parallel lines and perpendicular lines. illustrate the interior and exterior of an angle. measure line segments. compare line segments by observation, by tracing, using ruler and divider. measure a given angle. classify angles as acute, obtuse, right, straight, refl ex, zero and complete angle. defi ne curves and diff erentiate between open and closed curves.

Concept Building• Students are already familiar with the concept of point, line, line segment, angle, etc.• Explain the measuring of geometry, “geo-metric’, ‘measurement of earth’ and the use of

geometry to defi ne point, line, plane, etc.

Basic Geometrical Terms; Intersecting and Parallel Lines• To start by explaining point, line, line segment, ray and plane given on page 156. Do

the following activity. Draw a point in the board and ask students to measure its length, breadth and height. Now, tell them a point has no length, breadth and height.

• To explain diff erence between line, line segment and ray call any 6 students and make them stand, two each on the three points marked on the fl oor.

• Now, ask the two standing at the point A to walk in the opposite direction as much distance as they want. Now explains the concept of a line and that if has no defi nite length.

• Now its the turn of the students at the point B. Ask one of them to move same distance in any direction but a fi xed distance as 8 steps and the other keeps standing their. Join these points and now measure the distance between them. Th is is a line segment. As line segment has a fi xed

AB

C

A1 A2

57

length and two end points. Standing student represents initial point and the student who moved represents the terminal point.

• Now third, pair of students one keeps standing at the point C and the other moves in the any direction. Now explain them the concept of a ray and that of has one fi xed end, no fi xed length.

• To teach incidence properties in a plane mark a point on the fl oor and ask a group of students to gather at this point. Now direct them to move in di� erent directions or two each forming a pair in directions opposite to each other.

D2

A2

B2

C2

D1

C1

B1

A1

E1

E2

• Now, explain the concept an infi nite number of lines can be drawn passing through a given point.

• Draw two points on the black/white board.• Now, ask the class how many lines can be drawn joining these two points. Here, the

answer is 1.• Exactly one line can be drawn passing through two diff erent points in a plane.• Ask each student to raise his/her hand straight above and give them the idea of

parallel lines.• Now, ask them to cross there hands. Th is represent intersecting lines. Two

intersecting lines have one point in common.• Explain collinear points, concurrent lines given on page 158.• Use related examples given in the textbook to make them the concept in a better way.• Ask them to do Exercise 11.1.

Angles; Comparing Line Segments; Measurement of Line Segments• To introduce angles stand in front of the class and keep one hand on top of the other.

Now start moving one hand keeping the units sticking to each other, i.e., in the same position. Now introduce the concept of an angle and tell them that angle is the amount of rotation between two rays of at the initial point.

• Next draw an angle and mark some points on its arms, some inside and some outside.

58

Explain interior of an angle, exterior of the angle by using the concept given on page 160 from the book.

• Ask the students to do Exercise 11.2.• Demonstrate how to compare two line segments.• Use Divider and ruler and demonstrate how to measure the length of a line segment.• Instruct them to do Exercise 11.3.

Measuring angles• To explain what is the magnitude of an angle and how to measure an angle using

protractor use page 164.• To introduce right angle, straight angle, acute angle, etc. use some realistic examples. For

example, we can use hands of the clock.• Defi ne the related terms of topic from the textbook.• Ask them to do Exercise 11.4.• To reinforce ask the students to do related Try � ese section, Life Skills question 2,

Values give on page 168, Maths Lab Activity given on page 169 and Lets Link given on page 170.

Curves• To introduce curves ask each students to take a slip of paper and draw anything without

lift ing these slips and display on the board as you will get variety of results, for example as shown.

• Now explain straight and curved lines, open and closed curves, simple curve, polygons, etc.

• Draw a closed curve. Mark some points inside, some outside and some on the curve. Explain interior and exterior of a curve.

• Ask them to do Exercise 11.5.To revise the concepts learnt uses the section Let’s Revise given on the page 167.For recapitulation of the important points use Let’s Recap section given on page 168.For assessment of the concepts learnt use Multiple Choice Question given on page 167 and Testing Zone given on page 170.

59

1. Draw a rough � gure and label suitably in each of the following cases: (a) Point M lies on PQ . (b) XY and PQ intersect at T. (c) Line l contains E and F but not G. (d) OP and OQ meet at O.

2. Draw the rough diagrams to illustrate the following (a) Open curve (b) Closed curve

3. Draw a polygon and shade its interior.

4. Illustrate, if possible, each of the following with a rough diagram. (a) A closed curve that is not a polygon. (b) A polygon with two sides.

5. Fill in the blanks. (a) If there is a point common to two lines drawn, we say that the two lines ________

at the common point. (b) When three or more lines in a plane are passing through a point, then lines are

called __________________. (c) Th ree or more points in a plane are said to be _________, if they all lie on the

same line. (d) Two lines in a plane either intersect at exactly one point or are ________.

6. From your surroundings give the examples of: (a) concurrent lines (b) intersecting lines (c) parallel lines (d) an obtuse angle

7. Classify the following curves as open or closed. (a) (b) (c)

(d) (e)

Worksheet 1

60

1. Draw rough diagrams of two angles such that they have (a) one point in common. (b) two points in common. (c) three points in common. (d) four points in common. (e) one ray in common.

2. Classify the following angles as acute, straight, right obtuse, re� ex, zero and complete angles.

(a) 103° (b) 68° (c) 175° (d) 210° (e) 360°

(f) 90° (g) 0° (h) 91° (i) 180° (j) 71°

(k) 358° (l) 180.5°

3. In the given � gure name

(a) three line segments

N

B

AD

E M

F

(b) three rays

4. State which of the following statements are true (T) or false (F). (a) Th e sum of angles around a point is 360°. (b) An acute angle is always less than 90° and greater than 0°. (c) An obtuse angle is always greater than 90° and less than 180°. (d) An angle whose measure is equal to 90° is called a straight angle. (e) An angle whose measure is equal to 0° is called a complete angle. (f) An angle greater than 180° and less than 360° is called a refl ex angle. (g) A line is a set of all points which have length only, i.e., no breadth, no height.

Worksheet 2

61

Understanding Elementary Shapes

12Learning Objectives

Students will be able to identify polygons. classify polygons on the basis of its sides. name six parts of a triangle, i.e., 3 sides and 3 angles. classify triangles by considering the lengths of their sides and measure of their

angles. understand medians and altitudes of a triangle. learn various terms of quadrilaterals. classify quadrilaterals as square, rectangle, parallelogram, etc. illustrate the interior and exterior of a triangle and quadrilateral. identify and defi ne a circle and its parts; interior and exterior of a circle.

Concept Building• Students are already familiar with the concepts of angles plans fi gures such as triangle,

square, rectangle, circle.• Recapitulate these concepts with the help of some examples.

Polygons; Types of Polygons• Recap open and closed curve and inform them that a simple closed curve bounded by

three or more line segments is called a polygon. Discuss this sides, vertices and diagonal from the related sections.

• Instruct students to do Exercise 12.1.• Distribute some ice cream sticks, or straws or match sticks and ask them to make

polygons.• Now pick up each polygon and discuss its sides, vertices and diagonals. Also discuss

convex and concave polygons.• Instruct them to do Exercise 12.2.• For reinforcement ask them to do the Values section from the textbook.

62

Triangle• Defi ne triangle is a polygon made with three line segments. Ask students to make triangles

with match sticks. Discuss its sides, vertices angles, interior and exterior triangle.• Defi ne altitude and median of triangle.• Instruct the students to do the Exercise 12.3 given on page 176.

Classi� cation of Triangles• Discuss classifi cation of a triangle on the basis of its sides and angles.• Ask students to do the Exercise 12.4.• To reinforce ask them to do the sections Hots questions 1 and Maths Lab Activity given

on page 188.

Quadrilaterals• From the polygons that students have made pick up the polygon with 4-sides and classify

them as quadrilateral.• Discuss its sides angles, diagonals adjacent and opposite angles convex and concave

quadrilateral.• Ask them to do Exercise 12.5.

Types of Quadrilaterals• Draw a quadrilateral on the board and discuss the classifi cation as a rectangle square,

trapezium, etc.• Use examples given in the related section to make them understand the concept in a

better way.• To reinforce ask them to do the sections Let’s Link given on page 188 and HOTS Q3. • Instruct them to do Exercise 12.6 from the textbook.

Circle• Introduce circle and its parts with the help of activity given on page 183.• Defi ne the terms related to the topic.• Use Remember section to point out the important facts related to the topic.• Defi ne concentric circles, arc, segment and sections.• To reinforce ask them to do the related Try Th ese section and Exercise 12.7 from the

textbook.• To revise the concepts learnt do the section Lets Revise given on page 186.• To recapitulate the main points of the chapter use Lets Recap section given on page 187.• Use Multiple Choice Questions given on page 186 and Testing Zone section given on

page 187 and conduct a quiz contest in the class.

63

1. Observe the given � gure and

(a) identify three triangles on the fi gure.

(b) write the names of seven angles.

(c) write the names of six parts of triangle ABC.

(d) which of the two triangles have ∠B as common.

2. Draw a rough sketch of a quadrilateral PQRS. State

(a) two pairs of opposite sides.

(b) two pairs of opposite angles.

(c) two pairs of adjacent sides.

(d) two pair of adjacent angles.

3. Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them. Is the meeting pint of the diagonals in the interior or exterior of the quadrilateral.

___________________________________________________________________ ___________________________________________________________________

4. State whether the following statements are true (T) or false (F). (a) A triangle having all three sides equal is called an equilateral triangle. (b) Th e sum of angles of a triangle is 360°. (c) Th e line segments joining the opposite vertices of a quadrilateral are called its

diagonals. (d) If a line segment joining any two points in the interior of a quadrilateral does not

lie completely within it, then it is a convex quadrilateral, otherwise it is a concave quadrilateral.

(e) A parallelogram whose all sides are equal is called a rhombus. (f) A quadrilateral in which the pair of opposite sides are parallel, is called a

trapezium. (g) Th e perimeter of a circle is known as the diameter. (h) Two or more circles are said to be concentric, if they have the same centre.

A

B C

D

Worksheet 1

64

1. From the � gure, identify. (a) centre of the circle (b) three radii (c) a diameter (d) a chord (e) two points in the interior (f) a point in the exterior (g) a sector (h) a segment

2. Write yes (Y) or no (N) to answer the following questions. (a) Is every diameter of a circle is also a chord? (b) Is every chord of a circle is also a diameter?

3. State whether the following statements are true (T) or false (F). (a) Two diameters of a circle will necessarily intersect. (b) Th e centre of a circle is always in its interior.

4. Draw a circle and mark (a) Its centre (b) a radius (c) a diameter (d) a minor sector (e) a major segment (f) an arc (g) a point in its interior (h) a point in its exterior

5. Fill in the blanks.

(a) If the two sides of a polygon have a common end point, then these sides are called _______ sides of the polygon.

(b) A polygon is said to be ________ if sides are not equal and angles are not equal.

(c) Th e point of intersection of three altitudes of a triangle is called ________.

(d) Th e point of intersection of the three medians is G, which is known as ________.

(e) A triangle having any two sides equal is called an ________ triangle.

M

B

A

O

C

ND H

LT

Worksheet 2

65

UnderstandingThree-Dimensional Shapes

13Learning Objectives

Students will be able to describe diff erent 3D shapes, such as cuboid, cube, cylinder, sphere, cone, prism and

pyramid. describe diff erent elements, i.e., faces, edges and vertices of 3D shapes. identify and draw nets for cube, cuboid, cylinder, cone and tetrahedron.

Concept Building• Students are already familiar with the concept of plane fi gures.• Recapitulate these concepts with the help of some examples.

Types of 3D Shapes(Prisms, Pyramids, Solids with Curved Surfaces)• Introduce and explain with examples the basics of three-dimensional shapes.• Ask the students to identify the edges, faces and vertices of a solid.• Instruct them to collect some three-dimensional shapes from their surroundings.• From the collected objects, separate classify the diff erent objects.• Group the objects with similar shapes, and introduce then name as cuboid, cube, cylinder,

cone, sphere, prism and pyramid.• Ask the students to fi nd number of vertices, faces and edges of the solids of diff erent

shapes.• Introduce students with diff erent type of prism and pyramid based on their shape of

base.• Defi ne types of prisms and pyramids on the basis of their properties.• To reinforce ask the students to do the sections Life Skills and Maths Lab Activity

section from the textbook.• Ask the students to do the sections Try � ese and Exercise 13.1 from the textbook.

Nets• Take any box having a shape of cube or cuboid and made up of same hard paper. • Cut it along the edges as required and open the box.

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• Ask the students to observe the fl at surface so obtained.• Introduce in this way the net of the solid so obtained.• Also show them by folding diff erent segments of the fl at surface thus we can obtain the

solid again. • In this way, student will be able to draw the net of any solid.• Th us, by cutting and posting the required solid can be obtained.• To reinforce ask the students to do the Maths Lab Activity section from the textbook.• Instruct the students to do the Exercise 13.2 from the textbook.To revise the concepts learnt in the chapter students should do Let’s Revise, Values and HOTS sections from the textbook.Use Multiple Choice questions and Testing Zone sections to conduct a quiz contest in the class. Use the section Let’s Recap to revise the key points of the concepts.

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1. A cube looks like a square box. Draw a cube and labeled it. Also, name its each faces, vertices and edges.

2. For a cuboid � ll in blanks given below.

(a) It has _____________faces.

(b) Each face has _____ edges.

(c) Each face has _____ vertices.

(d) It has _____ edges.

(e) It has _____ vertices.

3. A triangular pyramid has a triangle as its base. It is also known as tetrahedron. Now answer the following.

(a) How many faces does a tetrahedron has?

(b) How many edges does a tetrahedron has?

(c) How many vertices does a tetrahedron has?

4. A square pyramid has a square as its base. Now answer the following.

(a) How many faces does a square pyramid has?

(b) How many edges does a square pyramid has?

(c) How many vertices does a square pyramid has?

5. A triangular prism looks like the shape of a kaleidoscope. It has triangle as its base.

(a) How many faces does a kaleidoscope has?

(b) How many edges does a kaleidoscope has?

(c) How many vertices does a kaleidoscope has?

Worksheet 1

68

1. Match the following:

(a) (i)

(b) (ii)

(c) (iii)

(d) (iv)

(e) (v)

(f) (vi)

2. Draw the nets of cube and cuboid in the space given below:

Worksheet 2

69

Constructions14Learning Objectives

Students will be able to construct circles of given radius using compasses. construct a line segment of the given length. construct the copy (congruent) of a given line segment. construct perpendicular to a line, through a point on it (using scale and compasses). construct perpendicular to a line, through a point not on it. construct perpendicular bisector of a line segment. construct di� erent angles, their bisectors. construct copy (congruent) of a given angle.

Concept Building• Students are already familiar with basic geometrical tools.• Read the Basic Geometrical Tools section to recapitulate these concepts.• Introduce students the basic geometrical tools such as ruler, divider, compasses,

protractor, set squares and their functions.

Construction of a line segment• Discuss the process of measuring the line segments by using ruler as well as by divider.• Ask students to draw a line segment of any measure, then measure its length by using

ruler and divider.• Explain the process of constructing a line segment by using ruler and a pair of compasses.• Now, construct two line segments PQ and RS of any length. Th en, draw a ray MN longer

than the total length of PQ and RS. Using compasses, measure and cut off MC = PQ and CT = RS along MN, i.e., MT = MC + CT = PQ + RS.

• Similarly, ask them to draw a line segment of measure MG = PQ - RS• Ask the students to do the Exercise 14.1 from the textbook.

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Perpendicular Lines; Construction of Perpendicular Lines; Drawing Perpendicular Bisector of a Given line segment• Explain the process of constructing perpendicular on a given line segment at a point on

it by using ruler and set squares as well as by using ruler and compasses. • Demonstrate how to construct a perpendicular on a given line segment from a point

outside it by using ruler and set squares as well as by using ruler and compasses.• Also, demonstrate how draw a perpendicular bisector of a line segment• Instruct the students to do the Exercise 14.2 from the textbook.

Construction of circle; Construction of angles using set squares• Bring some circular objects to the class.• Demonstrate how to draw a circle using these objects.• Now provide each student a circular object or ask them to fi nd any circular object from

their surrounding in the class and draw a circle on a sheet of paper.• Now, demonstrate how to draw a circle using ruler and compasses.• Explain the process of construction of ‘angles’ by using set squares, by using protractor

and by using ruler and a pair of compasses.• Also, discuss the process of drawing angle bisector of a given angle.• For example, fi rst draw an angle of 50°, then using ruler and compasses draw the bisector

of the angle. • Use the examples given in the textbook to explain the process and strengthen the concepts

to the students.• Instruct the students to do the Exercise 14.3 from the textbook.• To reinforce ask the students to do the Maths Lab Activity and Values sections from the

textbook.• To revise the concepts learnt in the chapter students should do Let’ Revise, Let’s Link

and HOTS sections from the textbook.Use Multiple Choice questions and Testing Zone sections to conduct a quiz contest in the class. Use Let’s Recap section to revise the key points of the concepts.

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1. Draw a line segment of length 7.5 cm by using a ruler.

2. Construct a line segment AB of length 6.5 cm. From this, cut AC of length 4.3 cm. Measure the length of BC.

3. Given, AB of length 7.4 cm and CD of length 4.1 cm. Construct a line segment XY such that the length of XY is equal to the di� erence of the lengths of AB and CD. Verify the length of XY by measuring it using ruler.

4. Draw any line segment PQ. Take any point R on it. � rough R, draw perpendicular to PQ. (Use ruler and set squares).

5. Draw the perpendicular bisector of XY whose length is 10.2 cm.

(a) Take any point N on the bisector drawn. Examine whether NX = NY.

(b) If M is the mid-point XY, what can you say about the lengths of MX and XY?

6. Draw a line segment of length 12.4 cm. Using compasses, divide it into four equal parts. Verify the each length by actual measurement.

7. Construct angles of the following measures using ruler and protractor.

(a) 44° (b) 70° (c) 121° (d) 139°

8. Construct angles of the following measures using ruler and compasses.

(a) 60° (b) 22.5° (c) 150° (d) 180°

9. Draw an angle of measure 110° and bisect it. Also, � nd the measure of each angle.

10. Construct the circles with the following radii.

(a) 5 cm (b) 7 cm (c) 5.5 cm (d) 8.2 cm

Worksheet 1

72

1. Draw an angle of measure 153° by using protractor. Also, construct its bisector.

2. Using set squares construct the following angles.

(a) 30° (b) 60° (c) 45° (d) 150°

3. Construct angles of the following measures using ruler and compasses.

(a) 60° (b) 30° (c) 90° (d) 75°

(e) 120° (f) 150° (g) 135° (h) 45°

4. Draw an angle of measure 45° and bisect it.

5. Draw an angle of measure 50°. Make a copy of it using only a straight edge and compasses.

6. Draw a circle of radius 4.5 cm.

7. Draw a circle and any two of its diameters.

If we join the end points of these diameters, what is the fi gure so obtained?

What fi gure is obtained if the diameters are perpendicular to each other?

How do we check our answer?

8. Given XY of length 6 cm and MN of length 3.5 cm. Construct a line segment PQ such that the length of PQ is equal to the sum of the lengths of XY and MN. Verify the length of PQ by measuring it using ruler.

9. An angle PQR is given, whose measure is not known. Construct another angle ABC such that its measure is twice that of angle PQR.

Worksheet 2

73

Symmetry15Learning Objectives

Students will be able to understand the meaning of symmetry. fi nd out whether the given objects are symmetrical or asymmetrical. understand the meaning of line symmetry and axis of symmetry. know and see symmetry with respect to a line, in objects used in day-to-day life,

alphabets, architecture, nature, geometrical fi gures and numerals. know about fi gures with one or more lines of symmetry and draw line(s) of

symmetry. understand refl ection (mirror image) and complete the given half fi gure using the

concept of refl ection.

Concept Building• Students are already familiar with symmetrical and asymmetrical objects.• Bring some pictures of symmetrical objects in the class.• Show these pictures one by one to the class and ask if these are symmetrical or not.• Read the Introduction section to recapitulate these concepts.

Line of symmetry (Mirror Re� ection, Symmetry in Geometrical Figures, Symmetry in Regular Polygons)• Read the related section from the textbook. • Defi ne a fi gure which is identical on both the sides of a line, is said to be symmetrical

about the line.• When a symmetrical object is folded along the line of symmetry, the two parts

superimpose, i.e., fall on one another exactly.• Draw an isosceles triangle on the board. Demonstrate how to draw line of symmetry of

this triangle. • Ask them to fi nd some other examples of fi gures having exactly one line of symmetry.• For this the teacher can give examples of some letters of English alphabet.• Use the Activity given on page number 213 to explain the concept of mirror refl ection.

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• Use the Remember section to point out the important facts related to the topic.• Use the Common Error section to avoid the common mistakes done by the students

while performing to draw lines of symmetry of a given shape.• Defi ne the concepts of symmetry in regular and irregular polygons.• To reinforce ask the students to do the related Try � ese, Life Skills, Values and

Exercise 15.1 sections from the textbook.

Creating Symmetrical Figures• Read the related sections from the textbook. • Demonstrate how they create symmetrical fi gures using water colours or graph papers.• To reinforce ask the students to do the related Try � ese section from the textbook.• To reinforce ask the students to do the Maths Lab Activity section from the textbook.• Ask the students to do Exercise 15.2 from the textbook.To revise the concepts learnt in the chapter students should do Let’s Revise and HOTSsections from the textbook.Use Multiple Choice Questions and Testing Zone sections to conduct a quiz contest in the class. Use Let’s Recap section to revise the key points of the concepts.

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1. List any four symmetrical objects that you seen from your home or school.

2. Draw a triangle which has

(a) exactly one line of symmetry.

(b) exactly three lines of symmetry.

(c) no line of symmetry.

3. On a squared paper. Sketch the following:

(a) A triangle with a horizontal line of symmetry but no vertical line of symmetry

(b) A quadrilateral with both horizontal and vertical lines of symmetry.

(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.

(d) A hexagon with exactly two lines of symmetry.

(e) A hexagon with six lines of symmetry.

4. Draw all possible lines of symmetry in each of the following symmetrical shapes.

(a) (b) (c)

(d) (e) (f)

(g) (h)

Worksheet 1

76

1. Draw the line of symmetry in each of the following letters.

C F H GK P T Z

Also, name the letters which do not have any line of symmetry.

2. State whether the following statements are True or False.

(a) A square has two lines of symmetry. ___________

(b) A rectangle has two lines of symmetry. ___________

(c) An isosceles trapezium has one line of symmetry. ___________

(d) An equilateral triangle has no lines of symmetry. ___________

(e) Every diameter of a circle is a line of symmetry for the circle. ___________

(e) A rhombus has two lines of symmetry. ___________

(f) A line segment has two lines of symmetry, its perpendicular ___________ bisector and the line segment itself.

(g) An angle has one line of symmetry, which is its bisector. ___________

3. Draw all possible lines of symmetry in each of the following shapes if possible.

(a) (b) (c)

(d) (e) (f)

Worksheet 2

77

Perimeter and Area of Plane Figures

16Learning Objectives

Students will be able to understand the concept of simple closed fi gures with their applications in daily life. derive the formula of the perimeter of a rectangle, square and other regular fi gures. calculate the area using a graph paper and a squared paper. calculate the area of a rectangle and a square using a formula. apply the knowledge of area in daily life.

Concept Building• Students are already familiar with the concept of plane fi gures, perimeter and area.• Give some examples and recapitulate these concepts.• Explain the concept of curve and its diff erent shape such as open curve, closed curve,

simple curve, simple closed curve, etc.• Draw some examples of these curves on the blackboard. • Now ask the students to identify the types of curve as asked by your from the blackboard.

Perimeter• Bring a string, ruler, meter scale, tape, etc. to the class.• Demonstrate how to fi nd perimeter of an object.• Defi ne the perimeter of a plane fi gure is the measure of length of its boundary.• Develop the formulae for calculating the perimeter of the fi gures like rectangle, square,

triangle and equilateral triangle. • Draw their attention to the fact that to fi nd the perimeter of a plane fi gure (with/without

formulae) fi rst convert all the sides of the plane fi gure into the same unit.• Use the Remember section to point out the important facts related to the topics.• Use examples given in the textbook to make them understand the concept in a better

way.• To reinforce ask the students to do the Exercise 16.1, Exercise 16.2 and Exercise 16.3

from the textbook.

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Area; Finding Area Using a Graph Paper; Area of a Rectangle; Area of a Square• Go through the related section from the textbook.• Explain the meaning of area by using some real life examples.• Defi ne area is the amount of surface enclosed between the boundary of a plane fi gure.• Recognise students the diff erent units of area such as cm², m², dm², etc.• Bring squared sheet to the class and distribute at least sheet to each student.• Ask the students to draw any plane fi gures on their sheets.• Explain the rules associated with the concept of fi nding area of plane fi gures (regular or

irregular) using squared sheet paper.• Use the related examples given in the textbook to make them understand the concept.• Develop the formulae for calculating the area of the fi gures like rectangle and square. • Write the formulae for calculating the area of a square and a rectangle.• Ask the students to observe the interrelation between the diff erent units of area.• Use examples given in the textbook to make them understand the concept in a better

way.• To reinforce ask the students to do the Exercise 16.4 and Exercise 16.5 from the textbook.To revise the concepts learnt in the chapter students should do the Let’s Revise, Life Skills, Values, Let’s Link, Maths Lab Activity and Hots sections from the textbook.Use Multiple Choice Questions and Testing Zone sections to conduct a quiz contest in the class. Use Let’s Recap section to revise the key points of the concepts

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1. Measure and write the lengths of the four sides of a page of your notebook. � e sum of the lengths of the four sides

= PQ + QR + RS + SP

= ____ cm + ____ cm + ____ cm + ____ cm = ____ cm

What is the perimeter of the page?

2. Find the perimeter of the following � gures:

(a) Perimeter = AB + BC + CD + DA = ____ + ____ + ____ + ____ = ____

A 40 cm

40 cm

10 cm10 cm

D

B

C

(b) Perimeter = AB + BC + CD + DA = ____ + ____ + ____ + ____ = ____

A6 cm

6 cm

6 cm6 cm

D

B

C

3. A piece of wire is 108 cm long. What will be the length of each side if the wire is used to form

(a) a square (b) an equilateral triangle (c) a regular hexagon

4. Find the perimeters of the rectangles whose lengths and breadths are given below. (a) 5 cm, 3 cm (b) 8.1 cm, 6.2 cm (c) 13 m, 9.5 m

5. Find the perimeters of the squares whose sides are given below. (a) 7 cm (b) 4.5 cm (c) 60.5 m

6. Each side of a square � eld is 25 m. Find the (a) perimeter of the square fi eld. (b) cost of fencing the fi eld at the rate of `25 per metre.

Worksheet 1

80

1. Find the perimeter of the following � gures:

(a) Perimeter = AB + BC + CD + DE + EF + FG + GH + HA

= ____ + ____ + ____ + ____ + ____ + ____ + ____ + ____ = ____

(b) Perimeter = AB + BC + CD + DE + EF + FA

= ____ + ____ + ____ + ____ + ____ + ____ = ____

2. Find the perimeter of a rectangle whose length and breadth are 120 cm and 1 m respectively.

3. Find the perimeter of a regular pentagon with each side measuring 7 cm. 4. Rani runs around a square � eld of side 75 m. Tony runs around a rectangular

� eld with length 160 m and breadth 105 m. Who covers more distance and by how much?

5. Find the area of a square plot of side 12 m. 6. � e area of a rectangular piece of cardboard is 91 sq. cm and its length is 13 cm.

What is the width of the cardboard? 7. Subodh wants to cover the � oor of a room 6 m wide and 8 m long with square

tiles. If length of each tile is of 0.5 m, then � nd the number of tiles required to cover the � oor of the room.

8. Find the area of each shaded region. Given, each square is of 1 sq. cm. (a) (b) (c)

Worksheet 2

81

Data Handling17Learning Objectives

Students will be able to understand the meaning of data. collect data through various sources. organise the given data. represent data in tabular form using tally marks. interpret the given pictograph. represent given data using pictograph. interpret the given bar graph. represent the data using bar graph.

Concept Building• Students are already familiar with the concept data and representation of data.• Give some examples and recapitulate these concepts.

Data; Organisation of Data; Tally Marks• Discuss the need and fi eld of data handling in real life.• Defi ne the information in numerical facts are called data. • Discuss the process of collection and representation of data.• Explain the data can be arranged in serial order, ascending order and descending order.• Ask students to collect data of age, qualifi cation of his/her family member and to

represent in ascending or descending order.• Explain the process of constructing the frequency distribution table.• Introduce tally marks, frequency etc.• Use examples given in the textbook to make them understand the concept in a better

way.• Instruct them to do Exercise 17.1 from the textbook.

Pictograph; Reading and Interpreting a pictograph; Drawing a pictograph• Bring a pictograph in the class.

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• Discuss with class how to read and interpret the graph.• Now ask some questions based on the graph one by one to the class.• Now provide a chart to each student and ask each student to make same cut-outs on their

own choices related to the pictograph.• Take information about the choices of favourite subjects of the students and write it on

the board.• Demonstrate how to draw a pictograph for the information recorded on the board.• Use the examples given in the textbook to make them understand these concepts.• For more practice ask the students to do Exercise 17.2 from the textbook.

Bar Graph; Interpreting a bar graph; Drawing a bar graph• Say the students that bar graph is another way of representation of data. We can read

(interpret) the bar graph to get information also based on the information (data) we can construct the bar graph.

• Demonstrate how to draw a bar graph for the pictograph they have already made.• Clarify to them that a bar graph can be horizontal or vertical.• Draw their attention to the fact that do not forget to label both the axis of the graph and

writing title of the bar graph.• Use examples given in the textbook to make the students better understand the concept

of interpreting and drawing a bar graph.• To reinforce ask the students to do the Values section from the textbook.• Instruct the students to do Exercise 17.3 from the textbook.To revise the concepts learnt in the chapter students should do Let’s Revise, Let’s Link, Hots and Maths Lab Activity sections from the textbook.Use Multiple Choice Questions and Testing Zone sections to conduct a quiz contest in the class. Use Let’s Recap section to revise the key points of the concepts.

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1. In a mathematics test, the following marks were obtained by 40 students. Arrange these marks in a table by using tally marks.

7 2 4 7 5 5 5 4 4 2 6 96 4 8 2 6 6 1 8 8 5 8 43 9 10 6 8 6 7 4 5 6 9 75 5 6 7

(a) Find how many students scored marks equal to or more than 7. (b) How many students scored marks less than 4? 2. Following are the choice of ice cream � avours of 30 students of Class VI. Vanilla, Kesar Pista, Mango, Chocolate, Chocolate, Ladoo, Kesar Pista, Mango,

Orange, Chocolate, Mango, Vanilla, Vanilla, Chocolate, Mango, Kesar Pista, Vanilla, Chocolate, Mango, Orange, Orange, Kesar Pista, Chocolate, Kesar Pista, Vanilla, Mango, Mango, Chocolate, Vanilla, Kesar Pista, Vanilla, Vanilla.

(a) Arrange the names of ice creams in a table using tally marks. (b) Which ice cream is liked by the most number of students?

3. � e pictograph given below shows the number of milk bottles sold each day in a dairy. Use the information from the graph and answer the following.

Milk bottles soldDay Number of milk bottles

Monday

Tuesday

Wednesday

Th ursday

Friday

Key: = 500 milk bottles Now answer the following questions. (a) Which of the two days the dairy sold minimum number of milk bottles? (b) How many more bottles of milk were sold on Friday than Th ursday?

Worksheet 1

84

1. Total number of animals in � ve villages are as follows:

Village A Village B Village C Village D Village E90 130 100 50 70

Prepare a pictograph of these animals using the symbol (∆) to represent 10 animals and answer the following questions.

(a) How many symbols represent animals of village E? (b) Which village has the maximum number of animals? (c) Which village has more animals: Village A or Village C? 2. Total number of students of a school in di� erent years is shown in the following

table.

Years 2011 2012 2013 2014 2015Number of Students 400 550 450 600 650

(a) Prepare a pictograph of students using one symbol ( ) to represents 100 students and answer the following questions.

(i) How many symbols represent total number of students in the year 2012? (ii) How many symbols represent total number of students in the year 2013? (b) Prepare another pictograph of students using any other symbol each representing

50 students. Which pictograph do you fi nd more informative?

3. A survey of 150 students was done to � nd which activity they prefer to do in their free time.

Preferred activity Number of studentsPlayingReading story bookWatching TVListening to musicPainting

6035302015

(a) Draw a bar graph to illustrate the above data taking scale of 1 unit length = 5 students. (b) Which activity is preferred by the most number of students other than playing? (c) Which two activities are preferred by the same number of students? (d) Which activity is preferred by the most number of students?

Worksheet 2

85

General Instructions: (i) All questions are compulsory. (ii) Th e question paper consists of 28 questions divided into four sections A, B,C and D. Section A consists of 8 questions of 1 mark each. Section B consists of 6 questions of 1 mark each. Section C consists of 10 questions of 1 mark each. Section D consists of 4 questions of 1 mark each. (iii) Th ere is no overall choice. However an internal choice has been provided in some

questions. Attempt only one options in such questions.

SECTION - A 1. What is the shape of a footballs. 2. Defi ne regular polygon. 3. What kind of angle 260° is? 4. Write the name of the plane shape which has countless number of lines of symmetry. 5. What is the sum of interior angles of a triangle? 6. Perimeter of a square = 4 × ______ 7. Length and breadth of a rectangular garden are ‘a’ and ‘b’ respectively. Use these

dimensions to fi nd the perimeter of the garden. 8. Defi ne tetrahedron.

SECTION - B 9. Find the number of sides, vertices and faces in a hexagonal prism. 10. With the help of ruler and compasses, construct and angle of measure 45°. 11. Complete the following table.

Shape Number of line(s) of symmetryEquilateral triangle

Rhombus

MathematicsModel Test Paper 2

Time: 2½ hoursClass 6

Total Marks: 70

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12. Draw the net of a cuboid.13. Find the perimeter of the following fi gure.

30 m

30 m

30 m 20 m15 m

15 m10 m

10 m

10 m10 m

14. In a game of hitting a target out of 10 chances for 20 students is given as follows. 5 7 6 2 4 9 1 3 0 3 5 8 5 10 6 2 4 4 3 7 Prepare a frequency distribution table for the given data.

SECTION - C 15. Find the number of lines of symmetry for the following shapes. (a) (b)

16. In following fi gure, ABCDE is a regular pentagon. (a) What kind of triangle is AED according to angles? (b) What kind of quadrilateral is ABCD?

A

B

CD

E

17. Draw a circle with MN = 10 cm as diameter. 18. Find the area of the following fi gures. (a) (b)

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19. Th e number of cows in fi ve cities of a country is depicted by the given pictograph.

City Number of cows

Delhi

Mumbai

Lucknow

Kolkata

Chennai

Key: One = 15000 cows

Observe the pictograph and answer the following questions. (a) Which city has the minimum number of cows? (b) Is the number of cows in Lucknow less than the number of cows in Delhi? (c) How many cows are there in all? 20. Use ruler and compasses to draw the following angles. (a) 90° (b) 135° 21. Th e area of a rectangular park is 248 sq. m. If the length of the park is 16 m, fi nd the

breadth of the park. or Find the area of a square fi eld of side 900 m². 22. Draw a line segment AB = 8 cm. Mark a point P on it. Th rough, point P, draw a

perpendicular to AB by using ruler and compasses only. 23. Find the number of right angles turned through by the hour hand of the clock when

it goes from (a) 12 to 3 (b) 5 to 11 24. Write the special names of the following. (a) Square prism (b) Rectangular prism (c) Circular pyramid

88

SECTION - D 25. Draw a circle of radius 4.9 cm and centre O. Draw a chord PQ of length 6 cm. Shade

the major segment of the circle.26. Th e bar graph given below shows the eye colours of a group of students.

2

4

6

8

10

12

14

16

18

20

Student’s eye colour

Eye colour

Num

ber o

f Stu

dent

s

Blue

Black

Brown

Green

Now observe the graph and answer the following questions. (a) How many students have blue eyes? (b) Which eye colour do most students have? (c) Which eye colour do least students have? (d) How many students were there in the group?27. Tarun wants to cover the fl oor of a room 6 m wide and 8 m long by squared tiles.

If each square tile is of side 2 m, then fi nd the number of squared tiles required to cover the fl oor of the room.

28. With reference to the adjacent fi gure (a) Write the name of the solid. (b) How many vertices does it have in all? (c) How many faces does the solid have? (d) Name all the vertical edges. (e) Name all the horizontal edges.

D

A

E C

B

E`

D`

A` B`

C`

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Answer KeyChapter-1Worksheet-11. (a) 1 (b) 1000 (c) 100 (d) 100 (e) 1000 (f) 50 (g) 6000 (h) 0.3 (i) 0.004 (j) 257000 (k) 0.67 (l) Roman (m) 1000 (n) DC2. (a) (i) 1000 hundred (ii) 1000 thousand (iii) 10 crore (b) 0; No (c) 1: Yes (d) Place value: 70,000; Face value : 7 (e) 4,508,004

Worksheet-21. (a) 8 (b) 5 (c) 7 (d) 22. (a) Greatest : 876320 Smallest : 203678 (b) Greatest : 984310 Smallest : 1034893. 8617414. 3269486 females5. (a) Sum : 73200 Diff erence : 92 (b) Sum : 73000 Diff erence : 2926. (a) 5700 (b) 50007. (a) 458 (b) 789 (c) 1425 (d) 8018. (a) T (b) F (c) F (d) F (e) T

Chapter-2Worksheet-11. (a) 405 × 395 (b) 15 (c) 15; 15 (d) 24 (e) 1002. 21422, 21423, 21424, 214253. 04. 225. (a) 428542 (b) 100442 (c) 410172376. (a) 77 (b) 5 (c) 31240447. (a) 1408 (b) 41408. (a) 2970000 (b) 16500 (c) 431000 (d) 169500 (e) 10000009. 31800 10. ̀ 250 11. 349

Worksheet-21. (a) T (b) T (c) F (d) F (e) T (f) F (g) F (h) T (i) F (j) F (k) F2. 123456 × 8 + 6 = 987654 1234567 × 8 + 7 = 98765433. (a) 5 + 7 = 12; 5 × 7 = 35; 0 + 1 = 1; 0 × 1 = 0 (b) 0 + 2 = 0 + 2; 0 × 2 = 2 × 0; 4 + 6 = 6 + 4; 4 × 6 = 6 × 4 (c) 3 × (0 × 5) = (3 × 0) × = 0; 3 + (0 + 9) = (3 + 0) + 9; (8 + 2) + 1 = 8 + (2 + 1); (7 × 2) × 11 = 7 × 0 = 284. 30 cartons

Chapter-3Worksheet-11. (a) F (b) F (c) T (d) F (e) T (f) F (g) F (h) F (i) F (j) F (k) T (l) F (m) T (n) T2. (a) prime (b) 2, 5 and 11 (c) two (d) three or more (e) 43. 17 and 71; 37 and 73; 79 and 97

Worksheet-21. Number Divisibility test

2 3 4 5 6 8 9 10 11128 Yes No Yes No No Yes No No No990 Yes Yes No Yes Yes No Yes Yes Yes

1586 Yes No No No No No No No No275 No No No Yes No No No No Yes

6686 Yes No No No No No No No No639210 Yes Yes No Yes Yes No No Yes Yes429714 Yes Yes No No Yes No Yes No No

2856 Yes Yes Yes No Yes Yes No No No3060 Yes Yes Yes Yes Yes No Yes Yes No

406839 No No No No No No No No No

2. (a) 20 (b) –54 (c) 56 (d) 17 (e) 45 (f) 185 (g) 59

90

Chapter-4Worksheet-11. (a) No (b) Yes (c) No (d) Yes2. (a) HCF : 4, LCM : 24 (b) HCF : 5, LCM : 140 (c) HCF : 4, LCM : 520 (d) HCF : 8, LCM : 1056 (e) HCF : 2, LCM : 180 (f) HCF : 5, LCM : 840 (g) HCF : 3, LCM : 5148 (h) HCF : 5, LCM : 3003. (a) HCF : 10, LCM : 70 (b) HCF : 25, LCM : 150 (c) HCF : 14, LCM : 294 (d) HCF : 11, LCM : 1089 (e) HCF : 5, LCM : 4620 (f) HCF : 24, LCM : 144 (g) HCF : 30, LCM : 600 (h) HCF : 34, LCM : 4084. 14 5. 4 6. Less than 99999 = 99996 Greater than 99999 = 1000087. 24 8. 29. Yes; since, LCM is divisible by HCF.

Worksheet-21. (a) Yes (b) Yes (c) Yes (d) No2. (a) HCF : 5, LCM : 10 (b) HCF : 7, LCM : 105 (c) HCF : 14, LCM : 168 (d) HCF : 10, LCM : 720 (e) HCF : 15, LCM : 90 (f) HCF : 13, LCM : 676 (g) HCF : 5, LCM : 600 (h) HCF : 25, LCM : 18003. (a) HCF : 11, LCM : 99 (b) HCF : 5, LCM : 2040 (c) HCF : 2, LCM : 816 (d) HCF : 13, LCM : 1287 (e) HCF : 12, LCM : 60 (f) HCF : 30, LCM : 180 (g) HCF : 2, LCM : 15300 (h) HCF : 7, LCM : 12604. 185. 176. Greater than 55000 = 55020 Less than 55000 = 549157. 129780 stones8. Yes; LCM is divisible by HCF.9. 300

Chapter-5Worksheet-11. (a) +8200 m (b) –520 m (c) +`200 (d) –`4002. (a) –1°C (b) +25°C (c) +18°C (d) –4°C (e) +22°C

3. (a) –1, –2, –3, –4, –5, –6, –7 (b) (c) (d) (e) 4. (a) 14 (b) 12 (c) 201 (d) 6545. (a) –52 (b) –30 (c) +91 (d) +1126. (a) –100 (b) 6347. (a) 24 (b) 848. –85 9. Actual profi t = `800

Worksheet-21. (a) –8 (b) –1 (c) –17 (d) –62. (a) –218 (b) 0 (c) 63 (d) –463. (a) 2 (b) 45 (c) –31 (d) –264. (a) 5 (b) (–19) (c) 0 (d) 23 (e) 26 (f) (–52)5. (a) < (b) < (c) < (d) <6. 137. –708. 10°C

Chapter-6Worksheet-1

1. (a) 0 14

12

24

44

(b) 0 99

89

79

69

59

49

39

29

19

(c) 0 14

7

137

127

117

107

97

87

77

67

57

47

37

27

17

2. (a) 257 (b) 15

8 (c) 277

(d) 353 (e) 68

9

3. (a) 615 (b) 6

15 (c) 1230

(d) 1845 (e) 18

45

4. (a) 912 (b) 34

91

5. (a) 712 (b) 43 (c) 6

7

(d) 15 (e) 14

6. (a) (v) (b) (i) (c) (iv)

(d) (iii) (e) (ii)

7. 56

8. (a) 516 (b) 313

360 (c) 7 112

Worksheet-21. (a) No (b) No (c) Yes (d) No

2. (a) 113 (b) 27 (c) 2

3 (d) 1115

(e) 32 (f) 2

3 (g) 27 (h) 17

5

3. (a) 410 (b) 0 (c) 8

21 (d) 727

4. (a) 2312 (b) 5 (c) 711

12 (d) 512

5. 125 km

6. In Both Classes same fraction of students getting fi rst class.

Chapter-7Worksheet-11. H T O . Tenths Hundredths

(a) 1 7 . 2(b) 0 . 4(c) 1 0 . 9(d) 2 0 3 . 7

2. (a) 6.1 (b) 300.23 (c) 14.8 (d) 100.02 (e) 500.2

3. (a) 25 (b) 27

10 (c) 1

(d) 165 (e) 64

5 (f) 432

4. (a) 406.05 (b) 8.0655. (a) Zero point zero one (b) One point three zero (c) One hundred seven point fi ve four (d) Ten point zero two

(e) Zero point zero one two6. (a) 0.3 (b) 0.18 (c) both are equal (d) 1.339 (e) both are equal (f) 0.077. (a) 4.768 (b) 9.658 (c) 248.5198. (a) 0.75 (b) 2.025 (c) 102.059. (a) 76.28 (b) 990.0910. 250.75 11. ̀ 697

Worksheet-21. (a) 0.03 (b) 0.7 (c) 5.42 (d) 0.076 (e) 0.854

2. (a) 3410 (b) 6

10 (c) 25100

(d) 4012100 (e) 2015

10003. (a) `0.06 (b) `0.60 (c) `0.15 (d) `6.15 (e) `40.754. (a) 0.17 m (b) 0.04 m (c) 2.45 m (d) 9.41 m5. (a) 0.4 cm (b) 3.3 cm (c) 12.5 cm (d) 6.5 cm6. (a) 0.005 km (b) 0.050 km (c) 6.666 km (d) 80.008 km7. (a) 29.232 (b) 42.356 (c) 14.075 (d) 312.89 (e) 27.438. (a) 3.536 (b) 8.78 (c) 14.53 (d) 3.627 (e) 68.921 (f) 2.134

Chapter-8Worksheet-11. (a) 4x (b) 3x (c) 5m (d) 2x (e) 7x (f) 3y (g) 4m (h) 2m2. 60y 3. 6s 4. (c) and (f)5. (a) x + 5 (b) y – 3 (c) 7y (d) y ÷ 6

(e) –x – 4 (f) 2(–y) (g) –x–4

(d) (–y) × (–9)6. (a) x3 × y2 (b) m2 × n3 (c) 169 × y4 (d) 36 × x7 × y8 × z9 7. (a) 60x3y4 (b) 100a8b8

92

Worksheet-21. (a) Th e cost of a book is three times the cost of a

notebook. (b) Th e number of marbles in Abhay’s box is

seven times the number of marbles he puts on table.

(c) Th e students of the school is 25 times the strength of our class.

(d) Raghu’s uncle is 4 times as old as he and his aunt is 3 years less than 4 times as old as he.

2. (a) Age of Aman 2 years ago. (b) Age of Aman 4 years aft er. (c) 4 more than 5 times the age of Aman.3. (a) Th ree times the number of students like

football in a class. (b) Half the number of students like football in

the class.4. u + 3, u × 3, u ÷ 3, u – 3, 3 ÷ 4, 3 – u 5. (a) x ÷ 3 (b) y ÷ 12 (c) 21 m (d) 7s (e) a + b (f) 40 – l 6. (a) Number of girls in our school is the number

of boys in our class. (b) Amal has 4 times the number of cookies eaten

by him. (c) Total number of plants in a garden in 3 times

the number of rows in the garden.7. (a) x × x × x × x × x × y × y × y (b) 2 × 2 × a × a (c) 2 × 2 × 3 × m × m × m × n × n × n × n × p × p

× p × p × p (d) 2 × 2 × 3 × 5 × 5 × a × a × a × a × a × b × b ×

b × b × b × c × c × c × c × c

Chapter-9Worksheet-11. (a) (t + 7) years (b) (t – 3) years (c) 7t years (d) (7t – 3) years

(e) 52t + 8 years

2. (a) x; (e) m; (g) t; (h) m 3. (a) b = 16 (b) x = 14 (c) x = 9 (d) y = 3

4. (a) m = 63 (b) x = 284 (c) x = 3 (d) y = 355. Son = 20 years, Daughter = 10 years.

Worksheet-21. (a) 15 (b) 13 (c) 10 (d) 16 (e) 2 (f) –22. x 1 2 3 4 5 6 7 8 9 10 ....

x + 10 11 12 13 14 15 16 17 18 19 20 .... Th erefore, x = 6, for x + 10 = 16.

3. (a) m = 354 (b) y = 6 (c) –255

16 (d) y = 1458

4. 16, 18, 205. Length = 18 cm, breadth = 12 cm6. 20, 40 7. 11 8. 48, 56, 64

Chapter-10Worksheet-11. (a) 8 : 12 or 2 : 3 (b) 15 : 35 or 3 : 52. (a) 10

20 = 24 = 3060 = 12; Yes

(b) 2127 = 28

36 = 79 = 5672

3. (a) 2 : 3 (b) 7 : 5 (c) 11 : 30 (d) 5 : 8 (e) 6 : 25 (f) 5 : 11 (g) 3 : 7 (h) 1 : 34. (a) 2 : 3 < 6 : 5 (b) 1 : 3 > 1 : 4 (c) 4 : 5 < 5 : 4 (d) 12 : 14 > 5 : 6 (e) 3 : 7 > 2 : 8 (f) 4 : 20 < 8 : 245. Sony = 24 pens, Reena = 16 pens6. (a) 3 : 1 (b) 10 : 3 (c) 13 : 6 (d) 15 : 17. 18 8. 10

Worksheet-21. (a) Yes (b) No (c) No (d) Yes (e) Yes (f) No2. (a) F (b) T (c) T (d) T (e) F (f) T3. (a) x = 40 (b) x = 34. (a) x = 5 (b) x = 95. (a) 30 (b) 0.286. (a) 75 (b) 2.8

93

7. `120 8. `1929. Swarup made more runs per over.

Model Test Paper 1Section A1. Profi t of `125 2. 15

73. a = 4 4. Th ree point four fi ve5. 1 : 36. Yes, 526592 is divisible by 11.7. Two hundred sixty-fi ve million three hundred

two thousand two hundred twenty-nine.

8. 1110986543210 7

4 + 3 = 7

Section B9. 5.36 10. 776

11. 79 12. 1563 = 5

2113. –4, –3, –2, –1, 0, 1, 2, 3, 414. 3.060 L

Section C15. 99960 16. 45.45517. 304, 340, 403, 430 18. 1.519. Yes, 12, 10, 6 and 5 are in proportion.20. Rakesh works for a longer time.21. 6 22. (a) 3090000 (b) 4802

23. A. O. = 410 < 35 < 54 < 75 < 11

4

D. O. = 114 < 75 < 54 < 35 < 4

1024. (a) a + 15 (b) 3b – 6 (c) 4x + 4

Section D25. 34506 26. ̀ 136427. 20 cm 28. 22 km 900 m29. (a) T (b) T (c) F (d) F

Chapter-11Worksheet-1

1. (a) M

QP (b) Y

P

QTX

(c) F

GLE

(d) P

Q

O

2. (a) (b)

3.

4. (a) (b) not possible

5. (a) intersect (b) concurrent (c) collinear (d) parallel6. (a) Ashoka Chakra (b) Two roads crossing each other (c) Railway track (d) Golf stick7. (a) Open (b) Closed (c) Closed (d) Closed (e) Open

Worksheet-2

1. (a) A C

BD

(b) P

Q R

S

(c) A

B C

DE (d) M

N P

OAB

(e) A

N P

OAB

2. (a) Obtuse (b) Acute (c) Obtuse (d) Refl ex (e) Complete (f) Right (g) Zero (h) Obtuse (i) Straight (j) Acute (k) Refl ex (l) Refl ex

3. (a) AB, AE, BD, (b) AN, EM, DF4. (a) T (b) T (c) T (d) T (e) F (f) T (g) F

Chapter-12Worksheet-11. (a) ∆ABD, ∆BCD, ∆ABC (b) ∆BAD, ∆ABC, ∆ABD, ∆BDC, ∆DCB, ∆CBD,

∆ABC (c) ∆ABC, ∆BCA, ∆CAB, side AB, side BC,

side CA (d) ∆ABD and ∆DBC

94

2. (a) PQ and SR, PS and QR (b) ∠P and ∠R, ∠Q and ∠S (c) PQ and PS, RQ and RS (d) ∠P and ∠S, ∠S and ∠R3. PR and QS, Meeting point of the

diagonals lie in the interior of the quadrilateral PQRS.

4. (a) T (b) F (c) T (d) F (e) T (f) F (g) F (h) T

Worksheet-21. (a) O (b) OD, ON, OC (c) CD (d) AM (e) O and L (f) T (g) Section DONH (h) segment AMB2. (a) Y (b) N3. (a) T (b) T4. (a) 0 (b) OC (c) AB (d) sector OBQC (e) segment MSN (f) arc MTN (g) L (h) G5. (a) adjacent (b) irregular (c) orthocentre (d) centroid (e) isosceles

Chapter-13Worksheet-11. Faces: ABCD, PQRS, ADSP,

BCRQ, ABQP, DCRS Vertices: A, B, C, D, P, Q, R, S Edges: AB, BC, CD, DA, PQ,

QR, RS, SR, AP, DS, BQ, CR2. (a) 6 (b) 4 (c) 4 (d) 12 (e) 83. (a) 4 (b) 6 (c) 44. (a) 5 (b) 8 (c) 55. (a) 5 (b) 9 (c) 6

Worksheet-21. (a) (iv) (b) (iii) (c) (vi) (d) (i) (e) (ii) (f) (v)2. Cube Cuboid

Chapter-15Worksheet-11. Human face, a leaf, Tajmahal, butterfl y2. (a)

(Isosceles triangle)

(b)

(Equilateral triangle) (c) (Scalene triangle)

3. (a) (b)

(c) (d)

(e)

4. (a) (b)

(c) (d)

(e) (f)

(g) (h)

Worksheet-21. C F H G

K P T Z F, G, K, P and Z2. (a) False (b) True (c) True (d) False (e) True (f) True (g) True (h) True3. (a) (b) (c)

Q

R

P

S

Q

R

P

S

A M

T

NC

QB

OS L

A BC

RS

F

D

Q

95

(d) (e) (f)

Chapter-16Worksheet-11. Do it yourself.2. (a) = 40 cm + 10 cm + 40 cm + 10 cm = 100 cm (b) = 6 cm + 6 cm + 6 cm + 6 cm = 24 cm3. (a) 27 cm (b) 36 cm (c) 18 cm4. (a) 16 cm (b) 28.6 cm (c) 45 m5. (a) 28 cm (b) 18 cm (c) 242 m6. (a) 100 m (b) `2500

Worksheet-21. (a) 15 m + 8 m + 12 m + 30 m 12 m + 8 m + 15 m

+ 45 m = 145 m (b) 100 m + 120 m + 90 m 80 m + 65 m + 45 m =

500 m2. 440 cm 3. 35 cm4. Tony covers more distance by 230 m.5. 144 sq.m 6. 7 cm 7. 192 tiles8. (a) 9.5 sq. cm (b) 8.5 sq. cm (c) 8 sq. cm

Chapter-17Worksheet-11. Marks

obtainedTally Marks Number of

students

1 12 33 14 65 76 87 58 59 3

10 1

(a) 14 (b) 15

2. (a) Ice Cream Flavour

Tally Marks Number of students

Vanilla 8Kesar Pista 6

Mango 7Chocolate 7

Orange 3 (b) Vanilla3. (a) Tuesday and Th ursday (b) 1750 more milk bottles were sold on Friday

than Th ursday.

Worksheet-21. Village Number of animal

VanillaKesar Pista

MangoChocolate

Orange Key : = 10 animals (a) 107 (b) Village B (c) Village C2. Year Number of students

2011

2012

2013

2014

2015

Key : = 100 students (a) (i) 5 and half (ii) 4 and half (b) Year Number of students

2011

2012

2013

2014

2015

Key : one = 50 students Th e second graph is more informative.

96

3. (a)

10

0

20

30

40

50

60

70

80

x

y

Activities preferred by students in their free time

Play

ing

Read

ing s

tory

book

Watc

hing

TV

Liste

ning

to m

usic

Pain

ting

(b) Reading storybook (c) Listening to music and painting (d) Playing

Model Test Paper 2Section A1. Sphere2. A polygon having all sides and interior angles

equal.3. Refl ex angle 4. Circle 5. 180°6. Side 7. 2(a + b)8. A tetrahedron is a pyramid whose base is a

triangle.

Section B9. Sides = 18, vertices = 12, faces = 8 10. Do it yourself.11. Shape Number of line (s) of symmetry

Equilateral triangle

3

Rhombus 212. 13. 180 m

14. Number of times hitting a

target

Tally Marks Number of students

0 11 12 23 34 35 36 27 28 19 1

10 1

Section C15. (a) 4 (b) 216. (a) Isosceles triangle (b) Isosceles trapzium17. Do it yourself18. (a) 5 sq. unit (b) 5 squ. unit19. (a) Lucknow (b) Yes (c) 510000 cows20. Do it yourself. 21. Breadth = 15.5 m23. (a) 1 right angle (b) 2 right angles

24. (a) cube (b) Cuboid (c) Cone

Section D25. Do it yourself. 26. (a) 4 (b) Black (c) Green (d) 3427. 12 tiles28. (a) Pentagonal prism (b) 10 (c) 7 (d) AA’, BB’, CC’, DD’, EE’ (e) AB, BC, CD, DE, EA