Maths Quest-5 Teacher Manual - SARASWATI HOUSE Material/978-93-5… · 3. Multiplication, Division and their Applications 14 4. Factors 18 5. Multiples 22 6. Fractions 26 7. ... Make

Teacher’sManual

MathsQuest

5

Kalpana Gairola

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

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

R

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

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First published 2016

ISBN: 978-93-5199-700-9

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.

Printed at: Vikas Publishing House Pvt. Ltd., Sahibabad (Uttar Pradesh)

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

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

Teacher’s Manual

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

Lesson plans

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

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

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

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

Practice material

MCQs, 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 MCQs, 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.

1. Place Value 5

2. Addition, Subtraction and their Applications 10

3. Multiplication, Division and their Applications 14

4. Factors 18

5. Multiples 22

6. Fractions 26

7. Decimals 31

Model Test Paper 1 36

8. Symmetry and Patterns 38

9. Geometry 43

10. Measurement 47

11. Perimeter, Area and Volume 52

12. Time and Temperature 57

13. Mapping Skills 61

14. Data Handling 65

Model Test Paper 2 69

Answer Key 71

ContentsContents

5

Learning Objectives

Students will be able to ➢ recall the concept of numbers up to 6 digits and rounding o� numbers ➢ read, understand and build 7-digit and 8-digit numbers ➢ � nd the place value and face value of a digit in the given number ➢ � nd the predecessor and successor of a large number ➢ compare 7-digit and 8-digit numbers ➢ form the greatest and the smallest 7-digit and 8-digit numbers with the given digits ➢ understand the International System of writing 7-digit-8-digit numbers ➢ round o� numbers to the nearest 10, 100 and 1000 ➢ develop Roman numbers

Concept Explanation • Recall 6-digit numbers and rounding o� numbers using the Gear Up section.• Write a 7-digit number on the board and discuss the place value of each digit. Start from

the ones place and when you cross the hundreds place, insert a comma to di� erentiate between the ones and thousands periods. Use a di� erent colour to show the digits in the thousands period. Use a third colour to show the digits in the lakhs period. Also, explain how to read these numbers. Repeat the process with other examples. Write the numbers in standard and expanded forms both.

• Repeat the above process to introduce 8-digit numbers. Introduce the new period, i.e., the crores period.

• Use page 10 to explain the place value and face value of a number.• For practice, students should do Check Point 1.1 on page 10..• Explain the rules of comparing and ordering of numbers using solved examples given on

pages 11 and 12.• Use page 12 to explain predecessor and successor.• � e teacher can write any 7 digits on the board. Ask students to form the greatest and the

smallest numbers using these digits. Ask them to note the rules of forming the greatest and the smallest numbers, i.e., to form the greatest number, the digits are arranged in descending or decreasing order and to form the smallest number, the digits are arranged in ascending or increasing order. Now take examples with 0 as one of the digits. Same procedure can be used for 8-digit number.

1 Place Value

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Two students can be asked to step forward. � ey can be given 7 or 8 digits. One can form the greatest number and one can form the smallest number. � is can be repeated with di� erent pairs of students.

• To reinforce, ask them to do Check Point 1.2.• For further reinforcement, Growing with Values on page 15 will be helpful. Also discuss

the drawbacks of increasing population.• � e teacher can get some clippings of the newspaper reports and explain the International

System of Numeration.• � e teacher can compare the Indian and International Systems to make students

understand these more clearly.• For practice, students should do Check Point 1.3 on page 16. For reinforcement of the

systems of numerations that they have learnt, use Maths Lab Activity on page 22 as well.• Divide the class into two teams each with a captain. Now assign one system of numeration

(Indian and International) each to each team. Write a 7-digit number on the board. Both the teams have to write the number in their notebooks according to their assigned system of numeration with commas in the correct places. Now the captain of each team will come and write the number as per their assigned system of numeration on the board.

• Start giving examples where we use rounded o� numbers. Revise the rules of rounding o� using pages 17, 18 for the same.

• For reinforcement, ask students to do Check Point 1.4 on page 19.• Review the seven letters that are used to denote the Roman numbers and tell students the

rules of the formation of Roman numbers. Give students lots of practise on converting Roman numbers into Hindu-Arabic numbers and vice versa.

• For practice students should do Check Point 1.5 on page 20. • For further reinforcement, let students do the Brain Workout section.• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths

with Science) and Test Yourself sections.

Multiple Choice Questions

Tick (√) the correct options. 1. When we add 1 to the largest 7-digit number, we get the smallest (a) 5-digit number (b) 6-digit number (c) 7-digit number (d) 8-digit number 2. Face value of 7 in 3,47,84,359 is (a) 7 (b) 7,00,000 (c) 70,000 (d) 7,00,00,000

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3. Place value of 9 in 8,92,47,553 is (a) 9,00,000 (b) 90,00,000 (c) 9,00,00,000 (d) 9 4. � e successor of 4,32,97,200 is (a) 5,32,97,200 (b) 4,32,97,201 (c) 4,32,97,199 (d) 4,33,97,200 5. 1 lakh in International System of Numeration is (a) 1 million (b) 1 thousand (c) 10 thousands (d) 100 thousands

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1. Put commas and rewrite the numbers in the Indian and International Systems of Numeration.

Number Indian System International system(a) 369512(b) 2397010(c) 32954602(d) 60032051

2. Write the place value of the underlined digit in both the Indian and the International Systems of Numeration.

Number Indian System International system(a) 2389435(b) 70453271

3. Write the expanded forms of (a) 3,97,20,407 ____________________________________________________ (b) 4,49,00,006 ____________________________________________________

4. Make the smallest and the greatest 7-digit numbers using the digits 7, 5, 3, 6, 8. Each digit must be used at least once and the digits may be repeated.

(a) Greatest __________ (b) Smallest __________

5. Write Roman Numerals for (a) 63 : __________ (b) 45 : __________ (c) 99 : __________ (d) 72 : __________

6. Use the correct sign (>, <, =). (a) 61,04,876 ___ 16,40,876 (b) 9,36,48,121 ___ 9,36,84,121 (c) 76,050,403 ___ 76,050,433 (d) 36,56,438 ___ 36,56,438

7. Round o� to the nearest thousand. (a) 88,645 (b) 9,999 (c) 26,428

Worksheet 1

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1. Choose the correct answer. (a) � e place value of the seventh digit from the right of a number is (i) Ten lakhs (ii) Ten thousands (iii) Millions (iv) Both (i) and (ii) (b) 2,11,34,678 is bigger than which of the following numbers. (i) 2,34,678 (ii) 2,21,34,678 (iii) 34,500,000 (iv) 2,11,34,679

2. Give the number names and the expanded forms in the system in which these numbers are written.

(a) 4,30,47,906 ____________________________________________________ (b) 28,610,706 ____________________________________________________

3. Write the Hindu-Arabic numerals for (a) XL : __________ (b) LX : __________ (c) LVII : __________ (d) XCVIII : __________

4. Arrange in the order mentioned. (a) Ascending 27,27,345; 27,27,745; 2,72,72,745; 2,07,745

_______________________________________________________________ (b) Descending 5,67,06,432; 5,76,06,432; 5,67,80,234; 6,67,80,243

_______________________________________________________________

5. � ere were 7231 birds in the Sultanpur Bird Sanctuary in October 2014. Round o� to the nearest 1000.

___________________________________________________________________

6. � e circulation of a newspaper in a city of India is 487321. Round o� to the nearest 100.

___________________________________________________________________

Worksheet 2

10

2 Addition, Subtraction and their Applications

Learning Objectives

Students will be able to ➢ add and subtract 7- and 8-digit numbers, both with and without regrouping ➢ learn the properties of addition and subtraction ➢ learn the shortcut method of addition

• understand problem solving with the help of keywords • use models to � nd missing numbers

➢ know the concepts of pro� t and loss

Concept Explanation • Use the Gear Up section on page 24 to revise the concept of addition and subtraction.• Tell students that adding 7- and 8-digit numbers is same as adding 5- and 6-digit

numbers. With the help of some examples explain the same to them.• Recall the properties of addition.• With the help of the example given on page 25, tell them about the shortcut method of

addition.• Tell students that subtracting 7- and 8-digit numbers is same as subtracting 5- and 6-digit

numbers. With the help of some examples explain the same to them.• Recall the properties of subtraction.• For practice, ask students to do Check Point 2.1 given on page 27.• Tell students the technique to compute mentally using the compensation strategy. Tell

them how one of the addends or the minuend and subtrahend can be changed to the multiples of 10 or 100 before doing the operation.

• Give a simple example of 18 + 13. Tell them that adding 2 to 18 will make it 20. � ey also have to subtract 2 from 13, which will make it 11. So now they can easily add 20 + 11= 31. Tell them that they have to take care that while adding a number to one of the addends they have to subtract the same number from other addend.

• Ask students to do Check Point 2.2 given on page 28.• Tell students the technique of problem solving with the help of keywords. Tell them

about the various keywords used in both the operations.• For practice, ask students to do Check Point 2.3.

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• Make students familiar with using models for � nding missing numbers while doing addition and subtraction sums.

• Ask them to do the Crack it section on page 31 for further practice.• Explain to students the terms cost price, selling price, pro� t and loss.• Use various examples given in the related section to compute cost price, selling price,

pro� t and loss. • Give them an example. Suppose a student got a chart paper for `10 and crayons for `30.

Now the student made a beautiful, colourful drawing on the chart paper and sold it to his friend for `50. Now ask students about the money he made. Tell them this is pro� t. Also tell them about CP and SP. Similarly, give an example of loss.

• Reinforce the concept and values in students through the Growing with Values section.• To make students understand the concept and importance of pro� t and loss, do Maths

Lab Activity given on page 36 with them.• Ask students to do Check Point 2.4 for further practice.• For further reinforcement, let students do the Brain Workout section.• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths



Tick (√) the correct options. 1. 4875 + 3297 = ______ + 4875 (a) 4875 (b) 3297 (c) 0 (d) 1 2. 9287 + 0 = _____ (a) 9287 (b) 0 (c) 9288 (d) 9286 3. 38245 – 0 = _____ (a) 38245 (b) 0 (c) 38244 (d) 38246 4. 62875 – 62875 = _____ (a) 62875 (b) 0 (c) 62876 (d) 62874 5. SP = CP + _____ (a) SP (b) CP (c) Pro� t (d) Loss

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1. Add or subtract as required. (a) 3,54,942 + 99,370 (b) 2,29,834 – 87,595

2. Fill in the boxes. (a) 8 3 2 5 6

+ 1 0 4 0 51 0 0 7 1 1

(b) 8 5 6 0 5 9– 0 2 5 0 6 0

5 0 0 7 0 0

3. Jayati bought a house. She paid `2,18,670 from her savings. She took a loan of `1,50,450 from a bank to pay the rest of the money. What was the cost of the house?

___________________________________________________________________

4. Raghav bought a computer and a printer for `1,15,499. � e cost of the computer was `85,789. What was the cost of the printer?

___________________________________________________________________

5. By how much is 2,35,678 greater than 99,999?

___________________________________________________________________

6. What should be added to 85,672 to get 2,32,456?

___________________________________________________________________

Worksheet 1

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1. Fill in the blanks. (a) 49875 + 0 = __________ (b) 942876 + 7421973 = 7421973 + __________ (c) 1428750 + 1 = __________ (d) 7342895 – 0 = __________ (e) 5347291 – __________ = 5347291

2. Subtract using the compensation strategy. (a) 48 – 18 __________________________________________________ (b) 115 – 25 __________________________________________________

3. Reena bought a cycle for `5678 and sold it again for `5795. Find her pro� t or loss.

___________________________________________________________________

4. Smriti bought a laptop for `28000. She spend `4500 on loading a so� ware. She then sold it for `35500. Find her pro� t or loss.

___________________________________________________________________

5. Do as directed. (a) Loss = `210 `SP = 85, Find CP. (b) Pro� t = `155 `CP = 70, Find SP. (c) Loss = `500 `CP = 1650, Find SP. (d) Pro� t = `250 `SP = 1260, Find CP.

6. A man bought a cooler for `2,500. He spent `500 on polishing it and `250 on changing its pump. If he got a pro� t of `100, how much did he sell it for?

___________________________________________________________________

Worksheet 2

14

3 Multiplication, Division and their Applications

Learning Objectives

Students will be able to ➢ recall the division terms and multiplication facts ➢ learn the multiplication of large numbers by 2- and 3-digit numbers ➢ multiply numbers having zeroes ➢ recall the properties of multiplication ➢ learn to divide 5- and 6-digit numbers by 1- and 2-digit numbers ➢ recall the properties of division ➢ understand the concept of averages ➢ learn about problem solving with the help of keywords ➢ use multiplication and division models in solving sums

Concept Explanation • Recall the division terms and multiplication facts using the Gear Up section.• Using the examples given on page 40, explain to students the multiplication of large

numbers by 2- and 3-digit numbers. Demonstrate to them how multiplication is done in parts and how all these parts are added up to get the � nal answer.

• Explain to the students multiplication with numbers having zeroes. Give examples wherein the number is multiplied by 10 and its multiples. Use example given on page 41 to show how a number can be multiplied by a number with 0 in the tens place.

• Recall the properties of multiplication.• For further practice on the concepts taught, ask students to do Check Point 3.1.• Ask students to do Growing with Values and discuss with them the about how we should

treat stray animals.• Explain to students the division of 5- and 6-digit numbers by 1- and 2-digit numbers.

Tell them that it is done the same way as done for 3- and 4-digit numbers.• Recall the properties of division.• For further practice, ask students to do Check Point 3.2.• Give some examples from real life where we use averages. Heights of the students in the

class can be taken as an example. You can � nd the average height of the class (or boys and girls) and make them understand the concept of averages.

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• Tell them how to calculate averages using the formula. Use the Tidbits section to reinforce the formula.

• Do the Maths Lab Activity given on page 51 with hem to further reinforce the concept of averages in them.

• For further practice, ask students to do Check Point 3.3.• Explain to students how to solve multiplication and division problems based on certain

keywords.• Give various real-life examples to students and ask them to tell whether they have to

divide or multiply based on the keywords given.• Help students develop multiplication and division models for solving sums.• Ask students to solve the Crack it section and Check Point 3.4 on page 48 for further

practice.• Explain the concept of DMAS to students. Ask students to do the related Crack it section

on page 49.• For further reinforcement, let students do the Brain Workout section on page 45.• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths



Tick (√) the correct options. 1. 479 × 386 = ___ × 479 (a) 479 (b) 1 (c) 0 (d) 386 2. 3762 × 1 = ____ (a) 3762 (b) 1 (c) 0 (d) 3763 3. 2 ÷ 1 = _____ (a) 3 (b) 1 (c) 2 (d) 21 4. 7 ÷ 7 = _____ (a) 7 (b) 49 (c) 14 (d) 1 5. A company manufactures 392 toys in one day. How many toys can it manufacture

in 5 days? (a) 392 + 5 (b) 392 – 5 (c) 392 ÷ 5 (d) 392 × 5

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1. Fill in the blanks. (a) 4967280 × 0 = ___________ (b) 3849743 × 1 = ___________ (c) 329 × 5874 = 5874 × ___________ (d) 49 × (37 × 55) = (49 × 37) × ___________ (e) 587321 ÷ 1 = ___________ (f) 82987 ÷ 82987 = ___________ (g) 0 ÷ 312976 = ___________

2. Fill in the blanks. (a) 487316 × 10 = ___________ (b) 92718 × 100 = ___________ (c) 3287 × 200 = ___________ (d) 457 × 1000 = ___________

3. Look at the problems and decide whether to divide or multiply. Tick (√) the right option.

(a) A laptop costs `20,000. What is the cost of 9 such laptops? (i) Multiply (ii) Divide (b) `4892 is to be divided equally among 4 students. How much money will each get? (i) Multiply (ii) Divide

4. A shopkeeper placed 1,80,000 books on 90 racks uniformly. How many books did the shopkeeper place on each rack?

___________________________________________________________________

5. � ere are 4,625 bags of sugar in a store room. Each bag weighs 63 kg. What is the total quantity of sugar in the store room?

___________________________________________________________________

Worksheet 1

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1. � e height of 3 trees in Monu’s garden is 6 m, 8 and 7 m, respectively. What is their average height?

___________________________________________________________________

2. In three tests of 50 marks each, Sahil scored 47, 44 and 41. What were his avearage marks?

___________________________________________________________________

3. Which least number should be subtracted from 5680 so that the result is exactly divisible by 45?

___________________________________________________________________

4. Which least number should be added to 5680 so that it is exactly divisible by 45.

___________________________________________________________________

5. Simplify: 50 × 3 + 200 ÷ 5

___________________________________________________________________

Worksheet 2

18

4 Factors

Learning Objectives

Students will be able to ➢ understand the divisibility rules ➢ know about prime and composite numbers ➢ learn about prime factorisation ➢ explain the highest common factor (HCF) and � nd it using common factors, prime

factorisation method, and long division method

Concept Explanation • Use the Gear Up section to recall the concepts of factors, common factors and factor

trees.• Explain the divisibility rules to students with the help of various examples. � e teacher

can play a quiz in the class by dividing the class into teams an asking each team whether a number is divisible by another according o the divisibility rules.

• To further reinforce the concept, ask students to do Check Point 4.1.• Explain the concept of prime and composite numbers to students using page 57. Also

make them understand how to � nd prime numbers between 1 and 100 using Sieve of Eratosthenes. Give students activity of � nding prime numbers between various numbers say between 35 and 65.

• Help them answer the questions based on the above given on page 58.• Tell students the concept of prime factorisation. Also explain to them that prime

factorisation can be found out by the factor tree method and the division method.• Use the common error given on page 59 to help them avoid mistakes they might make

while doing prime factorisation.• Ask students to do Check Point 4.2 for further practice.• Tell students what highest common factor or HCF is.• Explain the three methods that can be used to � nd the HCF – using common factors,

using prime factorisation method and using long division method.• Again divide the class into three groups with a captain each. Now assign one method

each to each group. Give them a set of numbers say 24, 48. Now ask each group to � nd the HCF by their assigned method. � e captain of the team that � nishes � rst can stand up and tell the answer. Other teams can then verify their answers.

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• To further reinforce the concept and instill the values, ask students to do the Growing with Values section. Stress on the importance of plants.

• Do the Maths Lab Activity given on page 64 to help students further understand the concept of HCF.

• For further reinforcement, let students do the Brain Workout section on page 63.• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths



Tick (√) the correct options. 1. 8264 is divisible by (a) 3 (b) 9 (c) 2 (d) 7 2. 921 is divisible by (a) 3 (b) 9 (c) 2 (d) 7 3. Prime factorisation of 56 is (a) 4 × 2 × 7 (b) 8 × 7 (c) 2 × 2 × 2 × 7 (d) 2 × 2 × 2 × 2 × 7 4. HCF of 24 and 28 is (a) 1 (b) 2 (c) 4 (d) 8 5. � e smallest and the only even prime number is (a) 1 (b) 2 (c) 4 (d) 6

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1. Name the following. (a) � e number that has exactly two factors, 1 and the number itself. ___________ (b) � e highest of the common factors of two or more numbers. _____________ (c) A number that has more than 2 factors. _____________

2. List all the prime numbers between 16 and 39.

___________________________________________________________________

3. Write the number which is prime as well as an even number.

___________________________________________________________________

4. Draw a factor tree to � nd the prime factorisation of 63.

___________________________________________________________________

5. Find the common factors of 20 and 52.

___________________________________________________________________

6. Put () for divisible and () for not divisible.

Divisible byNumber 2 3 4 5 6 9 10

(a) 75(b) 126(c) 275(d) 996(e) 2430(f) 66660

Worksheet 1

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1. Circle the numbers that are:

(a) Divisible by 2 : 21 32 44 57 63 78 80

(b) Divisible by 5 : 15 29 35 50 99 110 119

(b) Divisible by 10 : 38 50 65 70 90 114

2. Find the prime numbers between 70 and 100.

___________________________________________________________________

3. Find the prime factorisation of 212 using the factor tree method.

___________________________________________________________________

4. Find the prime factors of 68 using the division method.

___________________________________________________________________

5. Find the HCF of 24, 36, 48 using the prime factorisation method.

___________________________________________________________________

Worksheet 2

22

5 Multiples

Learning Objectives

Students will be able to ➢ learn about multiples and their properties ➢ know how to � nd multiples ➢ understand the concept of lowest common multiple (LCM) ➢ know about the properties of multiples ➢ use prime factorisation to � nd LCM of two or more numbers ➢ understand the relationship between LCM and HCF

Concept Explanation • Use the activity given in the Gear Up section to introduce the students to the concept of

multiples.• Explain what are multiples and reinforce the properties of multiples giving examples.• Do the Maths Lab Activity given on page 74 to reinforce the property that LCM of two

co-prime numbers is their product.• Also tell them how they can � nd multiples. Give them activities wherein they can � nd

the multiples of given numbers.• Explain to them what is the least common multiple (LCM). Let them make a grid with

the multiples of 2 and 3. Now ask them to strike o� the common multiples. Now ask them to � nd the smallest multiple out of these struck o� multiples. Tell them that this is the LCM.

• Tell them that LCM can be found out by prime factorisation method and short division method.

• Explain each process in detail. Divide the class into two groups. One method of � nding LCM can be assigned to each group. Give them a set of numbers, say, 15, 20, 30. Now ask each group to � nd the LCM by their assigned method. � e captains of the team then can announce the LCM and check if their answers match.

• For more practice, ask students to do the Crack it section on page 70. • Make them understand the relationship between HCF and LCM.• Divide the class into two teams. Write two numbers on the board, say 24 and 56. Now

one team has to � nd out the HCF of these numbers and the other team has to � nd the LCM of these numbers. � ey can then check if the HCF x LCM is equal to the product of the two numbers written on the board.

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÷• Ask students to do Check Point 5.2 for more practice,• To further reinforce the concept, ask students to do the Growing with Values section.

Discuss with them about ways and means in which underprivileged children can be helped.

• For further reinforcement, let students do the Brain Workout section on page 72.• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths



Tick (√) the correct options. 1. � e � rst even multiple of 9 is (a) 9 (b) 18 (c) 27 (d) 36 2. LCM of 2 and 3 is (a) 2 (b) 3 (c) 6 (d) 5 3. Co-prime numbers are the two numbers whose HCF is (a) 1 (b) 0 (c) 2 (d) 3 4. Product of two numbers = HCF × _____ (a) Prime number (b) Co-prime number (c) Factors (d) LCM 5. � e HCF of two numbers is 4 and LCM is 40. If one of the numbers is 20, the other

number is (a) 2 (b) 6 (c) 8 (d) 10

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1. Choose the correct answer. (a) Every number is a multiple of (i) 0 (ii) 1 (iii) 2 (iv) All of these (b) Two numbers 41 and 13 have no common factors. � eir LCM is (i) 4 + 13 (ii) 41 × 13 (iii) 41 – 13 (iv) 41 ÷ 13

2. Find the four multiples of: (a) 6 (b) 13 (c) 20

3. Find the LCM. (a) 18, 24 (b) 8, 18 (c) 12, 15, 30

4. � e product of two numbers is 300. If their LCM is 60, � nd their HCF

___________________________________________________________________

5. � e product of the HCF and LCM of two numbers is 726. If one of the numbers is 22, what is the other number?

___________________________________________________________________

6. Find the LCM of 28 and 42 using the prime factorisation method.

___________________________________________________________________

7. Find the LCM of 20, 35, 40 using the short division method.

___________________________________________________________________

Worksheet 1

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1. Find out if it is true or false: (a) 275 is a multiple of 3. (b) 389 is a multiple of 7. (c) 567 is a multiple of 9.

2. Find out the � rst four odd multiples of (a) 9 ______________________________ (b) 7 ______________________________ (c) 11 ______________________________

3. Find out the LCM of the following using the prime factorisation method. (a) 48, 72 _________________________________________ (b) 55, 105 _________________________________________

4. � e HCF of two numbers is 760 and LCM is 4800. If one of the numbers is 480, � nd the other number.

___________________________________________________________________

5. Breads come in packages of 12 and cheese slices come in packages of 10. What is the least number of packages of each that can be bought to be able to make cheese bread with no bread or cheese slices le� over?

___________________________________________________________________

6. Kanchan baked 30 oatmeal cookies and 48 chocolate cookies. She wants to divide the cookies into identical containers, so that each kind of container has the same number of each kind of cookie. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need?

___________________________________________________________________

Worksheet 2

26

6 Fractions

Learning Objectives

Students will be able to ➢ the concept of fractions and the terms associated with it ➢ understand the meaning of equivalent fraction ➢ identify and � nd equivalent fractions ➢ reduce a fraction to its lowest terms ➢ compare and order like and unlike fractions ➢ add and subtract like and unlike fractions ➢ add and subtract mixed fractions ➢ multiply two fractions ➢ � nd the reciprocal of a fraction ➢ divide a fraction by a whole number ➢ divide a fraction by another fraction

Concept Explanation • Use the Gear Up section to revise fraction, and proper, mixed, unit, improper, like and

unlike fractions.• To explain equivalent fractions, take rectangular papers as shown below. Colour them in

di� erent colours.

Rectangle A shows that 12 has been coloured.

Rectangle B shows that 24 has been coloured.

Rectangle C shows that 36 has been coloured.

• Ask the students to observe how much of each shape has been coloured. Expected answer is that equal portion of the rectangles has been coloured. Now explain to them that ½, 2/4 and 3/6 represent the same fraction and are called equivalent fractions. Tell them that equivalent fractions have the same value. Use pages 77 and 78 to explain further.

• Ask students to do Check Point 6.1 for further practice.• Teach reducing fractions to their lowest terms by either dividing the both the numerator

and denominator by their common factors till they cannot be divided further, or by simply dividing by their HCF in one step.

A B C

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÷• Ask students to do Check Point 6.2 for further practice.• For comparison of fraction, take six paper plates of equal size. Make them as shown

below.

12

13

14

16 1

81

• In fact, these can be kept as a permanent teaching aid and can be used to teach equivalent fractions comparison of fractions as well as addition and subtraction of fractions.

• Now use pages 81 to 83 for teaching comparison of fractions. • For reinforcement, ask students to do Check Point 6.3.• Teach students to do operations on fractions. Ask them to do Check Point 6.4 to Check

Point 6.10 for practice.• Do the Maths Lab Activity given on page 98 to make students understand addition and

subtraction of fractions through a grid. • Explain to them what is multiplicative inverse or reciprocal.• Place some chits containing fraction problems involving all four operations in a box.

Divide the class into four teams. Now ask one member of each team to come and pick a chit with a fraction problem and solve it. � e right answer earns the team a point. � e game can continue till all the students have got a chance and there is a clear winner.

• Ask students to do the Brain Workout section given on page 96 to further reinforce the concept.

• Help students do the Growing with Values section and discuss with them the importance of honesty.

• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths



Tick (√) the correct options.

1. Equivalent fraction of 37 is

(a) 921 (b) 9

14 (c) 621 (d) 6

28

2. Simplest form of 3244 is

(a) 711 (b) 8

21 (c) 811 (d) 9

11

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3. 79 + 20

9 = ______

(a) 2718 (b) 27

81 (c) 279 (d) 27

19

4. 245 – 13

5 = ______

(a) 115 (b) 19

5 (c) 215 (d) 2

5

5. 4 ÷ 16 = ______

(a) 46 (b) 6

4 (c) 14 (d) 24

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1. Fill in the missing numbers to make the statements true.

(a) 29 = 14

00 (b) 311 = 00

33

2. Write two equivalent fractions of the following.

(a) 38 _____________ (b) 9

16 _____________

3. Compare the following pairs of fractions using <, > or =.

(a) 56 _____ 23 (b) 8

6 _____ 129

(c) 47 _____ 11

17

4. Reduce to their lowest terms.

(a) 1218 _____________ (b) 20

36 _____________

(c) 4896 _____________ (d) 64

78 _____________

5. Add/Subtract.

(a) 57 + 12 + 5

14 (b) 320 – 4

30

(c) 2025 – 4

10 (d) 68 – 14

6. Find the product.

(a) 25 × 79 _____________ (b) 3

8 × 45 _____________

7. Find the reciprocals of:

(a) 413 _____________ (b) 7

21 _____________

(c) 819 _____________

Worksheet 1

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1. Tick the correct answer.

(a) 498 = ___________

(i) 6 81 (ii) 6 1

8 (iii) 8 16 (iv) 1 6

8

(b) 5 17 as an improper fraction is

(i) 367 (ii) 35

7 (iii) 351 (iv) None of these

(c) � e largest fraction among

57 , 5

11, 58 , 5

12 is

(i) 57 (ii) 5

11 (iii) 512 (iv) 5

8

2. Find the sum of 12, 34 and 58. _____________________

3. Find the di� erence of 45 and 310 _____________________

4. Simplest form of 6391 is _____________________

5. Find the product of 57 and 1415 _____________________

6. Multiplicative Inverse of 811 is _____________________

7. Solve 314 ÷ 2

7 _____________________

8. Sunidhi bought 4 12 kg apples for `315. Find the cost of 1 kg apples.

___________________________________________________________________

Worksheet 2

31

7 Decimals

Learning Objectives

Students will be able to ➢ recap the concepts of decimals, tenths and hundredths ➢ understand thousandths ➢ understand place value chart of decimals ➢ understand and build equivalent decimals ➢ understand the meaning of like and unlike decimals ➢ convert like to unlike decimals and vice versa ➢ compare and order the value of two or more decimals ➢ add and subtract decimals ➢ round o� decimals ➢ multiply decimals with whole numbers ➢ multiply decimals by a decimal ➢ divide decimals by a whole number

Concept Explanation • Use the Gear Up section to recall the concepts of decimals with tenth and hundredths.

Teaching aids used to teach place value can be used to teach place value chart of decimals also.

• Use plain squares as well as squares with markings of tenths on them. Explain to the students that the plain shapes express wholes. Now ask students to colour 3 strips of the tenths sheets. Now students can be asked to represent this as a fraction. � e fraction is

written as a mixed number 1 310. Tell them that this can be written as a decimal number

1.3. Explain to them the role of the decimal point which is placed between a whole number and the fractional number. Also emphasise on the fact that every numeral a� er decimal point is less than a whole.

• � e Maths Lab Activity given on page 122 can be done to further reinforce the concept.• Use the place value chart on page 102 to introduce the thousandths place.• Use the decimal numbers place value chart on page 102 explain relation between tenths,

hundredths and thousandths.

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• Give each student a decimals place value chart. Call out a few decimal numbers and ask the students to arrange them in the place value chart given to them. � e partners can then exchange and the teacher shows them the correct representations. � e partners correct each other’s chart.

• Ask students to do Check Point 7.1 for further practice..

• Use the square grids as shown on page 105 to explain the concept of equivalent decimals.

• Use the Crack it section given on page 106 to make students practice the concept of equivalence.

• Use pages 106 and 107 for explaining like and unlike decimal and changing of unlike to like decimals and vice a versa.

• To explain comparison of decimals, use the square grids shown on page 107.

Ask students to do Check Point 7.2 for further practice.

• Explain the operations on decimals using relevant examples from the text and ask students to do the related Check Points.

• Divide the class into two teams. Each student in Team A will have a decimal problem on one of the operations and the students in the other team will have the answers each. Once one student reads out a problem, the student with the answer from the other team has to stand up. � is activity can also be timed. � e roles can be revered for the next round of game.

• To teach rounding o� and estimation, use page 113 and 114.

• Explain the concept of multiplying and dividing with money and the unitary method to the students.

• Let some students act as shopkeepers and some as customers. � e shopkeepers will keep more than 1 object at a � xed price, e.g., 2 erasers for `40.50. � e customer is allowed to buy only 1 item a� er computing the price of the same. � e roles can be reversed a� er one round. � is will reinforce the concept of the unitary method.

• Ask students to do the Brain Workout section given on page 122.

• Encourage students to do the Growing with Values section and discuss the values related to it, that is, kindness and empathy towards animals.

• For overall recapitulation, let students go through the Flashback section.

• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths with GK) and Test Yourself sections.

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1. 4371000 in the decimal form would be

(a) 4.37 (b) 43.7 (c) 437 (d) 0.437 2. 38.579 in fraction would be

(a) 38579 (b) 38579

1000 (c) 38579100 (d) 38579

10 3. 3.47, 2.29, 8.32 are (a) Equivalent decimals (b) Like decimals (c) Unlike decimals (d) None of these 4. 59.7 can be rounded o� to (a) 57 (b) 59 (c) 97 (d) 60 5. 367.25 × 100 = ____ (a) 3.6725 (b) 36725 (c) 36.725 (d) 3672.5

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1. Choose the correct answer. (a) � e decimal 32.754 is read as (i) three two point seven hundred � � y-four (ii) three-two point seven � ve four (iii) thirty-two point seven hundred � � y-four (iv) thirty-two point seven � ve four (b) Which is greater in value? (i) 0.6 (ii) 0.06 (iii) 0.60 (iv) Both (i) and (iii)

2. Fill in the blanks.

Decimals Like or unlike Equivalent or not equivalent

(a) 3.90, 3.09, 3.99(b) 2 tenths, 20 hundredth,

200 thousandths(c) 14.14, 25.25, 36.36

3. Compare the decimals using <, > or =. (a) 3.8 ___ 3.81 (b) 9.07 __ 9.069 (c) 2 + 0.15 __ 3.05

4. Solve. (a) 9.999 + 1.111 ____________ (b) 4.1 – 3.191 ____________ (c) 0.17 × 5 ____________ (d) 16.1 ÷ 7 ____________ (e) 8.46 ÷ 3 ____________ (f) 3.5 ÷ 1000 ____________ (g) 3.75 × 10 ____________ (h) 4.009 × 1000 ____________ (i) 9.808 × 100 ____________ (j) 0.898 × 10 ____________

Worksheet 1

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1. Tick (√) the correct options. (a) 10 × 0.1 is (i) 10.1 (ii) 1.1 (iii) 1.0 (iv) 0.01 (b) 0.4 divided by 8 is (i) Q = 0, R = 0.4 (ii) Q = 0, R = 4 (iii) Q = 0.5 (iv) Q = 0.05

2. Do as directed.

(a) 310 (write as decimals) ______________

(b) 0.07 (write as fraction) ______________ (c) 9.3201 (write in the expanded form) ______________

(d) 700 + 80 + 3 + 110 + 4

100 (write in the short form) ______________

3. Fill in the blanks with >, < or = to make the statements true. (a) 4.07 ___ 4.70 (b) 14.173 __ 15.631 (c) 8.4 __ 8.40 (d) 92.1 __ 92.01

4. Fill in the blanks. (a) 49.7 ÷ 10 = ________ (b) 6.818 ÷ 100 = ________

(c) 51.87 ÷ 1000 = ________ (d) 0.697 ÷ 0.697 = ________

5. � e cost of 10 egg is `36.95. What is the cost of 1 egg.

___________________________________________________________________

6. A tailor used 12.72 m of cloth to make 8 shirts. How much cloth was used in making 18 such shirts.

___________________________________________________________________

7. Anuja saved `52.75 from her pocket money. Her sister Oorja saved `24.95. Who saved more money? How much more?

___________________________________________________________________

Worksheet 2

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1. Fill in the blanks. (1 × 7 = 7) (a) 1 crore = ________ millions (b) SP = CP + ________ (c) 25 ÷ 5 × 2 + 8 = ________ (d) A number which has more than two factors is called a ________ number. (e) � e � rst even multiple of 5 is ________ .

(f) 49 _____ 8

11 (put >, < or =)

(g) 89.7 will be rounded o� to ________ .

2. Write the period and the place value of the underlined digits. (1 × 3 = 3) (a) 85,932,674 (b) 79,290,005 (c) 80,075,882

3. Add/Subtract using the compensation strategy. (2 × 2 = 4) (a) 98 + 65 (b) 115 – 27

4. Multiply: (2 × 2 = 4) (a) 48907 × 327 (b) 592871 × 309

5. Divide. (2 × 2 = 4) (a) 928764 ÷ 14 (b) 72865 ÷ 15

6. Find the HCF of 25, 55 and 75 by prime factorisation method. (2 × 1 = 2)

___________________________________________________________________

7. Find the LCM of 9, 27 and 49. (2 × 1 = 2)

___________________________________________________________________

MathematicsModel Test Paper 1

Time: 2 hoursClass 5

Total Marks: 50

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8. Find the product. (2 × 2 = 4)

(a) 57 × 3

11 (b) 38 × 2

7

9. Divide. (2 × 2 = 4)

(a) 8 11 ÷ 11

8 (b) 1424 ÷ 5

2

10. Multiply. (2 × 2 = 4) (a) 3.37 × 5.4 (b) 6.257 × 0.09

11. Divide. (2 × 2 = 4) (a) 31.2 ÷ 8 (b) 3.948 ÷ 4

12. Solve. (4 × 2 = 8) (a) Smriti bought a scooty for `45,585. She bought its accessories for `3975 and

spent another `2824 on getting it delevered to her house. She sold the scooty a� er 2 months for `69,875. Find her pro� t or loss.

(b) � e population of a village is 87260. 1 out of 10 person is educated. How many people are educated?

(c) Surabhi wants to cut two ribbons of lengths 350 cm and 375 cm into pieces of equal lengths without any wastage. Find the greatest possible length of the ribbons.

(d) In a month, Sudhir goes to school by cycle for 110 of the days and rest of the days

he goes by school bus. How many days does Sudhir go by bus? (1 month = 30 days)

38

8 Symmetry and Patterns

Learning Objectives

Students will be able to ➢ understand symmetry and lines of symmetry ➢ understand turns and create patterns based on turns ➢ identify shapes that have quarter and half turns ➢ recognise nets of shapes ➢ draw cubes and cuboids using isometric dot papers

Concept Explanation • Use the Gear Up section to recall the concept of symmetry.• Use pictures from old magazines and cut-outs of di� erent geometrical shapes, and by

using the method of folding, introduce the concept of line of symmetry.• Show them the shapes and � gures with multiple lines of symmetry.• Explain the meaning of vertical and horizontal lines of symmetry using suitable examples.• Do Maths Lab Activity given on page 141 to further reinforce the concept of symmetry.• Draw an irregular � gure on the board. Use a mirror to draw its re� ected shape. Tell

students that the re� ected shape starts from the line of symmetry. • To reinforce, ask them to do Check Point 8.1.• Explain to them the concept of turns.• Take a paper plate. Divide it into four equal parts. Colour two out of four parts in same

colour as shown. Press a thumbpin in the centre and � x it on a � annel board and turn it. Let students decide whether it looks the same a� er a quarter turn or half a turn.

• Fix a paper cut-out of a right angled triangle on the board with the help of a thumbpin. Flip it to show its re� ected image.

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• Next, turn the triangle a quarter turn and then a half turn. Ask students to observe the turns carefully.

Quarter turn Half turn

• For further practice, ask students to do Check Point 8.2.• Draw a pattern on the board based on turns and explain it to the students.• Now ask students to create a pattern based on the turns in their notebooks.• Bring a cube-shaped box, say a cake box, to the class. Open it up in front of students to

show them the net of the cube.• Ask students to observe and open up di� erent packaging like that of a toothpaste, soap,

etc. and observe the nets of these shapes. Ask them to bring these to class as well for display.

• Teach students to draw cubes and cuboids on an isometric dot paper as shown on page 138. Tell them about di� erent perspectives as well.

• Ask students to do the Brain Workout section given on page 139.• Help them to do the activity given in the Growing with Values section and instill in them

love for their grandparents.• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths

with English) and Test Yourself sections.



1. � e mirror image of

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

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2. � e line of symmetry of is

(a) (b) (c)

3. What comes next? ________

(a) (b) (c)

4. Net of a cylinder is

(a) (b) (c)

5. How the � gure will look a� er a quarter turn clockwise.

(a) (b) (c)

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1. Tick (√) the correct options. (a) � e number of lines of symmetry that shapes have varies between (i) 1 and 2 (ii) 1 and 4 (iii) 1 and unountable (iv) 0 and uncountable (b) Which of these shapes will look the same a� er a quarter turn? (i) Circle (ii) Square (iii) Rectangle (iv) Both (i) and (ii)

2. Each of these � gures has more than one line of symmetry. Mark the lines of symmetry.

(a) (b) (c)

3. A� er how many quarter turns each of these will look the same as the original. (a) 8 ______ (b) 1 ______ (c) (d)

______ ______ 4. Complete the patterns.

(a) ________ (b) ________

(c) ________ (d) ________

5. Match the following.

(a) (i) cube

(b) (ii) cylinder open on both ends

(c) (iii) open box

(d) (iv) cone open at the bottom

Worksheet 1

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1. (a) Which of these shapes are symmetrical? Draw the lines of symmetry.

(i) (ii) (iii)

(b) Draw the re� ection of the given shapes.

(i) (ii) (iii)

2. Draw how these letters will look a� er these turns.

Letter 14 turn 1

2 turn

(a) B (b) F(c) C(d) K

3. Tick (√) the ones that would look the same a� er a half turn.

(a) (b)

____________ ____________

(c) (d)

____________ ____________

Worksheet 2

43

9 Geometry

Learning Objectives

Students will be able to ➢ develop the concepts of line, ray, line segment ➢ learn about angles and types of angles ➢ measure and construct angles with the help of a protractor

Concept Explanation • Introduce geometry by recalling polygons and open and closed � gures in the Gear Up

section.• Clean out the blackboard so that it is completely blank. Now with the chalk, put a small

dot on the board and tell students that this is a point.• � en draw several points close to each other. Now join the dots with a line. Keep

extending the line on both the sides to show that the line goes on endlessly.• Now introduce the line segment by showing it to be a part of the line that is already

there on the board. With a di� erent coloured chalk, mark out two end points of the line segment.

• Introduce the symbols to name point, line and line segment.• Similarly introduce the ray and its symbol.• Explain to students what is an angle and how to name an angle.• To introduce the concept of an angle, take two strips of a thick paper and place them

one on the top of the other. Push a drawing pin at one end on the thick cardboard or old book.

• You should be able to move these that are � xed at one end. Now move these to explain acute, obtuse and right angles. Use pages 146 to 148. To reinforce use try these on page 99 and 100.

• Ask students to do Check Pont 9.2 and Check Point 9.3 for further practice.• Do Maths Lab Activity with students to further reinforce the concept of angles.• Show students how to measure and construct angles using a protractor.• For practice, ask them to do Check Point 9.4 and Check Point 9.5.• For further reinforcement, ask students to do the Brain Workout section given on page

155.

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with English) and Test Yourself sections.


Tick (√) the correct options. 1. An angle that is a quarter of a full revolution: (a) Right angle (b) Acute angle (c) Obtuse angle 2. An angle less than a right angle: (a) Obtuse angle (b) Acute angle (c) Straight angle 3. An angle more than a right angle and less than a straight angle: (a) Obtuse angle (b) Acute angle (c) Straight angle 4. An angle equal to two right angles: (a) Obtuse angle (b) Acute angle (c) Straight angle 5. An angle equal to four right angles: (a) Acute angle (b) Complete angle (c) Straight angle

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1. Which of these is always correct for an acute angle? (a) its arms are very small. (b) its measure is less than 90°. (c) its measure is greater than 90°. (d) both (i) and (ii).

2. How many right angles make up a straight angle? (a) 1 (b) 2 (c) 3 (d) 4

3. Name each angle in two ways. Measure each angle and say what type it is?

(a)

B C

A

(b) F C

E

(c) RP O

_______________ _______________ _______________

4. Draw an angle with a measure 75°.

___________________________________________________________________

5. Name the line segments in the following � gures.

(a)

B

C

A

(b) R

QP

S

T

6. Measure the following angle with the help of a protractor.

B C

A

_________________________

Worksheet 1

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1. State whether the line segments are perpendicular to each other or not. (a) A

DC

B

(b) P R

Q S ___________ ___________

2. How many angles are formed in the given � gure. Name them

__________________________________________________________________

S

PQ

R

3. Name the vertex and arms of each angle.

(a)

B C

A (b)

Q R

P (c)

y z

x

4. Write T for true and F for false. (a) A line has no end point. (b) A ray has a � xed length. (c) An angle has two arms. (d) A 90° angle is also called a right angle. (e) A circle can have two centres.

5. Draw and label a line, a line segment and a ray.

___________________________________________________________________

6. Fill in the blanks. (a) A line has no end points while a ________ has one end-point. (b) A ________ has 2 end points. (c) For xyz, the vertex is ________ . (d) An obtuse angle has a measure between ________ and ________.

Worksheet 2

47

10 Measurement

Learning Objectives

Students will be able to ➢ review various units of measurement ➢ understand the relation between the di� erent units of length ➢ convert one unit of length into another ➢ use decimals to express length ➢ understand the relation between di� erent units of mass ➢ convert one unit of mass into another ➢ use decimals to express mass ➢ relate di� erent units of capacity ➢ convert one unit of capacity into another ➢ use decimals to express capacity ➢ add and subtract measures of lengths, mass and capacity ➢ estimate measures

Concept Explanation • Introduce the concept of units using the Gear Up section.• Introduce them to the decimal place value chart on length on page 160. Using this chart,

explain how a unit is 10 times less than the unit to its le� and 10 times more than the unit to its right.

• Also explain to them that for converting smaller units to larger units, we divide. And for converting larger units to smaller units, we multiply.

• Once the students understand this concept, hold a quiz on conversion in the class. � is will reinforce the concept of conversion of units in students.

• Use examples given in the book to tell students about the use of decimals in expressing length.

• Ask students to do Check Point 10.1.• Introduce them to the decimal place value chart on mass on page 163. Using this chart,

explain how a unit is 10 times less than the unit to its le� and 10 times more than the unit to its right.


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• Use examples given in the book to tell students about the use of decimals in expressing mass.

• Ask students to do Check Point 10.2.• Introduce them to the decimal place value chart on capacity on page 165. Using this

chart, explain how a unit is 10 times less than the unit to its le� and 10 times more than the unit to its right.



• Use examples given in the book to tell students about the use of decimals in expressing capacity

• Ask students to do Check Point 10.3.• Give students examples from real life where we have to estimate measures. For example,

height of a student, weight of the ti� n box, capacity of a water bottle, etc. Tell them that this estimate is close to the actual value. Tell them that for estimating close to the actual value, it is necessary that they have to have a strong understanding of the units.

• Make a table as shown below on the board. Now ask students to estimate the measure. � en ask them to measure and � nd the actual measure and see how close they were to actual measure.

Object Estimated measure Actual measureA pencilA dusterA student’s weightWater or milk in a glassLength of an eraser

• Do the Maths Lab Activity given on page 170 to make students understand the importance of units.

• Ask students to do Growing with Values given on page 168 and instill in them love and care for elders.



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Tick (√) the correct options. 1. 16 km = ______ hm (a) 160 (b) 1600 (c) 1.6 (d) 16 2. 457 dam = ______ m (a) 45.7 (b) 4.57 (c) 4570 (d) 45700 3. 9372 mg = ______ g ______ mg (a) 93, 72 (b) 937, 2 (c) 9372, 0 (d) 9, 372 4. 9 kL = ______ L (a) 9000 L (b) 900 L (c) 90 L (d) 9 L 5. 9 cups of 0.5 L capacity each have a total capacity of (a) 45 L (b) 0.45 L (c) 450 L (d) 4.5 L

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1. Tick (√) the correct options. (a) Best suited unit to measure the weight of a house� y is (i) kilogram (ii) gram (iii) milligram (iv) hectogram (b) 2 L 300 mL × 4 is equal to (i) 8 L 200 mL (ii) 9 L 100 mL (iii) 9 L 200 mL (iv) 8 L 1200 mL

2. Convert. (a) 8 km into hm _____________ (b) 4 m into mm _____________ (c) 8630 g to kg _____________ (d) 7 L into mL _____________

3. Add/Subtract. (a) 12 m 56 cm + 5 m 72 cm _______ (b) 37 km 832 m – 15 km 948 m _______ (c) 16 kg 372 g + 32 kg 804 g _______ (d) 25 kg 520 g – 17 kg 840 g _______ (e) 50 L 630 mL + 21 L 890 mL _______ (f) 63 L 156 mL – 34 L 475 mL _______

4. (a) A teapot has 2.5 L of tea. It is poured in cups with a capacity 250 mL each. How many cups can be � lled?

_______________________________________________________________ (b) 1.35 m of cloth is required for making a pair of shorts and 1.75 m for making a

shirt. How much cloth is required to make 2 pairs of shorts and 2 shirts?

_______________________________________________________________ (c) Mrs Gokhale bought 1 kg 500 g apples, 1 kg 225 g oranges and some mangoes. If

the fruits she bought weighed 4.450 kg, how many kilograms of mangoes did she buy?

_______________________________________________________________

Worksheet 1

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1. Tick (√) the correct options. (a) To convert kilogram to gram you will (i) multiply by 1000 (ii) divide by 1000 (iii) multiply by 100 (iv) divide by 100 (b) 7 m 6 dm is equal to (i) 7.6 m (ii) 0.76 m (iii) 76 m (iv) 760 m

2. Convert. (a) 800 m into hm ______ (b) 12 hg into g ______ (c) 7 L into dL ______

3. Add/Subtract (a) 32 kg 250 g – 18 kg 600 g ______ (b) 15 km 275 m + 18 km 803 m ______ (c) 44 L 92 mL + 11 L 853 mL ______ (d) 16 km 112 m – 7 km 207 m ______ (e) 16 kL 256 L + 27 kL 903 L ______ (f) 52 g 925 mg + 36 g 125 mg ______

4. Madhu purchased a 12 m cloth. She used 4 m to make her Salwar kameez, 2 m to make a shirt and 1 m 20 cm to make a pair of pants. Find the total length of the cloth le� with Madhu?

___________________________________________________________________

5. A horse was given 1 kg 750 g of food everyday. What quantity of food is required for 7 days.

___________________________________________________________________

6. A fountain pen can be � lled 10 times from a bottle containing 1 litre of ink. How much ink can be � lled in the fountain pen at one time?

___________________________________________________________________

Worksheet 2

52

11 Perimeter, Area and Volume

Learning Objectives

Students will be able to ➢ revise the concept of area and perimeter ➢ develop formula for calculating perimeter of a rectangle and a square ➢ develop formula for calculating area of a rectangle and a square ➢ � nd the area of a triangle ➢ focus on the di� erent units of area ➢ measure the area of irregular shapes ➢ explore relationship between area and perimeter ➢ develop the concept of volume ➢ use unit of volume, i.e., cubic units ➢ develop the formula to calculate volume of a cube and a cuboid

Concept Explanation • To review the area of a closed � gure, use the Gear Up section.• Distribute the cut-outs of rectangles and squares of di� erent measurements to students.

Ask them for the following details.

Rectangle SquareS.

NoLength Breadth Perimeter =

(l + b)S. No Side P = 4 × side

1 12 23 34 4

• Verify the details mentioned above and arrive at the formula of the two, i.e., perimeter of a rectangle and a square using page 173 and 174.

• For practice, ask students to do Check Point 11.1.• Follow the same method for arriving at the formulea of the area of a rectangle and a

square.• For practice, ask students to do Check Point 11.2.

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• Teach students to � nd the area of a triangle using a rectangle and graph. Use pages 179 and 180 to explain the same.

• For practice, ask students to do Check Point 11.3.• Using graphs, � nd the area of irregular shapes and for practice, ask students to do Check

Point 11.4..• Help students to solve the examples on pages 182 and 183 to arrive at a relationship

between the area and the perimeter.• To introduce the concept of volume, take an empty carton. Open it to obtain its net. Now

fold it back to get the carton again. Now explain to the students that the space enclosed within the carton is the volume of the carton.

• Take a variety of containers like empty polypack, coke can, etc. Fill these with di� erent objects like kidney beans, sand, marbles, etc. Tell students that the number of marbles a container contains is its volume. Repeat with kidney beans too. � en discuss the need for the standard unit of volume.

• Take small cubes of plastic and � ll up a carton. Keep counting the cubes as they are being put inside the carton. Once that is done, write the volume of the carton in cubic units.

• For practice, ask students to do Check Point 11.5.• Use page 186 to arrive at the formulae for calculating volumes for a cube and a cuboid.• For practice, ask students to do Check Point 11.6.• Do the Maths Lab Activity given on page 190 to make students understand the importance

of perimeter, area and volume.• Ask students to do the Growing with Values section and instill in them values of helping

needy children in best possible way.• For further reinforcement, ask students to do the Brain Workout section given on page

188.• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths



Tick (√) the correct options. 1. Perimeter of a rectangle with length 12 cm and breadth 4 cm is (a) 48 cm (b) 16 cm (c) 32 cm (d) 120 cm 2. Perimeter of a square with side 7 cm is (a) 14 cm (b) 21 cm (c) 15 cm (d) 28 cm

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3. � e area of a rectangle with length 14 cm and breadth 5 cm is (a) 70 cm2 (b) 19 cm2 (c) 140 cm2 (d) 50 cm2

4. � e area of a square of side 9 cm is (a) 18 cm2 (b) 36 cm2 (c) 81 cm2 (d) 27 cm2

5. � e volume of a cubical box with each side measuring 5 cm is (a) 25 cu. cm (b) 15 cu. cm (c) 125 cu. cm (d) 1250 cu. cm

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1. Tick (√) the correct options. (a) Length of the boundary of a closed � gure is called its (i) Perimeter (ii) Area (iii) Capacity (iv) Measure (b) Perimeter of a rectangle with dimensions 9 cm and 4 cm is (i) 36 cm (ii) 72 cm (iii) 13 cm (iv) 26 cm

2. Find the side of the square whose perimeter is 72 cm.

___________________________________________________________________

3. Find the perimeter of the square whose side is 14 cm.

___________________________________________________________________

4. � e length of the side of a square mat is 1 m 25 cm. Find the area of the mat.

___________________________________________________________________

5. Find the area of a rectangle whose length is 16 cm and breadth is 10 cm.

___________________________________________________________________

6. Find the area of the shaded part. Each square = 1 sq. cm. (a) (b)

7. In the shape given here two lines are drawn. Draw two more lines so as to have its area as mentioned.

17 sq. cm

Worksheet 1

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1. How many small cubes of side 2 cm can be put inside a cubical box of side 8 cm?

___________________________________________________________________

2. � e space occupied by a solid is called its— (a) volume (b) area (c) perimeter (d) circumference

3. Find the volume fo the solid shown below if each represents 1 cm cube.

4. � e length, breadth and height of an iron trunk is 3 m, 1 m 15 cm and 30 cm, respectively. Find the volume of the trunk.

___________________________________________________________________

5. Find the volume of a sugar cube whose edge is 9 mm.

___________________________________________________________________

6. Which lunch box has greater volume — Shipra’s or Kunj’s? Measure of Shipra’s lunch box 12 cm, 10 cm, 6 cm.

_______________________________________________________________ Measure of Kunj’s lunch box 11 cm, 11 cm 6 cm.

_______________________________________________________________

Worksheet 2

57

12 Time and Temperature

Learning Objectives

Students will be able to ➢ develop the relationship between hours and minutes; minutes and seconds ➢ add and subtract measures of time ➢ calculate the starting time and the � nishing time of an event when the duration is

given ➢ calculate the � nishing or starting date of an event when the duration is terms of days

is known ➢ develop the understanding of temperature ➢ know the units of temperature

Concept Explanation • To recapitulate the relation between the 12-hour and 24-hour clocks, use the Gear Up

section given on page 193.• Take a real clock and explain the concept of minutes and seconds and also the relationship

between a minute and a second. You can also use a stopwatch to further reinforce the concept of seconds.

• Explain the conversion of di� erent units of time to students with the help of a clock.• Once the students become familiar with the concept, hold a quiz in the class on the

conversion of di� erent units of time.• For practice, ask students to do Check Point 12.1.• Teach students addition and subtraction of time using pages 196 to 198.• To reinforce, ask students to do Check Point 12.2.• Use a dummy clock to teach calculation of starting or � nishing time.• Ask students to do Check Point 12.3.• Using a calendar, explain to students how to calculate the starting or � nishing date or the

duration of days..• Ask students to do Check Point 12.4 for further practice.• Teacher can show a video or take a large cardboard cut-out of a thermometer to explain

the markings on the thermometer. Hold it horizontally and explain to the students that it can be compared to a number line and the markings start from 95°F and greater numbers are to the right. Need for recording temperature should be discussed.

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• A clinical thermometer can be brought to the class to display in the class.• Explain the Celsius and Fahrenheit scales.• To further reinforce the concept of temperature, ask students to record the minimum

and maximum temperatures of their cities from the newspapers for two weeks. • Ask students to do Check Point 12.5.• Help students do the Maths Lab Activity given on page 206 to help them learn how to

measure temperature. • Ask students to do Growing with Values and instill in them the value of empathy for

others.• For reinforcement, ask them to do the Brain Workout section given on page 205.• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths



Tick (√) the correct options. 1. � ere are _____ hours in 5 days. (a) 25 (b) 120 (c) 10 (d) 1200 2. 3 hours have ______ minutes. (a) 18 (b) 90 (c) 180 (d) 1800 3. A plane leaves Delhi at 6:45 am. � e � ight takes 3 hours and 15 minutes to reach

Mumbai. At what time will it reach Mumbai? (a) 9:45 am (b) 10:45 am (c) 10:00 am (d) 11:00 am 4. What was the last date of the summer vacation of it started on 2 May and lasted for

45 days? (a) 13 May (b) 14 May (c) 15 May (d) 16 May 5. Temperature in the morning was 35°C. In the evening it was 17°C. � e di� erence

in temperature was (a) 8°C (b) 18°C (c) 10°C (d) 17°C

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1. Tick (√) the correct option. (a) What is the reading on a thermometer when water starts freezing? (i) 0°F (ii) 0°C (iii) 32°F (iv) both (i) and (iii) (b) How many seconds are there in a day? (i) 24 seconds (ii) 60 × 60 seconds (iii) 24 × 60 seconds (iv) 24 × 60 × 60 seconds

2. Find the time. (a) 50 minutes a� er 11:25 am __________________ (b) 5 hour 10 minutes a� er 2:00 hours __________________ (c) 3 hours 50 minutes before 2:00 hours __________________ (d) 3 hour 45 minutes before 12:00 midnight __________________

3. Find the date. (a) 28 days before 26 January 2016 __________________ (b) 70 days a� er 1 July __________________

4. In the � ight time table, � ll in the missing entries.

S.No. Flight no. From—to Departuretime Arrival time Flight

duration(a) SG - 248 Goa to Mumbai 11:45 am 12:50 pm(b) AL - 776 Mubai to Kolkata 12:15 pm 2 h 35 min(c) 6E - 575 Delhi to Cochin 02:10 pm 3 h 5 min

5. At Amritsar, the maximum and minimum temperatures on a certain day were 33.8°C and 17.2°C, respectively. � e next day the maximum went up by 1.7°C and the minimum came down by 1.2°C. Find the maximum and the minimum temperatures on the next day.

___________________________________________________________________

Worksheet 1

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1. Tick (√) the correct option. (a) Boiling point of water is (i) 0°F (ii) 100°C (iii) 32°F (iv) 212°F

(b) 5 14 minutes is

(i) 5 minutes 25 seconds (ii) 5 minutes 30 seconds (iii) 5 minutes 15 seconds (iv) 5 minutes 0.25 seconds

2. � e maximum temperature in 8 Indian cities on 15 April 2015 was recoreded as follows.

Bengaluru: 29°C Chennai: 37°C Goa: 33°C Kolkata: 38°C Mumbai: 32°C New Delhi: 38°C Manali: 10°C Kodaikanel: 25°C (a) Your family is planning a one week holiday in April. Which city will you select?

Why? _______________________________________________________________ (b) If you had to go to Manali to visit an aunt, what kind of clothes will you carry? _______________________________________________________________

3. Sheela is a good tennis player. She spends 100 minutes every morning in tennis practice. She starts practising at 6:15 am. At what time does she end her practise?

___________________________________________________________________

4. All India School Cricket Tournament started at Mumbai on 25 Feburay 2016. It lasted for 18 days. When did it end?

___________________________________________________________________

Worksheet 2

61

13 Mapping Skills

Learning Objectives

Students will be able to ➢ understand what is a � oor plan ➢ understand how to read maps ➢ understand how to read directions in maps ➢ understand scales in maps ➢ understand the usefulness of keys in maps

Concept Explanation • Recall the directions with the help of the Gear Up section• Show students some pictures of � oor plans to make them understand about the � oor

plan and its uses.• Show an atlas to the class to introduce the concept of the map. Start with the identi� cation

of the location of India in the world map. � en in the map of India ask students to locate the city students live in.

• Show the scales used in the maps and tell them the importance of these. Draw a tree on the board. Tell them that this is not the actual size of the tree as it is impossible to draw the actual size. � en introduce scale here. Tell them how we can represent the actual size with the help of a scale.

• Next tell them about the directions and keys in the maps and their uses.• For practice, ask students to do Check Point 13.1 and Check Point 13.2.• To reinforce, ask students to do the Brain Workout section given on page 213.• Do the Maths Lab Activity given on page 214 to help students create a map on their own.• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths

with Art and Drawing) and Test Yourself sections.



1. If 1 cm = 1 m, then the actual length of 3 cm would be

(a) 1 m (b) 2 m (c) 3 m (d) 4 m

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2. If 1 cm = 10 m, then the actual length of 4.5 cm

(a) 4 m (b) 45 m (c) 0.45 m (d) 4.5 m

3. If 10 cm = 1 m, then scaled down length of 3.5 cm

would be

(a) 35 cm (b) 350 cm (c) 3500 cm (d) 3.5 cm 4. A list of symbols or colours used to illustrate objects on a map is called a (a) scale (b) compass rose (c) key (d) none of these 5. _________ gives us an idea about the actual size or actual distance of an object in

a map. (a) Scale (b) Compass rose (c) Key (d) None of these

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1. Enlarge this picture by drawing it on 2 cm square grid.

2. Reduce this picture by drawing it on 12 cm square grid.

3. Measure to � nd the scale used in the drawing.

Actual height of building = 48 m.

Worksheet 1

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Look at the map of India and � ll in the blanks.

INDIA POLITICAL

(a) In the map, the South direction is on the ________ . (top, bottom, right, le� ) (b) If you want to go from Madhya Pradesh to Kashmir you have to travel in the

________ direction. (c) � e state on extreme South of India is ________ . (d) If you have to travel from Madhya Pradesh to Gujarat, you have to travel in the

________ direction. (e) If you have to travel from Delhi to Assam, you have to travel in the ________

direction.

Worksheet 2

65

14 Data Handling

Learning Objectives

Students will be able to ➢ understand more about circle graphs ➢ use tally marks to collect data ➢ understand the basics of line graphs

Concept Explanation Recall the directions with the help of the Gear Up section• Recall bar graphs using the Gear Up section.• Introduce the concept of circle graph. Take a cut-out of a circle and divide it into 8

equal parts. Now distribute these parts to 8 students. Ask them to colour these as per their favourite sport. Use colour coding for various sports, like yellow for cricket, red for football, etc. � en collect these parts and keep the similar colour parts together to form the circle again. Now explain to students that this is a circle graph on favourite sports of 8 students. Now ask them questions based on these. Give more examples.

• For practice, ask students to do Check Point 14.1.• Introduce tally marks. On the board draw a table and build a tally grid on the board.

For this you may collect the data from the students, for example, their birthdays or their favourite colours, fruits, etc. Let the students help you make the tally marks on the board.

Favourite colour Tally marks Number of studentsYellow 2Green 5Red 4Blue 8

• Once this is done, the number of students having their favourite colours can be found by counting tally marks.

• For practice, ask students to do Check Point 14.2.• Use the example given on page 222 to explain line graphs to students. Various other

examples can be taken.• For practice, ask students to do Check Point 14.3.• For more practice on bar graphs and tally marks, do the Maths Lab Activity given on

page 225.

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• For further reinforcement, let students do the Brain Workout given on page 224.• For overall recapitulation, let students go through the Flashback section.• Help students do the Recreation Corner, Maths Connect (showing the connect of Maths



Tick (√) the correct options. � e line graph given below shows the number of days it rained during the rainy

season in a city of Kerala. Study the graph and answer the questions that follow.

JuneJuly

August

September

20

25

30

15

10

5

Num

ber o

f day

s

Months

1. Which was the wettest month? (a) June (b) July (c) August (d) September 2. Which month received the least rainfall? (a) June (b) July (c) August (d) September 3. Which two months received the same amount of rainfall (a) June, July (b) July, August (c) August, September (d) June, August 4. For how many days it did not rain in the month of June? (a) 20 days (b) 10 days (c) 5 days (d) 15 days 5. In which month did it rain for about half a month? (a) June (b) July (c) August (d) September

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1. � e circle graph shows the favourite subjects of 24 students of class 5. Read it and complete the given table.

Subject Fraction in circle graph

Number of students

Social ScienceScienceEnglishMaths

2. Draw a bar graph to represent the following data.

Subjects Hindi English Maths EVS SSTMarks obtain 70 85 90 65 75

3. Complete the following tally chart.

Favourite TV channel Tally Marks Number of

studentsDiscovery 9

Movies 13Music 10

Educational 6Cartoon 5

News 2

Maths

Social Science

EnglishScience

Worksheet 1

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1. � e line graph shows the day temperature of Delhi city in January, recorded from 6 am to 6 pm in 2 hour intervals. Answer the following questions.

(a) At what time was the day warmest? (b) At what time was it coolest? Why

6 am8 am

2 pm10 am

4 pm12 noon

6 pm

8

16

10

18

12

20

6

14

4

2

Tem

pera

ture

in °C

Time

2. � e monthly sale of books in a school book shop for the � rst 8 months is as follows:

Month Jan Feb March Apr May June JulySale 350 400 600 400 250 50 200

Draw a line graph to show the data.

(a) Which month had the maximum sale? _______________________________________________________________

(b) When was the sale the least? _______________________________________________________________

Worksheet 2

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1. Draw lines of symmetry for the following shapes. (2 × 3 = 6)

(a) (b) (c)

2. Complete the pattern if the shape turns half turn in each case. (2 × 3 = 6)

(a)

(b)

(c)

3. Identify and name the following angles. (2 × 3 = 6)

(a) (b) (c)

MathematicsModel Test Paper 2

Time: 2 hoursClass 5

Total Marks: 50

N O

M

R

Q Px

y z

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4. Use a protractor to measure each of the following angles: (2 × 3 = 6)

(a) (b) (c)

5. Convert: (1 × 3 = 3) (a) 8700 dam = _______ km (b) 3.9 kL = _______ L. (c) 1879 g = _______ mg.

6. Find the perimeter of a rectangular scarf whose length and breadth are 5 m and 67 cm, respectively. (3)

7. A square painting is 8 m long. Find its area. (3)

8. Find the volume of a box with each side measuring 6 cm. (3)

9. Ritika started from her house at 7:45 am. She took 50 minutes to reach her school. What time did she reach her school? (3)

10. � e actual length of the following is given. What will be their scaled down length. if 100 cm = 1 cm. (2 × 3 = 6)

(a) (b) (c)

11. Make a tally marks table to show the number of each fruit in the picture. (5)

N N

M

S

R

P

A

B C

9 m 7 m 12 m

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Answer KeyChapter-1Multiple Choice Questions (MCQ)1. (d) 2. (a) 3. (b) 4. (b) 5. (d)

Worksheet-11. Number Indian

SystemInternational

system(a) 369512 3,69,512 369,512(b) 2397010 23,97,010 2,397,010(c) 32954602 3,29,54,602 32,954,602(d) 60032051 6,00,32,051 60,032,051

2. Number Indian System

International system

(a) 2389435 20,00,000 2,000,000(b) 70453271 4,00,000 400,000

3. (a) 3,00,00,000 + 90,00,000 + 7,00,000 + 20,000 + 400 + 7

(b) 4,00,00,000 + 40,00,000 + 9,00,000 + 64. (a) 8887653 (b) 33356785. (a) LXIII (b) XLV (c) XCIX (d) LXXII6. (a) > (b) < (c) < (d) =7. (a) 89,000 (b) 10,000 (c) 26,000

Worksheet-21. (a) (i) (b) (i)2. (a) Four crore thirty lakh forty-seven thousand

nine hundred six. 4,00,00,000 + 30,00,000 + 40,000 + 7,000 +

900 + 6 (b) Twenty-eight million six hundred ten

thousand seven hundred six. 20,000,000 + 8,000,000 + 600,000 + 10,000 +

700 + 63. (a) 40 (b) 60 (c) 57 (d) 984. (a) 2,07,745; 27,27,345; 27,27,745; 2,72,72,7455. (b) 6,67,80,243; 5,76,06,432; 5,67,80,234;

5,67,06,4325. 7000 6. 487300

Chapter-2Multiple Choice Questions (MCQ)1. (b) 2. (a) 3. (a) 4. (b) 5. (c)

Worksheet-11. (a) 4,54,312 (b) 1,42,2392. (a) 8 3 2 5 6

+ 1 7 4 5 51 0 0 7 1 1

(b) 8 5 6 0 5 9– 3 2 5 2 6 0

5 3 0 7 9 9

3. `3,69,120 4. `29,7105. `3,35,677 6. `1,46,784

Worksheet-21. (a) 49875 (b) 942876 (c) 1428751 (d) 7342895 (e) 02. (a) 30 (b) 853. `117 4. `3,0005. (a) `295 (b) `225 (c) `1,150 (d) 1,0106. `3,350

Chapter-3Multiple Choice Questions (MCQ)1. (d) 2. (a) 3. (c) 4. (d) 5. (d)

Worksheet-11. (a) 0 (b) 3849743 (c) 329 (d) 55 (e) 587321 (f) 1 (g) 02. (a) 4873160 (b) 9271800 (c) 657400 (d) 4570003. (a) (i) (b) (ii)4. 2,000 5. 2,91,375 kg

Worksheet-21. 7 m 2. 44 3. 104. 35 5. 190

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Chapter-4Multiple Choice Questions (MCQ)1. (c) 2. (a) 3. (c) 4. (c) 5. (b)

Worksheet-11. (a) Prime number (b) Highest common factor or HCF (c) Composite number2. 17, 19, 29, 31, 373. 2 4.

63

3 21

3 75. 1, 2, 46. Divisible by

Number 2 3 4 5 6 9 10(a) 75

(b) 126

(c) 275

(d) 996

(e) 2430

(f) 66660

Worksheet-21. (a) Divisible by 2: 32, 44, 78, 80 (b) Divisible by 5: 15, 35, 50, 110 (c) Divisible by 10: 50, 70, 902. 71, 73, 79, 83, 89, 973. 212

2 106

2 53

4. 2 × 2 × 17

5. 12

Chapter-5Multiple Choice Questions (MCQ)1. (b) 2. (c) 3. (a) 4. (d) 5. (c)

Worksheet-11. (a) (ii) (b) (ii)2. (a) 6, 12, 18, 24 (b) 13, 26, 39, 52 (c) 20, 40, 60, 803. (a) 72 (b) 72 (c) 60

4. 5 5. 33 6. 84 7. 280

Worksheet-21. (a) false (b) false (c) true2. (a) 9, 27, 45, 63 (b) 7, 21, 35, 49 (c) 11, 33, 55, 773. (a) 144 (b) 11554. 7600 5. 60 6. 6

Chapter-6Multiple Choice Questions (MCQ)1. (a) 2. (c) 3. (c) 4. (a) 5. (d)

Worksheet-1

1. (a) 29 = 14

63 (b) 311 = 9

33

2. (a) 616 , 9

24 (b) 1832 , 27

483. (a) > (b) = (c) <

4. (a) 23 (b) 59 (c) 1

2 (d) 3239

5. (a) 147 (b) 1

60 (c) 25 (d) 12

6. (a) 1445 (b) 3

10

7. (a) 134 (b) 21

7 (c) 198

Worksheet-21. (a) (ii) (b) (i) (c) (i)

2. 178 3. 1

2 4. 913 5. 2

3

6. 118 7. 3

4 8. `70

Chapter-7Multiple Choice Questions (MCQ)1. (d) 2. (b) 3. (b) 4. (d) 5. (b)

Worksheet-11. (a) (iv) (b) (iv)2. Decimals Like or

unlikeEquivalent or not equivalent

(a) 3.90, 3.09, 3.99 Like Not equivalent(b) 2 tenths, 20 hundredth,

200 thousandthsUnlike Equivalent

(c) 14.14, 25.25, 36.36 Like Not equivalent

73

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0–

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%

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3. (a) < (b) > (c) >4. (a) 11.11 (b) 0.909 (c) 0.85 (d) 2.3 (e) 2.82 (f) .0035 (g) 37.5 (h) 4009 (i) 980.8 (j) 8.98

Worksheet-21. (a) (iii) (b) (iv)

2. (a) .3 (b) 7100 (c) 9 + 3

10 + 2100 + 1

1000 (d) 783.143. (a) < (b) < (c) = (d) >4. (a) 4.97 (b) .06818 (c) .05187 (d) 15. 3.695 6. 28.62 m 7. Anuja, `27.8

Model Test Paper-11. (a) 1 Hundred (b) Pro� t (d) 18 (e) composite (f) 10 (g) < (h) 902. (a) � ousands periods; 900,000 (b) Millions periods; 70,000,000 (c) Millions periods; 03. (a) 163 (b) 884. (a) 15992589 (b) 1831971395. (a) Q = 66340, R = 4 (b) Q = 4857, R = 106. 5 7. 1323

8. (a) 1577 (b) 3

289. (a) 64

121 (b) 730

10. (a) 18.198 (b) 0.56313 11. (a) 3.9 (b) 0.987 12. (a) Pro� t `17,491 (b) 8726 (c) 25 cm (b) 27 days

Chapter-8Multiple Choice Questions (MCQ)1. (c) 2. (a) 3. (b) 4. (a) 5. (c)

Worksheet-11. (a) (iv) (b) (iv)

2. (a) (b) (c)

3. (a) 2 (b) 4 (c) 2 (d) 2

4. (a) (b) (c) (d)

5. (a) (iii) (b) (iv) (c) (ii) (d) (i)

Worksheet-2

1. (a) (i) (iii)

(b) (i) (ii) (iii)

2. Letter 1

4 turn 1

2 turn

(a) B B B

(b) F F F

(c) C

C C(d) K

K K

3. (d)

Chapter-9Multiple Choice Questions (MCQ)1. (a) 2. (b) 3. (a) 4. (c) 5. (b)

Worksheet-11. (b)2. (b)3. (a) ABC or B, acute angle (b) EFC or F, obtuse angle (c) PQR or O, straight angle4.

5. (a) AB, BC and CA (b) PT, TS, SR, RQ and QP6. 130°, 180°

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÷Worksheet-21. (a) Yes (b) No2. PSR, SRQ, RQP and QPS 3. (a) Vertex – B, Arms – AB and BC (b) Vertex – Q, Arms – PQ and QR (c) Vertex – y , Arms – xy and yz4. (a) T (b) F (c) T (d) T (e) F5. P Q

Line R

RayS

Line segmentx y

6. (a) ray (b) line segment (c) y (d) 90° and 180°

Chapter-10Multiple Choice Questions (MCQ)1. (a) 2. (c) 3. (d) 4. (a) 5. (d)

Worksheet-11. (a) (iii) (b) (iii)2. (a) 80 (b) 4000 (c) 8 kg 630 g (d) 70003. (a) 18 m 28 cm (b) 21 km 884 m (c) 49 kg 176 g (d) 7 kg 680 g (e) 72 L 520 mL (f) 28 L 681 mL4. (a) 9 (b) 6.20 m (c) 2 kg 175 g

Worksheet-21. (a) (i) (b) (i)2. (a) 8 (b) 1200 (c) 703. (a) 13 kg 650 g (b) 34 km 78 m (c) 55 L 945 mL (d) 8 km 905 m (e) 44 kL 159 L (f) 89 g 50 mg4. 4 m 80 cm 5. 12 kg 250 g 6. 100 mL

Chapter-11Multiple Choice Questions (MCQ)1. (c) 2. (d) 3. (a) 4. (c) 5. (c)

Worksheet-11. (a) (i) (b) (iv)2. 18 cm 3. 56 cm

4. 1.5625 m 5. 160 cm 6. (a) 10 sq. cm (b) 12.5 sq. cm7.

Worksheet-21. 64 2. (a) 3. 7 cm3

4. 1.035 m3 5. 729 mm3 6. Kunj’s lunch box

Chapter-12Multiple Choice Questions (MCQ)1. (b) 2. (c) 3. (c) 4. (c) 5. (b)

Worksheet-11. (a) (iv) (b) (iv)2. (a) 12:15 pm (b) 7:10 hours (c) 22:10 hours (d) 8:15 pm3. (a) 29th December (b) 9 September4. (a) 1 h 5 min (b) 9:40 am (c) 11:05 am5. 35.5°C and 16°C

Worksheet-21. (a) (ii) (b) (iii)2. (a) Manali (b) woollen clothes3. 7:554. 13th March

Chapter-13Multiple Choice Questions (MCQ)1. (c) 2. (b) 3. (a) 4. (c) 5. (a)

Worksheet-13. 1 cm = 8 cm

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÷Worksheet-2(a) bottom (b) south (c) Kerala (d) west (e) east

Chapter-14Multiple Choice Questions (MCQ)1. (b) 2. (d) 3. (d) 4. (b) 5. (d)

Worksheet-11.

Subject Fraction in circle graph

Number of students

Social Science 1/8 3Science 1/8 3English 1/4 6Maths 1/2 12

2. 100

908070605040302010

Hindi English Maths EVS SST

Mar

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btai

ned

Subjects

3. Favourite TV

channelTally

MarksNumber of

studentsDiscovery |||| |||| 9

Movies |||| |||| |||| 13Music |||| |||| 10

Educational |||| | 6Cartoon |||| 5

News || 2

Worksheet-21. (a) 2 pm (b) 6 am2.

700600500400300200100

Jan Feb Mar Apr May Jun Jul

(a) 6 March (b) June

Model Test Paper-21. (a) (b) (c)

2. (a) (b) (c)

3. (a) xyz (b) PQR (c) MNO5. (a) 87 (b) 3900 (c) 18790006. 11 m 34 cm 7. 64 m2

8. 216 cm3

9. 8:35 am 10. (a) 9 cm (b) 7 cm (c) 12 cm11.

Name Tally Marksbanana |||| ||||mango |||| ||||apple |||| ||||

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Documents

Maths Quest-5 Teacher Manual - SARASWATI HOUSE Material/978-93-5… · 3. Multiplication, Division and their Applications 14 4. Factors 18 5. Multiples 22 6. Fractions 26 7. ... Make