PT_G05_MA_WB_Text_2025_AY25-26

Practice • Solve • Succeed

Mathematics Workbook

Perfect

MATHEMATICS Workbook

Grade 5

Acknowledgements

Academic Authors: Muskan Panjwani, Anuj Gupta, Simran Singh

Creative Directors: Bhavna Tripathi, Mangal Singh Rana, Satish

Book Production: Sanjay Kumar Goel, Tauheed Danish, Vishesh Agarwal

Project Lead: Neena Aul

VP, Learning: Abhishek Bhatnagar

All products and brand names used in this book are trademarks, registered trademarks or trade names of their respective owners.

© Uolo EdTech Private Limited

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Book Title: Perfect Mathematics Workbook 5

ISBN: 978-81-982034-3-4

Published by Uolo EdTech Private Limited

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Preface

Mathematics thrives on practice, which is crucial for mastering concepts and building confidence. A regular engagement with mathematical problems helps students apply theoretical knowledge, identify areas for improvement, and enhance their critical thinking skills. With consistent practice, students can transform abstract ideas into tangible skills, paving the way for a deeper understanding and success in the subject.

The Perfect Mathematics workbooks are a set of practice books designed for students in Grades 1 to 8. One workbook is provided per grade. Aligned with the NCERT textbooks, these workbooks provide ample practice in the concepts covered in each grade, ensuring a strong foundational understanding of mathematics.

For younger learners (Grades 1 to 5), we have included Mental Mathematics worksheets designed to enhance rapid calculation skills, and avoid relying on calculators or written methods. These exercises promote quick thinking and boost students’ confidence in their mathematical abilities.

The workbooks support learners at all levels, providing opportunities to build problem-solving skills through questions aligned with Bloom’s Taxonomy. They also feature a diverse range of question types, including Fill in the blanks, True/False, MCQs, and both short and long answer questions. To foster critical thinking and analytical skills, each chapter includes dedicated challenge questions that push students to deepen their understanding and tackle more complex problems. Additionally, we have provided a Case Study at the end of each chapter, followed by scenario-based questions that encourage students to apply their theoretical knowledge in real-life situations, bridging the gap between classroom learning and practical application.

To facilitate self-assessment, answers to all questions are provided at the end of each workbook. This enables students to check their work and learn from their mistakes, fostering a growth mindset.

In addition, each workbook is aligned to its digital component, which contains immersive gamified experiences, video solutions and additional practice worksheets. Interactive exercises on the digital platform make learning experiential and serve to make abstract mathematical concepts more concrete.

We believe that the Perfect Mathematics Workbooks will be invaluable resources for students, helping them to not only master the curriculum but also develop a love for mathematics. Happy learning!

Rational

Numbers

QR Code: Digital resources aligned to the key concepts covered in the book.

Curriculum Alignment: Aligned with the topics covered in the NCERT textbooks for practice across chapters and topics.

Chapter Checkup: Chapter-end practice exercises aligned to different levels of Bloom’s Taxonomy.

Picture-based Questions: Questions featuring visual stimuli to foster comprehension and interpretation. 2

Challenge

Challenge: Critical thinking questions to enhance problem-solving and analytical thinking skills. Higher-order-thinking questions, in the form of assertive reasoning, and data-sufficiency questions.

Critical Thinking

1  A book has 400 pages. Raj finishes writing 100 pages in x minutes. Raju takes twice the time taken by Raj to write the next 150 pages. Vivek takes 2 hours more than half the time taken by Raju to write the remaining pages. The total time taken to write the book was 33 hours and 20 minutes. How much time is taken by Vivek to write the remaining pages (in hours)?

Case Study: Scenario-based questions for students to apply theoretical knowledge to real-world situations.

Urban Transport Tariffs

A company that provides transportation services charges different prices in different cities based on how many people live there. They also add a fixed fee for every ride, which stays the same no matter which city you are in. The table below shows how much they charge per kilometre and the fixed fee in City A and City B.

Answer

2  Read the statements and choose the correct option.

Assertion (A) – The difference of two numbers is 25. The larger number is x. The smaller number is x – 25. Reason (R) – Numbers which follow each other in order, without gaps, from smallest to largest like 12, 13, 14 and 15 are consecutive numbers.

1  The amount (x) paid by a customer travelling a distance of

a  Both A and R are true and R is the correct explanation of A

b  Both A and R are true but R is not the correct explanation of A

c  A is true but R is false

d  A is false but R is true

Numbers up to 8 Digits

Worksheet 1: All About 7-digit and 8-digit Numbers

1  Write the place value and face value of the underlined digit in the following numbers.

Number Place Value Face Value

a 7409230

b 8656023

2 Write the standard form of the numbers in the Indian and International number systems.

a 21643332

b 1200621

3  Write the number names and expanded form of the given numbers.

a 4,41,90,887

Number name:

Expanded Form:

b 81,085,432

Number name:

Expanded Form:

4  Write the numerals for the following number names.

a  Sixty lakh eight thousand ninety-eight b  Twenty million five hundred sixty-nine

c  Four million ninety thousand d  Eight crore one thousand two

5  Fill in the blanks.

a  10 million = crore b  1 million = lakh

c  1 crore = thousands d  There are zeroes in 20 million

6 The Amazon Rainforest covers approximately 2722000 square miles. Write the number in the Indian and the international number system.

a  Indian Number System  b  International Number System

7 Write the greatest 7-digit number that has the smallest odd digit at its hundreds, ten thousands and lakhs place.

Challenge

Critical Thinking & Cross Curricular

a  1980 b  1989 c  Both years d  Neither year 1

The Kumbh Mela is a major pilgrimage where Hindu pilgrims take the holy bath in the Ganges. The number of people who visited the Kumbh Mela in 1980 were 20,356,817 and those who visited in 1989 were 29,304,871. In which year did less than 25 crore people visit the Kumbh Mela?

Worksheet

2:

Comparing and Ordering Numbers

Which is smaller: 76,24,578 or 87,90,213?

Fill in the blanks with <, > or =.

a  35,72,123 35,78,123 b  63,45,789 63,45,789

c  2,86,73,451 57,81,290 d  6,24,58,110 6,24,59,211

Arrange the following numbers in ascending order and descending order.

a  1,00,36,782; 5,00,00,367; 8,87,21,460; 93,12,820

b  92,56,890; 36,81,910; 6,92,10,350; 8,26,00,031

Write the greatest and the smallest 7-digit numbers using all the digits only once. Greatest   Smallest

a  5, 3, 4, 0, 8, 9, 1

b  5, 7, 6, 2, 1, 3, 8

The total areas of 4 countries in sq. km are given below. Arrange the names in descending order of their area. Russia - 17,098,242; India - 3,287,590; China - 9,706,961; Australia - 7,692,024.

Use any of the digits 0 to 9, using each digit only once to form a 7-digit number that is closest to 40,00,000.

Worksheet 3: Rounding Off Numbers

Round off the following numbers to the nearest tens.

a  85,48,749

Round off the following numbers to the nearest hundreds.

a  1,25,89,183

Round off the following numbers to the nearest thousands.

a  8,97,00,110

b  6,07,85,888

b  87,52,368

b  5,89,89,929

The distance of the Moon from the Earth is 238,855 miles. What is the approximate distance between the Moon and the Earth when rounded off to the nearest thousand?

Critical Thinking & Cross Curricular

Rihan thinks of a number. He says that the number when rounded to the nearest thousands becomes 3,23,46,000. What is the smallest and the biggest possible number that Rihana could think of?

1 Rewrite the following numbers in figures and words using both the Indian and international number systems. Also, write their expanded form.

a  3507681

Indian Number System:

International Number System:

b  42087950

Indian Number System:

International Number System:

2  Write the numbers for the following number names in both number systems.

Number Name

a Sixty million seven hundred fifteen thousand two hundred thirty-nine

b Eight crore nine lakh fifty thousand two

3  Round off the following to the nearest tens, hundreds and thousands.

Numbers a  6,45,87,123 b  89,09,008

Nearest tens

Nearest hundreds

Nearest thousands

4  Fill in the blanks using <, > or =.

a  6,56,52,567 6,48,90,650 b  90,00,518 90,76,757

c  34,57,879 34,57,879 d  13,05,885 6,74,38,989

5  Arrange the following numbers in ascending order.

23,56,475; 9,08,04,365; 8,91,63,896; 90,87,687

1 Sanya wants to solve a 7-digit secret code in a safe. Use the given clues to help Sanya solve the secret code.

a  The digit in the hundreds and ones place is 6.

b  The digit in the lakhs place is 4 less than the digit in the ones place.

c The digit in the ten lakhs and ten thousands place is the smallest odd number.

d  The face value of the digit in the thousands place is 5.

e  The digit in the tens place is the biggest 1-digit number.

Code:

2 Write the greatest 8-digit odd number using only 5 digits. Do not repeat any digit more than twice.

Worksheet 5: Case Study

Population of Countries

The population of different countries is shown using a table. Read the data carefully and answer the questions.

1  Which country has the least population? a  Italy b  Germany c  Poland d  United Kingdom

2 Which country has the greatest population? a  Poland b  United Kingdom c  Italy d  Germany

3 Which country has approximately double the population than that of Poland?

4 Arrange the countries in ascending order as per their population.

Worksheet 6: Mental Maths

1 Tick () the correct answer.

a  What is the place value of 7 in the given number?

i  7 lakh ii  7 ten thousand iii  7 hundred iv  7 crore

b  Write in the Indian number system. 5 million —

i 5,00,000 ii  50,00,000 iii  500,000

2 Match the number to its respective rounded-off number to the nearest 100.

A

B

a 12,345,678 i 12,345,100

b 23,456,789 ii 23,456,500

c 12,345,123 iii 12,345,700

d 23,456,456 iv 23,456,800

3  Fill in the blanks.

a  6 lakhs is written as in the international number system.

b  2 million is written as in the Indian number system.

c thousands make a lakh.

4 The number 5,472,_15, when rounded off to the nearest 1000, gives 5,472,000. Which 2 of these could be the digits of the number?

a  5 b  8 c  0 d  4

5  Use the five given clues to form the 7-digit number.

a  Digit 4 is in the ten lakhs place.

b  Digit 1 is in the ten thousands place.

c  Digit 2 is in the tens place.

d  Digit 6 is in the ones place.

e  The digits in the remaining places are zero. The number is .

Operations on Numbers up to 6 Digits

Aligned to NCERT Chapter: Ch. 13: Ways to Multiply and Divide

Worksheet 1: Addition and Subtraction of Numbers up to 6 Digits

1  Write True (T) or False (F).

a  When the number is subtracted from itself, the difference is zero.

b  When 0 is subtracted from a number, the difference is zero.

c  When the order of the addends is changed, the sum remains the same.

d  The order of the numbers involved in subtraction can be changed.

2 Add the given numbers.

3 Subtract the given numbers.

4 Write the numbers in columns and add.

a  1,72,744 and 5,56,200

b  3,44,567, 78,456 and 39,894

5 Find the difference of the given numbers.

a  87,687 and 5789

b  5,68,978 and 3,21,098

6 What is the difference between the diameters of Jupiter and Saturn if Jupiter’s diameter is about 142,984 kilometres and Saturn’s diameter is about 120,536 kilometres.

Suhani adds two 5-digit numbers to get a 6-digit number. If the first number is 52,135, what range of values can the second number take?

Worksheet 2: Multiplication and Division of Numbers Up to 6 Digits

1 Write True (T) or False (F).

a  The divisor and remainder in a division sum can be the same.

b  The result of multiplication is called the multiplicand.

c  When a number is divided by another number, it is called the difference.

d  Anything multiplied by zero is zero.

2 Multiply the given numbers by 10, 100 and 1000.

56,567

3 Divide the given numbers by 10, 100 and 1000.

47,852

4 Find the product of the given numbers.

a  2675 × 23 b  4561 × 600 c  8795 × 895

5 Divide the given numbers.

a  26,486 ÷ 144 b  34,204 ÷ 274 c  45,436 ÷ 284

6 Mrs Gupta earns ₹78,562 every month. How much does she earn in 3 years?

1 Challenge ................................................................................................................................................................................................................ Critical Thinking

Shreya is organising an event. She wants to arrange chairs in rows for the attendees. Each row will have 2400 chairs and 380 rows. She additionally needs to set up another 150 rows, each containing 320 chairs. How many chairs does Shreya need in total?

Worksheet 3: Solving Expressions Using DMAS

1 Tick () the correct answer.

a  The order of DMAS

3 Alex has saved ₹120. He wants to buy a toy for ₹28 and a book. The book is half the price of the toy. How much money will he have left after buying the toy and the book?

The difference of 81 and 3 is added to the sum of their product and quotient. What is the resultant number?

Worksheet 4: Chapter Checkup

1 Find the sum of the given numbers.

a  56,789 and 23,456 b  9,87,654 and 45,774

2 Subtract the given numbers. a  54,676 and 34,575 b  8,64,826 and 96,537

3 Multiply the given numbers by 10, 100 and 1000. a  896 b  4546 c  6457

4 Divide the given numbers by 10, 100 and 1000. a  2100 b  4086 c  51,200

5 Find the product of the given numbers.

6 Divide the given numbers using long division. a  6789 and 432 a  54,767 and 231

7 Simplify.

8 Raj and his team are census workers, whose job is to collect the population. In Ghaziabad city, there are 3,81,53,154 men, 3,15,31,873 women and 6,81,231 children. How many people are there in Ghaziabad?

9 Isha is planning a road trip that covers a total distance of 7500 km. She plans to drive 150 km each day. In how many days will Isha complete the trip?

10 There are 5565 mangoes. The number of oranges is twice the number of mangoes. How many oranges will each box contain if the shopkeeper keeps an equal number of oranges in 5 cartons?

11 Shreya had ₹45,000 in her bank account. She got her salary and the amount in her bank account became three times what it was before. She donated ₹14,500 to an emergency relief fund for the soldiers on the Indian border. How much money was left in her bank account? Have you ever collected funds for a charity event?

Challenge Critical Thinking & Cross Curricular

1 The population of Hassan is 1,88,000. The population of Mysore city is 12,61,000.

Read the statements and answer the question given below.

Statement 1: The population of Belgaum is 7,83,000, which is 5,95,000 more than the population of Hassan.

Statement 2: The population of Hassan and Belgaum together is less than the population of Mysore. Is statement 1, 2 or both true?

2 Ravi has two bank accounts A and B. The combined balance of the two accounts is ₹8,75,632. What is the balance in account B?

Read the statements and choose the correct option.

Statement 1: The balance in Account A is ₹3,56,289.

Statement 2: Account B has more balance than account A.

a  Statement 1 alone is sufficient to answer.

b  Statement 2 alone is sufficient to answer.

c  Both statements together are sufficient to answer.

d  Both statements together are not sufficient to answer.

Worksheet 5: Case Study

Rice Production

Our country is the largest rice-producing country. Most of the states in our country produce rice, and most of the rice varieties are exported to different parts of the world. The table shows the amount of rice produced by the state in 2 months.

Karnataka

Tamil Nadu

Bihar

Madhya Pradesh

5,04,975 kg

8,20,965 kg

7,05,136 kg

4,94,814 kg

1 The total weight of the rice produced by Karnataka and Bihar is

2 Write True or False.

a  Tamil Nadu produces 4,67,870 kg more rice than Madhya Pradesh.

b  Karnataka produces 3,15,990 kg less rice than Tamil Nadu.

3 Tamil Nadu wants to deliver 78,432 kg of rice in 456 bags to a relief camp. What will be the weight of rice in each bag?

Worksheet 6: Mental Maths

1 Add the numbers.

a  4321 + 1000 = b  1234 + 200 = c  5679 + 300 = d  2599 + 1 =

2 Write True or False.

a 3999 + 1 = 3000. b 4800 + 6 = 800.

c 2500 × 100 = 2,50,000. d 2599 – 499 = 2100.

3  Divide.

4  Subtract and choose the correct answer.

a  9876 – 2000 i  9867 ii  7876  9676  8876

b  2375 – 300 i  2000 ii  1375  2075  2300 iii iv iii iv

Factors and Highest Common Factor

Aligned to NCERT Chapter: Ch� 6: Be My Multiple, I’ll be Your Factor

Worksheet 1: Factors of a Number

1  Find the factors of the numbers using the multiplication method. a  14 b  34 c  37

2 Find the factors of the numbers using the division method. a  15 b  41 c  63

3 Sort the given numbers as prime or composite numbers.

4 How many prime numbers are there between 10 and 20? List them.

5 Mycobacterium tuberculosis is a bacteria which is responsible for tuberclosis. It has a slower replication time and typically divides every 17 minutes (approx.). How many factor are there for the number 17?

An event manager is getting chairs arranged for a stage show. He wants to put the same number of chairs in rows as the total number of rows. How many chairs will be there in each row, if he has 169 chairs?

Worksheet 2: Concept of Divisibility

1 Circle the numbers that are divisible by 2. a  11 b  24 c  38 d  49 e  160

2 Circle the numbers that are divisible by both 5 and 10.

3 Circle the numbers that are divisible by 3.

4 Circle the numbers that are divisible by 9.

5 A secret passage has a number lock. Below are the clues to the correct number needed to open the lock. Which of the given numbers shows the secret code?

• The number is divisible by 3 and 5.

• The number has 0 as the last digit.

6 Anu is distributing gifts to the poor kids in her neighborhood. There are 10 kids in all. She has 40 pencils, 20 erasers, 55 candies and 20 notebooks. Which are the items that she can divide equally among the kids? Era has 324 blueberry cupcakes and 135 chocolate cupcakes. Can she put them in identical groups of 9 cupcakes without having any cupcakes left over? Give a reason for your answer.

Worksheet 3: Prime Factorisation

1 Which of the following represents the prime factorisation of 80?

2 Which of the following has 2 × 2 × 3 × 3 × 5 × 7 as its prime factorisation?

a  1206 b  1222 c  1260 d  1360

3 Draw factor trees to find the prime factorisation of the given numbers. a  8 b  20 c  24

4 Find the prime factorisation of the following using the division method. a  16 b  22 c  30

5 The Earth completes its revolution around the Sun in 365 days. What are the prime factors of 365?

1 Challenge

Samantha has 132 flowers that she wants to arrange in vases. She wants to place an equal number of flowers in each vase. How many vases did she use if the number of vases that she used was the largest prime factor of 132?

Worksheet 4: Finding the HCF

1  Find the common factors for the 2 numbers. a  13, 36 b  21, 16

2 Find the HCF by finding all the factors.

a  16, 24 b  15, 90

3 Draw factor trees to find the HCF of the given numbers.

a 12, 15 b 26, 65

4 Find the HCF of the following numbers by using the long division method.

a 18, 24 b 14, 84

5 The length, breadth and height of a box are 75 cm, 85 cm and 95 cm, respectively. Find the length of the longest tape which can measure the three dimensions of the box exactly.

The Central Food Technological Research Institute primarily focuses on helping people preserve and create new organic food and liquids. Siya, a research student, wants to create a juice made from 36 litres of lime juice, 45 litres of lemon juice and 72 litres of mint juice. Find the largest container that can measure the contents of the juice an exact number of times.

Worksheet 5: Chapter Checkup

1 Sort the numbers as prime or composite numbers.

2 Find the factors of the numbers using the multiplication method.

3 Find the factors of the numbers using the division method.

4 Use the divisibility rules to check if the given numbers are divisible by 2, 3, 5, 9, 10.

5 Draw factor trees to find the prime factorisation of the given numbers.

6 Use the repeated division method to find the prime factorisation of the numbers. a  75 b  21

7 Find the common factors of each pair of numbers.

a  25, 45 b  75, 125

8 Find the HCF by finding all the factors.

9 Find the HCF using the prime factorisation method. 16, 60 34, 38

10 Find the HCF of the following numbers by using the long division method.

a  36, 63 b  119, 187

11 Rainwater harvesting is a simple technique of collecting, filtering and subsequently storing rainwater into reservoirs or tanks. Two tanks contain 250 litres and 425 litres of rainwater, respectively. What will be the maximum capacity of a bucket that can measure the water in both tanks an exact number of times?

12 Neeta wants to distribute refreshments at a party. She has 240 cupcakes and 160 sandwiches. She wants to equally distribute the food items among her classmates in packets. What is the maximum number of packets she can make, and what will be the contents of each?

Challenge

1 Find the greatest number that divides 178 and 128, leaving a remainder of 8 in each case.

2 I am twice the number that divides two numbers without leaving any remainder. One number is 2 more than half a century, and the other number is 16 more than a century.’ Who am I?

Worksheet 6: Case Study

Colourful Gems

Jewellery making is an art. The stones used in making a jewel goes through a lot of chemical processes. Rubies are red in colour and are made from the corundum mineral. Emerald is made from beryl mineral and it is green in colour. Pearls are obtained below the sea and are white in colour. Jade comes in vibrant colours and is obtained from jadeite.

A jeweller has a few pearls, emerald, ruby and jade. He customises jewellery according to the needs of the customer.

1 A customer asks him to make a pearl bracelet with an odd number of strings. The total number of pearls in the bracelet is 72. If the number of strings is also a prime number, then which of these can be the number of strings? a  8 b  9 c  7 d  3

2 A girl asks the jeweller to use emeralds and rubies to make bangles. The jeweller has 18 rubies and 24 emeralds. What is the maximum number of stones he can use in each, such that the number of rubies and emeralds are equal in the bangles?

a  2 b  6 c  3 d  9

3 The jeweller decides to use 24 jades and 36 emeralds to make identical necklaces without any stones left. What is the greatest number of necklaces that the jeweller can make?

Worksheet 7: Mental Maths

4  Write True or False.

a Every number greater than 2 can be written as the sum of two prime numbers.

b Every odd number greater than 5 can be written as the sum of 3 prime numbers.

c  The factor of a number can be greater than the number.

Multiple and Least Common Multiples

Worksheet 1: Finding Multiples

1  Write the first 5 multiples of the given numbers.

8

2 Is 7209 a multiple of 9? Justify.

3 The kumbh mela is a major pilgrimage and festival in Hinduism. The ‘Purna Kumbh mela’ is organised every 12 years. The last Purna Kumbh mela was organised in 2013. When will the next three Purna Kumbh melas be organised?

4 Select any number with 0 in its ones place and write its first ten multiples. State whether the multiples are odd or even.

5 Cicadas are large and winged insects known for their distinct, loud sound. Two species of cicadas emerge from the ground every 13 years and 17 years, respectively. If both species emerged in 2021, will they emerge together over the next century?

A and B are two numbers. A is the factor of B. Can A also be the multiple of B? Give an example to explain your answer.

Worksheet 2: Common Multiples

Which of the following is a common multiple of 25, 75 and 50?

75

Find the common multiples of the given numbers. Write their LCM. a  12 and 15 b  9 and 63 c  5 and 55

Which of these will have the same lowest common multiple as 4 and 15?

a  4 and 20 b  6 and 25 c  5 and 12 d  8 and 30

The U.S. presidential elections are held every 4 years, while Senate elections are held every 6 years. If both elections are held in 2024, in which year will they next occur together again?

Ravi thinks of a number. He says that the third multiple of that number is equal to half the third multiple of 24. What number was Ravi thinking of?

Worksheet 3: LCM by Prime Factorisation Method

Find the prime factorisation of the numbers.

a  35 and 75 b  44 and 88

These numbers have already been factorised for you. Find the LCM of the pairs given below.

8 = 2 × 2 × 2 25 = 5 × 5 16 = 2 × 2 × 2 × 2

a  8, 10 b  8, 16 c  16, 10 d  25, 10

Find the LCM of the given numbers using the prime factorisation method.

a  36, 45 b  63, 105 c  72, 96 and 108

This year, my age is a multiple of 7. Next year, it will be a multiple of 8. I am older than 20 but younger than 80. How old am I?

Worksheet 4: LCM by Short Division Method

Find the LCM using the short division method. a  21, 24 b  25, 30 c  32, 48

Rohit finds the common prime factors of 42 and 56 using short division as shown below. He says that the LCM of 42 and 56 is 28. Is he right? Why or why not?

Jupiter takes around 12 years to revolve around the Sun while Saturn takes around 30 years to revolve around the Sun. If Jupiter, Saturn and the Sun are in a straight line at the beginning of their revolution cycle, after how many years will they be in their original positions again?

Read the statements and choose the correct option.

Assertion (A): Anna takes 8 minutes to complete one round, and Sylvia takes 12 minutes. If both start cycling at the same time and move in the same direction, they will meet at the starting point after 24 minutes.

Reason (R): The least common multiple (LCM) of 8 and 12 is 24.

a  Both A and R are true, and R is the correct explanation of A.

b  Both A and R are true, but R is not the correct explanation of A.

c  A is true, but R is false.

d  A is false, but R is true.

Worksheet 5: Word Problems

Narendra attends drawing classes which are scheduled once every seven days, starting from the 7th of August. He marks all the dates on a calendar. Write the dates that he will mark for the classes scheduled in the month of August.

There are 12 boys and 18 girls in Mrs. Mehra’s maths class. Each activity group must have the same number of boys and the same number of girls. What is the greatest number of groups Mrs. Mehra can make if every student must be in a group?

A milkman has 75 litres of milk in one can and 45 litres in another. What is the maximum capacity of a container which can measure the milk in either container an exact number of times?

On every fifth visit to a restaurant, you receive a free beverage. On every tenth visit you receive a free appetizer.

a If you visit the restaurant 100 times, on how many visits will you receive both a free beverage and a free appetizer?

b  At which visit will you first receive a free beverage and a free appetizer?

Worksheet 6: Chapter Checkup

1 Colour the multiples of 9 in the number chart shown below.

2 Ajit picked a number and multiplied it by 7. Which of the following numbers cannot be the result of this multiplication?

3  What will be the 9th multiple of the numbers given?

4  Select the common multiples of 30 and 45 from the following options.

30 = 30, 60, 90, 120, 150, 180, 210, 240, …    45 = 45, 90, 135, 180, 225, …

a  Only 180 b  90, 180 c  Only 90 d  30, 45

5 In the following table, the prime factorisation of two numbers A and B is given. Complete the table by finding the LCM of A and B.

a 2 × 3 × 3

× 5 × 7

b 2 × 3 × 5 3 × 3 × 5

c 2 × 3 × 3 × 7 2 × 3 × 11

6  Find the LCM of the given numbers using prime factorisation.

a  5, 9, 15 b  25, 40, 60

7  Find the LCM by the short division method.

a  12, 20 and 32

b  93, 62 and 120

8 Three bells ring at intervals of 20 minutes, 30 minutes and 45 minutes respectively. After how many minutes will the bells ring together?

Challenge

1 A teacher asks the students to name any number that has 75 as a multiple. Rahul says 15, Sahil says 25, and Ajay says 12.

Which of the statements given below is correct regarding this scenario?

a Rahul and Ajay are correct. b Ajay and Sahil are correct.

c Rahul and Sahil are correct.

d Only Rahul is correct.

2  Read the given statements. Choose the correct option.

Assertion (A): The LCM of 3 and 9 is 9.

Reason (R): The LCM of any two numbers is always greater than their HCF.

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, but R is not the correct explanation of A.

c A is true, but R is false.

d A is false, but R is true.

Worksheet 7: Case Study

Coordinating for a Cause

Riya and Samir are school friends. They live at equal distance from their school but in opposite directions. They use the local bus to go to their school. Riya’s bus arrives every 15 minutes, while Samir’s bus arrives every 20 minutes. For Earth Day, they decided to plant trees together, outside the school, to increase awareness about saving the environment. For this, they wanted to reach the school at the same time. The buses arrived at their respective bus stands at 8:00 a.m. but both of them missed their buses. Answer the given questions.

1  How often do the buses arrive at the same time?

a  Every 30 minutes b  Every 60 minutes c  Every 75 minutes d  Every 90 minutes

2 When should Riya and Samir take the next bus so as to reach school at the same time? a

3 When they finished planting trees, Riya said, “The number of trees I planted is a multiple of 2.” Samir said, “The number of trees I planted is a multiple of 5.” They both planted the same number of trees. What is the lowest multiple of trees planted that is common to both?

4 Have you ever taken part in such plantation drives? Give a reason for your answer.

Worksheet 8: Mental Maths

1 Fill in the blanks.

a  The lowest common of 4 and 10 is 20.

b  12, 24, 36 and 42 are the multiples of .

c  The 7th multiple of 8 is .

d  LCM of 9 and 90 is .

2 Circle the numbers below that are common multiples of 6 and 12.

Which is the smallest among these common multiples?

3  Fill in the table below. Number

a  75

b  100

c  120

4 I am a multiple of 70. I am between 300 and 500. I am 20 more than a multiple of 100. Who am I?

Fractions

Aligned to NCERT

Chapter:

Ch. 5: Parts and Wholes

Worksheet 1: Reviewing Fractions

1  Are the given pairs of fractions like or unlike?

a 4 7 and 1 4 b 5 8 and 4 8 c 1 4 and 1 5 d 3 7 and 5 7

2 Classify the following fractions as proper fractions, improper fractions or mixed numbers. Write P, I or M. a 461585171297122684 , , 4, , 5, , , , 6, , , 7,15 52758111539291797 b461585171297122684 , , 4, , 5, , , , 6, , , 7,15 52758111539291797 c 461585171297122684 , , 4, , 5, , , , 6, , , 7,15 52758111539291797 d 461585171297122684 , , 4, , 5, , , , 6, , , 7,15 52758111539291797 e 461585171297122684 , , 4, , 5, , , , 6, 52758111539291797 f 461585171297122684 , , 4, , 5, , , , 6, , , 7,15 52758111539291797 g 461585171297122684 , , 4, , 5, , , , 6, , , 7,15 52758111539291797 h 461585171297122684 , , 4, , 5, , , , 6, , , 7,15 52758111539291797 i 461585171297122684 , , 4, , 5, , , , 6, , , 7,15 52758111539291797 j 461585171297122684 , , 4, , 5, , , , 6, , , 7,15 52758111539291797

3  Match the mixed numbers and the improper fractions of the same value.

4  Convert between improper and mixed fractions. a 14 3 = b 58 7 = c 27 5 = d 45 6 =

5 87 rice packets are distributed among 5 families during floods. How many packets of rice does each family get? Express your answer as a mixed number.

Sanchita gives a puzzle to her sister. Read the clues and write the fraction that Sanchita is talking about.

a The fraction has a prime denominator and is an improper fraction.

b The mixed number 7 2 6 shows the same fraction.

Worksheet 2: Equivalent Fractions

Find any two equivalent fractions by using multiplication for each of the given fractions.

Find any two equivalent fractions by using division for each of the given fractions.

Express the given fractions in their lowest form.

Look at the coloured grid. Write the fraction shown by each colour. Which set of fractions are equivalent?

Worksheet 3: Comparing and Ordering Fractions

Compare the following fractions using >, <, =.

Put a tick () for the statements which are correct and a cross () for the statements which are wrong.

Arrange the given fractions in descending order.

3131 ,,, 8456

Shashank studied for 6 13 hours while Reshma studied for 11 23 hours. Who studied for a longer duration?

Rakesh, Roshan, Swati, and Prerna were assigned a task each. They completed the task in 4 6 hours, 7 8 hours, 1 hour and 2 3 hours, respectively.

Which of the following statements is false regarding the given scenario?

Statement I: Rakesh and Prerna took the same amount of time.

Statement II: The time taken by Roshan is less than that of Prerna but more than that of Swati.

Statement III: Swati took the most amount of time.

Statement IV: The time taken by Roshan is less than that of Swati but more than that of Rakesh or Preeti.

Worksheet 4: Chapter Checkup

1 Convert the given mixed numbers into improper fractions.

2  Convert the given improper fractions into mixed numbers.

3  Find any three equivalent fractions using multiplication.

4  Find any three equivalent fractions using division.

5  Write the following fractions in the simplest form.

6  Compare the fractions and put the correct symbol >, <, =. a 1 2 2 and 14 5 b 4 6 5 and 34 4 c 24 3 and 8

7  Arrange the following fractions in ascending order. a 5141 ,,, 12256 b 1331 ,,, 5582

8 Reading books is a relaxing activity, that reduces stress levels and enhances brain connectivity. Three friends, Alex, Bailey, and Casey borrowed some books from the library. Alex took 1 4 , Bailey took 3 8 , and Casey took 3 12 of the total borrowed books. Who took the least fraction of the borrowed books and who took the greatest fraction?

9 The approximate population of the 6 continents of the world as fractions are given below. Arrange them in ascending order. Asia: 3 5 , Australia: 1 80 , Europe: 7 80 , Africa: 7 40 , South America: 1 20 , North America: 3 40

1 If 4 fractions 1 2 , 3 8 , 5 4 and 5 6 are placed on the number line, which fraction will be to the extreme left?

Thinking

2 Read the statements and choose the correct option.

Assertion (A): 1 2 > 1 3 > 1 4 .

Reason (R): In unit fractions, the denominators are compared. The smaller the denominator, the smaller the fraction.

a  Both A and R are true and R is the correct explanation of A.

b  Both A and R are true but R is not the correct explanation of A.

c  A is true but R is false.

d  A is false but R is true.

Worksheet 5: Case Study

Sorting Recyclables

Mrs Gupta’s class is learning about recycling and the importance of sorting waste correctly. For their science project, they decide to organise a recycling drive. The students need to sort paper, plastic, and glass into different bins.

The bins are labelled with different fractions representing how full they can be before being emptied: Paper Bin: 3 6 full; Plastic Bin: 3 4 full; Glass Bin: 4 5 full

Tanvi, one of the students, notices that the fractions on the bins look different but wonders if they might actually be the same. Answer these questions:

1 Which of the following fractions is equivalent to the paper bin?

2 Which option shows the fractions from the bins arranged in ascending order?

3 The fraction of the glass bin is equivalent to 10 .

Worksheet 6: Mental Maths

1  Write True or False.

a 3 5 and 8 5 are like fractions.

b 2 4 and 5 9 are not unlike fractions.

2 Name the fraction as proper, improper or mixed.

1 8

3 Which of these are equivalent to the fraction shown by in the picture?

4  The fraction 100 1000 in the its simplest form is a b. What are the values of a and b?

Operations on Fractions

Wholes

Worksheet 1: Adding Fractions

1  Circle the pair of fractions in each problem which add together to make 1.

a 1235 ,,, 4444 b 1512 ,,, 8824 c 38124 ,,, 7212114 d 2151512 ,,, 5102535

2  Add the fractions and write the answer in the simplest form.

a 5 10 and 4 9 b 4 5 and 3 15 c

3 A basket has 2 1 5 kg of mangoes. Rajiv puts 2 2 5 kg more mangoes in it. What is the total weight of the mangoes in the basket?

Worksheet 2: Subtracting Fractions

1  Find the difference.

a 64 55 b 6514 126 c 171521 714

Earth’s atmosphere is composed of many gases. The atmosphere is composed of about 39 50 nitrogen and about 21 100 oxygen. What is the fraction of all the other gases in the atmosphere?

Challenge

Raghuveer purchased 4 types of fruit weighing 3 7 4 kg. He purchased 1 1 2 kg of apples, 1 2 4 kg of pears, 2 1 3  kg of oranges and some litchis.

Statement 1: The total weight of apples and pears is 3 1 2 kg.

Statement 2: The weight of litchis bought is 2 1 3 kg.

a Only statement 1 is true.

b Only statement 2 is true.

c Both the statements 1 and 2 are true.

d Both the statements 1 and 2 are false.

Worksheet 3: Multiplying Fractions

1

the fractions using fraction strips.

3 Answer the questions.

a  What is 3 4 of 2 hours? b  How many days are 2 7 of 1 week?

4 Sushen and his friends ate 3 4 of a cake at his party. The total weight of the cake was 2 kg. What weight of cake was eaten?

5 A car has 50 litres of petrol in its fuel tank. 3 5 of the fuel is used up to travel from one place to another. What quantity of fuel is left in the fuel tank? What should we do to utilise fuel efficiently?

6 Create a word problem to multiply a whole number by a fraction. The capacity of a cylindrical tank in a kitchen is 40 litres. It is 4 5 full of water. Nisha used a quarter of this volume of water while cooking food. If Nisha needs 28 litres of water to wash all the utensils, will she be able to do so? 1 Challenge

Worksheet 4: Dividing Fractions

1  Find the reciprocal of the given fractions.

3 Ravi has 21 kg of rice. He packs the rice in packets of 3 4 kg each. How many such packets does he pack?

4  How many

Worksheet 5: Chapter Checkup

1 Find the multiplicative inverse of the given fractions.

2 Write True or False.

a  The reciprocal of every fraction is a proper fraction.

b  0 ÷ any fraction = 0.

c  The reciprocal of 0 is 0.

d  The multiplicative inverse of any fraction is always greater than 1.

3  Add the given fractions.

4  Subtract the fractions and express the answer in its simplest form.

5  Multiply to find the product. Also, write the answer in its simplest form. a 5 6 9 ×

14 15 5 ×

23 98 ×

6  Divide and find the quotient.

7 Delhi is the capital city of India. The age distribution in Delhi is given as; Children − 29 100, Adults − 13 20 and Elderly people 3 50. What fraction of the population of Delhi are not children?

8 A boy was travelling to his grandmother’s home. He travelled 41 7 km by bicycle, 23 4 km on foot and 101 2 km by car. What is the total distance covered by him?

9 Radhika purchased 20 m of cloth. She used 112 5 m of cloth for the curtains and 35 6 m of cloth for a bed sheet. How much cloth does she have left?

1 A recipe requires 5 6 cup of grated cheese. With the help of 6 cheese cubes, you get 3 5 of the amount you need. How much more grated cheese (in cups) do you need? How many more cheese cubes should you grate?

2 Read the given statements. Choose the correct option.

Assertion (A): Shefali has 2000 marbles, out of which 1 4 are red and the rest are green. 2 5 of the red marbles are defective. The total number of non-defective red marbles is 300.

Reason (R): To add two unlike fractions, first the denominator is made the same by finding the equivalent fractions and then the numerators are added.

a  Both A and R are true and R is the correct explanation of A.

b Both A and R are true but R is not the correct explanation of A.

c A is true but R is false.

d A is false but R is true.

Worksheet 6: Case Study

Sonia's Summer Diary

It is summer holidays for Sonia. Her mother signed her up for different social service classes. Sonia goes to a different class each day of the week. The table below shows how much time Sonia spends in each class. Read the table and answer the questions.

1 How much time does Sonia spend in Community Clean-up Programs in the entire week?

2 If Sonia wants to add another 1 1  2 hours for a gardening and farming class on Sunday, how many fewer hours will she spend in the class on Sunday than on Wednesday?

3 Sonia’s friend Misha goes to animal care and welfare classes but spends 45 minutes less time there than Sonia. How much time does Misha spend in the class?

Worksheet 7: Mental Maths

1 Which of these fractions add up to 3 8 to make 1?

2  Write true or false.

a  The reciprocal of 7 is 1 7.

b  The multiplicative inverse of 7 12 is 14 24

c  The reciprocal of 1 12 is 1 12 .

d  The multiplicative inverse of 8 15 is 15 8

3 Solve mentally.

Introduction to Decimals

Worksheet 1: Reading and Writing Decimals

1  Write the decimals in words.

a  45.5

c  42.14

2 Write the decimal numbers.

a  Four hundred thirteen and two tenths b  Seventy-two point three three

c  Fifty-two and four hundred two thousandths

3  Shade to show the decimals and then write them in words.

4  Write the expanded form of the given decimal numbers.

a 45.1

b 45.13

5 Write in decimal form. a  4 + 1 10

Worksheet 2: Fractions, Decimals and Percentages

1  Convert the fractions into decimal numbers and percentages.

9 10 b 8 25

2  Rewrite the decimals as fractions and percentages. a 1.3 b 12.54 c 32.120

3  Write any two equivalent decimals for the given decimal numbers.

a  187.2 b  87.02

c  963.14 d  189.221

4  Write as fractions, decimals and percentages.

a Two and one tenth

b Thirty-five hundredths

c Five hundred twenty-four thousandths

5  Insert >, < or = in the blanks.

6 In 2021, Shivraj Dhananjay Thorat registered his name in the Asia Book of Records by covering a distance of 455.89 km in a day. Express the distance covered in expanded form.

Challenge

1

Use the digits 9, 0, 8, 9, 7 and write two numbers between 0.9975 and 0.9998.

Worksheet 3: Like and Unlike Decimals

1

Which of the following are a group of like decimals?

a  1.2, 5.4, 8.9, 6.54, 1.3

c  7.89, 7.2, 64.594, 45.2, 56.5

2

Convert the unlike decimals into like decimals.

a  13.15, 1.2

c  4.8, 1.526

Critical Thinking

b  2.23, 4.26, 4.89, 4.2, 6.584

d  81.564, 78.512, 453.125, 486.154, 86.15

b  3.48, 1.2

d  1.4, 47.584

Convert the fractions into like decimals.

a 12 20 , 1 5

b 14 40 , 5 10

The value of different currencies in terms of Indian rupees can be given as:

Japanese Yen = ₹0.54; Canadian Dollar = ₹60.9; US Dollar = ₹83.394. Convert all decimals into like decimals.

Consider the fractions 1 2, 8 25, 7 8, 29 40. Which of the following options is correct for the given fractions?

Statement 1: 8 25 = 0.320 and 29 40 = 0.725

Statement 2: 1 2 and 7 8 when converted to decimal numbers are like decimals.

Statement 3: The descending order for 1 2, 8 25, 7 8, 29 40 arranged as like decimals is 0.875 > 0.725 > 0.500 > 0.320

a  Only statement 1 is correct. b  Both statements 1 and 2 are correct.

c  Both statements 1 and 3 are correct. d  All the statements are correct.

Worksheet 4: Comparing, Ordering and Rounding off Decimals

Colour and compare using >, < or =.

Write if True (T) or False (F).

a If the digit in the tenths place is 5, then the number rounds up to the nearest whole number.

b 12.2 rounds up to 13 when rounded to the nearest whole number.

c  99.9 rounds up to 100 when rounded to the nearest whole number.

Find the greater decimal number. Use the <, > or = symbol.

Round off the numbers to the nearest whole number.

Arrange the decimal numbers in ascending order. a  14.14, 14.1, 14.01, 14.101 b  84.56, 84.5, 84.6, 84.55, 84.65

Round off the numbers to the nearest whole number first and put the correct symbol <, >, =.

In May 2023, Bangalore Urban recorded 205.8 mm of rainfall. What is 205.8 rounded off to the nearest whole number?

Challenge

Is an equal to 15 when rounded to the nearest whole number? 1

Decide whether the given statement always answers the given question.

Statement: A decimal number a is greater than 14.5.

Worksheet 5: Chapter Checkup

1 Shade the grid and write the expanded form of the decimals.

2 Write the decimal number in words.

a  15.2:

b  176.801:

3 Write as decimal numbers.

a  Forty point one zero one: b  One hundred three and five hundredths:

c Four hundred twenty and eleven thousandths: d  Thirty-one and five thousandths:

4 Convert the fractions into decimal numbers and percentages.

a 1 8 b 4 5

5 Identify the number by which the decimal has to be multiplied and then convert it into a fraction and percentage.

a  12.6

b  25.315

6 Round off the decimal numbers to the nearest whole number.

7 Arrange the numbers in descending order.

a  1.3, 1.31, 1.2, 1.33

b  19.4, 19.44, 19.54, 19.501

8 Regular cycling strengthens leg muscles, improves joint mobility, and enhances overall body flexibility. Mr Raj and his family took part in a bicycle race. The time taken by each of them is given below. Who won the race?

Raj: 14.3 minutes   Rekha: 15.2 minutes   Utkarsh: 13.92 minutes   Ali: 13.99 minutes

Challenge

Critical Thinking

1 Look at the numbers shown below. Which number does not follow the pattern? 0.9, 0.91, 0.93, 0.97, 1 and 1.05

2 Read the statements and identify which of the following options is correct.

Assertion (A): The decimal number 0.78 is less than the decimal number 0.7801.

Reason (R): When comparing two decimal numbers, the number with more digits to the right of the decimal point is always larger.

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, and R is not the correct explanation of A.

c A is true, but R is false.

d A is false, but R is true.

e Both A and R are false.

Worksheet 6: Case Study

Vertical Marvels

John got a school project in which he had to find the heights of multiple skyscrapers of the world. John made a list of 6 skyscrapers. Based on the list of the height of the skyscrapers, answer the questions given below.

Name Merdeka 118 CITIC Tower Jin Mao

1 Which of the following skyscrapers is the shortest?

Lotte World

a  Merdeka 118 b  CITIC Tower c  Jin Mao Tower d  Wuhan Greenland Centre

2 Which of the following skyscrapers is the tallest? a  Shanghai Tower b  CITIC Tower c  Lotte World Tower d  Merdeka 118

3 What is the ascending order of the heights of the given skyscrapers?

4 What are the heights of the to wers when rounded to the nearest whole number?

5  Write the expanded form of the heights of the skyscrapers.

Worksheet 7: Mental Maths

1 Tick () the correct answer.

a What is nine thousandth in decimal form?

b In the given digit, which digit is in the hundredths place?

2 Write the digit in the tenth's place.

3 Fill in the blanks with >, < or =.

4 Express as decimals.

Operations with Decimals

1 Add the tenths and hundredths visually and find the sum.

2 Subtract visually and find the difference.

3 Add the numbers using the column method.

4 Subtract using the column method.

5 Ramesh is a milkman. He has two cows. One is a Gir cow and the other is a Sahiwal cow. The Gir cow yields 13.4 litres of milk in a day while the Sahiwal cow yields 8.55 litres of milk in a day. How much more milk does the Gir cow yield than the Sahiwal cow?

Challenge ................................................................................................................................................................................................................

Rahul was adding two numbers whose sum was 10. The first number was greater than 4 while the second number was greater than 5. Both the numbers have only one decimal place. How many combinations such as these could Rahul have added? 1

Worksheet 2: Multiplying Decimals

1 Multiply the decimal number by the whole number visually.

2  Multiply.

3  Compare using >, < or =.

4 How many Indian rupees are the same as 1000 Euros? (1 Euro = ₹89.19)

Challenge

Rashmi and Sneha are solving a maths problem. Each of them thinks of a number between 1 to 5 and writes it on a piece of paper. The division of their number was 1.25. They forgot to mention who thought of which number. Rashmi said she thought of a whole number while Sneha mentioned she thought of a number which had two decimal places. Which numbers did they both think of? 1

Worksheet 3: Dividing Decimals

1  Divide the given decimal numbers visually.

0.8 ÷ 4

2  Fill in the blanks. a  15.6 ÷ 10 =

32.561 ÷ 1000 =

3  Find the quotient.

120.6 ÷ 6

51.23 ÷ 100 =

23.1 ÷ 1000 =

1.6 ÷ 8

1.2 ÷ 100 =

2 ÷ 10 =

4 How many pounds should Hari take with him to England, if the total expenses for the trip add up to ₹1,04,200? (Given: 1£ = ₹104.2 approximately)

Challenge Critical Thinking

1

Mr Agarwal went from England to Germany. He had 1000 Pounds with him. How many Euros will he get in exchange for 1000 pounds? (Refer to the table for conversion of currencies)

Worksheet 4: Chapter Checkup

1 Add or subtract the numbers visually. a  0.23 + 0.47 b  1.4 – 0.62

2 Find the product of the numbers visually. a  6 × 0.2

3  Add or subtract the numbers using the column method.

5 × 0.6

4  Fill in the blanks.

5  Fill in the blanks.

6  Find the product of the numbers.

12 × 1.54

7  Divide to find the quotient.

9 × 32.14

8 Raj wants to buy a DVD player for $47.85, a DVD holder for $21.36 and a stereo for $22.01. If he has $90, how much more money does he require?

9 George’s friend returned from the USA. He exchanged $168 for Indian currency. If he has to give $1 for every $20 as a tax for the exchange, what amount of Indian currency does he have? ($1 = ₹89.12)

10 Rohan owns a carpool agency that takes people from Meerut to Gurgaon everyday. If the cars run for 4 hours each day and consume 6.5 L of petrol each hour, for how many days will the cars run with 130 litres of petrol?

Challenge

Critical Thinking

1 John’s weight is 0.89 times that of Harry’s and Harry’s weight is 0.56 times that of Jacob’s. If Jacob weighs 51.25 kg, what is John’s weight?

2 Read the statements and choose the correct option.

Assertion (A): When multiplying two decimal numbers, the product is always less than both of the original numbers.

Reason (R): Multiplying any two numbers between 0 and 1 results in a number that is smaller than each of the original numbers.

Options:

a  Both A and R are true, and R is the correct explanation of A.

b  Both A and R are true, but R is not the correct explanation of A.

c  A is true, but R is false.

d  A is false, but R is true.

e  Both A and R are false.

Worksheet 5: Case Study

Patterns and Impacts: Analysing Rainfall in Indian Cities – 2023

In 2023, India experienced diverse weather patterns across its various cities. The government meteorological department recorded the rainfall in several major cities to analyse the effects of these patterns. The data is essential for urban planning, agricultural forecasts, and water resource management.

Read the questions and answer.

1 What is the total rainfall in Mumbai, Delhi and Bangalore?

mm

2 Find the difference in rainfall between Chennai and Kolkata.

3 If the rainfall in Pune doubles next year, how much rainfall is expected in the next year?

4 Find the difference between the rainfall in Mumbai and the total rainfall in Delhi, Bangalore and Chennai combined.

5 Why is it important for us to save rain water?

Worksheet 6: Mental Maths

1 Find the answer without solving.

a 0.6 + 0.13 = b 0.67 + 0.66 = 2  Solve.

a  15.8 ÷ = 0.0158 b  23 ÷ 1000 =

3 Answer the questions.

a  What should be added to 0.329 to get 4.000?

b  What should be added to 5 to get 6.5?

c  What should be subtracted from 1.8 to get 1.0?

d  What should be subtracted from 45.13 to get 30.13?

4 Fill in the blanks with <, > or =.

Lines and Angles

to NCERT Chapter: Ch. 1: Shapes and Angles

Worksheet 1: Types of Lines

1  Name the given figures as a intersecting lines, parallel lines, line or ray. a b c d

2 Write T for true and F for false.

a  A line segment AB can be denoted as AB.

b  A ray CD can be denoted as CD.

c  A line PQ can be denoted as PQ.

d  Two parallel lines are denoted by the symbol ||.

3  Select the word that best describes the given figures.

4 Look at the figure and answer the given questions.

a  Name all the points and lines in the figure.

b  Write the name of a line segment.

c How many rays are there in the figure? Write their names.

True or False: Only one line segment can be drawn between two given points. Justify the statement using a figure.

Worksheet 2: Types of Angles

Label the arms and vertex of the given angle.

Name the angles of the given figures.

Look at the figure and the angles ∠1, ∠2, ∠3 and ∠4 that are marked. Which of them are obtuse angles?

Look at the given figure and answer the questions.

a What type of angle do you get if you remove sticks OC, OD, OF, OG and OA?

b If the stick OA is removed, what type of angle is formed by sticks OB and OG?

c Count the number of angles

between

and OE. Name them.

Worksheet 3: Measuring and Drawing Angles

Name the angles as right, acute, obtuse or straight.

Measure each angle using a protractor.

Draw the given angles using the inner scale of a protractor.

Challenge Critical Thinking

Look at the figure. Identify and estimate the angle formed when the striker hits the coin through the centre.

Striker

Worksheet 4: Triangles, Quadrilaterals and Polygons

Write the names of each of the polygons.

a b c d

Match the shapes with the number of angles they have.

a b c d three five nine seven

Write T for True and F for False.

a  A quadrilateral has 4 sides.

c  A pentagon has five sides.

b  An octagon has eight angles.

d  A rhombus has five sides.

The Tower of Winds in Athens was constructed in 50 BCE. The shape of the building has 8 sides and 8 angles. Name and draw the shape.

Answer the riddle: I am a closed shape. I have twice the number of sides and angles than a triangle has. Who am I?

Count the number of triangles and quadrilaterals in the given figure.

Worksheet 5: Chapter Checkup

1 Which word among line, line segment and ray best describes the figure?

A B

2 Look at the figure and write if true or false.

a  AC is a line segment.

b  PQ and RS are sets of parallel lines.

c  CS is a line.

3  Write the names of the angles made by the given figures.

4  Look at the given figure and name the angles as right, straight, acute or obtuse.

a ∠ AOC

b ∠ AOD

c ∠ AOF

d ∠ BOF

e ∠ BOC

5  Write the measure.

6  Measure the given angles using a protractor. a b c d

7  Draw the given angles using the outer scale of a protractor. a  65° b  115°

8  Write the names of the polygons. Also, write the number of sides and angles they have. a b

Name:

Number of sides:

Number of angles

9  Tick () the polygons that have one or more right angles.

Name:

Number of sides:

Number of angles

10 The Museum of Deva has displayed an over-2000-year-old bronze matrix of Sarmizeugetusa, which was found in 2013. Name and draw the shape of the matrix shown.

Challenge

1 Read the statements and choose the correct option.

Statement I: If two lines are perpendicular, then they intersect at a right angle.

Critical Thinking

Statement II: Perpendicular lines are lines that intersect at a 90° angle, forming four right angles at their intersection point.

a Both assertion and reason are true.

b Both statements are false.

c Statement I is true but Statement II is false.

d Statement I is false and Statement II is true.

2 Look at the figure. Rearrange the sticks to form 5 squares. You can move only 2 sticks.

Worksheet 6: Case Study

A tangram is a puzzle made of 7 polygons. It is widely used among children to create different shapes and designs. Look at the design given below and answer the questions.

1  How many triangles are there in the figure?

2 What shape is formed when 2 right angle triangles and a parallelogram are placed together?

a  Square b  Rectangle c  Pentagon d  Hexagon

3 Can a circle be formed using the shapes in a tangram?

a  Yes b  Can’t say c  No d  None of these

4 Draw a fish using a square and 4 triangles.

Worksheet 7: Mental Maths

1 Write True or False.

a  A line or line segment passes through a dot.

b  Parallel lines intersect at a point.

c  A ray cannot be extended indefinitely in one direction.

d  Perpendicular lines meet at right angles.

2  Fill in the blanks.

a  The angle between 0° and 90° is called angle.

b  The angle between 0° and 180° is called angle.

c  The angle formed at 90° is called angle.

3  Match the time with the angle formed by the hands of the clock.

a  3:00 Obtuse angle

b  6:00 Straight angle

c  3:10 Right angle

d  3:55 Acute angle

Patterns and Symmetry

Worksheet 1: Extending and Creating Patterns

1  Which of these do not show a pattern?

2 Observe and extend the pattern.

3  Identify the rule for the given rotating pattern. Draw the next three units and colour them.

4 Identify and write the rule for the rotating patterns. Is there any pattern which is not following any rule? If yes, give your answer with a reason.

5 Use the given shapes to draw rotating patterns. The pattern should rotate clockwise at right angles.

Worksheet 2: Growing and Tiling Patterns

Which of these is not a tiling pattern? Give your answer with a reason.

Reason: Colour to complete the tile.

Draw the picture that comes next in each growing or reducing pattern.

Worksheet 3: Number Patterns

Look at the numbers and write the rule describing each pattern.

a  15, 19, 23, 27, 31, 35

b  6, 8, 10, 12, 14, 16, 18

c  1, 4, 9, 16, 25, 36, 49

Use the given code to find the numbers.

Create a magic triangle with a sum of each side that is equal to 12.

Worksheet 4: Symmetry in Plane Shapes and Solids

Draw the lines of symmetry for the given figures.

Write True or False.

b

Draw the lines of symmetry (if any) for the given letters.

a  When two halves look identical, they are called asymmetrical.

b  The letters F, G, J and L have two lines of symmetry.

c  The number 8 has 2 lines of symmetry.

d  The number 3 has a horizontal line of symmetry.

Complete the missing half of each of the shapes across the mirror line.

Ayan is an architect who creates layouts of houses. He was constructing 2 flats facing each other that are identical to each other. He lost the layout of one of the flats. Can you help Ayan by colouring the grid to show the flat?

Worksheet 5: Chapter Checkup

1 Tick () the figures that are symmetrical.

2 Draw all the possible lines of symmetry for the given figures.

3  Draw the reflection of the figures across the mirror line.

5  What will come next in the given patterns? Draw two figures for each.

6 Complete the tiling patterns by drawing 4 more shapes.

8 Generate number patterns with 5 terms following the given rules.

a  Start with 1 and add the double of itself.

b  Start with 15 and add 3 and 5 alternately.

4  In a certain language, the letters are coded as follows. Find the code for the word LEMON.

7 Examine the number pattern below. Write the next three numbers in the pattern. Also, write the rule followed. 331, 316, 301, 286, 271, , , Rule:

9 Fill in the missing numbers.

37 39 42 46 51

10 Mihir gets pocket money every month. He saved ₹20 in January, ₹40 in February, ₹80 in March, ₹160 in April and so on. How much money did he save in August?

11 Emily is hiking in the mountains. On the first day, she takes 100 steps. On the second day, she takes 120 steps, then 150 on the third day, 190 on the fourth day and so on. How many steps will she take on the sixth day?

Challenge

1 Look at the pattern below. Which number will replace the question mark?

2 In the question given, read the two statements marked as Assertion (A) and Reason (R). Choose the correct option.

Assertion: Tara is following a fitness regime. On the first day, she takes 20 steps. On the second day, she takes 25 steps, then 32 on the third day, 41 on the fourth day and so on. She will take 65 steps on the sixth day.

Reason: Tara is increasing the number of steps by 5 each day.

a  Both A and R are true, and R is the correct explanation of A.

b  Both A and R are true, but R is not the correct explanation of A.

c  A is true, but R is false.

d  A is false, but R is true.

Worksheet 6: Case Study

Imagine you are visiting the magnificent Taj Mahal. This 17th-century white marble mausoleum located on the banks of the Yamuna River in Agra, India, is a UNESCO World Heritage site famous for its beauty and intricate details.

Explore how symmetry plays a role in its design by answering these questions.

1 Which of the following shapes is most prominent in the Taj Mahal's design?

a  Triangle b  Rectangle c  Pentagon

2 The Taj Mahal has four identical minarets surrounding the main dome, reflecting perfect rotational symmetry. True or False?

3 If you draw an imaginary line down the centre of the Taj Mahal, both sides will mirror each other. This is called .

4  The Taj Mahal complex has 3 lines of symmetry. (Yes/No)

5  What can you do to help maintain cleanliness during your visit to Taj Mahal?

Worksheet 7: Mental Maths

1 Look at the pattern. Choose the next term in the given patterns.

2  Find the next term in the given patterns.

a  2, 4, 8, 16, b  A, AB, ABC, A, AB, ABC, A,

3 Find the rule in the given pattern. 5, 10, 20, 40, 80 Rule:

4 Which of these show the correct reflection of the given figure?

c  5, 15, 35, 65,

5  Write True or False.

a  3 × 4, 4 × 5, 5 × 6, 6 × 7 is a reducing pattern. b  A has no lines of symmetry.

c  A has one line of symmetry. d  A has one line of symmetry.

Length and Weight

Worksheet 1: Understanding Lengths Aligned to NCERT Chapters:

1 Esimate the length of these items. Measure the actual lengths. Find the difference.

a Pencil

Estimated Length:

Actual Length:

Difference: b Eraser

2 Write the lengths of the given objects. a b

Estimated Length:

Actual Length:

Difference:

3  Convert the given measurements.

4  Complete the table.

5 Find the measurement of the pencil.

6 Rajni went to buy skirts. If 3 m 586 cm of cloth is required for one skirt, then how much cloth is needed for 6 such skirts?

A rat was chewing up 2 cm of a cardboard each day. The owner removed the cardboard after one week. How much of the cardboard sheet was eaten in 1 week?

Worksheet 2: Understanding Weights

Circle the best estimate of the weight of the objects.

Convert the measurements.

Convert the weights into bigger units and smaller units.

By the time a kitten is about 4 months old, it weighs about 1688 g. What is its weight in kg?

An egg has a mass of 40 g. How many eggs can be bought in 1 kg?

A truck can carry 8 cartons of packed food. If they weigh 32 kg 448 g in total, then what is the weight of each carton?

Quintal and tonnes are also units of measuring weight. 1 quintal is 1,00,000 g and 1 tonne is 1000 kg. How many quintals is 1 tonne?

Worksheet 3: Chapter Checkup

Guess the best units of length (m or cm) and weight (kg or g) for the given objects.

Measure the objects.

James has some cotton candy which is 3 cm longer than the cotton candy shown below. How long is James’ cotton candy?

How much longer is the red straw than the blue straw?

Convert the lengths. a  8 m into km

4 hm 35 m into hm c  1232 m into mm

Convert the weights.

5 kg into g

5487 g into mg

A baby koala is called a joey. A young joey weighs about 0.38 kg. How much is that in g?

A lift in a building is allowed to carry up to 260 kg in weight. The people listed below want to enter the lift. Their weights are mentioned.

Amit: 85 kg

Priya: 70 kg

Can they enter the lift together? Why?

Priyanshi: 58 kg

Raju: 80 kg

9

Create a word problem to add weights of two objects.

Challenge

1  What is Meenakshi’s weight in grams? Read the clues and answer.

a  Meenakshi’s weight is half of her grandmother’s weight.

b If you add the smallest 2-digit number to 28 less than the smallest 3-digit number, you will get the grandmother’s weight in kilograms.

2 What is Riya’s father’s weight? Choose the correct option that answers the question.

Statement 1: The father’s weight is three times the difference between Nita’s weight and Riya’s weight. Statement 2: Nita’s weight is 36 kg and Riya’ weight is one-third of Nita’s weight.

a  Statement 1 alone is sufficient to answer.

b Statement 2 alone is sufficient to answer.

c  Statements 1 and 2 together are sufficient to answer.

d Statements 1 and 2 together are not sufficient to answer.

Worksheet 4: Case Study

Bannerghatta National Park is a famous national park in India. A small portion of the national park has become the Bannerghatta Biological Park. The fauna in the park include lions, tigers, bears, elephants and many more.

1 Write the unit used to measure the lengths of the given animals.

a  The unit used to measure the length of a tiger.

b  The unit used to measure the length of a butterfly.

2 The weight of a male leopard is 72 kg and the weight of the hyena is 55,000 g. Which of these is true?

a  The difference in weight is 1700 g. b  The difference in weight is 1.7 kg.

c  The difference in weight is 170 g. d  The difference in weight is 17,000 g.

3 The park has two enclosures that were merged. The length of enclosure 1 was 8894 m and the length of the second enclosure was twice the length of enclosure 1. The new enclosure is divided into 2 pieces where one piece has a length of 20,000 m and the other has the play area. What is the length of the play area?

4 The tigers and lions have to be shifted to sanitise the place. The van can accommodate animals up to 300 kg. The weight of a tiger is 72 kg and that of a lion is 176 kg. How many animals can be shifted in one trip?

5 How can you help to save flora and fauna near you?

Worksheet 5: Mental Maths

1 Tick () the estimate length of the pencil.

2 Tick () the estimate weight of an apple. 50 grams or 200 grams

5 cm or 12 cm

3  Choose and tick () the estimated weight of 10 apples in terms of bags of flour. = 3 bags of flour

4  Measure lengths.

a If a pencil is 7 cm long and you have 5 pencils lined up end to end, their total length is cm.

b A book is 25 cm long. If you have 3 such books, their total length is .

c If a ruler measures 30 cm, 2 rulers placed end to end is cm.

d You have a piece of string that is 45 cm long. If you cut it in half, the length of each piece is .

5  Measure weights.

a  A cat weighs 3 kg. The weight of 4 such cats is .

b  A book weighs 250 grams, the weight of 6 such books is kilograms.

Perimeter and Area 12

Aligned to NCERT Chapters: Ch 3: How Many Squares?; Ch 11: Area and Its Boundary

Worksheet 1: Perimeter of Squares and Rectangles

1  Find the perimeter of the given objects.

a 20 cm

2 Find the perimeter of the squares of the following measurements.

a s = 32 m

b s = 53 cm

3  Find the perimeter of the rectangles of the following measurements.

a l = 12 cm, b = 15 cm

4  Find the missing sides.

b l = 55 m, b = 85 m

a Rectangle with length = 32 mm, breadth = ?, Perimeter = 112 mm b  Square with Perimeter = 148 mm, side = ?

5 A farmer needs to fence his square-shaped garden. The distance from one corner to the next corner is 45 m. How much wire would he require to fence the entire garden?

6 Shade squares on a square grid to form 2 rectangles with a perimeter of 24 cm.

1 Challenge

The length of a rectangle is three times its breadth. If the perimeter of the rectangle is 32 metres, find its length and breadth.

Worksheet 2: Area of Squares, Rectangles and Triangles

1 Which unit would you prefer to find the area of the following?

a  blackboard

b  a book

c  classroom

d  your school

2 Find the area of the rectangles of the given measurements.

a l = 15 cm, b = 22 cm

e  your city

f  lake

g  table

h  a farmer’s field

b l = 58 m, b = 70 m

3 Find the area of the squares of the given measurements.

a s = 56 m

b s = 67 cm

4 Advita wants a new carpet for her room. If her room measures 12 m by 12 m, then how much carpet does she need to cover the entire floor?

5 Take each side of a square on the squared paper as 1 unit. Find the area of the triangles.

6 Find the area of the given compound shapes.

7 Use squared paper to show rectangles or squares with these measurements. Find the measurement that is not given for the following shapes.

a  Perimeter = 36 cm, Area = ?

b  Area = 24 sq. cm, Perimeter = ?

8 A rectangle has a length of 8 metres and a breadth that is one-fourth of its length. A square has a side length that is twice the breadth of the rectangle. Which shape has a larger area?

A rectangle is cut into 2 squares. The perimeter of each square is 36 cm. What is the perimeter of the rectangle? 1 Challenge

Worksheet 3: Chapter Checkup

1 Find the perimeter and area of the following rectangles.

2 Find the perimeter and area of the following squares.

3  Complete the given table.

S. No.ShapesLength/sideBreadthPerimeter

a Rectangle

b Square

c Rectangle34 m

4  Find the area of the following triangles in square units.

5 Find the area of the following compound figures.

6 This shape is made from five squares that are all the same size. If the area of the figure is 80 sq. cm, then its perimeter is:

52

7 Humayunʹs Tomb was built in memory of the second Mughal Emperor Humayun. It features a central platform that is square in shape and measures approximately 300 feet on each side. What is the area of the platform?

Three rectangular tiles having the same length and breadth are placed as shown. If the perimeter of each tile is 22 cm, find the perimeter of the shape formed.

If the length and width of a rectangle doubles, the area of the rectangle also doubles. Is this statement true? Explain your answer.

Worksheet 4: Case Study

The School Map

Farah’s school is very big, with many rooms and a playground. One day, she and her friends noticed a large square-shaped map of the school on the bulletin board in the reception area. Intrigued, they studied the map, which showed the different sections of the campus. Here the size of the classrooms was the same. They looked closer, and they wondered about what the areas of the rooms in the building were. Inspired, they decided to calculate the perimeter and areas of different sections to better understand their school’s layout.

1  What is the total area covered by all four classrooms ?

a  56 sq. m b  168 sq. m c  224 sq. m d  280 sq. m

2  Which area is bigger: the staff room or the art room?

3 If the layout is square in shape, what is the area of the school?

a  100 sq. m b  1444 sq. m c  1000 sq. m d  144 sq. m

4 What is the area of the entire school except for the area of the square shaped ground?

Worksheet

5: Mental Maths

1 State True or False.

a The perimeter of a square with each side of length 4 cm is 16 cm.

b The perimeter of a rectangle with length 8 cm and width 3 cm is 11 cm.

c The area of a square with side length 5 cm is 25 square cm.

d The area of a rectangle with length 10 cm and width 3 cm is 30 square cm.

2 What is the area of each of these rectangles drawn on a centimetre grid?

3  Choose the correct answer.

a What is the perimeter of a square with each side 9 cm?

i  27 cm ii  36 cm iii  18 cm

b What is the side of a square with area 36 cm?

i  8 cm ii  12 cm iii  6 cm

c What is the area of a triangle with a base of 7 cm and height of 8 cm? i  28 square cm

35 square cm

12 square cm

4  One-word answer questions.

a A triangle has an area of 15 square cm and a base of 5 cm. What is the height?

b A rectangle has an area of 24 square cm and a length of 8 cm. What is the width?

Capacity and Volume

1  Circle the best estimate of the given objects.

2 Convert the given measurements.

3  Complete the given table.

2 Rhea wants to fill an almirah that measures 3 m by 2 m by 1 m with cartons of old clothes. What is the volume of the almirah?

3 A big box that measures 10 cm by 15 cm by 6 cm is packed with smaller boxes. What is the volume of the bigger box?

4 A fish tank is emptied to fill it with cubical boxes. If the fish tank is 30 cm by 22 cm by 10 cm, then find its volume.

Challenge

Tina is making a building with cube-shaped blocks. The base of the building showing the number of cubes to be placed at the base is shown by the figure. The structure is 6 blocks high and each level has the same shape and number of blocks. What is the volume of Tina’s structure in cubic units?

Worksheet 3: Chapter Checkup

1  Tick () the best estimate.

Glue

b  Paint in a bucket

c  Ketchup in a bottle

2 Sahil filled 500 mL of water in a jug. Sahil put 6 matchboxes in it. The water level rose to 800 mL. What is the volume of 1 matchbox?

3  Read and write the amount of coloured water in each of the jugs.

4  Colour the beakers up to the amount of water written with each beaker.

5  Find the length, breadth, and height of the solids by counting the number of cubes.

6 Convert the measurements.

980 mL into L

7  Find the volume of the figures.

6869 L into mL

9796 dL into L

8 Ashish had two flasks. One flask can hold 850 mL of water, and the other flask can hold 1 L 250 mL of water. How much water can the flasks hold together? Do you drink 2 litres of water every day?

9  The containers are partly filled with unit cubes. Find the volume of each container.

10 5 cups of water can fill a bottle, and 5 cups of water can fill a bowl. 5 bottles of water can fill a jug while 3 jugs and 7 bowls of water can fill a pail. If each cup holds 90 mL of water, what is the capacity of the pail?

1 Jassi is fond of building blocks. He glues 8 cubes together to make a block as shown. Now, he wants to make a block that is 6 small cubes long, 5 small cubes wide and 4 small cubes high. He wants to use the smallest number of cubes possible, by leaving the largest possible hollow space inside the block such that it looks like a box. How many blocks will he use?

2  Read the statements and choose the correct option.

Assertion: The volume of a cube will always be greater than the volume of a cuboid.

Reason: The volume of a cube is l × l × l, and the volume of a cuboid is l × b × h

a  Both assertion and reason are true.

b The assertion is true, and the reason is the correct explanation for the assertion.

c The assertion is true, but the reason is not the correct explanation for the assertion.

d The assertion is not true, but the reason is true.

Worksheet 4: Case Study

Amul (Anand Milk Union Limited) is a dairy federation run by the Gujarat Cooperative Milk Marketing Federation Limited. Amul was founded on December 19, 1946. It is a major producer of diary products like milk, curd, paneer, different types of cheese, ice cream, chocolates and many more.

1 Write True or False.

a The volume written on the buttermilk packet will be less than 10 mL.

b  The volume written on the pack of milk will be in mL.

2 The volume of the flavoured milk is 0.45 L. The volume of the flavoured milk in mL is

3 Amul produces paneer which is distributed across the country. It produces 15,000 kg of paneer from 45,000 litres of milk. How much milk will be required to produce 30,000 kg of paneer in a day?

4 Amul cheese is a famous vegetarian cheese worldwide. The dimension of a 400 g pack of cheese is 7 cm × 3 cm × 4 cm. If the company packs 10 such packs in a box, what should be the minimum height of the box?

5 Milk is one of the dairy products that gives us calcium. Calcium is very important for bones and teeth. Do you drink milk every day? If yes, how much mL do you have in a day?

Worksheet 5: Mental Maths

1  Convert the given measurements.

a  6 daL to L b  213 dL to L

c  6000 L to hL d  6 L to cL

2 Look at the image and find the volume of the marble.

3  Tick () the shape that has volume of 10 cu. cm.

Volume of the marble is .

a b c d

4  Look at the image. Which of these is the volume of the cube?

a  30 cu. cm.

3-D Shapes on Flat Surfaces

Aligned to NCERT Chapter: Mapping Your Way Boxes and Sketches

Worksheet 1: 3-D Shapes

1  Circle the shape that is a:

a Cube                       b Cuboid

2  Write the number of vertices, edges and faces for the given shapes.

a Cone Vertices = , Edges = , Faces =

b Sphere Vertices = , Edges = , Faces =

c Square Prism Vertices = , Edges = , Faces =

d Cylinder Vertices = , Edges = , Faces =

3  What shape am I?

a I have 8 vertices, 6 flat faces and 12 edges.

b I only have 1 face.

c I have edges but no vertex. d I have a curved face and a vertex.

4  Draw a cone on a square grid.

5 Rohan and Simi have pitched a tent each, for themselves, as shown in these pictures. Name the shapes of the tents. What is similar and different in their tents?

Rohanʼs tent Simiʼs tent

1 A prism has two identical flat faces. Can a cylinder also be considered as a prism? Why or why not?

Worksheet 2: Nets of 3-D Shapes

1 Identify the shape for which the net is drawn.

2  Draw the net of the given shapes.

3 Rishi and Megha made the net of a square-based pyramid. Who made the net correctly? Explain your answer with reasons.

a Rishi’s drawing b Megha’s drawing

Challenge Critical Thinking

A dice has P, Q, R, S written in a clockwise order on the adjacent faces and T and U at the top and bottom faces respectively. When R is on the top, what will be at the bottom?

Worksheet 3: Views of Cube Structures

1 If you look at this object from the front, what will you see?

Front view

2 Draw the views of these figures. a Right-side view of b Top view of

3 This table is made of many cubes joined together. Draw and label three different views of the table.

4 Mehar has made a shape using her building blocks. Count and write the number of building blocks she used to make the shape.

1

Dice are cubes with dots on each face. The opposite faces of a dice always have a total of 7 dots on them. If the front view shows 4 dots and the left side view shows 5 dots, how many dots will be shown on the back view and the right side view?

Worksheet 4: Reading Maps

1 Look at the map and answer the questions.

a The hospital is to the of the airport.

b The hotel is to the of the bank.

c The airport is to the of the school.

2 On a map, the distance between two cities is 5 cm. Taking the scale as 1 cm = 25 km, what would be the actual distance between these two cities?

3 What is the actual distance between the complex and the college?

4 What is the length and width of the cupboard, table and desk? Map scale: 1 square = 2 m

Mihir goes to the stadium for football practice after school. On the map, his house is 2 cm from the school and the stadium is 2 cm farther from the school. What is the actual distance from his house to the stadium if the scale of the map is 1 cm = 3 km?

Worksheet 5: Floor Plans and Deep Drawings

1 Look at the floor map of the house and label the doors and windows.

2 Draw the floor plan for the given deep drawing.

3 Which room will you be in if you enter through the back door?

1 Rakesh made the floor plan of his house which is shaped like a cuboid. He had 4 windows on each side of his house. How many windows can he not show in the deep drawing of his house? Draw a floor map and a deep drawing to show the same.

Worksheet 6: Chapter Checkup

1  Join the corners of these figures and write the name of the solid.

2 A globe is like a round map that shows us how the Earth looks from space, with all the continents, countries and oceans. How many faces, vertices and edges does a globe have?

Vertices = , Edges = , Faces =

3  Fill in the blanks.

a A pattern that can be cut and folded to make a model of a 3-D shape is called a

b A special way of drawing a house to show its length, width and height is called a

c  The 2-D representation of the map of a house is called a .

4  Identify the shapes and write the number of faces, edges and vertices of each shape.

5  Draw the net of these shapes. a b

6  Draw the top, front and side views of the figures.

7  Match the distance on the map with the actual distance, if the scale of the map is 1 cm = 8 km.

on the map

e

8 The floor plan of a library is ready. Draw the doors and windows on the deep drawing of the library.

a  Is there any window which you could not show on the deep drawing? Circle them.

b  How many windows were you able to show on the deep drawing?

9 Look at the layout of Ruchi’s apartment. How many times bigger is the bathroom than closet 1?

10 Ben goes from his house to May’s house and then to Jule’s house. What is the total distance covered by Ben?

Benʼs house Wayneʼs house Tonʼs house Jessleʼs house Patʼs house 2 cm 3 cm Danʼs house

Carlʼs house Mayʼs house 4cm Juleʼs house

Scale: 1 cm on the paper = 3 km

Challenge

1 What is the minimum number of only flat faces a solid can have? Name the solid.

2  Draw the front, top and side view of a cone surmounted on a sphere.

Worksheet 7: Case Study

Tale of Three Viewpoints

A new building was made. It was taller than the buildings around it. Right in front of it was a small building. Three people were looking at the small building from different spots. Person 1 was looking at it from the top of the tall building. Person 2 was looking from the side of the building in the nearby park. Person 3 was looking from the front. This is shown in the picture below.

1 is Person ’s perspective.

2 is Person ’s perspective.

3  Write the views as seen by the 3 persons as front, side or top view. Person 1 Person 2 Person 3

4  What safety measures do you think Person 1 should take?

Worksheet 8: Mental Maths

1 Write True or False.

a A cylinder has 2 curved surfaces and 2 curved edges.

b A cone has 1 flat face and 1 curved surface.

c A cube and a cuboid have the same number of flat faces.

d A sphere has 1 edge and 1 vertex.

2 Write the name of the 3-D shapes of the nets shown below.

3  Look at the figure and tick the front view of the given figure. Top

4  Choose the correct floor plan for the given deep drawing.

Figure 1 Figure 2 Figure 3

Time and Temperature

Worksheet 1: Converting Between Units of Time

1  Convert into minutes. a 3 hours

2  Convert into seconds. a 5 minutes b 8 minutes c 9 minutes 10 seconds

3 Match the seconds with their conversions.

a 240 seconds 5 minutes 50 seconds

b 480 seconds 8 minutes 40 seconds

c 350 seconds 4 minutes

d 440 seconds 9 minutes 10 seconds

e 520 seconds 7 minutes 20 seconds

f 550 seconds 8 minutes

4 A flight from Delhi to London takes around 8 hours and 30 minutes. How many minutes is the journey?

Sarah’s teacher asked her to practise on the piano for 1 hour and 50 minutes a day. She practised for 55 minutes in the morning and 50 minutes in the evening. Which statement is true regarding this situation?

Statement 1: Sarah practised for the same duration as asked by the teacher.

Statement 2: Sarah should practise 5 more minutes to complete the duration requested by the teacher.

Worksheet 2: Calculating Duration and Time

1 What is the duration between the times shown on the two clocks?

2 Solve.

a 4 hours 30 min + 6 hours 20 min

b 7 hours 5 min − 5 hours 30 min c 3 weeks 10 days + 6 weeks 5 days

3 If it’s 2:40 p.m. now, what time will it be 35 minutes later? Show the time on a clock.

4 If a meeting started at 9:30 a.m. and ended at 12:45 p.m., how long did the meeting last in hours and minutes?

5 A new museum opened on 25 October 2020, and closed on 15 February 2022. For how many months and days was the museum open?

Meera’s school bus arrives at her bus stop at 8:10 a.m. every morning. Meera takes 15 minutes to get ready and needs to reach the bus stop at least 5 minutes before the bus arrives to maintain social distancing at the bus stop during the COVID-19 pandemic. It takes her 10 minutes to walk to the bus stop. At what time should she wake up to ensure she catches the bus on time? 1

Worksheet 3: Temperature

1 Choose the correct temperature.

a The temperature of a cup of hot coffee is around i 30°C. ii 85°C.

b What is the possible temperature of a snowman? i 0°C ii 50°C

2  Look at the thermometer and write the temperature.

3 Convert.

4 The temperatures in different cities at different times are as follows. Answer the questions based on the data.

a Which place is the coolest?

b Which place is the hottest?

c What is the difference between the temperatures in Delhi and Shimla?

d How many degrees will the temperature need to rise in Bangalore to reach 25°C?

5 The highest temperature ever recorded in India was 51.0°C in Phalodi, Rajasthan while the lowest temperature ever recorded was –60.0°C in Drass, Jammu and Kashmir. What is the difference between the highest and the lowest temperatures in India? Give your answer in Fahrenheit.

In a city somewhere, something incredible happens with the temperature. On a particular day of the year, the temperature reads the same on both the Celsius and Fahrenheit scales. The relationship between Celsius (°C) and Fahrenheit (°F) is given by the formula:

Can you figure out at what temperature the values of °C and °F are the same?

Worksheet 4: Chapter Checkup

1 Convert the time into smaller units.

2 Convert.

3 A flight departs from New Delhi at 10:00 a.m. and takes 6 hours and 30 minutes, including a stopover, to reach Chennai. How many minutes does the flight take to reach its destination?

4 Prashant was 5 years 4 months old when he first went to school. Today he is 12 years 3 months old. For how long has he been going to school?

5 The doctor advised Kunal to take his medicine every 75 minutes. How many times did Kunal take the medicine in 12 hours?

6 Sara is in an air-conditioned room with a room temperature of 32°C. If she decreases the temperature by 2°C every minute, how many minutes will it take to reach 16°C?

Read the assertion and reason, and choose your answer from the given options.

Assertion: Priya has taken 15 days leave from her office. Her holidays will start on Saturday, 25 June. The holidays end on Sunday, 10 July.

Reason: The number of days in the month of July is 31.

a Both Assertion and Reason are true, and the Reason is the correct explanation of the Assertion.

b Both Assertion and Reason are true, but the Reason is not the correct explanation of the Assertion.

c The Assertion is true, but the Reason is false.

d The Assertion is false, but the Reason is true.

Vishesh was travelling from New Delhi to London. It takes 9 hours 35 minutes for a flight to reach London from New Delhi. The flight departs from Delhi airport at 6:00 a.m. (according to Indian standard time). What will be the time in London when the flight lands if London’s time is 5 hours 30 minutes behind Indian standard time?

Worksheet 5: Case Study

Monitoring Climate Change

In a coastal town, scientists are studying the effects of climate change on the local environment. One aspect they are investigating is the change in temperature over the past few decades. Thus, for the past 30 years, researchers have been recording daily temperatures in the town. They have noticed a gradual increase in the average temperature over this period.

Data:

a  In 1990, the average daily temperature was 20°C.

b  In 2020, the average daily temperature was 24°C.

Answer the following questions:

1 What was the average daily temperature in 1990? a  20°C b  24°C c  22°C d  18°C

2 By how many degrees has the average daily temperature increased from 1990 to 2020? a  2°C b  4°C c  6°C d  10°C

3  The average daily temperature in 2020 was °C.

4 If the same trend follows, the temperature in 2050 would be °C.

5 The average daily temperature in the coastal town has decreased over the past 30 years. True / False

6 How do you think understanding changes in temperature over time can help us take better care of the environment?

Worksheet 6: Mental Maths

1 Multiple choice questions.

a  Which of the given cities has the maximum temperature?

i  Pune, 27°C ii  Bhopal, 36°C iii  Bangalore, 18°C  iv  Delhi, 48°C

b  Which of the given cities has the minimum temperature?

i  Pune, 27°C ii  Bhopal, 36°C iii  Bangalore, 18°C  iv  Delhi, 48°C

c  6 p.m. on a 24-hour clock is

i  6:00 hours ii  18:00 p.m. iii  18:00 hours  iv  6:00 p.m.

2 Fill in the blanks.

a The time 3 hours after 7:45 p.m. is .

b 15:00 hours on a 12-hour clock is .

c The duration from 11:30 a.m. to 2:30 p.m. is .

d The time from 7:00 a.m. to 7:00 p.m. is hours.

3  Write True or False.

a  The freezing point of water is 0 °C.

b  The water at 100°C is safe to drink.

c The difference between 3 years 3 months and 2 years 2 months is 1 year 1 month.

d  The formula to convert from °C to °F is to multiply by 9 5 and add 32.

4  Convert the temperatures from °C to °F using the given formula.

°F = (°C × 1.8) + 32

a  10 °C = b  20 °C =

5  Convert.

a  2 minutes 30 seconds = seconds. b  90 seconds = minutes seconds.

c  240 seconds = minutes. d  10 minutes = seconds.

Ch� 1: The Fish Tales

Ch� 4: Parts and Wholes

Ch� 10: Tenths and Hundredths

Ch� 13: Ways to Multiply and Divide

Worksheet 1: Unitary Method

1  Fill in the blanks.

a  If the cost of one candy is ₹5, then the cost of 7 candies will be ₹ .

b If Lisa received ₹240 as pocket money for 4 weeks, the amount of money she received every week was ₹ .

c  Riya saved ₹600 in 3 months. She saved ₹ every month.

2 Find the cost of 20 candles at ₹15 per dozen. (1 dozen = 12 units)

3 Suhani went to purchase cloth for her centre table. If 3 4 metres of cloth cost ₹54. Find the cost of 1 2  metre of cloth.

4 In 1947, at the time of India's independence, the price of gold was approximately ₹88.62 per 10 grams. What was the price of 100 grams of gold that time?

You have ₹50 to spend on school supplies. Pencils are priced at ʺBuy 2, Get 1 Freeʺ at ₹2 each. How many pencils can you buy without exceeding your budget?

Worksheet 2: Profit or Loss

1 Fill in the blanks.

a  The amount of money that a seller spends to pay for an item is called the

b  When the cost price is higher than the selling price, then there is a .

c When the selling price is than the cost price, then the seller is said to have gained a profit.

d  A flower vase is sold at ₹725 for a profit of ₹225. Its cost price is .

2 Raj set up his shop at the book fair. He sold a book for ₹540 and earned ₹30 on the book. Was my cost price more or less than the selling price?

3 Find the missing element.

a  SP = ₹1100   Profit/Loss =

1

c  SP = ₹940

= CP = ₹1100

b  Profit = ₹240   SP =

A shopkeeper buys 3 kg of oranges for ₹510 and 4 kg of apples for ₹456. He sells the oranges at ₹32 per kg. At what price (per kg) should he sell the apples so that he is able to recover his loss and break even (no profit - no loss)?

Worksheet 3: Word Problems on Money

1 Sahil sold his TV for ₹30,000 at a profit of ₹1563. Find the CP of the TV.

2 A shopkeeper bought 20 pencil boxes for ₹480. If he sold each pencil box for ₹50, calculate the profit or loss on each pencil box.

3 At a trade fair, a merchant bought 15 kg of spices for ₹3000 and sold them for ₹250 per kg. Did he make a profit or a loss? How much was the profit or loss on each kilogram?

4 Ayan bought an old smartphone for ₹5620. He spent ₹530 to repair it. He then sold the smartphone to his friend for ₹6150. Did Ayan make a profit or a loss, and how much?

5 Bicycles produce no emissions, making them an eco-friendly mode of transport. Aryan bought a new bicycle for ₹7830 and spent ₹270 on its transportation. He then sold the bicycle for ₹8000. Find the profit or loss. What are the other benefits of cycling?

Challenge

1

The exchange rate between Singapore and India was: 1 SGD = ₹62.5. Tanya takes a loan of 2000 SGD from a friend living in Singapore. In how many months will Tanya pay off the loan if she pays ₹5000 per month to her friend?

Worksheet 4: Chapter Checkup

1  State True or False.

a  Selling price is the amount of money a seller pays to buy an item for his store.

b  When CP < SP, the seller makes a profit.

c  Priya bought a bag for ₹350 and sold it for ₹400. She made a profit.

d  If the cost of 5 pencils is ₹30, then the cost of one pencil will be ₹8.

2  Calculate the profit or loss. a  CP = ₹167 and SP = ₹185 b  CP = ₹36 and SP = ₹29 c  CP = ₹147 and SP = ₹125

3 Kanika sold 20 bulbs for ₹15 each at a profit of ₹5 on all the bulbs. What was the cost price of each bulb?

4 Amit purchased two tea sets for ₹780 and ₹675. He sold both of them for ₹1450. Did he make a profit or a loss? How much was it?

5 A retailer bought 30 shirts for ₹200 each and 20 shirts for ₹100 each. He sold all of them for ₹300 each. Calculate the total profit or loss made by the retailer.

6  Which of these will be a better buy? 4 pencils for ₹24      Or       10 pencils for ₹50

7 A store bought 7 phones at ₹2100 each. They want to sell them at a total profit of ₹700. What should be the selling price of each phone?

1 Read the question below. Which of the statements is true?

3 workers can paint a house in 6 days for ₹9000. They divide the amount equally among themselves.

Statement 1: Each worker gets paid ₹500 every day.

Statement 2: In 1 day each worker will get 1 3 of the total amount.

2 Diya spent 1 5 of her salary on rent, 1 4 of what was remaining on food. Then she spent 1 3 of what was left on clothes and transport. She saved the remaining ₹5000. What was Diya’s salary?

Worksheet 5: Case Study

Shreya's Stamp Collection

Shreya works at a busy shopping centre. In her first year, she earned 2 valuable stamps. In her second year, she worked harder and earned twice as many stamps as she did in the first year. Shreya decided to sell all her stamps. Each stamp was worth ₹450, and she sold them at a profit of ₹50 per stamp.

Answer the questions given below:

1  Shreya collected stamps in her second year.

2 If Shreya sold all her stamps, how much money did she make? a  ₹1000 b  ₹2250 c  ₹3000 d  ₹4500

3 How much would she have sold her stamps for, if she had sold each of them at a loss of ₹25? a  ₹100 b  ₹225 c  ₹300 d  ₹425

4 Why do you think it is important to work hard and try to improve like Shreya did in her second year?

Worksheet 6: Mental Maths

1 Multiple-choice questions.

a If 5 pencils cost ₹15, how much does 1 pencil cost? i  ₹2 ii  ₹3 iii  ₹5  iv  ₹10

b If a book costs ₹12 and is sold for ₹15, what is the profit? i  ₹2 ii  ₹3 iii  ₹5  iv  ₹7

If a watch is bought for ₹4000 and sold for ₹4550, what is the profit?

i  ₹500 ii  ₹550 iii  ₹450  iv  ₹4550

2 Fill in the blanks.

a If you buy a toy for ₹250 and sell it for ₹230, the loss is ₹ .

b If 5 tickets cost ₹2000, then 1 ticket costs ₹ .

c The cost price of an item is ₹50, and profit is ₹60. The selling price is .

d If 8 markers cost ₹24, then 1 marker costs ₹ .

3  Determine if there is profit or loss.

a CP > SP. b CP = SP.

c CP = ₹450, SP = ₹ 500 d SP = ₹5, CP = ₹ 6

4 Suppose you have a wallet that doubles the money every hour. If you have ₹5, how much money will you have after 5 hours?

5 A book costs ₹80. If you get a coupon that gives you ₹25 off the book, how much do you pay after using the coupon?

Aligned to NCERT Chapter: Ch. 12: Smart Charts

Worksheet 1: Single and Double

Bar Graphs

1 The bar graph represents the number of students in different sections of Grade 5 of a school. Which section has the least and the most students?

Least-

Most-

2 Recycling is the process of taking old or used materials and turning them into new products instead of throwing them away. The students of Grade 5 conducted a “Green Choices” project where they collected data on the number of plastic bottles recycled over 5 days.

Day 1—20; Day 2—15; Day 3—18; Day 4—25; Day 5—22

Create a horizontal bar graph to represent the data.

3 The fifth-grade students at Green Valley Elementary School conducted a survey to find their favourite book genres. They asked 60 students to choose their favourite books. Here is the data they collected:

4 The number of carnival tickets sold to adults and children on certain days of a week are shown on the bar graph. Read the graph and answer the questions.

a What is the difference between the tickets sold to children on Sunday and those sold on Friday?

b What is the total number of tickets sold throughout the four days?

c How many more tickets were sold on Sunday as compared to Saturday?

5 Create two more questions on the bar graph given in Q4.

................................................................................................................................................................................................................

Refer to the bar graph in Q4 and answer the given question. On Monday, Tuesday and Wednesday, the total number of tickets sold to adults was two-thirds of the total number of tickets sold to adults on Saturday and Sunday. The total number of tickets sold to children was four-fifths of the total number of tickets sold to children on Friday and Saturday. How many total tickets were sold in the three days?

Worksheet 2: Reading and Drawing Pie Charts

1 Riya gets a fixed amount of pocket money from her parents, and she uses it responsibly. The pie chart shows the uses of pocket money managed by Riya.

a What activity consumes the largest portion of her pocket money?

b If she receives ₹100 as pocket money, how much money goes towards savings?

c If she decides to spend only 1 10 of her pocket money on snacks/food, how much money is that approximately?

2 Rohan recorded the time he spends on different activities during 12 hours over the weekend. Here is the data he collected:

Playing: 3 hours Studying: 4 hours Watching TV: 2 hours Reading: 3 hours

a  Find the fractions and angles for the data.   b  Draw a pie chart and label the data.

3 In a survey of 60 students, they were asked about their favourite sports. The results are as follows: 15 students like soccer, 12 students prefer basketball, 10 students enjoy swimming and the rest are into tennis. Create a pie chart to represent this data.

4 Read the pie chart showing the data for 200 students and answer the questions.

a How many students are interested in Maths?

b If 40 students are interested in Science, what fraction of the total students does this represent?

c If 10 students are interested in EVS, what fraction of the students are interested in EVS?

5 Create a question based on the pie chart given in Q4.

The pie chart shows the global energy consumption. If the total global energy consumption is 13,000 million tonnes then how much total energy is consumed by nuclear and renewables combined?

a 1625 million tonnes       b 1040 million tonnes

c 1560 million tonnes       d

Worksheet 3: Reading Line Graphs

1 The graph shows Kavya’s internet usage across five days.

On which days did she spend the maximum number of hours on the internet?

2 The line graph shows the number of persons who visited different cities on a certain day. Name the cities visited by the most and the least number of people.

3 Gulmarg is a beautiful hill station and popular tourist destination located in the Baramulla district of Jammu and Kashmir, India. The line graph represents the weekly minimum temperature readings (in °C) of Gulmarg for five weeks. Study the graph carefully and answer the questions.

a What was the temperature recorded during the second week?

b In which week was the highest temperature recorded?

c What was the temperature difference between the first and the last week?

Mohit’s father runs a clothing factory. The total sale of clothes from the factory is shown. Read the graph and answer the questions.

a In which month did the sales cloth double of that in May?

b What were the average sales over the period of five months?

Worksheet 4: Chapter Checkup

1 An organisation conducted a survey on pets to find the favourite pets in a certain locality. They asked 60 families about their preferences and created a bar graph to represent the results. Look at the graph and fill in the blanks.

a families like cats.

b families prefer birds and rabbits as their pets.

c The number of families who like dogs as pets is more than the number of families who like fish as pets.

2 The graph shows the number of pages read by boys and girls for five days of a week. Read the graph and answer the questions.

a On which day did boys and girls read an equal number of pages?

b Who reads more pages on Wednesday?

c What is the difference in the total number of pages read by girls and by boys?

3 The data represents the sale of refrigerators by a showroom in the last six months. Draw a horizontal bar graph.

a  What is the area of the Pacific Ocean?

b What is the total area of the Indian and the Atlantic Oceans?

c How much more is the area of the Antarctic Ocean than the Arctic Ocean? 0 Monday Number of Pages 5 10 15 20

4 The total area of the oceans on the Earth is about 362 million sq. km. The pie chart shows the area of the 5 oceans on Earth.

5 The data shows the number of hours spent by Kunal on different activities in a day. Draw a pie chart for the given data.

6 Read the graph showing the amount of fruit sold in a week. Answer the questions.

a On which day did the fruit seller sell 15 kg of fruit?

b How many kilograms did he sell together on Saturday and Sunday?

c What is the difference between the sales of the initial 4 days and the last 3 days?

7 Read the graph showing the temperature of different cities. Answer the questions.

a  Which is the hottest city?

b  Which is the coldest city?

c What is the temperature in Chennai?

d Which city has a temperature of 10℃?

8 In a music class, students were asked about their favourite musical instruments. Out of 40 students surveyed, 12 students liked the guitar, 10 liked the piano, 8 enjoyed playing the drums and the remaining students liked other instruments. Draw a pie chart to represent the data.

1 A fertiliser is a substance added to soil or plants to help them grow better and stronger. The bar graph shows the production of fertilisers by a company over the years. If the production in 2003 was twice of that of 1998, and in 2004, it was 8 6 of 1997, then what is the total production of fertilisers over the span of 10 years?

2 600 students were surveyed on their favourite foods. Read the pie chart and identify the options that are not true.

a 375 students have Indian food as their favourite food.

b 60 students have Mexican food as their favourite food.

c 90 students have Italian food as their favourite food.

d 85 students have Chinese food as their favourite food.

Worksheet 5: Case Study

Wildlife in India

Ruhaan is a wildlife biologist. He studies animals and other wildlife and how they interact with their ecosystems. Ruhaan collected data on the number of tigers and elephants for the year 2022 in different states of India and drew a bar graph on it. Read the bar graph and answer the questions.

1  What is the total number of tigers in the 4 states? a  198 b  202 c  204 d  200

2 What is the difference between the number of tigers and elephants in the 4 states altogether? a  30 b  35 c  38 d  43

3 Draw a horizontal bar graph to represent the same data.

4 Which state had 12 more elephants than tigers?

5 How can we conserve endangered (a species that is at serious risk of extinction) species like tigers and elephants?

Worksheet 6: Mental Maths

1 Look at the given pie chart to answer the below questions.

a How much would Nitin spend on bus fare if he had ₹100? i 7 ii 12 3 10

b Which two expenses have their total more than food? i Bus fare and Clothing ii Clothing and Utilities Utilities and Bus fare Utilities and Others

2 A bar graph shows the number of books read by students in different grades.

a Which two grades read a total of 150 books?

b If each grade reads 10 more books next month, how many books will Grade 3 have read in total?

3 A student is tracking their daily study hours over a month to observe how their study time varies from day to day. Which type of graph would be most appropriate?

a  Pie chart b  Bar graph c  Line graph

4 A line graph shows the monthly sales (in units) of a toy company from January to June.

a In which month did the company experience the largest drop in sales compared to the previous month? i  January ii  March iii  April

b What is the total number of units sold by the company from January to June?

Answers

Chapter 1

Worksheet

1

1. a. 9000; 9 b. 50000; 5

2. a. Indian System: 2,16,43,332; International System: 21,643,332

b. Indian system: 12,00,621; International System: 1,200,621

3. a. 4,00,00,000 + 40,00,000 + 1,00,000 + 90,000 + 800 + 80 + 7 Four crore forty-one lac ninety thousand eight hundred eighty-seven

b. 80,000,000 + 1,000,000 + 80,000 + 5000 + 400 + 30 + 2

Eighty-one million eighty-five thousand four hundred thirty-two

4. a. 60,08,098 b. 20,000,569 c. 4,090,000 d. 8,00,01,002

5. a. 1 b. 10 c. 10,000 d. 7

6. a. Indian number system- 27,22,000 b. International number system- 2,722,000

7. 91,19,199

Challenge 1. Option a

Worksheet 2

1. 76,24,578  2. a. < b. = c.

3. a. Ascending order: 93,12,820 < 1,00,36,782 < 5,00,00,367 < 8,87,21,460

Descending order: 8,87,21,460 > 5,00,00,367 > 1,00,36,782 > 93,12,820

b. Ascending order: 36,81,910 < 92,56,890 < 6,92,10,350 < 8,26,00,031  Descending order: 8,26,00,031 > 6,92,10,350 > 92,56,890 > 36,81,910

4. a. 98,54,310; 10,34,589 b. 87,65,321; 12,35,678

5. Descending Order = Russia, China, Australia, India Challenge 1. 39,87,654

Worksheet 3

1. a. 85,48,750 b. 6,07,85,890

2. a. 1,25,89,200 b. 87,52,400

3. a. 8,97,00,000 b. 5,89,90,000

4. 239,000 approximately Challenge 1. 3,23,45,500 and 3,23,46,499

Worksheet

4: Chapter Checkup

1. a. Indian system: 35,07,681; Thirty-Five Lakh Seven Thousand Six Hundred Eighty-One; 30,00,000 + 5,00,000 + 7000 + 600 + 80 + 1; International system: 3,507,681-Three Million Five Hundred Seven Thousand Six Hundred Eighty-One; 3,000,000 + 500,000 + 7000 + 600 + 80 + 1

b. Indian system: 4,20,87,950; Four Crore Twenty Lakh Eighty-Seven Thousand Nine Hundred Fifty; 4,00,00,000 + 20,00,000 + 80,000 + 7000 + 900 + 50

International system: 42,087,950; Forty-Two Million Eighty-Seven Thousand Nine Hundred Fifty; 40,000,000 + 2,000,000 + 80,000 + 7000 + 900 + 50

2. a. 6,07,15,239; 60,715,239 b. 8,09,50,002; 80,950,002

3. a. 6,45,87,120; 6,45,87,100; 6,45,87,000

b. 89,09,010; 89,09,000; 89,09,000

4. a. > b. < c. = d. <

5. 23,56,475 < 90,87,687 < 8,91,63,896 < 9,08,04,365

Challenge 1. 12,15,696  2. 9,98,87,765

Worksheet 5: Case Study

1. Option c  2. Option d  3. Germany

4. Poland, Italy, France, United Kingdom, Germany

Worksheet 6: Mental Maths

1. a. (iv) 7 crore  b. (ii) 50,00,000

2. a. 12,345,678 → 12,345,700, b. 23,456,789 → 23,456,800

c. 12,345,123 → 12,345,100 d. 23,456,456 → 23,456,500

3. a. six hundred thousand; b. 20 lakhs; c. 100

4. c. 0 d. 4  5. 40,10,026

Chapter 2

Worksheet 1

1. a. True b. False c. True d. False

2. a. 89,285 b. 2,64,859 c. 15,54,313

3. a. 91,660 b. 71,092 c. 9,21,018

4. a. 7,28,944 b. 4,62,917

5. a. 81,898 b. 9,31,609

6. 22,448 kilometres

Challenge 1. 47,865 to 99,999

Worksheet 2

1. a. False b. False c. False d. True

2. a. 5,65,670; 56,56,700; 5,65,67,000

b. 4,78,520; 47,85,200; 4,78,52,000

3. a. 2500; 250; 25 b. 35,400; 3540; 354

4. a. 61,525 b. 27,36,600 c. 78,71,525

5. a. Quotient = 183; Remainder = 134 b. Quotient = 124; Remainder = 228 c. Quotient = 159; Remainder = 280

6. ₹28,28,232

Challenge 1. 1,39,200 chairs

Worksheet 3

1. a. (ii) b. (ii)

2. a. 168 b. 272 c. 3171

3. ₹78

Challenge 1. So, the resultant number is 348.

Worksheet 4: Chapter Checkup

1. a. 80,245 b. 10,33,428

2. a. 20,101 b. 7,68,289

3. a. 8960; 89,600; 8,96,000 b. 45,460; 4,54,600; 45,46,000

c. 64,570; 6,45,700; 64,57,000

4. a. Quotient = 210; Quotient = 21; Quotient = 2, Remainder = 100

b. Quotient = 408, Remainder = 6; Quotient = 40, Remainder = 86; Quotient = 4, Remainder = 86

c. Quotient = 5120; Quotient = 512; Quotient = 51, Remainder = 200

5. a. 29,32,848

6. a. Quotient = 237; Remainder = 20

7. a. 27 b. 76 8. 7,03,66,258 people  9. 50 days   10. 2226 oranges in each carton

11. ₹1,20,500

Challenge 1. Both statements are true.  2. Option a

Worksheet 5: Case Study

1. 12,10,111 kg  2. a. False  b. True

3. 172 kg

Worksheet 6: Mental Maths

1. a. 5321 b. 1434 c. 5979 d. 2600

2. a. False b. False c. True d. True

3. a. 12 b. 120 c. 1200 d. 12,000

4. a. (ii) b. (iii)

Chapter 3

Worksheet 1

1. a. 1, 2, 7 and 14 b. 1, 2, 17 and 34 c. 1 and 37

2. a. 1, 3, 5 and 15 b. 1 and 41 c. 1, 3, 7, 9, 21 and 63

3. Prime numbers: a, c, g, i

Composite Number: b, d, e, f, h, j

4. 4 prime numbers - 11, 13, 17 and 19  5. 2 factors

Challenge 1. The chairs will be arranged in 13 rows with 13 chairs in each row.

Worksheet 2

1. b, c, e  2. d, e  3. a, b, d  4. a, b  5. 660 6. pencils, erasers and notebooks

Challenge 1. Yes, because both 324 and 135 are divisible by 9.

Worksheet 3

1. b  2. c  3. a. 8 = 2 × 2 × 2 b. 20 = 2 × 2 × 5

c. 24 = 2 × 2 × 2 × 3

4. a. 16 = 2 × 2 × 2 × 2 b. 22 = 2 × 11 c. 30 = 2 × 3 × 5

5. 5, 73, 365

Challenge 1. 11

Worksheet 4

1. a. 1 b. 1  2. a. 8 b. 15

3. a. 3 b. 13 4. a. 6 b. 14

5. 5 cm

Challenge 1. 9 litres

Worksheet 5: Chapter Checkup

1. Prime Numbers: b and c

Composite number: a and d

2. a. 1, 2, 4, 8 and 16 b. 1, 2, 4, 5, 10 and 20

c. 1, 2, 3, 4, 6, 8, 12 and 24

3. a. 1, 2, 4, 7, 14 and 28 b. 1, 2, 3, 4, 6, 9, 12, 18 and 36

c. 1, 2, 4, 7, 8, 14, 28 and 56

4. a. divisible by 5 b. divisible by 3

c. divisible by 2, 3, 5, 9 and 10 d. divisible by 2, 5 and 10

5. a. 88 = 2 × 2 × 2 × 11 b. 102 = 2 × 3 × 17

6. a. 75 = 3 × 5 × 5 b. 21 = 3 × 7

7. a. 1,5 b. 1, 5, 25

8. 4  9. 2  10. a. 9 b. 17

11. 25 litres  12. 80; 3 cupcakes; 2 sandwiches

Challenge 1. 10 is the greatest number that divides 178 and 128 leaving remainder as 8.

2. HCF is 4. Twice the HCF is 4 × 2 = 8. So, the number is 8.

Worksheet 6: Case Study

1. d  2. b

3. 12 necklaces

Worksheet 7: Mental Maths

1. 3, 9 2. 45 3. 3

4. a. True b. True c. False

Chapter 4

Worksheet 1

1. a. 8, 16, 24, 32, 40 b. 11, 22, 33, 44, 55 c. 21, 42, 63, 84, 105

2. Yes, 7209 is completely divisible by 9.

3. 2025, 2037, 2049  4. Answers may vary. Sample answer 10, 20, 30, 40, 50, 60, 70, 80, 90, 100; Even.  5. No

Challenge 1. Yes A can also be a multiple of B. For example, if B = 8, the factors are 1, 2, 4, 8. If A = 1, 2 or 4, it cannot be B’s multiple but if A = 8, it becomes a multiple of B which is also 8.

Worksheet 2

1. d  2. a. 60 b. 63 c. 55

3. c  4. 2036

5. Answers may vary. Sample answer.

A shopkeeper sells candles in packet of 12 and candle stands in packets of 8. what is the least number of candles and candle stands Rita should buy so that there will be one candle for each candle stand?

Challenge 1. 12

Worksheet 3

1. a. 35 = 5 × 7; 75 = 3 × 5 × 5 b. 44 = 2 × 2 × 11; 88 = 2 × 2 × 2 × 11

2. a. 40 b. 16 c. 80 d. 50  3. a. 180 b. 315 c. 864

Challenge 1. 63 years

Worksheet 4

1. a. 168 b. 150 c. 96

2. No, Rohit’s calculation is incorrect, as he didn’t consider all the prime factors.  3. 60

Challenge 1. a. Both A and R are true, and R is the correct explanation of A.

Worksheet 5

1. August 7, 14, 21, 28.  2. 6 groups 3. 15 litres

4. Answers may vary. sample answer.

Three pieces of ribbons 42 cm, 49 cm and 63 cm long need to be divided into the same length. What is the greatest possible length of each ribbon?

Challenge 1. a. 10 visits b. 10th visit

Worksheet 6: Chapter Checkup

1. 9, 18 and 27  2. a

3. a. 63 b. 81 c. 99 d. 117

4. b  5. a. 630 b. 90 c. 1386

6. a. 45 b. 600  7. a. 480 b. 3720

8. 180 minutes

Challenge 1. c. Rahul and Sahil are correct.    2. a

Worksheet 7: Case Study

1. b. Every 60 minutes   2. d. 9:00 a.m.

3. 10  4. Answers may vary.

Worksheet 8: Mental Maths

1. a. multiple b. 12 c. 56 d. 90

2. 24, 48, 60, 84. Smallest multiple- 24

3. a. Yes, No b. Yes, Yes c. No, No

4. 420

Chapter 5

Worksheet 1

1. a. Unlike fractions b. Like fractions  c. Unlike fractions

d. Like fractions

2. Proper fractions: a. 41212 ,,. 51529 , g. 41212 ,,. 51529 , j. 41212 ,,. 51529

Improper fractions: b. 658179 ,,,. 25113 , d. 658179 ,,,. 25113 , f. 658179 ,,,. 25113 , h. 658179 ,,,. 25113

Mixed numbers: c. 157 4,5,6. 789 , e. 157 4,5,6. 789 , i. 157 4,5,6. 789 3.

5. 2 17 5

Challenge 1. 22 3

Worksheet 2

1. Answers may vary, sample answers:

a. 1218 , 1421 b. 1218 , 3045 c. 2233 , 3451

2. Answers may vary. Sample answers:

a. 63 , 105 b. 72 , 288 c. 1510 , 2114

3. a. 2 5 b. 3 7 c. 1 3

4. a. 28 b. 56 c. 2 d. 70 5. d.

6. Answer may vary. Sample answer. = =

Challenge 1. Green- 1 6, Pink - 3 18 or 1 6 , Blue - 1 4 or 3 12, Purple - 1 6, Yellow- 1 4 or 3 12; Green, pink and purple are equivalent. Yellow and blue are equivalent.

Worksheet 3

1. a. < b. < c. > d. <  2. a.  b.  c.  d. 

3. a. 3311 5846 >>> b. 8131 9283 >>>

4. Reshma   Challenge 1. Statement II

Worksheet 4: Chapter Checkup

1. a. 15 2 b. 17 3 c. 103 8 d. 51 8

2. a. 2 4 4 b. 1 8 5 c. 1 24 6 d. 11 4 19

3. Answers may vary. Sample answers: a. 468 ,, 121824 b. 234 ,, 182736 c. 101520 ,, 162432

4. Answers may vary. Sample answers: a. 842 ,, 1263 b. 1284 ,, 21147 c. 25155 ,, 653913

5. a. 3 4 b. 11 14 c. 3 5

6. a. 114 2 25 < b. 434 6 54 < c. 24 8 3 =

7. a. 1514 61225 <<<  b. 1313 5825 <<<

8. Least: Alex and Casey; Greatest: Bailey   9. Australia < South America < North America < Europe < Africa < Asia

Challenge 1. 3 8 2. Option c

Worksheet 5: Case Study

1. b  2. a  3. 8 10

Worksheet 6: Mental Maths

1. a. True b. False  2. a. Proper

b. Improper c. mixed fraction d proper 3. option c

4. a = 1, b = 10

Chapter 6

Worksheet 1

Worksheet

Challenge 1. No

Worksheet

Worksheet 5: Chapter Checkup

4m

Challenge 1. 1 3 cup; 4 cheese cubes  2. b

Worksheet 6: Case Study

1. c  2. b  3. 113 20 hours

Worksheet 7: Mental Maths

1. Option c

2. a. true  b. false  c. false   d. true

3. a. 18  b. 28  c. 1  d. 3 2

Chapter 7

Worksheet 1

1. a. forty-five point five or forty-five and five tenths b. twelve point three or twelve and three tenths c. forty-two and fourteen-hundredths or forty-two point one four

2. a. 413.2  b. 72.33  c. 52.402

3. a. 1.6

One and six-tenths. or one point six b. 1.72

one point seven two or one and seventy-two hundredths or one point seven two

4. a. 40 + 5 + 1 10 or 40 + 5 + 0.1 b. 40 + 5 + 1 10 + 3 100 or 40 + 5 + 0.1 + 0.03

5. a. 4.1  b. 489.982

Worksheet 2

1. a. 0.9, 90%  b. 0.32, 32%

2. a. 13 10 , 130%   b. 627 50 = 1254%   c. 803 23 = 3212%

3. Answers may vary. Sample answers. a. 187.2 = 187.20 = 187.200 b. 87.02 = 87.020 = 87.0200 c. 963.14 = 963.140 = 963.1400 d. 189.221 = 189.2210 = 189.22100

4. a. 21 10 , 2.1, 210%  b. 7 20 , 0.35, 35%   c. 131 250 , 0.524, 52.4%

5. a. >  b. <  c. =

6. 400 + 50 + 5 + 8 10 + 9 100 or 400 + 50 + 5 + 0.8 + 0.09

Challenge 1. 0.9978 and 0.9987

Worksheet 3

1. None

2. a. 13.15, 1.20  b. 3.48, 1.20  c. 4.800, 1.526   d. 1.400, 47.584

3. a. 0.6 and 0.2 b. 0.35 and 0.50

4. 0.540, 60.900 and 83.394

Challenge 1. Option c

Worksheet 4

1.

2. a. True  b. False  c. True

3. a. 4.2  b. 15.67  c. 87.654

4. a. 3  b. 8  c. 48  d. 15

5. a. 14.01 < 14.1 < 14.101 < 14.14

b. 84.5 < 84.55 < 84.56 < 84.6 < 84.65

6. a. <  b. =  c. =  d. <

7. 206

Challenge 1. No

Worksheet 5: Chapter Checkup 1. a. 1.2 = 1 + 0.2 = 1 + 2 10

1.48 = 1 + 0.4 + 0.08 = 1 + 48 10100 +

2 a. fifteen and two-tenths or fifteen point two b. one hundred seventy-six and eight hundred one thousandths or one hundred seventy-six point eight zero one

3. a. 40.101 b. 103.05 c. 420.011 d. 31.005

4. a. 0.125, 12.5%  b. 0.8, 80%

5. a. 63 10; 5 ; 1260%  b. 5063 1000; 200 ; 2531.5%

6. a. 1  b. 100  c. 100  d. 1000

7. a. 1.33 > 1.31 >1.3 > 1.2   b. 19.54 > 19.501 > 19.44 > 19.4

8. Utkarsh won the race.

Challenge 1. 0.97   2. Option c

Worksheet 6: Case Study

1. Option c   2. Option d

3. Jin Mao Tower, Wuhan Greenland Centre, CITIC Tower, Lotte World Tower, Shanghai Tower, Merdeka 118

4. 679 m; 528 m; 421 m; 599 m; 476 m; 632 m

5. 678.9 = 600 + 70 + 8 + 9 10

527.7 = 500 + 20 + 7 + 7 10

420.5 = 400 + 20 + 5 10

599.1 = 500 + 90 + 9 + 1 10

475.6 = 400 + 70 + 5 + 6 10

632.0 = 600 + 30 + 2

Worksheet 7: Mental Maths

1. a. (ii)  b. (i)

2. a. 3  b. 5

3. a. >  b. >   c. =  d. <

4. a. 0.9 b. 0.09 c. 0.099 d. 0.999

Chapter 8

Worksheet 1

1.

2.

3. a. 35.9  b. 79.19  c. 117.882

4. a. 3.2  b. 0.58  c. 110.803

5. 4.85 litres

Challenge 1. 9

Worksheet 2 1.

2. a. 456  b. 1547.8  c. 63,157  d. 10  e. 179.34 f. 438.987  3. a. <  b. =  c. <

4. ₹89,190

Challenge 1. 3; 3.75

Worksheet 3

1. a. 0.2 b. 0.2

2. a. 1.56  b. 0.5123  c. 0.012  d. 0.032561 e. 0.0231  f. 0.2  3. a. 20.1  b. 9.13  c. 5.415   4. 1000 pounds

Challenge 1. 1166.72 Euros

Worksheet 4: Chapter Checkup

1. a. 0.7 b. 0.78

2. a. 1.2

b. 3 3. a. 63.123  b. 46.34  c. 33.48  d. 51.792

e. 518.755  f. 114.921  4. a. 10  b. 1000  c. 100

d. 10  e. 1000  f. 1000  5. a. 4.701  b. 100  c. 1000   d. 1000  e. 0.0142  f. 100  6. a. 18.48  b. 58.518   c. 289.26

7. a. 18.4  b. 12.35  c. 30.02   8. $1.22  9. ₹14,259.2  10. 5 days

Challenge 1. 25.543 kg  2. option c

Worksheet 5: Case Study

1. Option c 2. Option a 3. 1444.6 mm 4. 790 mm 5. Answers may vary.

Worksheet 6: Mental Maths

1. a. 0.73  b. 1.33

2. a. 1000 b. 0.023  3. a. 3.671 b. 1.5 c. 0.8 d. 15

4. a. < b. <

Chapter 9

Worksheet 1

1. a. Parallel lines  b. Ray  c. Intersecting lines

d. Line  2. a. False  b. False  c. True

d. True  3. Line segment, Parallel lines, Point, Ray

4. a. A, B, C, D, E, F; ,, ACCBAB

b. Answers may vary. Sample answer FD

c. 1 ray, BE Challenge

1. True     Q P Q P

Worksheet 2

1. Answers may vary. Sample answer

2. a. ∠PQR, ∠RQP or ∠Q  b. ∠LMN, ∠NML or ∠M

c. ∠XYZ, ∠ZYX or ∠Y  3. ∠1 and ∠3

4. Acute, Obtuse, Straight, Obtuse

Challenge 1. a. obtuse angle b. straight angle

c. 2 acute angles

Worksheet 3

1. a. Acute angle  b. Obtuse angle  c. Right angle

d. Acute angle  2. a. 74°  b. 115°  c. 152°  d. 120°

3. a. 50° b. 85° c. 100°

d. 145°

Challenge 1. Students will draw a straight angle.

Worksheet 4

1. a. Quadrilateral  b. Nonagon  c. Hexagon

d. Decagon  2. a. nine  b. three  c. seven

d. five   3. a. True  b. True  c. True  d. False

4. octagon  5. Hexagon

Challenge 1. Triangles -15 Quadrilaterals -5

Worksheet 5: Chapter Checkup

1. a. Line  b. Ray  c. Line segment  d. Line segment

2. a. True  b. False  c. False

3. a. Acute angle  b. Right angle  c. Straight angle

d. Obtuse angle

4. a. acute  b. right  c. straight  d. obtuse  e. acute

5. a. 150°  b. 130°  c. 170°

6. a. 120°  b. 155°  c. 57°  d. 90°

7. a. 65° b. 115°

8. a. Heptagon; 7 sides, 7 angles b. Octagon; 8 sides, 8 angles

9. a, d   10. Hexagon

Challenge 1. Option a 2.

Worksheet 6: Case Study

1. option c  2. option b  3. option c

4. Figures may vary. Sample figure.

Worksheet 7: Mental Maths

1. a. true  b. false  c. false  d. true

2. a. acute  b. obtuse  c. right

3. a. right angle  b. straight angle  c. acute angle   d. obtuse angle

Chapter 10

Worksheet 1

1. c

2.

3.

The pattern is rotating 90° in clockwise direction.

4. a. 45° Clockwise  b. 90° Clockwise

5.

Challenge 1.

Worksheet 2

1. b. Reason - Tiling pattern forms when a single unit or shape repeats over and over again without leaving any gaps. In option b there is a gap in pattern. Hence option b is not a tiling pattern.

2.

4. b; Answers may vary. Sample answer.

Challenge 1.

Worksheet 3

1. a. Adding 4 to each term.  b. Adding 2 to each term.

c. The pattern has squares of natural numbers.

2. a. 53453  b. 89012  c. 14523

3. Answer may vary. Sample answer: 12 2 6 1 54 3

Challenge 1. 14

Worksheet 4

1. a. 2 lines of symmetry  b. Asymmetrical

c. 1 horizontal line of symmetry

d. Many lines of symmetry.

2. a. no line of symmetry  b. c. no line of symmetry   d.

a. A b. H c. T d. Asymmetrical.

4. a. False  b. False  c. True  d. True

5. Answer may vary. Sample answer: a. b.

Challenge 1.

Worksheet 5: Chapter Checkup

4. 2 1 4 16 8   5. a. b. 6. a. b. c.

7. 256, 241, 226; 15 is subtracted each time.

8. a. 1, 3, 9, 27, 81  b. 15, 18, 23, 26, 31

9. a. 57, 64, 72, 81, 91  b. 75, 69, 62, 54, 45

10. ₹2560  11. 300 steps

Challenge 1. 28  2. Option c- A is true but R is false.

Worksheet 6: Case Study

1. b. Rectangle  2. True  3. reflectional symmetry

4. No  5. Dispose of trash in designated bins, and avoid bringing items that can cause litter.

Worksheet 7: Mental Maths

1. a  2. a. 32 b. AB c. 105  3. Each number is double the previous number.  4. d  5. a. False b. False

c. False d. True

Chapter 11

Worksheet 1

1. Answers may vary, Sample answer.

a. 15 cm; 13 cm; 2 cm b. 3 cm; 5cm; 2 cm

2. a. 5.5 cm b. 2.7 cm 3. a. 4.5 cm b. 0.547 cm

c. 1.056 km 4. a. 45.1 m b. 16,080 mm c. 280 m 5 dm

5. 0.0001 km 6. 53 m 16 cm

Challenge 1. 14 cm

Worksheet 2

1. a. 30 g b. 85 g c. 70 kg d. 100 g  2. a. 0.079 kg

b. 9,75,000 mg c. 46,77,000 g 3. a. 6.01 kg; 6010g b. 16.08 g; 16,080 mg c. 547.006 kg; 5,47,600 mg 4. 1.688 kg

5. 25 eggs 6. 4 kg 56 g

Challenge 1. 10 quintals is 1 ton

Worksheet 3: Chapter Checkup

1. a. m; kg b. cm; g c. m; kg  2. a. 12.5 cm b. 17.9 cm

3. 14.2 cm  4. 4.5 cm  5. a. 0.008 km

b. 4.35 hm c. 12,32,000 mm  6. a. 5000 g

b. 4.64 g c. 54,78,000 mg  7. 380 g

8. No, because their overall weight is 293 kg which is greater than the carrying limit of the lift.

9. Answers may vary. Sample answer: Ana buys 23.5 kg of rice and 18.25 kg of flour. How much rice and flour did she buy in all?

Challenge 1. 41,000 g 2. Option c

Worksheet 4: Case Study

1. a. cm b. mm

2. option d

3. Length of the play area = 6,682 m

4. The van can shift 4 tigers or 1 tiger and 1 lion in a trip

5. Answer will vary.

Worksheet 5: Mental Maths

1. 12 cm 2. 200 grams 3. 1 bag

4. a. 35 cm b. 75 cm c. 60 cm d. 22.5 cm

5. a. 12 kg b. 1.5 kg

Chapter 12

Worksheet 1

1. a. 80 cm b. 300 cm

2. a. 128 m b. 212 cm

3. a. 54 cm b. 280 m

4. a. 24 mm b. 37 mm  5. 180 m

6. Answers may vary. Sample answers. 10

Challenge 1. B = 4 m, L = 12 m

Worksheet 2

1. a. sq. cm b. sq. cm c. sq. m d. sq. m e. sq. km f. sq. m

g. sq. cm h. sq. m  2. a. 330 sq. cm b 4060 sq. m

3. a. 3136 sq. m b. 4489 sq. cm  4. 144 sq. m

5. a. 17.5 sq. units b. 6 sq. units

6. a. 96 sq. cm b. 33 sq. cm

7. Answers may vary. Sample answers: a.

Area = 80 sq. cm  b. Perimeter = 22 cm

8. Both shapes have same area.

Challenge 1. 54 cm

Worksheet 3: Chapter Checkup

1. a. 64 cm; 252 sq. cm b. 96 m; 567 sq. m

c. 164 m; 1617 sq. m  2. a. 320 cm; 6400 sq. cm b. 128 m; 1024

sq. m c. 180 m; 2025 sq. m  3. a. 40 cm; 128 cm

b. 105 m; 11,025 sq. m c. 28 m; 952 sq. m 4. a. 12 sq. units

b. 4 sq. units c. 10 sq. units  5. a. 39 sq. m  b. 78 sq. m

c. 64 sq. cm   6. c  7. 90,000 sq. feet

Challenge 1. 44 cm  2. No.

Worksheet 4: Case Study

1. c. 224 sq. m  2. Staff-room  3. b. 1444 sq. m

4. 1120 sq. m

Worksheet 5: Mental Maths

1. a. True b. False c. True d. True

2. a. 15 b. 4 c. 12 d. 9

3. a. ii b. iii c. i

4. a. 6 cm b. 3cm

Chapter 13

Worksheet 1

1. a. 5 mL b. 3 L  2. a. 0.658 L b. 84,37,000 mL

3. a. 8.060 L b. 3289 cL c. 4012 L 3 dL

Challenge 1. Yes

Worksheet 2

1. a. 16 cu. units b. 8 cu. units c. 80 cu. units  d. 36 cu. units   2. 6 cu. m  3. 900 cu. cm

4. 6660 cu. cm

Challenge 1. 144 cubic units

Worksheet 3: Chapter Checkup

1. a. 50 mL b. 20 L c. 500 mL  2. 50 mL  3. 800 mL, 200 mL, 300 mL, 700 mL, 500 mL

4. 50

5. a. 4,4,4  b. 8,2,3  6. a. 0.980 L b. 68,69,000 mL

c. 979.6 L

7. a. 12 cu. units  b. 44 cu. units c. 15 cu. units

8. 2 L 100 mL 9. a. 112 cu. unit b. 63 cu. unit  10. 9 L 900 mL

Challenge 1. 96 small cubes 2. Option d

Worksheet 4: Case Study

1. a. false b. true 2. 450 mL  3. 90,000 L

4. The box should have a minimum height of 40 cm to pack the 10 boxes

5. Answers may vary

Worksheet 5: Mental Maths

1. a. 60 L b. 21.3 L c. 60 hL d. 800 cL

2. 50 mL 3. option d 4. option c

Chapter 14

Worksheet 1

1. a.  b.

2. a. Cone: Vertices = 1, Edges = 1, Faces = 2

b. Sphere: Vertices = 0, Edges = 0, Faces = 1

c. Square prism: Vertices = 8, Edges = 12, Faces = 6

d. Cylinder: Vertices = 0, Edges = 2, Faces = 3

3. a. Cube or Cuboid  b. Sphere  c. Cylinder  d. Cone 4.

5. Similarity: 5 faces

Difference: Rohan’s tent has a triangular base, and Simi’s tent has a rectangular base.

Challenge 1. No, even if a cylinder has two identical faces, it is not considered a prism due to its curved surface.

Worksheet 2

1. a. Square pyramid b. Cylinder c. Cone  d. Hexagonal pyramid

2. a. b. 3. Megha

Worksheet 6: Chapter Checkup

1. a. b. c. Cube Cylinder Cuboid

2. Faces = 1, Vertices = 0, Edges = 0

Challenge 1. P

Worksheet 3

1.

3. Front view Side

Top

3. a. Net b. Deep drawing c. Floor plan

4. a. Cylinder: Faces = 3; Edges = 2; Vertices = 0 b. Cube: Faces = 6; Edges = 12; Vertices = 8

15 building blocks Front view Side view Top view

Challenge 1. 3 and 2

Worksheet 4

1. a. south b. east c. west  2. 125 km  3. 24 km

4. Cupboard = 2 m, 8 m; table = 6 m, 4 m; desk = 2 m, 6 m Challenge 1. 12 km

Worksheet 5

32 km b. 64 km c. 120 km d. 200 km e. 256 km   8. Answer may vary. Sample answers

view

view

9. 3 times   10. 21 km

Challenge 1. 6, Cube  2.

Worksheet 7: Case Study

1. 2  2. 3  3. person 1- top, person 2 - side, person 3 - front

4. Answers may vary. Sample answer: Person 1 should stay away from the edge and hold onto something sturdy.

Worksheet 8: Mental Maths

1. a. false b. true c. true d. false

2. a. cuboid b. cuboidal prism c. triangular prism

3. Students will tick figure 3

4. option d

Chapter 15

Worksheet 1

1. a. 180 minutes b. 240 minutes c. 140 minutes

2. a. 300 seconds b. 480 seconds c. 550 seconds

3. a. 4 minutes b. 8 minutes c. 5 minutes 50 seconds

d. 7 minutes 20 seconds e. 8 minutes 40 seconds

f. 9 minutes 10 seconds  4. 510 minutes

Challenge 1. Statement 2 is true.

Worksheet 2

1. 1 hour  2. a. 10 hours 50 min b. 1 hour 35 min

c. 11 weeks 1 day

Worksheet 6: Mental Maths

1. a. iv b.iii c. iii

2. a. 10:45 pm b. 3 pm c. 3 hours d. 12 hours

3. a. True b. False c. True d. True

4. a. 50 b. 68

5. a. 150 seconds b. 1 min 30 seconds c. 4 mins d. 600 seconds

Chapter 16

Worksheet 1

1. a. 35 b. 60 c. 200  2. ₹25  3. ₹36

4. ₹886.2

Challenge 1. 37 pencils

Worksheet 2

1. a. CP b. loss c. greater d. ₹500

2. Your cost price was less than the selling price.

3. a. ₹0 b. ₹1340 c. ₹160

Challenge 1. ₹217.5

Worksheet 3

1. ₹28,437   2. Profit, ₹26  3. He made profit. Profit on each kg is ₹50.  4. Neither profit nor loss  5. Loss, ₹100

Challenge 1. 25 months

Worksheet 4: Chapter Checkup

1. a. False b. True c. True d. False

2. a. Profit, ₹18 b. Loss, ₹7 c. Loss, ₹22

3. ₹14.75  4. Loss; ₹5  5. Profit; ₹7000

6. 10 Pencils for ₹50  7. ₹2200

Challenge 1. Statement 1 is true.

2. Divya’s salary was ₹12,500

3. 3:15 p.m.  4. 3 hours 15 minutes

5. 15 months 21 days

Challenge 1. 7:40 a.m.

Worksheet 3

1. a. ii b. i  2. a. 26°C b. 35°C c. 42°C,  d. 12°C

3. a. 95 °F b. 26.6 °C c. 113°F 4. a. Srinagar

b. Chennai c. 29.7°C d. 3.8°C 5. 231.8 °F

Challenge 1. –40°

Worksheet 4: Chapter Checkup

1. a. 7200 seconds b. 5400 seconds

2. a. 86 °F b. 79.44 °C  3. 390 minutes

4. 6 years 11 months  5. 9 times  6. 8 minutes

Challenge 1. Option b  2. 10:05 a.m.

Worksheet 5: Case Study

1. a. 20°C 2. b. 4°C 3. 24°C 4. 28°C 5. False

6. Answers may vary.

Worksheet 5: Case Study

1. 4  2. c  3. d  4. Answer will vary.

Worksheet 6: Mental Maths

1. a. ii b. ii c. ii

2. a. ₹20 b. ₹400 c. ₹110 d. ₹3

3. a. Loss b. No profit no loss c. Profit d. Loss

4. ₹160 5. ₹55

Chapter 17

Worksheet 1

1. V-A, V-C

2.

Day 5

Day 4

Day 3

Day 2

Number of Plastic Bottles Recycled Da y

Day 1

0246 810121416182022242628

4. a. 35 tickets b. 715 tickets c. 35 tickets

5. Answer may vary. Sample answer.

Q1. What is the number of adult tickets sold in the 4 days?; Q2. What is the difference in the number of children tickets sold on Thursday to that on Sunday.

Challenge 1. 280 tickets

Worksheet 2

5. Answer may vary. Sample answer. How many more students are interested in sports than Maths?

Challenge 1. 1560 million tonnes

Worksheet 3

1. Wednesday and Thursday  2. Most = Pune; Least = Goa

3. a. 8°C b. Week 1 c. 8°C

Challenge 1. a. April b. 6800

Worksheet 4: Chapter Checkup

1. a. 15 b. 19 c. 2

2. a. Thursday b. Boys c. 3 pages   3.

010 20 304050

of Refrigerators

6. a. Friday b. 65 kg c. 5 kg

7. a. Jaipur b. Ooty c. 15°C d. Bangalore

Worksheet 5: Case Study

1. Option b

2. Option c

3.

Telangana State 90 100

Andra Pradesh Bihar

010203040 50607080

Number of Elephants/Tigers Elephants Tiger

4. Andhra Pradesh

5. Answers may vary.

Worksheet 6: Mental Maths

1. a. option iii b. option ii

2. a. Grade 1 and Grade 4 b. 35

3. option c

4. a. option iii b. option iv

Rajasthan

About the Book

Perfect Mathematics workbooks are aligned with the latest NCERT textbooks and are NCF 2023 compliant. Aligned with NEP 2020, this workbook bridges abstract concepts to real-world applications by offering questions that enhance a child's mathematical skills. The workbook has hundreds of practice questions, ample writing space for clear responses and a variety of question types. Perfect Mathematics workbooks also provides a mental maths worksheet for each chapter for Grades 1 to 5. This book supports learners at all levels, providing opportunities to build critical thinking skills through questions and activities aligned with Bloom’s Taxonomy. For those seeking a greater challenge, the workbook includes thought-provoking higher order questions that push learners to apply, analyse and evaluate their concept knowledge.

Key Features

• Curriculum Alignment: Aligned with the lates NCERT textbooks and educational standards such as the NCF 2023.

• Mental Maths: In-built mental maths worksheets for Grades 1 to 5 to help students improve their ability to perform calculations rapidly without relying on calculators or written methods.

• Practice Questions: A wide variety of practice questions to reinforce concepts.

• Question Types: Includes a variety of question types like Fill in the Blanks, True or False, MCQs, and Short and Long answer questions.

• Challenge: Critical thinking questions to enhance problem-solving and analytical thinking skills. Higher order thinking questions in the form of assertive reasoning and data sufficiency questions.

• Case Study: Scenario-based questions to apply theory to real-life situations.

• Answer Key: Answers to all the questions at the end of the book.

• QR Codes: Digital integration through the Uolo app to promote self-learning and practice.

About Uolo

Uolo partners with K-12 schools to provide technology-enabled learning programs. We believe that pedagogy and technology must come together to deliver scalable learning experiences that generate measurable outcomes. Uolo is trusted by over 15,000+ schools across India, Southeast Asia and the Middle East.

ISBN 978-81-982034-3-4