PT_G06_MA_WB_SS_AY25

Practice • Solve • Succeed

Mathematics Workbook

Perfect

MATHEMATICS Workbook

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 6

ISBN: 978-81-982034-9-6

Published by Uolo EdTech Private Limited

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CIN: U74999DL2017PTC322986

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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.

Worksheet 3: Chapter Checkup

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.

Worksheet 4: Chapter Checkup

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

3

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)?

Worksheet 5: Case Study

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 Key: Answers to all the questions in the book at the end of the book.

AnswersAnswers

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.

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

These chapters are not included in the new NCERT books, although they have been recommended by the National Curriculum Framework (NCF). The teachers have the discretion to decide whether to cover them based on the needs of their students.

Patterns in Mathematics 1 0

Worksheet 1: Whole Numbers and Natural Numbers

1  Write the next 5 whole numbers after 13,214.

2  Find the predecessor and successor of the numbers.

3 New Delhi is the one of the largest cities in India, covering an area of approximately 1484 square kilometres. What are the predecessor and successor of 1484?

4  Fill in the blanks with a whole number to make the following statements true.

452 × 0 =

6567 × 1 = c  (4 × 7) × 10 = 4 × (7 × )

785 × 45 = 785 × ( – 5) e  14 × (10 + 12) = (14 × ) + (________ × 12) f  9875 ÷ 1=

5  Locate the missing points on the number line below.

6  Write the results of the number line representation in each case.

7  Evaluate using the number line.

a  15 + 7

b  14 – 9

c  18 ÷ 3

d  2 × 5

8  Replace the letter by a suitable whole number to make the statements true:

a  41 ÷ 41 = x b  0 ÷ y = 0

c  (36 − 25) ÷ p = 11

(144 ÷ 12) × r = 12

9 The total surface area of the Earth is 510 million square km. Of this total surface, 357 million square km is covered by water, and the rest is covered by land. Use the distributive property to calculate the area covered by land.

10  What is the distance between the points on the number line?

a  0 and 12

b  6 and 16

c  3 and 20

11 Adi was baking cookies. Out of 15 cookies that he baked, 7 got burnt. Find the number of cookies that were not burnt, using the number line.

12 A class of 20 students decides to contribute ₹5 each for a donation camp. Find the total amount of money contributed, using the number line.

13  What is the smallest whole number? How many whole numbers are there between 67 and 75?

Challenge

1 Find the product of the successor and predecessor of the largest six-digit number.

1 Look at the given pattern. Draw the next term in the pattern.

2  Find the missing numbers.

a  5, 7, 12, 14, 19, , 26 b  2, 3, 6, 18, 108, c  1, 8, 27, , 125

3  Draw the missing term in the pattern.

4  Study the pattern and write the next two steps. 1 × 1 = 1

5  Study the patterns and write the next 3 steps.

6 Aman gets ₹99 for 1 task. For 3 tasks, he gets ₹999, for 5 tasks, he gets ₹9999 and for 7 tasks, he gets ₹99,999. How much will he get for 13 tasks?

7 Look at the pattern. Write the rule followed in the pattern. How many rectangles will the fifth shape in the pattern have?

8  Solve and establish a pattern.

a  45 × 9 b  45 × 99

c  45 × 999 d  45 × 9999

9 The Fibonacci series was introduced to the West by the Italian mathematician Leonardo of Pisa. It is a sequence in which each number is the sum of the two preceding numbers. What are the next two numbers in the Fibonacci series: 1, 1, 2, 3, 5, 8, , ?

10  Create your own pattern using shapes.

Challenge

Critical Thinking

1 There are 7 students standing in a line. Each student has some pencils, so that the number of pencils each student has is double the number of pencils the student in front has. How many pencils does the 7th student have if the first student has 1 pencil?

Worksheet 3: Chapter Checkup

1 Write the successor and predecessor of the numbers.

2 Study the patterns and write the next two steps.

× 2 – 2 = 2220

c  11 × 3 – 2 = 31

111 × 3 – 2 = 331

1111 × 3 – 2 = 3331

3 Solve on a number line.

a 5 + 5 + 5

b 20 ÷ 4

c 4 × 5

4 What will be 6th shape in the patterns shown below?

d  11 × 4 – 2 = 42

111 × 4 – 2 = 442

1111 × 4 – 2 = 4442

5 Look at the given pattern. Write the rule for the given pattern. How many dots will the fourth shape in the pattern have?

6 How many dots will come in the fifth pattern?

7 Create your own pattern using different shapes.

8 Find the number which when divided by 65 gives 9 as a quotient and 5 as a remainder. Did you use any property? Name it.

9  Solve using the distributive property. a  550 × 45 – 550 × 15

865 × 12 + 865 × 45 c  420 × 36 – 420 × 23

630 × 25 − 630 × 15

10 A rectangular playground is 324 m long and 220 m wide. How much distance will Vicky cover going 4 times around it? Which property did you use to solve the problem?

1 Read the statements given below and choose the correct option.

Assertion (A): The sum of 100, 150 and 100 is 15,00,000.

Reason (R): If a, b and c are three whole numbers then, (a + b) + c = a + (b + c).

Choose the correct option:

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

b Both A and Rare true, but R is not the correct explanation for A.

c A is true, but R is false.

d A is false, but R is true.

2 Look at the pattern. Draw the next term of the pattern.

Worksheet 4: Case Study

Warli Art

Warli art is a tribal art mostly created by tribal people from the North Sahyadri Range in Maharashtra, India. These paintings use a set of basic geometric shapes such as a circle, triangle and square. These shapes are symbolic of different elements of nature.

1 The shapes used in the pattern above are

2 Choose the correct number of shapes in the first figure in the pattern shown above.

a 1 triangle and 2 circles

c 2 triangles and 1 circle

b 3 circles and 2 triangles

d 2 triangles and 2 circles

3 Write the rule followed by the pattern shown above.

4 What will be the next term in the pattern shown above?

5 Create your own Warli pattern using squares, triangles and circles.

Lines and Angles 02

Worksheet 1:

Aligned to NCERT Topic/s:

2.1 Point 2.2 Line Segment 2.3 Line 2.4 Ray

1  Which of these represents a line?

a  H b GH c OP d KL

2  Which of these is true about rays?

a  They lack thickness.

c  They only extend in one direction.

3  Check whether the statements are true or false.

a  A line extends in two directions.

c  A line segment is part of a ray.

4  Write the length of the given line segments. a b

5 Draw line segments of the lengths given.

b  They have a fixed length.

d  They have only two end points.

b  A plane has a definite size.

d  A ray has more endpoints than a line.

a   5.2 cm b   7.7 cm

c   61 mm d   35 mm

6  Which of the following is the shortest length?

7 A road of length 23 km was constructed. What is the length of the road in these units?

a metres b centimetres c decametres d hectometres

8 The Great Wall of China is around 20,000 km long. How many cm will it be on a map if you use the scale 1 cm = 5000 km?

Challenge

1 Look at the map with airports. If there are direct flights between every single pair of airports, how many total flight routes would be shown on the map if we draw a line segment to represent each possible flight connection?

Worksheet 2: Aligned to NCERT Topic/s:

1 Which of the following is an incorrect representation of an angle? Cross out the angle.

2  Classify the following angles as acute, obtuse or reflex angles. a  36°:

3  Which of the following objects is perpendicular to the ground?

a  Bat kept on the floor: b  Clock hands at 3:00:

c  A boy leaning against the wall: d  A book kept on a table:

4  Measure the given angles. Write their measure.

5  In the figure shown here, recognise the adjacent angles.

6 Write the difference between the measures of the angles formed by the blue arm and red arm with the black arm in each case.

7  What fraction of a full rotation should the minute hand of a clock travel to go from the numbers:

a  5 to 8?

b  3 to 7?

c  11 to 5? d  9 to 6?

8  Draw adjacent angles to ∠NMZ so that:

a  B lies in the interior of the new angle, but not A and D.

b  Both A and B lie in the interior region of the new adjacent angle.

c  Only C lies in the interior region of the new adjacent angle.

9 Adho Mukha Svana Yogasana commonly known as downward-facing dog, is a yoga pose that helps in strengthening the arms, shoulders and back muscles. In the Adho Mukha Svana Yogasana, your hands and feet create angles. Estimate how many degrees are in the angle made by the body in the given figure. Is it closer to a right angle or away from it?

10  Which direction would you be facing if your initial position is:

a  north and you take a 1 2 turn, anticlockwise?:

b  south and you complete 1 4 of a turn, clockwise?:

c  east and you turn three‐fourths, clockwise?:

11  Draw two angles ∠XOY and ∠AOB on point O. Mark four points such that:

a  They are interior to ∠XOY only.

b  They are interior to ∠AOB only.

12 Cycling is an activity that strengthens the heart muscle and improves blood circulation. If Reena's bicycle makes four and a half turns then how many right angles does it turn?

Challenge

1 Rohit has a job interview scheduled at 3:00 p.m. He wants to make sure that he leaves two hours early. What angle will the minute and hour hands make on the clock when he should be leaving his house?

Worksheet 3: Understanding Polygons

1 List the vertices, sides and angles in the triangle.

2 Classify the triangles as equilateral, isosceles or scalene, given the lengths of their sides.

a  6 cm, 7 cm, 9 cm:

b  15 cm, 15 cm, 15 cm: c  19 cm, 23 cm, 29 cm:

d  9 cm, 11 cm, 9 cm: e  18 cm, 31 cm, 27 cm: f  3 mm, 3 mm, 3 mm:

3  Classify the triangles according to the measures of the angles.

a  60°, 40°, 80°:

b  65°, 85°, 30°:

c  130°, 20°, 20°:

d  90°, 40°, 50°: e  110°, 25°, 45°: f  60°, 60°, 60°:

4 Rani drew a rough map of 5 cities in Indian states using triangles as given below. Colour the scalene (red), equilateral (blue) and isosceles (yellow) triangles in the figure.

5 Sam and Maria work in an old-age home that has 2 triangular parks for the elderly to walk in. The first garden measures 7 metres, 7 metres and 10 metres and the second measures 5 metres, 6 metres and 7 metres. Identify the types of triangle formed by their gardens. Do you help old people?

1 Consider the following statements:

a  Every equilateral triangle is necessarily an isosceles triangle.

b  Every right-angled triangle is necessarily an isosceles triangle. The correct statements are –

i  Only a ii  Only b iii  Both a and b iv  Neither a nor b

Worksheet 4: Classification of Quadrilaterals

1 List the names of sides and vertices in the given quadrilaterals. Name all the adjacent and opposite sides in them.

2 Draw and name the diagonals of the quadrilaterals given below.

3  Name the quadrilateral with the features given.

a  All sides are of equal length and all angles measure 90°.

b  Opposite sides are parallel and opposite angles are equal.

c  Two pairs of adjacent sides are of equal length, and one pair of opposite angles is equal.

4  Draw two quadrilaterals and mark the points A, B, C, D, E and F in each quadrilateral such that:

a  only A, B and C are in the interior. b  only B, D, E and F are in the exterior.

5 In an archaeological survey, which is a methodical investigation to locate and document cultural artifacts and sites within a specific area, a mysterious patch of land was found with four statues at the corners. The archaeologist, curious about the shape of the land, measures the angles formed at each statue.

∠ ABC = 80°, ∠ BCD = 100°, ∠ CDA = 75°, and ∠ DAB = 105°.

a  Is the patch of land a convex or a concave quadrilateral?

b  Can the quadrilateral land be a rectangle or a square?

c  Can the quadrilateral land be a parallelogram? Why?

1 The quadrilateral formed by joining the midpoints of the sides PQ, QR, RS, SP of a quadrilateral PQRS is Draw 2–3 quadrilaterals to find the answer.

a  a trapezium but not a parallelogram b  a quadrilateral but not a trapezium

c  a parallelogram d  a rhombus

Worksheet 5: Polygons and Their Features

1 Which of these is a regular polygon?

a  Square

c  Scalene triangle

2  List the names of all the sides and vertices of the polygon.

3  Draw an irregular polygon with the number of sides given.

b  Rectangle

d  Right-angled triangle

4 Raj chose to build a logo in the shape of a polygon for his company. Read the clues and guess the type of polygon and the number of sides in it.

a  All the sides and angles in his polygon are equal.

b  He can draw 9 diagonals in his polygon.

5 Sarah and Alex are participating in a school project to study the effects of sunlight on plant growth. Sarah has a garden in the shape of a hexagon. She plants two sunflower plants on each side of her garden. Alex has an octagon-shaped garden. He plants one sunflower plant on each side of the garden. Who has more sunflower plants and how many more?

1 Six friends, A, B, C, D, E and F, are sitting around a hexagon-shaped table. Each friend sits at a corner of the hexagon and faces the centre. Who is sitting opposite to D?

Here are the clues to figure out who sits opposite D: A is sitting two seats to the left of F. B is sitting next to both C and D. E is sitting two seats to the left of D.

Worksheet 6: Understanding Circles

1 Tick (✓) the simple curves.

2 Classify the curves as open or closed curves.

3 Colour the minor segment in red and major segment in blue.

4  Which of the following represents concentric circles?

5  Which of these does not have a finite length? a  chord b  arc c  diameter d  secant

6  Mark one point each on the interior, exterior and boundary of the curve.

7  Draw closed curves that cross themselves the number of times given.

8  Using a compass, construct circles with the given measures. a  radius = 3 cm b  Diameter = 8 cm

9  Draw 2 simple and 2 non-simple curves.

10  Find the circumference of the circles with the following radii. Take π = 22 7 .

11 Find the value of the radius for the following circumference. Take π = 22 7 .

12 The Ashoka Chakra, a significant symbol in India, features prominently on the Indian national flag. The chakra has 24 spokes and is a perfect circle. The circumference of the Ashoka Chakra on a replica flag is 3.14 metres. Calculate the radius of the chakra. (Take π = 3.14)

1 Read both the statements given below and choose the correct option.

Assertion (A): Chord, secant, sector, segment and radius are the parts of a circle.

Reason (R): The centre of the circle is always in the interior of the circle.

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: Chapter Checkup

1 Count the number of line segments in the figures.

2  Identify the polygon with the given number of sides.

3  Draw the line segments of these lengths.

4  Look at the points marked. Create new angles such that: a  Only A, E, D and F are in the interior of the angle.

5  Draw two adjacent angles to the given angle ∠XOY.

Only B, C, D and E are in the interior of the angle.

6  Classify the angles as acute, obtuse or reflex.

a  26° = b  256° = c  79° = d  129° =

7  Draw an irregular polygon with the given number of sides.

a  3

b  6

8  Tick simple curves among the figures. a b c d

9  Identify open and closed curves among the figures. a b c d

10  Classify the triangles as equilateral, isosceles or scalene.

a  7 cm, 7 cm, 10 cm: b  14 cm, 15 cm, 16 cm :

11  Classify the given triangles according to the measure of the angles.

a  70°, 30°, 80°:

b  45°, 85°, 50°:

c  29 cm, 29 cm, 29 cm :

c  120°, 20°, 40° :

12  A clock shows the time as 12 o' clock. What is the angle that the hour hand moves through when the time is:

a  3:00 o' clock?: b  6:00 o' clock?: c  12:00 o' clock?: d  9:00 o' clock?:

13  What orientation will you have if you are initially facing:

a  West and making 1 2 of a revolution clockwise?

b  North and completing 1 4 of a revolution anticlockwise?

14  RSTU is a square whose diagonals bisect at Q. Find as asked.

a  Name the diagonals of this square.

b  Name any four right angles found.

15 The figure MNOP is a kite. Answer the questions. Give reasons.

a Is MN equal to PM? O P M N Q

b Is ∠MNQ equal to ∠MPQ?

c Is ∠ONQ equal to ∠OPQ?

Challenge

1 How many quadrilaterals do you see in the figure?

2 Read the assertion and reason and choose the correct answer from the options.

Assertion (A): In an isosceles trapezium, the non-parallel sides are equal in length.

Reason (R): A trapezium is a quadrilateral with exactly one pair of parallel sides.

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.

Worksheet 8: Case Study

Tracking Time with Shadows

Sundials are ancient timekeeping devices that use the position of the sunʼs shadow to tell time. Throughout the day, the shadow of the gnomon moves around the dial, indicating different times.

In the morning, the shadow forms an acute angle with the dial markings. At noon, the shadow ideally forms a right angle or something close to it. In the evening, the shadow forms an obtuse angle.

Answer the following questions.

1 What type of angle is formed by the shadow of the gnomon in the morning? a  Acute angle b  Right angle c  Obtuse angle d  Straight angle

2 At what time of day does the shadow of the gnomon form a right angle with the dial? a  Morning b  Noon c  Afternoon d  Evening

3 In the , the shadow of the gnomon forms an acute angle.

4 In the evening, the shadow of the gnomon forms an angle.

5 The angle of the gnomon affects the types of angles formed by the shadow throughout the day. (True/False)

Number Play 0 3

Worksheet 1: Aligned to NCERT Topic/s: 3.1 Numbers Can Tell Us Things 3.2 Supercells

3.3 Patterns of Numbers on the Number Line

3.4 Playing with Digits

Look at the height of these children.

Now, in the box, write the number of taller children that each child has next to them. Look at the example below and then answer the questions.

Write ‘1’ if there is only one taller child standing next to them.

Write ‘2’ if both the children standing next to them are taller.

Write ‘0’ if neither of the children standing next to them are taller.

a  Write the number in the box under each student.

b  How many children will have the number 1 written in their boxes?

c  Can any two children standing next to each other say the same number?

d  Is it possible to arrange the children in such a way so that all would have only 0s? Give a reason for your answer.

There are 10 rods given below. Each rod will take a number depending on the height of the sticks next to it .

Write ‘1’ above a rod if there is only one taller rod next to it.

Write ‘2’ above a rod if both the rods next to it are taller.

Write ‘0’ above a rod if neither of the rods next to it are taller.

a  How many rods take the number 0?

b  How many rods take the number 1?

c  How many rods take the number 2?

a A cell is called a supercell if the number in it is larger than its adjacent cells. Read the number in each cell and colour the cell if it is a supercell.

Fill the table below such that we get as many supercells as possible. Colour the supercells. Use numbers between 100 and 1000 without repetitions.

Mark the missing numbers on the given number line. Find the smallest and the largest number.

Smallest Number = Largest Number =

Look at the pattern on the number line. What numbers would the letters A, B and C be?

Write four 4-digit and four 5-digit numbers using the digits 1 to 9. 4-digit numbers: , , , 5-digit numbers: _____________________, , ,

Look at the pattern. Find 3 more sets of numbers that add up to 16.

7 + 6 = 16

2 + 5 + 9 = 16

6 + 8 + 2 = 16

1 How many times will the digit 5 occur when you count from 1 to 100?

3.6 The Magic Number of Kaprekar

3.7 Clock and Calendar Numbers

3.8 Playing with Number Patterns

Write two 3-digit number that are palindromes.

Look at the addition.

3 7 7 3

1 1 0 0 1 1

1 2 1

The number 37 was added to its reverse 73. The steps of reversing and adding were repeated till we got a palindrome. Now, take the number 75 and follow the same process till you get a palindrome.

Read the steps and solve till you get the same number. What do you notice when you keep repeating the steps?

a  Take any 4 digits.

b  Form the largest and the smallest numbers using these digits.

c  Subtract the smallest number from the largest number.

d  Now, use the digits of the difference and repeat steps 1 to 3.

In how many rounds will the number 6198 reach the Kaprekar constant?

The date 22/02/2022 reads the same from left to right and right to left. Write one more date that reads the same way.

The time 12:21 is a palindrome number. Write two more examples of time that show palindrome numbers.

Write two 5-digit numbers that, when added, give the number 53,736.

1 Find the number using the given clues.

Clue 1: I am a 6-digit even number.

Clue 2: I am a 6-digit number with the digit 6 in the ones place.

Clue 3: My tens digit is 1 less than my ones digit.

Clue 4: My thousands digit is 2 less than the lakhs digit.

Write a pattern by using the given rule.

Rule: Start with any number. If the number is even, take half of it. If the number is odd, multiply it by 3 and add 1. Repeat. , , , , , ,

Estimate to find the answer quickly.

a  The number of hours spent in school are

b  The distance between the classroom and the principal’s office in meters is

1 Find the rule in the given pattern. What will be its 13th term?

3, 7, 13, 21, 31

Rule: 13th Term:

4: Chapter Checkup

Time: 15:51 1 2

Write two 4-digit number that are palindromes.

The date and time given below shows palindrome numbers. Write one more date and time that shows palindrome numbers.

Date: 23/01/1032

Look at the addition. Take the number 93 and follow the same process till you get a palindrome.

Use the numbers given in the box to reach 33,000. Both addition and subtraction can be used.

Write two 4-digit numbers that when added give the number 5654.

Show the steps to make number 2389 reach the Kaprekar constant?

7

Find the total number of dots on the dice by solving it mentally.

Challenge

1 What is the value of A if the given number is a palindrome?

2 Assertion (A): The number 56981718965 is a palindrome.

Reason (R): All palindromic numbers are symmetric and can be read the same way forwards and backwards.

a  A is true, but R is false.

b  A is false, but R is true.

c  Both A and R are true, and R is the correct explanation for A.

d  Both A and R are true, but R is not correct explanation for A.

Worksheet 5: Case Study

In many countries, vehicle registration numbers are a combination of letters and numbers. A particularly interesting scenario occurs when these numbers form a palindrome—a sequence that reads the same forwards and backwards. The rarity of such palindromic numbers makes them desirable for collectors, and even special auctions are sometimes held for these unique registrations.

1 Write 2 palindromic numbers between 500 and 999?

2 If a vehicle registration number is a four-digit number, give any 3 registration numbers that are palindromes?

3 A vehicle registration number is AB12321BA. Is this number a palindrome? Explain why or why not.

4 How many steps are needed to turn 87 into a palindrome by reversing the digits and adding the numbers repeatedly? Solve to show the answer.

Data Handling and Presentation

Worksheet 1: Aligned to NCERT Topic/s:

4.1

Collecting and Organising Data

1  State True or False.

a  Raw data is the organised form of data.

b  The arrangement of numbers in ascending or descending order is called an array.

c  Five as tally marks is represented as .

d  Frequency is always the same for every observation in data.

2  Draw tally marks for the given numbers.

3 The Mughal emperors were a succession of rulers who controlled significant regions of the Indian subcontinent from the early 16th to the 19th century. The prominent Mughal emperors included Babur, Humayun, Akbar, Jahangir, Shah Jahan and Aurangzeb. Each of them engaged in several major wars, with their totals being 3, 3, 5, 3, 4 and 6 wars, respectively. Create a frequency distribution table using tally marks to represent this data.

4 Fruits are naturally sweet and provide a quick source of energy, making them a great snack to keep us active throughout the day. Prepare a tally marks table for the favourite fruit of some children.

Orange, Apple, Banana, Guava, Litchi, Litchi, Orange, Apple, Banana, Banana, Apple, Guava, Guava, Apple, Litchi, Guava, Banana, Apple, Banana, Apple, Litchi, Orange, Apple, Orange, Litchi, Banana, Banana, Guava, Apple, Litchi, Banana, Orange, Banana, Apple, Litchi, Guava, Orange, Banana, Litchi, Apple, Apple, Apple, Orange, Banana, Litchi

5 The ages of 30 students at a school are shown below. 10, 11, 14, 12, 13, 11, 12, 13, 14, 10, 10, 12, 13, 14, 13, 12, 10, 11, 13, 14, 10, 12, 13, 14, 12, 10, 12, 13, 14, 10 Make a frequency distribution table for the data and answer the questions.

a  How many students are 12 years old?

c How many students are less than 13 years old?

b  How many students are 14 years old?

d How many students are more than 11 years old but less than 14 years old?

1 The tally marks table shows the animals in five shelter homes.

a If the scale of the tally marks is changed from one tally mark representing one animal to one tally mark representing two animals, how will the new tally marks for the ‘Pet Rescue Centre’ be represented?

Name of Shelter Home Number of Animals

Happy Tails Shelter

Paws Place

Furry Friends Home

Animal Haven Pet Rescue Centre

b If the number of animals in ‘Animal Haven’ increases to 15, how will this change be represented if one tally mark represents five animals?

= 1000 fans

a  How many fans were manufactured in May?

b  How many fans were manufactured in January?

c  In which month were the most fans manufactured and how many?

d  How many more fans were manufactured in April than in February?

4 The table has data from the National Centre for Seismology (NCS) showing the approximate number of earthquakes in a country from 2013 to 2022. Draw a pictograph for the given data.

5  Create a question on the pictograph made in Q5.

Challenge

Critical Thinking

1 Rina is designing a detailed pictograph where she uses a different number of pictures each week. In Week 1, she drew 9 pictures when 1 picture = 30 flowers. In Week 2, she used 7 pictures when 1 picture = 45 flowers. In Week 3, she drew 5 pictures when 1 flower = 45 flowers, and in Week 4, she used 12 pictures when 1 flower = 40 flowers. If she decides that each picture will represent 60 flowers going forward, how many pictures would she need to represent the flowers for Week 1, Week 2, Week 3, and Week 4?

4.4 Drawing a Bar Graph

1 In a city, the average power supply from generators, instead of being constant, was fluctuating.

a The power supply from the generators was at its highest during the time .

b The power supply from the generators was at its lowest during the time

2 The data shows the number of members in various families of a colony. Draw a bar graph to represent the data. Scale: 1 division = 10 families

3 The bar graph shows the expenditure of a family on various items in a month. Study the bar graph and answer the questions.

a  What was the expenditure on food?

b On which item did the family spend the least, and how much?

c On which item did the family spend the most, and how much?

d What was the total expenditure of the family?

4 Create two questions based on the bar graph drawn in Q2.

1 The bar graph shows the population of three nearby towns in the year 1975 and the year 2015. Read the statements and choose the correct option.

Assertion (A): Arsenal had the smaller increase in population from 1975 to 2015 compared to Cottage and Britannia.

Reason (R): The graph shows that Arsenal's population bar increased by only one division between 1975 and 2015.

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

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

c  A is true, but R is false.

d  A is false, but R is true.

Worksheet 4: Chapter Checkup

1 The data shows how people go to their office. Make a data frequency table for the data using tally marks.

walk, bus, bike, walk, bike, bus, walk, car, walk, bike, bike, bus, walk, walk, walk, car, bus, walk, bus, bus, walk, car, car, walk, walk, train, bike, bus, walk, walk

2 Draw a tally-marks table for the following shapes.

3 The frequency data table shows the favourite subject of students. Read the table and answer the questions.

a  Which subject is the favourite of the most students?

b  How many students like English?

c  Which is the least chosen subject?

d  What fraction of the total students like Maths?

Subject Tally Marks

Science

Maths Technology

English

4 The bar graph shows the number of saplings planted by a farmer in different blocks of a farm. Study the bar graph and answer the questions.

Planted by a Farmer

a  How many saplings were planted in block C?

b  How many saplings were planted in block D?

c In which block were the most saplings planted?

d How many saplings in total were planted by the farmer?

Saplings

5 India has eight Union Territories. Here is the bar graph representing the approximate area of 5 of the Union Territories. Read the bar graph and answer the following questions:

a  Which Union Territory has the largest area?

b  Which Union Territory has the smallest area?

c What is the area of the National Capital Territory of India?

d What is the total area covered by all the Union Territories?

6 Create a new question on the graph shown in Q5.

7 The pictograph shows the number of ice creams sold by an ice-cream vendor in different months of the year. Read the pictograph and answer the questions.

a How many ice creams were sold in the month of March?

b In which month were the most ice creams sold and how many?

c What is the difference in the number of ice creams sold in January and May?

d What number of ice creams were sold in total?

8 The data shows the number of bedsheets manufactured by a power loom factory in different weeks of a month. Draw a bar graph to represent the data.

Chandigarh

Lakshadweep

PuducherryDelhi DadraandNagarHaveli andDamanandDiu

9 The data shows the number of mangoes sold by various shopkeepers. Draw a pictograph to represent the data.

Shopkeeper Sohail Ashraf Mahmood Raju Vivek Number of Mangoes 9000 4500 6000 7500 10,500

Challenge

1 Read the bar graph and the statements given below. Choose the correct option.

Statement 1: Dealership 4 sold more cars than Dealership 1 but fewer than Dealership 2.

Statement 2: The total number of cars sold by the 4 dealerships is 140.

a  Statement 1 is true but statement 2 is false.

b  Statement 1 is false but statement 2 is true.

c  Both statements 1 and 2 are true.

d  Both statements 1 and 2 are false.

2 The pictograph represents the number of students participating in different extracurricular activities at school.

a If 60 students participate in other activities, how many symbols should be used in the pictograph to represent this?

Number of Cars

b If the key of the pictograph changes to each symbol representing 5 students, how would this affect the representation of chess and music?

Key: = 10 students

Critical Thinking

c What will be the key if there were 35 students participating in drama and you need to use the same number of symbols as used in the given pictograph?

Worksheet 5: Case Study

School Garden Project

Ms Kapoor, a teacher at Sunshine Elementary School, started a garden project with her class. Over five months, students planted different types of flowers—roses, sunflowers, tulips, daisies and marigolds. Each month, they recorded the number of flowers planted and represented the data using a pictograph. The pictograph uses a flower symbol, where each symbol represents 10 flowers.

1  In which month were the most sunflowers planted?

2 How many marigolds were planted in February?

30

50

60

40

3 In which month were the most tulips planted? How many tulips were planted that month?

4 Compare the number of daisies planted in February and May. Which month had more, and by how many?

5 Should we unnecessarily pluck flowers? Why or why not?

Prime Time 05

1  Write all the factors of the given numbers.

a  20:

b  26:

c  36:

d  88:

2  Write the first six multiples of each of the given numbers.

a  37:

b  62:

c  84:

d  99:

3  The product of two numbers is 24. Their sum is 14. Find the numbers.

4  Find two numbers of which the difference is 1 and the product is 72.

5  Shade the square grids to show factor pairs of the given numbers.

a  Factor pairs of 15 b  Factor pairs of 14

1 Raj claims to have 100 rupees, all in 2-rupee coins. Roy claims to have 67 rupees, all in 5-rupee coins. Who is wrong? Give a reason for your answer.

Worksheet 2: Aligned to NCERT Topic/s:

5.2 Prime Numbers

5.3 Co-prime

numbers for safekeeping treasures

5.5 Divisibility Tests

Determine whether the given numbers are even or odd. Write “E” for even and “O” for odd next to each number. a  42

Identify if there are any perfect numbers among the numbers given below. Write Yes/No. a  57:

Write True or False for the given statements.

a  25 is an even number.

b  17 is a prime number.

c  6 is a composite number.

d  13 and 17 are twin prime numbers.

Write all the prime numbers within each range given below. Create a co-prime pair from each range.

a  40 to 50

b  60 to 70

c  10 to 30

d  0 to 10 Write all pairs of twin primes between 60 and 90.

Check the divisibility of the given numbers by 2, 3, 4, 5, 6, 8, 9 or 10.

990 2484

41,870 9,12,048

Give a number divisible by:

a  2 but not 6 b  both 6 and 8

c  both 11 and 9 d  3 but not 2

Draw square grids to show all the factor pairs of 14. Write if 14 is a prime or composite number. Give a reason for your answer.

A maths teacher asks students to organise themselves into two groups based on whether their roll numbers are prime or composite. How many students are there in each group if there are a total of 36 students in the class having roll numbers 1 to 36?

Write a question on your own using the divisibility test for 11.

and 8 are co-primes or not.

Challenge

1 Find two prime numbers which can be expressed as the sum of 4 different prime numbers.

1 Worksheet 3: Aligned to NCERT Topic/s: 5.4 Prime Factorisation

Show the prime factorisation of each of the given numbers.

b  252 = 2 × 6 × 3 × 7 2

State whether these are prime factorisations or not.

a  189 = 3 × 3 × 21

Find the prime factors of 345. Arrange them in ascending order.

Express each number as the product of its prime factors by using a factor tree.

210

293

816

952

Find the prime factors of 560. Arrange them in ascending order. Calculate the product of the two smallest prime factors.

Write the smallest 5-digit number and express it in terms of its prime factors.

A biologist, a scientist who studies living organisms and their interactions with the environment, wants to organise several samples of bacteria into rectangular petri dishes for an experiment. Should the biologist have 56 samples or 63 samples of bacteria, if the samples are to be arranged into 4 rows?

Challenge

Critical Thinking

1 Find the smallest positive integer that can be expressed as the product of four distinct prime numbers and is greater than 100.

Worksheet 4: Working with LCM and HCF

Find the HCF of the numbers.

a  By listing factors.

i  48, 84 ii  30, 45

iii  18, 27 iv  36, 72, 108

b  By prime factorisation.

i  20, 30 ii  30, 45

45, 75 iv  54, 90, 126

c  By repeated division.

i  48, 60 ii  63, 105

iii  72, 96, 120

iv  65, 132

Find the LCM of the numbers.

a  By listing their multiples.

i  60, 20 ii  15, 35

iii  4, 8, 12

iv  12, 16

b  By the prime factorisation method.

i  16, 30, 42 ii  28, 44, 132

iii  16, 28, 40, 77

iv  20, 25, 30, 50

c  By the division method.

i  11, 22, 36 ii  96, 128, 240

iii  9, 12, 36, 54

iv  102, 170, 136

The highest common factor (HCF) of two numbers is 18, and their least common multiple (LCM) is 126. One of the numbers is 54. What is the other number?

If 25 is the HCF of two numbers, can the LCM of those numbers be 780? Explain.

What is the maximum number of Sundays that can occur in the first 57 days of the year?

Find the greatest number that can divide 655 and 889 leaving a remainder of 7 in each case.

Find the greatest number that can divide 77, 263 and 462 leaving remainders 5, 7 and 6, respectively.

1 The product of two numbers is 2028 and their H.C.F. is 13. How many such pairs of numbers are possible?

Worksheet 5: Word Problems on LCM and HCF

Shaini is making gift bags for a party. She has 64 toy cars and 80 action figures. She wants to make identical gift bags with the same numbers of toy cars and action figures in each. If she wants to make the greatest number of gift bags possible without having any items left over, then how many gift bags can she make?

A toy store has three toy-making machines. Machine X produces toys every 25 minutes, Machine Y every 35 minutes and Machine Z every 40 minutes. After how much time will all three machines complete their work simultaneously?

Cattle farming involves raising cows primarily for milk production, ensuring proper nutrition and health to maximise milk yield. A farmer has 72 cows and 36 bales of grass. He wants to make identical groups such that each group has an equal number of cows and an equal number of bales of grass. What is the maximum number of groups he can make?

Different plants have varying watering needs which is crucial for their health. Sansevieria requires watering every 18 days, while Euphorbia milii needs it every 12 days. If the gardener waters all the plants today, after how many days will he need to water them together again?

A carpenter has wooden planks of lengths 54 cm, 72 cm and 90 cm. What is the maximum length he can cut these planks into, with no wastage?

1 Read the statements and choose the correct option.

Assertion (A): If three cyclists start at the same point and ride around a circular track with different lap times, they will all meet at the starting point together after the LCM of their lap times.

Reason (R): The LCM of the lap times represents the first time all events will coincide.

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: Chapter Checkup

List all the factors of the numbers.

The product of two numbers is 36, and their sum is 13. Find the numbers. Are they co-primes? If so, use thread art to show this. 1 2 3

Write each number as the product of its factors by using a factor tree.

Find the HCF of the numbers.

a  By prime factorisation.

i  36, 48 ii  42, 56

b  By repeated division.

i  54, 72 ii  77, 121

Find the LCM of the numbers.

a  By the prime factorisation method.

i  18, 35, 49 ii  24, 36, 120

b  By the division method.

i  14, 28, 42 ii  80, 112, 200

A library has 30 history books, 45 science books and 60 literature books. They want to arrange these books on shelves so that each shelf contains an equal number of each type of book. What is the maximum number of books they can place on each shelf?

The traffic lights at three different road crossings change after every 40 seconds, 60 seconds and 80 seconds, respectively. If they change simultaneously at 7 am, then at what time will they change simultaneously again?

A garden has three sprinklers that operate at intervals of 20 minutes, 25 minutes and 30 minutes, respectively. What is the minimum amount of time one would have to wait to observe all three sprinklers operating simultaneously in the garden?

1  Find the smallest number from which if 15 is subtracted, the result is exactly divisible by 9, 12, 18, 21, 27 and 36.

2  Read the question and decide which of the statements are required to answer it.

The LCM and HCF of two numbers are 360 and 18 respectively. What is the second number?

Statement 1: The first number is 72.

Statement 2: The second number is 72 more than the HCF.

a Statement 1 alone is sufficient, but Statement 2 alone is not sufficient.

b Statement 2 alone is sufficient, but Statement 1 alone is not sufficient.

c  Either of the statements are sufficient.

d Both statements together are not sufficient.

Worksheet 7: Case Study

Geography Time!

Geographers studying transportation routes between cities need to calculate the optimal distances for road networks. Understanding factors and multiples helps them determine efficient distances and connections. In a region with three major cities—City A, City B and City C—urban planners are designing a highway system to connect these cities efficiently.

Answer the following questions:

1 The distance between City A and City C is 150 kilometres. If a new railway line is built, connecting City A and City C with a station at every 25 kilometres, how many railway stations will be needed along the route?

3

2 A cargo shipment departs from city A every 30 minutes and a parcel shipment departs from there every 40 minutes. If both shipments depart at 10 a.m., then when will they next depart at the same time?

3 The highway system is designed such that the distance between City A and City B is a multiple of the distance between City B and City C.

a  True b  False c  Incomplete information

4  What is one step one can take to make the city greener?

Perimeter and Area

1  Find the perimeter of the figures.

2  Find the perimeter of a rectangle of length 30 cm and breadth 12 cm.

3  Use a piece of thread to form a square figure with a perimeter of 164 cm. What is the length of the side of the square?

4 An isosceles triangle has a perimeter of 57 cm. If the measure of the unequal side is 17 cm, then what will be the measure of each of the two equal sides?

5  A piece of string is 42 cm long. What would be the length of each side if the string is used to form a  an equilateral triangle? b  a regular heptagon?

6  A rectangular piece of glass measures 3 m 25 cm by 1 m 42 cm. What is its perimeter?

7  On a square grid, draw 2 rectangles with the same perimeter.

8 The length and breadth of a rectangular football field are 77 m and 52 m, respectively. If a player takes two and a half rounds of the field, what is the distance covered by the player?

9 The perimeters of two squares are 40 cm and 60 cm respectively. What will be the side of the square whose perimeter is equal to the sum of the perimeters of these two squares?

Challenge

1 A square is cut out from a bigger square. Will the perimeter increase or decrease? Justify your answer with an example.

1  Find the area of a square of which the side is 7 cm.

2  Find the length of the rectangle with area 375 sq. cm and breadth 25 cm.

3  Find the area of the shapes in sq. cm.

4  The area of a triangular frame is 1125 sq. cm. If its height is 25 cm, what is the length of its base?

5 Draw a square that has a perimeter of 12 cm. Draw a rectangle with the same perimeter having a length of 4 cm. Which shape has a greater area?

6  Find the perimeter and area of the figures.

1 How much will the area of a square increase if its perimeter is doubled?

Worksheet 3: Perimeter and Area Problems

1  The area of the floor of a rectangular kitchen is 130 sq. m. If the length of the kitchen is 10 m, then find its perimeter.

2 Yash wants to install strip lights around the edges of his square-shaped ceiling and paint it white. He needs 84 metres of strip lights. Calculate the area he needs to paint.

3 A triangular garden has two sides measuring 15 metres and 20 metres. The perimeter of the triangle is 60 metres. What is the length of the third side of the garden?

4 Pooja is planning to decorate the walls of her room with stickers. How many stickers with dimensions 8 cm and 13 cm are required to fit in a rectangular region of perimeter 552 cm and length 120 cm?

5  Create a word problem on finding the area of a rectangle when its perimeter and one of the sides are given.

1 A community hall consists of a square room and a triangular stage that shares its base with the square room. The side length of the square room is 10 metres. The stage is an isosceles triangle with its two equal sides being half the length of the base. Find the perimeter of the entire hall.

Worksheet 4: Chapter Checkup

1  Find the perimeter of the given figures.

2  Find the area of the figures.

3  Find the area of a tabletop with length 21 cm and breadth 19 cm.

4  How many square tiles of length 12 cm will be needed to cover a square of length 3 m?

5 Suhani has a rectangular sheet of paper with a perimeter of 50 cm. The length of the sheet is 10 cm. She cuts the sheet along the diagonal to get two triangles. What is the area of each triangle so formed?

6  A piece of thread is 72 cm long. What will be the length of each side if the thread is used to form a square?

7  Sunita and Ramesh bought plots as shown. Whose plot has the greater area and perimeter?

Plot

Sunita’s

Ramesh’s Plot

8  A square of 144 sq. m area can be divided into how many rectangles of size 2 m × 1 m?

9 Find the cost of painting a rectangular piece of cardboard at the rate of 25 paise per sq. cm. The length and breadth of the cardboard are 80 cm and 1 4  m, respectively.

10 Sailesh runs around a square park of side 88 m 3 times a day while Renu runs around a rectangular park of side 30 m by 70 m five times a day. Who runs the longer distance every day?

11 Kanika wants to place a carpet in her bedroom as shown. The area to be carpeted is shaded green. How many sq. m of carpet does she need for the shaded portion?

12  Draw two rectangles that have different perimeters but the same area.

Challenge

1 Read the statements and choose the correct option.

Critical Thinking

Assertion (A): 1500 bricks of 40 cm by 40 cm can be used to construct a particular wall whose length and breadth are 16 m and 15 m, respectively.

Reason (R): Area of a rectangle is given as the product of its length and breadth.

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

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

c  A is true, but R is false.

d  A is false, but R is true.

2 If the areas of two rectangles are 20 square cm and 12 square cm, respectively, what will be the perimeter of a rectangle whose area is equal to the sum of the areas of these two rectangles? Assume that the new rectangle has dimensions such that its length is twice its breadth.

Worksheet 5: Case Study

A 2BHK apartment is a type of residential unit or flat that includes 2 bedrooms (B), 1 Hall (H) and 1 kitchen (K). Neha purchased a beautiful 2BHK apartment for her parents. The master plan of the apartment is as shown below. Look at the floor plan carefully and answer the questions.

1 What is the area of the flat?

a 80 square feet

c 150 square feet

b  160 square feet

d 1500 square feet

2 If the area of the hall is 480 square feet and its length is 40 feet, what is its perimeter?

3 If the width of Bedroom 1 is 16 feet, what is the width of the kitchen?

4 What would be the cost of tiling the floor of the kitchen if its length is 10 feet and the cost of tiling is ₹120 per square feet. (Hint: Use the measures calculated in the above questions.)

5 What gift would you like to give to your parents when you grow older?

Fractions

Worksheet 1: Aligned to NCERT Topic/s:

7.1 Fractional Units and Equal Shares

7.2 Fractional Units as Parts of a Whole

7.3 Measuring Using Fractional Units

7.4 Marking Fraction Lengths on the Number Line

7.5 Mixed Fractions

7.7 Comparing Fractions

1  Write the fraction of the shaded part.

2  Colour to show the fraction.

3  Classify the fractions as proper fractions, improper fractions or mixed numbers.

4  Represent the fractions on a number line.

a 1 6

b 14 11

c 2 3 7

d 1 1 8

5  Circle the larger fraction.

a 5 7 and 3 7 b 2 8 and 6 8

c 7 8 and 11 14 d 4 5 and 12 20

6  Compare the fractions using appropriate symbols (>, < or =).

7  Arrange the fractions in ascending order.

8 In school A, 480 students passed out of 500, whereas in school B, 550 students passed out of 600. Write the fraction of students who passed in both schools. In which school did the greater fraction of students pass?

1 You have a birthday brownie in a circular shape and have to divide it into 8 equal pieces by making 3 cuts only. How do you do it? What fraction of the whole brownie will each piece be?

Worksheet

2: Aligned to NCERT Topic/s: 7.6 Equivalent Fractions

1  Convert between improper fractions and mixed numbers. a 15 4 b 38 7

2  Reduce the following fractions into their simplest forms.

3  Identify whether each pair of fractions is equivalent or not. Write Yes or No. a 4 5 and 12 15 b 1 3 and 5 21 c 7 8 and 14 24 d 2 9 and 12 54

4  Write two equivalent fractions for the fractions. a 4 5 b 3 7 c 36 48 d 228 144

5  Write the equivalent fraction for the given fractions.

a 5 9 with denominator 81

c 18 24 with denominator 4

b 17 19 with numerator 85

d 36 72 with numerator 3

6 The small intestine in an average human body is about 38 5 m and is actually the largest intestine based on length. Write this length as a mixed number.

7 Renu has baked 100 cookies and wants to divide them equally among her 3 siblings. What will be the share of each sibling? Express your answer as a mixed fraction. Do you think equal sharing is fair?

1 Minal asked her brother to guess the fraction based on the given clues:

a  The numerator is three less than twice the denominator.

b  When you add 1 to both the numerator and the denominator, the fraction becomes 2 3

2 How many more boxes need to be shaded to make the fraction shown by the figure equivalent to the other 2 fractions?

� �

Worksheet 3: Aligned to NCERT Topic/s:

7.8 Addition and Subtraction of Fractions

1  Add the fractions and reduce the fractions, if necessary. a 1 7 + 2 7

c 3 7 + 2 14

2  Subtract the fractions and give the answer in simplified form.

3 What do we get if we subtract the difference of 4  1 5 and 2  1 10 from the difference of 8  2 3 and 5  1 9 ?

4 While studying different types of trees present in the Himalayan foothill forest, researchers found that 1 4 of the trees are conifers (plants that are conically shaped to survive during snowfall), while 1 4 of the trees are deciduous (plants that shed their leaves during the winter to survive). Combine these fractions to describe the total proportion of trees that are either conifers or deciduous.

5  An empty box weighs 2  6 7 kg. An iron pan weighing 5  2 3 kg is placed inside it. What is the total weight of the box?

6 Sophia is baking cookies for a school fundraiser. She’s making two batches of cookies. In the first batch, she uses 3 5 cup of sugar, and in the second batch, she uses 1 5 cup of sugar. Find how much sugar Sophia used in total for both batches of cookies.

Challenge

Critical Thinking & Cross Curricular

1 In caffeine, a fraction of 1 12 constitutes oxygen atoms, 1 6 are nitrogen atoms and 5 12 are hydrogen atoms. The rest of the atoms consist of carbon. What fraction of caffeine’s atoms are oxygen, nitrogen or carbon?

a  The numerator is three less than twice the denominator.

b  When you add 1 to both the numerator and the denominator, the fraction becomes 2 3 .

Worksheet 4: Chapter Checkup

1 Convert the mixed numbers into improper fractions.

2 Convert the improper fractions into mixed numbers.

15 4

3 Find any three equivalent fractions.

4 Write the following fractions in their simplest form.

5 Check whether each pair of fractions is equivalent or not.

21 3 and 8

6 Solve and reduce to their simplest forms.

7 Shweta has 4 5 kg of sugar. She uses 3 4 kg to make a sweet dish. How much sugar does she have left?

8 Radha purchased 40 m of cloth. She used 2 5 m cloth for the curtains and 3  3 4 m cloth for the bed sheet. How much cloth does she have left?

1 Read both the statements given below and choose the correct option.

Assertion: 21 84 and 12 56 are equivalent fractions.

Reason: Two fractions a b and c d , (b, d = 0) are equivalent if their simplest form is the same.

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 Assertion is true, but Reason is false.

d Assertion is false, but Reason is true.

Worksheet 6: Case Study

The Fitness Regime

Ravi is a dedicated athlete who spends 5 12 of the day training for physical fitness. He splits his training time among various art forms to improve his overall skills. Out of the 5 12 of the day, he spends 1 4 of his training time on martial arts, 1 3 of his training time on dance and the rest of the time on yoga.

Answer the following questions.

1 How much of the day does Ravi spend on martial arts?

2 What fraction of the day does Ravi spend on dance?

3 Ravi spends hours of his training time on yoga.

4 Arrange the activities in ascending order of their practice time.

5 What are the benefits of doing physical activities? Which physical activity do you do?

Playing with Constructions

Worksheet 1: Aligned to NCERT Topic/s:

8.1 Artwork

8.2 Squares and Rectangles

8.3 Constructing Squares and Rectangles

8.4 An Exploration in Rectangles

8.5 Exploring Diagonals of Rectangles and Squares

1  Use a ruler to draw line segments of the given length.

5.4 cm

6.1 cm

cm

7.2 cm

2  Construct line segments of the lengths given using a compass and a ruler.

3  Construct a copy of the line segments.

4  Construct a square of length 5 cm using a ruler and a compass.

5  Construct a figure made up of a square and a circle of any measure.

6 Construct a rectangle measuring 12 cm in length and 4 cm in breadth. Split the rectangle into 3 equal squares.

Challenge

Critical Thinking

1 Can we construct a square with a length of one diagonal given as 6 cm? Give a reason for your answer and show the construction if the construction is possible.

Worksheet 2: Aligned to NCERT Topic/s:

1  Draw the given angles with the help of a protractor.

a  20° b  35°

c  50° d  165°

2 The return of light from a medium is called reflection. The angle of reflection of a mirror is 60°. Draw the angle and its bisector.

3 Construct the following angles using only a ruler and compass.

a  60° b  90°

4 Draw the angles of given measures. Construct their angle bisectors. Write the measure of the two new angles formed.

a  80° b  136°

5 Draw a line segment PQ of length 6.5 cm and mark a point R on the line. Construct a perpendicular to PQ passing through R using a ruler and compass.

6 Copy the given angles in your notebooks. Construct their angle bisectors. Write the measure of the two angles formed. a b c

Challenge

1 Read the statement and choose the correct option. Give a reason.

Statement 1: There can be more than one angle bisector to any given angle.

Statement 2: The angle bisector of an angle is also its line of symmetry.

a  Only Statement 1 is true.

b  Only Statement 2 is true.

c  Both Statement 1 and Statement 2 are false.

d  Both Statement 1 and Statement 2 are true.

Worksheet 3: Chapter Checkup

1 Use a ruler and compass to construct line segments of the given measures. a  PQ = 3.6 cm b  AB = 8.2 cm

2 Construct a line segment EF with a length of 10.2 cm. From EF, cut off EG, which measures 3.8 cm. Determine the length of FG.

3 Construct a line segment DE of length 4.6 cm. Construct a perpendicular to DE passing through a point on DE using a ruler and a compass.

4 Given ST = 4.7 cm and UV = 6.2 cm, construct a line segment as given:

a  WX = 3UV – 2ST b  AB = 3ST + 2UV

5 The outline of the new parliament building in India is shown. Construct a single line segment that equals the total length of any two sides in the given shape using a ruler and compass.

6 Construct a rectangle of length 5 cm and a diagonal of length 9 cm using a ruler and compass.

7 Construct the given figures using a ruler and compass.

8 Draw angles of the given measures using a protractor. a  27° b  73°

9 Draw the given angles and construct their angle bisector.

a   42° b   71°

10 Draw a line segment JK = 5.1 cm. Mark two points X and Y on the line segment so that X is 1 cm away from J, and Y is 2 cm away from K. Draw perpendiculars to JK passing through X and Y.

11 Draw a quadrilateral ABCD with sides of any suitable length. Construct the perpendicular bisectors of all four sides using a ruler and a compass. Do the perpendicular bisectors intersect at a common point? Explain your findings.

Challenge

1 Read the assertion and the reason supporting the assertion. Choose the correct option.

Assertion (A): Two lines intersecting at a point at 90° can look like alphabet ‘L’.

Reason (R): Both lines are perpendicular to each other.

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

b  Both A and R are false.

c  Both A and R are true.

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

2 Anna drew a linear pair of angles. She constructed angle bisectors to both angles. Are the bisecting rays perpendicular to each other? Give a reason for your answer.

Worksheet 4: Case Study

Angle Explorer

A sundial made up of a flat plate and a rod is a horological device that tells the time of the day based on the apparent position of the sun in the sky. The length of the rod in a sundial is 45 cm. At 4 o' clock an angle of 120° is formed by the shadow with the rod.

Jantar Mantar, located in Jaipur, features the world's largest stone sundial.

1 If the scale is 5 cm = 1 mm, what would be the length of the rod in the sundial when drawn on paper?

a  10 mm

b  9 mm

c  45 mm

2 Construct a line segment to show the rod of the sundial using the scale as 5 cm = 1 mm.

d  450 mm

3 If the scale is 1 unit = 2°, how many units will be equal to the measure of the angle bisector of the angle mentioned above?

4 Construct the angle mentioned above. Also draw its angle bisector.

Symmetry

Worksheet 1: Aligned to NCERT Topic/s: 9�1 Line of Symmetry

Draw an isosceles triangle. How many lines of symmetry does it have?

2

Line 1 and line 2 are drawn to show the lines of symmetry in each figure. Write which is the correct line of symmetry in each figure.

Draw the lines of symmetry for each of the figures. 3 Write four letters with 2 or more lines of symmetry. 4

1 Check if the given figure is symmetrical. If not, then which part prevents the given figure from being symmetrical? How can you make this figure symmetrical without removing it?

Copy the figure in your notebooks. Draw the reflection of the figures along the mirror line.

Guess the word:

Suhani wrote a 3-letter word in her notebook. If you look at its mirror image along the horizontal mirror line, you will see the word ‘WOW’. What is the original word?

Draw the reflection symmetry of the following on a square grid.

Write the order of rotational symmetry for the given figures.

The logo shown means ‘Recycle’. Write the angle of symmetry for the given logo.

1 Which colour is incorrectly shaded in the mirror image?

Worksheet 3: Chapter Checkup

The Eiffel Tower, designed by Gustave Eiffel, was constructed for the 1889 World’s Fair in Paris, celebrating the 100th anniversary of the French Revolution. Does it have lines of symmetry? Draw to show.

Draw the lines of symmetry in the letters and numbers.

Draw lines to match the letters with their respective boxes on the basis of the lines of symmetry each letter has.

no line of symmetry 1 line of symmetry more than 1 line of symmetry

Write True or False.

a  There is 1 one line of symmetry in the letter T.

c  All quadrilaterals have 4 lines of symmetry.

b  A regular pentagon has 5 lines of symmetry.

d  A semicircle has one line of symmetry.

Are the lines of symmetry marked on the given figures, correct? If not, draw the correct lines of symmetry.

Complete the figures to make them symmetrical along the line of symmetry.

Draw the reflection symmetry of the following on squared paper.

Read the given statements and choose the correct option.

Assertion (A): A regular hexagon has six lines of symmetry.

Reason (R): A line of symmetry divides a shape into two identical shapes.

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.

A girl walks in a pattern on a map, starting from her house and walking north for 3 blocks, then west for 4 blocks, south for 3 blocks and finally east for 4 blocks, returning to her house. The path she traces forms a shape. How many lines of symmetry does it have?

Worksheet 4: Case Study

A Nature Walk

Mrs Sharma is the class teacher of grade 6. The students in her class are on a nature walk in the nearby park to explore the concept of symmetry. The students are excited as they gather different natural objects like leaves, flowers, butterflies, and even take pictures of trees. They observe these items carefully to identify lines of symmetry and mirror images.

1 Shubham observed a butterfly with beautiful wings. How many lines of symmetry does this butterfly have?

2 Maya collects different leaves and folds them to find lines of symmetry. Which of the following leaves shows a line of symmetry?

3 A student found a flower broken in half. He places it in front of a mirror to see what it originally looked like. Help him complete the drawing of the flower he found.

4 Choose one of the symmetrical objects you find in nature. Draw it and indicate its line of symmetry.

The Other Side of Zero Integers

Worksheet 1: Aligned to NCERT Topic/s: 10.1 Bela’s Building of Fun

1  Write the situations in terms of integers. Write their opposites as well. a Going 10 km to the east b Spending ₹1000 c Payal gets 5 apples

2  Represent the given integers on a number line.

3  Given below is a number line representing integers. Write the integers corresponding to the points.

4  Write the predecessor and successor of the following integers.

5  If you move 4 numbers to the left of 1 on a number line, what integer would you reach?

6  Write all the integers between the integers given.

a  –3 and 4 b  –5 and 0 c  1 and 6 d  –9 and –4 e  –15 and –8

7 Write the absolute value of the integers.

a  8 b  –10 c  25 d  –35 e  –65

8 Look at the pattern of integers. Identify the rule and fill in the blanks.

a  –13, –16, –19, –22, b  18, 12, 6, c  –30, –32, –34,

9 Compare using the >, < or = sign.

a  –26 –33 b  –15 –12 c  47 –47

d  14 18 e  –51 –15

10  Write the integers in ascending order.

a  –2, 5, 9, –8, –10 b  –6, –11, 16, 20, –7 c  14, –9, 13, –15, 23

11 The Indian Meteorological Department is the primary agency for weather forecasting. A weather report showed the temperatures of certain cities as 5°C, –3°C, 12°C, –7°C, 18°C and 2°C. Arrange the temperatures in ascending order.

Critical Thinking

1 Find the greatest integer that should fill the box to make the sentence true.

Worksheet 2: Aligned to NCERT Topic/s: 10.2 The Token Model

1  Draw tokens to show the addition of the given integers. Write the answers.

a  +5 + (+6) b  –1 + (+7)

2 Draw number lines to show the addition of the given integers. Write the answer.

a  6 and 4 b  –6 and –4

3 Write the addition sentence shown by the number lines.

b

4 Fill in the blanks.

a  12 + (–14) = b  –16 + (–18) = c  –25 + 63 =

d  52 + (–45) = e  125 + (–256) = f  (–365) + (–145) =

5  Simplify.

a  (–9) + 12 + (–15) b  18 + (–25) + 28

c  –32 + (–14) + (–35) d  36 + (–78) + (–14) + 63

6 The temperature of a city was recorded at 42°C on Monday. The temperature fell by 15°C on Tuesday and fell by a further 7°C on Wednesday. Find the temperature recorded on Wednesday.

Challenge

1  Look at the expression: 1 – 2 + 3 – 4 – 5 + 6 + 7 – 8 + 9

a  Solve the above expression.

b  Change one ‘−‘ to ‘+’ to get the answer as 11.

1  Draw tokens to show the subtraction of the given integers. Write the answers.

a   +11 – (+5)

a  15 from –36 b  –48 from –42 c  –52 from 69 Worksheet 3: Aligned to NCERT Topic/s:

b   –9 – (–5) c   –6 – (–7)

2  Draw number lines to show the subtraction.

a   –3 – (–4) b  (–10) – (5)

3  Subtract.

4  Subtract the integers and match the answers.

a  –125 – (–253)  777

b  236 – (–541)  –790

c  –365 – (425)  –157

d  –414 – (–257)  128

5  Fill in the blanks using the properties of integers.

a   –90 + 1 = b  25 – = 25

c  –35 + 0 = d  32 – 15 =

6  Subtract the sum of 623 and –584 from the sum of –795 and 475.

7 The lowest point in Africa is Lake Asal, at 153 m below sea level, and the highest point in Africa is Mount Kilimanjaro, at 5895 m above sea level. What is the difference of these elevations?

8 Pooja had a balance of `–1250 in her bank account due to some penalties. If she wants to make the balance in her bank account `5000, how much money does she need to deposit in her account?

9 A submarine is 2514 feet below sea level. An aeroplane is 10,500 feet above sea level. What is the distance between the submarine and the aeroplane?

10 Complete the boxes.

1 Anu and Piya are playing a game where they are going up and down the stairs. Anu goes up 4 steps and comes down 2 steps. Piya goes up 3 steps and comes down 1 step. Who reaches the top first if there are a total of 20 steps?

Worksheet 4: Chapter Checkup

1 Solve the given problems using tokens.

a  +3 + (+8) b  −2 + (+7)

2 Circle the integer which is to the left of the other on the number line.

a  –2, 5 b  13, 18 c  8, –8 d  –13, –17 e  25, 36

3 The table shows the temperatures of some places in India on a certain day.

Place

Temperature

Chennai 31° above 0°

Ladakh 5° below 0°

Pune 18° above 0° Sonamarg 8° below 0°

a  Write the temperatures in the form of integers.

b  Name the coldest and the hottest place.

4  Which point will be marked as −2 on the number line?

5  Tick () the integers that are given in their absolute values. a  9    b  +12    c  –36    d  57

6 Write the predecessor and successor of the following integers.

a  –8 b  –26 c  –38 d  45

7 Which of the statements is true?

a  +8 is larger than –16 b  +16 is smaller than +8

c  –8 is larger than +16 d  +16 is smaller than –8

8 How many positive integers lie between –5 and 0?

9 Which set of integers is written in ascending order?

a  –25, –65, 28, 63, 100

b  –22, –18, –15, 16, 36

c  29, 15, –9, –16, –32 d  –32, –17, –19, 42, 48

10 Add the integers.

a  –25 and 36 b  –142 and –48

11 Muskan burnt 480 calories working out on a treadmill and an additional 260 calories by skipping. She indulged in a sweet that had a calorie count of 500. How many calories did she lose or gain?

12 On a hot summer day, the temperature in a desert was 132°F. It dropped to –250°F on a windy day. What is the difference between the two temperatures?

13 Priya uses an online wallet for shopping which allows her to shop for anything up to `750 even if she has no balance in the account. She wanted to purchase a dress for `1000, and her account balance was `–125. She added `1500 to her account. What is the balance in the account after the purchase of the dress?

14 In a test of 50 questions, +6 marks is given for each correct answer, –1 mark is given for each incorrect answer and 0 for not attempting. Manoj completed this test with 40 correct answers and 6 incorrect answers. Find the marks obtained by Manoj in the test.

Challenge

Critical Thinking & Cross Curricular

1 The construction dates of the worldwide landmarks are given below. AD is represented by positive numbers and BC by negative numbers. Write the following differences in descending order.

(A – D), (C – B), (D – E), (C – D), (A – E)

2 Read the statements and choose the correct option.

Assertion (A): On a number line, 3 and −3 are equidistant from 0.

Reason (R): The absolute value of both 4 and −4 is the same.

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

Climate Zones: A Comparison

The average temperature varies across the countries. Some countries are warmer, whereas some countries are colder. The table shows the average temperatures of a few countries across the world.

1 The average temperature of Qatar is than the average temperature in Russia.

a 24.23°C more

c 31.81°C more

b 24.23°C less

d 31.81°C less

2 Arrange the countries in ascending order of the average temperature.

3 Which country among Russia and Greenland is warmer, and by how much?

4 Does it get colder or warmer when the temperature rises? Why?

Large Numbers and Operations

Worksheet 1: Understanding Large Numbers

1 Write the face value (FV) and the place value (PV) of the coloured digits in the numbers written in the Indian number system.

a  38,57,64,999

b  27,89,73,653

FV: _____________ PV: _____________ FV: _____________ PV: _____________

c  18,90,37,890

d  81,87,50,658

FV: _____________ PV: _____________ FV: _____________ PV: _____________

e  58,76,03,653 f 20,56,78,450

FV: _____________ PV: _____________ FV: _____________ PV: _____________

2  Write the expanded form of the numbers.

a  24,85,67,835:

b  56,42,86,604:

c  93,27,59,191:

3  Write the number names for the numbers.

a  23,34,26,578

b  74,36,54,679

c  46,57,68,979

4  Write numbers for the number names.

a  Sixteen crore twenty-six lakh ninety-two thousand one hundred forty-three:

b  Sixty-five crore twenty-two lakh forty-four thousand nine hundred:

c  Eighty crore ninety-nine lakh forty thousand two hundred one:

5  In a number 76,47,56,229, the digits 5 and 4 are interchanged to form a new number. Answer the questions.

a  Will there be a change in the face values of 5 and 4?

b  What will be the new place values of 5 and 4?

c  What is the difference of the place values of 5 in the new number and the original number?

6 The first state-controlled lottery emerged in Kerala in 1967. Mary won a lottery with a ticket bearing the 9-digit number 272545619. Rewrite the number using commas. Write its number name and expanded form.

7  The distance from Jupiter to Saturn is 64,62,70,000 km. Write the distance in words.

Challenge

1 Form the smallest 9-digit numbers using all odd digits at least once. Write the number as a number name.

Worksheet 2: International Number System

1 Write the face value and the place value of the coloured digits in the numbers written in the international number system.

a  179,043,456

FV: _____________ PV: _____________

c  385,876,243

FV: _____________ PV: _____________

e  754,750,213

FV: _____________ PV: _____________

2  Write the expanded form of the numbers.

a  248,567,465:

b  787,135,436:

c  932,542,191:

3  Write the number names of the numbers.

a  345,768,979:

b  575,123,389:

c  978,764,224:

4  Write numbers for the number names.

b 205,145,450

FV: _____________ PV: _____________

d  580,398,653

FV: _____________ PV: _____________

f  807,973,436

FV: _____________ PV: _____________

a  Eight hundred twenty-six million one hundred twenty thousand sixty-six

b  One hundred ninety-two million five hundred four thousand sixteen

c  Seven hundred eighteen million seven hundred ten thousand one hundred fifty-six

5  Arrange the following numbers in ascending order.

a  100,356,782; 500,040,367; 887,210,460; 931,124,820

b  927,516,890; 360,841,910; 692,180,350; 826,020,031

c  500,216,138; 604,503,821; 650,241,567; 945,241,823

6  Arrange the following numbers in descending order.

a  826,374,510; 871,926,345; 670,814,256; 450,070,921

b  423,516,789; 801,210,450; 962,115,108; 678,203,001

c  543,343,867; 967,208,891; 788,216,134; 578,206,010

7  Write the greatest 9-digit number and the smallest 9-digit number, using all the digits only once.

a  5, 3, 4, 0, 8, 9, 1, 7, 2 b  5, 7, 6, 2, 1, 0, 4, 3, 8 c  1, 9, 3, 5, 6, 2, 4, 8, 7

8 Write the greatest 9-digit number and the smallest 9-digit number, using all the digits by repeating the greatest digit only once.

a  2, 7, 1, 0, 8, 6, 4, 5 b  8, 3, 9, 4, 7, 1, 6, 5 c  7, 5, 2, 0, 4, 9, 3, 1

Challenge

1 I am a 9-digit number. All my digits are non-zero and distinct.

- My ones digit is four times the tens digit. The tens digit is 1.

- The sum of the ones and the tens digits is equal to the sum of the hundred thousands and millions digits.

- The sum of the ten thousands and the thousands digits is equal to double the hundreds digit.

- The millions digit is greater than the hundred thousands digit, and the ten thousands digit is 2 more than the thousands digit.

- The digit at the hundred millions place is the largest digit.

- The digit at the ten millions place is the remaining digit.

Which number am I?

Worksheet 3: Estimation in Large Numbers

1  Do as directed.

a  Round off to the nearest 10

b  Round off to the nearest 100

c  Round off to the nearest 1000

2 Solve to find the estimated answer by rounding off to the nearest 100.

a  4356 + 9120

c  8900 − 5220

89,174 + 23,589

79,174 − 23,543 e  215 × 956

3 Reeti bought a suit for ₹3659, a saree for ₹6342. Find the estimated amount she paid for the two items (Round off to the highest place). If she also bought a bedsheet and paid around ₹12,000 to the shopkeeper, what was the aproximate price of the bedsheet?

1 A number is formed by interchanging the digits 6 and 1 in 4,65,271. On rounding it off to the nearest ten, we get 4,15,280. If the original number is rounded off to the nearest hundred, then what is the difference of the original rounded-off number and the new rounded-off number?

2 Srikant estimated a number to the nearest ten and got the answer 5,67,790. What are the smallest and greatest possible numbers that can make Srikant’s answer correct?

Worksheet 4: Operations on Large Numbers

1  Solve the problems.

a  8,79,436 – 3,24,255

b  56,47,658 – 21,432

c  4,37,548 + 2345 + 7,65,675

2  Solve.

a  54,76,587 × 40

c  65,78,598 ÷ 3

d  76,98,608 + 23,13,542 + 2313 + 498

b  3,24,543 × 120

d  9,87,98,706 ÷ 9

3  Solve to find the answer.

a  402 – 118 + 180 ÷ 45 × 162 b  168 ÷ 14 × 22 – 210 + 185

c  15 × 35 ÷ 3 7 + 20 d  35 ÷ 5 × 9 + 7 × 30 ÷ 3

4  Which number when added to 46,98,799 gives 95,34,657?

5  Find the missing digits.

6  The product of two numbers is 5,87,69,880. If one of the numbers is 30, then find the other.

7  The quotient of two numbers is 9,04,35,460. If one of the numbers is 20, what is the other number?

8 Ajay travels a distance of 18 km 685 m from his house to his office. He travels in the metro two times a day. How much distance in metres will he cover in 5 days?

9 The distance at a particular time between Mercury and Earth is 9,63,77,000 km, and the distance between Earth and Jupiter is 6,56,96,000 km. Assuming that Mercury, Earth and Jupiter formed a straight line, find the total distance between Mercury and Jupiter.

Challenge

1 The numbers are following a sequence. Find the sequence and fill in the next numbers. 4,03,804; 4,02,804; 4,03,304; ; 4,02,804; ; 4,02,304

2 Insert brackets to make the calculations true.

Worksheet 5: Chapter Checkup

1 Rewrite the numbers in figures and words, using both the Indian and the international number systems. Also, write their expanded forms. a 350427681

c 635658421

d 901500084

2  Write the numbers for the number names.

a Four hundred sixty million seven hundred twenty-two thousand two hundred thirty-nine

b Sixty-three crore twelve lakh fifty-eight thousand one hundred forty-three

c Eighty crore nine lakh fifty thousand sixty-two

d One hundred million one hundred thousand thirty-nine

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

a 656,502,567 648,900,650

c 900,760,518 900,768,757

4  Arrange the following numbers in ascending order.

a 67,23,56,475; 19,08,04,365; 68,91,63,896; 76,90,87,687

b 676,162,895; 676,817,980; 435,406,576; 324,335,678

c 87,12,63,256; 65,45,12,845; 97,12,36,125; 65,78,15,325

5  Round off the numbers to the nearest ten, hundred or thousand.

a Ten 7,65,378 65,408   57,67,883

c Thousand 9,03,426 83,211   47,69,865

6  Simplify the problems.

a [72 – 36 ÷ 6 × 2] + (30 – 22) + 5

b 9 [8{12 – 7 + 5}] × 8

c 888 × [370 ÷ {65 + (18 ÷ 2)}] d 60 + 13 – {(5 × 1 2 × 10) – 75 ÷ (17 – 2)}

7  Solve and find the answers.

a 19,87,654 + 8,23,901

b 98,74,320 – 43,71,001

c 49,26,115 × 50 d 6,81,279 ÷ 3

e 67,589 – 23,543 + 13,678 f 90,800 + 32,552 – 45,765

8 A certain 9-digit number has only eights in the ones period, only sevens in the thousands period and only fours in the millions period. Write the number in figures and words, using both number systems.

9 An e-commerce company sold 76,578 books in the first month of the year 2000. Estimate the number of books that the company will sell in the whole year if the company sells an equal number of books each month.

10 Form the greatest and smallest 9-digit numbers, using the digits 1, 3, 6, 8, 4, 9, 0, 2 and 5 only once. Also, form the greatest and the smallest 9-digit numbers using all of these digits except 0. Arrange the numbers in both ascending and descending order.

11 A shipping company has a fleet of 35 cargo ships, each capable of carrying 27,850 tonnes of cargo. These ships are divided into three fleets: Fleet A, Fleet B and Fleet C. Fleet A has 9 ships, Fleet B has 12 ships and Fleet C has the remaining ships. Find:

a the total cargo capacity of Fleet A and Fleet B combined.

b the total cargo capacity of Fleet C.

c the total cargo capacity of all 3 fleets.

1 In 15,87,12,528 how many times is the value of 5 in the crores place to that of the value of 5 in the hundreds place?

2 Read both the statements given below and choose the correct option.

Assertion (A): The number 6468 rounded off to the nearest hundred is 6500.

Reason (R): To round off a number, if the digit at the tens place is 5 or more, then the number is rounded off to the nearest 100 by increasing the hundreds digit by 1 and replacing each digit on its right by 0.

a A is true, but R is false.

b A is false, but R is true.

c Both A and R are true, and R is the correct explanation for A.

d Both A and R are true, but R is not correct explanation for A.

Worksheet 7: Case Study

Health Benefits of Grapes

Grapes are delicious fruits that offer health benefits like lowering cholesterol and blood sugar levels. They are a rich source of copper and vitamin K. The table shows the grapes production in different countries in the year 2022.

1 The quantity of grapes produced in Italy rounded off to the nearest thousand is

2 Write True or False.

a The total quantity of grapes produced in India and Chile together is about 58,00,000 tonnes.

b France has produced about 20,00,000 tonnes more than Türkiye.

3 What is the total amount of grapes produced in Türkiye and Chile?

4  How much more grapes are produced in France than in India?

5 Write the number name of the quantity of grapes produced by Türkiye in the international number system.

3-D Shapes

Worksheet 1: Features of 3-D Shapes

Tick () the correct option.

a  Which of the figures is not a solid figure?

cube

b  How many faces does a triangular pyramid have? i  3

c  What is the shape of a dice?

i

d  How many vertices does a heptagonal pyramid have? i  7

Name the shape of the objects.

a b c d

Fill in the blanks.

a  A has 2 circular edges.

b  All the faces of a are identical.

c  A pentagonal prism has more edges than vertices.

d  A and a have square bases.

The Pyramids of Giza were royal tombs built for three different pharaohs. Their shape was that of a square pyramid. How many faces, edges and vertices do they have?

Draw two cubes side by side. Write the number of faces, edges, and vertices of the solid shape formed.

Match the shapes with their features.

a  6 faces

b  12 edges and 7 vertices

c  1 vertex and 2 faces

d  16 edges

e  7 faces and 10 vertices

Octagonal pyramid

Cone

Cuboid

Pentagonal prism

Hexagonal pyramid

1 Pyramids generally have an equal number of faces and vertices, and their number of edges is two less than twice the number of faces or vertices. If a pyramid has 8 vertices, what is the name of this solid?

Worksheet 2: Nets of 3-D Shapes

Write the names of the solid shapes for which the nets are shown. a b c d

Fill in the blanks.

a  A has no net.

b  The net of a cylinder has faces.

c  A cubical box is open from the top. The net of the box has faces.

d  A square pyramid has square/s and triangles in its net.

Which of these is the net of an octagonal pyramid?

given.

a  Cuboid

c  Cone

b  Triangular pyramid

d  Pentagonal pyramid

1 Rajan placed a square pyramid on top of an open cube-shaped box with the same side length as the square base. How many faces, edges and vertices does this new shape have?

Worksheet 3: Chapter Checkup

What are the number of faces, edges and vertices in the shapes given?

Fill in the blanks.

a  A pentagonal pyramid has edges and vertices.

b  The difference of the number of vertices and number of faces of a decagonal prism is .

c  The total number of edges in a heptagonal prism is .

Which of these are NOT prisms?

a  Cone

b  Cube

Write the number of faces and their types in each of the shapes.

a  Square prism

b  Heptagonal pyramid

c  Hexagonal prism

Given is the net of a cube. What colour face will be opposite the:

c  Cuboid

a  blue face?

b  orange face?

Jenna is participating in an origami competition. She wants to create a paper model of a triangular prism, using a net. Draw the net of a triangular prism.

David is a packaging designer. He is tasked with creating a unique gift box in the shape of a rectangular prism. Draw the net of a rectangular prism.

Choose the correct shape of the nets given.

Challenge

1 Read the statements and choose the correct option.

Assertion (A): A cube and a cuboid are both examples of rectangular prisms.

Reason (R): A cube has all its faces as squares, whereas a cuboid has faces that are all rectangles but not necessarily squares. Choose the correct option:

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

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

c  A is correct, but R is incorrect.

d  A is incorrect, but R is correct.

2 The sum of the numbers on the opposite faces of a dice always equals 7. Draw the dots on the net of the dice.

Worksheet 4: Case Study

Our Community Garden Shed

The local community centre is planning to build a garden shed to store tools and equipment. The shed will be constructed using various 3-D shapes to maximise space and functionality.

The community needs your help to understand the features and nets of these shapes to ensure the shed is well-designed.

1 The shed will be a rectangular prism with tin sheets all around to form the walls and the ceiling. How many tin sheets do they need?

2 Colour the walls pink and the ceiling red in the net of the shed. Cross out the part that does not form the walls and the ceiling.

3 On top of the shed, there will be a design in the shape of a rectangular pyramid. Which of the following statements correctly represent the shape?

a  It has 5 faces, 5 edges and 8 vertices. b  It has 5 faces, 8 edges and 8 vertices.

c  It has 8 faces, 5 edges and 5 vertices. d  It has 5 faces, 8 edges and 5 vertices.

4  How are a rectangular prism and a rectangular pyramid different?

5 The community centre wants to make sure the shed is environmentally friendly. How can they do that?

Decimals 3 1

Worksheet 1: Representing and Converting Decimals

Identify the decimal represented by the shaded part and represent it on a number line.

Write the given numbers in decimal form.

600 + 6 + 4 10 + 6 100

Express the decimals as fractions in their simplest form.

Write the decimal number represented by A, B, C and D.

Write the decimals as mixed fractions.

a  3.24

b  5.12 c  2.052

Convert the given decimals into like decimals.

a  1.54 and 15.021

c  1.1 and 4.65

Identify the greatest decimal number.

a  15.4, 15, 15.14, 15.41

c  12.810, 12.82, 12.815, 12.825

Arrange the given decimal numbers in ascending order.

a  7.3, 8.37, 7.23, 8.32

c  97.08, 97.18, 97.2, 97.8

Express the amount using decimals.

a  In kilograms –3 kg 68 g, 14 kg 50 g, 5 kg 5 g, 725 g, 45 g

b  54 and 48.021

d  18.054 and 97

b  178.1, 178.2, 1.78, 178.15

d  15.151, 15.015, 15.51, 15.5

b  58.37, 58.73, 58.45, 58.54

d  18.1, 18.101, 18, 18.11

b  In kilometres –4 km 15 m, 8 km 40 m, 3 km 4 m, 750 m, 15 m

1 Sejal, Vidhi, Ansh and Shiva each have a tablet. The table shows the screen sizes. Vidhiʼs tablet has the biggest screen. Anshʼs tablet screen is bigger than Sejalʼs but smaller than Shivaʼs. What is Anshʼs tablet screen size?

Worksheet 2: Addition and Subtraction of Decimals

Add the decimals. a  5.7, 4.6, 8.97 and 5.35

Subtract the decimals.

Compare using >, < or =.

14.2, 15.3, 14.51 and 18.33

1.1, 2.22, 3.333 and 4.444

Simplify the decimals.

It rained 4 mm on Monday, 3.5 mm on Tuesday, 3.75 mm on Wednesday and 4.2 mm on Thursday. How much did it rain in total on the 4 days?

Pawan goes to a jewellery store. He buys a 20 g 45 mg gold chain and a ring of 12.5 g in weight. What weight of jewellery did he buy? Write your answer in grams.

1 You mix 32.89 grams of citric acid and 11.889 grams of boric acid in a glass container for an experiment. You place the container on a balance and find the total weight to be 123.03 grams. What could be the reason?

Worksheet 3: Multiplication and Division of Decimals

Multiply the decimal number with the whole number.

× 4

Multiply the decimal number with the decimal number.

1.2 × 5.3

2.6 × 23.5

Divide the decimal number by the whole number.

12.3 × 51.31

Divide the decimal number by the decimal number.

Challenge

1 Question: Is Suvarna getting enough protein each day?

Statements:

1 Doctors recommend that sixth graders should eat about 5 ounces of protein each day. One serving of yogurt has 0.6 ounces of protein.

2  Suvarna, a sixth grader, eats 2.5 servings of yogurt each day.

Options:

a Statement 1 alone is enough to answer the question, but statement 2 alone is not enough.

b  Statement 2 alone is enough to answer the question, but statement 1 alone is not enough.

c Both statements together are enough to answer the question, but neither statement alone is enough.

d  Each statement alone is enough to answer the question.

e  Statements 1 and 2 together are not enough to answer the question.

Worksheet 4: Chapter Checkup

Write the expanded form of the decimal numbers.

a  5.23 b  12.056

c  507.633

Convert the fractions into decimals.

a  45  1 2 b 145 8

Express the decimals as fractions in their simplest form.

a  51.26 b  6.814

c  12.508

Arrange the decimal numbers in descending order.

a  15.1, 15, 15.05, 14.95 b  1.23, 1.2, 1.331, 1.303

c  153.32, 153.23, 152.1, 153.233

Solve. a  1.5 + 1.555 b  0.998 – 0.712

1.2 × 6.7

d  492.36 ÷ 6 e  5.9 × 47.6

In a long-jump competition, Rachna jumped 3.6 m, Nina jumped 3.65 m and Rohini jumped 3.55 m. Who jumped the farthest?

1 A smartphone plan costs ₹45 for the first 100 text messages in a month plus an additional ₹0.10 per text message. If you send 275 text messages in a month, what is the total cost?

2 A toy store sells two types of toys: Type A for ₹129.90 and Type B for ₹97.50. If the store sold a total of 60 toys and the total revenue was ₹7567.20, how many of each type of toy were sold?

3 Read the statements and choose the correct option.

Assertion (A): The sum of 23.56 and 78.4 is 101.96.

Reason (R): When adding decimal numbers, the decimal points do not need to be aligned; you simply add the numbers as if they were whole numbers.

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

Space Explorations!

In the vast expanse of space, astronomers use a special unit of measurement called an astronomical unit (AU) to describe distances within our solar system. One astronomical unit is the average distance between the Earth and the Sun, approximately 149.6 million kilometres. This makes it easier to compare the distances of planets from the Sun without dealing with extremely large numbers.

Let us look at the average distances of the planets from the Sun in AU:

Answer the following questions:

1 What is the average distance of Mars from the Sun in astronomical units (AU)? a  1.00 AU b  1.52 AU c  5.20 AU d  9.58 AU

2 If you add the distances of Mercury and Earth from the Sun, what is the result in AU? a  1.11 AU b  1.39 AU c  1.52 AU d  2.00 AU

3 The distance of Jupiter from the Earth is AU.

4 Arrange the following planets in ascending order of their distances from the Sun: Mars (1.52 AU), Venus (0.72 AU), Neptune (30.05 AU) and Uranus (19.22 AU).

Introduction to Algebra 4 1

Worksheet 1: Algebra and Patterns

Find the general rule for each of the number patterns. Then find the 18th term.

a  2, 4, 6, 8, 10, …

b  3, 6, 9, 12, 15, …

c  6, 11, 16, 21, ...

d 3, 8, 13, 18, 23, …

Find the rule in terms of variables for the matchstick pattern and write the number of matchsticks used in the 50th shape. Draw the next shape for the pattern.

Shape 1

Shape 2

b

Shape 3

Shape 1

Shape 2

What is the rule for each of the number patterns?

a  3, 5, 7, 9, …

Complete the table, write the rule, and answer the question. A bakery makes 10 cupcakes an hour.

b  5, 8, 11, 14, …

Shape 3

Shape 4

Hours 1 2 3 4 5 6 7 8

Cupcakes 10 20 30

Write the rule to work out the number of cupcakes this bakery produces within a certain amount of time.

How many cupcakes will it make in 1 day?

Write the general rule to find the area of a rectangle. 5

Challenge

1 The perimeter of two pieces of land is written as 4a + 5a where a is the side of each shape. How will you write the perimeter of the new shape formed when they are joined on one side?

Worksheet 2: Algebraic Expressions

1 2

Sort these into arithmetic expressions or algebraic expressions.

a  7 × 2 + 3 − 2 b  7x + 5

c  12y d 10y – 6x

Write down the terms of the algebraic expressions.

a x + y b  2a + 3b – c

c x + y + 2z

Write algebraic expressions for the statements.

a  3 added to 6m b  10 subtracted from n

c  15 times x d  Twice the product of x and y

e  9 multiplied by y added to 1

Solve the algebraic expression for the value x = 2, y = 4 and z = 9.

a x(y + 8)

f Thrice of y added to the difference of x and 3

(x + z)(xy – z) c xy – 9zx

A year has 12 months. How many months are there in u years. Write the algebraic expression and find the value of the expression for u = 13.

After sharing x pencils with your friend, you are still left with 7 pencils. What was the total number of pencils before sharing?

Challenge

1 The images show the expression for the parts and whole model. Fill in the missing parts of the expressions.

Worksheet 3: Algebraic Equations

Write the linear equations for each of the statements.

a  When we add 3 to a number, we get 12.

b  When 7 is taken away from a number, it leaves 2.

c  When 7 is taken away from twice a number, it leaves 3.

d  2 added to the product of a number and 4 gives 26.

The denominator of a fraction exceeds the numerator by 5. If 3 is added to both, the fraction becomes 3 4 . Write an equation to represent this situation.

Seventy-two people signed up for the soccer league. After the players were evenly divided into teams, there were 6 teams in the league and x people in each team. Write an equation to represent this situation.

Write a statement for each of the equations. a  4x + 5 = 9

2n + 1 = 5 c  12a – 7 = 5

3(y + 1) = 12

Solve the equations using the transposition method. a x + 6 = 10

5 = a + 2

−7 = x + 4

m – 12 = 3

4 + k – 7 = 2

Challenge

1 The sum of three consecutive multiples of 8 is 192. Find the numbers.

Worksheet 4: Chapter Checkup

Find the general rule which shows the number of matchsticks required to make the patterns. Use a variable to write the rule. Draw the shape for the next pattern.

If zero is added to a number or a number is added to zero, the result is the number itself. Generalise this property of numbers using a variable.

Write the algebraic expression for the situations.

a  4 added to 3 times x b  2 subtracted from 2 times y

c  4 less than the quotient of x by 3 d y is divided by 5 and the quotient is added to 6

State which of these are linear equations.

a  2x + 5 = 9  b  9x + 4 > 5  c  2y + 7 = 9

Solve the algebraic expression for x = 3, y = 7 and z = 5.

a  5x + 9y b  6xy – 2yz + 10

c  9xz –1 5 yz d  11yz + x + 4y

The lengths, in cm, of the sides of a triangle are 3x – 5, 2x – 1 and x + 1.

a  Write down an expression, in terms of x, for the perimeter of the triangle.

b  If the perimeter of the triangle is 31 cm, find the value of x

Write your own situation based statements for the given equations. Solve the equations using the transposition method.

a x + 30 = 50

b  6x – 3 = 9

Ajit has some marbles. Badri has twice as many marbles as Ajit. Charu has 5 more marbles than Badri. In total they have 55 marbles. How many marbles does Charu have?

Sahil has x drawing sheets. Rahul has 2 less than Sahil, while Aryan has 6 more than Sahil. Find out how many sheets Rahul and Aryan have in total. Also, find the total number of sheets that the three of them have.

1 Read the statements and choose the correct option.

Assertion (A): The equation for `3 subtracted from t to equal to 5’ is written as t – 3 = 5.

Reason (R): Any equation like the above, is a condition on a variable. It is satisfied only for a definite value of the variable.

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 false, but R is true.

d  A is true, but R is false.

2 Sia bought a new multi-door refrigerator for ₹90,000. The value of the refrigerator decreases by ₹3000 per year. In how many years will the price of the refrigerator be half its original price?

Worksheet 5: Case Study

Economics is a social science that studies production, distribution and consumption of goods and services. It also deals with the demand and supply of products. The price for supplying the product (P) is equal to the sum of the delivery charge (C) and the cost of making Q pieces.

1 The delivery charge is ₹300. The cost of making each piece is ₹30. Write the expression for the price for supplying the product.

a P = ₹300Q + ₹30

c P = ₹300 − ₹30Q

b P = ₹300 + ₹30Q

d ₹300Q + ₹30

2 If the value of Q is 4, find the price for supplying products.

3 The demand of the product is written as D, and the cost is written as C. Demand is half the cost. Write the expression if the cost rises 4 times.

4 What should be the value of the quantity in Q1 for the delivery charge to be equal to the product of quantity and cost of making one piece?

Introduction to Ratio and Proportion

Worksheet 1: Ratios and Their Applications

Write True or False.

a  A ratio can have units, depending on the types of quantities being compared.

b  In 3 : 5, the consequent is 5.

c  The terms of a ratio a : b are called the antecedent and consequent, respectively.

d  10 : 2 is the same as 2 : 10.

e  10 litres of water can be compared with 10 km.

Write the given ratios in their simplest form.

a  48 : 72 b  400 cm : 6 m c  1.5 kg : 750g

d  25 L : 750 mL e  9 hours : 540 min f  ₹100 : 10000 paise

Find three equivalent ratios for the ratios.

a  5 : 7

4 : 9 c  12 : 16 d  6 : 15

8 : 11

9 : 17

Compare and fill in the blanks with <, > or =. a  5 : 3 3 : 4 b  3 : 5 2 : 9 c  4 : 7 5 : 8

Match the ratios with their simplest forms.

a  480 : 32

b  378 : 105

c  138 : 111

d  42 : 280

Apoorv has a basket of apples. He has 16 red apples and 24 green apples. What is the ratio of the number of red apples to the number of green apples?

At a pet care centre, there are 30 dogs, 20 cats and 10 birds. What is the ratio of the number of cats to the total number of animals? How should we treat animals?

In Sarah's garden, there are 15 roses, 10 tulips and 5 lilies. Find the ratio of:

a  The number of roses to the number of tulips.

b  The number of lilies to the number of roses.

c  The number of tulips to the number of roses and lilies.

Madhav visited the Mysore Zoo, officially known as Sri Chamarajendra Zoological Gardens in Karnataka, India, and observed various animals. On the information board, he read that the average weight of a male tiger is about 220 kg, and that of a one-horned male rhino is about 2200 kg. Find the ratio of the weight of a tiger to that of a rhino.

1 Adventure tourism is booming in India. As per a recent survey, the ratio of rafting rentals to bungee rentals at a store is 10:7 in Rishikesh. If the number of bungee rentals doubles and the number of rafting rentals stays the same, then the number of bungee rentals is how many times the number of rafting rentals?

Worksheet 2: Proportion and Their Applications

Which sets of numbers are in proportion?

a  4, 5, 12, 15

c  15, 5, 12, 4

Check and state if true or false.

a  17 : 8 : : 1 : 3

c  21 : 4 : : 84 : 16

b  8, 5, 9, 6

d  9, 5, 18, 10

b  5 : 15 : : 3 : 9

d  7 : 12 : : 21 : 36

Create a proportion for each set. Use only 4 numbers from each set.

a  3, 13, 9, 16, 39

c  7, 21, 2, 4, 12

Find the missing numbers in the proportions given.

a  2 : x : : 5 : 10

c x : 16 : : 12 : 24

Find the fourth proportional to:

a  12, 4, 9

b  42, 5, 7, 3, 18

d  28, 14, 8, 56, 2

b  3 : 6 : : 9 : x

d  1 : 3 : : x : 12

b  2, 6, 1

c  9, 3, 6 d  32, 8, 24

Find the third term when the given terms are in continued proportion. a  9, 3 b  2, 4 c  16, 36 d  36, 42

The second, third and fourth terms of a proportion are 21, 45 and 63. Find the first term.

If x, 9 and 3 are in continued proportion, then find the value of x.

Challenge

1 To win a relay race, Riya must run 300 metres before her opponent runs 280 metres. Riya runs at a pace of 75 metres every minute. Her opponent runs at a pace of 15 metres every 12 seconds. Who wins the race?

Worksheet 3: Unitary Method

If the cost of 12 pens is ₹108, what is the cost of 20 such pens?

Raj can cycle at a speed of 2 km/h. How long will it take him to cover 8 km?

The cost of 125 postcards is ₹375. How many postcards can be purchased for ₹180?

Amit is employed under the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA), which guarantees 100 days of wage employment to rural households. He works for 5 days in a month and receives a salary of ₹1350 for his work. How many months will it take him to earn ₹12,150?

The temperature increased by 25℃ in the last 100 days. If the rate of temperature increase remains the same, how many degrees will the temperature increase in the next 16 days?

A school needs to transport its students on a field trip to an old age home, to teach students about empathy and compassion. 3 school buses can carry 120 students. How many school buses are required to transport 1000 students?

Challenge

1 A recipe requires 3 cups of flour to make 10 cookies. If you want to make 30 cookies, how many cups of flour are needed, considering that an extra 10% of flour is required due to adjustments in the recipe?

Worksheet 4: Chapter Checkup

A supermarket has 45 packets of potato chips, 66 packets of banana chips and 32 packets of corn chips. What is the ratio of:

a  Potato chips to corn chips? b  Banana chips to the total number of chips?

Write the ratios in their simplest form.

a  8 m : 700 cm

c  5 L : 750 mL

Find four equivalent ratios for the ratios given.

a  3 : 8

c  11 : 15

Compare and fill in the blanks with <, > or =. a  8 : 11

c  5 : 12

min

Which of the ratios are not in proportion? a  14 : 20 : : 28 : 40 b

If a box contains 24 red stamps and 36 blue stamps, what is the ratio of red to blue stamps in its simplest form?

If 12 : x : : 6 : 36, find the value of x.

If 9, 12 and x are in continued proportion, then find the value of x.

Reshma went to market to buy eggs. The cost of 4 dozen eggs is ₹288. What is the cost of 15 such eggs?

If the ratio of pencils to pens in a box is 4 : 5, and there are 36 pencils, how many pens are there?

The present age of a mother is 36 years, and that of her daughter is 20 years less than the age of the mother. What is the ratio of the age of the mother after 12 years to the age of the daughter 10 years ago?

1 The ratio of first and second class fares between two stations is 3:2. The number of passengers travelling first and second class are in the ratio 1: 15. If ₹26,400 is collected as the total fare, then what is the amount collected from the first class passengers?

2 Read the statements and choose the correct option.

Assertion (A): If the ratio of the mass of zinc to copper in an alloy is 7:5 and the total mass of the alloy is 120 kg, then the mass of zinc in the alloy is 70 kg.

Reason (R): The mass of zinc in the alloy can be calculated using the formula part of zinc total parts × total mass

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

Wildlife Study!

India's rich wildlife is a national treasure. Dedicated conservation efforts, from establishing national parks to community-led initiatives, are steadily bringing back endangered species and restoring fragile ecosystems. Suppose you are studying two renowned wildlife sanctuaries in India to analyse the ratios and proportions of various species for a school project focused on conservation efforts.

Sanctuary 1: Ranthambore National Park

Tigers: 60

Leopards: 20

Sanctuary 2: Bandhavgarh National Park

Tigers: 80

Answer the following questions:

Leopards: 15

Deer: 200

Deer: 250

1 How many tigers are there in Ranthambore National Park per 100 deer?

2 Bandhavgarh National Park has how many less leopards than Ranthambore National Park?

5

3 In Ranthambore National Park, the ratio of tigers to leopards is

4 True or False: Bandhavgarh National Park has a higher proportion of deer to total animals compared to Ranthambore National Park.

5 What should you keep in mind while visiting wildlife sanctuaries?

Answers

Answers

Chapter 1

Worksheet 1

1. 13,215; 13,216; 13,217; 13,218; 13,219

2. a. Predecessor = 66,777 Successor = 66,779

b. Predecessor = 54,556 Successor = 54,558

c. Predecessor = 86,456 Successor = 86,458

d. Predecessor = 89,664 Successor = 89,666

e. Predecessor = 97,563 Successor = 97,565

3. 1483, 1485

4. a. 0 b. 6567 c. 10 d. 50 e. 10, 14 f. 9875

5. a. 30, 50, 70, 90; b. 100, 150, 200, 225, 250

6. a. 20 + 10 + 10 + 10 + 10 = 60 b. 18 – 3 – 3 – 3 – 3 – 3 = 3

7. a. 22 b. 5 c. 6 d. 10

8. a. 1 b. y can be any non-zero whole number c. 1 d. 1

9. 153 million square km

10. a. 0

b.

c.

11. 8 cookies  12. ₹100 13. 0; 7

Challenge 1. Successor: 10,00,000; Predecessor: 9,99,998; Product = 9,99,99,80,00,000

Worksheet 2

1.

2. a. 21 b. 1944 c. 64

3.

4. 1111 × 1111 = 1234321  11111 × 11111 = 123454321

5. 1 × 11 + 1 = 12 1 × 12 + 1 = 13 1 × 13 + 1 = 14 2 × 8 + 1 = 17 2 × 10 + 1 = 21 2 × 12 + 1 = 25 12 × 11 + 2 = 134 12

6. ₹9,99,99,999

7. The first shape has 6 rectangles; the next shape has 11 rectangles and the next shape has 16 rectangles. So, the rule followed by the pattern is to add 5 rectangles every time.

The third shape has 16 rectangles.

The fourth shape will have, 16 + 5 = 21 rectangles. The fifth shape will have, 21 + 5 = 26 rectangles. So, the fifth shape will have 26 rectangles.

8. a. 405 b. 4455 c. 44955 d. 449955

Pattern: 405, 4455, 44955, 449955, 4499955, 44999955…

9. 13, 21  10. Answer may vary. Sample answer

Challenge 1. 64 pencils

Worksheet 3: Chapter Checkup

1. a. 1,54,697; 1,54,699 b. 2,54,894; 2,54,896

c. 5,45,976; 5,45,978 d. 6,45,711; 6,45,713

2. a. 11111 × 1 – 2 = 11109; 111111 × 1 – 2 = 111109

b. 11111 × 2 – 2 = 22220; 111111 × 2 – 2 = 222220

c. 11111 × 3 – 2 = 33331; 111111 × 3 – 2 = 333331

d. 11111 × 4 – 2 = 44442; 111111 × 4 – 2 = 444442

3. a. 0

5. The rule is to add 3 more dots in the next shape in the sequence. The fourth shape in the pattern will have 15 dots.

6. 49 dots

7 . Answer may vary. Sample answer.

8. 590; Multiplication by 9

9. a. 16,500 b. 49,305 c. 5460 d. 6300

10. 4352 m, Distributive property

Worksheet 4: Case Study

1. Triangles and circles

2. Option c

3. The rule is a man and a woman are repeated alternatively.

4. The next term will have 1 man and 1 woman.

5. Answers may vary. Sample answer:

12. 18 right angles

Challenge 1. 30º

Worksheet 3

1. Vertices: T, R, S Sides: TR or RT, TS or ST, RS or SR Angles: ∠T or ∠RTS or ∠STR, ∠R or ∠TRS or ∠SRT, ∠S or ∠TSR or ∠RST

2. a. Scalene b. Equilateral c. Scalene d. Isosceles

e. Scalene f. Equilateral  3. a. acute-angled triangle

b. acute-angled triangle c. obtuse-angled triangle d. right-angled triangle e. obtuse-angled triangle f. acute-angled triangle

4.

Chapter 2

Worksheet 1

1. c  2. c  3. a. True b. False c. True d. False

4. a. 2.7 cm b. 3.9 cm c. 5.7 cm

5. Students will draw line segment of lengths, 5.2 cm, 7.7 cm, 61 mm, 35 mm.

6. b  7. a. 23,000 m  b. 23,00,000 cm c. 2300 dam d. 230 hm  8. 4 cm Challenge 1. 6

Worksheet 2

1. Option c    2. a. Acute angle b. Obtuse angle  c. Reflex angle d. Acute angle

3. Option b

4. ∠P = 34º; ∠Q = 66º; ∠R = 67º  5. ∠QON and ∠QOR

6. a. 25º b. 45º

7. a. 1 4 b. 1 3 c. 1 2 d. 3 4

8. a. X

9. Close to a right angle.

10. a. South b. West c. North

5. First Garden – isosceles triangle Second Garden – scalene triangle

Challenge 1.  Option i

Worksheet 4

1. a. Sides (PQ, QR, RS, SP) vertices (P,Q, R, S); Adjacent sides: (PS, SR), (RQ, QP), (SR, RQ), (QP, PS) Opposite sides: (PS, QR), (SR, PQ)  b. Sides(AB, BC, CD, DA) vertices (A, B, C, D); Adjacent sides: (AB, BC), (BC, CD), (CD, DA), (AD, AB) Opposite sides: (AB, CD), (AD, BC) c. Sides (JK, KL, LM, MJ) vertices (J, K, L, M); Adjacent sides: (JM, ML), (ML, LK), (LK, KJ), (KJ, JM)  Opposite sides: (JM, KL), (ML, JK)   2. a. Diagonals: BD, AC  b. Diagonals: SU, VT c. Diagonals: MK, JL  3. a. Square b. Parallelogram c. Kite

4. Figures may vary. a. A B

F       b. A B C E

E

F

5. a. Convex quadrilateral b. No, c. No, since the opposite angles of the quadrilateral are unequal.

Challenge 1.  Option c

Worksheet 5

1. a  2. Vertices: A, B, C, D, E, F, G, H Sides: AB or BA, BC or CB, CD or DC, DE or ED, EF or FE, FG or GF, GH or HG, HA or AH

3. Figures may vary. Sample figures.

a. b. c.

4. Regular hexagon  5. Sarah, 4 sunflowers

Challenge 1.  A

Worksheet 6

1. a & c  2. a. Closed curve b. Open curve c. Open curve  d. Open curve e. Closed curve

3. a.  b.  c.  d.

4. d  5. d   6. Boundary of the curve

Exterior of the curve P Q R

7. Figures may vary. Sample figure. a. b.

Interior of the curve

8. a. 3 cm   b. 4 cm

9. Answer may vary. Sample answer. Simple curves Non-Simple curves

10. a. 44 cm b. 52.8 cm c. 132 cm d. 308 cm

11. a. 10.5 cm b. 14 cm

12. 0.5 m

Challenge 1.  (b) Both A and R are true, but R is not the correct explanation of A.

Worksheet 7: Chapter Checkup

1. a. 9 b. 8 c. 5 d. 7

2. a. Quadrilateral b. Octagon c. Pentagon d. Heptagon

3. Students will draw line segments of length 4.6 cm, 77 mm, 6.9 cm and 2.2 cm.

4. Figures may vary. Sample Figure.

a. X B C O Y G F D E A   b. F

5.

Acute angle

b. Reflex angle

c. Acute angle

d. Obtuse angle

9. Closed curve: a, c Open curve: b, d  10. a. Isosceles

b. Scalene c. Equilateral  11. a. acute-angled triangle

b. acute-angled triangle c. obtuse-angled triangle

12. a. 90º b. 180º c. 0º d. 270º  13. a. East b. West

14. a. RT and SU b. ∠RST, ∠STU, ∠TUR, ∠URS  15. a. Yes, the adjacent angles of a kite are equal. b. Yes, the angles to the opposite sides of an isosceles triangle are equal. c. Yes, the angles to the opposite sides of an isosceles triangle are equal

Challenge 1. 15  2.  Option B

Worksheet 8: Case Study

1. Option a  2. Option b  3. morning  4. obtuse

Worksheet 1

b. 4 children c. Yes

d. Yes. When all the children standing in a row are of the same height.

4. Answers may vary. Sample answer.

5.

Smallest Number = 55,306; Largest Number = 55,906

6. A = 8500; B = 9500; C = 10,500

7. 4-digit numbers: 1234, 2359, 5679, 8235; 5-digit numbers: 45,891; 12,789; 31,596; 48,862

8. 6 + 10 = 16; 5 + 4 + 7 = 16; 6 + 4 + 6 = 16

Challenge 1. 20 times

Worksheet 2

1. Answers may vary. Sample answer. 626, 505

2.  7 5

7 1 3 2 2 3 1

3 6 3

3. Answers may vary. Sample answer. Digits 6, 1, 9, 3

9631 – 1369 = 8262

8622 – 2268 = 6354

6543 – 3456 = 3087

8730 – 378 = 8352

8532 – 2358 = 6174

7641 – 1467 = 6174

We are getting the same number again and again. This is the Kaprekar constant.

4. 7 rounds

5. Answers may vary. Sample answer: 31/02/2013

6. Answers may vary. Sample answer: 04:40; 15:51

7. 12531 + 41,205 = 53,736

8. Answers may vary. Sample answer: 72,500 − 30,000 + 2500 = 45,000

Challenge 1. 654456

Worksheet 3

1. 280 2. 132 dots

3. Answers may vary. Sample answer:   52, 26, 13, 40, 20, 10, 5

4. Answers may vary.

Challenge 1. Rule: The difference between the terms is increasing by 2 each time. 183

Worksheet 4: Chapter Checkup

1. Answers may vary. Sample answer: 4664, 1991

2. Answers may vary. Sample answer:   Date: 22/02/2022Time: 13:31

3. 9 3

4. Answers may vary. Sample answer:   60,000 – 20,000 – 10,000 + 3000 = 33,000

5. Answers may vary. Sample answer:

2341 + 3313 = 5654

6. Digits = 2,3,8,9

9832 – 2389 = 7443

7443 – 3447 = 3996

9963 – 3699 = 6264

6642 – 2466 = 4176

7641 – 1467 = 6174 (Kaprekar constant)

7. 110 dots

Challenge 1. 4  2. c

Worksheet 5: Case Study

1. Answers may vary. Sample answers: 505 and 727

2. Answers may vary. Sample answers: 1221, 2332, 4554, 6886

3. Yes the registration number AB12321BA is a palindrome since it reads the same way forward and backwards.

4. 4 steps: 87 + 78 = 165. 165 + 561 = 726. 726 + 627 = 1353. 1353 + 3531 = 4884 which is a palindrome.

Chapter 4

Worksheet 1

1. a. False b. True c. False d. False

2. a. |||| |||| |||| ||||

b. |||| |||| |||| |||| |||| ||

c |||| |||| |||| |||| |||| |||| |

d. |||| |||| |||| |||||||| |||| |||| |||| ||

3.  Name of Mughal emperor Tally Marks Babur ||| Humayun ||| Akbar |||| Jahangir ||| Shah Jahan |||| Aurangzeb |||| | 4.  Fruit Tally Marks Orange |||| || Apple |||| |||| || Banana |||| |||| | Guava |||| | Litchi |||| ||||

5.  Age Number of Student Tally Marks 10 7 |||| || 11 3 |||

7 |||| ||

7 |||| || 14 6 |||| | a. 7 students b. 6 students c. 17 students d. 14 students

Challenge 1. a. |||| b. |||

Worksheet 2

1. Brand A Brand B Brand C Brand D Brand E

Key: = 500 soaps

2. a. 1500 bulbs b. 300 bulbs c. 3900 bulbs

d. Tuesday, 1500 bulbs e. 14,700 bulbs

3. a. 4500 fans b. 5500 fans c. June, 8000 fans d. 500 fans

4.  Year Number of earthquakes

5. Answer may vary Sample answer. How many more earthquakes occured in 2015–2016 than that in 2013–2014?

Challenge 1. Week 1: 4.5 pictures; Week 2: 5.25 pictures; Week 3: 3.75 pictures; Week 4: 8 pictures

Worksheet 3

1. a. 09:00-10:00 b. 08:00-09:00

2.

3. a. ₹7000 b. Clothes; ₹6000 c. Rent; ₹9000 d. ₹37,250

4. Answers may vary. Sample answer.

a. How many families have more than 2 members in their family?

b. How many families have less than 5 members in their family?

Challenge 1. Option c

Worksheet 4: Chapter Checkup

1.

3. a. Maths b. 14 students c. Science d. 17 54

4. a. 30 saplings  b. 33 saplings c. Block B d. 173 saplings

5. a. Delhi b. Lakshadweep c. 1500 square km d. 2750 sq. km

6. Answers may vary. Sample answer. What is the area of Chandigarh?

7. a. 675 ice creams b. May; 1200 ice creams

c. 750 ice creams d. 4275 ice creams

= 1000 mangoes

Challenge 1. c  2. a. 6 symbols b. The students participating in chess will be shown by 10 faces and the students participating in drama will be represented by 4 faces. c. 7 students

Worksheet 5: Case Study

1. Option b  2. Option c  3. April; 40  4. May, 10

5. No. Answers may vary. Sample answer. We should refrain from unnecessary flower plucking as it disrupts the garden's ecosystem. We should admire their beauty in situ to protect plant health.

Chapter 5

Worksheet 1

1. a. 1, 2, 4, 5, 10, and 20 b. 1, 2, 13, and 26 c. 1, 2, 3, 4, 6, 9, 12, 18, and 36 d. 1, 2, 4, 8, 11, 22, 44, and 88  2. a. 37, 74, 111, 148, 185, and 222 b. 62, 124, 186, 248, 310, and 372 c. 84, 168, 252, 336, 420, and 504 d. 99, 198, 297, 396, 495, and 594

3. 2 and 12  4. 9 and 8

5. a.  15 × 1 3 × 5 5 × 3 1 × 15   b.  7 × 2 2 × 7 1 × 14 14 × 1

Challenge 1. 2 is a factor of 100 but 5 is not a factor of 67. So, Roy is wrong.

9.  Sohail Ashraf

Mahmood Raju Vivek Key:

Worksheet 2

1. a. E b. O c. E d. O  2. 28 is a perfect number. 3. a. False b. True c. True d. False

4. a. 41, 43, 47; Sample answer. 41 and 43 b. 61, 67; Sample answer. 61 and 67 c. 11, 13, 17, 19, 23, 29; Sample answer. 11 and 13 d. 2, 3, 5, 7; Sample answer. 2 and 3  5. 71, 73

6. 990, 2484, 41,870 and 9,12,048 are divisible by 2. 990, 2484 and 9,12,048 are divisible by 3. 2484 and 9,12,048 are divisible by 4. 990 and 41,870 are divisible by 5. 990, 2484, and 9,12,048 are divisible by 6. Only 9,12,048 is divisible by 8. 990 and 2484 are divisible by 9. 990 and 41,870 are divisible by 10.

7. Answers may vary. Sample answers: a. 14 b. 48 c. 99 d. 9

8. Factors of 14 = 1, 2, 7, 14. 14 is a composite number since it has more than 2 factors.

14 × 1 = 14

1 ×

9. Prime numbers: 11 and Composite numbers: 24

10. Answers may vary. Sample answer. Is 1331 divisible by 11? 11. 20

No, 20 and 8 are not co-primes.

Challenge 1. Answers may vary. Sample answers. 2 + 3 + 5 + 7 = 17; 2 + 3 + 5 + 13 = 23

Worksheet 3

1. a. 126 = 2 × 3 × 3 × 7 b. 882 = 2 × 3 × 3 × 7 × 7 c. 6241 = 79 × 79

d. 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 192  2. a. No  b. No

3. 3, 5, and 23  4. Students will draw the factor trees.

a. 210 = 2 × 3 × 5 × 7 b. 293 = 1 × 293

c. 816 = 2 × 2 × 2 × 2 × 3 × 17 d. 952 = 2 × 2 × 2 × 7 × 17

5. 560 = 2 × 2 × 2 × 2 × 5 × 7  Order: 2, 5, 7 Product: 10

6. 10,000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5  7. 56 samples

Challenge 1. 210

Worksheet 4

1. a. (i) 12 (ii) 15 (iii) 9 (iv) 36  b. (i) 10 (ii) 15 (iii) 15 (iv) 18 c. (i) 12 (ii) 21 (iii) 24 (iv) 1  2. a. (i) 60 (ii) 105 (iii) 24 (iv) 48  b. (i) 1680 (ii) 924 (iii) 6160 (iv) 300 c. (i) 396 (ii) 1920 (iii) 108 (iv) 2040  3. 42  4. No 5. 9  6. 18  7. 8

Challenge 1. 4 pairs

Worksheet 5

1. 16 gift bags  2. 1400 minutes  3. 36 groups  4. 36 days

5. 18 cm

Challenge 1. Option a

Worksheet 6: Chapter Checkup

1. a. 1, 2, 3, 4, 6, 8, 12 and 24 b. 1, 2, 3, 5, 6, 10, 15 and 30  c. 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 d. 1, 2, 4, 19, 38 and 76

2. Students will draw factor trees. a. 267 = 3 × 89

b. 315 = 3 × 3 × 5 × 7 c. 539 = 7 × 7 × 11 d. 714 = 2 × 3 × 7 × 17

3. 4 and 9; Yes. 9 8 7 6 5 4 3 2 1

4. a. (i) 12 (ii) 14 b. (i) 18 (ii) 11

5. a. (i) 4410 (ii) 360 b. (i) 84 (ii) 2800

6. 15 books  7. 7:04 a.m. 8. 300 minutes

Challenge 1. 771  2. Option c

Worksheet 7: Case Study

1. Option d 2. 12 p.m. 3. Option c

4. Answer may vary.

Chapter 6

Worksheet 1

1. a. 37 cm b. 34 cm  2. 84 cm  3. 41 cm 4. 20 cm  5 a. 14 cm b. 6 cm  6. 9.34 m

7. Answers may vary. Sample answers: 2 cm 5 cm 4

8. 645 m  9. 25 cm

Challenge 1. The perimeter will remain the same. For example, if a square of side length 5 cm is cut from a bigger square of side length 10 cm, the perimeter which was originally 40 cm is now also 40 cm.

Worksheet 2

1. 49 sq. cm  2. 15 cm  3. a. 30 sq. cm b. 47 sq. cm

4. 90 cm  5. The square has the larger area.

6. a. P = 104 cm, A = 192 sq. cm b. P = 48 units, A = 63 sq. units

Challenge 1. Area increaes 4 times.

Worksheet 3

1. 46 m  2. 441 sq. m  3. 25 m  4. 180 stickers

5. Answer may vary. Sample answer: Maria has a rectangular garden. She knows the perimeter of the garden is 40 metres, and one of the sides measures 12 metres. To find out how much area she needs to plant flowers, calculate the area of the garden.

Challenge 1. 40 m

Worksheet 4: Chapter Checkup

1. a. 48 cm b. 22 cm  2. a. 18.5 sq. units b. 31 sq. units

3. 399 sq. cm  4. 625 tiles  5. 75 sq. cm  6. 18 cm

7. Ramesh’s plot has the greater area and perimeter.

8. 72  9. ₹500  10. Sailesh  11. 50 sq. m

12. Answers may vary. Sample answers:   4 9 12 3

Challenge 1. Option a 2. 24 cm

Worksheet 5: Case Study

1. Option d  2. 104 feet  3. 14 feet  4. ₹16,800

5. Answer may vary. Sample answer.

Chapter 7

Worksheet 1

1. a. 3 4 b. 6 16 c. 10 20 d. 5 9

2. Answers may vary. Sample answers. a. b. c.  d.

3. Proper

Each

Worksheet 2

1.

Equivalent

4. Answers may vary. Sample answers:

6. 73 5 m  7. 33 1 3 cookies

Challenge 1. 1 2 2. one

Worksheet 3

1. a. 3 7 b. 7 c. 4 7 d. 3 19 110 2.

Challenge 1.  7 12

Worksheet 4: Chapter Checkup

1. a. 21 2 b. 17 3 c. 100 23 d. 15 8

2. a. 33 4 b. 83 5 c. 206 7 d. 5 2 17

3. Answers may vary. Sample answers: a. 15 21 , 10 14 , 20 28 b.

33

,

,

5. a. Not equivalent b. Not equivalent c. Not equivalent d. Not equivalent  6. a. 2 5 b. 3 1 3 c. 5 9 d. 2  17 58

7. 1 20 kg  8. 3517 20 m

Challenge 1. Option d

Worksheet 6: Case Study

1. b  2. c 3. 41 6 4. Martial arts < Dance < Yoga

5. Answers may vary.

Chapter 8

Worksheet 1

1. a. A B 5.4 cm  b. P Q 6.7 cm

c. X M 6.1 cm  d. L Y 7.2 cm

2. a. A B 4.3 cm  b. D E 5.6 cm

c. G H 3.9 cm  d. P Q 2.7 cm

3. Students will construct line segments of the same length as AB, PQ and MN.

4.  5 cm 5 cm 5 cm 5 cm S H J I

5. Figure may vary. Sample figure.

Challenge 1. Yes, we can construct a square by drawing a perpendicular to the diagonal.

Worksheet 2

Challenge 1. Option b

An angle can have only one unique angle bisector. The angle bisector divides the angle into two equal parts, making it the line of symmetry for that angle.

Worksheet 3: Chapter Checkup

5. Figures may vary. Sample figure.

8. a.

9. a.  A B 42° 21° D C

b.  A B 35.5° 71° D C

10.  1 cm 2.1 cm 2 cm J X Y K 11. No  A B D C

Challenge 1. Option d

2. Yes, the bisecting rays are perpendicular to each other. A linear pair of angles is formed when two adjacent angles add up to 180°.

Let’s denote the two angles as ∠A \angle A∠A and ∠B \angle B∠B.

Let ∠A = x and ∠B= 180° − x

The bisector of ∠A = x 2 and the bisector of ∠B = 180° − x 2

Sum of angles formed by the bisectors = x 2 + 180° − x 2 = x + 180° − x 2 = 180° 2 = 90°

Since the sum of two angles formed by the bisectors is 90°, the bisecting rays are perpendicular to each other.

Worksheet 4: Case Study

1. Option b

2. A 9 mm B

3. Angle formed by the shadow = 120°

Measure of angle bisector = 60°

2° = 1 unit

60° = 60° 2° = 30 units

30 units will be equal to 60°

4.

Chapter 9

Worksheet 1

1. One line of symmetry

2. a. Both l1 and l2 b. Both l1 and l2 c. Neither l1 or l2

3. a. b. c. d.

4. H, I, O and X

Challenge 1. The lower right portion is missing a hole towards the centre. We can make it symmetrical by drawing another hole.

Worksheet 2

1. b. 2. a.  b.    c.

d.

3. MOM  4. GOVERNMENT OF INDIA

5. a. MIRROR b. SYMMETRY c. REFLECTION d. MATHEMATICS

6. a.  b.

c.

7. a. 2 b. 6 c. 3 d. 1

8. The logo has 3 angles of symmetry. The angles of symmetry are 120°, 240°, 360°.

Challenge 1. Blue and Yellow  2. 2

Worksheet 3: Chapter Checkup

1. Yes, the figure has one line of symmetry.

Z S 3 D 8 U

3. no line of symmetry 1 line of symmetry more than 1 line of symmetry

Worksheet 4: Case Study

1. Option b  2. Option b 3.

4. a. True b. True c. False d. True

5. a. Yes b. Yes  c. No

6. a.   b.  c. 7.

8. a.  b.

Challenge 1. Option a  2. 2

4. Figures may vary. Sample figure.

Chapter 10

Worksheet 1

1. a. +10 km, −10 km b. −₹1000, +₹1000 c. +5 apples,−5 apples

2.

3. A = −6, B = −9, C = −2, D = 3, E = 6, F = 1  4. a. 16, 18 b. −13, −11 c. 24, 26 d. −89, −87 e. 124, 126  5. −3

6. a. −2, −1, 0, 1, 2, 3 b. −4, −3, −2, −1 c. 2, 3, 4, 5 d. −8, −7, −6, −5 e. −14, −13, −12, −11, −10, −9  7. a. 8  b. 10 c. 25 d. 35 e. 65

8. a. Three places on the left of the number line; –25 b. Six places to the left on the number line; 0 c. Two places on the left of the number line; –36  9. a. > b. <, c. > d. <, e. <  10. a. −10 < −8 < −2 < 5 < 9 b. −11 < −7 < −6 < 16 < 20 c. −15 < −9 < 13 < 14 < 23 11. −7°C < −3°C < 2°C < 5°C < 12°C < 18°C

Challenge 1. 6

Worksheet 2

+ + + + + + + 6

2. a. 10 b. −10

Worksheet 3

Worksheet 4: Chapter Checkup

1. a. + + + + + + + + + + + 11

b.  + + + + + + + 5

2. a. –2 b. 13 c. –8 d. –17 e. 25

3. a. +31°, –5°, +18°, –8° b. Coldest: Sonamarg; Hottest: Chennai

4. E  5. a and d  6. a. −9, −7 b. −27, −25 c. −39, −37 d. 44, 46  7. a. +8 is larger than –16  8. None  9. b 10. a. 11 b. −190  11. Burnt or lost 240 calories  12. 382°F 13. ₹375  14. Manoj obtained 234 marks in the test.

Challenge 1. Descending order = (C – B), (C – D), (D – E), (A – D), (A – E)

2. Option b

Worksheet 5: Case Study

1. Option c

2. Greenland, Russia, Austria, Brazil, Qatar

3. Russia is warmer than Greenland by 14.89°C

4. It gets warmer as the temperature rises because the energy and heat in the environment increases.

Chapter 11

Worksheet 1

1. a. 7; 7,00,000 b. 7; 70,000 c. 9; 90,00,000

d. 1; 1,00,00,000 e. 8; 8,00,00,000 f. 2; 20,00,00,000

2. a. 20,00,00,000 + 4,00,00,000 + 80,00,000 + 5,00,000 + 60,000 + 7000 + 800 + 30 + 5 b. 50,00,00,000 + 6,00,00,000 + 40,00,000 + 2,00,000 + 80,000 + 6000 + 600 + 4 c. 90,00,00,000 + 3,00,00,000 + 20,00,000 + 7,00,000 + 50,000 + 9000 + 100 + 90 + 1

3. a. twenty-three crore thirty-four lakh twenty-six thousand five hundred seventy-eight b. seventy-four crore thirty-six lakh fifty-four thousand six hundred seventy-nine c. forty-six crore fifty-seven lakh sixty-eight thousand nine hundred seventy-nine

4. a. 16,26,92,143 b. 65,22,44,900 c. 80,99,40,201

5. a. No b. 50,00,000; 40,000 c. 49,50,000

6. 27,25,45,619 = 20,00,00,000 + 7,00,00,000 + 20,00,000 + 5,00,000 + 40,000 + 5000 + 600 + 10 + 9 Number name: twenty-seven crore twenty-five lakh forty-five thousand six hundred nineteen 7. sixty-four crore sixty-two lakh seventy thousand

Challenge 1. Smallest 9-digit number = 11,11,13,579

The successor of the number 11,11,13,580

The predecessor of the number 11,11,13,578

Worksheet 2

1. a. Face value = 9, place value = 9,000,000 b. Face value = 2, place value = 200,000,000 c. Face value = 8, place value = 800,000 d. Face value = 8, place value = 80,000,000 e. Face value = 0, place value = 0 f. Face value = 7, place value = 70,000  2. a. 200,000,000 + 40,000,000 + 8,000,000 + 500,000 + 60,000 + 7000 + 400 + 60 + 5 b. 700,000,000 + 80,000,000 + 7,000,000 + 100,000 + 30,000 + 5000 + 400 + 30 + 6 c. 900,000,000 + 30,000,000 + 2,000,000 + 500,000 + 40,000 + 2000 + 100 + 90 + 1

3. a. three hundred forty-five million seven hundred sixty-eight thousand, nine hundred seventy-nine b. Five hundred seventyfive million one hundred twenty-three thousand three hundred eightynine c. nine hundred seventy-eight million seven hundred sixty-four thousand two hundred twenty-four

4. a. 826,120,066 b. 192,504,016 c. 718,710,156

5. a. 100,356,782 < 500,040,367 < 887,210,460 < 931,124,820

b. 360,841,910 < 692,180,350 < 826,020,031 < 927,516,890

c. 500,216,138 < 604,503,821 < 650,241,567 < 945,241,823

6. a. 871,926,345 > 826,374,510 > 670,814,256 > 450,070,921

b. 962,115,108 > 801,210,450 > 678,203,001 > 423,516,789

c. 967,208,891 > 788,216,134 > 578,206,010 > 543,343,867

7. a. Greatest 9-digit number = 98,75,43,210, smallest 9-digit number = 10,23,45,789 b. Greatest 9-digit number = 87,65,43,210, smallest 9-digit number = 10,23,45,678 c. Greatest 9-digit number = 98,76,54,321, smallest 9-digit number = 12,34,56,789

8. a. Greatest 9-digit number = 88,76,54,210, smallest 9-digit number = 10,24,56,788 b. Greatest 9-digit number = 99,87,65,431, smallest 9-digit number = 13,45,67,899 c. Greatest 9-digit number = 99,75,43,210, smallest 9-digit number = 10,23,45,799

Challenge 1. The number is 953,286,714

Worksheet 3

1. a. i. 40,540 ii. 94,270 iii. 2,54,770 iv. 20,45,540

b. i. 8,09,800 ii. 23,98,800 iii. 3,80,08,000 iv. 89,74,53,500

c. i. 4,90,000 ii. 31,41,000 iii. 1,03,09,000 iv. 30,47,58,000

2. a. 13,500 b. 1,12,800 c. 3700 d. 55,700 e. 2,00,000 f. 6,18,80,000 g. 7 h. 4.4  3. About ₹2000

Challenge 1. 50,020  2. 5,67,785 and 5,67,794

Worksheet 4

1. a. 5,55,181 b. 56,26,226  c. 12,05,568 d. 1,00,14,961

2. a. 21,90,63,480 b. 3,89,45,160  c. 21,92,866  d. 1,09,77,634

3. a. 932 b. 239 c. 1245 d. 133

4. 48,35,858

5. a. 2 2 2 7 5 0 2 + 7 2 8 1 2 2 8 0 = 7 5 0 3 9 7 8 2

6. 19,58,996  7. 1,80,87,09,200

8. Ajay travels a distance of 1,86,850 m in 5 days.

9. 16,20,73,000 km

Challenge 1. 4,02,304; 4,01,804

Each number is first decreasing by 1000; then increasing by 500.

2. a. (6 + 5) × 3 – 1 = 32 b. 3 + 4 × (8 – 4) = 19

c. 10 × (8 – 4) + 1 + 5 = 46

Worksheet 5: Chapter Checkup

1. a. Indian system: 35,04,27,681 = thirty-five crore four lakh twentyseven thousand six hundred eighty-one, 30,00,00,000 + 5,00,00,000 + 4,00,000 + 20,000 + 7000 + 600 + 80 + 1

International system: 350,427,681 = three hundred fifty million, four hundred twenty-seven thousand, six hundred eighty-one, 300,000,000 + 50,000,000 + 400,000 + 20,000 + 7000 + 600 + 80 + 1

b. Indian system: 42,08,79,502 = forty-two crore, eight lakh, seventynine thousand, five hundred two, 40,00,00,000 + 2,00,00,000 + 8,00,000 + 70,000 + 9000 + 500 + 2

International system: 420,879,502 = four hundred twenty million, eight hundred seventy-nine thousand, five hundred two, 400,000,000 + 20,000,000 + 800,000 + 70,000 + 9000 + 500 + 2

c. Indian system: 63,56,58,421 = sixty-three crore fifty-six lakh fiftyeight thousand four hundred twenty-one, 60,00,00,000 + 3,00,00,000 + 50,00,000 + 6,00,000 + 50,000 + 8000 + 400 + 20 + 1

International system: 635,658,421 = six hundred thirty-five million, six hundred fifty-eight thousand four hundred twenty-one, 600,000,000 + 30,000,000 + 5,000,000 + 600,000 + 50,000 + 8000 + 400 + 20 + 1

d. Indian system: 90,15,00,084 = ninety crore, fifteen lakh, eightyfour, 90,00,00,000 + 10,00,000 + 5,00,000 + 80 + 4

International system: 901,500,084 = nine hundred one million five hundred thousand eighty-four, 900,000,000 + 1,000,000 + 500,000 + 80 + 4

2. a. 460,722,239 b. 63,12,58,143 c. 8,09,50,062 d. 100,100,039  3. a. > b. > c. < d. =

4. a. 19,08,04,365 < 67,23,56,475 < 68,91,63,896 < 76,90,87,687 b. 324,335,678 < 435,406,576 < 676,162,895 < 676,817,980 c. 65,45,12,845 < 65,78,15,325 < 87,12,63,256 < 97,12,36,125

5. a. Ten: 7,65,380; 65,410; 57,67,880; b. Hundred: 2,34,600; 43,300; 1,23,35,000; c. Thousand: 9,03,000; 83,000; 47,70,000;

6. a. 73 b. 5760 c. 4440 d. 53  7. a. 28,11,555 b. 55,03,319 c. 24,63,05,750 d. 2,27,093 e. 57,724 f. 77,587  8. 444,777,888; International number system: four hundred forty-four million, seven hundred seventy-seven thousand, eight hundred eighty-eight; Indian number system: 44,47,77,888 = forty-four crore forty-seven lakh seventy-seven thousand eight hundred eighty-eight 9. 9,24,000 books

10. Greatest 9-digit number: 98,65,43,210, smallest 9-digit number: 10,23,45,689; Greatest 9-digit number (except 0): 99,86,54,321, smallest 9-digit number (except 0): 11,23,45,689

Ascending order: 10,23,45,689 < 11,23,45,689 < 98,65,43,210 < 99,86,54,321

Descending order: 99,86,54,321 > 98,65,43,210 > 11,23,45,689 > 10,23,45,689

11. a. 5,84,850 tons b. 3,89,900 tons c. 9,74,750 tons

Challenge 1. Option c  2. 1,00,000 times

Worksheet 7: Case Study

1. 84,38,000

2. a. True   b. True

3. 65,67,686 tonnes

4. 27,98,950 tonnes.

5. Four million, one hundred sixty-five thousand Chapter 12

Worksheet 1

1. a. ii b. ii c. i d. ii  2. a. Cuboid b. Cylinder c. Cone

d. Cube  3. a. cylinder b. cube c. 5 d. cube, square pyramid  4. 5 faces, 8 edges and 5 vertices. 5. Cuboid. 6 faces, 12 edges and 8 vertices.

6. a. Cuboid b. Hexagonal pyramid c. Cone d. Octagonal pyramid e. Pentagonal prism

Challenge 1. Heptagonal pyramid.

Worksheet 2

1. a. Hexagonal pyramid b. Triangular pyramid c. Cube d. Cylinder  2. a. sphere b. 3 c. 5 d. 1, 4

3.

4. Answer may vary. Sample answer: a.  b.  c.  d.

5. Answer may vary. Sample answer: a.  b.  c.  d.

6. Triangular pyramid  7. Triangular prism

Challenge 1. 9 faces, 16 edges and 9 vertices.

Worksheet 3: Chapter Checkup

1. a. 6 faces, 10 edges, 6 vertices b. 6 faces, 12 edges, 8 vertices  c. 2 faces, 1 edge, 1 vertex d. 10 faces, 24 edges, 16 vertices

2. a. 10, 6 b. 8 c. 21  3. a. Cone  4. a. Total number of faces = 6; 4 rectangular, 2 square shaped b. Total number of faces = 8; 7 triangular, 1 heptagon shaped c. Total number of faces = 8; 6 parallelograms, 2 hexagons

5. a. Red   b. Grey

6. Answer may vary. Sample answer:

7.  Answer may vary. Sample answer:

8. Triangular pyramid Cone Cylinder Square pyramid

9. a. Octagonal pyramid b. Cube c. Pentagonal pyramid d. Pentagonal prism

Challenge 1. Option a     2.

Worksheet 4: Case Study

1. Option a     2. 3. Option d

4. All 6 rectangular faces in a rectangular prism, and only 1 rectangular face in a rectangular pyramid.

5. Answers may vary. Sample answer: The community centre can make the shed environmentally friendly by using recycled materials for building it.

Chapter 13

Worksheet 1

1.  a. 1.3 1 2 1.3

2. a. 606.46 b. 39.087 c. 840.201 d. 1248.16

3. a. 6 25 b. 59 100 c. 13 20 d. 1 8 e. 9 40 f. 64 125

4. A = 0.8, B = 1.4, C = 3.4, D = 4.6

5. a. 3 6 25 b. 5 3 25 c. 2 13 250

6. a. 1.540 and 15.021 b. 54.000 and 48.021 c. 1.10 and 4.65  d. 18.054 and 97.000  7. a. 15.41 b. 178.2 c. 12.825 d. 15.51

8. a. 7.23 < 7.3 < 8.32 < 8.37 b. 58.37 < 58.45 < 58.54 < 58.73

c. 97.08 < 97.18 < 97.2 < 97.8 d. 18 < 18.1 < 18.101 < 18.11

9. a. 3.068 kg, 14.05 kg, 5.005 kg, 0.725 kg, 0.045 kg b. 4.015 km, 8.04 km, 3.004 km, 0.75 km, 0.015 km

Challenge 1. 8.7 inches

Worksheet 2

1. a. 24.62 b. 62.34 c. 11.097

2. a. 2.5 b. 1.72 c. 0.229  3. a. > b. = c. <

4. a. 123.91 b. 172.11 c. 810.907 d. 99.871 e. 41.363 f. 76.163

5. 15.45 mm  6. 32.545 g

Challenge 1. The extra weight was the weight of the container.

Worksheet 3

1. a. 204.8 b. 113.4 c. 1729

2. a. 6.36 b. 61.1 c. 631.113

3. a. 15.2 b. 23.9 c. 41.3

4. a. 2.3  b. 8.9 c. 12.6

5. 20.88 sq. feet

Challenge 1. c. Both statements together are enough to answer the question, but neither statement alone in enough.

Worksheet 4: Chapter Checkup

4. a. 5 + 0.2 + 0.03 or 5 + 2 10 + 3 100

b. 10 + 2 + 0.05 + 0.006 or 10 + 2 + 5 100 + 6 1000

c. 500 + 7 + 0.6 + 0.03 + 0.003 or 500 + 7 + 6

5. a. 45.5 b. 18.125 c. 12.6  6.

+ 3

7. a. 15.1 > 15.05 > 15 > 14.95 b. 1.331 > 1.303 > 1.23 > 1.2  c. 153.32 > 153.233 > 153.23 > 152.1  8. a. 3.055 b. 0.286  c. 8.04 d. 82.06 e. 280.84 f. 2427.505  9. Nina

Challenge 1. ₹62.5  2. Type A = 53; Type B = 7  3. Option c

Worksheet 5: Case Study

1. b. 1.52 AU  2. b. 1.39 AU  3. 4.20 AU

4. Venus (0.72 AU), Mars (1.52 AU), Uranus (19.22 AU), Neptune (30.05 AU)

Chapter 14

Worksheet 1

1. a. 2n; 36 b. 3n; 54 c. 5n + 1; 91  d. 5n − 2; 88

2. a. 3n; 150

b. 7n; 350

3. a. 2n + 1 b. 3n + 2 4. Hours 1 2 3

7 8 Cupcakes 10 20 30 40 50

80 10n; 240 cupcakes

5. A = l × b

Challenge 1. 7a

Worksheet 2

1. a. Arithmetic expression  b. Algebraic expression   c. Algebraic expression  d. Algebraic expression

2. a. x and y b. 2a, 3b, –c c. x, y, 2z d. x, –6z e. 2x, 5

f. 4 3 x, 2 g. 5abc, –2ab, 7ac h. 2ab, 4ac, –6c  3. a. 3 + 6m

b. n – 10 c. 15x  d. 2xy e. 9y + 1 f. 3y + (x – 3)

4. a. 24 b. −11 c. −154 d. 1 4 5. 12u; 156  6. x + 7

Challenge

1. a.  k 10 k + 10

b.  9 k k k k k k k k k k

d.  k 4 k

Worksheet 3

1. a. x + 3 = 12 b. x – 7 = 2 c. 2x – 7 = 3 d. 4x + 2 = 26

2. X + 3 x + 8 = 3 4 3. 6x = 72

4. Answers may vary. Sample answers: a. When we add 5 to the product of 4 and a number, we get 9. b. When we add 1 to twice a number, we get 5. c. When 7 is taken away from the product of 12 and a number, we get 5. d. Three times the sum of a number and 1 gives 12.  5. a. 4 b. 3 c. 15 d. −11 e. 5 f. 4

Challenge 1. The numbers are 56, 64 and 72.

Worksheet 4: Chapter Checkup

1. a.

Rule: 4n

b.  Rule: 4n + 2

2. 0 + x = x = x + 0  3. a. 3x + 4 b. 2y – 2 c. x 3 – 4 d. 6 + y 5

4. a. Linear b. Non-Linear c. Linear

5. a. 78 b. 66 c. 128 d. 416  6. a. (6x – 5) cm b. 6 cm

7. Statements may vary. Sample statements. a. Raj has some money and after receiving ₹30, he has a total of ₹50. How much money does he have originally?; 20 b. Six times a number reduced by 3 gives 9. What is the number?; 2  8. 25 marbles 9. 2x + 4; 3x + 4

Challenge 1. Option a  2. 15 years

Worksheet 5: Case Study

1. Option b

2. ₹420

3. D = 2C

4. The quantity has to be 10.

Chapter 15

Worksheet 1

1. a. False b. True c. True d. False e. False

2. a. 2:3 b. 2:3 c. 2:1 d. 100:3 e. 1:1 f. 1:1

3.  Answer may vary. Sample answer: a. 10:14, 15:21, 20:28

b. 8:18, 12:27, 16:36 c. 24:32, 36:48, 48:64 d. 12:30, 18:45, 24:60 e. 16:22, 24:33, 32:44 f. 18:34, 27:51, 36:68

4. a. > b. > c. < d. < e. < f. = 5. a. 15:1 b. 18:5 c. 46:37 d. 3:20 6. 16:24  7. 20:60  8. a. 15:10 b. 5:15 c. 10:20

9. 1:10

Challenge 1. 1.4 times

Worksheet 2

1. a, c, d,  2. a. False b. True c. True d. True

3. Answer may vary. Sample answer: a. 3:13::9:39 b. 7:42::3:18 c. 7:21::4:12 d. 2:14::8:56

4. a. 4 b. 18 c. 8 d. 4 5. a. 3 b. 3 c. 2 d. 6

6. a. 1 b. 8 c. 81 d. 49 7. 15 8. 27

Challenge 1. Riyaʹs opponent

Worksheet 3

1. a. ₹180  2. 4 hours  3. 60 postcards  4. 9 months

5. 4℃  6. 25 buses

Challenge 1. 9.9 cups

Worksheet 4: Chapter Checkup

1. a. 45:32 b. 66:143  2. a. 8:7 b. 6:7 c. 20:3

3. Answers may vary, sample answer: a. 6:16, 9:24, 12:32, and 15:40 b. 10:18, 15:27, 20:36, and 25:45 c. 22:30, 33:45, 44:60, and 55:75  4. a. < b. < c. <  5. b, c 6. 2:3  7. 72  8. 16 9. ₹90  10. 45  11. 8:1

Challenge 1. ₹2400 2. Option a

Worksheet 5: Case Study

1. a. 30  2. a. 5  3. 3:1  4. True

5. We should observe wildlife from a distance, avoid disturbing their natural habitats, follow park rules and regulations, and learn about conservation efforts to protect these animals and their environments.

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 978-81-982034-9-6