Have you ever shared a chocolate with your friend? Or divided a pizza among family members?
When we share things equally, we are actually using the concept of fractions!
In this chapter, we will learn about sharing and measuring things by dividing them into equal parts. We will explore how to identify and create halves, quarters, and other fractions, and understand how these concepts apply in our daily lives.
Parts and Wholes
Let’s begin with a story about two sisters, Ikra and Samina, who needed to share a drawing sheet.
Ikra and her little sister, Samina, decide to make a drawing, but they are left with a single drawing sheet. Ikra wants to share the paper by dividing it in half, but Samina insists on having a bigger part of the paper. Ikra thought for a moment and proposed a solution.
What Samina didn’t realize was that one half and two quarters are actually the same amount!
This is one of the fascinating things about fractions that we’ll learn in this chapter.
So let’s dive into the world of fractions and discover how sharing and measuring help us understand the parts that make up a whole!
When an object is divided into two equal parts, each part is called a half. We write half as 1/2. Some are divided into halves correctly, and some are not. Can you identify in below image which ones are divided into halves correctly?
For a shape to be divided into halves correctly, the two parts must be exactly equal in size and shape.
When you fold one part over the other, they should match perfectly.
Yes, all shapes can be correctly halved.
Understanding Quarters
When an object is divided into four equal parts, each part is called aquarter. We write quarter as 1/4.
Each shape, given alongside, is divided into 4 equal parts. One out of the 4 equal parts is shaded. Each shaded part of the shape is one-fourth of the whole.
Try yourself:
What is each part called when an object is divided into two equal parts?
A.Third
B.Whole
C.Half
D.Quarter
View Solution
Many Ways to Make Halves and Quarters
Making Halves
Students are asked to fold or cut a rectangular paper into two equal parts — called halves. This helps children understand that:
A half means dividing a shape into 2 equal parts.
There is more than one way to do it — horizontally, vertically, or even diagonally.
No matter how it’s folded, the goal is always to get two equal parts of the whole.
A rectangular paper can be divided into two equal parts (halves) in several different ways:
Vertical Division: Drawing a vertical line down the middle
Horizontal Division: Drawing a horizontal line across the middle
Diagonal Division: Drawing a diagonal line from one corner to the opposite corner
All these methods create two equal parts, so they all correctly divide the rectangle into halves.
Making Quarters
Students are asked to draw or fold the paper in five different ways to get ¼ (one-fourth) parts. See that the same rectangle can be split in many ways, yet all parts must be equal.
This introduces students to the fraction ¼, helping them understand that a quarter means one out of four equal parts.
DING DONG BELL!!
Sumedha’s mother gives her and Vinayak one dhokla (a yummy snack) and says to share it.
They cut it into 2 equal parts. Each one gets ½ (one-half) of the dhokla. 2 halves make one whole dhokla.
Now Kumar arrives, so they need to share again.
They divide the dhokla into 3 equal parts. Each one gets ⅓ (one-third) of the dhokla. 3 one-thirds make one whole dhokla.
Sumedha’s cousin Paridhi comes. Time to share again!
They cut the dhokla into 4 equal parts. Each one gets ¼ (one-fourth) of the dhokla. 4 one-fourths make one whole dhokla.
Now Idha joins! More friends, smaller pieces.
They divide the dhokla into 5 equal parts. Each one gets ⅕ (one-fifth) of the dhokla. 5 one-fifths make one whole dhokla.
Idha says she doesn’t want her piece and gives it to Sumedha!
Sumedha had ⅕ and got one more ⅕ from Idha. So now she has ⅕ + ⅕ = 2⁄5 of the dhokla.
This story teaches us about fractions through sharing dhokla. As more friends join, the dhokla is divided into more equal parts—like halves, thirds, fourths, and fifths. We learn that:
A fraction is a part of a whole.
More people means smaller pieces.
Fractions can be added.
Try yourself:
What do we call each part when an object is divided into four equal parts?
A.Fifth
B.Half
C.Quarter
D.Third
View Solution
My Flower Garden
Idha has seeds of 5 different flowering plants—Rose, Mogra, Lily, Marigold, and Jasmine. She decides to plant them equally in her garden. That means each flower will take up 1 out of 5 parts, or 1/5 of the total garden space.
Initial Plan:
Each of the 5 plants gets 1/5 of the garden:
Rose = 1/5
Mogra = 1/5
Lily = 1/5
Marigold = 1/5
Jasmine = 1/5
Revised Plan:
Idha has very few Lily seeds, so she decides not to plant Lily and instead uses that space to plant Roses again.
Now, the garden looks like this:
Rose = 2 parts → 2/5 of the garden
Mogra = 1/5
Marigold = 1/5
Jasmine = 1/5
Lily is no longer planted.
From the final layout:
Mogra = 1/5
Marigold = 1/5
Jasmine = 1/5
Rose = 1/5 + 1/5 = 2/5
So, each part of the garden represents a fraction of 1/5, and combining parts gives larger fractions like 2/5.
Comparing Fractions
Sometimes we need to compare fractions to determine which one is larger or smaller.
Let’s learn how to compare fractions.
When comparing fractions, we use symbols like:
“>” means “greater than”
“<” means “less than”
“=” means “equal to”
Let’s look at an example comparing 1/4 and 1/2:
We can see that 1/2 covers more area than 1/4, so 1/2 > 1/4.
Answer: 1/2, 1/3, 1/4
Note: When comparing fractions with the same numerator (the top number), the fraction with the smaller denominator (the bottom number) is larger.
Let Us Find Fractions in Our Surroundings
Fractions are everywhere around us! Let’s explore some everyday situations where we can find and use fractions.
Kadamba is excited to know where we use fractions in daily life. She found some examples below. Help her find more examples and try to draw the images of the same in your notebook.
Examples of Fractions in Daily Life:
Food: When we divide a pizza into 8 slices, each slice is 1/8 of the whole pizza.
Time: Half an hour is 1/2 of an hour, and 15 minutes is 1/4 of an hour.
Money: 50 paise is 1/2 of one rupee, and 25 paise is 1/4 of one rupee.
Measurements: Half a meter is 1/2 of a meter, and 250 ml is 1/4 of a liter.
Some Solved Examples
Example 1:There are 12 cookies. What fraction of cookies will each child get if there are 3 children?
Sol: Total number of cookies = 12
Number of children = 3
Number of cookies each child will get = 12 ÷ 3 = 4
Fraction of the total cookies each child will get = 4/12 = 1/3 (after simplifying)
Example 2: Fill in the with < or >.
Example 3: Arrange the following fractions in ascending order.
(a) Since, 1 < 3 < 5 < 6 < 7. The fraction with the smaller numerator names the smaller fraction.
Here, the fractions in ascending order are
(b)The fraction with the greater denominator names the smaller fraction.
Here, the fractions in ascending order are
Example 4: A chocolate bar is cut into 5 equal parts. Arjun eats 2 parts and then eats 1 more. What fraction of the bar did he eat?
Sol: First he ate = 2/5
Then he ate = 1/5
Total eaten = 2/5 + 1/5 = 3/5
Example 5: Raj got 6 out of 12 questions correct in a quiz. What fraction of questions did he get right? Simplify the answer.
In this chapter, we will explore the fascinating world of large numbers, particularly focusing on thousands and how they relate to our daily lives. From counting people at community events to understanding place values, we’ll discover how numbers beyond 1000 are represented in the Indian number system.
Thousand Waterfall
Thousands of water droplets make up this magnificent waterfall – an example of thousands in nature
Let’s begin with a practical example!
Jaspreet and Gulnaz are organizing a langar (community lunch) at their neighborhood Gurudwara.
They expect around one thousand (1000) people to attend.
Throughout the event, they keep track of how many people come at different times: 52 people, 145 people, 325 people and 508 people.Community lunch organised by Jaspreet and Gulnaz
By the end of the day, they need to count how many people in total were served food.
This requires understanding how to work with numbers in the hundreds and thousands.
Place Value System
The Indian number system, which was discovered in India around 2000 years ago, allows us to write all numbers using just ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This system is now used around the world!
A place value chart helps us see how much each digit in a number is worth based on where it is located.
In the Indian system, numbers are grouped into hundreds, thousands, lakhs, crores, and so on. Here’s a breakdown:
Units: The first three digits from the right are the units, tens, and hundreds.
Thousands: The next two digits are the thousands.
Lakhs: The next two digits are the lakhs.
Crores: The digits after lakhs are the crores.
Indian Place Value Chart
Example 1: How can we break down the number 12,34,567 using the Indian place value system? Sol: We break the number from right to left like this:
Circle as many groups of 10 Ones or 10 Tens as possible. Write the final number against the following pictures.
a)
b)
c)
Try yourself:
What do we call the next two digits after hundreds in the Indian number system?
A.Lakhs
B.Thousands
C.Crores
D.Tens
View Solution
Numbers Beyond 1000 ( One Thousand)
Let’s learn about big numbers — numbers that are more than 1000!
What is 1000?
1000 is made up of:
1 Thousand
0 Hundreds
0 Tens
0 Ones So, 1000 = 1 thousand + 0 hundred + 0 ten + 0 one
We use special blocks called Dienes Blocks to show numbers. But drawing big blocks is hard! So, we use tokens to show the same numbers.
Let’s Make the Number 1001
Look at this:
We have 10 orange tokens of 100 each → 100 × 10 = 1000
And 1 pink token → 1That means: 1000 + 1 = 1001
Let’s Write It in the Place Value Table:
1 Thousand + 0 Hundred + 0 Ten + 1 One = 1001
Comparing Numbers
Comparing numbers means looking at two numbers and finding out which one is greater, smaller, or if they are equal.
We use three special signs to compare:
Greater than ( > ) Example: 7 > 5 (7 is bigger than 5)
Less than ( < ) Example: 3 < 9 (3 is smaller than 9)
Equal to ( = ) Example: 4 = 4 (Both numbers are same)
Let’s compare 3012 and 3102.
Thousands: Both numbers have 3 thousands. So we go to the next digit.
Hundreds:
3012 has 0 hundreds
3102 has 1 hundred
Since 1 hundred is more than 0 hundreds,
So, 3102 > 3012
Try yourself:What do we get when we regroup 10 ones?A.1 TenB.1 HundredC.1 ThousandD.1 OneView Solution
Q1: Compare the numbers 425 and 452. Which one is larger?
Sol: Step 1: Both numbers have 3 digits, so we need to compare the digits.
Step 2: Compare the hundreds digit: Both have 4 in the hundreds place.
Step 3: Compare the tens digit: 2 in 425 and 5 in 452.
Since 5 > 2, we know that 452 > 425.
Therefore, 452 is larger than 425.
Q2: Arrange the numbers 789, 798, 879, 897, 978, 987 in ascending order (smallest to largest).
Sol: Ascending order means arranging numbers from the smallest to the largest.
Let’s arrange these numbers:789, 798, 879, 897, 978, 987
Step 1: Look at the Hundreds PlaceHundreds Place
All numbers start with 7, 8, or 9.
789 and 798 start with 7 → smallest group
879 and 897 start with 8
978 and 987 start with 9 → biggest group
Step 2: Compare numbers within each group
Group starting with 7:
789 < 798
Group starting with 8:
879 < 897
Group starting with 9:
978 < 987
Solved Examples
Example 1: Write the number 1,234 in expanded form and identify the place value of each digit.
Sol: Step 1: Identify the place value of each digit.
1 is in the thousands place
2 is in the hundreds place
3 is in the tens place
4 is in the ones place
Step 2: Write the expanded form by multiplying each digit by its place value.
1 × 1000 = 1000
2 × 100 = 200
3 × 10 = 30
4 × 1 = 4
Step 3: Add all the values to get the expanded form.
1,234 = 1000 + 200 + 30 + 4
Example 2: Arrange the numbers 1,025, 1,205, 1,052, and 1,520 in descending order (largest to smallest).
Sol: Step 1: Compare the thousands digit.
All numbers have 1 in the thousands place, so we need to compare the hundreds digit.
Step 2: Compare the hundreds digit.
1,025 has 0 in the hundreds place
1,205 has 2 in the hundreds place
1,052 has 0 in the hundreds place
1,520 has 5 in the hundreds place
Since 5 > 2 > 0, we know that 1,520 is the largest, followed by 1,205.
Step 3: For numbers with the same hundreds digit (1,025 and 1,052), compare the tens digit.
1,025 has 2 in the tens place
1,052 has 5 in the tens place
Since 5 > 2, we know that 1,052 > 1,025.
Step 4: Arrange all numbers in descending order:
1,520, 1,205, 1,052, 1,025
Example 3: Find the next three numbers in the pattern: 825, 850, 875, …
Sol: Step 1: Identify how the numbers change from one to the next.
From 825 to 850: The number increases by 25
From 850 to 875: The number increases by 25
Step 2: Apply the same pattern to find the next three numbers.
After 875, adding 25 gives us 900
After 900, adding 25 gives us 925
After 925, adding 25 gives us 950
So the next three numbers in the pattern are 900, 925, and 950.
By understanding these concepts, you can confidently work with larger numbers and apply this knowledge to solve real-world problems. Remember, mathematics is not just about numbers; it’s about understanding the patterns and relationships that help us make sense of the world around us.
In this chapter, we will explore the fascinating world of patterns that surround us in our daily lives. From counting objects to arranging money, from identifying even and odd numbers to recognizing patterns in arrangements – patterns are everywhere!
Patterns help us organize information, make predictions, and solve problems more efficiently. They are the building blocks of mathematics and help us understand the world around us. Whether you’re counting coconut trees or arranging coins in groups, patterns make these tasks easier and more fun.
Coconut Trees arranged in a patternCoins in Patterns
Let’s dive into the world of patterns and discover how they shape our understanding of numbers and arrangements!
Let’s Begin with a Story
Let us Count – Raju’s Pattern Adventure
Raju loved to collect and organize things. One day, while helping his grandmother in the kitchen, he noticed something interesting about the way she arranged fruits in a basket.
“Grandmother, why do you always place the fruits in this circular pattern?” Raju asked.
His grandmother smiled and replied, “Patterns help us organize things better, Raju. Look at how I’ve arranged these fruits – one apple in the center, surrounded by eight oranges. This pattern not only looks beautiful but also helps me count them easily.”
Raju was fascinated. He began to notice patterns everywhere – in the arrangement of trees in the garden, in the design of floor tiles, and even in the way his teacher organized students for group activities.
Soon, Raju started creating his own patterns with different objects. He realized that patterns make counting easier and help us understand relationships between numbers.
Just like Raju, let’s explore various patterns in our daily life and learn how they help us understand mathematics better!
Patterns with Money
Money provides an excellent way to understand patterns and practice counting. Let’s explore some interesting money patterns.
Pattern 1: Flower Pattern with Coins
In this pattern, coins are arranged in a flower-like shape with one coin in the center and coins arranged around it.Flower – Shape Pattern
Pattern 2: Rectangle Pattern with Notes and Coins
In this pattern, notes and coins are arranged in a rectangular shape.
Rectangular Shape pattern
Try yourself:
What did Raju’s grandmother say about patterns?
A.They help organize things better.
B.They are only for counting money.
C.They make everything look the same.
D.They are not useful in daily life.
View Solution
Two Ways of Arranging Coins
Shirley and Shiv arranged their coins in the following ways. Let’s examine the number of coins in each arrangement.
Shirley arranged her coins in groups of 3, 5, 7, etc. These are odd numbers.
Shiv’s Arrangement (Even Numbers)
Shiv arranged his coins in groups of 4, 6, 8, etc. These are even numbers.
This arrangement helps us understand the concept of odd and even numbers, which we’ll explore in more detail in the next section.
Even and Odd Numbers
Even Numbers
Look at the number 4 on the left side of the image. There are 4 ice cream cones.
We can divide them into two equal groups:
2 cones in one group
2 cones in the other group
That means 4 is an even number because it can be split equally into two groups with nothing left over.
So, Even numbers are numbers that can be divided into two equal parts.
Examples of even numbers: 2, 4, 6, 8, 10
Odd Numbers
Now look at the number 5 on the right side. There are 5 cupcakes.
When we try to divide them into two groups:
2 cupcakes go in one group
2 cupcakes go in the second group
But 1 cupcake is left over
That means 5 is an odd number because it cannot be split into two equal groups without something being left out.
So, Odd numbers are numbers that cannot be divided equally into two parts.
Examples of odd numbers: 1, 3, 5, 7, 9
Try yourself:
What type of numbers did Shirley use to arrange her coins?
A.Odd numbers
B.Even numbers
C.Prime numbers
D.Fractional numbers
View Solution
Q1: Do you think all numbers in the times-2 table are even?
Sol: Yes, all numbers in the times-2 table are even numbers. This is because when we multiply any number by 2, we are essentially creating pairs, which is the definition of an even number.
For example:
1 × 2 = 2 (1 pair)
2 × 2 = 4 (2 pairs)
3 × 2 = 6 (3 pairs)
4 × 2 = 8 (4 pairs)
5 × 2 = 10 (5 pairs)
Sol: The times-3 table follows a pattern of odd, even, odd, even, and so on:
1 × 3 = 3 (odd)
2 × 3 = 6 (even)
3 × 3 = 9 (odd)
4 × 3 = 12 (even)
5 × 3 = 15 (odd)
This happens because when we multiply an odd number by 3, we get an odd number, and when we multiply an even number by 3, we get an even number.
Q2: Are there more even or odd numbers between 1 and 100?
Sol: Let’s analyze this systematically:
Even numbers between 1 and 100: 2, 4, 6, 8, …, 98, 100
Odd numbers between 1 and 100: 1, 3, 5, 7, …, 97, 99
Counting them:
Even numbers: 2, 4, 6, …, 98, 100 → 50 numbers
Odd numbers: 1, 3, 5, …, 97, 99 → 50 numbers
Therefore, there are an equal number of even and odd numbers between 1 and 100.
Sol: The possible 2-digit numbers are:
16 (which is even because it ends in 6)
61 (which is odd because it ends in 1)
Let’s Try!
This activity helps us understand that a number is even if its last digit is even, and a number is odd if its last digit is odd.
Some Solved Examples
Example 1: Rahul has 5 ₹10 notes, 3 ₹5 coins, and 7 ₹2 coins. How much money does he have in total?
Sol: Amount from ₹10 notes = 5 × ₹10 = ₹50
Amount from ₹5 coins = 3 × ₹5 = ₹15
Amount from ₹2 coins = 7 × ₹2 = ₹14
Total amount = ₹50 + ₹15 + ₹14 = ₹79
Example 2: Sita has 45 candies. She wants to distribute them equally among her friends. Can she distribute them equally among 2 friends? What about 3 friends? Explain your reasoning.
Sol: For 2 friends:
45 ÷ 2 = 22 remainder 1
Since there is a remainder, she cannot distribute them equally among 2 friends.
For 3 friends:
45 ÷ 3 = 15 remainder 0
Since there is no remainder, she can distribute them equally among 3 friends, giving 15 candies to each friend.
This is because 45 is an odd number (not divisible by 2) but is divisible by 3.
Example 3: Observe the given pattern and draw the next three shapes in this pattern.
Sol:
This is an example of a repeating pattern with a cycle of 3 shapes.
Imagine you’re playing a fun game of hide and seek with your best friends at school. You’re hiding under a table, behind the curtain, or maybe inside the cupboard. You’re trying hard not to giggle or make a sound!
Now suddenly, someone finds you! You ask, “How did you see me?!” They smile and say, “I was looking from the top!”
That’s right! Things look very different when we look at them from different sides—from the top, from the front, or from the side. Just like in video games or puzzles, where you have to look at the whole scene carefully to find clues.
This chapter is all about seeing and understanding the space around us in a fun and smart way! You will learn:
The difference between a top view, side view, and front view of the same object. A book may look like a rectangle from the top, but just a line from the side!
Using positions like left, right, top row, middle row, first column, etc., we’ll learn how to describe exactly where something is—just like giving clues in treasure hunts!
How to use and draw maps and follow paths.
Views of Objects
Objects can be seen from different angles: top view, front view, and side view.
The same object looks different depending on the view.
For example, a brick drawn by Mini, Bholu, and Rani looks different because each child drew a different view (top, front, or side).
The top view (Bholu’s drawing) shows the shape from above, the front view (Mini’s drawing) shows the face from the front, and the side view (Rani’s drawing) shows the side of the object.
Example of a 3D Shape:
A 3D shape can be viewed from the top, from the side and from the front and these views can be combined to visualise what the solid looks like. Thus, we see that a cuboid appears to be rectangle, when viewed from any direction. Now, let us see the different views of a car, which is a 3D shape.
Try yourself:
What is a top view of an object?
A.The shape seen from above
B.The face seen from the front
C.The side seen from the left
D.The back seen from behind
View Solution
Identifying Views
Different objects can be recognized by their views.
For example, a tree looks like a circle from the top and a triangle from the front.
Drawings of objects like chairs, tables, pencils, erasers, and bottles show different shapes based on their views.
Example 1:Mini draws her water bottle from three views. Top view: Circle, Side view: Rectangle and Front view: Rectangle.
Ans: Mini’s bottle is shaped like a cylinder. Cylinders look like:
A circle from the top
A rectangle from the front and side
Try it Yourself! Take a matchbox or pencil box and draw it while looking at it from the top, front, and side. Each view gives a different picture!
Understanding Positions in a Grid What is a Grid?
A grid is a table made of rows and columns. It helps us show the position of objects clearly. Each square in the grid has its own place using:
Rows (go left to right)
Columns (go up and down)
We can use grids to give clues, draw objects, and find positions—just like in a game!
In this activity:
One player hides a treasure (thinks of an object in the grid).
The other player tries to find it by following clues and steps like:
“Take 2 steps up and 1 step left.”
“Now you are still 2 steps away!”
Grid Game
Here are the clues given by Rani to fill the grid:
An eraser at the top right corner → That’s Row 3, Column 3
A pencil in the top left corner → That’s Row 3, Column 1
An apple in the middle of the second row and second column → That’s Row 2, Column 2
A water bottle in the third row and second column → That’s Row 1, Column 2
A football is already drawn in the bottom left corner → That’s Row 1, Column 1
You keep following the clues until you reach the treasure!
Grid Game – Treasure Hunt
For Example: Let’s see how Jagat and Mini are playing.
Jagat thinks of a Mango.
Drone Around the School
Gyan brought a drone—a small flying camera—that can take pictures from above. He used it to take a top view of the school, and now his friends can see the whole school from the sky!
The drone helps us see:
Buildings
Playground
Paths and parks
Classrooms and school areas
This is called a top view—it’s like looking down at the school from the sky!
Try yourself:
What shape does a water bottle look like from the top?
A.Circle
B.Rectangle
C.Triangle
D.Square
View Solution
Exploring Paths and Directions
A sight map provides a visual layout of a place, such as a school, showcasing various areas like classrooms, a stage, and a kitchen.
On a map, we can trace different paths to navigate from one location to another, like going from the Grade 4 classroom to the stage.
These paths can differ in length, with some being shorter and more direct than others.
Directions are given using terms like left, right, up, or down to help someone find their way. For example, to get to the mid-day meal kitchen from the entrance, you would turn left and follow the designated path.
It’s important to note that in grid games or maps, diagonal movements are not permitted.
Example 2: Fill in the table below by writing the correct top view and side view for each object:
In this chapter, we will explore the exciting world of shapes that surround us in buildings, objects, and even nature. From your pencil box to the tallest towers—everything is made up of different shapes. But have you ever thought about what makes a cube different from a cylinder, or how a circle is made?
Let’s build with Diksha!
Diksha visited famous monuments in Delhi, like:
India Gate
Qutub Minar
Akshardham
Jantar Mantar …and many more!
She saw how big and beautiful these buildings were.
Now she wants to build a small model of India Gate using her wooden blocks.
What Is a Model?
A model is a small copy of something big — like a mini version of a real building!
You can use shapes like cubes, cylinders, and rectangles to make a building model with blocks.
Let’s Build a Model Using Blocks!
India Gate is made using blocks
1. What parts are in your model? Ans: The model has a roof made of blue and orange blocks, two pillars or walls on the sides, and a base made with green blocks.
2. Why did you choose those parts? Ans: Because the real India Gate also has a big top part like a roof, two tall pillars or sides, and a strong base to stand on.
3. What shapes can you use? Ans: You can use cubes and rectangles for the roof and walls, and square blocks for the base. This model does not use curved shapes like the real India Gate.
4. How is your model similar to the real building? Ans: The model has a large top section like the India Gate, an open space in the middle like the archway, and pillar-like blocks on the sides.
5. How is it different from the real building? Ans: The model is made of colorful plastic blocks instead of stone. It doesn’t have any carvings or small details. It also looks more like a simple house than an actual arch.
Q:What is common in all these bricks? A: They are all solid and mostly shaped like rectangular blocks. They are strong and used to build things.
Understanding Shapes
We are going to learn following things in this chapter which are as follows:
Shapes are figures or objects that have a specific form or outline. They can be flat (2D) or have volume (3D). Shapes are everywhere around us and help us describe the world.
Look around your classroom or home — can you name some objects that have shapes?
Ans: Yes! A clock (circle), a notebook (rectangle), a dice (cube), and a ball (sphere).
1. 2D Shapes (Two-Dimensional)
These are flat shapes with only two dimensions – length and width.
Examples of 2D Shapes:
Examples of 2-D Shapes
1. Circle
Round shape with no corners or edges.
Example: A coin.
2. Square
Four equal sides and four right angles.
Example: A chessboard square.
3. Rectangle
Opposite sides are equal, with four right angles.
Example: A book cover.
4. Triangle
Three sides and three corners.
Example: A slice of pizza.
2. 3D Shapes (Three-Dimensional)
These shapes have three dimensions – length, width, and height.
Examples of 3D Shapes:
1. Cube:
All sides are squares.
It has 6 faces, 12 edges, and 8 corners (vertices).
Example: Rubik’s cube.
2. Sphere:
No edges or corners.
It’s perfectly round in all directions.
Example: Soccer ball.
3. Cylinder:
Two identical flat circular ends and one curved side.
It has 2 edges and no corners.
Example: Soup can.
4. Cone:
One circular base and a single vertex (point).
It has 1 edge.
Example: Party hat.
5. Rectangular Prism (Cuboid):
Faces are rectangles.
It has 6 faces, 12 edges, and 8 vertices.
Example: brick.
Try yourself:
What type of shapes are flat and have only length and width?
A.3D Shapes
B.2D Shapes
C.Geometric Shapes
D.Angles
View Solution
Sorting 3D Shapes
3D shapes, unlike 2D shapes, have depth in addition to height and width. This extra dimension gives 3D shapes their unique properties and allows them to occupy space. Let’s delve into the different types of 3D shapes and their characteristics.
1. Cube
A cube is a 3D shape that has 6 faces, all of which are squares.
It has 8 corners (also known as vertices) where the edges meet.
A cube also has 12 edges, which are the lines where two faces meet.
Some examples of a Cube shape are:
2. Cuboid
A cuboid is similar to a cube but has 6 faces that are rectangles.
It also has 8 corners and 12 edges, just like a cube.
A cuboid is also known as a rectangular prism.
Some examples of Cuboid are:
3. Triangular Prism
A triangular prism has 5 faces, 2 of which are triangles and 3 are rectangles.
It has 6 corners and 9 edges.
Some examples of Triangular Prism are:
4. Square Pyramid
A square pyramid has 5 faces, with 1 square base and 4 triangular faces.
It has 5 corners and 8 edges.
Some examples of Square Pyramid are:
5. Triangular Pyramid
A triangular pyramid, also known as a tetrahedron, has 4 triangular faces.
It has 4 corners and 6 edges.
Some examples of Triangular Prism are:
Try yourself:
What shape has 6 faces that are all squares?
A.Cube
B.Cuboid
C.Triangular Prism
D.Square Pyramid
View Solution
6. Sphere
A sphere has 1 curved face and no edges or corners.
Some examples of Sphere are:
7. Cylinder
A cylinder has 2 flat circular faces, 1 curved face, and 2 edges where the curved face meets the circular faces.
Some examples of Cylinder are:
8. Cone
A cone has 1 flat circular face, 1 curved face, and 1 edge where the curved face meets the circular face.
Some examples of Cone are:
What’s the difference between a prism and a pyramid?
A prism has two same-shaped flat faces (top and bottom).
A pyramid has only one flat base, and all sides are triangles that meet at a point.
Parts of 3D Shapes
1. Face
A face is a flat surface on a 3D shape.
In the image, the square labeled “face” is one of the cube’s flat sides.
2. Edge
An edge is the line where two faces meet.
In the image, the arrow labeled “edge” points to one such line between two faces.
3. Vertex and Vertices
A vertex is a point where three edges meet. It is also known as a corner.
The green dots in the image show the vertices.
When there is more than one corner, we use the word vertices.
As you can observe, the faces of a cube and cuboid are flat, whereas a cylinder, cone and sphere have curved faces.
Now, let us find out how many faces, edges and corners does each shape have. For a cube and cuboid, pick up a die and a geometry box and count the number of faces, edges and corners. You will notice that both the cube and cuboid have 6 faces, 12 edges and 8 corners.
Now, from the figure given above, try to count the same for cone, cylinder and sphere. You will find that: A cylinder has 3 faces (2 flat, 1 curved), 2 edges and 0 corners. A cone has 2 faces (1 flat, 1 curved), 1 edge and 1 corner. A sphere has only 1 curved surface.
Euler’s Formula. This formula describes the relationship between the number of faces (F), corners (V), and edges (E) in many 3D shapes. For convex polyhedra, the formula is F + V – E = 2. This mathematical relationship helps in understanding the properties of 3D shapes.
Try yourself:
How many edges does a cylinder have?
A.2
B.3
C.0
D.1
View Solution
Nets of 3D Shapes
A net is a two-dimensional layout that can be folded to form a three-dimensional shape. It shows how the surfaces of a 3D object are connected.
Example. The net of a cube consists of 6 squares, which when folded along the edges, form the faces of the cube. Similarly, the net of a cuboid is made up of 6 rectangles that fold to create the rectangular faces of the cuboid.
Take a die or any other cube and trace all its faces on a sheet of paper. What is the shape of all the six faces? They are all squares of the same size. Thus, you see that a cube can be made from six squares joined together in a particular manner.
We have many more nets (arrangements of these squares) that can be folded up to form a cube. We can also form nets with 5 square faces. In this case it will be a box with no lid.
When Lines Meet
An angle is made when two lines meet at a point. This point is called the corner or vertex.
Angles are found in every shape we see — from the chair you sit in the house to the corner of your book!
Right Angle: An angle that measures 90 degrees, resembling the corner of a square.
Acute Angle: An angle smaller than a right angle.
Obtuse Angle: An angle larger than a right angle.
Shapes with Straws
Triangles: Shapes with three sides that can have acute, right, or obtuse angles.
Similarly you can try with Rectangular shape.
Q: What result we will get?
Ans: All corners in a rectangle are right angles.
Let’s Summarise:
Try yourself:
What shape do all six faces of a cube have?
A.Squares
B.Rectangles
C.Pentagons
D.Triangles
View Solution
Sorting Shapes
By Faces: A face is the flat surface of a 3D shape. Just like how a dice has 6 flat sides, each flat side is called a face.
By Edges: An edge is where two faces meet. It’s like the corner of a box or the side of a triangle.
By Angles: An angle is where two lines or edges meet. Angles are found in flat (2D) shapes like triangles and rectangles.
Some Solved Examples
Q1: Mira sees a coin, a book, and a pizza slice. What shape is each one?
Ans:
A coin is a circle(round with no corners).
A book is a rectangle (opposite sides equal).
A pizza slice is a triangle (3 sides and 3 corners).
Q2:Which of these shapes has a curved surface: cube, cone, or sphere?
Ans: Cone and sphere have curved surfaces. A cube has only flat faces.
Q3:A cuboid has 6 faces, 8 corners, and 12 edges. Does it follow the rule: Faces + Vertices – Edges = 2?
Tick the question that is the most appropriate for finding the ‘most liked subject’?
Ans:
Why do you think so? Discuss with your friends and teacher.
Ans: Do it Yourself!
Anjali and Rohan recorded the children’s answers (responses) to the above question as follows: They wrote M for Mathematics, L for Languages, T for The World Around Us, A for Arts and P.E. for Physical Education.
Look at the children’s responses above and answer the following questions:
The number of children who like Mathematics the most is _____________ .
The number of children who like Language the most is ____________ .
The number of children who like The World Around Us the most is ___________ .
The number of children who like Physical Education the most is ___________ .
The number of children who like Arts the most is _____________ .
Ans:
The number of children who like Mathematics the most is 10.
The number of children who like Language the most is 8.
The number of children who like The World Around Us the most is 7.
The number of children who like Physical Education the most is 11.
The number of children who like Arts the most is 9
Page No. 205
Let’s fill the above information in this table. Ans:
Q: Now look at the above table and answer the following questions:
What is the most common favourite subject among the children? ________________
What is the least common favourite subject among the children? ________________
Ans:
The most common favourite subject is Physical Education (P.E.) with 11 children choosing it.
The least common favourite subject is The World Around Us with 7 children choosing it.
There are the following two ways to display the information.
Which way of displaying information is easier to understand and why? ____________ Ans: The table (option 2) is easier to understand because it clearly shows the number of children for each subject in an organized way. It is simple to compare the numbers directly, unlike the list (option 1), which requires counting each response.Page No. 206
Colourful Golas
During school lunch break children rush to eat gola of their favourite colour.
Rohan and Anjali record the golas eaten by different children. They want to eat the one that is most eaten by others.
They both start recording the golas eaten by the children.
Look at the information given above. Colour the line drawing of the golas appropriately. Q1: Which colour ice gola do the children eat: (a) the most (b) the least Ans: (a) The most: Yellow colour ice gola (b) The least: Blue colour ice gola How do you know? I counted the golas for each colour. Yellow has the highest count (10), and blue has the lowest count (5).
Q2: Which colour gola would Anjali and Rohan have bought? Ans: Anjali and Rohan would have bought the yellow colour gola because it is the most popular.
Q3: Which colour golas did boys eat the most? Ans: Boys ate the most yellow colour golas.
Q4: Which colour golas did girls eat the most? Ans: Yellow
Q5: Which of the ways of representing data did you use to answer these questions and why? Ans: I used the pictures of golas to count how many of each colour were eaten by Rohan and Anjali. This way was easy because I could see and count the golas directly to find the most and least eaten colours.Page no. 207
Activity – Chess or Cricket
Find out from your classmates how many of them play only chess, only cricket, both or neither.
Now let us organise the above data in the table.
Ans: Example done for students.
Answer these questions based on the data collected from your grade.
Q1: Who plays Chess the most? (Boys/Girls) Ans: Add the number of children who play:
Only Chess and
Both Chess and Cricket
For Girls: 5 (only Chess) + 2 (both) = 7 girls For Boys: 3 (only Chess) + 5 (both) = 8 boys So the answer is: Boys
Q2: Who plays Cricket the most? (Boys/Girls) Ans: Add those who play:
Only Cricket and
Both games
For Girls: 4 + 2 = 6 girls For Boys: 6 + 5 = 11 boys So the answer is: Boys
Q3: How many children play both types of games? Ans: Just add the “Both” row:
Girls: 2
Boys: 5
Total: 2 + 5 = 7 childrenPage No. 208
Bal Mela
Anjali and Rohan have recorded the number of people who ate fruit chaats and sandwiches in the Bal Mela over three days, using a Pictograph.
Let us Do
Q1: Complete the table.
Ans:
Q2: On which day were the most sandwiches sold? Ans: Day 3
Q3: Which item had the highest sale on Day 2? Ans: Sales of fruit chaats on day 2 = 12 Sales of sandwiches on day 2 = 16 The difference in the sales of both items = 16 – 12 = 4. Hence, sandwiches had the highest sale on day 2.
Q4: Complete the table given below. Circle the day that had the highest sales. Ans:
Q:Fill the yellow boxes with 1-digit numbers (multiplicands and multipliers) such that you get the products given in the white boxes.
Fill the remaining white boxes with appropriate products.
Ans:
Q: The product of the numbers in each row is given in the orange boxes. The product of the numbers in each column is given in the blue boxes. Identify appropriate numbers to fill the blank boxes.
Ans:
Times 10
Q: Match each problem with the appropriate pictorial representation and write the answer. Ans:
Q: How many pebbles are there in this arrangement? _______
This is a 5 × 15 arrangement. There is an easy way to find this product by splitting the arrangement. Ans: Let’s break it down: 5 × 15 can be split as 5 × 10 and 5 × 5. 5 × 10 = 50 5 × 5 = 25 Now add them: 50 + 25 = 75 pebbles. So, the blanks are filled as: 5 × 15 = 5 × 10 and 5 × 5 = 50 + 25 = 75 pebbles.
Page 186
Recall the times-tables that we created in Grade 3. Now construct a times-15 table. You may use the arrangement given below and split the columns into 10 and 5 for ease of counting, as shown on the previous page.
Q1: What patterns do you see in this table? Ans: Each answer is 15 more than the last:
Start at 15, then 30, 45, 60, 75, …
1 × 15 = 15, the number of pebbles in the first row. 2 × 15 = 15 + 15 = 30 i.e., the number of pebbles in the both first and second row 3 × 15 = 15 + 15 + 15 = 45, i.e., the number of pebbles in the first three rows
The last digit alternates between 5 and 0:
15 (5), 30 (0), 45 (5), 60 (0), …
Q2: Compare the times-15 table with the times-5 table. What similarities and differences do you notice?Ans:
Similarity:
1. They follow a pattern:
In the 5-times table, numbers go up by 5 each time.
In the 15-times table, numbers go up by 15 each time.
2. Increae in the difference
The subtraction answers increase by 10 each time:
10, 20, 30, 40, 50…
Difference:
Each successive number in the times-15 table is three times larger than the corresponding number in the times-5 table.
Q3: Construct other times-tables for numbers from 11 to 20, as you did for 15. Ans: To make times-tables from 11 to 20, multiply each number by 1, 2, 3, up to 10. For example:
Q4: As you compared the times-5 table with the times-15 table, compare the times-1 table with the times-11 table, the times-2 table with the times-12 table, and so on. Share your observations. Ans: 1. Times-1 vs. Times-11
2. Times-2 vs. Times-12
3. Times-3 vs. Times-13
…… repeat the same for 14, 15, 16, 17, 18, 19 and 20
Here is an arrangement of wheels. To count the total number of wheels, Tara splits them into two equal groups.
Similarly, 6 × 14 can be obtained by splitting the arrangement into two equal groups.
We have seen how to calculate 3 × 14 and 6 × 14 by splitting and doubling. Can we construct the times-14 table by splitting and doubling? Try! Solution: Yes, we can construct the times-14 table by splitting and doubling.
What other times tables can be constructed by splitting into equal groups and doubling? Give examples. Solution: We can construct 8, 10, 12, 16, 18, 20, etc. times tables by splitting into equal groups and doublings.
Q: A small bus can seat 20 people. How many people can be seated in 12 buses? Now let us do 12 × 20. Solve the following problems. Share your thoughts. Q: 24 × 40 = _______ Ans: First, break 24 into 20 + 4. Then, 20 × 40 = 800 and 4 × 40 = 160. Add them: 800 + 160 = 960. So, 24 × 40 = 960.
Q: 50 × 60 = _______ Ans: 50 × 60 means 5 tens × 6 tens. So, 5 × 6 = 30, then 30 × 100 = 3000. So, 50 × 60 = 3000.
Q: 70 × 80 = _______ Ans: 70 × 80 means 7 tens × 8 tens. So, 7 × 8 = 56, then 56 × 100 = 5600. So, 70 × 80 = 5600.
Page No. 190
A Day at the Transport Museum
Amala, Raahi and Farzan are visiting the “Transport Museum”. This museum has a collection of different modes of transport used by people in India. It includes several vehicles from the olden days. Raahi spots a toy train. She figures out that each coach can seat 14 children. The toy train has 15 coaches.
Q:How many children can be seated in the toy train? Ans: 15 × 14 = (10 × 10) + (10 × 4) + (5 × 10) + (5 × 4) = 100 + 40 + 50 + 20 = 210.
Page 191
Q:She wonders how many coaches will be needed for the 324 children from her school. Remember, each coach can seat only 14 children. Ans: 324 ÷ 14
Ans: 23 coaches, 2 children remain (need 24th coach).
Page No. 192
Let Us Solve
Q:Also, identify remainder (if any) in the division problems. (a) 25 × 34 Ans:
(b) 16 × 43 Ans:
(c) 68 × 12 Ans:
(d) 39 × 13 Ans:
(e) 125 ÷ 15 Ans:Thus, when 125 is divided by 15, we get (5 + 3) = 8 with remainder 5.
(f) 94 ÷ 11 Ans: Thus, when 94 is divided by 11, we get (2 + 3 + 3) = 8 with remainder 6.
(g) 440 ÷ 22 Ans:
So, 440 ÷ 22 = 10 + 10 = 20
(h) 508 ÷ 18 Ans: Thus, when 508 is divided by 18, we get (10 + 10 + 5 + 3) = 28 with remainder 4.
Q: Find the answers in Set A. Examine the relationships between the problems and the answers in Set A carefully. Then use this understanding to find the answers in Set B.
Ans:
Ans:
Ans:
Let Us Solve
Q:Also, identify remainder (if any) in the division problems. (a) 237 × 28 Ans:
(b) 140 × 16 Ans:
(c) 389 × 57 Ans:
(d) 807 ÷ 24 Ans: When 807 is divided by 24, we get 10 + 10 + 10 + 2 + 1 = 33, with remainder 15.
(e) 692 ÷ 33 Ans: When 692 is divided by 33, we get 10 + 10 = 20, with remainder 32.
(f) 996 ÷ 45 Ans: When 996 is divided by 45, we get 10 + 10 + 2 = 22, with remainder 6.
Dividing by 10 and 100
Q: A farmer packs his rice in sacks of 10 kg each. (a) If he has 60 kg of rice, how many sacks does he need?
Ans: Each sack holds 10 kg of rice. So we divide:
60 ÷ 10 = 6
⇒ He needs 6 sacks.
(b) If he has 600 kg of rice, how many sacks does he need?
Ans: Each sack holds 10 kg of rice. So we divide:
600 ÷ 10 = 60
⇒ He needs 60 sacks.
Ans: Each sack holds 100 kg of rice. So we divide:
600 ÷ 100 = 6
⇒ He needs 6 sacks.
Ans:
60 ÷ 10 = 6 sacks
600 ÷ 10 = 60 sacks
600 ÷ 100 = 6 sacks
Page No. 198
Q:Find the answers to the following questions. Share your thoughts in grade. 40 ÷ 10 = _________ Ans: 40 ÷ 10 = 4
Think and answer. Write the division statement in each case.
Q1. Manku the monkey sees 870 bananas in the market. Each bunch has 10 bananas. How many bunches are there in the market? Ans: Total bananas in the market = 870 Number of bananas in each bunch = 10 Number of bunches in the market = 870 ÷ 10 = 87 Division statement: 870 ÷ 10 = 87
Q2. Rukhma Bi wants to distribute ₹1000/- equally among her 10 grandchildren on the occasion of Eid. How much money will each of them get? Ans: Number of grandchildren of Rukhma Bi = 10 Amount distributed by Rukhma Bi = ₹ 1000 Amount of money received by each grandchild = ₹ 1000 ÷ 10 = ₹ 100 Division statement: 1000 ÷ 10 = 100
Let Us Solve
Q1: The oldest long-distance train of the Indian Railways is the Punjab Mail which ran between Mumbai and Peshawar. Its first journey was on 12 October 1912. Do you know how many coaches it had on its first journey? It had 6 coaches: 3 carrying 96 passengers and 3 for goods. (a) How many people travelled in each coach on the first journey? (b) This train has been running for 106 years now. It runs between Mumbai, Maharashtra and Ferozepur, Punjab. It has 24 coaches. Each coach can carry 72 passengers. How many people can travel on this train? Ans:(a) Number of coaches carrying passengers in train = 3 Number of peoples in train = 96 People travelled in each coach = 96 ÷ 3
96 ÷ 3 = 10 + 10 + 10 + 2 = 32 Thus, 32 people travelled in each coach. ⇒ 32 people travelled in each passenger coach.
(b) Number of coaches in train = 24 Number of passengers in each coach = 72 Number of people travel in the train = 24 × 72
⇒ 1728 people can travel on this train now.
Page No. 199
Q2: Amala and her 35 classmates, along with 6 teachers, are going on a school trip to Goa. They are using the double-decker “hop on hop off” sightseeing bus to explore the city.
(a) 2 people can sit on every seat of the bus. There are 15 seats in the lower deck and 10 in the upper deck. How many seats will they need to occupy? Are there enough seats for everyone?
(b) Find the total cost of the tickets for all children.
(c) What is the cost of the tickets for all teachers?
Ans: (a) Total people: 35 Students + 6 Teachers = 41 people.
Seats needed: 41 ÷ 2 = 20 (1 extra person needs 1 seat).
Total seats: 15 (lower) + 10 (upper) = 25
Yes, there are enough seats for everyone. Since, the total number of seats is more than the required number of seats occupied.
(b) Ticket price for each child = ₹ 359 Total cost of the tickets for all children = 36 × ₹ 359
Total coat of tickets for all children = ₹ 12,924
(c) Ticket price for adult = ₹ 899 Total cost of the tickets for all teachers = 6 × ₹ 899
Q3: Kedar works in a brick kiln. (a) The kiln makes 125 bricks in a day. How many bricks can be made in a month? (b) Each brick is sold in the market for ₹9. How much money can they earn in a month? Ans: (a) Assume 30 days Number of bricks made in a day = 125 So, number of pricks can be made in a month = 30 × 125
⇒ Therefore, 3750 bricks can be made in a month
(b) Price of each brick = ₹ 9 Money earned in a month = ₹ 9 × 3750
Q4: Chilika lake in Odisha is the largest saltwater lake in India. It is famous for the Irrawaddy dolphins. Boats can be hired to go see the dolphins. The trip from Puri includes a bus ride followed by a boat ride. Eight people will be going on the trip.
A bus ticket from Puri to Satapada costs ₹60.
A two-hour boat ride for 8 people costs ₹1200.
How much money do we need to spend on each person?
Q5: Find the multiplication and division sentences below. Shade the sentences. How many can you find?
Ans:
250 × 4 = 1000
50 × 20 = 1000
5 × 22 = 110
52 × 20 = 1040
104 × 6 = 624
30 × 15 = 450
50 × 19 = 950
1000 × 6 = 6000
55 × 101 = 5555
99 × 7 = 693
200 × 16 = 3200
35 × 9 = 315
931 ÷ 10 = 93
4 × 26 = 104
Q6: Solve
(a) 35 × 76
Ans:
(b) 267 × 38 Ans:
(c) 498 × 9 Ans:
(d) 89 × 42 Ans:
(e) 55 × 23 Ans:
(f) 345 × 17 Ans:
Following above table method, we can solve below questions as well.
(g) 66 × 22 Ans:
(h) 704 × 11 Ans:
(i) 319 × 26 Ans:
(j) 459 ÷ 3 Ans:
Thus, when 459 is divided by 3, we get 100 + 50 + 3 = 153 with no remainder.
(k) 774 ÷ 18 Ans:
So, 774 + 18 = 10 + 10 + 10 + 10 + 3 = 43
(l) 864 ÷ 26 Ans:
Thus, when 864 is divided by 26, we get (10 + 10 + 10 + 3 = 33) with remainder 6.
In a similar manner, we can solve remaining questions also.
(m) 304 ÷ 12
Ans: Thus, when 304 is divided by 12, we get (10 + 10 + 5 = 25) with remainder 4.
(n) 670 ÷ 9 Ans:
Thus, when 670 is divided by 9, we get (50 + 20 + 4 = 74) with remainder 4.
(o) 584 ÷ 25 Ans: Thus, when 584 is divided by 25, we get (10 + 10 + 2 + 1 = 23) with remainder 9.
(p) 900 ÷ 15 Ans: Thus, when 900 is divided by 15, we get (10 + 10 + 10 + 10 + 10)
(q) 658 ÷ 32 Ans:
Thus, when 658 is divided by 32, we get (10 + 10 = 20) with remainder 18.
(r) 974 ÷ 9 Ans:
Thus, when 974 is divided by 9, we get (100 + 5 + 2 + 1 = 108) with remainder 2.
Page No. 201
Chinnu’s Coins
Q1: Five friends plan to visit an amusement park nearby. Each of them uses different notes and coins to buy the ticket. The cost of the ticket is ₹750.
Bujji has brought all notes of ₹ 200.
And Munna has brought all notes of ₹50.
Whereas Balu has brought all notes of ₹20.
And guess what, Chinnu has all coins of ₹5.
And Sansu has all coins of ₹2.
(a) Find out how many notes/coins each child has to buy the ticket. Ans: Bujji: ₹750 ÷ ₹200 = 3 notes and ₹150 left → Needs 4 notes (₹800), will get ₹50 back.
Munna: ₹750 ÷ ₹50 = 15 notes
Balu: ₹750 ÷ ₹20 = 37 notes and ₹10 left → Needs 38 notes (₹760), will get ₹10 back
Chinnu: ₹750 ÷ ₹5 = 150 coins
Sansu: ₹750 ÷ ₹2 = 375 coins
(b) Which of these children will not receive any change from the cashier? Ans: Munna, Chinnu, and Sansu will not receive any change from the cashier.
(c) How long would the cashier take to count Chinnu’s coins? Ans: 150 coins at ~2 seconds each = 150 × 2 = 300 seconds = 5 minutes.
Q2: Observe the following multiplications. The answers have been provided. In each case, do you see any pattern in the two numbers and their product? For what other multiplication problems will this pattern hold? Find 5 such examples. Ans: We observe that, the ones digit of the product is the product of ones digits of the multiplicand and multiplier, and the tens digit of the product is the sum of ones digit of the multiplicand and multiplier.
Other such examples are
Page No. 202
Q3: Assume each vehicle is travelling with full capacity. How many people can travel in each of these vehicles? Match them up. Ans:
Q1: Notice the number of days in February in the years 2024 and 2025.
Number of days in Feb 2024 = _____________
Number of days in Feb 2025 = _____________
Ans:
Number of days in Feb 2024 = 29 Days
Number of days in Feb 2025 = 28 Days
Page No. 176
Q2: Fill in the blanks with consecutive leap years before and after 2024. Ans: A leap year occurs every 4 years. 2016, 2020, 2024, 2028, 2032, 2036
Q3: We know that most years have 365 days. How many days would a leap year have? Ans: Leap year: 365 + 1 = 366 days.
Q4: Write the names of the months when you celebrate your favourite festivals.Ans: Example festivals:
Q5: Answer the following questions by writing the appropriate days of the week: (a) Today: ___________ (b) Yesterday: ___________ (c) Tomorrow: ___________ (d) Day after tomorrow: ___________ (e) Day before yesterday: ___________ Ans: Assume today is Friday, April 25, 2025: (a) Today: Friday (b) Yesterday: Thursday (c) Tomorrow: Saturday (d) Day after tomorrow: Sunday (e) Day before yesterday: Wednesday
Q6: July 1 is a Monday. Write the dates for the next two Mondays. Ans: July 1: Monday.
Each day of a week comes exactly 7 days after the previous occurrence of the same weekday. So, the dates for the next two Mondays will be
Next Monday: July 1 + 7 = July 8. Following Monday: July 8 + 7 = July 15.
Q7: Laali is born on 04/07/2014 and Chotu is born on 04/12/2019. Who is older among the two and how much? Ans: Laali: Born 04/07/2014. Chotu: Born 04/12/2019. Compare: 2014 < 2019, Laali is older. Difference: From 04/07/2014 to 04/12/2019. Years: 2019 − 2014 = 5 years. Months: July to December = 5 months. Days: Same day (4th), so 0 days. Laali is older by 5 years, 5 months.
(a) Laali will turn 5 years old on ______________. Ans: Born: 04/07/2014. 5 years old: 04/07/2014 + 5 years = 04/07/2019.
(b) Chotu’s 10th birthday will be celebrated on Ans: Born: 04/12/2019. 10th birthday: 04/12/2019 + 10 years = 04/12/2029.
Q8: Check the manufacturing and expiry dates on the wrapper of any biscuit packet. (a) How old is the packet of biscuits? Ans: Example: Manufacturing: 01/01/2025, Today: 25/04/2025. Duration: From 01/01/2025 to 25/04/2025.
Q9: Notice the day on which July 15 falls in your calendar. Now find out what day is August 15? September 15? October 15? What pattern do you notice? Share in grade. Ans: Assume July 15, 2024, is a Monday (calendar check). August 15: 31 days later (July 15 to August 15). 31 ÷ 7 = 4 weeks, 3 days. Monday + 3 = Thursday. September 15: 31 days later (August 15 to September 15). Thursday + 3 = Sunday. October 15: 30 days later (September 15 to October 15). 30 ÷ 7 = 4 weeks, 2 days. Sunday + 2 = Tuesday. Pattern: Days shift by 2–3 days per month (30–31 days).
Now choose a date and look up the day on which it falls. Challenge your friends to guess what day will the same date fall in the following month. Ans: Do it Yourself!
Page No. 177 (Let Us Explore)
Q1: Find out when the year begins in each of these calendars. Ans:
Hindu Calendar – Starts with Chaitra (March/April)
Islamic Calendar – Starts with Muharram (Moves each year; in 2025, it starts in July/August)
Sikh Calendar (Nanakshahi) – Starts with Chet (March/April)
Q2: Check how the names of the months in these calendars correspond to the months in the English calendar. Ans:
Hindu Calendar:
Chaitra ≈ March/April
Vaishakha ≈ April/May
And so on…
Islamic Calendar:
Muharram, Safar, etc.
These months move about 10 days earlier every year because it follows the moon.
Sikh Calendar:
Chet ≈ March/April
Vaisakh ≈ April/May
And so on…
Q3: Identify the months from the Hindu/Islamic/Sikh or any other calendar in which some of the important festivals of the community fall. Ans:Hindu Festivals:
Diwali – Kartika (October/November)
Holi – Phalguna (February/March)
Islamic Festivals:
Eid al-Fitr – Shawwal (April/May in 2025)
Eid al-Adha – Dhu al-Hijjah (June/July in 2025)
Sikh Festivals:
Vaisakhi – Vaisakh (April)
Guru Nanak Jayanti – Kartik (November)
Q4: Identify the dates of the new moon and full moon in your community’s calendar every month. Do you notice any pattern? Ans: In the Hindu calendar,
Purnima means full moon
Amavasya means new moon
These come about 15 days apart
In the Islamic calendar,
The new moon marks the start of a new month
The lunar cycle (from new moon to next new moon) is about 29.5 days, so there is a clear pattern.
Q5: How are the full moon or new moon days named in your community’s calendar? Ans:Hindu Calendar:
Purnima – Full Moon
Amavasya – New Moon
Islamic Calendar:
The new moon starts each month (e.g., 1st Muharram)
Sikh Calendar:
The new month begins on Sangrand
Special days like full moons are observed during religious occasions
Page No. 178
Look at the picture below. It shows the time spent on different activities by a doctor. Write the number of hours spent on each activity in the space provided. Then, find the total number of hours between 6 o’clock morning to 6 o’clock evening and 6 o’clock morning of the next day.The total number of hours is ________ . Ans:
Total: 6 AM to 6 PM = 12 hours.
Full day: 6 AM to next 6 AM = 24 hours.
Page No. 180
Fill in the blanks by writing time in the appropriate format.Ans:
Page No. 181
Raghav leaves home at 8:20 AM and returns back at 8:35 AM. How much time has he taken?Ans: From 8:20 AM to 8:35 AM.
Minutes: 35 − 20 = 15 minutes.
Let Us Do
Q1: Show the appropriate times on the clock as per instructions. (a) Raghav started doing his homework at 10:20 AM. He took 25 minutes to finish it. Show the time that he finished his homework.Ans:
(b) Muneera starts reading a story at 4:15 PM. She finishes reading it in 45 minutes. Show the time that she finished reading the story.Ans:
Start: 4:15 PM.
Add 45 minutes: 4:15 + 45 = 4:60 = 5:00 PM.
Ans: 5:00 PM.
(c) Akira leaves for school at 8:00 AM. She reaches school in 15 minutes. Ans:
(d) Who do you think is correct? Is there any relation between 1 hour and 60 minutes?
Ans: Both are right!
Akira says she spent 1 hour (from 8:00 to 9:00).
The other person says 60 minutes.
As, 1 hour = 60 minutes
Observe the shaded portions Ans:
Page No. 183
Q: Find out how much time you take to (a) boil milk Ans: Example: Boiling milk takes ~10 minutes.
(b) fill water from tap in a bucket Ans: Example: Filling a bucket takes ~10 minutes.
Q: What activities can you do in 5 minutes? Ans: Examples: Brush teeth, tie shoes, eat a snack, read a page.
Let Us Check
Three friends read time from a clock. Who is right? Discuss the error and explain how one reads the clock correctly.Ans:First Row: Big Hand at 12, Small Hand at 4
Correct Time: 04:00
Rani is correct.
Second Row: Big Hand at 7, Small Hand at between 5 and 6
Is it a symmetrical pattern? Where would you draw the line that divides this design into two equal halves? Isn’t this line called the line of symmetry? Ans: Yes, folding paper and pressing spreads ink evenly, creates mirror images. Yes, there is a line of symmetry along the fold (vertical center).
2. Making a paper airplane
Follow the steps.
(a) Mark the line of symmetry in Fig. 3, Fig. 4, and Fig. 5.
Ans:
(b) How many lines of symmetry can you see in Fig. 8? Ans:
One line of symmetry.
(c) Where will you place a mirror to see the reflection of the right half side of Fig. 8? Will it look the same as the left half side? Ans: Place mirror: Along vertical line of symmetry (center).
Reflection: Yes, right half reflects to match left half (symmetrical).
Along center; yes, same.
(d) Fly the plane. Ans: Action: Follow folding steps and fly the plane.
(e) Will the plane fly if there is no line of symmetry? Ans: No symmetry: Plane may be unbalanced, affecting flight.
(f) Try to make an asymmetrical plane. Ans: Fold unevenly (e.g., one wing larger).
Create uneven folds.
(g) Fly both the planes and see which plane flies for a longer time. Ans: Symmetrical plane: Likely flies longer due to balance.
Asymmetrical plane: May wobble or crash sooner.
Symmetrical plane flies longer.
(h) Share your observations with your friends. Ans: Observation: Symmetrical plane flies better; asymmetrical plane is unstable.
3. Holes and Cuts
Mini has made this design by folding and cutting paper.
Now it’s your turn! Take a square sheet of paper. Do as instructed below.
Let us see what Rani is making. Rani takes a piece of paper and folds it twice.
She makes a straight cut at the corner and cuts out two squares on two sides as shown in the picture.
Challenge 1: Where would the hole and cut appear when you open the paper?Ans: When the paper will open, the hole and cut appear as follows:
Challenge 2: Fold a piece of paper once; put two cuts in the middle as shown. How many sides will this shape have when you open the folded paper?Ans: The shape have 4 sides.
Challenge 3: Fold a paper twice. Where would you cut to make a square hole in the center of the paper? How many cuts are required?Ans: Do it Yourself.
4. Complete the designs belowAns: Do it Yourself.
Page no. 167
Let Us Do
Symmetry in shapes
Q1: Look at the shapes given along the border. Draw these shapes on the dot grid. Which of the shapes are symmetrical? Draw the lines of symmetry.Ans:
All shapes are symmetrical as by drawing a line of symmetry, it divides the figures into equal parts.
Page 168
Q2: Games with a Mirror (a) Where should we place the mirror in shape A to get the shapes given below? Ans:
(b) Circle the numbers whose mirror image is the same number.Ans:
Which digits from 0 to 9 have the same mirror image?
Ans: 0, 1 & 8 will have same mirror images and 3 (in some digital fonts).
Make some 4-digit numbers such that the mirror image is the same number. Where would you keep the mirror in each case? How many such numbers can you make?
Ans: Some examples of the 4-digit numbers that have the same mirror images are: 1881, 8118, 1001, 8008, etc. We will keep the mirror to the left or right side of the number in each case.
(c) Make similar questions and ask your friends to guess the numbers. Ans: Do it Yourself!
Page 169
Q3. What do you notice about the letters written on the ambulance? Why are they written this way? Discuss.Ans: The word “AMBULANCE” is written backward (like in a mirror) on the front of the ambulance.
Why?
So drivers in cars ahead see it correctly in their rearview mirror and move out of the way quickly!
It is written CAT and the mirror has been kept horizontally below the word.
Can you identify these words? Where will you place the mirror to read the following words correctly?Ans:
Now, you try to write some words/names in this way and challenge your friends to guess them.
Ans: Do it Yourself!
Q4. Complete the following to make symmetrical shapes.
Ans:
Page 170
Q5: Observe the shapes. How many sides does each shape have?
How many lines of symmetry does each shape have? You may trace these shapes and check the lines of symmetry by folding the shapes.Ans: Do it Yourself!Tiling the Tiles
Here are some patterns with tiles. Identify the repeating unit (tile) and continue the patterns.Ans: Do it Yourself!
Page 171
Tiles at the Tile Shop
Bablu Chacha makes beautiful tiles of the kinds shown below. Design creative tiles of your own in the spaces given below. You may use a rangometry kit or shape cutouts.
Q1: Which shapes have you used to make the tiles?
Ans: Do it Yourself!
Q2: Which of the tiles are symmetrical? Draw the lines of symmetry (if any). Ans:
Q3: Make more tiles by joining two or more shapes. Trace them in your notebook to create paths with no gaps or overlaps. Ans: Do it Yourself!
Q4: Look at the following shapes. What do you notice? Discuss.Ans: Both are identical. The difference is of the colour pattern.
Page No. 172
Let Us Do
Q1: Make floor patterns with your tile. Mini has made a floor pattern as shown below.Ans: Do it Yourself!
Q2: Making a catty wall!
Create more of these tiles. Some ideas to make creative wall patterns are given below.
Ans: Do it Yourself!
Q3: Let us go on a nature walk (Project time)
Go for a nature walk to a nearby park or around your school with your teacher or your parents. Observe the patterns, designs, or symmetry around you carefully. Collect leaves, petals, and flowers that have fallen on the ground.
You have played a version of this game in the chapter ‘Vacation with my Nani Maa’ in Grade 3. We will add either 1 or 2 each time to reach the target number 10.
Can you win the game if(a) The other player has reached the total of 6 and it is your turn?
Ans: Yes, we can win the game. Add 1 bringing the total to 7. On other player’s tun n, the opponent can add either 1 or 2. T-f he/she adds 1, the total becomes 8 and or.i our turn, we can add 2 to reach 10 and win. If he/ she adds 2, the total becomes- 9 and on our turn, we can add 1 to reach 10 and win.
(b) The other player has reached the total of 7 and it is your turn?
Ans: No, we cannot win. We can add either 1 or 2. If we add 1, the total becomes 8 and the other player can a dd 2 to reach 10 and win. If we add 2, the; total becomes 9 and the other player can add 1 to reach 10 and win.
(c) The other player has reached the total of 8 and it is your turn?
Ans: Yes, we can win. Add 2, bringing the total to 10 and we will win. Play the game to reach other target numbers (like 10, 11 or 12) by adding 1 or 2 each time.
Q: Can you find a number in each case when you are sure that you can win?
Ans: Suppose, if other player has reached the total 9 and its our turn, we can add 1 to reach 10 and win. Similarly, we can find some numbers in each case when we are sure that we can win if the target number is 11 or 12. For example, if the target number is 11 and the other player has reached the total 7 and its our turn. Then we can add 1 to reach 8. The other player can either add 1 or 2. If they add 1 the total becomes 9 and in our turn we can add 2 to win.
If the player add 2, the total becomes 10 and in our turn we can add 1 to reach 11 and win. Similarly, if the target number is 12 and the other player has reached the total 8 and its our turn, then we can be sure to win.
Page No. 150
Addition Chart
Q1: Identify some patterns in the table.
Following are some patterns that can be observed in the table.
Any number plus 0 remains the same.
The sum increases by 2 when moving diagonally.
Each row and column increase by 1 as we move right or down, respectively.
The table mirrors itself across the main diagonal.
Q2: Observe the cells where the number 9 appears in the table. How many times do you see number 9? What about other numbers?
Ans: There are ten 9’s in the table.
Following are the patterns of appearance of the numbers.
Each number appears one more time than its value till the number 12 and then the appearances of numbers start decreasing symmetrically.
Q3: Are there any rows or columns that contain only even numbers or only odd numbers? Explain your observation.
Ans: Every row and column in the table has both odd and even numbers. This happens because adding two even numbers or two odd numbers gives an even number as resulf while adding one odd and one even number gives an odd number as result.
Q4: Look at the window frame highlighted in red colour in the table. (a) Find the sum of the two numbers in each row.
Ans: Sum of 10 and 11 = 10 +11 = 21 Sum of 11 and 12 = 11 + 12 = 23
(b) Find the sum of the two numbers in each column. What do you notice? Ans: Sum of 10 and 11 = 21 (in column) Sum of 11 and 12 = 23 Again we get numbers 21 and 23 as result.
(c) Now, find the sum of the numbers in each of the two diagonals marked by arrows. What do you notice? Ans: Sum of 10 and 12 = 22 Sum of 11 and 11 = 22 The sum of the numbers in two diagonals is same.
(d) Now, put the red window frame in other places and find the sums as above. What do you notice?
Ans: If we put the window frame in any two consecutive numbers in row and column, the sum of rows and columns will change but the difference between the sum of any two rows, columns and diagonals will remain the same.
Q5: Identify some patterns and relationships among the numbers in the blue window frame.
Ans: In the blue window frame, numbers in each row and in each column are same and the difference between the sum of numbers of each row and each column is 3.
Page No. 151
Reverse and Add
(a) Take a 2-digit number say, 27. Reverse its digits (72). Add them (99). Repeat for different 2-digit numbers.
27 + 72 = 99.
45 + 54 = 99.
19 + 91 = 110.
Ans: Sums like 99, 110, etc.
(b) What sums can we get when we add a 2-digit number with its reverse?
Ans: Let’s add some 2-digit numbers and their reverse to identify any pattern. 10 + 01 = 11 = 1 × 11 11 + 11 = 22 = 2 × 11 12 + 21 = 33 = 3 × 11 13 + 31 = 44 = 4 × 11 . . . . . 18 + 81 = 99 = 9 × 11 99 + 99 = 198 = 18 × 11 We can observe that, when we add a 2-digit number with its reverse, we get a number that can be obtained in the times-11 table.
(c) List down all numbers which when added to their reverse give (i) 55
Ans: 14 + 41 = 55, 32 + 23 = 55, 50 + 05 = 55 Thus, all the numbers that, when added to their reverse give 55 are 14, 23, 32, 41 and 50.
(ii) 88
Ans: 17 + 71 = 88, 26 + 62 = 88, 35 + 53 = 88 44 + 44 = 88, 80 + 08 = 88 Thus, all the numbers that, when added to their reverse give 88 are 17, 26, 35, 44, 53, 62, 71, and 80.
(d) Can we get a 3-digit sum? What is the smallest 3-digit sum that we can get?
Ans: Yes, we can get a 3-digit sum by adding a 2-digit number and its reverse. The smallest such 3-digit number is 110. As, 19 + 91 = 110.
Fill in the blanks with appropriate numbers. (a)
Ans:
(b) Ans:
(c)
Ans:
Page 154
How Many Animals? (Continued)
Q3: Maharashtra has 444 tigers. Madhya Pradesh has 341 more tigers than Maharashtra. Uttarakhand has 116 tigers more than Maharashtra. (a) How many tigers does Madhya Pradesh have? Ans:
So, Madhya Pradesh has 785 tigers.
(b) How many tigers does Uttarakhand have?
Ans:
Therefore, there are 560 tigers in Uttarakhand.
(c) How many tigers does Madhya Pradesh and Uttarakhand have?
Ans:
So, there are 1345 tigers in Uttarakhand and Madhya Pradesh.
(d) How many tigers are there in total across the three states? Ans:
So, there are 1789 tigers across the three states.
Page 156
More or Less?
1. Assam has 5719 elephants. It has 3965 more elephants than Meghalaya. How many elephants are there in Meghalaya? 1754 elephants are there in Meghalaya.
2. The population of leopards as per the 2022 census was 8820 in the Central India and the Eastern Ghats. It had increased by 749 in comparison to the number of leopards in 2018 in the same region. How many leopards were there in 2018? _________ leopards were there in 2018.
Write the number of animals on this map based on the data from the problems in the previous pages.
Ans:
Elephants: Karnataka (6049), Kerala (3054), Assam (5719), Meghalaya (1754).
Q1: The board in the ticket office in the Kaziranga National Park shows the following:(a) How many more visitors came in December than in November?
Ans: Number of visitors in December = 8591 Number of visitors in November = 6415 The difference between the number of visitors in these two months = 8591 – 6415 = 2176 Therefore, 2176 more visitors came in December than in November.
(b) The number of visitors in November is 1587 more than October. How many visitors were there in October?
Ans: Number of visitors in November = 6415 Since the number of visitors in November is 1587 more than October. Therefore, the number of visitors in October = 6415 – 1587 = 4828. Thus, there were 4828 visitors in October.
Q2: In a juice making factory, women make different types of juices as given below:(a) The number of bottles of guava juice is 759 more than the number of bottles of pineapple juice. Find the number of bottles of guava juice.
Ans: Number of bottles of pineapple juice = 1348. Number of bottles of guava juice is 759 more than number of bottles of pineapple juice. Number of bottles of guava juice = 1348 + 759 = 2107 Therefore, the number of bottles of guava juice is the number of bottles of guava juice.
(b) The number of bottles of orange juice is 1257 more than the number of bottles of guava juice and 1417 less than the number of bottles of passion fruit juice. How many bottles of orange juice are made in a month?
Ans: The number of bottles of guava juice = 2107. Number of bottles of orange juice is 1257 more than the number of bottles of guava juice. Number of bottles of orange juice = 2107 + 1257 = 3364 Therefore, 3364 bottles of orange juice is packed in a month.
(c) Is the total number of bottles of guava juice and orange juice more or less than the number of bottles of passion fruit juice? How much more or less?
Ans: Total number of bottles of guava juice and orange juice = 2107 + 3364 = 5471 Number of bottles of passion fruit juice = 4781 ∵ 5471 -4781 = 690 Thus, the number of bottles of guava juice and orange juice is 690 bottles more than passion fruit juice.
Page 158
Let Us Do (Continued)
Q3: In a small town, the following vehicles were registered in the year 2022. Find the number of vehicles as per the conditions given below. (a) The number of buses is 253 more than the number of jeeps. How many buses are there in the town? Ans: Number of jeeps = 6304 Number of buses = 253 more than 6304 = 253 + 6304 = 6557 Therefore, there are 6557 buses in the town.
(b) The number of tractors is 5247 less than the number of buses. How many tractors are in the town? Ans: Number of buses = 6557 Number of tractors = 5247 less than 6557 = 6557 – 5247 = 1310 Therefore, there are 1310 tractors.
(c) The number of taxis is 1579 more than the number of tractors? How many taxis are there? Ans: Number of tractors = 1310 Number of taxis = 1579 more than 1310 = 1579 + 1310 = 2889 Therefore, there are 2889 taxis.
(d) Arrange the numbers of each type of vehicle from lowest to highest. Ans: We have, Jeeps: 6304; Buses: 6557; Tractors: 1310; Taxis: 2889. The order of these numbers from the lowest to the highest is: 1310, 2889, 6304, 6557.
Answer: Tractors, Taxis, Jeeps, Buses
Q4: Solve (a) 1459 + 476 Ans: 1459 + 476 = 1935.
(b) 3863 + 4188 Ans: 3863 + 4188 = 8051.
(c) 5017 + 899 Ans: 5017 + 899 = 5916.
(d) 4285 + 2132 Ans: 4285 + 2132 = 6417.
(e) 3158 + 1052 Ans: 3158 + 1052 = 4210.
(f) 7293 − 2819 Ans: 7293 − 2819 = 4474.
(g) 3105 − 1223 Ans: 3105 − 1223 = 1882.
(h) 8006 − 5567 Ans: 8006 − 5567 = 2439.
(i) 5000 − 4124 Ans: 5000 − 4124 = 876.
(j) 9018 − 487 Ans: 9018 − 487 = 8531.
Page 159
Let Us Do (Continued)
Q5: The children in a school in Chittoor are planning to organise a Baal Mela in their school. Raju, Rani and Roja decided to raise some money to make arrangements for the mela. The money is available in notes of 500, 100, 50, 10 and coins of 5, 2 and 1. They decide to put the money in the School Panchayat Bank.
Help each of the children fill the deposit slip given below.
Different combinations of notes can give the same amount. Can you guess a possible combination of notes they might have? Fill in the amounts appropriately.
Total in words: Two thousand forty-five.
Ans: Raju’s slip completed as shown.
Page 160
Let Us Do (Continued)
1. Rani
2. Roja
Page 161
Let Us Solve
Q1: Solve Ans:
Q2: Arrange the following in columns and solve in your notebook.(a) 3683 − 971 Ans: 3683 − 971 = 2712.
(b) 8432 − 46 Ans: 8432 − 46 = 8386.
(c) 4011 − 3666 Ans: 4011 − 3666 = 345.
(d) 5203 − 2745 Ans: 5203 − 2745 = 2458.
(e) 1465 + 632 Ans: 1465 + 632 = 2097.
(f) 3567 + 77 Ans: 3567 + 77 = 3644.
(g) 8263 + 3737 Ans: 8263 + 3737 = 12000.
(h) 5429 + 3287 Ans: 5429 + 3287 = 8716.
Page 162
Let Us Solve
Q1: Find easy ways to solve the following problems.(a) 8787 − 99 Ans: 8787 − 100 + 1 = 8688.
(b) 4596 + 104 Ans: 4596 + 100 + 4 = 4700.
(c) 3459 + 21 Ans: 3459 + 20 + 1 = 3480.
(d) 5010 + 95 Ans: 5010 + 100 − 5 = 5105.
(e) 4990 + 310 Ans: 4990 + 300 + 10 = 5300.
(f) 7844 − 15 Ans: 7844 − 20 + 5 = 7829.
(g) 260 + 240 Ans: 260 + 240 = 500.
(h) 1575 − 125 Ans: 1575 − 100 − 25 = 1450.
(i) 3999 + 290 Ans: 3999 + 300 − 10 = 4289.
Q2: Use the signs <, =, > as appropriate to compare the following without actually calculating.Ans:
Q3: Use the given information to find the values. Ans:
Q3: Fill the squares with the numbers 1-9. The difference between any two neighbouring squares (connected by a line) must be odd.Ans:
Yes, we can fill the squares in many ways.
No, it is not possible to fill the squares such that the difference between any two neighbouring squares is even. This happens because the difference of either two odd numbers is even or two even numbers is even, means we cannot fill any even number that is connected to an odd number and vice versa, that is not possible in the given connected squares.
Diagonal Division: Drawing a diagonal line from one corner to the opposite corner
Community lunch organised by Jaspreet and Gulnaz
And 1 pink token → 1That means: 1000 + 1 = 1001
Classrooms and school areas
Munna: ₹750 ÷ ₹50 = 15 notes
Chinnu: ₹750 ÷ ₹5 = 150 coins
Sansu: ₹750 ÷ ₹2 = 375 coins
