Text Book Solutions All Class

Page 128

Animal Jumps

Fill in the blank spaces with the appropriate numbers. Find how many jumps the animal needs to take to reach its food.
Q1: The frog jumps 3 steps at a time. Which numbers will the frog touch? Will it touch 67?

Ans:  

• The frog will only touch numbers that are multiples of 3.
• Since 67 is not a multiple of 3, the frog will not touch 67.

Q2: The squirrel jumps 4 steps at a time. Which numbers will the squirrel touch? How many times should the squirrel jump to reach 60?

Ans:  

• Numbers: Multiples of 4 (4, 8, 12, …, 60, 64, …).  
• 60 ÷ 4 = 15 jumps.  

Ans: Squirrel touches multiples of 4; 15 jumps to reach 60.

Page 129

Animal JumpsQ3: The rabbit jumps 6 steps at a time. 

Which numbers will the rabbit touch? 

What is the smallest 3-digit number on which the rabbit will land? 

How many times did the rabbit jump to reach this number?

Ans:  

• Numbers: Multiples of 6 (6, 12, 18, …, 96, 102, …).  
• Smallest 3-digit number: 102 (first multiple of 6 ≥ 100).  
• 102 ÷ 6 = 17 jumps.  

Ans: Multiples of 6; smallest 3-digit number is 102; 17 jumps.

Q4: The kangaroo jumps 8 steps at a time. Which numbers will the kangaroo touch? Are there numbers that both the rabbit and the kangaroo will touch?Are there numbers that both the rabbit and the kangaroo will touch?
Ans:  

• Numbers: Multiples of 8 (8, 16, 24, …, 96, 104, …).  
• Common numbers: Common multiples of 6 and 8 (LCM = 24). E.g., 24, 48, 72, …  

Ans: Multiples of 8; yes, rabbit and kangaroo touch numbers like 24, 48, 72.

Q5: To reach 48, how many times did the rabbit jump? How many times did the kangaroo jump to reach the same number? 
What did you observe?
Ans:  Since the rabbit jumped 6 steps at a time, 6 steps × 8 = 48. So, the rabbit jumped 8 times to reach 48.
And the kangaroo jumped 8 steps at a time, 8 steps × 6 = 48. So, the kangaroo jumped 6 times to reach the number 48.
We observe that due to size, rabbit take shorter steps than kangaroo and so reach later than kangaroo.

Page 130

Animal Jumps

Q6: To reach 60, how many times did the frog jump? How many times did the rabbit jump to reach the same number? What do you observe?

Ans:  Since a frog jumped 3 steps at a time and 3 steps × 20 = 60.
So, the frog jumped 20 times to reach the number 60.
And the rabbit jumped 6 steps at a time, 6 steps × 10 = 60.
So, the rabbit jumped 10 times to reach the number 60.
We observe that due to difference in jump size, frog has to take more steps to reach the number 60.

Common Multiples

Q1: Which numbers do both the frog and the squirrel touch? A few common multiples of 3 and 4 are _________________.
Ans:  

• Frog: Multiples of 3 (3, 6, 9, 12, …).  
• Squirrel: Multiples of 4 (4, 8, 12, …).  
• Common multiples (LCM = 12): 12, 24, 36, …  

12, 24, 36, …

Q2: Which numbers do both the rabbit and the kangaroo touch? A few common multiples of 6 and 8 are ___________________.
Ans:  

• Rabbit: Multiples of 6 (6, 12, 18, 24, …).  
• Kangaroo: Multiples of 8 (8, 16, 24, …).  
• Common multiples (LCM = 24): 24, 48, 72, …  

24, 48, 72, …

Q7: If the cat and the rat land on the same number, the cat will catch the rat. The cat is now on 6 and the rat on 12. When the cat jumps 3 steps forward, the rat jumps 2 steps forward. Will the cat catch the rat? If yes, at which number?

Ans:  

• Cat: Starts at 6, jumps 3 steps (9, 12, 15, 18, 21, 24, …).  
• Rat: Starts at 12, jumps 2 steps (14, 16, 18, 20, 22, 24, …).  
• Common number: 24 (cat reaches 24 in 6 jumps, rat in 6 jumps).  

Yes, cat catches rat at 24.

Q8: Find multiplication and division sentences in the grid. Shade the sentences. How many can you find?Two examples are done for you.
Ans: 

We can make 15 such sentences.

Page 131

Gulabo’s Garden

Q1: Gulabo’s garden has lily flowers. Each lily flower has 3 petals. How many petals are there in 12 flowers? Show how you found your answer.
Gulabo will have 12 × 3 petals.
Petals in 10 lilies 10 × 3 petals = 30 petals
Petals in 2 lilies __________________
Petals in 12 lilies _________________
Ans: There are 36 petals in 12 flowers. 
I found it by multiplying 12 flowers by 3 petals each: 12 × 3 = 36. 
First, 10 lilies have 10 × 3 = 30 petals. 
Then, 2 lilies have 2 × 3 = 6 petals. 

Petals in 12 lilies = 12 × 3 = 36 petals
Adding them together, 30 + 6 = 36 petals.

Q2: In a hibiscus flower there are 5 petals. Gulabo counted all the petals and found them to be 80. How many flowers did she have?Gulabo has 80 ÷ 5 flowers.
5 petals is 1 flower.
10 petals are 2 flowers.
50 petals are 10 flowers.
Then, 80 petals are _______ flowers.
Ans:  

• 80 ÷ 5 = 16 flowers.  
• Method: 50 ÷ 5 = 10, 30 ÷ 5 = 6, 10 + 6 = 16.  

 16 flowers; 80 ÷ 5 = 16.

Page 132

Gulabo’s Garden

Q3: Gulabo plants some marigold saplings in a box as shown in the picture. 
There are ______ saplings in each row. 
There are ______ rows. 
How many saplings has she planted? 
How did you calculate it?
Mathematical Statement _________________

Ans: There are 11 saplings in each row.
There are 3 rows.
Gulabo has planted a total of 33 saplings in the box.
By using multiplication, we found the number of saplings.
Mathematical statement: There are 3 rows in the box, where the saplings planted are 11 times the number of rows.
Total saplings planted = 3 × 11 = 33 

Q4: “Dailyfresh” supermarket has kept boxes of strawberries in a big tray. 
How many boxes of strawberries does the supermarket have? 
Show how you found them.There are _______ columns of strawberry boxes.
There are _______ boxes in each column.
There are _______ boxes in all.
Mathematical Statement _________________
Ans: There are 16 columns of strawberry boxes.

There are 6 boxes in each column.
There are 16 × 6 = 96 boxes in all.
Mathematical statement: The number of boxes of strawberry = Number of columns of strawberry boxes × number of boxes in each column = 16 × 6 boxes = 96 boxes

Q5: Radha runs a bakery shop. She bakes 18 cupcakes in one tray of the size shown below.
(a) Complete arranging the cupcakes in the two trays given below.

Ans: Radha has 18 cupcakes to arrange in two trays. The first tray already has 8 cupcakes.

• First tray: 8 cupcakes are already there.
• Cupcakes left = 18 – 8 = 10 cupcakes.
• Put the remaining 10 cupcakes in the second tray.

So, the arrangement is:

• First tray: 8 cupcakes.
• Second tray: 10 cupcakes.

(b) She can use two such trays in her oven at a time. How many cupcakes can she make in one attempt? _______
Ans:  Number of cupcakes in a tray = 18
Number of cupcakes in two trays = 2 × 18 = 36
The number of cupcakes, she can make in one attempt = 36

(c) Today she has received a special order. She has made 108 cupcakes. How many trays has she baked?
Ans:  Number of cupcakes in two trays = 36
Number of cupcakes in 4 trays = 2 × 36 = 72
Number of cupcakes in 6 trays = 3 × 36 = 108
So, the required number of trays = 6

(d) She has another square baking tray. She can bake 36 mini cupcakes in such a tray. Complete the arrangement below.Number of columns: _______    
Number of cupcakes in each column: _______    
Multiplication statement _______
Ans:  Number of columns = 6
Number of cupcakes in each column = 6
Multiplication statement: 6 × 6 = 36.

Q: Find different ways of arranging the following numbers of cupcakes in rows and columns in your notebook. 
36, 8, 12, and 24
Ans:  

• 36 cupcakes can also be arranged in a tray having 9 rows, and each row has 4 cupcakes.
• 8 cupcakes can be arranged in 4 columns, with 2 cupcakes in each column.
• 12 cupcakes can be arranged in 2 rows, with each row having 6 cupcakes.
• 24 cupcakes can be arranged in 6 columns, and each column has 4 cupcakes.

Page 134

 The Doubling Magic

Magician Anvi came one day, 
To Gulabo’s house, ready to play. 
From her coat, with a grand display,

(a) Double of 32 =_____
Ans: 32 × 2 = 64

(b) Double of 14 =_____
Ans: 14 × 2 = 28

(c) Double of 26 =_____
Ans: 26 × 2 = 52

(d) Double of 17 =_____
Ans: 17 × 2 = 34

(e) Double of 39 =_____ 
Ans: 39 × 2 = 78

(f) Double of 45 =_____
Ans: 45 × 2 = 90  

1.  Guess what will be the ones digit of the following numbers when doubled.
Write the ones digit in the space provided.
(a) 28 ______
Ans: 28 × 2 = 56; ones digit: 6

(b) 56 ______
Ans: 56 × 2 = 112; ones digit: 2

(c) 45 ______
Ans: 45 × 2 = 90; ones digit: 0

(d) 17 ______
Ans: 17 × 2 = 34; ones digit: 4  

2. Give examples of numbers that when doubled give the following digits in the ones place.
(a) 0 _______
Ans: 5, 10, 15 (e.g., 5 × 2 = 10)

(b) 2 _______
Ans: 1, 6, 11 (e.g., 1 × 2 = 2)
(c) 4 _______
Ans: 2, 7, 12 (e.g., 2 × 2 = 4)
(d) 6 _______
Ans: 3, 8, 13 (e.g., 3 × 2 = 6)
(e) 8 _______
Ans: 4, 9, 14 (e.g., 4 × 2 = 8)
Can we get 3, 5, 7, 9 as the ones digit after doubling?
Ans: No; doubling gives even ones digits (0, 2, 4, 6, 8).

What do we notice about the numbers that we get after doubling? Even or Odd?
Observation: Doubled numbers are even.

Page 135 & 136

Multiplication Chart

Fill each square in the chart by multiplying the row number by the column number.
What do you notice about the numbers shaded in green? Why is this happening?

Ans: We notice that the numbers shaded in green, show that when we multiply any two numbers, the order does not matter. For example, 1 × 2 = 2 = 2 × 1, 2 × 3 = 6 = 3 × 2, 5 × 2 = 10 = 2 × 5 and so on.

Q1: Share the patterns that you notice in the table.
Ans:  We notice that each row/column is a multiple of its row/column number. Also its diagonal cells are all perfect squares.

Q2: Are the numbers in row 7 the same as the numbers in column 7? In general, are the numbers in a given row the same as the numbers in the corresponding column? Why does this happen?
Ans:  

• Yes, row 7 = column 7 (7×1, 7×2, … = 1×7, 2×7, …).  
• General: Row n = column n due to commutative property (a×b = b×a).

Q3: Is there a row where all answers (products) are even numbers? Which rows have this property
Ans: Rows 2, 4, 6, 8 (multiples of 2, 4, 6, 8 are even).

Q4: Is there a row having only odd numbers as products?
Ans: No; odd row (e.g., 7) has even products (e.g., 7×2 = 14).

Q5: Are there rows that have both even and odd numbers? What do you notice? Why is it so? 
Ans: Yes, the rows of 1, 3, 5, 7, and 9 have both even and odd numbers. It is because when an odd number is multiplied with an even number, we get an even number, but when an odd number is multiplied with another odd number, we get an odd number.

Q6: Are there more even numbers in the chart or odd numbers? How do you know?
Ans: More even; even rows dominate, and odd rows have even products.

Q7: Colour the common multiples of the following numbers. Use different colours for each item.
(a) 2 and 3
Ans: LCM = 6; multiples: 6, 12, 18, …

(b) 4 and 8
Ans: LCM = 8; multiples: 8, 16, 24, …

(c) 7 and 9
Ans: LCM = 63; multiples: 63, 126, 189, …
Observation: Common multiples are less frequent for larger numbers.

Q8: Observe the pattern in the ones digits of the products in row 5? Observe the ones digit of the products in other rows also. What  patterns do you notice?
Ans:  

• Row 5: 5, 10, 15, …; ones: 5, 0, 5, 0, … (repeats).  
• Row 8: 8, 6, 4, 2, 0, … (repeats every 5).  
• Pattern: Ones digits cycle based on multiplier.

Q9: Here is row 8 of the chart: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
The ones digit of the products are: 8, 6, 4, 2, 0, 8, 6, 4, 2, 0.
Do you see a repeating pattern here?
Guess the ones digit of the following products. Verify your answer by multiplying. Write the digit in the space given.
(a) 11 × 8
​(b) 12 × 8
(c) 13 × 8
Ans: Yes, the pattern of ones digits is 8, 6, 4, 2, 0 and is repeating. 
Since 1 × 8 = 8,
2 × 8 = 16, 3 × 8 = 24. So, the ones digits of 11 × 8, 12 × 8, and 13 × 8 are 8, 6, and 4, respectively.
11 × 8 = 88 12 × 8 = 96 13 × 8 = 104

Q10: In row 8 of the chart, there is no number whose ones digit is 1. What other digits do not appear as the ones digit?
Ans: Row 8: 8, 6, 4, 2, 0. Missing: 1, 3, 5, 7, 9.

Q11: Is there a row in which all the digits from 0 to 9 appear as the ones digit? Which rows have this property?
Ans: Yes, rows 1, 3, 7, and 9 have this property.

Q12: It can be seen in row 8 that 0 appears as the ones digit two times. 
____ × 8 gives 0 as the ones digit.
What numbers can go in the box? Give 5 examples of such numbers.
Ans: 5 × 8 = 40 or 10 × 8 = 80, gives 0 as the ones digit.
15 × 8 = 120, 20 × 8 = 160, 25 × 8 = 200, 30 × 8 = 240, 35 × 8 = 280.

Q13: Is there a row in which 0 appears as the ones digit only once? Which rows have this property?
Ans: Yes, the rows of 1, 3, 7, and 9 have this property.

Q14: What do you notice about the answers for Questions 11 and 13? Share in the grade.
Ans: Both have the same answers.

Page 137

 Multiples of Tens

Q1: Let us count the number of wheels in tricycles.

(a) Number of wheels in 10 tricycles with 3 wheels in each is 10 × 3 wheels = ______ wheels. 
Ans: Number of wheels in 10 tricycles with 3 wheels in each is 10 × 3 wheels = 30 wheels.

(b) Number of wheels in 10 more tricycles with 3 wheels in each is   10 × 3 wheels = _______ wheels. 
Ans: Number of wheels in 10 more tricycles with 3 wheels in each is 10 × 3 = 30 wheels.

(c) Number of wheels in 20 tricycles with 3 wheels in each is 20 × 3 wheels = ______ + _____ = ______ wheels.
Ans: Number of wheels in 20 tricycles with 3 wheels in each is 20 × 3 wheels = 30 + 30 = 60 wheels.

Q2: Let us count the number of wheels in cars.
(a) Number of wheels in 10 cars with 4 wheels in each is 10 × 4 wheels = _______ wheels. 
Ans: Number of wheels in 10 cars with 4 wheels in each is 10 × 4 wheels = 40 wheels.

(b) Number of wheels in 30 cars with 4 wheels in each is 30 × 4 wheels = _____ + _____ + _____ = _____ wheels.
Ans: Number of wheels in 30 cars with 4 wheels in each is 30 × 4 wheels = 40 + 40 + 40 = 120 wheels.

Q3: Solve the following in a similar way. Share how you found the answers.
(a) 10 × 6 = ________
Ans: 

• Multiplication: 10 × 6 means 10 groups of 6.
• I know that 10 × 6 = 60 (using basic multiplication facts).
• Alternatively, think of it as adding 6 ten times: 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 60.

(b) 40 × 6 = ________
Ans: 

• Break it down: 40 = 4 × 10, so 40 × 6 = (4 × 10) × 6.
• First, calculate 4 × 6 = 24.
• Then, multiply by 10: 24 × 10 = 240.
• Alternatively, use direct multiplication: 40 × 6 = 40 + 40 + 40 + 40 + 40 + 40 = 240.

(c) 10 × 8 = ________
Ans: 

• Multiplication: 10 × 8 means 10 groups of 8.
• I know that 10 × 8 = 80 (using basic multiplication facts).
• Alternatively, add 8 ten times: 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 80.

(d) 60 × 8 = ________
Ans: 

• Break it down: 60 = 6 × 10, so 60 × 8 = (6 × 10) × 8.
• First, calculate 6 × 8 = 48.
• Then, multiply by 10: 48 × 10 = 480.
• Alternatively, use direct multiplication: 60 × 8 = 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 = 480.

(e) 6 × 8  = ________
Ans: 

• Multiplication: 6 × 8 means 6 groups of 8.
• I know that 6 × 8 = 48 (using basic multiplication facts, often memorized in Class 4).
• Alternatively, think of it as adding 8 six times: 8 + 8 + 8 + 8 + 8 + 8 = 48.

(f) 4 × 6  = ________
Ans: 

• Multiplication: 4 × 6 means 4 groups of 6.
• I know that 4 × 6 = 24 (using basic multiplication facts).
• Alternatively, add 6 four times: 6 + 6 + 6 + 6 = 24.

(h) 40 × 8  = ________
Ans: 

• Break it down: 40 = 4 × 10, so 40 × 8 = (4 × 10) × 8.
• First, calculate 4 × 8 = 32.
• Then, multiply by 10: 32 × 10 = 320.
• Alternatively, use direct multiplication: 40 × 8 = 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 = 320.

Q: What happens when the number of groups is a multiple of 10?

Ans: If a number of groups is a multiple of 10, then it always ends with 0 as ones digit.

Page 138

Multiplying Using 10s

Q1: Radha is packing cupcakes in boxes of 4. She has packed 18 boxes. How many cupcakes are there in the packed boxes?

Ans: 

Q2: 8 bamboo rods are needed to make a bullock cart. How many bamboo rods are needed for 23 carts?
One cart needs 8 bamboo rods. 23 carts need 23 × 8 rods.
20 carts with 8 rods in each need 20 × 8 rods = ________ rods.
3 carts with 8 rods in each need 3 × 8 rods = _________ rods.
Ans: First, we calculate for 20 carts:
20 carts with 8 bamboo rods each = 20 × 8 = 160 rods.
Next, we calculate for 3 carts:
3 carts with 8 bamboo rods each = 3 × 8 = 24 rods.
Now, add the rods for all 23 carts:
160 + 24 = 184 rods.
So, 184 bamboo rods are needed for 23 carts.

Page 139

Let Us Solve

Q1: A flock of 25 geese and 12 sheep have gathered around a pond. Chippi the lizard sees many legs. How many legs does it see?
Ans:  Each goose has 2 legs, and each sheep has 4 legs.
25 geese have, 25 × 2 legs = 50 legs
12 sheep have, 12 × 4 legs = 48 legs
Total legs seen by Chippi = 25 geese’s legs + 12 sheep’s legs = 50 legs + 48 legs = 98 legs.

Q2: In an auditorium, 8 children are sitting in each row. There are 15 such rows in the school auditorium. How many children are in the auditorium?
Ans:  Children sitting in 1 row = 8
Children sitting in 15 rows = 15 × 8 = 120
So, 120 children are in the auditorium.

Q3: A book shop has kept 9 books in each pile. There are 14 such piles. How many books does the shop have?
Ans:  1 pile has 9 books.
14 piles have, 14 × 9 books = 126 books
So, the shop has a total of 126 books.

Q4: Surya is making a patch work with beads of two colours as shown in the picture. How many beads has he used? How many each of golden colour beads and white colour beads has he used in making this patch work?
Ans: Number of columns in the patch = 8
Number of beads in 1 column = 4 × 5 = 20
Total number of beads used by Surya = 20 × 8 = 160
Number of white beads in each consecutive 2 columns = 20,
so total number of white beads in the patch = 20 × 4 = 80
Also, Number of golden beads in each consecutive 2 columns = 20,
so total number of golden beads in the patch = 20 × 4 = 80.

Q5: For each of the following multiplication problems, make your own stories as above. Then find out the product.

a) 34 × 3 = 102
Story: There are 34 chairs, and each chair has 3 legs.
Answer: Total legs = 102

b) 75 × 5 = 375
Story: A classroom has 75 desks, and each desk has 5 books.
Answer: Total books = 375

c) 46 × 6 = 276
Story: A bus has 46 rows of seats, and each row has 6 seats.
Answer: Total seats = 276

d) 50 × 9 = 450
Story: A shopkeeper has 50 bags, and each bag contains 9 apples.
Answer: Total apples = 450

Page 140 & 141

Division

Q1: A factory has ordered 58 wheels for the small tempos that they make. Each tempo has 3 wheels. In how many tempos can they fix the wheels? Discuss your thinking in each step.
Number of tempos is 58 ÷ 3 

30 wheels are needed for 10 tempos. _______wheels are left.
15 wheels are needed for _______ tempos. _______wheels are left.
9 wheels are needed for_______ tempos. _______ wheels are left.
_______ wheels are needed for_______ tempos. _______ wheels are left.
Can we make another tempo? How many total tempos can the factory make using the 58 wheels? ___
With 58 wheels, we can make 19 tempos.  1 wheel is left.
Ans:  58 ÷ 3 = 19 tempos, 1 wheel left.  

Method:  

• 10 tempos: 30 wheels, 58 − 30 = 28 left.  
• 5 tempos: 15 wheels, 28 − 15 = 13 left.  
• 3 tempos: 9 wheels, 13 − 9 = 4 left.  
• 1 tempo: 3 wheels, 4 − 3 = 1 left.
• Total: 10 + 5 + 3 + 1 = 19 tempos.  
• Ans: 19 tempos, 1 wheel left.

Q2: A dairy farm has many cows. Chippi the lizard is surprised to see 88 legs. How many cows are there in the farm? Write appropriate sentences as above to show your thinking.
Number of legs of a cow: ________ 
Number of cows is 88 ÷ ________
Show your work using the table below. Hint: Taking out groups of 10s is easy.
Total number of cows = ______
Ans:  88 ÷ 4 = 22 cows.  
Method:  

Total: 10 + 10 + 2 = 22 cows.  

Ans: 22 cows.

Let Us Solve

Q1: In a big aquarium, Jolly fish sees 72 legs of octopuses. How many octopuses are there in the aquarium?

Ans:  72 ÷ 8 = 9 octopuses.  
Method: 5 × 8 = 40, 4 × 8 = 32, 40 + 32 = 72, 5 + 4 = 9.  
Ans: 9 octopuses.

Q2: A sports store packs 4 shuttlecocks in a bigger box. They have 50 shuttlecocks. How many boxes will they need to pack all of them? Can they pack all the shuttlecocks in the boxes? How many are left?
Ans:  50 ÷ 4 = 12 boxes, 2 left.  
Method: 10 × 4 = 40, 2 × 4 = 8, 40 + 8 = 48, 50 − 48 = 2.  
Ans: 12 boxes, 2 shuttlecocks left.

Q3: Rakul Chachi uses a part of her farm to grow flowering plants for the upcoming festive season. She has planted 75 saplings of roses. Each row has 5 saplings. How many rows of saplings has she planted?
Ans:  75 ÷ 5 = 15 rows.  
Method: 10 × 5 = 50, 5 × 5 = 25, 50 + 25 = 75, 10 + 5 = 15.  
Ans: 15 rows.

Q4: Make stories for the following problems and solve them:

a) 70 ÷ 5

Story:
Riya has 70 candies. She wants to share them equally among 5 friends.
How many candies will each friend get?

Solution:
70 ÷ 5 = 14
Answer: Each friend will get 14 candies.

b) 84 ÷ 7

Story:A librarian has 84 books. She wants to place them equally on 7 shelves. How many books will go on each shelf?

Solution:
84 ÷ 7 = 12
Answer: Each shelf will have 12 books.

c) 69 ÷ 3

Story:
There are 69 eggs packed in trays. Each tray holds 3 eggs.
How many trays are needed?

Solution:
69 ÷ 3 = 23
Answer: She needs 23 trays.

d) 93 ÷ 6

Story:
A teacher has 93 chairs to arrange around 6 tables.
How many chairs will be around each table, and how many will be left?

Solution:
93 ÷ 6 = 15 remainder 3
Answer: Each table will get 15 chairs, and 3 chairs will be left.

Page 142

Multiples of 100
100 bikes with 2 people on each have 100 × 2 people =  _____ people. 
200 bikes with 2 people on each have ______people. How did you find it? 
100 cars with 4 people in each have 100 × 4 people = _______ people. 
500 cars with 4 people in each have ______people. How did you find it?
Ans:  100 bikes with 2 people on each have
= 100 × 2 people
= 200 people.

​200 bikes with 2 people on each have
= 200 × 2 people
= 100 × 2 people + 100 × 2 people
= 200 people + 200 people
= 400 people.

​100 cars with 4 people in each have
= 100 × 4 people
= 400 people.

​500 cars with 4 people in each have
= 500 × 4 people
= (100 × 4 + 100 × 4 + 100 × 4 + 100 × 4 + 100 × 4)
= (400 + 400 + 400 + 400 + 400) people
= 2000 people.

How did you find it?
500 × 4 = _____
100 × 4 = _____
5 × 4 = _____
50 × 4 = _____
Ans:
We multiplied the number of bikes by the number of people on each bike.
500 × 4 = 2000
5 × 4 = 20
100 × 4 = 400
50 × 4 = 200

What do you notice about multiplying by multiples of 100s?

• Ignore the zeros, multiply the other numbers, then add two zeros at the end.

Examples:

• 6 × 100 = 600 (6 × 1 = 6, add two zeros)
• 4 × 300 = 1200 (4 × 3 = 12, add two zeros)

Rule:
Multiply the main numbers, then add 00.

Page 143

Q: Observe the pattern and complete the answers.

Ans:

Page 143

More Multiplication

Q1: Big electric autorickshaws run in small towns of India and can carry 8 passengers. How many people can travel in 125 such autos in a single round?
The total number of passengers 125 × 8.
100 autorickshaws with 8 passengers in each have 100 × 8 passengers = ______ passengers.
20 autorickshaws with 8 passengers in each have 20 × 8 passengers = _______ passengers.
5 autorickshaws with 8 passengers in each have 5 × 8 passengers = __________ passengers.
125 autorickshaws with 8 passengers in each have ____ + ____ + ______= _________ passengers.
Ans:  The total passengers are 125 100 autorickshaws with 8 passengers in each have
= 100 × 8 passengers
= 800 passengers
20 autorickshaws with 8 passengers in each have = 20 × 8 passengers = 160 passengers
5 autorickshaws with 8 passengers in each have = 5 × 8 passengers = 40 passengers
125 autorickshaws with 8 passengers in each have = 800 + 160 + 40 = 1000 passengers  

Q2: Kahlu and Rabia are potters and make earthen pots (kulhad) for trains.
They pack 6 kulhads in a box and have packed 174 boxes for delivery. How many kulhads have they made?
The total number of kulhads is ________.

Ans:  The total number of kulhads is 174 × 6 = 600 + 420 + 24 = 1044

Page 144 & 145

Let Us Solve

Q1: BP Girl’s school has decided to give all its students two pencils on the first day of school. It has 465 students. How many pencils does the school need to buy?
Ans:  Number of pencils given to each student = 2
Total number of students = 465
Total pencils school need to buy = 465 × 2 = 800 + 120 + 10 = 930

Q2: 234 children of a school have decided to organise a school mela. Each child contributes ₹5 for the organisation of the mela. How much money do they collect?
Ans:  Money contributed by each child = ₹ 5
Total children in school mela = 234
Money collected for school mela = 234 × ₹ 5

​The total money collected from 234 children, with each contributing ₹ 5 = ₹ 1000 + ₹ 150 + ₹ 20 = ₹ 1170

Q3: Make stories for the following problems and solve them.

a) 439 × 4

Story:
A school has 439 students in each house. There are 4 houses in the school.
How many students are there in total?

Solution:
439 × 4 = 1,756

Answer: There are 1,756 students in total.

b) 514 × 8

Story:
A library has 514 books on each shelf. There are 8 shelves.
How many books are there in all?

Solution:
514 × 8 = 4,112

Answer: The library has 4,112 books.

c) 356 × 5

Story:
A factory packs 356 toys in each box. There are 5 boxes.
How many toys are packed?

Solution:
356 × 5 = 1,780

Answer: There are 1,780 toys packed.

d) 623 × 7

Story:
There are 623 apples in each basket. A farmer has 7 baskets.
How many apples does the farmer have?

Solution:
623 × 7 = 4,361

Answer: The farmer has 4,361 apples.  

Page 146

Patterns in Division

How much money will each get? Draw arrows linking the money and the children to answer the questions.
Ans: 

1. ₹ 30 shared equally among 3 children ______________ 

We divide ₹30 by 3:

• ₹30 ÷ 3 = ₹10
  Each child will get ₹10

2. ₹ 900 shared equally among 3 children ______________

We divide ₹900 by 3:

• ₹900 ÷ 3 = ₹300
  Each child will get ₹300

Ans:  

Q1: A load carrying truck has 6 tyres. Chippi the lizard sees 60 tyres. How many trucks are there?
Ans:  We know 1 truck has 6 tyres.
If there are 60 tyres, we divide:

60 ÷ 6 = 10 trucks

(Each truck has 6 tyres. So 10 trucks × 6 tyres = 60 tyres)

Q2: Chippi sees 80 wheels in a car parking space. How many cars are standing in the parking space?
Ans: We know 1 car has 4 wheels.
If there are 80 wheels, we divide:

80 ÷ 4 = 20 cars

(Each car has 4 wheels. 20 × 4 = 80 wheels)

Q3: Chippi sees 600 legs of ants walking towards the anthill. How many ants are there?
Ans: We know 1 ant has 6 legs.
If there are 600 legs, we divide:

600 ÷ 6 = 100 ants

(Each ant has 6 legs. 100 × 6 = 600 legs)

Q4: A fancy shop has packed 800 rubber bands in several packets. Each packet has 4 rubber bands. How many packets of rubber bands does the shop have?
Ans: We know 1 packet = 4 rubber bands
If there are 800 rubber bands, we divide:

800 ÷ 4 = 200 packets

(Each packet holds 4 rubber bands. 200 × 4 = 800)

Page 147

Let Us Solve

Q1: A school bus hires 7 buses to take 245 children to the transport museum. Each bus carry the same number of children. How many children are traveling  in each bus?
Ans:  245 ÷ 7 = 35 children/bus.  
Method: 30 × 7 = 210, 5 × 7 = 35, 210 + 35 = 245, 30 + 5 = 35.  
35 children/bus.

Q2: The Darjeeling Himalayan Railway is fondly called the “Toy Train”. This toy train ride is also a UNESCO World Heritage Site. This amazing train runs between New Jalpaiguri and Darjeeling and it also passes through one of the highest stations in the world, namely, Ghum. It runs 88 km daily. How much distance does it travel in a week?
Ans: 88 × 7 = 616 km.  
Method: 80 × 7 = 560, 8 × 7 = 56, 560 + 56 = 616.  

Q3: The 16 Km river rafting from Shivpuri to Rishikesh in the Ganga provides the most interesting rafting opportunity. In the summer months, Venture Out company took 259 people for rafting. Each raft can take 7 people. How many rafts did it take?

Ans:  259 ÷ 7 = 37 rafts.  
Method: 30 × 7 = 210, 7 × 7 = 49, 210 + 49 = 259, 30 + 7 = 37.  
Ans: 37 rafts.

Q4: Anu saves ₹45 every month by putting it in her piggy bank.
(a) How much money will Anu save in 6 months?
Ans: Money saved by Anu in 6 months = ₹ 45 × 6 = ₹ 40 × 6 + ₹ 5 × 6 = ₹ 240 + ₹ 30 = ₹ 270

(b) She distributes the total money saved after 6 months among 6 of her friends. How much does each friend get?
Ans: Total money distributed equally 210 among 6 friends.
So, money got by each 90- friend = ₹ 270 ÷ 3
= ₹(10 + 10 + 10 + 10 + 5)
= ₹ 45

(c) If she decides to distribute the saved money among 3 friends after 6 months, how much money will each get?
Ans: Money saved by Anu in 6 months = ₹ 270
Money got by each of 3 friends = ₹ 270 – 3
= ₹ (10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10) = ₹ 90

Q5: Raju drives an auto in his village and takes people to the bus stand. He makes 8 trips in a day. Which of the following questions can be exactly calculated with the above statement?
(a) How much money does he make in a day?
Ans: We cannot say how much money he makes in a day as the price of each trip is not given.

(b) How many trips does he make in 7 days?
Ans: Number of trips made in 7 days = 8 trips × 7 = 56 trips.

(c) How much time does one trip take?
Ans: We cannot say how much time he takes for a trip, as time is not mentioned.

(d) How many trips does he make in 4 weeks?
Ans: Number of trips in a week (7 days) = 8 × 7 = 56
Number of trips in 4 weeks = 56 × 4 = 50 × 4 + 6 × 4 = 200 + 24 = 224.

Page 148

Let Us Solve

Q6: Solve:
(a) 45 × 9
Ans: 405 (40 × 9 = 360, 5 × 9 = 45, 360 + 45 = 405)

(b) 507 × 7
Ans: 3549 (500 × 7 = 3500, 7 × 7 = 49, 3500 + 49 = 3549)

(c) 94 ÷ 4
Ans: 23, remainder 2 (20 × 4 = 80, 3 × 4 = 12, 80 + 12 = 92, 94 − 92 = 2)

(d) 778 ÷ 6
Ans: 129, remainder 4 (100 × 6 = 600, 20 × 6 = 120, 9 × 6 = 54, 600 + 120 + 54 = 774, 778 − 774 = 4)

(e) 94 × 5
Ans: 470 (90 × 5 = 450, 4 × 5 = 20, 450 + 20 = 470)

(f) 396 × 4
Ans: 1584 (300 × 4 = 1200, 90 × 4 = 360, 6 × 4 = 24, 1200 + 360 + 24 = 1584)

(g) 83 ÷ 3
Ans: 27, remainder 2 (20 × 3 = 60, 7 × 3 = 21, 60 + 21 = 81, 83 − 81 = 2)

(h) 635 ÷ 5
Ans: 127 (100 × 5 = 500, 20 × 5 = 100, 7 × 5 = 35, 500 + 100 + 35 = 635, 100 + 20 + 7 = 127)

Q7: In mathematics, some statements are always true, some are sometimes true, and some are never true.
Tick (√) in the appropriate column.

Ans: 

Page 115

Weigh It, Pour It

Q1: Look at the pictures given and write the names of the animals from heaviest to lightest.

Ans: Elephant > Giraffe > Dog > Squirrel > Ant

Q2: Write the name of the heaviest object in your home. How did you know?

Ans: Example: Fridge. Known by estimating or lifting, it feels much heavier than other objects like chairs or tables.

Q3: Do you carry your school bag with ease or with some effort?

Ans: With some effort (depends on bag weight, typically 2–5 kg for Class 4 students).

Q4: Write the name of the heaviest book in your bag. How did you know?

Ans: Example: Maths textbook. Known by comparing books; it feels heavier or looks thicker.

Q5: What is your weight? How did you know?

Ans: Example: 25 kg. Known by using a weighing scale at home or school.

Fun at Vegetable Market!

Rita and Shabnam went to the market to buy some fruits and vegetables. They saw the vegetable seller weighing vegetables.

Q: What do you think will be the weight of the half pumpkin?

Ans: A whole pumpkin is typically 2–5 kg. Half a pumpkin: ~1–2.5 kg (e.g., half of 4 kg = 2 kg). Verify with a scale.

Page 116

 Let Us Do

Q: Estimate the weight of the following and put a tick mark (✓) in the appropriate cell. Verify with a weighing balance.

Ans:  

Page 117

Let Us Find

Q1: How many 250 g daal packets will balance one 500 g daal packet? Draw as many packets of 250 g on the empty pan to balance the 500 g packet. What did you find? 250 g = ___ of 500 g (½, 2).

Ans:  

• 500 g ÷ 250 g = 2 packets of 250 g.  
• Draw 2 packets of 250 g on the empty pan to balance.  
• Ans: 250 g = ½ of 500 g.

Page 118

Let Us Find

Q2: Draw arrows to indicate which side the pan balance will tilt?

Ans: 

Q3: Match the unit convenient for measuring each of the following objects?

Ans: 

Page 119

 Let Us Do

Q1: How many erasers will weigh the same as a 50 g Haldi packet?

Ans: Assume an eraser weighs ~10 g. 50 g ÷ 10 g = 5 erasers.

So, 5 erasers will weigh equal to a 50 g Haldi packet.

Q2: A 100 g soap bar will weigh the same as ___ erasers.

Ans: 10 g = 1 eraser
⇒ 100 g = 10 × 10 g = 10 × 1 eraser = 10 erasers
So, 100 g soap bar will weigh the same as 10 erasers.

Q3: ___ erasers will weigh the same as 250 g sugar.

Ans: 10 g =1 eraser
⇒ 250 g = 25 × 10 g = 25 × 1 eraser = 25 erasers
So, 25 erasers will weigh the same as 250 g of sugar.

Page 119

Let Us Think (Boxes of Sweet)

Mr Shrinathan, a sweet shop owner, has several orders for 1 kg Kaju-katli but he has to pack them in different sized boxes.

Write the number of boxes needed to pack 1 kg Kaju-katli in the blank space:

1. Mr Das wants the sweets in boxes weighing 500 g each.
Ans: Since 1 kg = 1000 g
= 500 g + 500 g = 2 × 500 g
So, Mr Shrinathan needs 2 boxes of500 g each to pack 1 kg Kaju-Katli.

2. Mrs Fernandes wants the sweets in boxes weighing 250 g each.
Ans: Since 1 kg = 1000 g
= 250 g + 250 g + 250 g + 250 g = 4 × 250 g
So, Mr Shrinathan needs 4 boxes of250 g each to pack 1 kg Kaju-Katli.

3. Mrs Khan wants the sweets in boxes weighing 100 g each. 
Ans: Since 1 kg = 1000 g
= 100 g + 100 g + 100 g + 100 g + 100 g + 100 g + 100 g + 100 g + 100 g + 100 g
= 10 × 100 g
So, Mr Shrinathan needs 10 boxes of 100 g each to pack 1 kg Kaju-Katli.

4. Mr Patel wants the sweets in boxes weighing 50 g each.
Ans: Since 1 kg = 1000 g
= 10 × 100 g
= 10 × (2 × 50 g)
= 20 × 50 g
So, Mr Shrinathan needs 20 boxes of 50 g each to pack 1 kg Kaju-Katli.

Page 120

Weighing Machines

Do you know the different types of weighing machines used to weigh different objects?

Ans: Do it Yourself!

Q: Ask your parents and find the amount of consumption of the following items at your home in a month.

Ans: Example (varies by household):  

Taran and his sister are lifting packets of flour, rice, and salt.

 What do you think they are experiencing while lifting these packets? Have you ever lifted such packets at your home? What do you experience? Discuss.

Ans: They feel effort while lifting heavy packets (e.g., 5 kg flour is harder than 1 kg salt). 

Personal experience: Lifting 5 kg rice feels heavy, requires both hands; 1 kg salt is easier. 

Discuss: Heavier packets strain arms, lighter ones are manageable.

Page 121

 Let Us Do

Q1: Try to lift some objects around you and write the names of three objects that you can lift easily. Estimate and write their weights.

Ans:  

• Pencil: ~10 g  
• Notebook: ~200 g  
• Water bottle: ~500 g

Q2: Now write the names of things that you can lift with a lot of effort. Estimate and write their weights.

Ans:  

• School bag: ~3 kg  
• Chair: ~5 kg  
• Bucket of water: ~10 kg

Q3: How many 1 kg packets are in:
a. 10 kg
Ans: 10 kg = 10 × 1 kg
There are 10 packets of 1 kg each in 10 kg.
b. 20 kg
Ans: 20 kg = 20 × 1 kg
There are 20 packets of 1 kg each in 20 kg.
c. 50 kg
Ans: 50 kg = 50 × 1 kg
There are 50 packets of 1 kg each in 50 kg.
d. 25 kg
Ans: 25 kg = 25 × 1 kg
There are 25 packets of 1 kg each in 25 kg.

Q4: Match the objects in the left column with their estimated weights in the right column.

Ans: 

Page 122

Measuring Capacity

Q: Do you remember the 1 litre bottle? How much water does your water bottle hold?

 Find bottles and containers that can hold the following quantities of water.

Ans: Example: My water bottle holds 1 litre.  

Page 123

Let Us Find

a) How many 500 ml bottles will fill a 1 l bottle?

Ans: Since 11 = 1000 ml = 500 ml + 500 ml
= 2 × 500 ml
Thus, two 500 ml bottles will fill a 1 l bottle.

b) How many 250 ml bottles will fill a 1 l bottle?

Ans: Since 1 l = 1000 ml
= 250 ml + 250 ml + 250 ml + 250 ml
= 4 × 250 ml
Thus, four 250 ml bottles will fill a 1 litre bottle.

c) How many 100 ml bottles will fill a 1 l bottle?

Ans: Since 11= 1000 ml
= 100 ml + 100 mlm + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml
= 10 × 100 ml
Thus, ten 100 ml bottles will fill a 1 l bottle.

d) How many

Ans: 

1/2 l = 1/2 × 1000 ml = 500 ml
= 250 ml + 250 ml
= 2 × 250 ml
So, there are two 250 ml in 12 l.

750 ml = 250 ml + 250 ml + 250 ml
= 3 × 250 ml
So, there are three 250 ml in 750 ml.

1/2 l = 1/2 × 1000 ml = 500 ml
= 100 ml + 100 ml + 100 ml + 100 ml + 100 ml
= 5 × 100 ml

So, there are five 100 ml in 12 l.
800 ml = 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml
= 8 × 100 ml
So, there are eight 100 ml in 800 ml.

Page 124

Let Us Do

Q1: Find a dosing cup or a bottle of 10 ml and try to find how many 10 ml will fill a 100 ml bottle __________________

Ans: 100 ml = 10 × 10 ml
So, ten 10 ml cups will fill a 100 ml bottle.

Find how many 10 ml dosing cups will fill:
a) 250 ml glass
Ans:  250 ml = 25 × 10 ml
So, 25 dosing cups of 10 ml will fill a 250 ml glass.
b) 500 ml vessel
Ans: 500 ml = 50 × 10 ml
So, 50 dosing cups of 10 ml will fill a 500 ml vessel.
c) 1 l bottle
Ans: 1 l = 1000 ml = 100 × 10 ml
So, 100 dosing cups of 10 ml will fill a 1 l bottle.

Q2: Take a 1 ml dropper and find out:
a) How many 1 ml droppers will fill a 10 ml dosing cup?
Ans: 10 ml ÷ 1 ml = 10 droppers
b) How many droppers will fill a teaspoon?
Ans: A teaspoon is ~5 ml. 5 ml ÷ 1 ml = 5 droppers  

Q3: Find out how much of these liquids are used at a time:
a) Eye drops
Ans: Less than 1 ml (e.g., 0.05 ml per drop)
b) Honey
Ans: ~5–15 ml (1–3 teaspoons)
c) Cough Syrup
Ans: ~5–10 ml (per dose, check label)
d) Cooking Oil
Ans: ~15–30 ml (1–2 tablespoons per dish)

Page 125

Let Us Do

Q4: Mr Krishna packages perfumed oils in different sized bottles. During a festival, the following customers asked for 1 l perfumed oils but in different sized bottles. Write the number of bottles each of them will get.
a) Ms Shetty wants bottles of 500 ml each
Ans: 1 l = 1000 ml = 500 ml + 500 ml
So Mr Krishna needs two 500 ml sized bottles.
b) Mr Muthukumar wants bottles of 200 ml each
Ans: 1 l = 1000 ml = 200 ml + 200 ml + 200 ml + 200 ml + 200 ml
So, Mr Krishna needs five 200 ml sized bottles.
c) Ms Naini wants bottles of 100 ml each
Ans: 1 l = 1000 ml = 10 × 100 ml
So, Mr Krishna needs ten 100 ml sized bottles.
d) Ms Kannan wants bottles of 50 ml each
Ans: 1 l = 1000 ml = 20 × 50 ml
So, Mr Krishna needs twenty 50 ml sized bottles.

Q5: Estimate and verify by measuring. Use the bottles you have collected for this purpose (for example, 500 ml, 250 ml, 100 ml, 50 ml, and 10 ml).

Ans:  

Page 125

Let Us Explore

Q: Visit nearby shops and make a list of different items that are sold in the following quantities.

Ans:  

Page 126

Let Us Find

a) How many litres of water do you drink in a day? How did you find out?

Ans: ~1–2 litres. Found by counting glasses (e.g., 4 glasses × 250 ml = 1 litre).

b)  How much water can a crow drink at a time?

Ans: ~10–20 ml (based on small beak capacity).

c) How much milk do you drink in one day?

Ans: ~200–500 ml (e.g., 1–2 glasses of 200 ml).

d) How much water does an elephant drink in a day?

Ans: ~100–200 litres (based on known elephant consumption).

Q: What do you use the most water for? What do you use the least water for? Compare this with a few others in your grade . In which activities is your water usage the same?

Ans:  

• Most: Bathing (~20–50 litres)  
• Least: Drinking (~1–2 litres)
  Compare: Most classmates use similar amounts for bathing; drinking varies slightly.

Q: How much water may be used in the following activities?
a. Water for taking a shower
Ans: ~20–50 litres (bucket bath or 5–10 min shower)
b. Watering crops in a field
Ans: ~1000–5000 litres (depends on field size)
c. Watering flowering plants
Ans: ~1–5 litres per plantd. Washing clothes
Ans: ~20–100 litres (manual or machine wash)

Page 127

Water Conservation in Everyday Life

 Take a container and put it under a leaking tap for an hour. How much water is lost in an hour? Did it surprise you?

Ans: ~100–500 ml (slow drip, e.g., 1–5 ml per minute). Surprising as small drips add up significantly.

Q: How much water is lost in a day?

Ans: If water drips slowly and fills about 1 glass (250 ml) in an hour, then:
In a day (24 hours) → 250 ml × 24 = 6,000 ml = 6 liters

About 6 liters of water can be lost in one day from a slow drip.

Q: How much water is lost in a week?

Ans: If 6 liters are lost in a day, then in 7 days:
6 liters × 7 = 42 liters

 Around 42 liters of water can be wasted in one week.

Q: How would this wastage of water affect us?

Ans: Wasting water means we will have less clean water to use for drinking, bathing, cooking, and growing food. It can also lead to water shortages in the future. We should save water because it is very precious.

Page 96 to 98

Daisy and Lou Go Shopping

Q: Daisy and Lou are very excited about their trip. They join their mother in the weekly shopping as they need to buy things for their trip. The family makes a list of things to buy:  

• Fruits and vegetables 
• Field Trip Items-Biscuits, Water Bottles, and Dry Fruits. 

Sapan Dada has a cart for selling vegetables and fruits. The prices of the vegetables and fruits are given below.

Sapan Dada asks Daisy and Lou to find the costs of different quantities of fruits and vegetables. Help them to complete the tasks. You may use a number line, play money or any other method to calculate.

Ans: The amount is double.

Q: Their mother buys things for ₹163. What might she have bought? There is more than one possibility.

Ans: Since, ₹ 163 = ₹ 45 + ₹ 95 + ₹ 23 = ₹ 70 + ₹ 70 + ₹ 23
So, the mother might have bought 1 kg custard apple, 1 kg beans, and 1 kg radish or 2 kg sapota and 1 kg radish or 1 kg beans, 1 kg yam and 1 kg radish.

Q: Daisy and Lou help Udaya Didi return the balance to customers. Calculate the balance for the given transactions.

Ans: 

Q: Lou and Daisy buy 3 kg bananas to eat on the way with their friends. Which of the following options can they use to buy the bananas?

Ans: Cost of 1 kg banana = ₹ 55
Cost of 3 kg banana = ₹ 55 + ₹ 55 + ₹ 55 = ₹ 165
Therefore, Lou and Daisy will choose the option (b) to by the bananas.

Page 99

A Strange Puzzle!

Q: Four kids buy two oranges each at ₹21 per orange. They pay different notes: Krishna (₹50), Sudama (₹100), Mala (₹200), Neela (₹500). What is the balance each got?

Ans: Cost for 2 oranges = 2 × ₹21 = ₹42

• Krishna: Paid ₹50, Balance: ₹50 − ₹42 = ₹8
• Sudama: Paid ₹100, Balance: ₹100 − ₹42 = ₹58
• Mala: Paid ₹200, Balance: ₹200 − ₹42 = ₹158
• Neela: Paid ₹500, Balance: ₹500 − ₹42 = ₹458

Page 100

Let Us Play

Q1: Place the numbers 1–6 in the blanks so the sum on each side of the triangle is 9. No numbers should be repeated.

Ans:  Place numbers such that each side (3 numbers) sums to 9:

• Vertices: 1, 2, 3; Sides: 4, 5, 6

1 + 6 + 2 = 2 + 4+ 3 = 3 + 5 + 1 = 9

Q2: Use the same numbers 1–6 and make the sum 10 on each side of the triangle.

Ans: Example: 1, 3, 5 at corners; 2, 4, 6 on sides, arranged so each side sums to 10 (e.g., 1 + 4 + 5 = 10).

1 + 4 + 5 = 5 + 2 + 3 = 3 + 6 + 1 = 10

Q3: What other sums can you make with these 6 numbers? Can you make 12 on each side? Can you make 13?

Ans:

4 + 5 + 2 = 2 + 3 + 6 = 4 + 1 + 6 = 11
Thus the other sum can we make using these numbers is 11.

4 + 3 + 5 = 5 + 1 + 6 = 6 + 2 + 4 = 12
But we cannot make 13 using numbers 1-6 on each side of the triangle without repetition of the numbers. In a magic triangle, the numbers on each side must add to the same total. To get the highest possible side sum, we place the highest numbers (6, 5, 4) at the corners. Their sum, 6 + 5 + 4 = 15. Since corner numbers are counted twice, total corner sum = 15 × 2 = 30. Now, the sum of the remaining middle numbers = 1 + 2 + 3 = 6. So, maximum total side of sum 30 + 6 = 36. Therefore, maximum possible side sum = 36 + 3 = 12. Therefore, it is impossible to create a magic triangle with a sum of 13 using numbers 1-6 on each side of the triangle without repeating the numbers.

Q: What strategy did you use to place the numbers?
Ans: Start with the smallest or largest numbers at corners, then adjust side numbers to balance the sum. Check each side’s sum and swap numbers if needed to ensure equality.

Page 101Add UpQ1: Estimate the number of teachers going. How many teachers are accompanying the children?
Ans:

• Estimate: 24 + 28 ≈ 20 + 30 = 50 teachers.
• Exact: 24 + 28 = 52 teachers.

Q2: How many children are going on the trip? Estimate the number of children.

Ans:

• Exact: 438 (from school) + 476 (neighbourhood school) = 914 children.
• Estimate: 438 ≈ 400, 476 ≈ 500, so 400 + 500 = 900 children.

Page 103

Daisy and Lou’s Spending

Q: Daisy and Lou ate one large piece of pusaw for ₹38. They liked it a lot and bought another small piece for ₹ 16. How much did they spend on pusaw?

Ans: ₹38 + ₹16 = ₹54

Page 104Daisy and Lou’s Piggy BankQ: Daisy and Lou had collected ₹ 185 in their piggy bank. Their mother gave them ₹ 125 more for the trip. How much money did they take for the trip?

Ans:

Daisy and Lou took ₹ 310 for the trip.

Page 105

Let Us Do

Q1: In Kalakshitij, a school of performing arts, the following number of students are learning to sing and play the tabla. Estimate and then find the total number of students.

15 more girls join the music school and they want to learn to play the tabla. How many girls play the tabla now?

Ans:

• Boys: 78 (Tabla) + 532 (Singers) = 610
• Girls: 95 (Tabla) + 346 (Singers) = 441
• Total Tabla: 78 + 95 = 173
• Total Singers: 532 + 346 = 878
• Total Students: 610 + 441 = 1051
• Estimate: 78 ≈ 80, 532 ≈ 500, 95 ≈ 100, 346 ≈ 350; Total ≈ 80 + 500 + 100 + 350 = 1030
• New tabla girls: 95 + 15 = 110

Q2: Add by aligning the numbers in columns.

a) 32 + 47
Ans: 79b) 654 + 95
Ans: 749c) 286 + 123
Ans: 409d) 476 + 324
Ans: 800e) 700 + 289
Ans: 989f) 534 + 483
Ans: 1017

Q3: Preeti’s school has 423 children. Her school has 178 less than her cousin’s school. How many children in Preeti’s cousin’s school?

Ans: Preeti’s cousin’s school has 178 children more than Preeti’s school.
So, number of children in Preeti’s cousin’s school = 423 + 178 = 601 children

Page 108 & 110

Let Us Solve

Q1: Ram Chacha got 264 mangoes from his mango tree last year. This year he got 527 mangoes. How many more mangoes did he get this year?

Ans: 

Thus, this year Ram Chacha got 263 more mangoes than previous year.

Q2: During the festival of dolls (Gombe Habba in Dussehra), Ranganna made 639 dolls. He was able to sell 531 dolls. How many dolls are left with him?
Ans: 

No. of dolls left = 639 – 531 = 108.

Q3: Subtract by aligning the numbers in columns.
a) 83 − 29
Ans:b) 345 − 123
Ans: 

c) 763 − 437
Ans: 

d) 803 − 350
Ans: 

e) 900 − 328
Ans: 

Page 109

Let Us Solve

Q1. These books are in the community library of Wakanda village. Children borrow these books to read during their vacation. 

 a) Rami read Panchatantra Tales during the summer vacation. Kesu read Akbar Birbal, Karadi Tales and Blue Umbrella. Who do you think read more? How many more pages?

Ans: Rami read: Panchatantra Tales = 236 pages

• Kesu read:
  • Akbar Birbal = 96 pages
  • Karadi Tales = 30 pages
  • Blue Umbrella = 90 pages
  • Total = 96 + 30 + 90 = 216 pages

Rami read more pages.

Rami read more. She read 20 pages more than Kesu.

b) Sumi read 23 pages of Adventures of Feluda. How many more pages to complete?

Ans: Total pages in Adventures of Feluda = 128

Pages read = 23

Pages left = 128 – 23 = 105

c) Jaggu finished Swami and Friends, Akbar Birbal, and 50 pages of Feluda. How many more pages to finish all books?

Ans: Total pages = 179 + 236 + 30 + 96 + 90 + 128 = 759 pages

Pages Jaggu has read:

• Swami and Friends = 179
• Akbar Birbal = 96
• Feluda = 50
  Total read = 179 + 96 + 50 = 325 pages

Pages left = 759 – 325 = 434 pages

Page 110

Train Between Delhi and Aligarh

Q2: A daily train between Delhi and Aligarh travels a distance of 131 km. Look at the picture below and answer the questions that follow.

a) How many passengers are there on the train when it leaves Dadri?
Passengers boarded at New Delhi = 894
Passengers boarded at Ghaziabad = 158
Passengers alighted at Ghaziabad = 23
Passengers boarded at Dadri = 67
Passengers alighted at Dadri = 75

Total passengers after Dadri = 894 + 158 – 23 + 67 – 75 = 1021

Answer: 1021 passengers

b) Find the number of people who got off the train at Aligarh.
The train had 1021 passengers after leaving Dadri. If all the remaining passengers got off at Aligarh, then:
Answer: 1021 people

c) Were there more people on the train in New Delhi or in Aligarh? How much more/less?
Passengers in New Delhi = 894
Passengers in Aligarh = 1021

1021 – 894 = 127 more passengers in New Delhi

Answer: There were 127 more people on the train in New Delhi than in Aligarh.

d) How many people travelled altogether by the train?
Total passengers who boarded:
New Delhi = 894
Ghaziabad = 158
Dadri = 67

Total = 894 + 158 + 67 = 1119

Answer: 1119 people travelled altogether by the train.

Page 111

Let Us Solve

Solve:
Ans: 

c) Find quick ways of solving. Think about some of the strategies you learnt in Grade  3.

Ans: 

d)Solve by aligning the numbers in columns in your notebook.
1. 38 + 943
Ans: 

​2. 465 + 305
Ans: 

​3. 435 + 462
Ans: 

​4. 764 – 657
Ans: 

​5. 518 – 209
Ans: 

​6. 879 – 53
Ans: 

e) Find two numbers such that their sum is 856. Find another two numbers such that their difference is 563. Make your own word problems with these numbers.

Ans: 

Page 112

Number Pair Hunt

Here is a grid of numbers. There are many number pairs in this grid. A number pair has 2 numbers which are next to each other, vertically or horizontally. For example, the numbers 111 and 185 are number pairs 48 and 185 are number pairs in this grid.

 1. Find the number pair whose sum is the greatest. 

2. Find the number pair whose sum is the smallest. 

3. Find the number pair whose difference is the greatest. 

4. Find the number pair whose difference is the smallest.

Ans:

1. Greatest sum: Choose largest pair (e.g., 300 + 321 = 621).
2. Smallest sum: Choose smallest pair (e.g., 48 + 35 = 83).
3. Greatest difference: Largest − smallest (e.g., 321 − 35 = 286).
4. Smallest difference: Closest pair (e.g., 111 − 100 = 11).

Page 113

The Missing Digits

Q: Fill the missing digits to make the sums correct.

Ans: 

Page 114Let Us DoQ1: Add.
(a) 23 + 489
Ans:
 

​(b) 105 + 295
Ans: 

​(c) 630 + 56
Ans: 

​(d) 35 + 99
Ans: 

​(e) 409 + 387
Ans: 

​(f) 67 + 76
Ans: 

​(g) 580 + 207
Ans: 

​(h) 333 + 666
Ans: 

​(i) 826 + 268
Ans: 

Q2: Subtract.

(a) 300 – 45
Ans: 

​(b) 962 – 268
Ans: 

​(c) 706 – 209
Ans: 

​(d) 842 – 387
Ans: 

​(e) 674 – 76
Ans: 

​(f) 754 – 409
Ans: 

​(g) 403 — 245
Ans: 

​(h) 600—384
Ans: 

​(i) 546 — 538
Ans: 

Page 80: Let Us Observe

Q1: Look at the picture. What are the students measuring? Put a tick mark (✓) if you find it being measured.

Ans: Length, Weight, and Temperature are measured by the students in the above picture.

Q2: What is being used to measure the height? What other tools can be used to measure height?
Ans: A measuring scale is used to measure height. Other tools include a ruler, height chart, or a meter stick.

Q3: Recall in Grade 3 you studied that lengths are measured in metres. Check and fill in the blanks whether the following are correct/incorrect for your classroom.
(a) The height of most of the students in my grade is more than a metre.
Ans: Correct (Most Class 4 students are taller than 1 meter.)

(b) The length of my arm is less than a metre.
Ans: Correct (An arm is usually less than 1 meter.)

(c) The height of the door of the grade is less than a metre.
Ans: Incorrect (A classroom door is usually more than 1 meter tall.)

(d) The breadth of the blackboard is more than a metre.
Ans: Correct (A blackboard is typically wider than 1 meter.)

Page 81: Let Us Do

1. Walk, Jump, and Crawl on 1, 5 and 10 m line

Draw lines of 1 m, 5 m, and 10 m on the floor of the classroom or outside in the playground. How will you make these lines? Think and share with your friends. Walk, jump, and crawl on the lines.
Ans: Do it Yourself!

Page 82: Let Us Do

2. Long Jump

Each child can participate in a long jump competition. How far have your friends jumped? Measure as accurately as possible using a combination of ropes. Who jumped the longest distance? Who has jumped the shortest?

 Fill the following table.

Ans:

Q3: Estimate how long and broad is your classroom. Measure and check.Ans: Estimate the classroom length and breadth (e.g., length ≈ 8 m, breadth ≈ 6 m). Use a measuring tape or meter rope to measure accurately. Compare your estimate with the actual measurement.

Page 83: Let Us Think: Guess the Length

Look at the pictures carefully and answer the questions.

Q1: What is the length of one bus in metres? What is the length of one cricket bat in metres?
Ans: A bus is about 15 meters long. A cricket bat is about 1 meter long.

Q2: How many buses would be equal to the length of two blue whales?
Ans: A blue whale is about 30 meters long. Two blue whales = 2 × 30 = 60 meters. A bus is about 15 meters. So, 60 ÷ 15 = 4 buses.

Q3: How many cricket bats will be needed to measure one whale?
Ans: A blue whale is about 30 meters. A cricket bat is about 1 meter. So, 30 ÷ 1 = 30 cricket bats.

Q4: If two ostriches stand one above another, their height will be equal to the height of
Ans: One ostrich’s height is 3 m.
Therefore, the heights of two ostriches are 3m + 3m = 6m
As we can see in the given picture, the crocodile’s length is also 6 metres.
Therefore, the two ostriches’ height will be equal to the length of one crocodile.

Q5: How many crocodiles will be equal to the length of a blue whale?
Ans: A crocodile is about 6 meters long. A blue whale is 30 meters. So, 30 ÷ 6 = 5 crocodiles.

Page 84: Let Us Observe

Chutki wants to keep track of the increase in height of her plant. Compare the metre rope with the measuring tape used by a tailor. Is the length of both the same or different? 

Ans: The meter rope and tailor’s measuring tape are both 1 meter long, so their length is the same. 

Observe the measuring tape carefully. What do you notice? 

Ans: The measuring tape has marks for centimeters (cm) and millimeters (mm), with numbers every 1 cm or 10 cm. These marks help measure small lengths accurately.

Discuss how these marks help us measure clearly.

Ans: The red bar (10 cm) repeats 10 times to make 1 meter.

Q: 1 metre (m) = 100 centimetre (cm), ½ m = ___ cm, ¼ m = ___ cm
Ans:  

• ½ m = 50 cm (½ × 100 = 50)  
• ¼ m = 25 cm (¼ × 100 = 25)

Page 85: Let Us Do

Q1: Measure each object using a scale. 

Write the names of the objects in increasing order of length.

Ans: 

Page 86: Let Us Do

Q2: Estimate the lengths of the following and compare your responses with your friends in the grade. Write some examples of things that can be lesser than or equal to 1 cm in length. Verify by measuring.Ans: 

Q3: Take three toy cars and find out how far each one can go. You can use a small wooden ramp, or you might like to make a ramp using any material that you have. Measure the distance each of your cars travels using measuring tape and write the answers in cm.
Ans: 

Page 87: Let Us Do

Q4: Find the longest and the shortest route in this treasure hunt. You can go around the obstacles but cannot jump over them. You can only walk on the yellow tiles and not on the grass. Can you find the length of your route in centimetres? Look for the 1 cm clue in the map.
Ans: Trace paths on yellow tiles, avoiding obstacles. Use the 1 cm clue to scale the map. Measure each route with a scale. Compare lengths to find the longest and shortest routes in cm.

Shortest Route: 16 cm.

Longest Route: 48 cm

Page 88: Let Us Do

Q5: Trace your hand on a piece of paper. Measure it using the scale. Length of my hand = ___ cm
Ans: Trace your hand on paper. Measure the length from the wrist to the tip of the middle finger with a scale. Record in cm (e.g., 15 cm).

Q6: Use your hand to estimate the measurement of any object. Convert into centimetres. Verify using the scale.Ans: 

Q7: Ashwin’s scale is broken. Can you help him to measure using this scale?
Ans: If the scale is broken (e.g., missing the start), align the object with the first visible mark (e.g., 2 cm) and subtract the starting mark from the end mark to find the length. If an object starts at 8 cm and ends at 14 cm, length = 14 – 8 = 6 cm.

And if an object starts at 12 cm and ends at 16 cm, length = 16 – 12 = 4 cm.

Q8: Fill the blanks on the number line below appropriately.Ans: 

Q9: The length of a board is 2 metres. Sonu has a decorative border sticker which is 20 cm long. How many such stickers are needed to cover the length of the board completely?

Ans: The board is 2 meters long.
1 meter = 100 cm, so 2 meters = 200 cm.
Each sticker is 20 cm long.
To find how many stickers are needed, divide the board’s length by the sticker’s length:
200 ÷ 20 = 10.
So, 10 stickers are needed to cover the board.

Metre and Centimeters

Ramu and Shamu are using a measuring tape to measure their own height.

 Ramu reads his height from the tape as 120 cm and Shamu reads it as 1 m 20 cm. 

Who is correct?

 Pinki says both are correct and draws this.

Ans: Ramu’s height = 120 cm
Shamu’s height = 1 m 20 cm
Since 1 metre = 100 cm,
Now, convert 1 m 20 cm into cm:
1 m 20 cm = 1 × 100 cm + 20 cm = 120 cm
Both measurements are the same.
Pinki is correct because both Ramu and Shamu have given the same height in different units.

Page 90: Let Us Do

Q1: Fill in the blanks: A kilometre is 1000 metres. 

i) 2 m = 200 cm

ii) ____ m = 400 cm
Ans: 4 m = 4 × 100 cm = 400 cm

iii) 6 m = _____ cm
Ans: 6 m = 600 cm

iv) _____ m = 800 m
Ans: 8 m = 800 cm (There is a mistake in the question)

b) Identify the wells with the same depth and match them.
Ans:

Page 90: Let Us Explore

Activity: Students will measure their height using a measuring tape. Make a table in your notebook and complete it.

Answer the following questions.

1. Height of the tallest child is _____.

2. Height of the shortest child is _____.

3. Number of children who are more than 1 m tall _____.

4. Number of children who are shorter than 1 m _____.

Ans: Do it Yourself!

Page 91: Fencing and Lacing

How many bricks will Bhola need to make the boundary?
Ans: 21 more bricks are needed to cover the boundary.

Page 92: Let Us Do

Q1: Bhola made the boundary of his gardens in the following ways. Circle the boundary that is longest.
Ans: Compare the boundaries of each garden by counting the sides or measuring with a scale. Circle the garden with the most sides or longest total length. 

Image 1: Bricks used – 12 + 12 + 7 + 7 = 38 bricks
Image 2: Bricks used – 4 x sides = 4 x 10 = 40 bricks
Image 3: Bricks used –  12 + 12 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 5 + 5 = 50 cm (longest)

Q2: Let us find the perimeter of some shapes using the dot grid. One is done for you.
a) Colour the boundary with the longest length in blue.
Ans: Count the dots along each shape’s boundary (1 dot = 1 cm). Colour the shape with the highest count in blue.

b) Colour the boundary with the shortest length in green.
Ans: Colour the shape with the lowest count in green.

c) Tick the shapes with the same length.
Ans: Tick shapes with the same number of dots along their boundaries.

Page 93: Let Us Do

Q3: Do any of the following shapes have the same perimeter? Tick them.
Ans: Measure each shape’s perimeter using a scale or count sides on a grid. 
1. Image A and C are Same: 12 cm
2. Image D, E and F are Same: 14 cm
3. Image B: 10 cm

Q4: Tick the garden with the minimum perimeter.Ans: Measure the perimeter of each garden. Tick the one with the smallest total length.

first fig. perimeter is 18 cm, second is 24 cm, third one is 20 cm.

Page 94: Let Us Do

Q5: Estimate and measure the perimeters of shapes around you using a scale and write them in the space given below.Ans: 

Q6: Draw three different shapes with perimeter of 20 cm.Ans: 

Page 63: Let Us Discuss

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.

Q1: Which part of the paper you would have chosen—one half or two quarters? Why?
Ans: I would choose one half. One half is the same as two quarters because two quarters (2 × 1/4 = 2/4 = 1/2). Both are equal parts of the paper.

Q2: Do you think Ikra shared the paper equally? Why? Try with a paper.
Ans: Yes, Ikra shared the paper equally. One half (1/2) is the same as two quarters (2/4). If you fold a paper in half or into four equal parts and take two parts, the size is the same.

Q3: How do you know that the paper has been divided equally?
Ans: The paper is divided equally if each part is the same size. For one half, fold the paper into two equal parts. For two quarters, fold it into four equal parts and take two. Both cover the same area.

Q4: Why do you think Samina chose two quarters of the paper?
Ans: Samina chose two quarters because she thought it sounded like a bigger part. She didn’t realize that two quarters (2/4) is the same as one half (1/2).

Page 63: Let Us Do

Q1: Samina has divided some figures into two parts. Colour the figures that are divided into halves correctly. How did you get the answer?
Ans: To find halves, each part must be equal in size. Check if the figure is divided into two equal parts. Colour only those figures where both parts are the same size. I got the answer by looking at the shapes and comparing the size of the two parts.

Q2: Divide the shapes into halves by drawing a line.
Ans: Draw a line through the middle of each shape so that both parts are equal in size. For example, for a rectangle, draw a vertical or horizontal line to split it into two equal parts.

Page 64: Let Us Do

Q3: Divide these shapes into 4 equal parts/quarters.
Ans: Draw lines to split each shape into four equal parts. For a rectangle, draw one vertical and one horizontal line to make four equal rectangles. For a circle, draw two lines through the center to make four equal sections.

Page 64: Let Us Try

Q4: In how many different ways can you fold/cut a rectangular paper in two equal parts? Try it with a rectangular paper.
Ans: You can fold or cut a rectangular paper in two equal parts in these ways:

1. Fold vertically to make two equal rectangles.
2. Fold horizontally to make two equal rectangles.
3. Fold diagonally from one corner to the opposite corner to make two equal triangles.
   There are at least three different ways.

Page 65: Let Us Do

Q2: Now try to draw and show five different ways in which we can fold/cut a rectangle into four equal parts (1/4 or quarter).
Ans: Five ways to fold or cut a rectangle into four equal parts:

1. Draw three vertical lines to make four equal vertical strips.
2. Draw three horizontal lines to make four equal horizontal strips.
3. Draw one vertical and one horizontal line to make four equal rectangles.
4. Draw two diagonal lines from opposite corners to make four equal triangles.

Q3: Match the following parts with their corresponding wholes.
Ans: 

Page 68: Let Us Discuss

Q1: What is Sumedha observing about her share as each guest comes in?
Ans: Sumedha observes that her share of dhokla gets smaller as more guests come. When shared with more people, each person gets a smaller piece.

Q2: In which situation will Sumedha get to eat more dhokla: when shared among 9 people or 11 people?
Ans: Sumedha will get more dhokla when shared among 9 people. If the dhokla is divided into 9 parts, each piece is bigger than when divided into 11 parts.

Q3: How many pieces of 1/6 would make a complete dhokla?
Ans: Six pieces of 1/6 make a complete dhokla because 6 × 1/6 = 6/6 = 1 whole.

Q4: What would be Sumedha’s share, if Idha and Vinayak both give their share of dhokla to her?
Ans: Idha’s share = 1/5
Vinayak’s share = 1/5
Sumedha’s total share = 1/5 + 1/5 + 1/5 = 3/5
So, Sumedha will get 3/5 of the dhokla if both Idha and Vinayak give their share to her.

Page 68: Let Us Do

Q1: How much dhokla would each person get if it was shared equally among 6 people? Try also with 8 people. Who will get the bigger pieces of dhokla? Draw and explain.
Ans:

• For 6 people: Divide the dhokla into 6 equal parts. Each person gets 1/6 of the dhokla.
• For 8 people: Divide the dhokla into 8 equal parts. Each person gets 1/8 of the dhokla.
• Explanation: The pieces are bigger when shared among 6 people because 1/6 is larger than 1/8. Draw a circle for the dhokla, divide it into 6 parts, and then into 8 parts to see that 1/6 is bigger.

Page 69: Let Us Do

Q2: Shade a portion of the dhokla to represent the fraction Sumedha would get when the dhokla is shared equally among the given number of people. Discuss why the fractions get smaller.
Ans: Divide the dhokla into equal parts based on the number of people and shade one part to show Sumedha’s share. For example, if 4 people, shade 1/4; if 5 people, shade 1/5. The fractions get smaller because as more people share the same dhokla, each person’s share becomes a smaller part of the whole.

Page 69: Let Us Discuss

Q1: Share your observations about the different pieces and the whole.
Ans: The whole is the complete object, like a dhokla or paper. When divided into equal pieces, each piece is a fraction of the whole. For example, 1/2 is one of two equal parts, and 1/4 is one of four equal parts. Smaller fractions mean more pieces and smaller sizes.

Q2: Take any two different pieces of the fraction kit and compare them. Discuss which one is smaller and why.
Ans: Take two pieces, like 1/3 and 1/4. Compare their sizes. 1/4 is smaller than 1/3 because the whole is divided into more parts (4 parts) for 1/4, so each part is smaller than when divided into 3 parts for 1/3.

Q3: Sumedha noticed that when a whole is equally divided in a larger number of parts, each part gets smaller. Do you agree with Sumedha?
Ans: Yes, I agree with Sumedha. When the whole is divided into more parts, each part is smaller. For example, 1/6 is smaller than 1/4 because 6 parts are smaller than 4 parts of the same whole.

Q4: Sumedha says, “When I join 5 pieces of 1/5, it makes a whole dhokla.” Try to do it yourself with your fraction kit.Ans: Yes, Sumedha is correct. Take 5 pieces of 1/5 from the fraction kit. When you join them, they make a whole dhokla because 5 × 1/5 = 5/5 = 1 whole.

Q5: Sumedha says that this part is one-third of the complete whole. Why is she saying so?
Ans: Sumedha says it is one-third because the whole is divided into three equal parts, and one part is shaded or taken. One-third (1/3) means one out of three equal parts of the whole.

Page 70: Let Us Try

Q1: ______ is greater than _________. (1/5, 1/4).
Ans: 1/4 is greater than 1/5. When the whole is divided into 4 parts, each part (1/4) is bigger than when divided into 5 parts (1/5).

Q2: ________ > __________. (1/9, 1/6).
Ans: 1/6 is greater than 1/9. When the whole is divided into 6 parts, each part (1/6) is bigger than when divided into 9 parts (1/9).

Q3: 1/6 _______ 1/8.
Ans: 1/6 is greater than 1/8. Same as above, 1/6 is larger because fewer parts mean bigger pieces.

Q4: ______ is smaller than _______ ( ______, _______).
Ans: 1/7 is smaller than 1/5.

Page 70: My Flower Garden

Mogra in 1/5 or one-fifth part of the garden. Marigold in part of the garden. 
Jasmine in 1/5 or one-fifth part of the garden. 
Rose in 1/5 and 1/5 part or a total of 2/5 (two-fifths) part of the garden. 1/5 or one-fifth 
Ans: The garden is divided into 5 equal parts (1/5 each).

• Mogra: 1/5
• Lily: 1/5
• Marigold: 1/5 (since 4 parts are used by Mogra, Rose, and Jasmine, 1 part remains)
• Jasmine: 1/5 (one of the remaining parts)
• Rose: 1/5 

Page 70: Look at the garden and answer the questions.

Mogra in part…….. 
Marigold in part……… 
Rose in 1/5 + 1/5 + 1/5 part or a total of 3/5 (three-fifths) part………
Ans:

• Mogra: 1/5 (one of the remaining parts)
• Marigold: 1/5 (one of the remaining parts)
• Rose: 3/5 (given as 1/5 + 1/5 + 1/5 = 3/5)

Look at the garden and answer the questions.

a) Marigold in ………..
Ans: The garden is divided into 5 equal parts (1/5 each).

• Marigold: 1/5

b) Rose: 4/5 (given as 1/5 + 1/5 + 1/5 + 1/5 = 4/5): True

Page 71: Let Us Do

Make a flower garden with seven flowering seeds—Mogra, Marigold, Jasmine, Rose, Lily, Hibiscus, and Periwinkle?

Ans: 

Page 73: Do It Yourself

Write the fractions for each of the toppings in the following dosas.
Ans: 

Make a dosa with 2/3 topping of Spicy onion, 1/3 of Classic potato.
Ans: Divide the dosa into 3 equal parts. Shade 2 parts for Spicy onion (2/3) and 1 part for Classic potato (1/3).

Make a dosa with 2/3 of Classic potato, 1/8 of Chilly paneer and 4/5 of Tangy tomato mix.
Ans: This seems incorrect as 2/3 + 1/8 + 4/5 exceeds 1. Assuming a typo, a possible correction is: Divide the dosa into 24 equal parts (LCM of 3, 8, 5). Shade 16/24 for Classic potato (2/3), 3/24 for Chilly paneer (1/8), and 19/24 for Tangy tomato (≈4/5, adjusted).

Page 73: Let Us Explore

Meena has 8 diyas. Colour 1/4 of her diyas red. To find 1/4, let us divide the number of diyas into 4 equal parts. Can you see how to divide the diyas into 4 equal parts? Now colour 2 diyas red.
Ans: Divide 8 diyas into 4 equal parts: 8 ÷ 4 = 2 diyas per part. One-fourth (1/4) of 8 is 2 diyas. Colour 2 diyas red.

Page 74: Let Us Do

Now let us try to find fractions for the situations given below. Circle the appropriate parts in the pictures.
Q1: There are 12 cookies. What fraction of cookies will each get if the number of children are as follows:
a) 3 children
Ans: 12 ÷ 3 = 4 cookies each. Fraction: 4/12 = 1/3.b) 6 children
Ans: 12 ÷ 6 = 2 cookies each. Fraction: 2/12 = 1/6.c) 2 children
Ans: 12 ÷ 2 = 6 cookies each. Fraction: 6/12 = 1/2.d) 4 children
Ans: 12 ÷ 4 = 3 cookies each. Fraction: 3/12 = 1/4.

Q2: Simran calls her school friends for her birthday party. 1/3 of her friends receive a hairband as their return gift. Place hairbands on 1/3 of her friends.
Ans: Count the number of friends. Divide by 3 to find 1/3. Place hairbands on that many friends. For example, if 9 friends, 1/3 = 3 friends get hairbands.

Q3: Draw flowers in 1/5 of the given number of pots.
Ans: Count the number of pots. Divide by 5 to find 1/5. Draw flowers in that many pots. For example, if 15 pots, 1/5 = 3 pots with flowers.

Page 75: Let Us Find Fractions in Our Surroundings

Q1: Yesterday, Mummy asked to divide a box of barfis into four equal parts. There are 16 barfis in the box. Draw a picture of 16 barfis and find 1/4 of the whole. How many barfis are in each part?
Ans: Draw 16 barfis in a 4×4 grid. Divide into 4 equal parts: 16 ÷ 4 = 4 barfis per part. One-fourth (1/4) is 4 barfis.

Q2: Rohan has a piece of ribbon to decorate his notebook. Mohan’s ribbon is one-fourth as long as Rohan’s ribbon. How long will Rohan’s ribbon be? Draw it. 

Ans: If Mohan’s ribbon is 1/4 of Rohan’s, Rohan’s ribbon is 4 times Mohan’s. Draw Rohan’s ribbon 4 times longer than Mohan’s. For example, if Mohan’s is 1 cm, Rohan’s is 4 cm.

Page 75: Try Yourself

Observe your surroundings and think of situations where we use fractions, and write any two of them in the space provided below.
Ans:

1. Dividing a pizza into 8 equal slices, each slice is 1/8.
2. Sharing 12 chocolates among 4 friends, each gets 3/12 = 1/4.

Page 76: Let Us Do

1. Take a rectangular piece of paper and fold the paper into three equal parts and then unfold it.

2. Colour one of the three equal parts as shown in the image.

3. Fold the paper back into three equal parts like before, and then fold it in half.

4. Observe the colored part. What is the fraction for the shaded part now? What does this mean?

5. Fold the paper again and check how the coloured part changes.

6. Write down what fraction you observe after each fold.

1/3 = 2/6 = ______ = ______ =______
Ans: Do it Yourself!

Page 77: Let Us Try

Take another piece of paper and try the same starting with two equal parts, and halving every time. Share the findings with your friends.
Ans: Take a piece of paper. Fold it in half to make 2 equal parts. Fold it in half again to make 4 equal parts. Keep folding in half each time. You get 8 parts, then 16 parts, then 32 parts. Each fold makes twice as many parts as before.

1/2 = 2/4 = 4/8 = 8/16 = 16/32

Page 77: Let Us Discuss

Observe the fraction chart and discuss the following questions. 

Q1: How many 1/4 s are equal to 1/2?
Ans: Two 1/4s equal 1/2 because 1/4 + 1/4 = 2/4 = 1/2, then answer is 2.

Q2: Is 2/3 less than or greater than 1/2?
Ans: 2/3 is greater than 1/2. 
Compare: 2/3 = 4/6, 1/2 = 3/6. 
Since 4/6 > 3/6, 2/3 is greater.

Q3: Ten pieces of 1/10 make a complete whole. Is this statement true?
Ans: Yes, true. Ten pieces of 1/10 make 10/10 = 1 whole.

Q4: Three pieces of 1/6 are equal to two pieces of 1/8. Is this true?
Ans: No, not true. 
Three pieces of 1/6 = 3/6 = 1/2. 
Two pieces of 1/8 = 2/8 = 1/4. 
Since 1/2 ≠ 1/4.

Q5: How many pieces of 1/8 make 1/4?
Ans: Two pieces of 1/8 make 1/4 because 1/8 + 1/8 = 2/8 = 1/4.

Q6: Find the pieces that you can put together to make another bigger piece.

Ans: Do it Yourself!

Page 78: Let Us Do

Q1: Bablu is playing with square shapes. He wants to cut them in such a way that each piece is equal in size. Circle the squares that have been cut into equal parts. Write the fraction for the shaded part, whenever possible.
Ans: Circle the squares where each piece is the same size. For example, if a square is divided into four equal parts and one is shaded, the fraction is 1/4. If it’s not equal, don’t circle it.

Q2: Check if the children’s claim below about the shaded parts of each of the pictures is correct. Circle the ones which you think are correct, cross out the ones which are not correct. You can draw additional lines to make the parts equal. Discuss your thinking.
Ans: Do it Yourself!

Q3: Identify the fractions represented by the coloured parts in the given pictures.

Q4: Identify the fraction of the whole that the blue parts make in each of the pictures given below.
Ans: Count the total parts and the blue parts. For example, if 3 out of 4 parts are blue, the fraction is 3/4.

Q5: Divide the following into equal parts and shade the appropriate parts in each.
Ans:

• Shade 2/3: Divide into 3 equal parts, shade 2.
• Shade 4/6: Divide into 6 equal parts, shade 4.
• Shade 1/4: Divide into 4 equal parts, shade 1.
• Shade 3/4: Divide into 4 equal parts, shade 3.

Page 39 (Let Us Do)

Q: Jaspreet and Gulnaz receive many donations.  The donations are shown in the table below. Write the number in each case.

Ans:

Page 40 (Let Us Do)

Ans: 

Q: Write the time and draw the number of people who had food at different time slots using HTO blocks as shown below.

The time slot when the most number of people came for lunch is _____________________.
The time slot when the least number of people came for lunch is _____________________.

Ans:

Ans: 

The time slot when the most number of people came for lunch is 1:30 to 2:00.
The time slot when the least number of people came for lunch is 12:00 to 12:30.

Let Us Do

Q1:
(a) Make 3-digit numbers using the digits 3 and 7. Write the numbers in the boxes given below. Circle the smallest and cross out the largest.Ans: The possible 3-digit numbers using digits 3 and 7 (with repetition allowed) are:

• Smallest number: 333 (circle this)  
• Largest number: 777 (cross this out)

(b) Make six 3-digit numbers using the digits 3, 5, 0, 8 such that all numbers are less than 550. You can repeat the digits.Ans:
Possible 3-digit numbers less than 550 using digits 3, 5, 0, 8 with repetition:

(c) Mark the numbers you made in 1(b) on the number line.Ans: 

Page 42 (Let Us Do)

Q2: Fill in the blanks with appropriate numbers.
(a) 
Ans:

(b)
Ans:

(c)
Ans:

(d) 
Ans:

(e) 
Ans: 

Page 43 (Let Us Do)

Let us see how they did it.
Q: How many people came for the community lunch? __________ 
Ans: 1032

Fill in the blanks with appropriate numbers.
Ans: 

Page 44 (Let Us Do)

Q3: Identify the range of numbers most suitable for the following situations. Share your thoughts.
Ans:  

Q: Identify things around you that are more than 1000 in number.
Ans: Examples of things with more than 1000 in number:  

• Grains of rice in a sack  
• Stars in the sky  
• Leaves on a large tree  
• People in a big city

Page 47 (Let Us Break Up One-Thousand)

Q:
(a) We are at 900. How much more to make 1000? __________.
900 + ____ = 1000
Ans: 900 + 100 = 1000
So, 100 more is needed.

(b) Mark 800. How much more to make 1000?
800 + ______ = 1000
Ans: 800 + 200 = 1000
So, 200 more is needed.

(c) Mark 850. How much more to 1000?
850 + ____ = 1000
Ans: 850 + 150 = 1000
So, 150 more is needed.

(d) Mark 760. How much more to 1000?
760 + _____ = 1000
Ans: 760 + 240 = 1000
So, 240 more is needed.

(e) Mark 400. How much less is 400 than 1000?
1000 – ____ = 400
Ans: 1000 – 600 = 400
So, 400 is 600 less than 1000.

(f): Complete the addition facts leading to 1000.

Ans: 

Page 48 (Grouping and Regrouping)

Look at the pictures below. Circle as many groups of 10 Ones or 10 Tens as possible. Write the final number against the following pictures.
Q1: 
Ans:

Q2: 
Ans: 200 + 50 = 250
2 Hundreds + 5 Tens + 0 Ones
= 250

Q3: 
Ans: 20 + 5 = 25
2 Tens + 5 Ones = 25.
Q4: 
Ans: 100 + 80 = 180
1 Hundred + 8 Tens + 0 Ones = 180

Page 49 (Grouping and Regrouping)
Circle groups of ten 1s, 10s, and 100s as many times as required in each of the following pictures. Fill in the empty boxes.
(a) Ans: 

(b) Ans: 

(c)
Ans: 

(d)
Ans:

(e) 
Ans: 

(f)
Ans:
Page 50 (Let Us Solve)
Identify and write the numbers for each of the following in your notebook. Draw pictures like these, if needed.

(a) 45 Ones 
(b) 39 Ones 
(c) 35 Tens 
(d) 86 Tens 
(e) 10 Tens and 1 Ones 
(f) 15 Tens and 23 Ones 
(g) 34 Tens and 12 Ones 
(h) 19 Tens and 10 Ones 
(i) 2 Hundreds, 13 Tens and 7 Ones
Ans: 
(a) 45
(b) 39
(c) 350
(d) 860
(e) 101
(f) 173
(g) 352
(h) 200
(i) 337

Page 51 (Numbers Beyond 1000 (One Thousand))

We will use tokens in place of Dienes blocks for larger numbers.

1 Thousand + 0 Hundred + 0 Tens + 1 Ones = 1001
Look at the table below and fill in the blanks.
Ans: 

Ans: 

Page 53 

Q: Write the numbers in a sequence—forward and backward as indicated.
(a) 
Ans: 

(b)
Ans:
 

(c) 
Ans: 

(d)

Ans: 

Page 54 (Let Us Play) 

Q: Make the place value slider. Children can take turns to increase or decrease the number as told.
(a) 1895 – increase the number by 1
Ans: 1895 + 1 = 1896

(b) 2785 – increase the number by 10
Ans: 2785 + 10 = 2795

(c) 3369 – decrease the number by 2
Ans: 3369 – 2 = 3367

(d) 5648 – decrease the number by 10
Ans: 5648 – 10 = 5638

(e) 6487 – increase the number by 20
Ans: 6487 + 20 = 6507

Page 54 (Let Us Think)

Q1: Ram wrote 7 Thousand 0 Hundreds 2 Tens 4 Ones as 724. Is this correct? Write the correct number.
Ans: 7 Thousand 0 Hundreds 2 Tens 4 Ones = 7000 + 0 + 20 + 4 = 7024
Ram’s number 724 is incorrect.
Correct number: 7024

Q2: Richa wrote 5 Thousand 6 Hundreds 0 Tens 3 Ones as 563. Is this correct? Write the correct number.
Ans: 5 Thousand 6 Hundreds 0 Tens 3 Ones = 5000 + 600 + 0 + 3 = 5603
Richa’s number 563 is incorrect.
Correct number: 5603

Page 55 (Number Line)

Q1: Which of these numbers lie between 2226 and 3226? Circle the correct answers.
Ans: Numbers between 2226 and 3226 are:
2236, 3126, 3216Q2:
(a) 1001 and 1038 are marked on the number line. Try to mark 1043, 1069, and 1084 on the same number line.
Ans: 

(b) Mark the following numbers on the number line below: 2025, 2080, 2175, 2245, 2295, 2310, 2390, 2430, 2460
Ans: 

(c) Mark the following numbers on the number line below: 5512, 5548, 5590, 5636, 5673, 5695
Ans: 

(d) Mark the following numbers on the number line below: 8679, 8990, 8923, 8763
Ans: 

Page 56 (Let Us Play)

Use the arrow cards (given at the end of the book) to make different numbers. Take turns giving a number for the grade to make using the arrow cards. Read aloud the number and express them in expanded form and in words.
3452 is made up of the cards 3000, 400, 50 and 2. 
The expanded form of 3452 is 3000 + 400 + 50 + 2. 
In words, 3452 is three thousand four hundred fifty two.
What cards are used to make 4085? Write it in expanded form and in words.
Ans: Cards used: 4000, 0, 80, 5

Expanded form: 4000 + 0 + 80 + 5

In words: Four thousand eighty-five

Page 56 (Find Me!)

Read aloud the numbers and locate them in the grid.

Ans:

Q1: The number 3782.
Ans: Already done

Q2: Two thousand five hundred and seventy-six.
Ans: 2576 is found in the grid

Q3: A 4-digit number with all digits the same.
Ans: 2222 is found in the grid:

Q4: The smallest 4-digit number in this table.
Ans: The smallest 4-digit number is 1011.

Q5: The largest 4-digit number in this table.
Ans: The largest 4-digit number is 9672

Q6: A number more than 5000 and less than 5200.
Ans: 5010 is found in the grid

Q7: A number between 5600 and 6300.
Ans: 5720 number between 5600 and 6300 in the grid.

Q8: A 4-digit number all of whose digits can be found on a die.
Ans: A die has digits 1 to 6. A possible number is 5321 

Page 57 (Let Us Solve)

Q1: Use tokens of 1s, 10s, 100s, 1000s to identify the numbers and write them in the table.
(a) 6 Tens and 22 Ones
Ans: 6 Tens = 60, 22 Ones = 22
Total = 60 + 22 = 82  

(b) 4 Tens and 12 Ones
Ans: 4 Tens = 40, 12 Ones = 12
Total = 40 + 12 = 52  

(c) 3 Hundreds, 14 Tens, and 8 Ones
Ans:3 Hundreds = 300, 14 Tens = 140, 8 Ones = 8
Total = 300 + 140 + 8 = 448  

(d) 12 Hundreds, 18 Tens, and 2 Ones
Ans: 12 Hundreds = 1200, 18 Tens = 180, 2 Ones = 2
Total = 1200 + 180 + 2 = 1382  

(e) 1 Thousand, 5 Hundreds, 10 Tens, and 17 Ones
Ans: 1 Thousand = 1000, 5 Hundreds = 500, 10 Tens = 100, 17 Ones = 17
Total = 1000 + 500 + 100 + 17 = 1617  

Q2A: Circle the number that is bigger.

Ans:  

• 30 or 300: 300 
• 6000 or 600: 6000  
• 6000 or 3000: 6000

Q2B: Circle the number that is smaller.

Ans:  

• 2 Ones or 2 Hundreds: 2 Ones
• 5 Tens or 2 Thousands: 5 Tens
• 7 Tens or 4 Hundreds: 7 Tens

Page 58 (Comparing Numbers)

Jaspreet and Gulnaz help to keep a record of the number of plates used in the Gurudwara every month. Use the signs <and> to find the month when a larger number of plates were used.

Ans: 

Q: Compare the numbers using the signs <and>.
Describe how you decided which number is the bigger one. Which position (Th, H, T, O) helped you to decide this?
Ans: 
3012 < 3102
3102 is bigger than 3012 because the hundreds place in 3102 has 1 hundred, while 3012 has 0 hundreds. The thousands, tens, and ones places are the same.

Page 58 (Let Us Do)

Compare the following pairs of numbers using < and >. Make a Th, H, T, O table, if necessary. Share your thoughts with the class.
(a) 2190 ______2910
Ans: 2190 < 2910
(Th: 2 vs 2, H: 1 vs 9, 1 < 9, so 2190 is smaller)

(b) 7087 ______ 7088
Ans: 7087 < 7088
(Th: 7 vs 7, H: 0 vs 0, T: 8 vs 8, O: 7 vs 8, 7 < 8, so 7087 is smaller)

(c) 1009______ 9001
Ans: 1009 < 9001
(Th: 1 vs 9, 1 < 9, so 1009 is smaller)

(d) 982 ______ 1024
Ans: 982 < 1024
(Th: 0 vs 1, 0 < 1, so 982 is smaller)

Q2: Order the prices of the following objects from smallest to biggest (increasing order)
Ans:

Q3: The following women international cricketers have played 200 ODIs (One-Day International Matches). Listed below are their scores. Arrange the runs scored by them in increasing order (from lowest to highest).
Ans: 4064 < 4814 < 5114 < 6002 < 7805

Page 60 (Let Us Do)

Q4: Arrange the following mountain ranges in decreasing order of height (from highest to lowest).

Ans: 

• K2: 8611 meters
• Kangchenjunga: 8586 meters
• Nanda Devi: 7816 meters
• Chaukhamba I: 7138 meters
• Mullayanagiri: 1930 meters
• Kalsubai: 1646 meters
• Bailadila Range: 1276 meters

Q5 Use the signs <, =, > to compare the following.
(a) 2 Tens + 4 Thousands + 3 Hundreds _____ 2043
Ans: 2 Tens + 4 Thousands + 3 Hundreds = 4000 + 300 + 20 = 4320
4320 > 2043

(b) 2 Tens + 4 Thousands + 3 Hundreds _____ 4320
Ans: 2 Tens + 4 Thousands + 3 Hundreds = 4320
4320 = 4320

(c) 2 Thousands + 9 Hundreds + 9 Tens + 9 Ones _____ 3000
Ans: 2 Thousands + 9 Hundreds + 9 Tens + 9 Ones = 2000 + 900 + 90 + 9 = 2999
2999 < 3000

(d) 15 Ones + 9 Tens + 3 Hundreds _____ 1593
Ans: 15 Ones + 9 Tens + 3 Hundreds = 300 + 90 + 15 = 405
405 < 1593

(e) 5000 + 30 + 4 _____ 5034
Ans: 5000 + 30 + 4 = 5034
5034 = 5034

(f) 5000 + 300 + 4 _____ 5340
Ans: 5000 + 300 + 4 = 5304
5304 < 5340

Q6 Fill the blanks with digits 0 –9 such that the numbers meet the condition.
(a): 7__ __3 < 768__
Ans:

• We have 7 _ _ 3 on the left and 768 _ on the right. The “<” means the first number must be smaller than the second.
• The first number starts with 7 and ends with 3, but the middle two spots are blank. The second number is 768 with one blank at the end.
• Both numbers start with 7, so we need to look at the next digits to make sure 7 _ _ 3 is smaller than 768 _.
• For 768 _, the last digit can be anything (like 7680, 7681, 7682, etc.). But we need to make the first number smaller.
• In 7 _ _ 3, the second digit (first blank) should be 0, 1, 2, 3, 4, 5, or 6. Why? Because numbers like 7033, 7133, 7233, up to 7633 are all smaller than 7680 (or any 768_ number).
• The third digit in 7 _ _ 3 can be anything (0–9), but the second digit is the important one to keep it smaller.

The first blank in 7 _ _ 3 can be 0, 1, 2, 3, 4, 5, or 6.

(b) 853__ < 8__3__
Ans: 

• We have 853 _ on the left and 8 _ 3 _ on the right. We need 853 _ to be smaller than 8 _ 3 _.
• Both numbers start with 8, so we look at the next digits.
• In 853 _, the second digit is 5. In 8 _ 3 _, the second digit is a blank.
• To make 8 _ 3 _ bigger than 853 _, the second digit of 8 _ 3 _ must be bigger than 5. So, it can be 6, 7, 8, or 9.
• That makes numbers like 863_, 873_, 883_, or 893_, which are all bigger than 853_ (like 8530, 8531, etc.).
• The last digits in both numbers can be anything (0–9), but the second digit of 8 _ 3 _ is what matters most.

The first blank in 8 _ 3 _ can be 6, 7, 8, or 9.

(c) __2__1 < 5__2__
Ans: 

• We have _ 2 _ 1 on the left and 5 _ 2 _ on the right. We need _ 2 _ 1 to be smaller than 5 _ 2 _.
• The second number starts with 5, so it’s like 502_, 512_, 522_, etc., depending on the blank.
• The first number has a 2 in the second spot and a 1 at the end, so it’s like _ 2 _ 1. The first and third digits are blank.
• Since 5 (in 5 _ 2 _) is bigger than anything starting with 1, 2, 3, or 4, we can make the first number start with a small digit like 1, 2, 3, or 4.
• For example:
  • If the second number is 502 _, the first number can be 1211, 2211, etc., because 1211 < 5020 or 2211 < 5020.
  • If the second number is 512 _, the first number can be 1211, 2211, etc., because 1211 < 5120 or 2211 < 5120.
• The third digit in _ 2 _ 1 and the last digit in 5 _ 2 _ can be anything (0–9), but the first digit of _ 2 _ 1 should be small.

The first blank in _ 2 _ 1 can be 1, 2, 3, or 4, and the first blank in 5 _ 2 _ can be 0, 1, 2, 3, or 4 to make pairs that work.

Example: If we pick 1211 and 5120, then 1211 < 5120, which is true!

Page 61 (Challenge!)

Q: There are 99 numbers strictly between 700 and 800 excluding 700 and 800. How many numbers are there strictly between 7000 and 8000? Circle the correct answer: 
Ans: Numbers between 700 and 800 (excluding 700 and 800) are 701 to 799, which is 799 – 701 + 1 = 99 numbers.
Numbers between 7000 and 8000 (excluding 7000 and 8000) are 7001 to 7999, which is 7999 – 7001 + 1 = 999 numbers.

Let Us Explore

Q1: Make as many four-digit numbers as possible using the digits 2, 3, 4, 7 without repetition. There are 24 different numbers possible. Find as many as you can and arrange the numbers in decreasing order in your notebook.
Ans: Using digits 2, 3, 4, 7 without repetition, the possible 4-digit numbers are (24 permutations):
7432, 7423, 7342, 7324, 7243, 7234, 4732, 4723, 4372, 4327, 4273, 4237,
3742, 3724, 3472, 3427, 3274, 3247, 2743, 2734, 2473, 2437, 2374, 2347
Arranged in decreasing order:
7432 > 7423 > 7342 > 7324 > 7243 > 7234 > 4732 > 4723 > 4372 > 4327 > 4273 > 4237 > 3742 > 3724 > 3472 > 3427 > 3274 > 3247 > 2743 > 2734 > 2473 > 2437 > 2374 > 2347

Q2: Compare with your friends to find what other numbers they have made. See if all of you together can come up with all the 24 numbers. How do you know that you have all possible such numbers?
Ans:  Do it Yourself!

Page 34: Let Us Count

Gundappa has some land with tall coconut trees.

Q1: How many coconut trees does Gundappa have?
Ans: Gundappa has 81 coconut trees.

Q2: How do you know?
Ans: I counted the number of trees in each row and each column. There are 9 rows and 9 columns. So, the total number of trees is 9 × 9 = 81.

Q3: Gundappa has plucked 5 coconuts from each tree. How many coconuts has he plucked?
Ans: Gundappa has plucked 81 × 5 = 405 coconuts.

Q4: Muniamma makes plates and cups. 

Number of cups = ________
Ans: In the first stack, from top to bottom, there are 11 cups. Similarly, in the second, third, fourth, fifth and sixth stacks, there are 10, 9, 9, 10 and 11 cups, respectively.
So, the total cups are:
11 + 10 + 9 + 9 + 10 + 11 = 60 cups

Muniamma has arranged coconut laddoos and milk peda in trays like this. All trays have the same arrangement. Trays are placed one on top of the other.

Q5: How many coconut laddoos are there in the trays?
Ans: Each tray has 13 coconut laddoos. There are 3 trays.
So, 13 × 3 = 39 coconut laddoos.

Q6: How many milk pedas are there in the trays?
Ans: Each tray has 12 milk pedas. There are 3 trays.
So, 12 × 3 = 36 milk pedas.Page 35: Patterns with Money

Shirley and Shiv arranged their play money in some nice patterns as shown below.

Q1: How much money? (Left pattern)
Ans: ₹80

Q2: How much money? (Right pattern)
Ans: ₹108

 Q3: How did you count them? 

Ans: Left Pattern:

 There are 4 coins of ₹10 and 1 coin of ₹20 and 4 coins of ₹5.
So, total money = (4 × 10) + 20  + (5 x 4)= ₹80.

Right Pattern:

₹2 coins = 4
₹5 coins = 8
₹10 notes = 6
So, total money = (4 × 2) + (8× 5) + (6 × 10) = 8 + 40 + 60 = ₹108.

Q4: Arrange play money of amounts ₹1, ₹2, ₹5, and ₹10 to show ₹36, ₹125, and ₹183. Ask your peers to tell how much it is.
Ans:To make ₹36:

• ₹10 notes × 3 = ₹30
• ₹5 coin × 1 = ₹5
• ₹1 coin × 1 = ₹1
• Total = ₹30 + ₹5 + ₹1 = ₹36

To make ₹125:

• ₹10 notes × 10 = ₹100
• ₹5 coin × 5 = ₹25
• Total = ₹100 + ₹25 = ₹125

To make ₹183:

• ₹10 notes × 15 = ₹150
• ₹5 coin × 5 = ₹25
• ₹2 coin × 4 = ₹8
• Total = ₹150 + ₹25 + ₹8 = ₹183

Page No 35: Two Ways

Shirley and Shiv arranged their coins in the following ways. Write the number of coins in the triangles.

Ans:

Q1: Describe Shiv’s arrangement and write his numbers.

Ans: Shiv has arranged his coins in even numbers. The numbers are 4, 6, 8, 12 and 14.

Q2: Describe Shirley’s arrangement and write her numbers.
Ans: Shirley has arranged her coins in odd numbers. The numbers are 1, 3, 5, 7, 11 and 17.

Q3: Identify numbers between 1 and 20 as even or odd. You may draw the pairing arrangement of the numbers.
Ans: Odd numbers between 1 and 20: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
Even numbers between 1 and 20: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

We can pair even numbers equally. Odd numbers always leave one unpaired.

Q4: Do you think all numbers in the times-2 table are even?
Ans: Yes, all numbers in the 2 times table are even.
For example: 2, 4, 6, 8, 10, 12… All these can be made into equal pairs without any left.Page 37: Crayons Arrangement

Q: Circle the odd numbers and put a square around each even number. Use the crayons arrangement, if needed.


Ans: The numbers given are 36, 37, 38, 39, 8, 5, 51, 52, 43, 69.

To check, pair crayons for each number. For example, 37 crayons leave one unpaired (odd), while 38 crayons can be fully paired (even).

Q: Explore your textbook and find out what Shirley has seen. Draw a square on the even numbers. Put a circle on the odd numbers.
Ans: Do it yourself.Page 38 – Crayons Arrangement (Continued)

Q: Identify which of the following numbers are even and which are odd. Explain your reasoning.
Ans: Even numbers: 30, 46, 78, 300, 154.

• Reasoning: These numbers can be paired completely. For example, 30 can be divided into 15 pairs (30 ÷ 2 = 15), so it is even.

Odd numbers: 67, 415, 99.

• Reasoning: These numbers cannot be paired completely. For example, 67 leaves one unpaired (67 ÷ 2 = 33 with remainder 1), so it is odd.

Q: Make two 2-digit numbers using the digits 1 and 6 without repetition. Identify the numbers as even or odd.
Ans:

• Numbers: 16, 61.
• 16 is even (can be paired, 16 ÷ 2 = 8).
• 61 is odd (cannot be paired, 61 ÷ 2 = 30 with remainder 1).

Q: Now choose any two digits and make 2-digit numbers in such a way that the numbers are even.
Ans: Choose digits 2 and 4.

• Numbers: 24, 42.
• Both are even: 24 ÷ 2 = 12 (paired), 42 ÷ 2 = 21 (paired).

Q: Are there more even or odd numbers between 1 and 100?
Ans: There are 50 even numbers and 50 odd numbers between 1 and 100.

• Even numbers: 2, 4, 6, …, 100 (50 numbers).
• Odd numbers: 1, 3, 5, …, 99 (50 numbers).
  So, there are an equal number of even and odd numbers.

Q: Shirley notices that both the numbers, before and after an odd number, are even.
Ans: This is true. For example, for the odd number 5, the number before (4) and after (6) are even. Odd numbers (e.g., 1, 3, 5, …) are not divisible by 2, while the numbers before and after (e.g., 4 and 6 for 5) are divisible by 2, making them even.

Q: Shiv wonders if both the numbers, before and after an even number, will be odd. What do you think? Check and discuss.
Ans: Yes, this is true. For example, for the even number 4, the number before (3) and after (5) are odd. Even numbers (e.g., 2, 4, 6, …) are divisible by 2, while the numbers before and after (e.g., 3 and 5 for 4) are not divisible by 2, making them odd.

Q: Choose any 10 numbers in order without skipping any (consecutive numbers). Write whether they are even or odd below each number. What do you notice? Discuss.
Ans: Choose numbers 20 to 29:

• 20 (even), 21 (odd), 22 (even), 23 (odd), 24 (even), 25 (odd), 26 (even), 27 (odd), 28 (even), 29 (odd).
• Notice: The numbers alternate between odd and even (even, odd, even, odd, even, …). This happens because each number increases by 1, switching between not divisible by 2 (odd) and divisible by 2 (even).

Where Are You Hiding?(Page 24)

Let Us DoQ1: Look at the picture and answer the following:
a. Which game are the children playing?
Ans: The children are playing ‘hide and seek’ game.

b. Who is looking from the top?
Ans: Jagat is looking from the top.

c. In Scene 1, if Rani faces towards the hut, will she be able to see who all are hiding near the hut? Discuss.
Ans: In scene 1, if Rani faces towards the hut, she will not be able to see who all are hiding near the hut because Bholu is hiding behind the tree and Mini is hiding behind the hut.

Discuss(Page 25)In Scene 4, can Mini see all the children playing the game? Discuss.
Ans: No, Mini can only see Bholu and Jagat.

Q2: Mini, Bholu, and Rani draw the same brick. Why are their drawings of the same brick different? Discuss.Ans: Their drawings are different because they drew the brick from different views. Mini drew the front view, Bholu drew the top view, and Rani drew the side view. Each view shows a different side of the brick.

Whose drawing shows the following views?

Ans:

Q3: Look at the pictures and name the objects. Also write which view of the object is given.

Ans: 

Q4. Jagat and Rani have made different drawings of the same objects. Match the views with the objects.
Look around you! Try to make drawings of objects, such as chairs, tables, pencils, erasers, birthday cap, and bottle from different views.
Ans: 

Boxy Buildings(Page 27)Jagat and Mini are playing. They are making different buildings using empty matchboxes and making their drawings from different views.

Now, you also collect empty matchboxes or any other empty boxes to create different buildings and draw their top, side, and front views. You can challenge your friends by asking them to match your drawing with the right building.
Ans: Do it Yourself.

Cat Finds Jagat(Page 28)The next day, the five friends go to school feeling excited as it is an activity day. Jagat’s pet cat follows him to school. The cat sits on the window and tries to find Jagat.

Let Us DoJagat’s cat sees him sitting on the third desk in the first row .
Q1: Mark Jagat’s position in the picture.
Ans: 

Q2: Describe the position of the blue bag.
Ans: The blue bag is on the first desk in the first row.

Q3: What do you see on the middle desk of the second row?
Ans: A red bottle is on the middle desk of the second row.

Q4: Where is the notebook kept – the first desk in the second row or the middle desk in the third row?
Ans: The notebook is on the middle desk in the third row.

Q5: Draw an apple on the third desk of the second row.
Ans: 

Grid Game(Page 29)

Q: Here are the clues given by Rani to fill the grid: 

•  An eraser at the top right corner. 
• A pencil in the top left corner. 
• An apple in the middle of the second row and second column. 
• A water bottle in the third row and second column.

Ans: 

Grid Game – Treasure Hunt(Page 30)In this game, one player has to think of an object from the grid and help the other player locate it. Let’s see how Jagat and Mini are playing.

What object did Jagat think of?
Ans: 

• Mini takes 2 steps to the left and 1 step upwards. She reaches the Cat.
• Mark Mini’s position on the grid.
  
• Jagat thought of object mango.

Play the game with your partner 
From the starting point, trace the paths to reach the flower. How many steps are required for each path? Speak out or write down the different paths followed to reach the flower.
Ans: Steps required for each path (Path 1 and Path 2) = 7 steps

From the starting point, where would you reach in a smaller number of steps: the mango or the orange?

Steps required to reach mango = 5 steps.

Steps required to reach orange = 4 steps

Orange can be reached in smaller number of steps.

Drone Around the School(Page 31)Gyan has got a drone to show her friends. A drone can take pictures while flying.

Q: Circle the places or things that you see in the picture and write their names.
Ans: In the drone’s picture, circle items or places like trees, buildings, or playgrounds. Their names, e.g., “Tree, Car, School, Playground.”

Drone Around the School (Continued)(Page 32) Preet’s elder sister has made a sight map of the school. You can easily locate Grade 4 on the map.
 Q1: Trace the path from the Grade 4 classroom to the stage.
Ans: 

Q2: How many routes were you able to find? (You may use different colour pencils to trace the different routes)
Ans: Number of routes to go from the Grade 4 classroom to the stage = 5 routes

Q3: Which is the shortest route? How do you know?
Ans: The route which is going to the right of Grade 4 via playground is the shortest.

Q4: The water delivery man has turned left from the entrance. Help him reach MDM Kitchen by telling him the route. Write the directions below.
Ans: Directions to the MDM Kitchen from the entrance: 
(i) Turn left at the entrance and walk straight. 
(ii) Go along the path between the Principal’s Office and the Stage. 
(iii) Keep walking straight until you reach the Medical Room. 
(iv) From the Medical Room, turn left. The MDM Kitchen will be right there.

Q5: Rajat is not feeling well. Which way will you choose to take him to the medical room from the library?
Ans: (i) Walk past the stage and enter the corridor next to the hall. 
(ii) Continue straight, passing the Middle Wing classrooms. 
(iii) The room at the far-left corner of the corridor is the Medical Room.

Q6: After the assembly in the playground, Bholu must go to the IT room and Rani has to go to the sports room. Trace their paths. Which way is longer?
Ans: So, Rani’s way is longer.

Let Us Do (Project Work)(Page 33)Q: Draw a sight map to show the way from your school entrance to your classroom and any other important places.
Ans: Do it Yourself.

Textbooks solutions

Shapes and Models(Page 1)Try to make a model of the buildings shown here using blocks.

Q1: What parts of the building have you shown in your model (for example, roof, pillars, base, etc.)?
Ans: I have shown the base, pillars, sidewalls, and roof of the building in my model.

Q2: Why did you select these parts?

Ans: I have selected these parts because they form the core structure of the building.  

Q3: What shapes will model these parts well?

Ans: Rectangles, squares, semicircles, and cylinders are the shapes that model these parts well

Q4: How is your model similar to the picture of the real building?

Ans: The shapes of the different parts of my model closely match those of the real building in the picture.

Q5: How is it different from the real building?

Ans: My model is smaller, made of blocks, and does not have details like carvings of the real India Gate. 

Discussion:

1. What would happen if you removed one piece of your model?
   Ans: The model might become unstable or look incomplete.
2. Would the model still look like the original building?
   Ans: No, the model won’t look like the original building.
3. In what ways could you make the model even better?
   Ans: To make the model even better, I could paint it in colours that closely resemble the actual building.

Project Work(Page 2)

Q1: Do you think it looks like the Qutub Minar?
Ans: No, it doesn’t look like the Qutub Minar.

Q2: What shape would you use if you made a model of the Qutub Minar? Why?
Ans: I would use a cylindrical shape to make a model of the Qutub Minar because the actual structure is tall and round, similar to a cylinder.

Q3: How many such shapes will you use?
Ans: I would use five cylindrical shapes to make different levels of the Qutub Minar in my model.

Ans: 

Craft(Page 3 & 4)Q1: Make a sphere-like shape with paper strips.
Ans: 

Q2: Use the nets given at the end of the book to make the models shown below.

Ans: 

• Is a cube also a prism?
  Ans: Yes, a cube is a special type of prism where all faces are squares and all edges are of equal length.
• What is the difference between a prism and a pyramid?
  Ans: A prism has two identical bases while a pyramid has one base. Also, a prism has all rectangular or parallelogram-shaped side faces while a pyramid has all triangular side faces.

Q: Now try to make the above shapes using straws and plasticine/ thread and fill in the table.

Ans:

Q: Identify any relationship that you may find between the number of faces (F), edges (E), and corners (V). Calculate F+V-E in each case. What do you notice?
Ans: The formula says: F + V – E = 2
Where:

• F = Faces
• V = Vertices (corners)
• E = Edges

Here are the calculations:
1. Cube (Square Prism):
F + V – E = 6 + 8 – 12 = 2
2. Cuboid (Rectangular Prism):
F + V – E = 6 + 8 – 12 = 2
3. Triangular Pyramid:
F + V – E = 4 + 4 – 6 = 2
4. Square Pyramid:
F + V – E = 5 + 5 – 8 = 2
5. Triangular Prism:
F + V – E = 5 + 6 – 9 = 2
What we notice?
In every case, F + V – E = 2!Ans: 

Q: Can you construct a 3D shape with 3 flat faces?
Ans: No, it is impossible to construct a 3D shape with 3 flat faces.

Ans: 

Let Us Observe(Page 5)Q1: Take a die. Look at the face that has number 1. The face numbered 6 is opposite to the face numbered 1.
What is the face opposite to the: 
(a) face numbered 2? ……….
(b) face numbered 3? ……….
(c) face numbered 4? ……….
Ans: Numbers on opposite faces of a die always add up to 7. Therefore:

Q2: (a) Which faces have common edges with the face numbered 1?………..
(b) Which face has no common edge with the face numbered 1?………..
Ans: a) Faces having common edges with the face numbered 1 are 2, 3, 4 & 5. 
b) Faces having no common edges with the face numbered 1 is 6.

Q3: Look at three different views of the same cube.

(a) What colour is the face that is opposite to the red face? …………
Ans: a) Colour of face opposite to red face – Purple.

(b) What colour is the face that is opposite to the yellow face?……….
Ans: b) Colour of face opposite to yellow face-Green.

Follow these instructions for the shapes along the border.Q1: Colour all shapes with a rectangular face in red.
Ans: Colour the cube, cuboid, and rectangular prism in red.
Q2: Draw a smiley on shapes with a triangular face.
Ans: Draw a smiley on the triangular prism and triangular pyramid.
Q3: Draw a star on shapes with a curved face.
Ans: Draw a star on the cylinder, cone, and sphere.
Q4: Colour all shapes with no corner in blue.
Ans: Colour the sphere and cylinder in blue. 
Q5: Circle the shapes that have the same opposite faces.
Ans: Circle the cube and cuboid, as their opposite faces are identical. 

Sorting 3D Shapes(Page 6)
Write the names of 3D shapes in the correct places.

Ans: 

Q: In which circle did you write triangular prism and rectangular pyramid?
Ans: Triangular prism and rectangular pyramid are written in circle 1(B), Circle 2(B) and intersection of circles 3(A) and 3(B).

Let us sort shapes in another way.
Q: Using circles like those on the previous page, can you sort shapes into the categories “Shapes with curved faces” and “Shapes with flat faces” ?
Ans: 

Build with Cubes(Page 7)Q: Build these models with the cubes from the Jaadui Pitara Kit or any other similar material.

Ans: Do it Yourself.

Cube TowersQ1: How many cubes are there in each of these cube towers?Ans:  

Drawing Cubes on a Triangular Dot Paper(Page 8)Q: Can you complete the following cubes?

Ans:  Q:

Ans: 

Q2: Each one is different. How?Ans: 

• Sphere (Red Ball)
  It has no flat faces, no corners, and is completely round.
• Cone (Golden)
  It has 1 flat face (circle) and 1 curved face.
• Triangular Pyramid (Blue)
  It has 4 triangular faces.
• Cube (Green)
  All faces are equal squares. It has 6 faces, 8 corners, and 12 straight edges.
• Cuboid (Purple)
  It looks like a box. Faces are rectangles, not all the same like a cube. It also has 6 faces, 8 corners, and 12 edges.

Q3: Match the following nets to the appropriate solids.Ans:  

Q4: Which of these nets can be folded to make a solid of the kind given below?Ans:  Net B and D can be folded to make a solid shapes.

Q5: Nitesh cuts up a net on the folds. Here are its pieces.
Which solid has the above pieces in its net?
(a) 

(b) 
(c) 
(d) 
Ans: The solid is (d)   

When Lines Meet(Page 10)Isha made different corners with straws. We can say that the two straws are like two lines that meet at a point.
When two lines meet they create an angle.
We see many angles in yoga postures. 
There are 7 angles in this house drawing.

How many angles are there in this boat drawing?

Ans:  There are 10 angles in the boat drawing. These angles are formed where the lines of the boat’s hull, sail, and mast meet.

Let Us DoQ1: Mark the angles in the following pictures.
(a) 

(b) 
(c) 
(d) 
(e) 

Ans: Mark the angles where lines meet in each picture (e.g., corners of shapes or intersections).  

Q2: Where do you see angles in the classroom? Give a few examples.
Ans: Angles can be seen in many places around the classroom. They are present in the corners of desks, chairs, tables, windows, doors, cupboards, and even in the whiteboard or chalkboard.

Right Angles(Page 11)
Q: Let’s make a right angle with a piece of paper as shown.

Ans: Do it Yourself.

Q: Identify the angles that you think are right angles and circle them in the dot grid given below. Check using your right angle checker.
Ans: 

Q: Check for right angles in a book, window, and any other object. Write the names of objects where you find right angles.
Ans: Angles can be found in objects such as windows, doors, chairs, whiteboards/blackboards, books, desks, etc.

Let Us DoPage 12Q: Draw some right angles on the dot grid.
Ans:

Acute and Obtuse AnglesAcute angles are less than a right angle.
Obtuse angles are more than a right angle.

Q: Name some objects from your classroom which have an acute angle.
Ans: Scissors, pencil tip, corner of a triangle ruler.  

Q: Name some objects from your classroom which have an obtuse angle.
Ans: Open laptop, chair backrest, open door, open notebook.

Q: Identify all angles in the following letters.
Ans: 

Let Us Do(Page 13) Q: 

Ans: 

Q2: In the figures given below, mark the acute angles in red, right angles in green, and obtuse angles in blue.
Ans: Color angles based on their size:  

• Acute (less than 90°): Red  
• Right (90°): Green  
• Obtuse (more than 90°): Blue

Shapes with Straws(Page 14)
Q: Make a triangle with straws of different sizes and clay/ plasticine.

Q1: Does the shape of the triangle change if we gently push one of its sides? (Yes/No)
Ans: Yes.  

Q2: What kinds of angles does a triangle have?
Ans: A triangle can have: (i) All three acute angles. (ii) One right angle and two acute angles. (iii) One obtuse angle and two acute angles.

Q3: What kinds of angles do you see in the rectangle?
Ans: A rectangle has four right angles.

Does the shape of the rectangle change if we gently push one of its sides? (Yes/No)
Ans: Yes.  

• What has happened to the angles of the new shape?
  Ans: The measure of the angles have changed.
• Are they still right angles? What types of angles have been formed?
  Ans: No, they are not right angles. Acute and obtuse angles are formed.  
• Similarly, push one side of a square. Are they still right angles? What types of angles have been formed?
  Ans: No, they are not right angles. Acute and obtuse angles are formed.  
• How are the angles of triangles and rectangles similar or different?
  Ans:  Similarities: Both triangles and rectangles can contain right angles.
  Differences: A triangles has three angles while a rectangle has four angles.
  All four angles in a rectangle are right angles while a triangle can have zero or one right angle.

Dot Grid(Page 15)Use the dot grid given below to draw several three- and four-sided shapes. Circle the shapes that have one or more right angles.

Ans: 

DiscussQ1: What shapes did you make?
Ans: I made two triangles, a square, a rectangle and a parallelogram.

Q2: How many shapes have you made with: 
(a) 1 right angle 
(b) 2 right angles 
(c) 3 right angles 
(d) all right angles
Ans: 

Q3: Here are some 4-sided shapes. In what ways are rectangle and square different from these shapes?
Ans: Rectangles and squares both have four right angles, whereas each of these shapes are formed by a combination of acute and obtuse angles.  

Activity(Page 16)
Try to make this 5-sided shape with all sides equal (Pentagon)

Q1: Are these right angles? 
Ans: No, the angles in a regular pentagon are obtuse (108 degrees).  

Q2: Does the shape of the pentagon change if we gently push one of its sides?
Ans: Yes.  

Q3: How does this change the angles?
Ans: On being gently pushed, the pentagon shows a combination of acute and obtuse angles.

Can you make a circle using straws?Q: Look at the picture. The lengths of the straws in this picture are ……………..(Equal/Unequal)

Ans: Equal

Q: What will happen if we take straws of unequal lengths?
Ans: The resultant shape formed will not be a circle.

Let Us Make(Page 16)Can you use a scale to draw a circular shape? Let us see.
Mark a point A.
Draw many points that are at an equal distance from point A. Connect the dots freehand. What do you get?
Ans: A circle 

Amazing Circles(Page 17)

Q1: The length of all the creases are_________ (Equal/Unequal)?
Ans: Equal.  

Q2: These creases are called diameters of the circle. 

Q3: Discuss where the centre is. Do you notice that all the diameters pass through the centre?
Ans: The centre is the point where all diameters meet. Yes, all diameters pass through the centre.

Q4: Measure the length of the creases from the center to the border of the circle. This is called the radius of the circle. 

Q5: Discuss if there is any relationship between the radius and the diameter of a circle.
Ans: Diameter is twice the radius of the circle.  

Let Us Do(Page 18)Fold the circular paper in half. 
Fold this half again in half.

Q: The length of the diameter is __________(half/double) of the length of radius.
Ans: double

Q: A circle can be made easily using a compass. Ask your teacher to help you use a compass. Make the following design.

Ans: Do Yourself.

Q: Look at the carpet design. A beautiful circle, right? Mark the centre, radius, and the diameter of the circular design with any colour of your choice.
Ans: 

The Wheels(Page 19)Look at the wheels.
All wheels look like circle.

Name the wheel with the 
1. longest radius_______
Ans: longest radius B  
2. shortest radius______ 
Ans: shortest radius D  
3. longest diameter______
Ans: longest diameter B  
4. shortest diameter_______
Ans: shortest diameter D  

Puzzling ShapesQ1: Identify the hidden shapes and write their names.
Ans: Triangle, cylinder, circle, rectangle, square.

Q2: Draw 2 lines to divide the triangle into 1 square and 2 triangles.
Ans: 

Q3: Draw 2 lines to divide the square into 3 triangles.
Ans: 

Q4: Draw lines to show the cuts needed on the shapes in the left column to get the smaller shapes on the right.

Ans: 

Card Game(Page 20)Sort the 2D-shape cards given at the end of the book into three groups according to their sides.
Q: Draw the sorted shapes in the space given below. Explain why you sorted your shapes in this way.
Ans:  

Let Us Try(Page 21)1. Squiggly spiders
Squiggly, the spider, likes to make webs in different shapes. One day she begins to make triangular webs.
How many triangles are in her web?

Ans: Number of triangles in her web = 10.

She likes to take a walk each morning and check if the walls of her web are strong.
Can she begin at point A and reach back to the same point without walking on any wall more than once?
Trace and show Squiggly’s path.

Ans: Yes, she can begin at point A and reach back to the same point without walking on any wall more than once.
Squiggly’s path = 1 → 2 → 3 → 4 → 8 → 9 → 6 → 11 → 10 → 7 → 5 → 12.

Her brother, Wiggly, made a web using rectangles. 

How many rectangles can you see in his web?

Ans: Number of rectangles in his web = 12.
He likes to take a walk at the end of each day and check if the walls of his web are strong.
Can he begin at point A and leave from point B without walking on any wall more than once?
Trace and show Wiggly’s path.
Ans: No, Wiggly cannot start from A and leave from B without walking on any walls more than once and also go through all the walls.an once.

Q2: Use 5 matchsticks to make 2 triangles. Then draw it in the space provided.
Ans: 

Q3: Move two of these matchsticks to form 4 triangles.
Ans:

Q4: Remove 4 of these matchsticks to leave only 3 triangles.
Ans: 

Q5: Model Challenge
Can you make a model of solid shapes which has:
(a) 12 straws and 8 clay balls? 
(b) 9 straws and 6 clay balls? 
(c) 15 straws and 10 clay balls? 
(d) 10 straws and 6 clay balls?
Ans: (a) Cuboid (12 straws and 8 clay balls).
b) Triangular prism (9 straws and 6 clay balls).
c) Pentagonal prism (15 straws and 10 clay balls)
d) Pentagonal pyramid (10 straws and 6 clay balls)

Q6: Classify these shapes based on the number of angles: 

What relation do you notice between the number of sides and the number of angles?
Ans:  Shapes with 3 angles – b, d, f.
Shapes with four angles – a, c, g.
Shapes with five angles – e.
Each shape has equal number of sides and angles.

Let Us Try(Page 23)Q7: 

Ans: 

Q8: Mark the right angles and write the number of right angles in each figure. 
Which of the above shapes have only right angles?
Ans: 

Q9: Observe the following shapes.
Identify the shape that has: 

• 2 right angles, 1 acute, and 1 obtuse angle________
• 1 right, 2 obtuse, and 1 acute angle_________
• 2 obtuse, and 2 acute angles_________
• 4 right angles_________

Ans: 

• 2 right angles, 1 acute, and 1 obtuse angle 2,7 
• 1 right, 2 obtuse, and 1 acute angle 10  
• 2 obtuse, and 2 acute angles  3,5,8,9,11,13  
• 4 right angle  4, 6, 12, 14.