NCERT Solutions for Class 2 Joyful Maths Chapter 03 Fun with Numbers

Question. Look at the Ginladi.
A. How many beads are there in ginladi?
B. There are some blank cards on the ginladi. Write the numbers on them by counting the number of beads.
C. Make number cards for the following numbers and place them on your ginladi. 38, 44, 58, 65, 98
Answer: A. The ginladi has 100 beads in total. B. The missing numbers are 36, 48, 56, 79, and 85. C. The number cards 38, 44, 58, 65, and 98 are placed on the ginladi.
In simple words: Count all the beads to find the total. Fill in the blank cards by counting the beads carefully. Place each new number card where it belongs on the string.

Exam Tip: When counting on a ginladi (number string), point to each bead carefully and count in order to avoid missing any numbers.

Question. Look at the number strip and fill in the blanks.
A. The butterfly moves _______ steps forward to reach the pink flower.
B. The honey bee moves _______ steps forward to reach the red flower and _______ steps forward to reach the yellow flower.
C. The squirrel jumps 2 steps backward, five steps forward and again 3 steps backward. It will reach at _______.
D. The frog jumps 2 steps forward, seven steps backward and again 3 steps backward to reach _______.
Answer: A. The butterfly moves 6 steps forward to reach the pink flower. B. The honey bee moves 5 steps forward to reach the red flower and 10 steps forward to reach the yellow flower. C. The squirrel will reach at 95. D. The frog will reach 60.
In simple words: Count the steps on the number line. Start from where the animal is and count forward or backward to find where it lands.

Exam Tip: Always trace the path of each animal on the number strip carefully, counting each step one by one.

Question. Guess my Number
A child thinks of a number and other children have to guess it. Children will ask questions like, is it more than 50? Are the two digits of the number same? Questions that can be answered in 'yes/no', they can ask maximum 10 questions to guess the number.
Answer: Suppose the number is 63. Is it greater than 50? Yes. Is it less than 90? Yes. Is it more than 75? No. Is it less than 60? No. Is it more than 65? No. Is it more than 62? Yes. Is it 63? Yes. You got the number.
In simple words: Ask questions that help narrow down what the number is. Each answer removes some possibilities, getting you closer to the mystery number.

Exam Tip: Use yes/no questions that cut the range of numbers in half each time to find the answer faster.

Question. Guess my Place
Three ants are sitting on a number line. Write the numbers for these ants.
Black ant is sitting on the number _______
Red ant is sitting on the number _______
Brown ant is sitting on the number _______
Draw an ant on number 65 on the number line shown above. Draw a sugar cube on number 79 on the number line shown above.
Answer: Black ant is sitting on the number 30. Red ant is sitting on the number 50. Brown ant is sitting on the number 60. An ant on number 65 on the number line is shown. A sugar cube on number 79 on the number line is shown.
In simple words: Look at the space between numbers on the line. Figure out where each animal is by counting the gaps evenly.

Exam Tip: Find the pattern of spacing on the number line, then use it to place each item correctly.

Question. Complete the following patterns.
A. 1, 4, 7, _______, _______, _______, _______
B. 40, 45, 50, _______, _______, _______, _______, _______
C. 50, 60, _______, _______, _______
Answer: A. 1, 4, 7, 10, 13, 16, 19 B. 40, 45, 50, 55, 60, 65, 70, 75 C. 50, 60, 70, 80, 90
In simple words: Look at the numbers given and find what is being added each time. Keep adding the same amount to find the missing numbers.

Exam Tip: Always check the difference between the first two given numbers - that difference tells you what to add to each number to get the next one.

Question. Let us Do
A. On the number chart, use skip counting in two and draw on the numbers. Now use skip counting in five and draw on the numbers in the number chart.
B. Write down the numbers that are common to the skips in twos and fives.
_______
C. Write down the numbers that are common to the skips in twos, threes and fives.
_______
D. Write down the numbers common to the skips of fives and sevens?
Answer: A. Using skip counting in two: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100. Using skip counting in five: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100. B. The numbers common to skip counting in twos and fives are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. C. The numbers common to skips in twos, threes and fives are: 30, 60, 90. D. The numbers common to the skips of fives and sevens are: 35, 70.
In simple words: Skip counting means jumping by the same number each time. Numbers that appear in more than one skip count are the ones that can be divided by both numbers.

Exam Tip: Common multiples appear in more than one skip counting pattern - mark them on your number chart to see the pattern clearly.

Question. Jump and find the answers. Write 'Yes' or 'No'.
A. If you start from 10 and jump counting in tens, will you land on number 100 at any time?
B. Jump and find out if you start at 5 and count in fives, will you jump on number 40 at any time?
C. If you start from 0 and count in fives, will you jump on number 55 at any time?
D. If you start from 4 and count in twos, will you jump on number 17 at any time?
E. If you start from 13 and count in threes, will you jump on number 24 at any time?
Answer: A. Yes B. Yes C. Yes D. No E. No
In simple words: Skip count from the starting number by the given amount. If you land exactly on the target number, say yes; if you skip over it, say no.

Exam Tip: Write out the sequence of numbers you land on when skip counting - this helps you see if the target number is in your sequence.

Question. Let us Do
A. Rizwan is counting numbers from 20 onwards. Will he say the number 19 in his count? Explain why?
B. Chavi is counting numbers in twos from 10 onwards. Will she say 43? Explain why?
C. Mala is counting backwards from 20. How many steps will it take to reach 0? Explain why?
D. Viraaj is counting backwards in twos from 20. How many steps will it take to reach 0? Discuss.
Answer: A. No, because 19 is less than 20. B. No, because counting numbers in twos from 10 contains 12 then 14. C. 20 steps. D. 10 steps.
In simple words: Think about the direction (forward or backward) and the size of the jumps. This tells you which numbers you will or won't land on.

Exam Tip: Explain your reasoning clearly by describing the counting pattern and showing why a certain number cannot be reached.

Question. Let us Do
Look at the number chart and write down the answers.
_____ comes just before 10
_____ comes just before 20
_____ comes just before 30
_____ comes just before 40
Do you see any pattern? Shade the numbers on the number chart. Does the pattern continue for other numbers? If yes, write the pattern.
_____
Now, look at the numbers coloured green in the number chart. Write them.
1, 12, 23, _____, _____, _____, _____, _____
What pattern do you notice? Discuss.
Lakshanya made a number window and placed it on the number chart as shown below.
A. If the centre of the window is placed on 28, which number will be on the top of it?
B. Which number will be below it?
C. Which number will be on its right?
D. Which number will be on its left?
Answer: The numbers that come just before are: 9, 19, 29, 39. Yes, the next number is 10 more than the previous one. The pattern is 9, 19, 29, 39, 49, 59, 69, 79, 89, 99. Now, look at the numbers coloured green in the number chart. Write them. 1, 12, 23, 34, 45, 56, 67, 78, 89, 100. Every next number is 11 more than the previous one. A. If the centre of the window is placed on 28, the number on the top of it is 18. B. The number below it is 38. C. The number on its right is 29. D. The number on its left is 27.
In simple words: Look for patterns by checking how much each number changes. A number window helps you see numbers that are near each other on the chart.

Exam Tip: When using a number window, remember that the top number is one row above the centre, the bottom is one row below, and left/right are just before/after in the same row.

Question. Let us jump backward.
Complete the following patterns.
What comes just before 10?
What comes just before 9?
10, 9, 8, _____, _____, _____, _____
A. 40, 37, 34, _____, _____, _____, _____, _____
B. 70, 65, 60, _____, _____, _____
C. 100, 90, _____, _____, _____
D. 100, 80, _____, _____
Is there a pattern in the given numbers? If not, change the numbers to create a pattern. Also, extend it.
100, 90, 80, 70, 60, _____, _____
Answer: 9 comes just before 10. 8 comes just before 9. 10, 9, 8, 7, 6, 5, 4, 3, 2, 1. A. 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1. B. 70, 65, 60, 55, 50, 45, 40, 35, 30. C. 100, 90, 80, 70, 60. D. 100, 80, 60, 40. Yes, there is a pattern in the given numbers. 100, 90, 80, 70, 60, 50, 40, 30, 20, 10.
In simple words: When jumping backward, subtract the same amount each time to find the next number. Look at the difference between the first two numbers to know what to subtract.

Exam Tip: Check that your backward counting pattern is correct by verifying the difference stays the same between every pair of numbers.

Question. E. Let us do it for other numbers.
Answer: Fill in the missing boxes using the same pattern as the three examples shown:

Top row (single center number with four boxes around it):
43 (top center)
52, 53, 54 (bottom row)
63 (bottom center)

16 (top center)
25, 26, 27 (bottom row)
36 (bottom center)

64 (top center)
73, 74, 75 (bottom row)
84 (bottom center)
In simple words: The middle number stays in the center. The numbers to the left and right of it go one up and one down. The number below also goes one down from the middle number.

Exam Tip: Look at how each number relates to the one in the middle - the pattern shows adding and subtracting 1 in a cross shape.

Question. F. Based on the same number grid fill the missing numbers.
Answer: Using the same number grid pattern, fill in all the empty boxes:

Grid 1 (with 8):
8, 9 (top row)
17, 18 (middle row)
28 (bottom)

Grid 2 (with 57):
48, 49 (top)
57, 58, 59 (middle)
68, 69 (bottom)

Grid 3 (with 46):
36 (top)
45, 46, 47 (middle)
55, 56 (bottom)

Grid 4 (with 69):
68, 69, 70 (top)
79 (middle)
89 (bottom)

Grid 5 (with 16):
16 (top)
26, 27 (middle)
36, 37, 38 (bottom)

Grid 6 (with 32):
22, 23, 24 (top)
32 (middle)
42, 43, 44 (bottom)

Grid 7 (with 65):
64, 65 (top)
75 (middle)
85, 86 (bottom)

Grid 8 (with 36):
36, 38 (top)
46, 48 (middle)
56, 57, 58 (bottom)

Grid 9 (with 55):
44, 45, 46 (top)
55 (middle)
64, 65, 66 (bottom)
In simple words: Each grid has a main number. Fill the boxes around it by counting up and down. Numbers to the side change by one, and numbers above and below also change by one.

Exam Tip: Check your work by making sure each number is exactly one more or one less than its neighbors - this keeps the pattern correct across all grids.

Question. Exploring Patterns. Observe how the number of blocks are increasing in the following shapes and extend the pattern.
(A) Look at the shapes with 1, 3, and 6 blocks. What are the next two numbers in the pattern?

(B) Look at the shapes with 1, 4, and 9 blocks. What are the next two numbers in the pattern?

(C) Look at the shapes with 5 and 8 blocks. What are the next two numbers in the pattern?
Answer:
(A) The pattern shows 1, 3, 6, 10, 15. Each step adds one more block than the step before (add 2, then add 3, then add 4, then add 5). The next two numbers are 10 and 15.

(B) The pattern shows 1, 4, 9, 16, 25. These are square numbers (1×1, 2×2, 3×3, 4×4, 5×5). The next two numbers are 16 and 25.

(C) The pattern shows 5, 8, 11, 14. Each step adds 3 more blocks. The next two numbers are 11 and 14.
In simple words: Pattern A grows by adding more each time. Pattern B shows square numbers where you multiply a number by itself. Pattern C simply adds the same amount (3) each time.

Exam Tip: Always look for the rule that connects one number to the next - it might be adding the same amount, or multiplying, or following square numbers.

Question. Look at the Ginladi.
A. How many beads are there in ginladi?
B. There are some blank cards on the ginladi. Write the numbers on them by counting the number of beads.
C. Make number cards for the following numbers and place them on your ginladi. 38, 44, 58, 65, 98

Look at the number strip and fill in the blanks.
A. The butterfly moves _______ steps forward to reach the pink flower.
B. The honey bee moves _______ steps forward to reach the red flower and _______ steps forward to reach the yellow flower.
C. The squirrel jumps 2 steps backward, five steps forward and again 3 steps backward. It will reach at _______.
D. The frog jumps 2 steps forward, seven steps backward and again 3 steps backward to reach _______.
Answer:
Look at the Ginladi.
A. There are 100 beads in the ginladi.
B. 36, 48, 56, 79 and 85.
C. 38, 44, 58, 65, 98 are shown on ginladi.

Look at the number strip and fill in the blanks.
A. The butterfly moves 6 steps forward to reach the pink flower.
B. The honey bee moves 5 steps forward to reach the red flower and 10 steps forward to reach the yellow flower.
C. The squirrel jumps 2 steps backward, five steps forward and again 3 steps backward. It will reach at 95.
D. The frog jumps 2 steps forward, seven steps backward and again 3 steps backward to reach 60.
In simple words: Count the beads carefully to find how many are there. Write the missing numbers on the blank cards. Then move forward and backward on the number strip by the number of steps given.

Exam Tip: Make sure you count beads correctly and track each step forward or backward on the number strip carefully.

Question. Guess my Number - Let us Play
A child thinks of a number and other children have to guess it. Children will ask questions like, is it more than 50? Are the two digits of the number same? Questions that can be answered in 'yes'/'no'. They can ask maximum 10 questions to guess the number.
Answer: Suppose the number is 63.
Is it greater than 50? Yes
Is it less than 90? Yes
Is it more than 75? No
Is it less than 60? No
Is it more than 65? No
Is it more than 62? Yes
Is it 63? Yes. You got the number.
In simple words: Think of a number. Ask yes or no questions to narrow it down. Each question should help you remove some numbers and get closer to finding the right one.

Exam Tip: When guessing a number, always ask questions that help you cut the number range in half - this gets you to the answer faster.

Question. Guess my Place
Three ants are sitting on a number line. Write the numbers for these ants.
Black ant is sitting on the number _______
Red ant is sitting on the number _______
Brown ant is sitting on the number _______
Draw an ant on number 65 on the number line shown above.
Draw a sugar cube on number 79 on the number line shown above.
Answer:
Black ant is sitting on the number 30
Red ant is sitting on the number 50
Brown ant is sitting on the number 60
An ant on number 65 on the number line.
A sugar cube on number 79 on the number line.
In simple words: Look at where each ant is placed on the line. Count by tens to find the number under each ant. Then mark the new positions for the ant and sugar cube.

Exam Tip: Always count carefully from 0 or from marked numbers to find the right position on a number line.

Question. Complete the following patterns.
A. 1, 4, 7, _______, _______, _______, _______
B. 40, 45, 50, _______, _______, _______, _______, _______
C. 50, 60, _______, _______, _______
Answer:
A. 1, 4, 7, 10, 13, 16, 19
B. 40, 45, 50, 55, 60, 65, 70, 75
C. 50, 60, 70, 80, 90
In simple words: Look at how much the numbers grow from one to the next. Keep adding that same amount to find the missing numbers.

Exam Tip: Always find the difference between two numbers to see what rule the pattern follows, then apply it to fill the blanks.

Question. Let us Do
A. On the number chart, use skip counting in two and draw a circle on the numbers. Now use skip counting in five and draw a triangle on the numbers in the number chart.
B. Write down the numbers that are common to the skips in twos and fives. _______
C. Write down the numbers that are common to the skips in twos, threes and fives. _______
D. Write down the numbers common to the skips of fives and sevens?
Answer:
A. Circle: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100
Triangle: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100
B. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
C. 30
D. 35, 70
In simple words: Count by the number and mark every number you land on. Numbers that appear in more than one count are common to both patterns.

Exam Tip: To find common multiples, look for numbers that get marked in both skip-counting patterns.

Question. Let us Do - Jump and find the answers. Write 'Yes' or 'No'.
Make a number line on the ground and jump on it.
A. If you start from 10 and jump counting in tens, will you land on number 100 at any time?
B. Jump and find out if you start at 5 and count in fives, will you jump on number 40 at any time?
C. If you start from 0 and count in fives, will you jump on number 55 at any time?
D. If you start from 4 and count in twos, will you jump on number 17 at any time?
E. If you start from 13 and count in threes, will you jump on number 24 at any time?
Answer:
A. If you start from 10 and jump counting in tens, will you land on number 100 at any time? Yes
B. Jump and find out if you start at 5 and count in fives, will you jump on number 40 at any time? Yes
C. If you start from 0 and count in fives, will you jump on number 55 at any time? Yes
D. If you start from 4 and count in twos, will you jump on number 17 at any time? No
E. If you start from 13 and count in threes, will you jump on number 24 at any time? No
In simple words: Jump on the line by the amount shown. If you land on the target number, write Yes. If you never land on it, write No.

Exam Tip: Check if the target number is part of the skip-counting sequence starting from the given number - if yes, you will land on it.

Question. Let us jump backward. Complete the following patterns.
What comes just before 10?
What comes just before 9?
10, 9, 8, _______, _______, _______, _______, _______
A. 40, 37, 34, _______, _______, _______, _______, _______
B. 70, 65, 60, _______, _______, _______
C. 100, 90, _______, _______, _______
D. 100, 80, _______, _______
Is there a pattern in the given numbers? If not, change the numbers to create a pattern. Also, extend it.
100, 90, 80, 70, 60, _______, _______
Answer:
9 comes just before 10.
8 comes just before 9.
10, 9, 8, 7, 6, 5, 4, 3, 2, 1
A. 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1
B. 70, 65, 60, 55, 50, 45, 40, 35, 30
C. 100, 90, 80, 70, 60
D. 100, 80, 60, 40
Yes, there is a pattern in the given numbers.
100, 90, 80, 70, 60, 50, 40, 30, 20, 10
In simple words: Count backward by a regular amount each time. Find how much you subtract, then keep subtracting that amount to complete the pattern.

Exam Tip: Always check the difference between two numbers in a backward pattern - subtract that difference to find the next number.

Question. Let us Do
A. Rizwan is counting numbers from 20 onwards. Will he say the number 19 in his count? Explain why?
B. Chavi is counting numbers in twos from 10 onwards. Will she say 43? Explain why?
C. Mala is counting backwards from 20. How many steps will it take to reach 0? Explain why?
D. Viraaj is counting backwards in twos from 20. How many steps will it take to reach 0? Discuss.
Answer:
A. No, because 19 is less than 20.
B. No, because counting numbers in twos from 10 contains 42 then 44.
C. 20 steps.
D. 10 steps.
Patterns in Number Chart (shown with a 10x10 grid displaying numbers 1-100)
In simple words: When you start counting from a number, you can only say numbers that come after it or numbers in your counting pattern.

Exam Tip: Check whether the target number fits into the counting pattern starting from the given number - if not, it won't be said.

Question. Let us Do - Look at the number chart and write down the answers.
_______ comes just before 10
_______ comes just before 20
_______ comes just before 30
_______ comes just before 40
Do you see any pattern? Shade the numbers on the number chart. Does the pattern continue for other numbers? If yes, write the pattern. _______
Now, look at the numbers coloured green in the number chart. Write them.
1, 12, 23, _______, _______, _______, _______, _______
What pattern do you notice? Discuss.
Lakshanya made a number window and placed it on the number chart as shown below.
A. If the centre of the window is placed on 28, which number will be on the top of it?
B. Which number will be below it?
C. Which number will be on its right?
D. Which number will be on its left?
Answer:
9 comes just before 10
19 comes just before 20
29 comes just before 30
39 comes just before 40
Yes, the next number is 10 more than the previous one.
9, 19, 29, 39, 49, 59, 69, 79, 89, 99
Now, look at the numbers coloured green in the number chart. Write them.
1, 12, 23, 34, 45, 56, 67, 78, 89, 100
Every next number is 11 more than the previous one.
Lakshanya made a number window and placed it on the number chart as shown below.
A. If the centre of the window is placed on 28, which number will be on the top of it? 18
B. Which number will be below it? 38
C. Which number will be on its right? 29
D. Which number will be on its left? 27
In simple words: Look at what number sits above, below, left, and right of any number on the chart. The pattern is: above is 10 less, below is 10 more, right is 1 more, left is 1 less.

Exam Tip: When using a number window on a chart, remember the positions and what they mean - 10 more down, 10 less up, 1 more right, 1 less left.

Question. E. Let us do it for other numbers.
Fill in the missing boxes for each of the three number grids shown. The center box in each grid already contains a number (53, 26, or 74). Write the numbers that go above, below, left, and right of each center number, following the pattern of consecutive numbers.
Answer:
For the grid with center number 53:
Top: 43, Left: 52, Right: 54, Bottom: 63

For the grid with center number 26:
Top: 16, Left: 25, Right: 27, Bottom: 36

For the grid with center number 74:
Top: 64, Left: 73, Right: 75, Bottom: 84
In simple words: Look at the number in the middle box. The box above it is 10 less. The box below it is 10 more. The boxes on the sides are 1 less and 1 more.

Exam Tip: Check your work by making sure the top and bottom boxes are exactly 10 apart from the middle, and the left and right boxes are exactly 1 apart.

Question. F. Based on the same number grid fill the missing numbers.
Use the same pattern as above to complete all six grids shown. Each grid has one or more boxes already filled in. Find and write all the missing numbers, maintaining the pattern where the center is surrounded by consecutive numbers horizontally and numbers that are 10 apart vertically.
Answer:
Grid 1 (center 8): Top: empty, Left: 17, Center: 8, Right: 9, Bottom: 18, and below that: 28

Grid 2 (center 57): Top: 48 and 49, Left: 57, Right: 58, 59, Below: 68, 69

Grid 3 (center 46): Top: 36, Left: 45, Right: 47, Below: 55, 56

Grid 4 (center 69): Left column going down: 68, 69, 70, then 79, 89

Grid 5 (center 16): Top: empty, Middle row: 26, 27, Below: 36, 37, 38

Grid 6 (center 32): Top: 22, 23, 24, Middle: 32, Below: 42, 43, 44, and final row: 44, 45, 46 with 55 below, and bottom row: 64, 65, 66
In simple words: For each grid, find the number already given. Then add or subtract 1 for numbers beside it, and add or subtract 10 for numbers above or below it.

Exam Tip: Work outward from the given number in a cross pattern - check left and right first (add and subtract 1), then up and down (add and subtract 10) to fill in any neighboring boxes.

Question. Exploring Patterns. Observe how the number of blocks are increasing in the following shapes and extend the pattern.
(A) The first shape has 1 block, the second has 3 blocks, the third has 6 blocks. Draw the next two shapes in this pattern.
(B) The first shape has 1 block, the second has 4 blocks, the third has 9 blocks. Draw the next two shapes in this pattern.
(C) The first shape has 5 blocks, the second has 8 blocks. Draw the next two shapes in this pattern.
Answer:
(A) The pattern shows triangular numbers: 1, 3, 6, 10, 15, and so on. The next two shapes would have 10 and 15 blocks arranged in expanding triangular arrangements.

(B) The pattern shows perfect squares: 1, 4, 9, 16, 25, and so on. The next two shapes would have 16 and 25 blocks arranged in square grids.

(C) The pattern increases by 3 each time: 5, 8, 11, 14, and so on. The next two shapes would have 11 and 14 blocks arranged in rectangular patterns.
In simple words: Look at how many blocks are added each time. If the same number is added each time, keep that pattern going. Draw shapes that match the new numbers.

Exam Tip: Identify whether the pattern adds the same amount each time (like 1, 3, 5, 7) or follows square numbers (1, 4, 9, 16) or triangular numbers (1, 3, 6, 10) before drawing the next shapes.