NCERT Textbook: Number Play

 Page 1


6.1 Numbers Tell us Things
What do the numbers in the ??gure below tell us?
Remember the children from the Grade 6 textbook of mathematics? 
Now, they call out numbers using a di??erent rule.
What do you think these numbers mean?
The children rearrange themselves and each one says a number 
based on the new arrangement.
Could you ??gure out what these numbers convey? Observe and try to 
??nd out.
NUMBER PLAY
6
Chapter-6.indd   127 Chapter-6.indd   127 4/12/2025   11:59:04 AM 4/12/2025   11:59:04 AM
Reprint 2026-27
Page 2


6.1 Numbers Tell us Things
What do the numbers in the ??gure below tell us?
Remember the children from the Grade 6 textbook of mathematics? 
Now, they call out numbers using a di??erent rule.
What do you think these numbers mean?
The children rearrange themselves and each one says a number 
based on the new arrangement.
Could you ??gure out what these numbers convey? Observe and try to 
??nd out.
NUMBER PLAY
6
Chapter-6.indd   127 Chapter-6.indd   127 4/12/2025   11:59:04 AM 4/12/2025   11:59:04 AM
Reprint 2026-27
Ganita Prakash | Grade 7 
The rule is — each child calls out the number of children in front of 
them who are taller than them. Check if the number each child says 
matches this rule in both the arrangements.
Write down the number each child should say based on this rule for 
the arrangement shown below.
Figure it Out
1. Arrange the stick ??gure cutouts given at the end of the book or 
draw a height arrangement such that the sequence reads:
(a) 0, 1, 1, 2, 4, 1, 5
(b) 0, 0, 0, 0, 0, 0, 0
(c) 0, 1, 2, 3, 4, 5, 6
(d) 0, 1, 0, 1, 0, 1, 0
(e) 0, 1, 1, 1, 1, 1, 1
(f) 0, 0, 0, 3, 3, 3, 3
2. For each of the statements given below, think and identify if it 
is Always True, Only Sometimes True, or Never True. Share your 
reasoning.
(a) If a person says ‘0’, then they are the tallest in the group.
(b) If a person is the tallest, then their number is ‘0’.
(c) The ??rst person’s number is ‘0’.
(d) If a person is not ??rst or last in line (i.e., if they are standing 
somewhere in between), then they cannot say ‘0’.
(e) The person who calls out the largest number is the shortest.
(f) What is the largest number possible in a group of 8 people? 
128
Chapter-6.indd   128 Chapter-6.indd   128 4/12/2025   6:16:31 PM 4/12/2025   6:16:31 PM
Reprint 2026-27
Page 3


6.1 Numbers Tell us Things
What do the numbers in the ??gure below tell us?
Remember the children from the Grade 6 textbook of mathematics? 
Now, they call out numbers using a di??erent rule.
What do you think these numbers mean?
The children rearrange themselves and each one says a number 
based on the new arrangement.
Could you ??gure out what these numbers convey? Observe and try to 
??nd out.
NUMBER PLAY
6
Chapter-6.indd   127 Chapter-6.indd   127 4/12/2025   11:59:04 AM 4/12/2025   11:59:04 AM
Reprint 2026-27
Ganita Prakash | Grade 7 
The rule is — each child calls out the number of children in front of 
them who are taller than them. Check if the number each child says 
matches this rule in both the arrangements.
Write down the number each child should say based on this rule for 
the arrangement shown below.
Figure it Out
1. Arrange the stick ??gure cutouts given at the end of the book or 
draw a height arrangement such that the sequence reads:
(a) 0, 1, 1, 2, 4, 1, 5
(b) 0, 0, 0, 0, 0, 0, 0
(c) 0, 1, 2, 3, 4, 5, 6
(d) 0, 1, 0, 1, 0, 1, 0
(e) 0, 1, 1, 1, 1, 1, 1
(f) 0, 0, 0, 3, 3, 3, 3
2. For each of the statements given below, think and identify if it 
is Always True, Only Sometimes True, or Never True. Share your 
reasoning.
(a) If a person says ‘0’, then they are the tallest in the group.
(b) If a person is the tallest, then their number is ‘0’.
(c) The ??rst person’s number is ‘0’.
(d) If a person is not ??rst or last in line (i.e., if they are standing 
somewhere in between), then they cannot say ‘0’.
(e) The person who calls out the largest number is the shortest.
(f) What is the largest number possible in a group of 8 people? 
128
Chapter-6.indd   128 Chapter-6.indd   128 4/12/2025   6:16:31 PM 4/12/2025   6:16:31 PM
Reprint 2026-27
Number Play
6.2 Picking Parity
Kishor has some number cards and is working on a puzzle: There 
are 5 boxes, and each box should contain exactly 1 number card. The 
numbers in the boxes should sum to 30. Can you help him ??nd a way 
to do it?
 
+ + + + = 30
Can you ??gure out which 5 cards add to 30? Is it possible? 
There are many ways of choosing 5 cards from this collection. 
 Is there a way to ??nd a solution without checking all possibilities? 
Let us ??nd out.
Add a few even numbers together. What kind of number do you get? 
Does it matter how many numbers are added?
Any even number can be arranged in pairs without any leftovers. 
Some even numbers are shown here, arranged in pairs.
 
As we see in the ??gure, adding any number of even numbers
will result in a number which can still be arranged in pairs 
without any leftovers. In other words, the sum will always be an 
even number.
Now, add a few odd numbers together. What kind of number do you 
get? Does it matter how many odd numbers are added?
Odd numbers can not be arranged in pairs. An odd number is one 
more than a collection of pairs. Some odd numbers are shown below:
 
129
Chapter-6.indd   129 Chapter-6.indd   129 4/12/2025   11:59:05 AM 4/12/2025   11:59:05 AM
Reprint 2026-27
Page 4


6.1 Numbers Tell us Things
What do the numbers in the ??gure below tell us?
Remember the children from the Grade 6 textbook of mathematics? 
Now, they call out numbers using a di??erent rule.
What do you think these numbers mean?
The children rearrange themselves and each one says a number 
based on the new arrangement.
Could you ??gure out what these numbers convey? Observe and try to 
??nd out.
NUMBER PLAY
6
Chapter-6.indd   127 Chapter-6.indd   127 4/12/2025   11:59:04 AM 4/12/2025   11:59:04 AM
Reprint 2026-27
Ganita Prakash | Grade 7 
The rule is — each child calls out the number of children in front of 
them who are taller than them. Check if the number each child says 
matches this rule in both the arrangements.
Write down the number each child should say based on this rule for 
the arrangement shown below.
Figure it Out
1. Arrange the stick ??gure cutouts given at the end of the book or 
draw a height arrangement such that the sequence reads:
(a) 0, 1, 1, 2, 4, 1, 5
(b) 0, 0, 0, 0, 0, 0, 0
(c) 0, 1, 2, 3, 4, 5, 6
(d) 0, 1, 0, 1, 0, 1, 0
(e) 0, 1, 1, 1, 1, 1, 1
(f) 0, 0, 0, 3, 3, 3, 3
2. For each of the statements given below, think and identify if it 
is Always True, Only Sometimes True, or Never True. Share your 
reasoning.
(a) If a person says ‘0’, then they are the tallest in the group.
(b) If a person is the tallest, then their number is ‘0’.
(c) The ??rst person’s number is ‘0’.
(d) If a person is not ??rst or last in line (i.e., if they are standing 
somewhere in between), then they cannot say ‘0’.
(e) The person who calls out the largest number is the shortest.
(f) What is the largest number possible in a group of 8 people? 
128
Chapter-6.indd   128 Chapter-6.indd   128 4/12/2025   6:16:31 PM 4/12/2025   6:16:31 PM
Reprint 2026-27
Number Play
6.2 Picking Parity
Kishor has some number cards and is working on a puzzle: There 
are 5 boxes, and each box should contain exactly 1 number card. The 
numbers in the boxes should sum to 30. Can you help him ??nd a way 
to do it?
 
+ + + + = 30
Can you ??gure out which 5 cards add to 30? Is it possible? 
There are many ways of choosing 5 cards from this collection. 
 Is there a way to ??nd a solution without checking all possibilities? 
Let us ??nd out.
Add a few even numbers together. What kind of number do you get? 
Does it matter how many numbers are added?
Any even number can be arranged in pairs without any leftovers. 
Some even numbers are shown here, arranged in pairs.
 
As we see in the ??gure, adding any number of even numbers
will result in a number which can still be arranged in pairs 
without any leftovers. In other words, the sum will always be an 
even number.
Now, add a few odd numbers together. What kind of number do you 
get? Does it matter how many odd numbers are added?
Odd numbers can not be arranged in pairs. An odd number is one 
more than a collection of pairs. Some odd numbers are shown below:
 
129
Chapter-6.indd   129 Chapter-6.indd   129 4/12/2025   11:59:05 AM 4/12/2025   11:59:05 AM
Reprint 2026-27
Ganita Prakash | Grade 7 
Can we also think of an odd number as one less than a collection 
of pairs?
This ??gure shows that the sum of two odd numbers must always 
be even! This along with the other ??gures here are more examples 
of a proof!
We can see that 
two odd numbers added 
together can always be 
arranged in pairs.
What about adding 3 odd numbers? Can the resulting sum be arranged 
in pairs? No. 
Explore what happens to the sum of (a) 4 odd numbers, (b) 5 odd 
numbers, and (c) 6 odd numbers.
Let us go back to the puzzle Kishor was trying to solve. There are 
5 empty boxes. That means he has an odd number of boxes. All the 
number cards contain odd numbers.
They should add to 30, which is an even number. Since, adding any 
5 odd numbers will never result in an even number, Kishor cannot 
arrange these cards in the boxes to add up to 30.
Two siblings, Martin and Maria, were born exactly one year apart. 
Today they are celebrating their birthday. Maria exclaims that the sum 
of their ages is 112. Is this possible? Why or why not?
As they were born one year apart, their ages will be (two) consecutive 
numbers. Can their ages be 51 and 52? 51 + 52 = 103.  Try some other 
consecutive numbers and see if their sum is 112.
The counting numbers 1, 2, 3, 4, 5, ... alternate between even and odd 
numbers. In any two consecutive numbers, one will always be even 
and the other will always be odd!
What would be the resulting sum of an even number and an odd 
number? We can see that their sum can’t be arranged in pairs and thus 
will be an odd number.
130
Chapter-6.indd   130 Chapter-6.indd   130 4/12/2025   11:59:05 AM 4/12/2025   11:59:05 AM
Reprint 2026-27
Page 5


6.1 Numbers Tell us Things
What do the numbers in the ??gure below tell us?
Remember the children from the Grade 6 textbook of mathematics? 
Now, they call out numbers using a di??erent rule.
What do you think these numbers mean?
The children rearrange themselves and each one says a number 
based on the new arrangement.
Could you ??gure out what these numbers convey? Observe and try to 
??nd out.
NUMBER PLAY
6
Chapter-6.indd   127 Chapter-6.indd   127 4/12/2025   11:59:04 AM 4/12/2025   11:59:04 AM
Reprint 2026-27
Ganita Prakash | Grade 7 
The rule is — each child calls out the number of children in front of 
them who are taller than them. Check if the number each child says 
matches this rule in both the arrangements.
Write down the number each child should say based on this rule for 
the arrangement shown below.
Figure it Out
1. Arrange the stick ??gure cutouts given at the end of the book or 
draw a height arrangement such that the sequence reads:
(a) 0, 1, 1, 2, 4, 1, 5
(b) 0, 0, 0, 0, 0, 0, 0
(c) 0, 1, 2, 3, 4, 5, 6
(d) 0, 1, 0, 1, 0, 1, 0
(e) 0, 1, 1, 1, 1, 1, 1
(f) 0, 0, 0, 3, 3, 3, 3
2. For each of the statements given below, think and identify if it 
is Always True, Only Sometimes True, or Never True. Share your 
reasoning.
(a) If a person says ‘0’, then they are the tallest in the group.
(b) If a person is the tallest, then their number is ‘0’.
(c) The ??rst person’s number is ‘0’.
(d) If a person is not ??rst or last in line (i.e., if they are standing 
somewhere in between), then they cannot say ‘0’.
(e) The person who calls out the largest number is the shortest.
(f) What is the largest number possible in a group of 8 people? 
128
Chapter-6.indd   128 Chapter-6.indd   128 4/12/2025   6:16:31 PM 4/12/2025   6:16:31 PM
Reprint 2026-27
Number Play
6.2 Picking Parity
Kishor has some number cards and is working on a puzzle: There 
are 5 boxes, and each box should contain exactly 1 number card. The 
numbers in the boxes should sum to 30. Can you help him ??nd a way 
to do it?
 
+ + + + = 30
Can you ??gure out which 5 cards add to 30? Is it possible? 
There are many ways of choosing 5 cards from this collection. 
 Is there a way to ??nd a solution without checking all possibilities? 
Let us ??nd out.
Add a few even numbers together. What kind of number do you get? 
Does it matter how many numbers are added?
Any even number can be arranged in pairs without any leftovers. 
Some even numbers are shown here, arranged in pairs.
 
As we see in the ??gure, adding any number of even numbers
will result in a number which can still be arranged in pairs 
without any leftovers. In other words, the sum will always be an 
even number.
Now, add a few odd numbers together. What kind of number do you 
get? Does it matter how many odd numbers are added?
Odd numbers can not be arranged in pairs. An odd number is one 
more than a collection of pairs. Some odd numbers are shown below:
 
129
Chapter-6.indd   129 Chapter-6.indd   129 4/12/2025   11:59:05 AM 4/12/2025   11:59:05 AM
Reprint 2026-27
Ganita Prakash | Grade 7 
Can we also think of an odd number as one less than a collection 
of pairs?
This ??gure shows that the sum of two odd numbers must always 
be even! This along with the other ??gures here are more examples 
of a proof!
We can see that 
two odd numbers added 
together can always be 
arranged in pairs.
What about adding 3 odd numbers? Can the resulting sum be arranged 
in pairs? No. 
Explore what happens to the sum of (a) 4 odd numbers, (b) 5 odd 
numbers, and (c) 6 odd numbers.
Let us go back to the puzzle Kishor was trying to solve. There are 
5 empty boxes. That means he has an odd number of boxes. All the 
number cards contain odd numbers.
They should add to 30, which is an even number. Since, adding any 
5 odd numbers will never result in an even number, Kishor cannot 
arrange these cards in the boxes to add up to 30.
Two siblings, Martin and Maria, were born exactly one year apart. 
Today they are celebrating their birthday. Maria exclaims that the sum 
of their ages is 112. Is this possible? Why or why not?
As they were born one year apart, their ages will be (two) consecutive 
numbers. Can their ages be 51 and 52? 51 + 52 = 103.  Try some other 
consecutive numbers and see if their sum is 112.
The counting numbers 1, 2, 3, 4, 5, ... alternate between even and odd 
numbers. In any two consecutive numbers, one will always be even 
and the other will always be odd!
What would be the resulting sum of an even number and an odd 
number? We can see that their sum can’t be arranged in pairs and thus 
will be an odd number.
130
Chapter-6.indd   130 Chapter-6.indd   130 4/12/2025   11:59:05 AM 4/12/2025   11:59:05 AM
Reprint 2026-27
Number Play
Since 112 is an even number, and Martin’s and Maria’s ages are 
consecutive numbers, they cannot add up to 112.
We use the word parity to denote the property of being even or odd. 
For instance, the parity of the sum of any two consecutive numbers is 
odd. Similarly, the parity of the sum of any two odd numbers is even.
Figure it Out
1. Using your understanding of the pictorial representation of odd 
and even numbers, ??nd out the parity of the following sums:
(a) Sum of 2 even numbers and 2 odd numbers (e.g., even + even 
+ odd + odd)
(b) Sum of 2 odd numbers and 3 even numbers
(c) Sum of 5 even numbers
(d) Sum of 8 odd numbers
2. Lakpa has an odd number of ?1 coins, an odd number of ?5 coins 
and an even number of ?10 coins in his piggy bank. He calculated 
the total and got ?205. Did he make a mistake? If he did, explain 
why. If he didn’t, how many coins of each type could he have?
3. We know that:
(a) even + even = even
(b) odd + odd = even
(c) even + odd = odd
Similarly, ??nd out the parity for the scenarios below:
(d) even – even =  ___________________
(e) odd – odd =  ___________________
(f) even – odd =  ___________________
(g) odd – even =  ___________________
Small Squares in Grids
In a 3 × 3 grid, there are 9 small squares, 
which is an odd number. Meanwhile, in 
a 3 × 4 grid, there are 12 small squares, 
which is an even number.
Given the dimensions of a grid, can you 
tell the parity of the number of small 
squares without calculating the product?
131
Chapter-6.indd   131 Chapter-6.indd   131 4/12/2025   11:59:05 AM 4/12/2025   11:59:05 AM
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