NCERT Textbook: Number Play | Mathematics (Maths) Class 6 PDF Download

 Page 1


NUMBER PLAY
3
Numbers are used in different contexts and in many different ways 
to organise our lives. We have used numbers to count, and have 
applied the basic operations of addition, subtraction, multiplication 
and division on them, to solve problems related to our daily lives. 
In this chapter, we will continue this journey, by playing with 
numbers, seeing numbers around us, noticing patterns, and learning 
to use numbers and operations in new ways.
 Think about various situations where we use numbers. List 
five different situations in which numbers are used. See what 
your classmates have listed, share, and discuss.
3.1 Numbers can Tell us Things
What are these numbers telling us?
Some children in a park are standing in a line. Each one says a number.
 What do you think these numbers mean?
 The children now rearrange themselves, and again each one 
says a number based on the arrangement.
Math 
Talk
Chapter 3_Number Play.indd   55 09-08-2024   16:33:11
Page 2


NUMBER PLAY
3
Numbers are used in different contexts and in many different ways 
to organise our lives. We have used numbers to count, and have 
applied the basic operations of addition, subtraction, multiplication 
and division on them, to solve problems related to our daily lives. 
In this chapter, we will continue this journey, by playing with 
numbers, seeing numbers around us, noticing patterns, and learning 
to use numbers and operations in new ways.
 Think about various situations where we use numbers. List 
five different situations in which numbers are used. See what 
your classmates have listed, share, and discuss.
3.1 Numbers can Tell us Things
What are these numbers telling us?
Some children in a park are standing in a line. Each one says a number.
 What do you think these numbers mean?
 The children now rearrange themselves, and again each one 
says a number based on the arrangement.
Math 
Talk
Chapter 3_Number Play.indd   55 09-08-2024   16:33:11
Ganita Prakash | Grade 6
56
Did you figure out what these numbers represent?
Hint:  Could their heights be playing a role?
A child says ‘1’ if there is only one taller child standing next to them. 
A child says ‘2’ if both the children standing next to them are taller. A 
child says ‘0’, if neither of the children standing next to them are taller. 
That is each person says the number of taller neighbours they have.
 Try answering the questions below and share your reasoning:
1.  Can the children rearrange themselves so that the children 
standing at the ends say ‘2’?
2.  Can we arrange the children in a line so that all would say 
only 0s?
3.  Can two children standing next to each other say the same 
number? 
4.  There are 5 children in a group, all of different heights. Can 
they stand such that four of them say ‘1’ and the last one says 
‘0’? Why or why not?
5.  For this group of 5 children, is the sequence 1, 1, 1, 1, 1 possible? 
6.  Is the sequence 0, 1, 2, 1, 0 possible? Why or why not?
7.  How would you rearrange the five children so that the 
maximum number of children say ‘2’?
Math 
Talk
Chapter 3_Number Play.indd   56 09-08-2024   16:33:13
Page 3


NUMBER PLAY
3
Numbers are used in different contexts and in many different ways 
to organise our lives. We have used numbers to count, and have 
applied the basic operations of addition, subtraction, multiplication 
and division on them, to solve problems related to our daily lives. 
In this chapter, we will continue this journey, by playing with 
numbers, seeing numbers around us, noticing patterns, and learning 
to use numbers and operations in new ways.
 Think about various situations where we use numbers. List 
five different situations in which numbers are used. See what 
your classmates have listed, share, and discuss.
3.1 Numbers can Tell us Things
What are these numbers telling us?
Some children in a park are standing in a line. Each one says a number.
 What do you think these numbers mean?
 The children now rearrange themselves, and again each one 
says a number based on the arrangement.
Math 
Talk
Chapter 3_Number Play.indd   55 09-08-2024   16:33:11
Ganita Prakash | Grade 6
56
Did you figure out what these numbers represent?
Hint:  Could their heights be playing a role?
A child says ‘1’ if there is only one taller child standing next to them. 
A child says ‘2’ if both the children standing next to them are taller. A 
child says ‘0’, if neither of the children standing next to them are taller. 
That is each person says the number of taller neighbours they have.
 Try answering the questions below and share your reasoning:
1.  Can the children rearrange themselves so that the children 
standing at the ends say ‘2’?
2.  Can we arrange the children in a line so that all would say 
only 0s?
3.  Can two children standing next to each other say the same 
number? 
4.  There are 5 children in a group, all of different heights. Can 
they stand such that four of them say ‘1’ and the last one says 
‘0’? Why or why not?
5.  For this group of 5 children, is the sequence 1, 1, 1, 1, 1 possible? 
6.  Is the sequence 0, 1, 2, 1, 0 possible? Why or why not?
7.  How would you rearrange the five children so that the 
maximum number of children say ‘2’?
Math 
Talk
Chapter 3_Number Play.indd   56 09-08-2024   16:33:13
Number Play
57
3.2 Supercells
Observe the numbers written in the table below. Why are some 
numbers coloured? Discuss.
200
577
626 345 790 694 109
43 79 75 63 10 29 28 34
198
A cell is coloured if the number in it is larger than its adjacent 
cells.  626 is coloured as it is larger than 577 and 345 whereas 200 is 
not coloured as it is smaller than 577. The number 198 is coloured as 
it has only one adjacent cell with 109 in it, and 198 is larger than 109.
 Figure it Out
1. Colour or mark the supercells in the table below.
6828
670 9435 3780 3708 7308 8000 5583 52
2. Fill the table below with only 4-digit numbers such that the 
supercells are exactly the coloured cells.
5346 1258 9635
3. Fill the table below such that we get as many supercells as possible. 
Use numbers between 100 and 1000 without repetitions.
4. Out of the 9 numbers, how many supercells are there in the table 
above? ___________
5. Find out how many supercells are possible for different 
numbers of cells. 
Do you notice any pattern? What is the method to fill a given 
table to get the maximum number of supercells? Explore and 
share your strategy.
Math 
Talk
Chapter 3_Number Play.indd   57 09-08-2024   16:33:13
Page 4


NUMBER PLAY
3
Numbers are used in different contexts and in many different ways 
to organise our lives. We have used numbers to count, and have 
applied the basic operations of addition, subtraction, multiplication 
and division on them, to solve problems related to our daily lives. 
In this chapter, we will continue this journey, by playing with 
numbers, seeing numbers around us, noticing patterns, and learning 
to use numbers and operations in new ways.
 Think about various situations where we use numbers. List 
five different situations in which numbers are used. See what 
your classmates have listed, share, and discuss.
3.1 Numbers can Tell us Things
What are these numbers telling us?
Some children in a park are standing in a line. Each one says a number.
 What do you think these numbers mean?
 The children now rearrange themselves, and again each one 
says a number based on the arrangement.
Math 
Talk
Chapter 3_Number Play.indd   55 09-08-2024   16:33:11
Ganita Prakash | Grade 6
56
Did you figure out what these numbers represent?
Hint:  Could their heights be playing a role?
A child says ‘1’ if there is only one taller child standing next to them. 
A child says ‘2’ if both the children standing next to them are taller. A 
child says ‘0’, if neither of the children standing next to them are taller. 
That is each person says the number of taller neighbours they have.
 Try answering the questions below and share your reasoning:
1.  Can the children rearrange themselves so that the children 
standing at the ends say ‘2’?
2.  Can we arrange the children in a line so that all would say 
only 0s?
3.  Can two children standing next to each other say the same 
number? 
4.  There are 5 children in a group, all of different heights. Can 
they stand such that four of them say ‘1’ and the last one says 
‘0’? Why or why not?
5.  For this group of 5 children, is the sequence 1, 1, 1, 1, 1 possible? 
6.  Is the sequence 0, 1, 2, 1, 0 possible? Why or why not?
7.  How would you rearrange the five children so that the 
maximum number of children say ‘2’?
Math 
Talk
Chapter 3_Number Play.indd   56 09-08-2024   16:33:13
Number Play
57
3.2 Supercells
Observe the numbers written in the table below. Why are some 
numbers coloured? Discuss.
200
577
626 345 790 694 109
43 79 75 63 10 29 28 34
198
A cell is coloured if the number in it is larger than its adjacent 
cells.  626 is coloured as it is larger than 577 and 345 whereas 200 is 
not coloured as it is smaller than 577. The number 198 is coloured as 
it has only one adjacent cell with 109 in it, and 198 is larger than 109.
 Figure it Out
1. Colour or mark the supercells in the table below.
6828
670 9435 3780 3708 7308 8000 5583 52
2. Fill the table below with only 4-digit numbers such that the 
supercells are exactly the coloured cells.
5346 1258 9635
3. Fill the table below such that we get as many supercells as possible. 
Use numbers between 100 and 1000 without repetitions.
4. Out of the 9 numbers, how many supercells are there in the table 
above? ___________
5. Find out how many supercells are possible for different 
numbers of cells. 
Do you notice any pattern? What is the method to fill a given 
table to get the maximum number of supercells? Explore and 
share your strategy.
Math 
Talk
Chapter 3_Number Play.indd   57 09-08-2024   16:33:13
Ganita Prakash | Grade 6
58
6. Can you fill a supercell table without repeating numbers such 
that there are no supercells? Why or why not?
7. Will the cell having the largest number in a table always be a 
supercell? Can the cell having the smallest number in a table 
be a supercell? Why or why not?
8. Fill a table such that the cell having the second largest number 
is not a supercell.
9. Fill a table such that the cell having the second largest 
number is not a supercell but the second smallest number is 
a supercell. Is it possible?
10. Make other variations of this puzzle and challenge your 
classmates.
Let’s do the supercells activity with more rows.
Here the neighbouring cells are those that are immediately to the 
left, right, top and bottom.
 The rule remains the same : a 
cell becomes a supercell if the 
number in it is greater than all 
the numbers in its neighbouring 
cells. In Table 1, 8632 is greater 
than all its neighbours 4580, 
8280, 4795 and 1944.
 Complete Table 2 with 5-digit 
numbers whose digits are ‘1’, 
‘0’, ‘6’, ‘3’, and ‘9’ in some order. 
Only a coloured cell should 
have a number greater than all 
its neighbours.
The biggest number in the table 
is ____________ .
Try
This
2430 7500 7350 9870
3115 4795 9124 9230
4580 8632 8280 3446
 5785 1944 5805 6034
Table 1
Table 2
96,301 36,109
13,609 60,319 19,306
60,193
10,963
Chapter 3_Number Play.indd   58 09-08-2024   16:33:13
Page 5


NUMBER PLAY
3
Numbers are used in different contexts and in many different ways 
to organise our lives. We have used numbers to count, and have 
applied the basic operations of addition, subtraction, multiplication 
and division on them, to solve problems related to our daily lives. 
In this chapter, we will continue this journey, by playing with 
numbers, seeing numbers around us, noticing patterns, and learning 
to use numbers and operations in new ways.
 Think about various situations where we use numbers. List 
five different situations in which numbers are used. See what 
your classmates have listed, share, and discuss.
3.1 Numbers can Tell us Things
What are these numbers telling us?
Some children in a park are standing in a line. Each one says a number.
 What do you think these numbers mean?
 The children now rearrange themselves, and again each one 
says a number based on the arrangement.
Math 
Talk
Chapter 3_Number Play.indd   55 09-08-2024   16:33:11
Ganita Prakash | Grade 6
56
Did you figure out what these numbers represent?
Hint:  Could their heights be playing a role?
A child says ‘1’ if there is only one taller child standing next to them. 
A child says ‘2’ if both the children standing next to them are taller. A 
child says ‘0’, if neither of the children standing next to them are taller. 
That is each person says the number of taller neighbours they have.
 Try answering the questions below and share your reasoning:
1.  Can the children rearrange themselves so that the children 
standing at the ends say ‘2’?
2.  Can we arrange the children in a line so that all would say 
only 0s?
3.  Can two children standing next to each other say the same 
number? 
4.  There are 5 children in a group, all of different heights. Can 
they stand such that four of them say ‘1’ and the last one says 
‘0’? Why or why not?
5.  For this group of 5 children, is the sequence 1, 1, 1, 1, 1 possible? 
6.  Is the sequence 0, 1, 2, 1, 0 possible? Why or why not?
7.  How would you rearrange the five children so that the 
maximum number of children say ‘2’?
Math 
Talk
Chapter 3_Number Play.indd   56 09-08-2024   16:33:13
Number Play
57
3.2 Supercells
Observe the numbers written in the table below. Why are some 
numbers coloured? Discuss.
200
577
626 345 790 694 109
43 79 75 63 10 29 28 34
198
A cell is coloured if the number in it is larger than its adjacent 
cells.  626 is coloured as it is larger than 577 and 345 whereas 200 is 
not coloured as it is smaller than 577. The number 198 is coloured as 
it has only one adjacent cell with 109 in it, and 198 is larger than 109.
 Figure it Out
1. Colour or mark the supercells in the table below.
6828
670 9435 3780 3708 7308 8000 5583 52
2. Fill the table below with only 4-digit numbers such that the 
supercells are exactly the coloured cells.
5346 1258 9635
3. Fill the table below such that we get as many supercells as possible. 
Use numbers between 100 and 1000 without repetitions.
4. Out of the 9 numbers, how many supercells are there in the table 
above? ___________
5. Find out how many supercells are possible for different 
numbers of cells. 
Do you notice any pattern? What is the method to fill a given 
table to get the maximum number of supercells? Explore and 
share your strategy.
Math 
Talk
Chapter 3_Number Play.indd   57 09-08-2024   16:33:13
Ganita Prakash | Grade 6
58
6. Can you fill a supercell table without repeating numbers such 
that there are no supercells? Why or why not?
7. Will the cell having the largest number in a table always be a 
supercell? Can the cell having the smallest number in a table 
be a supercell? Why or why not?
8. Fill a table such that the cell having the second largest number 
is not a supercell.
9. Fill a table such that the cell having the second largest 
number is not a supercell but the second smallest number is 
a supercell. Is it possible?
10. Make other variations of this puzzle and challenge your 
classmates.
Let’s do the supercells activity with more rows.
Here the neighbouring cells are those that are immediately to the 
left, right, top and bottom.
 The rule remains the same : a 
cell becomes a supercell if the 
number in it is greater than all 
the numbers in its neighbouring 
cells. In Table 1, 8632 is greater 
than all its neighbours 4580, 
8280, 4795 and 1944.
 Complete Table 2 with 5-digit 
numbers whose digits are ‘1’, 
‘0’, ‘6’, ‘3’, and ‘9’ in some order. 
Only a coloured cell should 
have a number greater than all 
its neighbours.
The biggest number in the table 
is ____________ .
Try
This
2430 7500 7350 9870
3115 4795 9124 9230
4580 8632 8280 3446
 5785 1944 5805 6034
Table 1
Table 2
96,301 36,109
13,609 60,319 19,306
60,193
10,963
Chapter 3_Number Play.indd   58 09-08-2024   16:33:13
Number Play
59
The smallest even number in the table is ____________.
The smallest number greater than 50,000 in the table is ____________.
Once you have filled the table above, put commas appropriately 
after the thousands digit.
3.3 Patterns of Numbers on the Number Line
 We are quite familiar with number lines now. Let’s see if we can 
place some numbers in their appropriate positions on the number 
line. Here are the numbers: 2180, 2754, 1500, 3600, 9950, 9590, 1050, 
3050, 5030, 5300 and 8400.
1000 2000
2180
2754
3000 4000 5000 6000 7000 8000 9000 10,000
  Figure it Out
  Identify the numbers marked on the number lines below, and label 
the remaining positions.
b.
9996 9997
a.
2010 2020
15,077 15,078 15,083
c.
86,705 87,705
d.
  Put a circle around the smallest number and a box around the 
largest number in each of the sequences above.
Chapter 3_Number Play.indd   59 09-08-2024   16:33:13