NCERT Book Class 6 Maths Number Play PDF Download

Chapter 3: Number Play

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.

Math Talk

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.

[Figure: Children standing in a line, each saying a number, See in your textbook]

Math Talk

What do you think these numbers mean?

The children now rearrange themselves, and again each one says a number based on the arrangement.

[Figure: Children rearranged in a different line, each saying a number, See in your textbook]

Teacher's Note

When you see numbers above the children, pause and think about what they could represent. Here, the numbers describe a property of each child's neighbours - specifically their heights. Do not assume the numbers count the children from left to right; instead, look for a pattern based on what you see in the picture and how the arrangement affects the numbers.

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.

Math Talk

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'?

3.2 Supercells

Observe the numbers written in the table below. Why are some numbers coloured? Discuss.

A cell is coloured if the number in it is larger than its adjacent cells. The number 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.

Teacher's Note

A supercell must be larger than all its adjacent neighbours. Cells at the edges have fewer neighbours than cells in the middle - a number at the edge only needs to be larger than the cells next to it within the table, not in imaginary cells outside. Check each number carefully by listing its actual neighbours before deciding if it is a supercell.

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.

   Math Talk

   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.

Key Points

• When numbers describe something about their neighbours, you need to look at the relationships between values, not just count positions or list them in order.
• A supercell is a number that is larger than every number adjacent to it in the table, whether the cell is at an edge or in the middle.
• The maximum number of supercells you can create depends on how many numbers you have and how you arrange them - there is a pattern to find.

This is a preview of the first 3 pages. To get the complete chapter, click below.