NCERT Class 7 Ganita Prakash 1 Chapter 06 Number Play PDF Download

Chapter 6: Number Play

6.1 Numbers Tell us Things

What do the numbers in the figure below tell us?

Remember the children from the Grade 6 textbook of mathematics? Now, they call out numbers using a different rule.

What do you think these numbers mean?

The children rearrange themselves and each one says a number based on the new arrangement.

[Figure: Children in two different arrangements, each calling out numbers, See in your textbook]

Could you figure out what these numbers convey? Observe and try to find out.

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: Stick figures of different heights in a line, See in your textbook]

Figure it Out

1. Arrange the stick figure cutouts given at the end of the book or draw a height arrangement such that the sequence reads:
   1. 0, 1, 1, 2, 4, 1, 5
   2. 0, 0, 0, 0, 0, 0, 0
   3. 0, 1, 2, 3, 4, 5, 6
   4. 0, 1, 0, 1, 0, 1, 0
   5. 0, 1, 1, 1, 1, 1, 1
   6. 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.
   1. If a person says '0', then they are the tallest in the group.
   2. If a person is the tallest, then their number is '0'.
   3. The first person's number is '0'.
   4. If a person is not first or last in line (i.e., if they are standing somewhere in between), then they cannot say '0'.
   5. The person who calls out the largest number is the shortest.
   6. What is the largest number possible in a group of 8 people?

Teacher's Note

The key to this puzzle is thinking about position, not just height. A child's number depends only on who is in front of them - it does not matter if there are taller children behind. When you work through the arrangements, trace from left to right and count carefully: for each child, how many taller children stand ahead in the line?

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 find a way to do it?

[Figure: Five empty boxes with a plus sign between each, equals 30, See in your textbook]

[Figure: Number cards showing 13, 9, 7, 11, 5, and 3 in different arrangements, See in your textbook]

Can you figure 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 find a solution without checking all possibilities? Let us find 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.

[Figure: Dots arranged in pairs to show even numbers, See in your textbook]

As we see in the figure, 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.

Teacher's Note

When you add even numbers, you always get an even answer. This is important for solving puzzles. If Kishor needs a sum of 30 (which is even) and he wants to add exactly 5 numbers, think about this: if he picks all even numbers, the sum stays even (good). But what if he picks some odd numbers? One odd number makes the sum odd, two odd numbers make it even again. Test this with the cards before you check every combination.

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:

[Figure: Dots arranged to show odd numbers with one leftover, See in your textbook]

Key Points

• When you add even numbers together, no matter how many, the result is always even.
• The sum of an odd number of odd numbers is always odd, and the sum of an even number of odd numbers is always even.
• You can use parity (whether a number is even or odd) to solve problems without checking every possibility.
• In the height puzzle, each child counts only the taller children who are standing in front of them, based on their position in the line.

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