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Numbers Tell us Things

Class 7 Maths · Chapter 6: Number Play · NCERT Ganita Prakash section 6.1

Learn

Seven friends stand in a line, one behind another. Each calls out a number using a rule: how many people in front of me are taller than me? The heights (in cm) are 140, 152, 135, 160, 128, 149, 131. They call out 0, 0, 2, 0, 4, 2, 5.

0, 0, 2, 0, 4, 2, 5

Check one: the 5th friend (128 cm) has 140, 152, 135 and 160 in front, all taller, so she says 4. The numbers tell us about the order of heights without telling us the heights. The first person always says 0, because nobody is in front.

Always, sometimes or never? The tallest person always says 0 (nobody in front is taller). But a person who says 0 is only sometimes the tallest: they might just be taller than everyone in front. In a line of 8, the largest possible number is 7: the last person, if shortest.

Make a line: to get 0, 1, 2, 3, 4, 5, 6, each person must be shorter than everyone in front, so stand from tallest to shortest. To get 0, 0, 0, 0 … stand from shortest to tallest. Try making 0, 1, 0, 1, 0, 1, 0 with friends!

Explore: always, sometimes or never?

  1. Sort the statements about the line game.

Remember

  • The rule turns heights into numbers that show the order without the actual heights.
  • Test a statement by searching for a line where it fails.

Quick check

Heights in a line are 150, 138, 155, 142 cm. What does the 4th person say?

  1. 2
  2. 1
  3. 3
  4. 0
Answer

2. In front of 142: 150 and 155 are taller, 138 is not.

Think about it

Can a line of 6 people call out 0, 1, 2, 0, 5, 5?

One answer

No. The 5th person has only 4 people in front, so they can say at most 4.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.