The Token Model

Class 6 Maths · Chapter 10: The Other Side of Zero · NCERT Ganita Prakash section 10.2

Learn

Ira and Zoya play with two kinds of tokens. A green token is worth +1 and a coral token is worth −1. Three green and one coral show 3 − 1 = +2.

A green and a coral together are worth +1 + (−1) = 0. That's a zero pair. Adding or removing zero pairs never changes the value. So +2 can also be 5 green and 3 coral.

5 − 3 = +2

Adding: put the tokens together, then cancel zero pairs. (+4) + (−6): 4 green with 6 coral → 4 pairs cancel, 2 coral are left → −2.

(+4) + (−6) = −2

Subtracting: take tokens away. (+3) − (+5): you have only 3 green, but must take away 5. Add 2 zero pairs first (the value is still +3), now take away 5 green: 2 coral are left → −2.

(+3) − (+5) = −2

Look: (+3) − (+5) = −2, and (+3) + (−5) = −2 as well. Taking away a number is the same as adding its opposite. So (−2) − (−6) = (−2) + (+6) = +4.

a − b = a + (−b)

Explore: play with tokens.

1. Show −4.
2. Show +2 using exactly 8 tokens.
3. Here are 2 green tokens (+2). Take away 5 green tokens. (Add zero pairs first!) What is left?

Remember

• Green = +1, coral = −1; a green and a coral make a zero pair (0).
• Subtracting a number = adding its opposite: 3 − 5 = 3 + (−5).

Quick check

What is (−5) + (+3)?

1. −2
2. +2
3. −8
4. +8

Think about it

Anjali says that when you add two integers, the answer is always bigger than both of them. Find an example that shows she is wrong.

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.