Additive & Multiplicative Thinking

Things can be compared in two ways.

Comparison by subtraction, or finding the difference is additive thinking.

Comparing by division or finding the ratio is multiplicative reasoning.

Before we get into the topic of thinking, give the following problems to your students. Let them discuss in groups and write down their answers & comments. The answers are given in the next page. Discuss the answers after they complete the chapters on additive and multiplicative thinking.

1. Ram and Govind are brothers. In 2019, their ages are 11 & 15 respectively. In future on their father’s 50thbirthday, Ram will be 16 years old. What will be Govind’s age at that time?

2. Ram pays Rs 40 to buy 2 dozen lemons. How much would he have to pay if he buys 4 dozen bananas?

3. Ram & Govind take a photograph in which they find that their respective heights (in the photo) are 3 & 4 cms respectively. They want a larger photo and ask the studio to enlarge the photo. In the enlarged photo Ram’s height is 4.5 cms. What would be Govind’s height in the enlarged photo?

4. Ram’s family is traveling to Tirupati. In the first hour, they cover 33 kms. If they travel at the same speed, how many kms will they cover in 3 hours?

5. Ram washes the family car, inside and outside every week and takes 2 hours to do it. In one of the weeks, Govind helps him and works with the same enthusiasm. How many hours would they then need to wash the car?

6. A shop is using a traditional (non-electronic) weighing scale. The shop keeper has correctly weighed 2 kgs of sugar and both the pans are at the same height. Then a child drops a ten-rupee coin in the pan which contains the sugar. What should be added to the other pan to make the pans come to the same height?

7. A ball is dropped from the terrace of a 18 story building. In the first second it drops by 32 ft. How much will it drop in the next second?

8. When Ram & Govind are 10 & 14 years of age their weights were 20 & 25 kgs. What will be their weights 5 years later?

9. A group of 20 monkeys were playing on 2 coconut trees. When Ram passes by the trees on his way to the shop, he would that 12 monkeys were playing in the taller tree and 8 in the shorter tree. When he returned back after 25 minutes, he found that 9 monkeys were playing on the taller tree. How many monkeys must be in the shorter tree?

10. Ram took a box of chocolates to share equally with his friends. Each one, including himself got 3 chocolates each. If there were more friends, what would happen to the share of chocolates each would have got?

We can classify the situations in the previous chapter as per the above framework.