Addition Metaphors 2

“More Than” situations

Here, one collection is described as having some things “More Than” the given collection. The following problem is an example.

Ram has 65 tokens. Lakshman has 5 tokens more than him. How many tokens does Lakshman have?

In Join situation, both collections were concrete and could be seen separately. In this situation, however, one of the collections is concrete but the “more than” amount is an abstract idea.

So, this idea cannot be acted out through direct role plays. It has to be introduced in several steps. First step would be to imagine a situation where Lakshman has “as many” tokens as Ram and find out how many tokens Lakshman would have. After this a simpler situation can be posed where Lakshman has 1 token more than Ram. By this process, slowly students realise that this is also an addition situation.

We had seen the situation with temperature and age as being counter examples for the Join situation. Both these make sense in “more than” situations as can be seen below.

Glass A has milk at 30 deg. The temperature of the milk in Glass B is 10 deg “more than” that of Glass A. What is the temperature of the milk in Glass B?

Ram is 15 years old. His brother is “Older to him” by 3 years. What is his brother’s age?

Like in Join situations, appropriate examples involving weight, volume, area, time, money etc can be given.

“More Than” situations require more complex thinking compared to Join situations. Hence, they are best taught from Class 2, after children have fully understood the meaning of Join.

Language Complexity

An additional difficulty is that in real life the idea of “more than” is conveyed by many other phrases, depending on the context, like “older /younger“, “hotter/ colder”, “bigger/ smaller”, “longer/ shorter”, “taller/ shorter”, “heavier/ lighter” etc. Teachers should train children in using vocabulary appropriate to the context.

In temperature situations “more colder” translates to “lesser temperature”!

The words used “word problems” in various contexts have been summarised in Chapter 9.7.

Tricky phrase- “Less Than”

We also have situations where the term “less than” actually translates into a “more than” idea requiring addition. Take the following example.

Ram got 65 tokens. Ram has 5 tokens less than Lakshman. How many tokens does Lakshman have?

Though the words of this problem are different the meaning is the same. Hence mechanical rules like “subtract if the word less occurs in the problem” can easily be misleading.

Use of the term “Put Together”

A term very commonly used in addition problems is “Put Together”. We have deliberately used the term “Join” for the following reason.

“Put Together” is the “process” by which any two collections are arithmetically added. In adding 2-digit numbers, we put the bundles together and the sticks together and find the resulting collection. However, this term has become synonymous with the entire concept of addition. This confusion of the process with the concept becomes a mental block to realising that addition also has a “more than” concept.

Hence, we will use” Join” to indicate the metaphor and “put together” to indicate the process.