Subtraction Metaphors 2

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Comparison situations

Here we compare one collection with another to find out the bigger and the smaller ones. In that process we can also know how much bigger or smaller is one collection as compared to the other. Let us see the following example.

Ram got 50 marks in Math and Shyam got 25 marks. Who got more marks and how much more?

Additive Comparison

In daily life we do two kinds of comparisons. This is called &ldquo;Additive Comparison&rdquo; which uses the idea of the difference.

The other kind of comparison is &ldquo;multiplicative comparison&rdquo;. In this we would say that Ram got twice as many marks as Shyam or Shyam got half the marks which Ram got. We will deal with this idea in chapters 10.5 & 10.6 on multiplication metaphors.

How much/ many more situations

Let us consider the following problem.

At the end of the year, class 35 Class 5A students will move to Class 6A. Class 6A has only 32 student chairs. How many more student chairs are required to seat all the students?

In this situation we have 2 (concrete or abstract) collections. The task is to find out how much should be added to the smaller collection to make it equal to the bigger collection.

Difficulty with this situation

The term &ldquo;more&rdquo; is usually associated with addition. In this subtraction situation, the term &ldquo;more&rdquo; is used but the operation required in subtraction. This is obviously a difficult concept for children to understand.

It would help if examples can be discussed from the life experiences of children themselves; the quantity of rice or milk that needs to be poured into a partly-filled container in order to fill it, finding the distance yet to be covered in the midst of a journey, the number of days still left from the school vacations etc.

Perils of mechanical rules

This also shows the perils of teaching a &ldquo;rule&rdquo; that if a problem has the word &ldquo;more&rdquo; then it is an addition problem. Understanding this situation is very important.

Use of the term &ldquo;Take Away&rdquo;

Like in the case of Put Together, we have avoided the term &ldquo;Take Away&rdquo; as it is both a process and concept also. Use of the term Separate makes it easier to internalise the other metaphors of subtraction.

Annexure 056A gives a list of vocabulary, commonly used in addition &amp; subtraction problems.

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