Multiplication Metaphors 2

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Scaling

Here the ratio of 2 collections is given. When one of the collections is known, then the value of the other collection can be worked out. Some examples are.

Ram got 8 presents for his birthday. Shyam got twice what Ram received. How many presents did Shyam receive?

Guavavas cost Rs 40 per dozen. Bananas cost half as much as Guavas. What was the price of Bananas?

The price of Guavas to Bananas was in the ratio 2:1. If Guavas cost Rs 40/ dozen, what would be the cost of bananas?

&ldquo;Scaling&rdquo; in multiplication is the inverse of &ldquo;Ratio&rdquo; in Division.

All maps show a scaling factor which shows the relation of the distance on the map to the actual distance.

Product

The idea of Product is best explained through examples.

The rate of bananas is Rs 40 /dozen. We want to purchase 3 dozen bananas. Hence, we would have to pay 40 X 3 = Rs 120. The rupee amount we have to pay is the product of the quantity and the rate of the rupee amount per unit quantity.

If we are travelling at the rate of 30 kms/hour, then in 4 hours we will cover 30 X4 kms.

Rate is a general term. Depending on the context it is given different names. In the first problem it is called &ldquo;Price&rdquo; and in the second it is called &ldquo;Speed&rdquo;.

Traditionally in Indian schools, Product is taught as part of &ldquo;Unitary Method&rdquo;.

Combinations

It is the number of different ways or combinations in which certain things can be arranged. It leads to ideas of probability, which is studied in the higher classes. &lsquo;Combinations&rsquo; also occurs in different forms in different contexts. The following problem gives one such simple form.

For his birthday, Ram gets 3 T Shirts of different designs and 4 trousers in different colours. In how many different combinations can he wear them? Working out all the combinations, we would find that there are 3 X 4 combinations.

It is suggested that the Combinations metaphor may be taught only in Middle School. It leads to an idea of the Cartesian Product used in higher mathematics.

The idea of combinations captures the essence of multiplication in a way &ldquo;put together&rdquo; does for addition.

Repeated Addition Procedure

We see that the idea of multiplication arises out of many life situations, other than &ldquo;repeated addition&rdquo;. Repeated addition is a procedure for getting the result of multiplying any two whole numbers. It is not a fundamental concept observable in the environment around us.

Unfortunately, &lsquo;repeated addition&rsquo; has become synonymous with multiplication, obscuring the other important metaphors.

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