Problems With Multiple Answers

There is a major difference between what are called “stand-alone computations” and word problems.

A stand-alone computation is purely mathematical. The only logic used here is mathematical logic. Computations have only one answer.

A word problem, however, is an event in real life described using numbers & computations.

Hence, a word problem, using the same computation, may have multiple answers depending on the context and what has been asked for. The logic to be used here is that related to real life situations.

This is particularly applicable to division word problems, which have in 2 results – the quotient & the remainder.

Let us take a computation like 14÷4.

The same computation may appear in several word problems, with different answers.

Problem Type 1

14 toys are being equally shared among 4 children. How many toys would each child receive?

The sharing has to be fair and toys cannot be partitioned.

The answer (from 14÷4 = 3) is that each child gets 3 toys.

We do not worry about the remaining toys.

Problem Type 2

Lakshmi goes to a giftshop with Rs 14, to buy some gifts. Each gift costs Rs 4. If she buys as many gifts as she can, how much money is she likely to be left with?

She can buy at the most 3 gifts, since 14÷4 = 3.

She will have Rs 2 still left with her. ( 14 - 3 X 4 = 2)

Problem Type 3

4 children are sharing 14 toffees among themselves. How many toffees would each friend receive?

Children do not mind biting a toffee & sharing a part of it.

Each child gets 3 1/2 toffees. (from 14 ÷4 = 3 1/2 )

Problem Type 4

14 members of a family are going on a trip by car. Each car can carry a total of 4 persons. How many cars would be needed for the trip?

14÷4 = 3 with a remainder of 2. Hence they would need 3 cars.

Since all members of the family need to be accommodated, they would need an additional car to accommodate the 2 remaining members.

They would need 4 cars. (3 +1 = 4)

Students in Grade 5, should be exposed to all these situations.