Problems with Multiple Answers

We have been fed on the myth that all problems in math have only one solution. And this is supposed to be “strength” of math is judging a person’s intelligence. It also makes the correction work of the teacher easier.

But math has a lot of problems which have multiple answers. These problems lead to multiple ways of thinking about them. They develop “critical thinking skills” of students. And we have seen that this is one of the important objectives of math education.

Let us see some examples.

Sorting & Classification

These are activities which can be started in pre-school.

Imagine a collection of 3 shapes; circles, squares & triangles. Each of these is in any one of 3 colours; red, green & yellow. Further these are made of 3 different materials – plastic, rubber & paper board.

Ask a child to classify them in to sets as per his idea. Except that the child has to explain to the teacher & his friends what the basis of classification was.

We can see that these materials can be classified as per 3 criteria – shape, colour and material. In any of these classification there would be a mix of shapes, colours & textures.

It is possible that children may come out with other criteria as per their “view point”. Here there are no correct answers, only appropriate explanations.

It enables a child to understand that the same piece can belong to different sets, depending on the criteria chosen.

Number Work

Consider the following problems.

1. Using only 3 digits; 3, 5 & 7 and form as many numbers as you can. Arrange all of them in increasing order.

2. Write as many 3-digit numbers as possible, such that the sum of the digits will always be 9.

3. Write as many addition problems where the total is 15.

4. Write 1, 2, 3 & 4 in that order, insert any operating symbol and gat as many results as possible. Example 1 + 2 + 3 + 4 = 10

Addition & Subtraction

1. □ □ □ – 1 2 7 = □ □ □

2. □ □ □ + 1 2 7 = □ □ □ where □ stands for any number from 0 to 9.

These 2 activities help a student to think critically about numbers and their relations. This strengthens number sense.

Division

1. Write a word problem involving 29 ÷8, where the answers can be

a. 3

b. 4

c. 5

d. 3.625

This activity brings out the difference between a numerical computation and a word problem which mirrors a life situation.

Patterns

How many different patterns, associated with arithmetic operations, can you see in the diagram given below.

(Insert a 6 X 6 array with symbols)

One example 6 + 6 + 6 + 6 + 6 + 6 = 36

This activity encourages students to think creatively about ways of visualising arithmetic operations.