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 started in pre-school. Imagine a collection of shapes; circles, squares & triangles. Each of these is in any one of r 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 what was the basis of classification. We can see that these materials can be classified as per 3 criteria – shape, colour and material. 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. 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. X X X – 1 2 7 = X X X 2. X X X + 1 2 7 = X X X Where X stands for anu numbers from 0 to 9 Division 1. Write a word problem involving 29 ÷8, where the answers can be a. 3 b. 4 c. 5 d. 3.625 Patterns How many different patterns, associated with arithmetic operations, can you see in the diagram given below. One example 6 + 6 + 6 + 6 + 6 + 6 = 36