Much of Mathematics teaching is actually about encouraging children to become more aware about patterns they find and to use them in their thinking. Illustrate this in the case of the situation given below by answering the questions given in questions (i), (ii) and (iii), below.

“A mathematics teacher in class 5 showed the following pattern in the class.

46 X 44 = 2024

63 X 67 = 4221

71 X 79 = 4909

She gave some time for the students to identify the pattern. After some time she asked the students to find the answer of "84 x 86" in one second. One student answered 7224. Based on this situation, answer the following question.

i) What is the pattern used by the student?

ii) Explain why it works?

iii) Describe how it helps to encourage mathematical thinking.

i) The pattern used by the student is based on the difference between the two numbers being multiplied. Specifically, the student subtracts 1 from each number and then multiplies the results. Finally, they place the product of the subtraction at the beginning and the square of 1 at the end of the result. For example:

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