Reversing the direction of the input and output in a number machine, the operator changes ( + into - and x into ÷ and vice versa). A number of exercises are provided. The lesson is suitable for KS2 pupils. The commutative property comes handy when solving a problem that seems to defy common sense; that is, when dividing a number by another the usual expectation is the answer to being smaller in magnitude than the number to be divided. Similarly, when multiplying two numbers one expects the answer to be larger in magnitude than both numbers that are to be multiplied. This puzzling situation arises because of the fact that dividing or multiplying by a number between -1 and 1 produces that effect.
A challenging situation is when one asks, what is 3 divided by a number and the answer is 4.
Using number machines idea and the commutative property one can get the answer. This is explained in one of the worksheets, and the interesting thing is, it is not beyond the level of KS2 pupils to understand it.
It is suggested that a calculator should be used first to explore the answer - in the interest of enhancing problem solving culture.
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