don steward
mathematics teaching 10 ~ 16

Friday, 11 November 2016

two numbers conjecture

this task is one from John Mason (Oxford and O.U.)
it is a great way to introduce the difference of two squares since the result just drops out
the powerpoint is here

to understand what is going on
and to test out the conjecture
students need to try some examples
firstly, they need to consider how to obtain an even number difference

then several student examples can be collected on the board
and general rules considered

be aware that some numbers have more than one representation as the difference of two squares

an initial purpose for the task might be for students to write down or recall square numbers (or they could be given a list)

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