don steward
mathematics teaching 10 ~ 16

Friday, 9 May 2014

warp and weft quadratic expansions

this task uses an idea from John Mason with Alan Graham and Sue Johnston-Wilder in their book 'developing thinking in algebra' [published by the Open University in 2005]

identifying patterns can help to establish a way to multiply out bracketed expressions

students can be asked to copy the information in one of the four arrays on each page 

they are then asked develop ideas about the patterns in the expressions, probably by looking at what changes and what stays the same as you go across or down the grid

they then complete the array i.e. replacing the stars with an appropriate expression
they can also extend the rows, to the left and right, and the columns, up and down

they could devise their own array

and they can also be asked to simplify the quadratic expressions (the middle terms)

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