median
don steward
mathematics teaching 10 ~ 16

Monday, 3 March 2014

windmills

this task involves producing diagrams that look a bit like a child's windmill

it is from Pat's blog (pballew)
and has some neat extensions (see on the blog)






you can start this application of Pythagoras task easily by asking students to draw a square inside another square
then join the corners in a "windmill" kind of a way

or ask them what is happening:
















students could find as many options as they can on 7 by 7 (or is it 6 by 6) dotty grids
and some options can be presented to show that the 'inside' square could have a length (or two) on the perimeter of the larger square:




















students are asked to find the squares of the four lengths
they should notice a rather neat result



















I think all of the options for this grid size are as follows:


 


















why these results are all even is an interesting enquiry as are the situations where you get the largest/least

proving a general result involves some slogging with brackets
and it might be helpful to know that


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