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Proof by markscheme

While marking my Y11 mocks this week I came across this nice algebraic proof question:

The first student had not attempted it. While looking at it I ran through it quickly in my head. Here is the method i used jotted down:

I thought, “what a nice simple proof”. Then I looked at the markscheme:

There seemed no provision made in the markscheme for what I had done. (Edit: It is there, my brain obviously just skipped past it) How did you approach this question? Please let me know via the comments or social media.

Anyway, some of my students gave some great answers. None of them took my approach, but some used the same as the markscheme:

And one daredevil even attempted a geometric proof…….

  1. March 18, 2019 at 3:02 am

    I admire the courage in trying for the geometric proof!

    I could kind of imagine doing at least a count-the-dots sort of proof, like by the difference between

    * * *
    * * *
    * * *


    * * * * *
    * * * * *
    * * * * *
    * * * * *
    * * * * *

    being (from rows) twice the smaller odd number, plus (from columns) twice the smaller odd number, plus the four dots in the square at the end. So that’s something that’s four more than a whole multiple of eight, plus four more. So, that’s a multiple of eight plus eight.

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