Counting Factors with Grade 7/8s

One of the great parts of my job as a split classroom teacher and division consultant is that I get to spend time in classrooms from grades six to twelve. This means I often need to be in one head space to teach my own Grade 12s and then switch gears to act with younger mathematicians. It also means that the classroom experiences are sporadic and involve teachers working in several different places in several different curricula. On this particular occasion, I was working with a 7/8 split class that had just finished a unit on perfect squares and divisibility …

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Induction Squared

I came across an interesting problem recently that I gave to my students in need of enrichment.  Given a square and the ability to divide that square into smaller squares, can you divide a square into ‘n’ smaller squares. The squares do not have to be the same size. For which values of ‘n’ is this possible? For which values of ‘n’ is this impossible? Students initial reaction was to draw a square and experiment. I cannot think of a better way to begin this problem. It is organic, and contains some very speedy deductions. We begin with suspicion of …

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