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Patterns and the inability of students to define “random”

November28

Here is an interesting pattern, noticed by our editors last night (that could be a hint?). What do you think it is? Is there a mathematical pattern to it? I put this to three different classes today (Grades 7,8 and 11) and they all struggled with the concept of “random” patterns in Mathematics. I posed the question. “How do we know that a pattern is random in Mathematics or Science?” Still no comments to this post which makes me wonder if this is a universal fault with our teaching and learning? If students are unable to define what a random means, then how can they define what we mean by “order”?? Hmm, this is perhaps getting too deep??? More on this picture soon, especially if you comment!

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y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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