It is always fun when I can look back at my past blog posts, see what I learned from a lesson, and reflect on student reasonings before I teach that same lesson again. This past week we were working on this lesson from last year: https://mathmindsblog.wordpress.com/2014/01/27/area-and-perimeter-of-squares-student-noticings/.

The lesson unfolded in much the same way, with the class patterns looking like this:

I anticipated all of them, however, like last year, there always has to be one that throws me a curve ball and leaves me math homework over Christmas vacation:)

The 5th statement looked like this in his math journal:

With these other noticings below it…

His explanation focused on the pattern of the fraction the perimeter is of the area. The numerator stayed a two and the denominator went up by one on every even dimension. I honestly didn’t know what to ask him because the question “Why is that happening?” seemed way to broad. He played around with building the squares and was not getting anywhere. I am thinking, after chatting with Christopher (@trianglemancsd) on Twitter, that focusing on the meaning of the fraction first may be the way to go??

Basically, I first have to sit down and reason about his on my own…gotta love math homework on vacation!

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TaffyHi – I thought I left a comment the other day about my thinking, But, now I do not see it here. Maybe I forgot to hit the words POST COMMENT!

Anyway, I was thinking about your students discovery and though – what does the area need to be multiplied by in order to obtain the perimeter? n^2 times what equals 4n? That factor turns out to be 4/n, which can also be written as 2 divided by (n/2). Notice how n/2 becomes a whole number when n is an even number. Great pattern sniffing by your student!!

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