Second day of school and all is well in Middle-School-Land. We have an abnormally well-behaved group of seventh graders this year (I say now, and promptly jinx it no doubt). Yesterday and today both sections of seventh grade have been working super productively and already are demonstrating amazing group-work skills. I have been so impressed with them.

And then today, during our discussion of a warm-up question in which they had to describe the perimeter of an 8-by-1 rectangle, one of my sections of 7th had the best impromptu Math Talk. I asked them to write a sentence describing the number of “toothpicks & tiles” in the figure displayed up on the SMARTboard. Most groups interpreted “sentence” to mean a number sentence, which turned out to be really cool because they all thought of different number sentences.

One girl had this totally wonky one. I had completely no clue (zip, zero, nada) as to where she was coming from. She described the perimeter as “2 times 6 plus 3 times 2”. Luckily I squashed my initial reaction, which was to say that this number sentence may have been equivalent to 18 but didn’t have a connection to the picture, and instead I asked her to explain her thinking. I was so glad that I did!

She explained that she had taken off the two ends, leaving her with a row of 6 squares (I’m paraphrasing here, she didn’t say it exactly like this), which is where the 2 times 6 came from. And then she looked at the two squares on each end and realized that she needed to count 3 of the edges on those squares, which accounted for the 3 times 2. Add those together and you’ve got the perimeter.

I thought that was so cool! I never in a million years would have thought of visualizing the perimeter in that way. The other groups were excited to share their ideas and it was just a great conversation. These kids are going to rock the Border Problem when we do it later on in the year. I’m really looking forward to that!

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