Day 15: Growing Shape Patterns

Today’s photo again comes from my Algebra 1 class. We’ve been accumulating different kinds of representations of number patterns:

  • verbal
  • symbolic
  • numeric (or tabular)
  • graphic (in the sense of graphing)
  • geometric (in the sense of pictures)

I introduced graphic representations yesterday; today we dug into geometric representations. We worked with what I call growing shape patterns. Nothing particularly innovative here, but I just love sharing this set of activities with kids. I start by having them make up a growing shape pattern of their own on graph paper. Then I give them the sheet in the photo with a shape pattern already there. Next, they gather data from the steps in the pattern and write formulas for area and perimeter. Then I ask them to come up with other things to count, tabulate, and model with symbols. Finally, they return to the patterns that they designed and analyze them in the same way.

I feel like all of this representation stuff is close to the heart of what algebra’s all about. Much of the rest is just details and hygiene. I’m really excited about the start we’re making on the year. I feel like my students are going to come away with a really robust picture of algebra and are just going to soar.

And yes, my student has made a mistake above. We’ll tackle that on Monday. Hooray! Mistakes are just opportunities for growth!

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