We did an awesome project today inspired by Fawn. Coming up on area of composite shapes, I needed a way for students to practice the composite-ness and the “splitting up” skill. A popular text book problem asks about pools and tiling/grass/etc around the pool in the yard, so I thought about having them draw a pool and do all that jazz, but I couldn’t really get that idea together.

A popular text book problem asks about pools and tiling/grass/etc around the pool in the yard, so I thought about having them draw a pool and do all that jazz, but I couldn’t really get that idea together. As it turns out, there’s this kinda big holiday called ~~Easter~~ Spring coming up, in which Hallmark has secularized another Christian holiday for a profit. So I had my kids make greeting cards at the end of class yesterday (after they worked on a “traditional” worksheet on area of composite shapes in groups) and photocopied them after school. I was pretty vague about what we would be using them for on purpose, which drove my students a little nuts. Some of the kids even came up to me after school yesterday to ask what the cards were for. Mostly, though, they liked the elementary school throwback to arts and crafts.

Today, the entirety of the class was devoted to this one question: How much of your card is left uncovered?

Here’s what my awesome students came up with:

My thoughts:

+’s

- Different ways of seeing- most students broke up the shapes and then subtracted those areas from the card area, but some broke up the non-covered areas to calculate it directly.
- Differentiation!!!!!!!!! Some students took a long time to figure out how to split their shapes, some students were able to do some but not all calculations, some were ready to start splitting into smaller shapes to be more precise, and some students were even able to finish all calculations and write a paragraph to explain their reasoning
- Foreshadowing of calculus: the smaller we split our shapes/the more shapes we calculate, the closer we can get to the actual area
- Using the document camera after about 5-10 minutes of work to show classmates’ examples helped tremendously
- I was able to have some students put fewer shapes on their card and other students put more shapes on (more differentiation!)
- Copy the cards! So helpful to have a paper version to draw on so they could still use their cards as cards
- Most students engaged

∆’s

- Some students had a hard time getting started- I ended up suggesting that they start by finding the covered area instead but a lot of them still didn’t understand what to do until their classmates presented their beginnings. Is this a problem? What other scaffolded questions could I ask to help students get started?
- How can I/ should I make the connection to calculus more explicit?

Materials:

Go to the dollar store. Not Target.

- Rulers
- Calculators
- Coloring supplies
- Colored notecards
- Foam sticky shapes
- Stickers