I’m very excited to share that I am stepping into a new role on my campus next year. I will be moving from the instructional coach role (working with teachers) to the academic support role (working with students). I’m super psyched about the change! I got a little glimpse of the future today as I subbed for the current academic support teacher and worked with a group of 5th graders on perimeter.
I started our session by asking students what they knew about perimeter. There were two reasons for this. First, it’s important to activate prior knowledge, but it also served as a formative assessment for me. Since I don’t routinely work with these kiddos, I wanted to quickly determine what they already knew about the topic. There was also, actually, a third reason. I love to hear students talk about math. I want to give them opportunities to engage in mathematical discussions and develop academic vocabulary.
I got lots of response–it’s the distance all the way around the shape, you add all the sides to find it, there’s a formula for it, etc.
So I drew a rectangle on the whiteboard and labeled it as shown.
I told students that mathematicians use what they already know to help them solve problems, and then I asked them to tell me what they knew about this figure that might help them find the perimeter. They knew it was a rectangle. Great! So, what do you know about a rectangle? Two sides are the same and the other two sides are the same. We added that information to the drawing as I explained that mathematicians like to get all their thinking down in writing.
Notice how I continually stress the habits that mathematicians employ in their work. With the model drawn and labeled, I asked the students to mentally calculate the perimeter. I then asked each student, in turn, for their solution. I didn’t just call on one student, I let each one respond. After they told their solution (which most correctly calculated as 22 in.), I asked them to tell me how they calculated it. Some said they added 7 + 7 and then 4 + 4 and then added the sums together to get 22. Others multiplied 7 x 2 and 4 x 2 and added the products together. As they explained, I added that academic vocabulary. Then I added, You know how I did it? I added 4 + 7 to get 11. I knew if these two sides had a sum of 11, then the other two sides did, too. I like doubles, so I did 11 + 11 and also got 22. They liked that. Later, as we did additional problems and they told me how they solved it, I asked them how I would have solved it, and they were able to explain my doubling strategy. 🙂
Time for more of a challenge. Next, I drew the following problem on the whiteboard.
Talk about wide eyes! So I brought them back to what do you know? Well, we know the measurements of the other sides, so we wrote them in.
I again asked them to mentally calculate the perimeter, and I called on each one in turn. I got some WILD answers! So I told them I was going to do something that would seem almost magical, and I covered up the fractions.
Then I asked, okay, what’s the perimeter now? 10. Then I uncovered one of the fractions. How about now? 10 1/2.