I am in the unique position over the next few weeks to see perimeter and area work in 3rd, 4th and 5th grade. It is so incredible to see the overlap across all three grade levels and, being a 5th grade teacher for so long, it is great for me to see where this work begins.
After planning with Hope and her student teacher, Lori, last week, we taught the lesson introducing perimeter today. On Friday, the students measured things around the room in different units of measure, having discussions about most appropriate units. For example, when measuring the length of the room would we use the same unit as we would for the width of our pencil eraser? Why?
Since I was not there for the lesson on Friday, I was super curious to just hear what students thought about when they heard the word “measuring.” I wrote the word on the board and away we went. They were very quick with benchmarks, equivalents and different dimensions we can measure. I did a terrible job with my picture, but I got a couple really interesting questions like, “Can we measure anything? Air?” and “Can we measure the corner angles of things like the carpet?” Also, after a student had shared that one yard is the same as your hip to your ankle, students questioned if that was true because of the different heights of people. All of these things are great for students to explore at later times!
Hope introduced the Investigations problem of an ant traveling around the edge of a piece of paper. To be honest, we were not thrilled with the context, but at the time we could not come up with anything snappy or original, so we went with it. We thought it was nice because, in inches, we could see if students measured to the half inch and also how they worked with the half inch when combining to find the perimeter. In hindsight, I am thinking a city map might have worked, however then the scale comes into play, so maybe not?? We let them choose the unit they thought would be appropriate, put them with a partner and they went off to work together. We were surprised to see most students using inches and when asked, thought that it would be “too many centimeters.” They seemed to chose units based on the biggest unit that still fits the object, but not thinking about precision and getting the smallest unit for that.
This is where I am continually amazed by what students know and intuitively do with mathematics.
It was interesting to see some pairs not know how to deal with the half,”not quite 9,” but know they only had to measure one side and then put “11” on the opposite side.
While another group had the 8 and one half written exactly like they said it “8 and 1 (one).5(half) inches.” Although written incorrectly, they dealt with it beautifully in their computation. However, I would want to bring up the equal sign in future share outs so they 8×2=16+1=17 would be written correctly. Does anyone use arrows in the elementary grades for this? 8×2–>16+1–>17? Or is it more appropriate for separate lines at this age?
When I walked up to this group I asked where the ant was walking because of their lines through the middle of the paper. They said around the outside but it is the same no matter where you draw the line. I asked them to show me the 8 inches and I left them to talk about the 1/2 inch.
Some students did not deal with the 1/2 inch but seeing the ways they found the perimeter and wrote their equations, I was able to see the formula for perimeter coming to life.
As students got finished with their first unit choice, we had them find the perimeter in another unit. It was nice to see the multiplication from their previous unit showing up a lot.
When I saw this one, I didn’t really know what to do with it. What do you with a 3rd grader using .5 as half? I asked them what .5 meant and they quickly said one half. They said one can be broken into .5 and .5 just like it can be broken into 1/2 and 1/2. That is so interesting to me and I would have loved to explore that conversation more, but with a whole class that is not ready to go there, I wrote it on the board and moved on.
As always, there is not enough time in a class period for me to talk about math with the kiddos. Tomorrow morning, students will journal about their strategy to find the distance the ant traveled. Since the majority of the class only measured two sides, we want to make explicit, through student sharing, why they didn’t have to measure all four sides in this case.
They next part of the lesson, which Hope and Lori will continue tomorrow, includes the students creating their own ant path on grid paper and finding the perimeter of that path. We are not going to dictate that the path must be a rectangle, but the ant must stay on the grid lines. We are hoping that this generates the conversation of when we can double the two sides and add them and when we can’t, assuming students draw irregular shape paths.