Something we have worked really hard to discover is perimeter and today we are going to build on that knowledge. See, last week you helped me figure out if I had enough fence to go around the perimeter of my yard for my dogs. Well, all of that grass inside of the fence is the area inside the fence. There are a lot of ways that we can find area, but today we’re going to use something we already know a lot about: square units.
I have a few examples on the board that I have students help me make sense of. I have the figures look like they are on grid paper to make counting the units inside the figure easier. It's important to not expect students to "get it" after a few examples, so make sure you have students work with a few additional examples to find both perimeter and area of each. This is time that you'll have to get a sense of who's struggling with this concept.
I am going to give each of you some square tiles and we are going to use them as our square units to figure out the area of a shape. I have some shapes for you to work on, and I want you to find both the perimeter and area of the figures.
Here I think it is important to reinforce the difference between area and perimeter. I find that it’s helpful to give students something that they can manipulate as they are building their understanding of a concept.
Research shows that gestures in math are effective learning tools. Area and perimeter lend themselves to hand movements - students can use their pointing finger to describe an area by air writing as they say the word, and wave their hands to show area.
Today I want you to use what you’ve been practice to find the area and perimeter of different, and bigger, shapes! Who can remind me of what area is? How do I find it? And what is perimeter? How to I find that? Great, off you go!
There are many students who confuse area and perimeter, so I wanted to give students concrete examples that they could write on as they were working through this activity. I try to make the beginning lessons of a concept very hands-on so that students can work through obstacles in how to determine the area of various figures (MP1).
I saw some great work from you guys today. Who can tell me something they noticed as they were working? Who came across some challenges?
Here I want to discuss how some students were counting each square, and how challenging that can be when the figure is very large. I also want students to share how they broke the figure up into smaller sections to make sense of the area.