Creative Teaching Tips and Ideas for Area and Perimeter Part 1 (EP 37)

Creative Teaching Tips and Ideas for Area and Perimeter Part One

Hey there, and welcome to another episode of Elementary Math Chat. Today’s episode will be another content-specific episode, and this time it’s going to be on area and perimeter. This is also going to be a two-part episode. So, this week, I’ll go through the first half of my area and perimeter unit, and then next week, I’ll go through the second half.

And don’t forget about my 24-review challenge by the 24th of the month, which is actually tomorrow. I know it takes a couple days for these reviews to appear once you write them. So, I think we’ll extend this until the end of the month. So, if you haven’t written one, there is still time to do so.

All right, so let’s go ahead and jump into this unit on area and perimeter. This was one of those units that one day, it’d be so easy for my students, and we’d all be enjoying it and connecting it to the real world. And the next day, it was like everything they learned went out the door and it was confusing and all the word problems. And wait, what is area? What is perimeter?

It’s not really that they’re challenging. It’s just that kids don’t have the real-world experiences that these types of questions refer to. So obviously, they’re going to mix up area and perimeter as they go through this unit.

So, that is definitely the most challenging part about teaching area and perimeter, and it’s also a huge focus that I put in each one of my lessons. So, we’ll talk about a couple of different ways that you can help your students with word problems.

So, let’s go ahead and start with my first lesson, and this was on perimeter. They learned about perimeter in third grade, so they were familiar with what it meant. But the big difference in fourth grade is learning how to use the formulas to find the perimeter of both squares and rectangles.

So, we started this lesson with a quick discussion about what it means to use a formula and how it’s similar to following a recipe. If you think about it with a recipe, you put the ingredients in. You follow the instructions, and in the end, you have a delicious casserole or dessert to enjoy.

Using a formula is really similar. You put your numbers in, those are your ingredients. You follow the instructions. Those are the operations like multiply, or add, or divide that are in your formula. And in the end, you have your answer.

I like to have a little fun with them on this next part, so I asked them, well what happens if you accidentally use two cups of water instead of two tablespoons of water? Or what happens if you get a little careless and you accidentally put salt in the recipe when you were supposed to use sugar?

The look on their faces when I ask them that question always makes me laugh. They’re like, ooh, disgusting, salt instead of sugar and way too much water! So, even they know that if you don’t follow a recipe, it’s not going to turn out the way you want it to.

And it’s the exact same thing with a formula. You’ve got to follow the formula exactly the way it’s written or your answer will not turn out the way you want it to. So, I always thought that was kind of a creative way to introduce them to a formula and have them connect it with something that they already know about.

The next part of my lesson was just another effort to tie in those real-world connections with perimeter. I showed them a picture of a fence, a border around a swimming pool, as well as a picture frame, and I asked them to tell me what they all had in common.

I let them talk to their neighbors for a minute or two, and during this time, I wrote a t-chart on the board. I swear every time I listen back to this it sounds like I’m saying chi-chart. But I’m saying the letter T; t-chart. Just wanted to make that clear.

But anyway, I wrote this on the board, and one side of the chart I labeled with area, and the other side I labeled with perimeter, so everything they were about to share with me I would put on the perimeter side. And by the end of the discussion, we had the words border, around, fence, frame, and edge on this list.

Here’s a quick tip, I don’t know if you know this one, but within the word perimeter is the word rim, and so that helps them remember that it’s the distance around a figure, not the inside like with area. So, we also added rim to that list.

This was a really great reference for them because whenever they came to a word problem, and they were unsure of whether to find the area or find the perimeter, they could look at this list for help. So, I kept this on my board for the entire unit.

The next idea I want to share with you is something that I did to not only introduce the three formulas for perimeter but also to show my students that formulas were nothing to be afraid of. They’re nothing to be intimidated by. I wanted them to discover that they were already using these formulas, even if they didn’t know it.

I knew that if I showed them a rectangle with very simple dimensions, they would be able to figure out all three ways to get the perimeter, and so that’s exactly what I did. I showed them a rectangle where one side was five inches, and the other side was 10 inches. So, then I asked them, okay, tell me what you remember from third grade? What is the perimeter of this rectangle? What is the distance around this figure?

Immediately, hands went in the air, they were excited, and they were about to jump out of their seats. They’re like, I know this, I know this! So, we all agreed in the end that the perimeter of this rectangle was 30 inches. So, I said, okay, everybody agrees that the perimeter of this rectangle is 30 inches, but then I asked them to explain how they got their answer.

And remember, my goal for this is for them to discover that they’re already using these formulas. I don’t want to have to be the person to introduce the formulas to them. I want them to tell me the formulas.

So, I asked them, all right, well, how did you solve this problem, and the majority of them added all four sides. That’s how they learned it in third grade. So, I added that formula to the board. But then I said, well, did anyone else solve it a different way? And of course, I had hands in the air, and some of them were like, well, I added the length and then added the width and then just doubled it. So, we tested it out, and sure enough, it worked. So, I wrote that formula on the board.

At this point, I get really excited because I’m like, wow, you guys, you have figured out two different ways to find the perimeter. Is there anyone who can figure out a third way? Now, I don’t know how many of them actually used this method the first time around. But again, since my numbers were so simple, they were able to figure it out.

You can double the length, double the width, and then add those two together. So, I wrote that third and final formula on the board. We checked it just to make sure that it did actually work, and that was how I introduced the three formulas for finding the perimeter of rectangles.

Let’s move on and talk about small groups real quick because this is a great opportunity to review concepts with fractions and decimals. You can either write these problems on the board, or I have a set of task cards that I’ll link in the show notes that also do this.

But instead of finding the perimeter of a rectangle with whole number dimensions, change the dimensions to mixed numbers, like a width of 2¼ centimeters, and a length of 3¾ centimeters. So, now they’re not only practicing finding the perimeter, but they also get practice with adding mixed numbers.

You can also include both fractions and decimals. For example, the length could be 5.6 feet in decimal form, and the width could be four and three-tenths feet in fraction form. So, that would give them a little more practice going back and forth between fractions and decimals.

I also think this makes perimeter a little more engaging. It can get a little boring if you’re just adding whole numbers the entire time and almost takes the thought process out of it. So again, either write these on your board, or you can grab the set of task cards that I made that already have these dimensions included.

So, that takes care of my tips for teaching perimeter. The next lesson in my area and perimeter unit was on area. I followed a similar format with this lesson. We started by reviewing the formulas for area, and when I say formulas, I mean for squares and rectangles. The area equals base times height, and then area equals side times side if they want to use that one for a square.

And I reminded them that they had to follow these formulas exactly. Oftentimes with area, they find the area, so they multiply the base times the height, and then they double it because that’s what they did when they found the perimeter. But going back to the recipe, you wouldn’t bake a cake and then put it in again for twice the amount of time. And the same applies to area. All you have to do is multiply the base times the height. That’s it, no doubling.

We then looked at a few real-world examples of area just like we did with perimeter. I showed a picture of someone installing wood floor planks, another of someone painting a wall, and then a third picture of someone laying carpet in a room. I asked them what these pictures all had in common, and we added those words to the t-chart under the area side.

Some students noticed that they were all flat surfaces, which is helpful to point out because area does measure two-dimensional figures. So, we added the word flat to our t-chart under area. They also noticed in every picture that someone was covering something, whether it was a wall that was being covered, a floor, something was being covered.

By the end of the conversation, we had the words cover, carpet, floor, tile, garden, paint, wallpaper, quilt, and square units all under the list of keywords for area. I forgot to mention this in the perimeter one, but I also had an example of both area and perimeter in this t-chart.

On the perimeter side, I bolded the outline of the rectangle to reinforce that it was measuring the distance around the figure. And for the area example, I shaded the rectangle to reinforce that it was measuring the inside. So, that was a good visual for them to have on this t-chart, and I would definitely recommend doing that on yours as well.

Now when it comes to your small group activity, I recommend doing the exact same thing I talked about with perimeter. The easiest way to do this is just to write these problems on the board. So, for fourth grade, I always made sure that one category required them to do double-digit multiplication. Another category had both three-by-one and four-by-one digit problems. And then another one would incorporate fractions. Again, such an easy and simple way to incorporate other skills into your area and perimeter unit.

All right let’s move on to the third lesson in my area and perimeter unit, and this one was on finding the area of combined rectangles. I think one of the biggest struggles with this concept is that the shapes in the workbook are so small, and it’s hard to learn this concept when you’re working with such small figures.

So, before we did anything in the workbook, I gave them each a handout that had two larger examples of combined rectangles, and this was in a sheet protector. So, they could use their Expo marker to write on the rectangles and draw their lines to divide them up in different ways, and we could also solve the problem in more than one way. That’s why I liked putting them in sheet protectors and using Expo markers. So, that was super helpful.

 Now remember, with these problems, context is so important. So, as we went through and solved the area of these combined rectangles, we talked about what they could represent. They could be a hallway and laundry room that you’re putting down tile for. They could be your bedroom and closet that you’re putting carpet down on. They could be your yard, maybe you’re putting down sod on the front yard and the side yard, and you need to know how many square feet you need.

So, even without actually using word problems, you can still connect these ideas to real life. I also did this further small group activity. But there they had four questions to solve instead of two, and those weren’t as big, they only took up a fourth of the page. But by that point, they had figured out how to solve them, and it was much easier to solve on a smaller scale.

All right, well, we have made it to the halfway point in my area and perimeter unit. So, I’m going to end this episode here, and next week, I’ll take you through the second half of this unit. Those lessons were on finding missing dimensions with both area and perimeter. Another lesson was on problem-solving with area, specifically multi-step problems. And then I’ll also share a little bit about what I did on my review day to help them prepare for the test. So, stay tuned for part two next week. 

So, let’s go ahead and wrap up with today’s teaching tip of the week. Today’s tip is for your lesson on converting units of measure, and it will help your students know when to multiply or when to divide when they’re converting units of measure. So, this is what it sounds like.

 When you go from a bigger unit to a smaller unit you multiply. When you go from a smaller unit to a bigger unit you divide. Well, that alone is not going to help them, so put arm motions along with it, and that will teach them whether they’re supposed to multiply or divide.

So, imagine, when you go from a bigger unit, put your arms out, to a smaller unit, bring your arms in, and cross them. So, you’re literally making the multiplication sign with your arms. Now the opposite. When you go from a smaller unit, start with your arms crossed, to a bigger unit or you can say larger unit there doesn’t matter, you’re gonna bring your arms out but you want to show them like a division sign and a fraction.

So again, when you go from a smaller unit, arms are crossed, to a larger unit, arms are out, you divide. So, from start to finish; when you go from a bigger unit to a smaller unit you multiply. When you go from a smaller unit to a bigger unit you divide.

I remember having kids taking their tests and I would see them doing the hand motions that go along with this. One of my former math coaches taught me that trick, so I think you’ll find it helpful as well. It’s a great way for them to determine when to multiply and when to divide when converting units of measure. 

All right, well, that is all for today’s episode. I hope you enjoyed it. Have a great week, and I will see you next Tuesday for part two of my area and perimeter unit.