Every year, many of my students seem to have difficulty grasping the idea of perimeter and area. I’ve found that the best way to help students learn the difference between the two while figuring out how to properly calculate each is to have them engage in several different hands-on activities. This week I’ll share with you how I introduce these important measurement concepts separately, then reinforce them with engaging cumulative activities that emphasize both area and perimeter.
Using straws cut into lengths of 2, 4, and 6 inches, along with pipe cleaners cut into 2-inch pieces, students explore perimeter by making polygons with sides of various lengths. They measure and record the lengths then draw the shapes in their math notebooks, annotating the length of each side along with the total perimeter. Using premeasured lengths makes it easier for me to quickly check if students are adding up the sides correctly as I walk around checking their work.
In this follow-up activity, students use rubber bands on geoboards to create shapes with different perimeters that I have written on the board. For example, I’ll ask them to make a square with a perimeter of 16, a triangle with a perimeter of 12, etc. To wrap up this activity, I ask students to create four different polygons and record the perimeter of each on their small dry erase boards. As I walk around, it is easy to see who has grasped the idea and who needs more time and practice.
While my students are out of the room, I use tape to craft seven large polygons. Each side is marked with a letter. Working in groups of three, students use yardsticks and tape measures to record the length of each side, and then they add them together. This activity really helps cement the notion that perimeter is the sum of individual sides added together.
After measuring the floor polygons, students move about the room measuring the perimeter of everyday items such as rugs, cabinet doors, their desks, etc., and recording them in their math journals along with an annotated diagram.
In the book Spaghetti and Meatballs for All! A Mathematical Story by Marilyn Burns, Mr. and Mrs. Comfort invite 32 people to a reunion. To accommodate their guests, they set up eight square tables to seat 4 people at each, one to a side. The guests, however, rearrange things so different-size groups can sit together. Mrs. Comfort protests, knowing the arrangements won’t work, but no one listens. After a great deal of confusion the guests realize Mrs. Comfort was right.
I read the first part of this book, up until the guests begin to move the tables, to my class. Then I tell the class that they are going to help Mrs. Comfort set her tables so everyone is happy. Each group of two students gets eight squares that represent the tables and 32 smaller squares for the guests. Students work very hard, and exasperation always gives way to delight when they realize that the only way to get 32 places at the table is with Mrs. Comfort’s original plan.
When students’ knowledge of perimeter is quite solid, introduce area. Using connecting math cubes or building blocks are great ways to have students create closed shapes that can be used to introduce area. The square-shaped blocks help students understand the notion of “square units” as we calculate the total number of blocks, or area, of their shapes. LEGO bricks also work very well here. Tip: I store math block manipulatives in plastic sandwich bags that contain 36 units. Students can grab a baggie, and we save lots of time counting out blocks for math.
Students always seem to focus closely on lessons that involve edible manipulatives because they know that when the work is done, they feast! We use these to compare and contrast the area and perimeter of different polygons. Students discover that the exact same 20 crackers can yield many different perimeters while the area always remains 20. You can count on your students' amazement when they discover the large perimeters they can create with zigzag designs. Whenever using edible manipulatives, I always keep my students with allergies in mind. My students with wheat, soy, and dairy allergies use Rice Chex instead of cheese crackers for worry-free edible math.
Students write their weekly word list on square centimeter graph paper and then calculate the area and perimeter of each word. Words with tall letters like b, d, and k, along with letters that hang down like g, p, and q, take up two spots. For example, the word “road” has an area of 5 sq. cm. and a perimeter of 12 cm. while “boat” has an area of 6 sq. cm. and a perimeter of 14 cm. I have also had students break their words up and sort them after writing them on the centimeter grid.
These two activities are always huge favorites with my students in math centers. First they use the square centimeter graph paper to write out their names. Next they find the area and perimeter of each letter and add those together to find the area and perimeter of their entire name. Students love to compare the sizes of their letters and names. Having your students in cooperative groups for this is key because when one student has trouble visualizing how a letter m can be made out of squares, a group member is always there willing to lend a hand.
Using the same square centimeter grid above, students get in touch with their inner artists as they create pieces of artwork and then determine their area and perimeter.
Our culminating activity is for students to create an area and perimeter neighborhood. I print and copy square-inch grids onto construction paper of different colors. After a bit of modeling, students select four different colors to create the house, roof, door, and windows. Drawing their polygons and cutting and fitting them together into a house shape requires them to use substantial problem-solving skills well before they even calculate the area and perimeter of each. Completed houses are displayed on a bulletin board along with a sheet that lists their name, the area and perimeter, and their favorite part of the project.
About a week after the houses are completed, I have students design trees for the display. Because a week has passed, this activity works as a review and reinforcement of their area and perimeter skills.
I hope the activities I've shared here have helped give you a few ideas of ways you can teach and reinforce area and perimeter with your students. If you have any great ideas for using manipulatives to teach math, I would love to read about them in the comments section below.