Understanding the difference between area and perimeter is one of those challenges many students and adults have. For some reason, the concepts and formulas of area and perimeter are just hard to remember. Possibly because most of us just don’t use them often enough. But – there is a way to help students easily learn area and perimeter and how to differentiate them!
What is the difference between area and perimeter?
The easiest way to explain this difference is with a picture that shows both measurements with one shape. I have seen some really great representations of this but the most common is a pasture with a fence around it. If you are doing this with your students any representation will work as long as it has an inside and an outside. So, feel free to be as creative as you want!
How do you measure perimeter?
Usually, we teach perimeter first. The concept and the formula are a little easier to learn and remember:
This one seems easier for students to understand and calculate especially if you start with unit squares. Here are the steps I teach my students when measuring for perimeter:
The reason I teach them to put a slash on each unit square is so that they count each one just once. This comes in really handy when I teach them to measure the sides of polygons with known and unknown lengths.
Next, they count the slashes and write the number on each side.
Finally, they use the formula Side + Side + Side + Side to calculate the total perimeter of the shape.
I like this method because it gives students a framework for finding the perimeter of any shape.
How do you measure area?
Once my students have learned how to find perimeter and have practiced with different shapes that include unit squares and those that don’t – we move on to learning how to measure the area of a shape.
Again, I go back to the picture of the classroom board that shows both measurements. This is the springboard for learning the formula of area. We talk about measuring all of the area inside of a shape.
The formula for area is:
Going back to the unit squares model, I give them this framework:
I like to start with labeling one side length and one side width.
To make sure students don’t mix up the formula for area with the formula for perimeter, we put a dot inside the squares along the length of the shape. (Remember, we used slashes across the lines to mark the perimeter.)
We count the dots along the length (=4) and along the width (= 4) and insert them into the formula for area.
Finally, we multiply the length (4) times the width (4) and the area is 16 square centimeters.
*When measuring for area of a shape, we use square centimeters.
How to practice measurement of area and perimeter
One of the best ways I have found for students to practice measuring perimeter and area is to give them activities that ask them to do both. By having to measure both, students learn to differentiate perimeter and area much quicker.
These are the task card activities that I have my students use. They have to find the area and perimeter of the shape BUT ALSO determine if the measurements given are correct. This error analysis practice is a meaningful way for them to practice area and perimeter that extends their conceptual knowledge and I think – clarifies the difference for them.
In addition, they will write to explain what the error is on each task card. What teacher doesn’t want their students writing to explain in math? It’s magical! They begin to be able to explain their thinking in writing which then transfers to their understanding.
This Area & Perimeter error analysis activity is really effective in a math center where students can get repeated practice finding errors and writing to explain.
I hope seeing how I teach area and perimeter with unit squares helps you – even just a little bit!
Want to know and learn more about error analysis? In this post, I share why I think it’s such a great way for students to master important math concepts: What I Wish Teachers Knew About Error Analysis.