BEFORE You Teach Students to Find Area and Circumference of a Circle

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It’s that time of year when students learn how to find the area and circumference of a circle. There’s a time of year for that? Of course. Pi Day is coming. That magical date of March 14th (3.14) when teachers everywhere talk about all things related to the number pi and circles.  Many teachers celebrate this occasion by teaching students to find the area and circumference of a circle. 

But before you do that lesson, give some thought to what prerequisite skills students will need to use. My students come to me with a variety of abilities but most of them have some serious gaps in their mathematical knowledge base, especially since the pandemic.  So, there are several skills I like to cover or review before we tackle finding the area and circumference of a circle. 

Circle Basics

First, we cover the basic idea of a circle. We talk about what it is from a geometric standpoint (a collection of points equidistant from a center point) and we practice naming its parts (center, radius, diameter, etc.) For my kinesthetic learners, I even teach them some gestures to go with those parts. We practice how to find the radius when you know the diameter and vice versa. I actually have a free digital activity for this. Click here to grab it. 

Practice converting radius and diameter before you teach students to find the area and circumference of a circle.

Difference Between Area and Circumference

Second, we talk about the difference between the circumference and the area. The circumference is a “fancy name” for the perimeter and only applies to a circle. We talk about how that can be hard to measure with a regular ruler. But if you use a string to wrap it around and then measure the string we can get a pretty good measurement. The area is how many squares on my graph paper it would take to cover the entire circle. We talk about how that’s a little hard to count because of the squares that get cut into pieces.

Discovering Pi

Next, depending on how much time you have in your pacing guide, you can do a “discovering pi” activity. Have the students measure different circular objects with their string and ruler. They can measure the circumference and the diameter and divide. They should notice that their answers are all pretty close together…3 point something. This is a great time to introduce or review the idea of an irrational number. 

Before teaching students to find the area and circumference of a circle, make sure they have a good understanding of pi.


Next, we talk about formulas. For many years, I took for granted that my students knew what a formula was and how to use one. I try to make sure they understand the idea that formulas show how things are related. We review some formulas they should have learned in previous years such as the formula for area of a rectangle or for area of a triangle. We talk about the idea of a variable and how to substitute numbers in for a variable in order to perform calculations. 


Finally, we review rounding with decimals. I don’t want my students to miss an area or circumference question on a standardized test just because they don’t remember how to round to the tenths or hundredths place. This is something I usually do through bellringers or warm ups as we are working our way to our circle unit. I used to think that students had just forgotten this skill but I have come to realize that many of them never learned it in the first place. I am sure their teachers covered it but for whatever reason it just didn’t click at that time. But now, years later, there are a lot of “Aha moments” as we practice this basic skill.

I like to use my self-checking digital activities for these warm ups and bell ringers so that students get instant feedback. You can click on the images below to purchase them. If you haven’t tried self-checking activities like these before click here for my previous blog post for all the reasons I love them.

Resist the Temptation

Sometimes it is tempting to just jump in and teach a topic like how to find area and circumference of a circle, especially when you are behind in your pacing guide. But if you take the time to review the prerequisite skills and base knowledge with students your lessons will go much smoother.

If you have some great ideas that you use in your classroom leave them in the comments below so that everyone can benefit from your knowledge. Or if you just found this post helpful. Let me know that also.

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