Understanding Area of a Circle Conceptually

Let's tackle Area of a Circle conceptually using a series of visual prompts to help students generate the formula for finding the area of ANY circle! We'll also show the circumference of a circle!

In this series of Math Is Visual Prompts, students are given the opportunity to wrestle with the idea of area – in particular the area of a circle – through a “Would You Rather” situation.

As always, the visuals provided as a consolidation are useful AFTER students are given the opportunity to work with these ideas concretely and after consolidating in the classroom through student work.

Let’s get started…

Spark Curiosity: Would You Rather…

Ask students “Would You Rather two 12 inch medium pizzas or one 18 inch large pizza?” to spark curiosity and pause where indicated in this video.

Area of a Circle - Pizza Comparison.007 Would You Rather 2 Medium Pizzas or 1 Large

What If You Want The Most Crust?

After they all share out, challenge them to think about whether they want to change their answer if you were looking for the situation with the most crust:

Area of a Circle - Pizza Comparison.011 What if you want the most crust

At this point, we want them to start digging in. Be sure to ask them to convince their neighbours as we want to move beyond just gut shot guesses.

This is a great opportunity for students to “play” with the idea of circumference as it relates to the diameter of a circle. As they may (or may not) be aware, the ratio of the circumference to the diameter is approximately 3.14:1.

Yes, it is π:1!

Area of a Circle - Pizza Comparison - Circumference GIF

As you see in the video, the winner in this case is the 2 medium pizzas.

Area of a Circle - Pizza Comparison.046 2 mediums has the most crust

What If You Want The Most Pizza?

Next, let’s ask students if they would still stick with 2 mediums if they want the most pizza.

Area of a Circle - Pizza Comparison.049 The Most Pizza Area of Circle

Again, have them convince their neighbours.

When consolidating, you can use two versions. One is purely spatial involving partitioning by creating a parallelogram out of the circles and then “covering it up“:

Area of a Circle - Pizza Comparison - Area of a Circle GIF

Now, to show covering it up:

Area of a Circle - Pizza Comparison - Area of a Circle Large Pizza Wins GIF

Students can also do this using measurements, noting that half of the circumference of each circle ends up being the “length” of the resulting parallelogram.

Area of a Circle - Pizza Comparison - Area of a Circle Full ConsolidationGIF

In the video, you also see some number sense strategies being used to promote number fluency.

For example, we decompose the slide length of 38 inches to 10 + 10 + 10 + 8 to make multiplication easier without resorting to a standard algorithm or a calculator:

Area of a Circle - Pizza Comparison.118 Consolidation

We also use a compensation strategy for the rectangle of the large pizza by multiplying 28.5 inches by 10 inches (instead of 9) and then subtract 1 group of 28.5 inches afterwards:

Area of a Circle - Pizza Comparison.123 Consolidation With Compensation

As you can see, in the end, the large pizza is the winner:

Area of a Circle - Pizza Comparison.126 Large Is Winner

Go ahead, have some FUN with your students as we learn the area of a circle. Remember, it’s all about the rectangle in the end!

How’d It Go?

Thanks for watching and reading!

Did you use this in your classroom or at home? How’d it go? Post in the comments!

Math IS Visual. Let’s teach it that way.

kylepearce3

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