# Area of a Circle Discovery Activity

When students are learning about area formulas, it helps to be able to SHOW them why each formula works.  I like to use paper to try to cut and rearrange paper so that students can actually see why each formula works.  When students see the manipulation for each formula, they can figure out the formula for themselves if they forget.

When I teach students about the area of a circle, I like to have them actually use paper to manipulate for themselves and then glue it in their interactive notebooks.  I've found that some students need to move the paper for themselves and when they put it in their notebooks, it helps them remember the activity later.  My favorite part about this area of a circle discovery activity is that it can be used well in a middle school or high school class.

## Area of a Circle Discovery Activity

First, cut out a circle.  You can draw a circle with a compass or you can print a circle from the computer.  Then, fold the circle in half horizontally and vertically.  Open the circle.  You should end up with a circle split into quarters.

Cut each quarter wedge.

Fold each wedge into quarters.  Cut each wedge on the fold lines.  You will end up with 16 wedges.

Now, take the small wedges and alternate them to form a rectangle, like below.

Use all 16 wedges to make a rectangle/parallelogram.

First, students realize that the area of the rectangle is the same as the area of the circle.  Students can then see that the base of the rectangle is half of the circumference.  Next, you can help explain that the base is the length of the radius multiplied by pi.

When I have my students do discovery activities in class, I like to have them answer questions after the activity to ensure that they have gathered all of the necessary information from the activity.  If you want to have your students answer questions about this activity, you can check out this FREE area of a circle discovery activity.  It would be perfect to have students glue these questions in their interactive notebooks on one side, and then tape the cut apart circle on the other side. 