Unit 5, Lesson 15
Area of a Circle
Accelerated 6
Preparation
Lesson Narrative
In this lesson, students see that the area of a circle can be found by multiplying . When we say area of a circle we technically mean “area of the region enclosed by a circle.”
Students estimate the area inside different circles on a grid. This helps reinforce their understanding of the concept of area as the number of unit squares that cover a region. They use tables and graphs to analyze the measurements (MP8). Students see that, unlike circumference, the area of a circle is not proportional to the diameter.
They then discover that unrolling a circle into a triangle shape suggests that area and circumference are related by the equation where is the area, is the circumference, and is the radius. Optionally, students can cut a circle into sectors and rearrange the sectors into a shape resembling a parallelogram to find a similar formula. Using algebraic reasoning, students construct and critique arguments that this is equivalent to or (MP3).
- Create a table and a graph that represent the relationship between the diameter and area of circles of various sizes, and justify (using words and other representations) that this relationship is not proportional.
- Show how a circle can be decomposed and rearranged to approximate a polygon, and justify (orally and in writing) that the area of this polygon is equal to half of the circle’s circumference multiplied by its radius.
Let's investigate the areas of circles.
Required Materials
Activity 2
Required Preparation
For the digital version of the activity, acquire devices that can run the applet.
Consider copying the blackline master onto different colors of paper. If different colors of copy paper are not available, the blackline master can be copied onto white paper and then construction paper can be used for the other sheet that the pieces are glued onto.