In this lesson, students begin working with the area of circles. 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.

The last activity is optional because it previews the relationship between area and radius, which will be explored in more depth in a later lesson. Students see that it takes a little more than 3 squares with side lengths equal to the circle’s radius to completely cover a circle, leading to an approximate formula: the area of a circle is a little bigger than . At this point, it is a reasonable guess that the exact formula is , but the next lesson will focus on using informal dissection arguments to establish this formula.