7.3 Measuring Circles

In this unit, students learn to understand and use the term “circle” to mean the set of points that are equally distant from a point called the “center.” They gain an understanding of why the circumference of a circle is proportional to its diameter, with constant of proportionality \(\pi\). They see informal derivations of the fact that the area of a circle is equal to \(\pi\) times the square of its radius. Students use the relationships of circumference, radius, diameter, and area of a circle to find lengths and areas, expressing these in terms of \(\pi\) or using appropriate approximations of \(\pi\) to express them numerically.