Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Students will learn the circumference and area formulas for a circle. Students will see two ways of deriving the area formula from the circumference formula. The first way is to cut out concentric rings, then arrange into a triangle, as seen here. The second way is to cut slices, then rearrange into a rectangle, as seen here.
Note: The MAA also posted the last challenge, but there was an error in their reasoning.