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. Next, students will learn how to find the area of composite figures involving semicircles. Following that, provide this challenge, then this one, then this one, then this one, and finally this one. Next, give your students this problem. After that, give your students this problem. Then give your students the easier variant of this problem. Next, give your students the challenges found here and here. Those two challenges are equally difficult, and thus can also be given in any order. Conclude by giving this riddle.