Students will learn how area and volume change when scaled along an axis. They'll first see this for rectangles and right rectangular prisms. Then they'll learn the area formula for ellipses, and how it's derived from stretching the unit circle. They should also see that when \(a = b\) they get the area formula for circles. After that, students will learn the volume formula for ellipsoids, and how it's derived from stretching the unit sphere. They should also see that when \(a = b = c,\) they get the volume formula for spheres.
This topic is not covered by the Common Core, but I think it should be.
Next, give your students these challenges:
Conclude by leading this investigation: