In a variety of ways, the student develops, applies, and justifies triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples. The student applies the concepts of similarity to justify properties of figures and solve problems. Students predict what would happen if they took a wire or string 1 foot longer than this circumference and formed a ring around the middle of the basketball, like the rings around Saturn. Using a thin metal wire, such as electrical wire, students cut a piece that is 1 foot longer than the circumference of the basketball. Students revisit their predictions about what could fit under the wire.
Students then calculate the actual distance from the surface of the basketball to the ring of wire.
Students calculate the actual distance from the surface of the earth to the imaginary ring and compare the results with those from the basketball questions. Each group of students is given the dimensions of a different rectangular prism and students calculate the total surface area and volume. Students double the height and compare the new total surface area and volume to those of the original solid. They repeat this process for the width, and then again for the length. Students write a conjecture about the effects on the total surface area and volume when one dimension of the prism is doubled.