The Common Core stresses the importance of students developing a deeper understanding of fundamental concepts and to discover/uncover the interrelatedness of mathematics. The discussion below can be used to demonstrate how a basic law of exponents is tied to the geometry of similar figures.
1) If the sides of 2 squares are in the ratio 2:1, show that their areas are in the ratio 4:1
(b) numerically by examining particular cases
• Squares and circles are of course special cases of similar figures. Beyond this investigation lies the BIG IDEA:
(m/n)^3 = (m^3)/(n^3)...