Mathematical contests should be decentralized to allow access to non competitive activities so as to enable students to participate and succeed in Mathematics. These activities should be compellingly interesting so that students enjoy learning about proofs and abstract structures rather than just solving problems.

Another way to divide a line segment discovered by Nathan Besteman is described along with Euclid's and the GLaD construction. The related projects and problems that teachers of geometry can assign to their students are also presented.

Diversity can be introduced in algebra without needing extra time. Explores three opportunities to encounter and engage diversity: (1) history; (2) multiple representations; and (3) object concept of function. (ASK)