Students will learn how even and odd numbers can be represented algebraically, then shown some proofs involving these representations, then asked to prove some things on their own. Theorems should include those involving addition, multiplication, and squaring. For example, prove the sum of two odd numbers is even. Prove the square of a number has the same parity. These proofs require nothing more than distributing, combining like terms, and applying properties of exponents. Conclude by giving your students this challenge.