Students will see several proofs of the AM-GM inequality. First, students will see three visual proofs.

Here's the first proof:

For the other two proofs, watch these videos by Micro Visual Proofs:

Next, students will see an algebraic proof.

AM/GM Inequality (2 of 2: Algebraic Proof) by Eddie Woo

Conclude by giving your students these challenges:

- Making a Difference by NRICH
- Gaxinta by NRICH
- 2008 AMC 8, Problem 15
- 2005 AMC 8, Problem 20

Remainders by NRICH: For the first two problems, replace "I'm thinking of a number," with "I'm thinking of a positive number." Do not give your students the challenging extension.