First, students will learn what the midpoint formula is, and how to use it.

Midpoint formula by Khan Academy

Midpoint formula by Khan Academy

Next, students will learn how the midpoint formula is derived.

Proof of Midpoint Formula by Davidson Online Math

One type of problem students should see is to find the other endpoint, given an endpoint and the midpoint. This is done by setting up and solving two equations.

Finding Endpoint Given Midpoint by Khan Academy

Next, give your students these challenges:

- 2018 Math Kangaroo Levels 3-4 Problem #21 by STEM4all
- Math Kangaroo 2017 Level 7-8 Problem #25 by STEM4all

\(A,\) \(B,\) \(C,\) \(D\) are the midpoints on a square of paper. \(E\) is the midpoint of \(\overline{CD}.\) Make the red and blue lines by folding. You can use a pencil to mark points or trace the fold lines you've already made. Making a few marks like this will help you greatly in making precise folds. Then cut along the red and blue lines to get four new shapes. Then rearrange the four shapes to make a triangle. What type of triangle is it?

Conclude by leading this investigation:

Area and Perimeter of Polyanimals

by MathPickle