Mathalicious: Cartogra-fail
Mathalicious

In this lesson, students approximate the areas of different landmasses by decomposing them into triangles and rectangles.

Real World Math: Exploratory Lessons - Four Color Map
Real World Math

This is a fairly simple puzzle for students to solve but it took over a century for it to be proven with computers. 

Illuminations: Handy Map
Illuminations (National Council of Teachers of Mathematics)

This lesson engages students in creating a map of their hands.

Siemens STEM Day: As Far As I Can Sea
Siemens STEM Day

In this activity, students will learn the different techniques used to map the ocean, and will practice using those techniques themselves in the classroom.