Last spring I wrote about Mathigon’s Map Coloring Challenge. That’s not the only map-based math lesson available from Mathigon. Mathigon’s lesson on spheres, cones, and cylinders incorporates map projections.
In Surface Area of a Sphere Mathigon includes an interactive diagram that illustrates the problem that cartographers have when trying to create maps of the world. The interactive diagram shows four map projections and the areas of the map that are distorted by each projection. Students can click on each of the map projections to see a comparison of an area on the 2D map to the same area on a globe. Overall, it’s a good way for students to see how two dimensional world maps can distort the size and scale of an area.
Mathigon’s Map Coloring Challenge asks students to use as few colors as possible to color in all 50 U.S. states without having the same color touching two states at the same time. For example, if I color New Hampshire purple, I can’t use purple on Vermont, Maine, New York, or Massachusetts but I could use purple on Pennsylvania.
On a related note the USGS offers a free map projections poster (link opens a PDF). You may also want to take a look at Projection Wizard as another tool for showing students how various projections distort the regions of the world.
Applications for Education
Years ago I did a hands-on lesson with students in which they used strips of paper to create a globe that was then laid flat so that they could see the difficulty in creating an accurate 2D map of the world. Mathigon’s Surface Area of a Sphere accomplishes a similar goal in an online format as does the Projection Wizard site mentioned above.