Visualizing in 3D

I introduced my precalculus students to vectors in 3D space yesterday. They have a hard time visualizing the 3-dimensional axis system, especially since the familiar XY-plane is now on the “floor”:

3D axes

To help them understand how 3D coordinates work, I paired the students up, and gave them a slip of paper that read:

This landmark is ( ______, ______, ______ )

steps from the northwest corner of Mr. Wert’s classroom.

Using the northwest corner of my room as the origin, they went all over campus and picked a spot to put their label on. They had to keep track of how many steps they walked in the x-direction, the y-direction, and the z-direction. Here’s an example:

3D landmark

Actively keeping track of their position using 3D coordinates really helped them understand how the x, y, and z coordinate system. works. After this, they were ready to work with vectors in 3 dimensions.

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