Understanding Cartesian Coordinates in Three Dimensional Space

Your math teacher is BORING, all they ever show you is X and Y! That is how I start of this lesson. I teach high school Advanced Manufacturing and Engineering. In my program we do a lot of work with CAD, CAM, CNC, and 3D printing. Unfortunately, most of my students come to me with very limited knowledge and experience in designing and manufacturing in 3D space. I have found Tinkercad a great place to start. So I created this lesson as an introduction to 3D cartesian coordinates as well as CAD.

Tinkercad

The first part of this lesson has students work in groups of two or three. I give them the XYZ Point 1 Number Line face down on the table. I tell them they are going to flip it over and write as many observations as they can about what they are looking at. The observations start really simple, "there's numbers", but soon grow more profound, "two are positive and one is negative", and slowly develop into predictions and assumptions about what they are looking at, "is it a point in space". Really fun to watch and facilitate!

Next I have the students open and start an account on Tinkercad. I give them a very brief overview of the basics, focusing on how the program is made for kids and if they hover over icons they say what function they perform. I explain the workplane, the view cube, the basic shapes, and most importantly, the ruler. I show them what happens when you add a shape without the ruler vs. with the ruler. I point out the they can see all three dimensions of the shape, as well as the distance from zero on all three axes. Then I tell them to put a sphere on the stage that has dimensions of 10mmx10mmx10mm XYZ, and turn it to blue.

This part is fun. I just tell them to plot the blue sphere where it belongs according to the Point 1 worksheet. The room erupts with some of the best academic discourse about math I have ever seen. I let them roll for a few minutes with probing questions, then I stop them and ask where should Zero be? After a little refresher on the old boring math teacher, and their XY coordinate planes, and how the quadrants work, they decide dead center on the workplane should be Zero. A quick discussion on how to find the center. I show them more detail on the ruler and how it can be rotated and mark mid point or end point, we want mid point. I then show them the XYZ Planes image and talk about plans vs. axes. Once this is done they get it in seconds.

This I normally do the next class period. Just like day one, they get the worksheet XYZ Points 1-8 and are instructed to list all observation they can. They are now way more knowledgeable about the 3D world and the conversations reflect it. They will soon realize it an object in space, and eventually most will realize it is a cube.

This time I introduce the duplicate tool and explain all the have to do is change the duplicated coordinates to the next point on the worksheet. Same as day one, the students are asked to plot the points in space and see if their predictions are correct.

For those who need a little extra challenge. Ask them first write all of the coordinates for an octahedron. Then build it in the center of cube so there are no shared points.

Have fun!