Yesterday we did a project exploring a common algebra mistake -> assuming that . That project is here:

Today I thought it would be fun to explore the same idea using 3d printing. During the day I made prints of the two surfaces

(i) , and

(ii) .

Here they are:

For the project I asked the boys to try to figure out what the two graphs looked like over the domain -2 < x < 2, and -2 < y < 2, and they showed them the shapes. Though not really by design, the choice of a square for the domain turned out to lead to an interesting discussion at the end.

Here's how the project went:

(1) What does look like?

(2) What does look like?

(3) What about the actual shapes surprises you?

I really enjoyed the combination of these two projects. Hopefully seeing the shapes of the surfaces becomes one little extra reminder that the two commonly confused expressions and are not the same.