Begin with lecture/discussion: Prompted by small white board question: “What are the properties of a rotation in 2 dimensions?”, students give conditions necessary for a matrix to result in rotations only.

Then teacher derives the specific components of rotation (and coincidentally reflection) matrices from the condition that they preserve lengths. Note: use lecture is a good opportunity to go back-and-forth between bra-ket language and matrices written as rows and columns of explicit components. rewrite this lecture as a follow-up to the components activities. Shorten!

Small whiteboard question: What matrix will result in a 3D rotation around the z-axis? Used volleyball to explain question. What matrix will result in a 3D rotation around the x-axis…y-axis?

Construction notes: Add a note and link and possibly a video clip about very small XYZ whiteboard used to help with analyzing rotation matrices in class.