Here’s a really easy way to break up a lecture-y day. After teaching on how to find the cross product for two vectors, ask them to figure out the angle between the cross product and one of the original vectors. Informally, on whiteboards. Mistakes are welcomed and celebrated (sometimes). Great practice of cross product, algebra, trigonometry, size of vectors, and the dot product angle formula.
Here’s some student work (some in progress, some completed with errors, and some completed without errors). Spoiler alert: It’s always fun to have some massive mess of variables all cancel out too!