CPM offers a pretty cool interface to informal language about rigid transformations. It's worth a look. Students worked in partners so that they could switch off. That way they could get feedback from their partner. It made students much more engaged. Then they copied down their solving steps after solving each puzzle.
Above, a student used 2 reflections for each to solve it quickly. I was impressed.
Above are the posters I made a few years ago and had a student color and decorate. It helps students see the relationship between the informal language of sliding, turning and flipping to translating, rotating, and reflecting.
As you can see, we reviewed 3 homework problems from the night before where they practicing solving a system using substitution (CPM calls it Equal Values method), solving for y, and a word problem that could be solved using a system of equations.