Compositions of rigid motions
- Where one motion is not enough — 3 tasks
- What a description has to name — 3 tasks
- Two motions, and the order they come in — 3 tasks
- Carrying one figure onto another — 6 tasks
- Two mirrors — 6 tasks
- Practice — 24 tasks
- Summary — 2 tasks
- Cool-down — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
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Carry ABC onto DEF: Right, Backwards, or Missing a Part? — Cut & Glue Sort 25–30 minutes, including the cutting · 5 sheets
12 students' answers to "describe two motions that carry triangle ABC onto triangle DEF", sorted into correct, the wrong way (it carries DEF onto ABC) and missing a part (no center, no direction, no line, no angle). Most wrong-way answers are right answers with their two sentences swapped, so only doing the motions tells them apart.
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Two Motions: Which Comes First, and Which Way? — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page: carry a point through two motions, undo two motions from where they land, and decide whether two orders give the same point. A wrong answer goes to a box that sends the student back, and the row of box numbers at the bottom is the check.
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Compositions: Even or Odd Reflections? — Mystery Picture 20–30 minutes · 4 sheets
25 squares, each a triangle and a copy carried there by rigid motions, their corners marked dot, circle, diamond: go around the marks of each, fill the square if they go the same way around (no reflection, or two) and leave it white if they go opposite ways (one reflection). The orientation count the lesson teaches first, with no arithmetic — and when every square is right, a picture appears.
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Compositions of Rigid Motions — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each with a point and two rigid motions — reflections, translations and rotations, two reflections in parallel mirrors and in crossing ones, and one sequence to undo. Every answer is a point. Doing the two motions in the other order lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.