Setting up a coordinate proof: placing a general figure
- A claim that agrees with every example — 3 tasks
- Naming a rectangle without numbers — 3 tasks
- Numbers settle one, letters settle all — 6 tasks
- Too much force, too little force — 6 tasks
- The same figure placed two ways — 5 tasks
- Practice — 23 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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What Does the Placement Force? Setting Up a Coordinate Proof — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each a placement with letters, like (−a, 0), (a, 0), (0, b). Students decide what it forces for every choice of letters: a right angle, two equal sides that meet at a corner, or neither. Hidden right angles, symmetric placements with negative letters, and general placements that only sometimes make a rectangle are all in the mix.
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Which Placement Is General? Setting Up a Coordinate Proof — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page. Each names a figure and gives two placements of it with letters, like (0, 0), (a, 0), (a + b, c), (b, c). Students pick the general one. Each wrong placement is a classic mistake: one letter doing two jobs, which forces too much, or a fourth corner with letters of its own, which forces too little. The row of box numbers at the foot is the check.
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General or Not? Placing a Figure for a Coordinate Proof — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each naming a figure and giving a placement of it with letters, like (0, 0), (a, 0), (a + b, c), (b, c). Students compute nothing. They decide whether the placement is general: it must give that figure for every choice of letters and force nothing extra. Fill it or leave it white, and a picture appears. The white squares are the classic mistakes: one letter doing two jobs, a right angle forced at the origin, a fourth corner with letters of its own.