Triangle proportionality and its converse
- The sliding seam — 3 tasks
- Which segment is compared with which — 3 tasks
- What the parallel cut does — 3 tasks
- Deciding whether the cut is parallel — 3 tasks
- Going Deeper — 6 tasks
- Practice — 26 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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Is the Cut Parallel, or Can You Not Tell? Triangle Proportionality — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 triangles, each with a segment across two sides and four lengths, and nothing saying the segment is parallel. Students decide from the numbers whether it is parallel to the third side, not parallel, or cannot be told. The pieces hold the mistakes that matter: a segment that only looks parallel, a piece-over-piece fraction compared with a piece-over-whole one, and the parallel segment's own length used as if it were a piece.
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A Piece, a Whole Side, or the Segment Across? Triangle Proportionality — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, all about one triangle with a segment parallel to one side. Each box gives three lengths and asks for a fourth: a piece, a whole side, or the third side. The wrong answers are the two costliest mistakes on this topic: putting the wrong lengths together in the proportion, and handing in a piece when the question asks for a whole side (or the reverse). The row of box numbers at the foot is the check.
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Is This Proportion True? Triangle Proportionality — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each one proportion written with the letters of one of three figures: fill the square if the proportion is true, leave it white if it is not. The white squares are the mistakes students really make: the parallel segment put in a proportion with two pieces, a piece-over-piece fraction mixed with a piece-over-whole one, and a segment that only looks parallel. When every square is right, a picture appears.
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Which Piece Goes With Which? Triangle Proportionality — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each one triangle with a segment cut across two sides. The cards give three lengths and ask for a piece, a whole side, or the segment across; two ask what length makes the segment parallel. Mixing a piece-over-piece fraction with a piece-over-whole one, stopping at the piece, or putting the segment across into a proportion with two pieces lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.