Slope criteria for parallel and perpendicular lines, and why they hold
- One line, one number — 3 tasks
- The pair that looks parallel — 3 tasks
- Read the slope before you judge — 3 tasks
- Two steps to a perpendicular slope — 3 tasks
- Going Deeper — 9 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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Perpendicular or Not? Slopes of Perpendicular Lines — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pairs of lines, given by slopes, by equations, by dots on square paper, or drawn on plain paper. Students sort each pair: perpendicular, not perpendicular, or cannot tell from the piece. Pairs with only the sign changed or only the fraction turned over, a pair that looks perpendicular and is not, and a vertical line with a horizontal one are all in the mix.
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Perpendicular Slopes: Opposite Reciprocals — Slope Criteria Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each giving a line by its slope or by its equation y = mx + b. Students find the slope of a perpendicular line by changing the sign and turning the fraction over. The wrong answers are the two halves of the lesson's commonest mistake: only changing the sign, and only turning the fraction over. The row of box numbers at the foot is the check.
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Perpendicular or Not? Slopes of Perpendicular Lines — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each giving two lines by their slopes or by equations solved for y. Students compute nothing: they check whether one slope is the other with its sign changed and turned over. Fill it or leave it white, and a picture appears. The white squares are the two halves of the commonest mistake: only turning the fraction over, and only changing the sign.
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Perpendicular Slopes: Opposite Reciprocals — Slope Criteria Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each giving a line by its slope or by its equation y = mx + b. Students find the slope of a perpendicular line in two steps, change the sign and turn the fraction over, and write it on a record sheet with a column for each step. Doing only one of the two steps lands on a card that sends the group back, and a clean run is 8 lines.