A curve built from a point and a line
- Eight measurements and one sentence — 3 tasks
- The point you do not have to measure — 3 tasks
- Which points belong — 3 tasks
- The condition becomes an equation — 3 tasks
- The rolling circle, and how the curve widens — 4 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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On the Parabola or Not? Focus and Directrix — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each telling something about a point P and a parabola given by its focus and directrix: P's coordinates, a fact about its distances, or a drawing with two marked lengths. Students sort each one: on the parabola, not on it, or cannot tell. A point that only looks as if it is on the curve, the focus itself, a vertical directrix and a slanted segment taken as the distance are all in the mix.
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The Equation of a Parabola from Its Focus and Directrix — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each giving the focus and the directrix of a parabola. Students find the vertex halfway between them and the signed number p, then pick the equation (x − h)² = 4p(y − k). Each wrong equation is a real mistake: p taken as the whole focus-to-directrix distance, p with the wrong sign, 1/(4p) in place of 4p, or the vertex put at the focus. The row of box numbers at the foot is the check.
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As Far from the Focus as from the Directrix? Parabolas — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each a drawing of a focus F, a directrix d, a point P and two marked lengths. Students measure nothing and compute nothing. They decide whether the two numbers show that P is as far from F as from d. Fill it or leave it white, and a picture appears. The white squares are the classic mistakes: a segment to the vertex instead of the focus, a slanted segment taken as the distance to the directrix, and two different distances.
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Points on a Parabola: Focus, Directrix and the Equation — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each giving a focus, a directrix and an x. Students find the vertex halfway between them, the signed number p, and the y of the point of the parabola, then check that the point is as far from the focus as from the directrix. Taking p as the whole focus-to-directrix distance, or giving it the wrong sign, lands on a card that sends the group back, and a clean run is 8 lines.