Deriving the equation of a circle
- The coverage map — 3 tasks
- Distance as a triangle, then run backwards — 3 tasks
- The check that settles it — 3 tasks
- Every circle — 3 tasks
- On, inside, outside, and why it is enough — 3 tasks
- Practice — 25 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 Circle or Not? Deriving the Equation of a Circle — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each giving a circle (by its equation, its center and radius, its center and a point, or a drawing) and a point P. Students test P with the equation: on the circle, not on it, or cannot tell because the piece does not give one circle. A drawn point that misses by 2% of the radius, and the classic sign and radius mistakes, are in the mix.
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Write It, Read It — Deriving the Equation of a Circle Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page. Each gives a circle one way and asks for it another: the equation from a center and a radius, the center or the radius from an equation, or the equation from a center and a point on the circle. Every wrong answer is one of the two classic mistakes: the signs of the center copied from the page, or the radius mixed up with its square. The row of box numbers at the foot is the check.
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Do They Match? Deriving the Equation of a Circle — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each with the equation of a circle and a center and radius. Students decide whether they match: the center from the signs in the brackets, the radius from the right side. Fill it or leave it white, and a picture appears. The white squares are the classic mistakes: signs copied from the page, the radius written without squaring, and the right side read as the radius.
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Center and Radius: Deriving the Equation of a Circle — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each giving the equation of a circle in standard form. Students read off the center or the radius, exactly, and walk to the card showing their answer. Copying the signs from the page, or taking the right side as the radius, lands on a card that sends the group back, and a clean run is 8 lines.