Arc length and radian measure
- Two riders, two quantities — 3 tasks
- The fraction, with no radius in sight — 3 tasks
- Arc length: a fraction of the way round — 3 tasks
- The radian: an arc divided by its radius — 6 tasks
- Going Deeper — 6 tasks
- Practice — 30 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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Same Measure, Same Length? Arc Measure and Arc Length — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each two arcs described in words: an angle in degrees or radians, and a radius or a diameter, or no radius at all. Students sort each pair: same length, different lengths, or cannot tell. The same measure does not mean the same length, and different measures can give the same length.
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Arc Length: How Far Around? Arc Length in Degrees and Radians — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a circle with an arc drawn heavy and the angle at the center marked, some in degrees and some in radians. The words give the radius or the diameter. Students find the arc length to the nearest tenth of a cm. The wrong answers are the two commonest mistakes: using the diameter as the radius, and using the other arc's angle. The row of box numbers at the foot is the check.
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One Radian: Is the Arc Longer Than the Radius? Radian Measure — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a circle with an arc drawn heavy and an angle in degrees or radians, or an arc length with the radius or the diameter. Students decide one thing: is the heavy arc longer than the radius? That is the meaning of one radian, about 57°. Fill it or leave it white, and a picture appears.
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Arc Length: How Far Around? Arc Length in Terms of π — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a circle with an arc drawn heavy and the angle at the center marked. The words give the radius or the diameter, and sometimes the marked angle belongs to the other arc. Students find the arc length as a fraction of 2πr, in terms of π. Using the diameter as the radius, or the other arc's angle, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.