Arcs and chords
- One rope, three ponds — 3 tasks
- The two lines nobody gave you — 3 tasks
- Congruent chords, congruent arcs — 3 tasks
- The converse, and the line that changes — 3 tasks
- Where the hypothesis earns its keep — 6 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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Congruent Chords, Congruent Arcs: Do the Marks Prove It? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each one or two circles with two chords and some marks, and a sentence: the chords are congruent, or the thick arcs are. Students sort each piece: the marks prove it, the marks prove it false, or the marks cannot tell, because nothing says the two circles have the same radius.
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Congruent Chords, Congruent Arcs: Arc Measures in a Circle — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a circle with two congruent chords marked by tick marks and two arcs measured. Students use "congruent chords cut congruent arcs" and the 360° around the circle to find a short arc, or the long arc named with three letters. The wrong answers are the two commonest mistakes: not sharing out the two congruent arcs, and giving the short arc for the long one. The row of box numbers at the foot is the check.
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Congruent Chords, Congruent Arcs: Do the Marks Prove It? — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each one or two circles with two chords, some marks, and a sentence: "The two chords are congruent" or "The two thick arcs are congruent." Students compute nothing: they decide whether the marks prove the sentence, which needs one circle or circles with the same radius. Fill it or leave it white, and a picture appears.
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Congruent Chords, Congruent Arcs: Arc Measures in a Circle — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a circle with two congruent chords marked by tick marks and two arcs measured. Students use "congruent chords cut congruent arcs" and the 360° around the circle to find a short arc, or the long arc named with three letters. Not sharing out the two congruent arcs, or giving the short arc for the long one, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.