Medians and the centroid
- The tray on one fingertip — 3 tasks
- A double can against a single one — 3 tasks
- Medians, and the point where they meet — 3 tasks
- How the centroid cuts a median — 3 tasks
- Proving it, and cutting it up — 6 tasks
- Practice — 24 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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Double It, Halve It, or Can You Not Tell? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each naming a triangle, its centroid and a midpoint, with one length given and another asked. Students do not work anything out: they decide whether to double the number, halve it, or whether nothing can be told. The last row holds the mistakes that matter: a point that is not the centroid, and two lengths on different medians.
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Long Piece or Short Piece? The Centroid — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, all about one triangle with its three medians and the centroid. Half the boxes give one length on a median and ask for another; half give two lengths as expressions in x and ask for a length. The wrong answers are the two costliest mistakes on this topic: turning the 2 to 1 ratio upside down, and handing in x instead of the length. The row of box numbers at the foot is the check.
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Is the Long Piece at the Corner? — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each naming a triangle, its centroid and one midpoint, with one sentence about the pieces the centroid cuts: twice, half, two thirds, one third, three times, or a ratio. Fill the square if the sentence is true. The white squares turn the ratio upside down, use a point that is not the centroid, or claim equal distances the centroid does not have. When every square is right, a picture appears.
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Which Piece of the Median Is Longer? — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each one tilted triangle with its three medians and the centroid. Each card gives one length on a median (the piece at the corner, the piece at the midpoint, or the whole median) and asks for another. Turning the 2 to 1 ratio upside down lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.