30-60-90 triangles
- Mirror it and get an equilateral triangle — 3 tasks
- How long can the altitude be? — 3 tasks
- Half of an equilateral triangle — 3 tasks
- Find the shorter leg first — 3 tasks
- Going Deeper — 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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30-60-90 Triangles: Is x Right? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 triangles drawn to scale, each with some angle marks, one length and a value for x. Students sort them: x is right; x is wrong (the √3 on the wrong side, or the wrong side doubled); or the marks do not show a 30-60-90 triangle, so nobody can tell, even though it looks like one.
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Where Does the √3 Go? 30-60-90 Triangles — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a 30-60-90 triangle drawn to scale with its angles marked, or an equilateral triangle cut by its altitude. Students find x from one given side, forward and backward. The wrong answers are the two costliest mistakes: putting the √3 on the wrong side, and starting from the given side instead of the shorter leg. The row of box numbers at the foot is the check.
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Which Side Is It? 30-60-90 Triangles — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a lettered triangle with two of its angles in words and a question: is this side the shorter leg, the longer leg, or the hypotenuse? No drawings, so the angles decide and not the look. Fill it or leave it white, and a picture appears.
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30-60-90 Triangles: Find the Shorter Leg First — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a 30-60-90 triangle drawn to scale with its angles marked, or an equilateral triangle cut by its altitude. One side is given and x is to be found, in all six directions. Putting the √3 on the wrong side, or starting from the given side instead of the shorter leg, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.