45-45-90 triangles
- The same number from every square — 3 tasks
- Cutting a square in half — 3 tasks
- From a leg to the hypotenuse — 3 tasks
- From the hypotenuse back to a leg — 3 tasks
- Going Deeper — 6 tasks
- Practice — 28 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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Multiply or Divide by √2? 45-45-90 Triangles — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each a marked triangle or a square in words, with one length given and one called x. Students sort them: x is the hypotenuse, so multiply by √2; x is a leg, so divide by √2; or the marks do not show a 45-45-90 triangle, so neither rule can be used. Most of the last row look exactly like 45-45-90 triangles.
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Times √2 or Divide by √2? 45-45-90 Triangles — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page. Each gives one length of a 45-45-90 triangle or a square, as a small marked drawing or in words, and asks for another. More boxes go backward, from the hypotenuse to a leg, than forward. The wrong answers come from going the wrong way: multiplying by √2 when the rule says divide, or dividing when it says multiply. The row of box numbers at the foot is the check.
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Do the Marks Show It? 45-45-90 Triangles — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a triangle with marks on it: right-angle marks, tick marks, matching arcs or printed degrees, and no lengths. Do the marks show a 45-45-90 triangle? Many white squares look exactly like one, but their marks do not prove it. Fill or leave white, and a picture appears.
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Times √2 or Divide by √2? 45-45-90 Triangles — Scavenger Hunt a full class period · 13 sheets
16 cards around the room. Each gives one length of a 45-45-90 triangle or a square and asks for another, as a marked drawing or in words. Every answer is exact, like 9√2. Multiplying by √2 when the rule says divide, doubling a leg, or using a perimeter as a side lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.