Pythagorean applications and triples
- Two numbers, no roles told — 3 tasks
- Which length is the hypotenuse — 3 tasks
- Add or subtract: the brace decides — 3 tasks
- What a triple is worth — 3 tasks
- Where the triples come from — 3 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.
-
Add, Subtract, or Neither? Pythagorean Applications — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 situations in words, each with two lengths and a question: a ladder on a wall, a wire from a pole, a walk east then north, a kite, a ramp, a tree and its shadow. Students sort them with no calculation: add the squares (the hypotenuse is asked for), subtract them (a leg is asked for), or the theorem cannot be used because the words make no right angle (a leaning wall, a hillside, a slanted tree).
-
Add the Squares or Subtract Them? Pythagorean Applications — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a situation in words with no drawing: a ladder on a wall, a wire from a pole, a walk east then north, a ramp. Students draw the right triangle, decide which length is the hypotenuse, and find the third side. The wrong answers are the two costliest mistakes: adding the squares when a leg is asked, and using a known triple in the wrong role. The row of box numbers at the foot is the check.
-
Add or Subtract? Pythagorean Applications — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a short situation in words (a ladder on a wall, a kite, a walk east then north, a ramp) with two lengths and a question. Is the length asked for a leg, so the squares are subtracted, or the hypotenuse, so they are added? No calculation: fill it or leave it white, and a picture appears.
-
Which Side Is the Hypotenuse? Pythagorean Applications — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a situation in words with no drawing: a ladder on a wall, a wire from a pole, a kite, a walk east then north. Students draw the right triangle, decide which length is the hypotenuse, and find the third side. Adding the squares where they must be subtracted, or using a known triple in the wrong role, lands on a card that sends the group back. A clean run is 8 lines on the record sheet.