Pythagorean Platforms

Teaching Notes for Educators

Students swing across a jungle by solving the Pythagorean theorem one written step at a time. Every canyon is a right triangle made from the scene itself, so the numbers always describe something they can see.

• The triangle: leg a (coral) is the distance straight across to the next platform, leg b (green) is how high the vine's anchor is above the explorer, and the hypotenuse c (blue) is the rope. The same three colors are used for every number on screen.
• One step per swing: students choose the right line of the written solution - plug in, square, add (or subtract), take the square root - and each correct line swings them forward. Each wrong choice is a common mistake with its own hint, such as adding the sides, doubling instead of squaring, or forgetting the square root.
• Why squares: a square is built on each side of the canyon triangle. As students work, the squares on the two legs fill with tiles and pour into the square on the rope, which they fill exactly - a visual proof of a² + b² = c².
• Answers you can see: the big swing lands one rope length below the anchor, drawn to scale, so short ropes keep the explorer high in the trees and long ropes swing low. After the final step, a slow-motion close-up labels all three sides and reveals the missing length.
• Five worlds: World 1 is the starting point: one question per canyon, where students count the 1-ft squares along the edge of the square on the rope and type its length - the hypotenuse, found by counting. World 2 walks through every step with unit tiles. Each world uses four different triangles (in Worlds 1 to 3: 3-4-5, 6-8-10, 5-12-13 and 9-12-15), so no question repeats within a world. World 3 is the challenge round: one side of the triangle isn't labeled, so students first count the 1-ft grid squares along it, choose each step from four answers (every wrong one a common mistake), type the final rope length, and work against a fraying-rope timer (20 seconds per choice on the first problem, 3 seconds less on each problem after), with fewer hints and squares that stay "?" until their areas are found. World 4 finds a missing leg - the distance to the next platform - from numbers carved on a temple door, with the same fraying-rope timer as World 3. World 5 is the summit challenge: bigger triangles (6-8-10, 5-12-13, 9-12-15 and 8-15-17), a random mix of rope and distance problems, and no answer choices, with step hints and a perfect-squares list for support - each step is a line of the solution with one number blanked out, and students type what belongs there.