What students learn
In a right triangle, a² + b² = c², where c is the hypotenuse. In the game:
- 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.
- Hypotenuse c (blue) is the rope.
The same three colors are used for every number on screen, so students always know which side a number belongs to.
A visual proof, built in
A square is built on each side of the 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. Students watch a² + b² = c² happen, which is the heart of the standard's "explain a proof" requirement.
The five worlds
- World 1: one question per canyon. Students count the 1-foot squares along the edge of the square on the rope and type its length. The hypotenuse, found by counting.
- World 2: every step of the solution, with unit tiles: plug in, square, add, take the square root.
- World 3: the challenge round. One side isn't labeled, so students count grid squares first. Four answer choices per step, every wrong one a common mistake, with a fraying-rope timer.
- World 4: find a missing leg, the distance to the next platform, from numbers carved on a temple door, with the same timer.
- World 5: the summit. Bigger triangles, a mix of rope and distance problems, and no answer choices: each line of the solution has a blank to fill in, with a perfect-squares list for support.
No triangle repeats within a world. The final step of each canyon is a slow-motion swing that labels all three sides, and the explorer lands one rope length below the anchor, drawn to scale.
Worked examples
Find the rope (hypotenuse): a = 6 ft, b = 8 ft
c² = 6² + 8² c² = 36 + 64 c² = 100 c = √100 = 10 ft
Find the distance (a leg): rope c = 13 ft, height b = 5 ft
a² + 5² = 13² a² + 25 = 169 a² = 144 a = √144 = 12 ft
Common mistakes the game catches
Each wrong choice in the game is a real mistake with its own hint:
Adding the sides (6 + 8 = 14) instead of adding their squares.
Doubling instead of squaring (6² = 12).
Forgetting the square root and stopping at c² = 100.
Adding when finding a leg (a² = 169 + 25) instead of subtracting. World 4 is built to practice this.
Ways to use it in class
- Printables. A free worksheet with an answer key and a two-to-a-page exit ticket match this game, ready to print or save as a PDF.
- Discover it. Start in World 1 before you name the theorem. Ask: "How did the two small squares relate to the big one?"
- Write every step. Students copy each chosen line into their notebook, so the game produces a full written solution.
- World per day. Worlds 1–2 on day one, 3 on day two, 4–5 for review.
- Exit ticket. "A 10-foot ladder leans against a wall with its base 6 feet out. How high does it reach?"
Discussion questions
- Why must the hypotenuse always be the longest side?
- Does a² + b² = c² work for a triangle without a right angle? Try 4, 5, 6.
- Why do long ropes make the explorer swing lower?
Real-world connections
Ladders against walls, TV screen sizes (measured on the diagonal), the shortest path across a park, ramps, roof pitch, and the distance between two points on a map grid all come from the Pythagorean theorem.
Standards
CCSS.MATH.CONTENT.8.G.B.6Explain a proof of the Pythagorean Theorem and its converse. (The squares on the legs pour into the square on the rope.)
CCSS.MATH.CONTENT.8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Access and privacy
No accounts, no student data. Students choose an explorer or a monkey to swing with, and finished worlds save in that browser. Plays with the keyboard alone, a mouse, or touch; on a phone, turn it sideways.