Slackrope Pythagoras — Cornell Notes (Printable)
- What is given?
- How to model with coordinates?
- Vertical drop?
- Horizontal distances to poles?
- Which right triangles?
- Pythagoras substitution
- Arithmetic and final units
- Pattern spotting
- Key justification sentence
- ACARA alignment
Oh my — cue the tiny bells. We set up the scene like a stage: the poles are at (0,15) and (14,15). The walker stands at (5,3). Simple, dramatic coordinates.
Given: Pole A at (0,15), Pole B at (14,15), Walker at (5,3). Heights in metres.
Model: Draw vertical drops from each pole to the walker to form two right triangles. The top of each pole is at y=15; the walker is at y=3.
Vertical drop: 15 − 3 = 12. (There — the short modelling line the teacher loves.)
Horizontal distances: From walker (x=5) to Pole A (x=0): 5 m. From walker to Pole B (x=14): 14 − 5 = 9 m.
Right triangles: Two right triangles with legs (5,12) and (9,12).
Use Pythagoras:
Left rope segment = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13 m.
Right rope segment = sqrt(9^2 + 12^2) = sqrt(81 + 144) = sqrt(225) = 15 m.
Total rope length: 13 + 15 = 28 m. Final answer: 28 m.
Patterns to notice: These are 5–12–13 and 9–12–15 Pythagorean triples. When you see those legs, neat integers often follow. Pattern spotting is power.
Key modelling sentence (justification): 15 − 3 = 12 shows the vertical drop — that connects the story to the algebra.
Teacher Rubric Notes (short, Ally McBeal style):
- Diagram & labelling (3/3): Poles and walker placed clearly; horizontal distances 5 and 9 and vertical drop 12 are labelled — very tidy.
- Correct Pythagoras setup (4/4): Both triangles chosen correctly and substitution is correct.
- Arithmetic & final answer with units (2/2): Integer results; total 28 m; units stated.
- Justification sentence (1/1): Add the single line 15 − 3 = 12 to finish the modelling — shows conceptual grasp.
ACARA v9 alignment (short): Measurement & Geometry — modelled situation with coordinates and applied Pythagoras (Years 7–9). Proficiencies: Fluency, Reasoning, Problem Solving.
Model with coordinates, note vertical drop 15 − 3 = 12, use Pythagoras on 5–12 and 9–12 triangles to get 13 and 15, then add: total rope length = 28 m.