Slackrope Walker — Cornell Notes (Age 13)
Cues / Questions
- What is the problem?
- How do I place coordinates?
- Which right triangles appear?
- How to apply Pythagoras twice?
- What needs labelling on the diagram?
- Common mistakes to avoid?
- One-sentence justification?
- ACARA v9 links & rubric?
Notes & Step-by-step Work
Problem restated: Two poles are 15 m tall and 14 m apart. A walker stands on the rope 5 m from the left pole and is 3 m above the ground. Model the rope as two straight segments from each pole top to the walker. Find the total rope length.
1. Choose coordinates (model)
Place the left pole top at (0,15) and the right pole top at (14,15). Place the walker at (5,3). (Why? This makes horizontal distances easy: 5 m from left, 9 m from right.)
2. Draw & label the diagram (must do)
Label horizontal distances: 5 m (left) and 9 m (right). Label vertical drop: 15 − 3 = 12 m. Mark right angles at the walker bases. (Label everything — that prevents the common slip of swapping 5 and 9.)
3. Compute left segment (left pole top to walker)
Horizontal = 5, Vertical = 12. Use Pythagoras:
Length_left = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13 m.
4. Compute right segment (right pole top to walker)
Horizontal = 9, Vertical = 12. Use Pythagoras:
Length_right = sqrt(9^2 + 12^2) = sqrt(81 + 144) = sqrt(225) = 15 m.
5. Total rope length
Total = 13 + 15 = 28 m. State units clearly.
One-sentence modelling justification (required)
Vertical drop = 15 − 3 = 12, so each triangle has vertical leg 12 m; horizontal legs are 5 m and 9 m.
Common error
Not labelling the horizontal segments (5 vs 9). Mark them on the diagram to avoid mixing them up.
ACARA v9 alignment (short)
Measurement & Geometry (Years 7–9): apply Pythagoras in right triangles, use coordinates to model geometry. Proficiencies: Fluency (accurate calculation), Reasoning (choose representation), Problem Solving (modelling real context).
Worked (algebra-style) — show every step
Left length = sqrt[(5 − 0)^2 + (3 − 15)^2]
= sqrt[5^2 + (−12)^2]
= sqrt[25 + 144]
= sqrt[169] = 13 m
Right length = sqrt[(14 − 5)^2 + (15 − 3)^2]
= sqrt[9^2 + 12^2]
= sqrt[81 + 144]
= sqrt[225] = 15 m
Total rope length = 13 + 15 = 28 m
Summary (bottom of Cornell page)
Summary sentence: Model the rope as two right triangles with vertical drop 15 − 3 = 12 m and horizontal legs 5 m and 9 m; Pythagoras gives lengths 13 m and 15 m, so the total rope length is 28 m.
ACARA v9-aligned Marking Rubric — (Ally McBeal cadence)
Listen — and I mean really listen — because this is where elegance meets evidence. You brought the drama of the courtroom and the crispness of a legal brief. The case files:
- Diagram & coordinates — 3 marks: Draw the scene (two pole tops at (0,15) and (14,15), walker at (5,3)). Mark the 5 m and 9 m horizontal distances and the 12 m vertical drop. If your diagram breathes, award full marks.
- Correct triangle setup & Pythagoras — 4 marks: Two correct distance formulas using (Δx)^2 + (Δy)^2 and proper substitution. No hesitation. Courtroom approved.
- Arithmetic & final sum with units — 2 marks: Clean square roots (13 and 15) and neat addition to 28 m. Units stated. The numbers must stand tall like witnesses.
- One-sentence justification — 1 mark: A single modelling sentence showing vertical drop = 15 − 3 = 12. That tiny sentence seals the argument.
ACARA mapping: Measurement & Geometry — applying Pythagoras, representing situations with coordinates. Proficiencies assessed: Fluency, Reasoning, Problem Solving. Total = 10 marks. Case closed.
Teacher comments (Carrie Bradshaw cadence — exemplary outcome)
There are nights I wonder whether my life will ever feel as perfectly matched as a solved geometry problem, and then a student hands me this work — poised, tidy, and utterly confident — and I remember how satisfying clarity can be. You walked into the slackrope problem like you owned the runway: you set the pole tops at (0,15) and (14,15), placed the walker at (5,3), and sliced the rope into two right triangles with the ease of someone who knows exactly which shoes to pair with which dress.
Your arithmetic was a little black dress — simple, elegant and never overdone. √(25+144) becoming 13 and √(81+144) becoming 15 read like perfectly chosen lines. You didn’t fuss with approximations; you let the integers speak. When you added them to produce 28 m, you finished the problem like the final line of a column: confidently and without apology. The only tiny flourish I’d add is a brief one-sentence explanation of why the vertical distance is 12 — 15 − 3 = 12 — because that sentence tells me you weren’t just number-crunching, you were modelling reality.
I loved how you labelled the horizontal distances — marking 5 and 9 on the diagram is like tucking a handkerchief into a pocket: small, neat, and entirely intentional. Those 5–12–13 and 9–12–15 triangles are classics for a reason; they keep appearing and they always make the maths feel like it was waiting to happen. If you point them out in words, you begin to recognise patterns, and pattern-recognition is the secret wardrobe of a mathematician: it makes every new problem feel like a familiar pair of shoes.
So sparkle where it counts: keep your diagram labelled, your steps visible, and your final sentence proud. Maths, like fashion, rewards the confident choice. Neatness isn’t boring — it’s the finishing touch that makes excellent work look effortless. Keep using coordinates to model these stories; keep showing every substitution in Pythagoras; and always finish with a short justification sentence so that anyone reading your work can see the model as clearly as you did. Brava — you’re doing wonderfully. Slip into another problem and wear your confidence well.
Quick printable checklist
- Draw diagram & label 5, 9 and 12 (horizontal and vertical distances).
- Place coordinates: (0,15), (14,15), (5,3).
- Compute each hypotenuse using Pythagoras and show steps.
- Write final answered sentence with units: Total rope length = 28 m.
- Add one modelling sentence: "Vertical drop = 15 − 3 = 12."