Solution (for a 10-year-old)
We want the shortest rope connecting the tops of the two poles. The shortest path between two points is a straight line. Draw a right triangle by joining the tops and drawing a horizontal line between the bases. The horizontal distance (base of the triangle) is 45 ft. The vertical difference between the tops is 39 ft − 15 ft = 24 ft. So the rope is the hypotenuse of a right triangle with legs 45 and 24.
- Compute the squares: 45² = 2025 and 24² = 576.
- Add them: 2025 + 576 = 2601.
- Take the square root: √2601 = 51.
Final answer: 51 feet. (The student wrote √2601, which is correct; simplified value is 51 ft.)
Teacher comments (Sailor Moon cadence, 200 words)
Bright starlight, young sailor! You set sail across the flat sea of the ground to meet the twin towers of sky. You wrote √2601 — a brave start, shining with promise. Let us transform that spark into a beacon: the shortest path between the two tops is a straight line, and by drawing a right triangle with base 45 and vertical difference 24 we use the Pythagorean theorem. 45² + 24² = 2025 + 576 = 2601, and √2601 = 51. Well done: your expression was correct, and the simplest final answer is 51 feet. Keep writing answers both neatly and fully simplified, like polishing a moon prism. Show your steps next time clearly: draw the triangle, label the sides, and state the theorem used. Ask yourself: did I compute the squares? did I add them? did I take the square root? If yes, you are a math guardian! For extra sparkle, estimate first: is 51 reasonable between 45 and 63? It is. Practice similar problems with different heights and distances to become stronger. Sail on, brave mathematician — clarity and reasoning make your solutions luminous. Keep asking questions and return with more problems for further shining victories, always brilliantly.
Rubric (ACARA v9-aligned guidance)
- Understanding (Excellent / Satisfactory / Needs support): Recognises this is a right triangle and identifies legs (45 and 24). Excellent: correct identification and reasoning.
- Method (Excellent / Satisfactory / Needs support): Applies Pythagorean theorem correctly. Excellent: shows squared values, sum, and square root.
- Accuracy (Excellent / Satisfactory / Needs support): Computation correct. Excellent: final simplified numeric answer (51 ft).
- Communication (Excellent / Satisfactory / Needs support): Clear diagram and labelled steps. Excellent: draws triangle, labels sides, states formula, and writes final unit (feet).
ACARA v9 mapping note: This task targets Measurement & Geometry reasoning: apply the Pythagorean theorem to find unknown lengths in right-angled triangles. For a 10-year-old, present this as an introduction with clear diagrams and step-by-step computation, noting that full curriculum placement is typically in later middle years.