Short explanation (for a 10-year-old):
Imagine the two pole tops as two points. The horizontal distance between their bases is 45 ft. One pole is 39 ft tall and the other is 15 ft tall, so the difference in their heights is 39 − 15 = 24 ft. That makes a right-angled triangle where the two legs are 45 ft (across the ground) and 24 ft (vertical difference). The shortest rope between the tops is the hypotenuse of that right triangle.
Use the Pythagorean theorem: hypotenuse = sqrt(45^2 + 24^2) = sqrt(2025 + 576) = sqrt(2601) = 51. So the shortest rope is 51 ft.
Evaluation of the student answer:
Student wrote: sqrt 2601. This is correct. Numerically, sqrt(2601) = 51, so the rope must be 51 ft long. The answer is accurate. To be fully clear, the student should show intermediate steps (vertical difference 24, show 45^2 + 24^2), and include units (ft).
Rubric (4-point scale):
- 4 Excellent: Correct method (Pythagoras), clear steps shown, correct calculation, units included (e.g., 51 ft).
- 3 Good: Correct result and method but missing one small detail (like an intermediate step or units).
- 2 Satisfactory: Some understanding shown but incomplete method or arithmetic errors; final answer may be incorrect.
- 1 Needs improvement: Little or no correct method; misunderstanding of triangle structure or arithmetic.
Using this rubric, the student earns a 4 if they add the small missing details (intermediate steps and units). As written (just "sqrt 2601") it demonstrates correct reasoning but is brief — score: 3.5/4 (rounded to 4 with brief correction).
ACARA v9 mapping: Aligned with Measurement and Geometry content — applying the Pythagorean theorem to solve problems (Year 5/6 level).
Teacher comments (200 words, in a Nigella Lawson cadence):
In the warm hush of a kitchen on a gentle afternoon, I admire how you set your maths out — simple, direct and honest. You saw two upright poles, a slice of open air between them, and you reached for the shortest line that joins their tops. That clarity is like butter melting into hot toast. You used Pythagoras — a classic, reliable recipe — and arrived at sqrt(2601). It is a beautiful number, exact and satisfying: it is 51 feet. This solution shows that you understand horizontal and vertical differences, and how they combine to make a right-angled triangle. To lift this further, always write the intermediate steps: 39 − 15 = 24 (vertical difference), 45 (horizontal distance), then sqrt(45^2 + 24^2) = sqrt(2025 + 576) = sqrt(2601) = 51 ft. That small habit is like adding a pinch of salt — it clarifies and deepens flavour. For next time, check units and label your diagram. Mapped to ACARA v9: Measurement and Geometry — investigate lengths and apply the Pythagorean theorem to solve problems (Year 5/6). Keep cooking with numbers; your intuition is deliciously on cue. Well-presented work like this invites more complex recipes — try varied numbers and enjoy discovery today.