Correct solution (brief):
Vertical displacement: 1/2 + 1/2 = 1 km. Horizontal displacement: 3/4 km. Distance from start = √(1^2 + (3/4)^2) = √(1 + 9/16) = √(25/16) = 5/4 km. The student wrote √(5/4) which equals √5 / 2 ≈ 1.118 km — not 1.25 km. The student’s answer is incorrect.
200‑word teacher comment (Amy Chua cadence):
You must be precise. The method is simple; sloppy notation cost you the correct answer. Add the vertical distances: 1/2 + 1/2 = 1 km. Treat the horizontal 3/4 km as the other leg of the right triangle. Apply Pythagoras without hesitation: distance = √(1^2 + (3/4)^2). Show your arithmetic: 1 + 9/16 = 25/16, so the square root is 5/4 km. Your written answer √(5/4) is algebraically different and therefore wrong. If you mean 5/4, write 5/4 or 1.25 km. Always include units. A correct solution needs three things: (1) identification of legs, (2) correct substitution into the formula, (3) simplification and units. Practice these three steps until they are automatic. Repeat similar problems varying fractions and decimals so your simplification and notation become flawless. I expect neat, complete answers next time — not ambiguous roots.
ACARA v9 mapping (conceptual):
- Mathematics — Measurement & Geometry: Apply Pythagoras' theorem to find lengths in right‑angled contexts and represent displacement in plane geometry.
- Skills: interpreting vector-like displacement, algebraic substitution, fraction arithmetic, simplifying square roots.
Rubric (summarised):
- Excellent (A): Correct distance 5/4 km; clear steps showing legs, substitution into √(a^2+b^2), correct simplification and units.
- Satisfactory (C): Correct method shown but minor arithmetic or notation slips; final value correct or clearly recoverable.
- Needs Improvement (E): Missing or incorrect identification of legs, wrong substitution, incorrect simplification (e.g. wrote √(5/4) instead of 5/4), or missing units.
Next steps: Practice three similar problems, write full steps each time, and check simplification. I will not accept ambiguous notation.