Teacher comment (100 words)
My dears, you’ve coaxed elegant geometry from a grid, noticing how right triangles hide like truffles beneath the surface. Use Pythagoras with gentle precision: square the legs, sum their sweetness, inhale the root. Trace possible paths slowly, check distances against 1, √10, 5, √5 in order, and savour each correct match. If a length resists, step back and try a different turn; sometimes the simplest route is the most delicious. Record your reasoning clearly so others can taste your logic. Celebrate neat sketches, accurate algebra, and the quiet thrill of a solved puzzle. Keep experimenting until your path sings brightly.
ACARA v9 alignment
- Mathematical content: Apply Pythagoras to solve problems with right-angled triangles and distances on grids.
- Working mathematically: Reasoning, choosing strategies, checking results and communicating solutions clearly.
Exemplar rubric (Nigella Lawson cadence)
Criteria: Understanding • Strategy & Reasoning • Accuracy • Communication & Representation
- Excellent (A): Understanding is sumptuous and complete; Pythagoras is applied confidently to every segment. Strategy is elegant and efficient, anticipating turns. Calculations are flawless; every distance matches the list in order. Diagram and notes are tidy and delectable, allowing another to follow your feast of logic.
- Proficient (B): Understanding is clear with minor hesitations. Strategy works well though one or two detours appear. Most calculations are correct; distances match with small checking. Diagram is neat and explanations are appetisingly clear.
- Developing (C): Partial understanding; Pythagoras is used but with occasional errors. Strategy is experimental and sometimes inefficient. Some distances are correct, others need rework. Diagram and working are present but need clearer labeling and explanation.
- Beginning (D): Understanding is limited; Pythagoras may be misapplied. Strategy is unclear or absent. Several distances are incorrect and calculations show gaps. Diagram is messy or missing key labels; reasoning is difficult to savour.
Teacher tip: encourage systematic checking of each leg by computing squared sums, sketching right triangles on the grid, and annotating lengths so the path reads like a recipe that anyone can follow.