Imagine the grid like a glossy baking tray and the points like plump cherries you must skewer in a specific order. We have five marked points: (5,0), (6,3), (1,3), (6,2), (3,2). The required consecutive distances are 1, √10, 5, √5. Use the Pythagorean theorem: distance between (x1,y1) and (x2,y2) is √((x2−x1)²+(y2−y1)²).
First a quick sniff for the pair that gives distance 1: only (6,3) and (6,2) are one unit apart (dx=0, dy=1 → √1 = 1). That suggests starting at (6,2) then (6,3). From (6,3) we need √10 next. Check (6,3) → (5,0): dx=−1, dy=−3 → (1+9)=10 → √10. Lovely. From (5,0) we need 5 next: (5,0) → (1,3): dx=−4, dy=3 → (16+9)=25 → √25 = 5. Finally from (1,3) we need √5: (1,3) → (3,2): dx=2, dy=−1 → (4+1)=5 → √5.
So the complete path (in order) is: (6,2) → (6,3) → (5,0) → (1,3) → (3,2). Check each step by squaring the differences to verify 1, 10, 25, 5. Draw straight segments between these points on your 7×7 grid to create the continuous path.
Teacher comments & exemplar rubric (ACARA v9) — in a Nigella cadence:
Imagine guiding each student like a slow stirring of a rich sauce: warm, precise, and celebratory. Learning focus (ACARA v9): use the Pythagorean theorem to find distances between points on a coordinate grid; select and order coordinates to match given lengths; justify reasoning with calculations. Success criteria: correct distances (show squared differences), clear sequence that matches 1, √10, 5, √5, and neat diagram.
Exemplars: Excellent (A): All distances correctly calculated with Pythagorean steps shown; path order valid; reasoning clear and concise; diagram labelled; reflection on why each step works. Satisfactory (B): Most distances correct; correct path found with minor omissions in justification or labelling. Developing (C): Some correct calculations; path attempt incomplete or incorrect ordering; limited explanations. Beginning (D): Major errors in distance calculation; no clear path; reasoning absent.
Feedback suggestions: praise accurate calculation, prompt students to square differences, check arithmetic, and encourage neat sketches. Extension tasks: challenge confident students to create their own Pythagorean Path; differentiate by providing hints: compute squared distances first, then match lengths. Celebrate curiosity, taste triumph, and keep practising. Return to methods with delight.