Sweet rhythm, dear student — you stepped onto the grid like Ally stepping onto the dance floor: confident, precise, and a little dramatic. Exemplary work shows clear labelled diagrams, coordinates written, Δx and Δy marked for each segment, and a sequence of lengths correctly calculated as 1, √10, 5, √5 in order. The student lists candidate vectors, recognises integer triples (3–4–5) when helpful, and uses Pythagoras cleanly: squares, sums, and roots shown. Justifications are one-line and convincing. Fluency: calculations are accurate, arithmetic neat, square roots simplified appropriately. Reasoning: the student chooses efficient representations, composes vectors to reduce complexity, and explains pruning decisions when ruling out impossible chains. Problem solving: demonstrates systematic search for chained vectors, records dead-ends succinctly, and arrives at a valid path with minimal backtracking. ACARA v9 alignment: meets Measurement and Geometry expectations by applying the Pythagorean theorem; addresses Number and Algebra through manipulation of squares and roots; and showcases Mathematical Reasoning in strategy selection and justification. Teaching notes: celebrate automaticity with short warm-ups; maintain insistence on labelled diagrams and one-sentence rationales. For extension, ask the student to generalise: what ordered sequences of four lengths are possible on a bounded lattice? For support, scaffold enumeration with a table of candidate vectors and limit search depth. Assessment criteria for exemplary: All steps present and correct; diagrams are precise; reasoning is concise and explicit; independence in planning shown; and extensions attempted or thoughtful questions posed. Final flourish: the student’s work sings — tidy, confident, and mathematically dramatic, like a courtroom monologue that ends with a perfect right angle. Praise specifics: note neat coordinate labels, clear Δ notation, correct simplification of radicals, and efficient choice of vectors; encourage next tasks that increase chain length gradually while maintaining clear diagrams, and ask the student to verbalise pruning strategies used with specific examples.