Development draft · local review needed

Day 13 · A residual measures mismatch, not cause · AC9M10ST03…Year 10 Maths · T1 W3–4 · Day 13 lesson

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Year 10 / Mathematics / Term 1 / Weeks 03 04

Part of the full two-week lesson sequence. Check the pack guide and taught point before teaching.

Open for this lesson: Pack guide · Fresh learner checks · Aids and text routes.

Teacher copy: This page may include teaching prompts or answer keys. Answer keys in this public library can be viewed by anyone. Give learners a clean prompt, use checks as formative evidence, and change a case locally when prior access matters.

Learner prompts

Goal: compare all nine drafts to the proposed M(x)=3x+2 and keep claims scoped. 25 = 2 + 5 + 7 + 7 + 4.

0–2: Say the line is the notebook's proposal, not a fitted physical law.
2–7: At x=2 the line predicts 8; drafts C/D list 8/9, residuals 0/+1. Define record − model, with clue-icon units.
7–14: Learners fill the residual ruler: A–I residuals 0,+1,0,+1,0,+1,0,+1,+5. At x=5, 22−17=+5. Discuss how one chosen line can describe the x=1–4 cluster but miss I.
14–21: Routes: move 0/+1/+5 number tiles next to draft letters; fill a table and calculate by hand; use a calculator then explain one subtraction orally/AAC. Every route states the sign and unit.
21–25: Exit “Does +5 show why I differs?” Look-for: no, only numerical mismatch. Next move: change a causal sentence into a question about the design decision.

Another setting: Invented picture-book scene counts versus caption counts. Optional/home: find one residual from an original mini-table.

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