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Day 14 · Rearrange a model to find the inputYear 8 Maths · T1 W3–4 · Day 14 lesson

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Year 8 / 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 · Sources and materials · Daily routes · Worked swaps · Fresh learner checks · Aids and text routes.

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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

Codes: AC9M8A01, AC9M8A03. Goal: rearrange C=8+5n, interpret n, and review a model assumption. Prepare: balance/rearrange mat.

  1. Launch · 2 min. A fictional club kit has an 8-token setup and 5 tokens per identical refill. n is a non-negative whole number of refills. Ask what C measures.
  2. Model · 5 min. From C=8+5n, subtract 8, divide by 5: n=(C−8)/5. For C=33, n=5; check 8+5×5=33. Not every C produces a valid whole refill count.
  3. Guided · 6 min. Given C=23, use the same form to get n=3. At C=24, calculation gives 16/5=3.2, outside this whole-refill model; discuss a possible unmodelled fee, not fractional refills.
  4. Practice · 6 min. D14-A/B/C use different fictional linear models; each finds an input, checks by substitution and states a domain/omitted-condition limit.
  5. Exit · 4 min. In C=8+5n, what would C=8 mean? n=0 refills; only setup tokens. A real club may have other conditions.
  6. Note · 2 min. If inverse order is swapped, substitute the candidate in the original. Keep algebra and model interpretation as separate evidence.

Later: Day14 extra tests a total that cannot represent a whole refill.

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