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Day 8 — A budget makes an inequalityYear 10 Maths · T1 W1–2 · Day 8 lesson

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Year 10 / Term 1 / Weeks 01 02 / Mathematics

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

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Codes: AC9M10A02, AC9M10A04. Goal: solve and interpret linear inequalities for whole-month commitments. Prepare: $1,000 practice cap, cost models.

  1. Ask · 2 min. “If the fictional cap is $1,000, does a solution of 9.5 months mean 9.5 payments are possible?” No: the model uses complete months.
  2. Model A · 5 min. 240+80m ≤ 1000 → 80m ≤ 760 → m ≤ 9.5; with whole months 0–12, maximum 9. Check A(9)=$960 and A(10)=$1,040.
  3. Guide B · 6 min. 480+50m ≤ 1000 → 50m ≤ 520 → m ≤ 10.4; maximum 10. Check B(10)=$980 and B(11)=$1,030.
  4. Apply · 7 min. A fictional planner needs 10 complete months. Students decide which plan fits the stated cap: B only, within this model. They must say what the calculation does not judge.
  5. Challenge · 3 min. Ask whether A at m=9 and B at m=10 is a fair price-only comparison for the same service duration. No; compare the same horizon.
  6. Exit · 2 min. Everyone writes A's maximum whole months and the pair of values that check the boundary.

Access: number-line inequality and table route; calculator as check after symbolic steps; oral explanation of whole-month boundary accepted.