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Day 6 — Turn a plan into an equationYear 10 Maths · T1 W1–2 · Day 6 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: AC9M10A04. Goal: formulate two linear cost models and say what their terms mean. Prepare: fictional device-hire brief and cost board.

  1. Context · 2 min. “This is an invented adult household choice. We compare simplified totals; no one will disclose personal finances or make a purchase.”
  2. Model · 5 min. Let m be complete months. A(m)=240+80m: $240 setup at m=0, then $80 per month. Write the parallel B(m)=480+50m with units.
  3. Guide values · 6 min. Calculate at m=4: A $560, B $680. Ask why multiplying setup by four would be wrong.
  4. Represent · 7 min. Learners fill a small table for m=0,4,8,10. Use the cost board or text table. Check A/B at 8 both $880 but with different cost structures.
  5. Assumptions · 3 min. Name one omitted real condition: actual contract, device quality, repair outcome or exit terms. Fixed monthly increase makes these linear within the model; real total cost might not be.
  6. Exit · 2 min. Everyone explains the 50 and 480 in B(m) and gives B(4) = $680.

Access: money counters, large text, typed formula, speech/AAC explanation. Do not require a home-budget story from the learner.

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