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Day 7 — Solve and read the crossing pointYear 10 Maths · T1 W1–2 · Day 7 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.

Open for this lesson: Sources and materials · Check guide.

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Codes: AC9M10A02, AC9M10A04. Goal: solve a pair of linear equations and interpret the graphical intersection. Prepare: cost models and axes 0–12 months, $0–$1,300.

Predict · 2 min. “Plan A starts cheaper but rises faster. Could the totals meet?” Ask for a reasoned guess.
Model algebra · 5 min. Set 240+80m=480+50m. Subtract 50m and $240: 30m=240, so m=8. Substitute: both $880.
Graph check · 6 min. Plot each plan at m=0 and m=8; straight lines meet at (8 months, $880). Discuss that the intersection means equal modelled cost, not equal service quality.
Independent comparison · 7 min. Compare m=6: A $720, B $780, so A cheaper by $60. Compare m=10: A $1,040, B $980, so B cheaper by $60. Ask why ordering reverses.
Error check · 3 min. Show 30m=240 → m=30/240. Repair the inverse operation and substitute to test 8.
Exit · 2 min. Everyone states the crossing coordinate with both units and one model limit.

Access: tactile crossing lines or paired value table; demonstrate equality by substitution without demanding visual graph reading.

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