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Day 8 — Compare two lines and a break-even pointYear 9 Maths · T1 W1–2 · Day 8 lesson

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Year 9 / Mathematics / Term 1 / Weeks 01 02

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

Open for this lesson: Pack guide.

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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.

Goal/materials: solve/interprete intersection and conditional advantage; C and D model card, plot and calculator.

  1. Notice, 3: Retrieve C(0)=12 and D(0)=24. Key: C lower at 0 whole hours under stated model.
  2. Model, 5: “Set 12+6h=24+4h. Subtract 4h and 12: 2h=12 ⇒ h=6. Both cost 48 at h=6.” Check by substituting both rules and matching graph intersection.
  3. Together, 8: At h=3, C=30, D=36; at h=8, C=60, D=56. Ask which is lower for each and why the steeper C line becomes higher after 6. Avoid ‘better for everyone’.
  4. Try, 6: Fresh training-room simulator F(h)=8+7h and G(h)=20+4h, h whole 0–7. Key: equal at h=4, both 36; at h=2, F22 vs G28, F lower. Learner checks algebra and context.
  5. Check, 3: “Which of C or D is lower at h=6?” Key: neither; equal at 48. If learner uses only starting charge, plot/compute h=6 and say ‘depends on h’.

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