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Day 7 — A gradient becomes a rate in contextYear 9 Maths · T1 W1–2 · Day 7 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: derive C(h)=12+6h from two invented plot points; blank plot, graph-check card.

  1. Notice, 3: Show fictional print-studio points (0,12),(4,36) with h in whole booked hours and C in credits/dollars. Ask for vertical change. Key: 24 credits.
  2. Model, 5: “Rate m=24/4=6 credits per hour; at h=0, cost is 12. Model C(h)=12+6h for 0–8 whole hours. This is a stipulated quote, not a live offer.” Plot points (0,12),(4,36),(8,60).
  3. Together, 8: Groups derive D(h) from (0,24),(4,40): rate 4, fixed 24. Plot (0,24),(4,40),(8,56). Name what the intercept and gradient mean in this fictional model.
  4. Try, 6: New bike-locker simulation E(h) through (0,5),(3,20). Key: rate 5 credits/hour, fixed 5, E(h)=5+5h; E(4)=25. Learner states domain if teacher stipulates h=0–6 whole hours.
  5. Check, 3: “Does a graph point at h=2.5 belong to our print-studio booking rule?” Key: no, booking domain is whole hours; a mathematical line can be drawn between points but a half-hour quote is not provided. If overlooked, re-read domain card.

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