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Day 18 · An inequality describes many allowed inputsYear 8 Maths · T1 W3–4 · Day 18 lesson

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Year 8 / Mathematics / Term 1 / Weeks 03 04

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

Open for this lesson: Pack guide · Sources and materials · Daily routes · Worked swaps · Fresh learner checks · Aids and text routes.

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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.

Learner prompts

Codes: AC9M8A02, AC9M8A03. Goal: solve a one-variable inequality and interpret its whole-number boundary. Prepare: graph/number-line board.

  1. Launch · 2 min. A fictional poster desk has 9 setup points and 5 points per poster, with 34 points available. Let n be whole posters, n≥0.
  2. Model · 5 min. 9+5n≤34 means within cap. Subtract 9, divide by positive 5: n≤5. Allowed whole counts are 0–5. Check boundary: at 5, 34; at 6, 39 and over cap.
  3. Guided · 6 min. Draw closed dot at 5 with arrow left on number line; cross out negative values by domain. On Cartesian axes, show y=9+5n and horizontal y=34; eligible integer points are at/below budget line.
  4. Practice · 6 min. D18-A/B/C: new cap and relation, each with algebra, two checks and a number-line/graph or precise verbal equivalent.
  5. Exit · 4 min. Explain the difference between ≤ and < at the boundary. With n=5, 9+5n≤34 true; 9+5n<34 false.
  6. Note · 2 min. If learner says only n=5, have them test n=4 and n=0; record solution set, not just maximum.

Later: Day18 extra uses an exclusive cap.

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