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Day 2 · Solve for an unseen overlapYear 11 Specialist Maths · T1 W1–2 · Day 2 lesson

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Year 11 / Specialist 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 · Practice cases · 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

Target: rearrange the two-set rule to recover an intersection and then a neither count. Prepare: B, two-set map.

  1. Launch · 2 min. State B's 40 total and 32 in at least one. Ask how many lie outside both before any formula.
  2. Model · 4 min. 32=22+18−x, so x=8 in both. Neither 40−32=8. Regions drawing-only 14 and music-only 10; 14+8+10+8=40.
  3. Guided reading · 5 min. Ask why 22+18−32 is nonnegative and no larger than 18. Use 8 to verify each original set count.
  4. Practice route · 7 min. Choose Day 2 route; solve x and neither, then use a four-region audit to explain reasonableness.
  5. Audit · 4 min. Repair “8 neither means 8 both.” They happen to match numerically here but represent different regions; a changed universe would separate them.
  6. Exit · 3 min. “Does B's 8 both include either single-group region?” Expected: no; those 8 selected both activities.

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