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Day 8 · Check all seven regionsYear 11 Specialist Maths · T1 W1–2 · Day 8 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: verify a three-set calculation by reconstructing exclusive regions and rejecting an impossible set claim. Prepare: C, region audit mat.

  1. Launch · 2 min. Ask whether a pairwise count of 4 in C means exactly 4 in A&R only. It includes the two all-three people.
  2. Model · 4 min. Centre 2; pair-only 2,1,3; single-only 7,4,3. Sum seven regions 2+2+1+3+7+4+3=22. Check A=7+2+1+2=12, R=4+2+3+2=11, C=3+1+3+2=9.
  3. Guided reading · 5 min. Propose a claim “A&R pair=1 while all-three=2.” It is impossible because the triple is a subset of the pair. Discuss that nonnegative region counts and subset bounds are reasonableness tests.
  4. Practice route · 7 min. Choose Day 8 route; reconstruct and audit C's seven cells and reject one impossible alternative.
  5. Audit · 4 min. Repair any negative region by revisiting whether a pair count already includes all-three.
  6. Exit · 3 min. “What is the minimum possible size of each pair in C?” Expected: at least 2, the all-three count; actual pairs are 4,3,5.

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