Target: derive and apply two-set inclusion–exclusion for a union when both set counts and overlap are known. Prepare: A, two-set map.
- Launch · 2 min. Ask whether 17 sketching plus 13 coding equals the number of distinct people in A.
- Model · 4 min. Put 5 “both” tokens into the overlapping region first. Then 12 sketch-only and 8 coding-only. The 5 both-tokens appeared in each set total, so
17+13−5=25distinct participants. - Guided reading · 5 min. Use A's universe 30. Add 5 neither; four disjoint regions sum 30. Explain why the neither group is outside the union, not inside a circle.
- Practice route · 7 min. Choose Day 1 route; give formula, region reconstruction, answer with people as units, and one sentence about double count.
- Audit · 4 min. Show claim
17+13=30 distinct participants. Learner locates the 5 repeated names and repairs to 25. - Exit · 3 min. “What is the union of A's two groups?” Expected: 25 people; 17+13−5 because both were counted twice.