Target: apply the addition principle only when alternatives are disjoint, and identify when overlap would break a plain sum. Prepare: D, sum-or-product chooser.
- Launch · 2 min. Ask whether one D participant books a studio session and an outdoor session. In this case they book exactly one.
- Model · 4 min. List S1/S2/S3 and O1/O2/O3/O4. Seven distinct outcomes exist:
3+4=7. A product 12 would describe a pair of sessions, not the stated one-session booking. - Guided reading · 5 min. Imagine one session appears on both lists. Name it once in the union; add the two list counts then subtract the shared option. Thus the addition principle's plain sum needs exclusive alternatives.
- Practice route · 7 min. Choose Day 4 route; count D, write the outcome set, and explain why 3×4 is wrong in this model.
- Audit · 4 min. Repair “OR always means add” using A: overlapping interests require subtraction.
- Exit · 3 min. “What would 3×4 count in D?” Expected: a pair with one studio and one outdoor session, a different decision.