Target: use the multiplication principle for two independent stages and explain why each first choice pairs with each second choice. Prepare: E, branch tree aid.
- Launch · 2 min. Ask whether one finished E label needs a shape, a caption, or both.
- Model · 4 min. Draw three shape branches; each has four caption leaves. Count leaves as 4+4+4=12, then compress to
3×4=12. - Guided reading · 5 min. Check a particular shape pairs with all four captions. Ask what changes if a shape cannot take one caption: the uniform product would overcount and branch counts must be added instead.
- Practice route · 7 min. Choose Day 6 route; show a tree/table or grouping, product and justification, with “finished labels” as units.
- Audit · 4 min. Repair
3+4=7: it counts single choices from either list, not a two-part label. - Exit · 3 min. “Why is 3×4 valid for E?” Expected: every one of three shapes can pair with every one of four captions.