Follow-up TPS for generalization (Think–Pair–Share leading into theory):

• Prompt (Think, 1–2 min): “For the 6-letter set {v,o,i,a,p,u} where letters are all different, how many 3-letter combinations can you form if repetition is not allowed? Write your reasoning.”
• Pair (3–5 min): “Explain to your partner why the count is 654, and produce one example set of three letters and show an explicit ordering.”
• Share (5–7 min): Ask pairs to place one example and the multiplication expression on the OneNote page. Teacher highlights the model: ‘number of options for position 1 × options for position 2 × options for position 3’ and links to the earlier concept: elementary case & favorable elementary case.

Differentiation & extensions:

• Support: permit one-step guided checklist, or let weaker students use colored counters to represent choices.
• Stretch: ask “If repetition is allowed, how does the count change?” (666) or “How many unique words can be formed that are not valid English words but count as different orderings?” (same count)
• Challenge: use Think–Pair–Square to compare permutations vs combinations, or to examine cases when letters repeat (e.g., A A B).

Assessment and recording:

• Require each pair to submit one clean solution on the OneNote “Homework answers” page (teacher’s model solutions page) and one student to briefly explain the model on camera or board.
• Formative check: teacher notes pairs’ reasoning mistakes on a simple checklist (OneNote or paper) — categories: counting error, logic gap, misapplied repetition rule.

Protocols for recording and using model solutions (consistent with your existing practice)

• Bring pre-made model solutions to class (as you do): put them on OneNote “Homework answers” or “Example assignments” tabs.
• When pairs share, add the chosen pair’s answer to the OneNote “Pair Answers” page. Leave it visible for the rest of the session.
• Keep both student responses and teacher model visible side-by-side — students compare and annotate their work.
• If using a table camera, photograph pair work and paste to OneNote; annotate and return to the group later.
• Who records? Assign students to be recorders on rotation OR let the teacher capture representative answers. Rotate to share the workload and to build student ownership.