Code: AC9M6N02. Goal: use a factor-array explanation to classify 1, 2, 12 and 16. Prepare: blank factor-array lab or text/tactile route, 16 counters/cards.
- Launch · 2 min. Ask whether a number can be both square and composite; collect a tentative answer without rating speed.
- Model · 5 min. Arrange 12 as
1 × 12,2 × 6,3 × 4; show factor pairs. Twelve has more than two positive factors, so composite. Arrange 16 as4 × 4; it is square and composite (2 × 8also works). Say why 1 has just one positive factor and 2 has exactly two. - Guided · 6 min. Learners use tiles, drawn cells or spoken factor pairs for 1 and 2, then check 16. Name the rule greater than 1 for both prime and composite. Do not call “odd” a prime test.
- Choice · 6 min. One D11-A/B/C route: each requires a correct classification and factor evidence.
- Exit · 4 min. “Is 16 prime because its square array looks special?” No, since 16 has factors 1, 2, 4, 8, 16. “Is 1 prime?” No, it has one positive factor.
- Note · 2 min. Save factor language and a diagram/spoken explanation. If labels are memorised without proof, reteach with a new array.
Home/extension: Make 12 with bottle-cap substitutes or sketch boxes; no purchase. Extension: explain why every positive square above 1 has at least factors 1, n, n² (for n>1, these are distinct).