Term 1 Week 7 · Multiplying a fraction by a fraction · CG Quarter 1, competency 8
| # | The misconception | Where it shows | What to do |
|---|---|---|---|
| 1 | "Multiplying makes it bigger" | §A and §B, by design | Nothing, until §D. It must be disproved by the learner's own hands |
| 2 | Counting only the second shading | §C.1 — learner says ½ × ½ = ½ | "Point at the piece with both marks. Only that one counts." |
| 3 | Adding instead of multiplying | ½ × ½ = 1 (or 2/4 read as "two quarters, so a half") | Go back to the sheet. "Show me the piece worth 1. There isn't one — the whole sheet is 1." |
| 4 | Multiplying the denominators but adding the numerators | ⅔ × ¾ = 5/12 | Count the doubly-shaded cells physically. Five cannot be produced by any count |
| 5 | Believing the order matters | Learner refolds because they "did it backwards" | The side-by-side comparison in §C.3 |
| 6 | Reading ⅔ × ¾ = ½ as an error | §C.4, last row | Have the pair explain their count to the class. Their count is right |
| 7 | "Of" means share out | §D onward | Deferred to Day 5, where it is taught directly. Do not open it today |