Term 1 Week 7 · Multiplying fractions, whole numbers and mixed numbers · CG Quarter 1, competency 11
| # | The misconception | Where it shows | What to do |
|---|---|---|---|
| 1 | Multiply the wholes, multiply the parts, put them together | §B, by design | Nothing, until §C.1. The rectangle is the correction |
| 2 | 2½ means 2 × ½ | Conversion at §C.3 gives 1 instead of 5/2 | "Read it aloud. Two AND a half. The plus is invisible but it is there." |
| 3 | 2½ = 3/2 — wrong denominator source | §C.3 | Count halves physically: two whole circles cut in half is four, plus one is five |
| 4 | A whole-number answer must be wrong | §C.4, rows 2, 3 and 5 | Have the learner explain their working. It is correct. Say so plainly |
| 5 | The answer must be bigger, because there are whole numbers | §C.4, row 2 (1½ × ⅔ = 1) | Grade 5's rule still holds: ⅔ is less than one, so it pulls the answer down |
| 6 | Improper fractions are errors to be fixed immediately | Learners convert back to mixed before multiplying | "Leave it improper until the very end. It is easier to multiply and there is nothing wrong with it." |
| 7 | Simplifying is optional | 20/6 left unsimplified | Not today's battle. Accept 20/6 with a note; Day 3 is where simplifying is taught properly |