Term 1 · Week 7 · Multiplying fractions, whole numbers and mixed numbers
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For the teacher. This is for a learner reading 2½ as 2 × ½, or converting it to 3/2. It is not a shortened copy of
worksheet.html — it is a different route to the same competency, starting further
back. Task 4 is the first mixed-number product on worksheet.html. Show each worked example first and let the learner copy the
method, never the answer. If task 1 will not come: If task 1 will not come, cut real halves — paper circles are enough — and count them aloud. The conversion is a count, not a rule.
1Read it aloud
— targets 2½ read as two times a half
Say: “Read it. I want to hear the word AND.”
Worked example.2½ is read two AND a half. The plus is invisible: 2 + ½.
3¼ is read ______________________________ and means ______ + ______
1⅔ is read ______________________________ and means ______ + ______
2Count the halves
— targets 2½ = 3/2 — the wrong denominator source
Say: “How many halves altogether? Count them.”
Worked example. 2½: two wholes cut in half is 4 halves, plus the 1 already there = 5 halves = 5/2.
3½ = ______ halves = ______/2
2⅓ = ______ thirds = ______/3
1¾ = ______ quarters = ______/4
3A fraction of a whole number
— targets reaching for a rule before a picture
Say: “Of means take that much of it.”
Worked example. ½ × 6: half of 6 is 3. Draw 6 dots and split them if you need to.
½ × 8 = ______
⅓ × 9 = ______
⅔ × 6 = ______
4Mixed number times a fraction
— targets multiplying wholes and parts separately
Say: “Convert first. Then multiply straight across.”
Worked example. 1½ × ⅔ = 3/2 × 2/3 = 6/6 = 1. A whole-number answer is allowed.
2½ × ½ = ______
1⅓ × ¾ = ______
Circle one: an answer that comes out a whole number is always wrong / sometimes right
Answer key — not printed on the learner's copy
three and a quarter, 3 + ¼ · one and two thirds, 1 + ⅔