Term 1 · Week 7 · Multiplying a fraction by a fraction
NameDate
For the teacher. This is for a learner who answers ½ × ½ = ½, or who expects every product to be bigger. 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 grid on worksheet.html, reached from folding rather than from notation. 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, fold real paper instead of drawing. The overlap has to be felt before it can be counted.
1Shade twice, count once
— targets counting only the second shading
Say: “Shade across. Now shade up and down. Which squares have both?”
Worked example. A 2 × 2 grid, one half shaded across and one half shaded down: 1 square of 4 carries both marks.
Grid A is 2 by 2. Shade half across, half down. Squares with both marks: ______ of ______
Grid B is 2 by 4. Shade half across, one quarter down. Squares with both: ______ of ______
Grid C is 3 by 3. Shade one third across, one third down. Squares with both: ______ of ______
2Write what you counted
— targets the leap from picture to symbol
Say: “Say the count as a fraction. Bottom first.”
Worked example. 1 square of 4 → ¼. The bottom is how many pieces the whole was cut into.
Grid A: ______ Grid B: ______ Grid C: ______
Write grid A as a multiplication: ______ × ______ = ______
3Without the grid
— targets dependence on drawing every time
Say: “You already know what the grid would do.”
Worked example. ½ × ⅓: the whole ends in 2 × 3 = 6 pieces, and 1 × 1 = 1 carries both marks → 1/6.
½ × ⅕ = ______
⅓ × ¼ = ______
⅔ × ½ = ______
4Bigger or smaller?
— targets "multiplying makes it bigger"
Say: “Answer before you work it out.”
Worked example. ¾ × ½: half of something is always less than the something, so the answer is smaller than ¾. It is 3/8.
⅔ × ¾ will be (circle one) bigger / smaller than ¾. It is ______
Write in words why multiplying by a fraction below 1 makes an answer smaller: ______________________
Answer key — not printed on the learner's copy
A: 1 of 4 · B: 1 of 8 · C: 1 of 9
¼, ⅛, 1/9 · ½ × ½ = ¼
1/10 · 1/12 · 2/6 (= ⅓)
smaller · 6/12 = ½ · because you are taking only part of it