Teacher: one page per learner, printed A4. Sections A, B and C
count toward Written Works; see assessment.md §1. The two shadings are
distinguished by hatch direction, so the sheet still works photocopied in grey.
The answer key at the foot of this page is screen-only and will not appear on the printout.
A Shade the grid — across for the first fraction, down for the second
first fraction (shade whole columns)second fraction (shade whole rows)= the product
1. ¾ × ⅔
shaded twice of =
2. ⅗ × ½
shaded twice of =
B Multiply — give the product, then the simplest form
Problem
Product
Simplest form
½ × ⅓
⅔ × ¾
⅗ × ½
⅞ × ⅔
¾ × ⅘
C Word problems — underline the word that tells you to multiply
⅔ of a ₱900 allowance is saved. ¼ of the savings goes on load.
How much goes on load?
A ribbon is ¾ m long. ⅔ of it is used.
How much is used?
D Which is smaller?
⅘ or ⅘ × ⅔
⅗ × 1 or ⅗
½ × ½ or ½ × ⅓
⅔ × ¾ or ⅔ × ⅘
E True or false?
Multiplying always makes it bigger.
½ × ⅓ is the same as ⅓ × ½.
To multiply fractions, add the denominators.
Two proper fractions give a product smaller than both.
★ The challenge
? × ? = ¼
Find two different pairs of fractions, both smaller than 1, whose product is
exactly ¼. and
In one sentence, explain why ⅘ × ⅓ is smaller than ⅓.
Answer key — screen only, not printed. A · 1. 6 of 12 = 6/12 = ½ · 2. 3 of 10 = 3/10 |
B · 1/6 → ⅙ · 6/12 → ½ · 3/10 → 3/10 · 14/24 → 7/12 · 12/20 → ⅗ C · 1. ⅔ × 900 = 600, then ¼ × 600 = ₱150 · 2. ⅔ × ¾ = ½ m.
The word to underline is of in both |
D · ⅘ × ⅔ · neither — they are equal · ½ × ⅓ · ⅔ × ¾ |
E · false · true · false · true ★ · 1. any two of ½×½, ¾×⅓, ⅔×⅜, ⅖×⅝, ⅚×3/10, ⅞×2/7 ·
2. any wording showing that ⅘ is less than one whole, so taking ⅘ of something leaves
less than you started with.
Item ★2 is the diagnostic — a learner can complete everything above it by rule and
still believe multiplication makes numbers bigger. Read the sentences first. Watch D2. "Neither" is the answer; ⅗ × 1 = ⅗. Learners who pick one of them have
applied "multiplying makes it smaller" without noticing the multiplier is exactly 1.