Teacher: one page per learner, printed A4. Sections A, B and C
count toward Written Works; see assessment.md §1. The rectangles in §A
are drawn to true proportion, so a learner who cuts them correctly can see which pieces are
large before computing anything. The answer key at the foot of this page is screen-only and
will not appear on the printout.
A Cut each rectangle into four — then label every piece and total them
1. 1½ × 2¼
← 1½ wide →
height 2¼
total =
2. 2⅓ × 1½
← 2⅓ wide →
height 1½
total =
B Convert — fill in whichever side is empty
Mixed number
Improper fraction
2¾
17/5
17/6
5¾
1⅞
C Multiply — show the improper form, then the simplest form
Problem
As fractions
Simplest form
2½ × 1⅓
1½ × ⅔
4 × 1¾
2¼ × 1⅕
1⅔ × 2⅖
D Estimate, then compute
3⅞ × 2⅛
estimate exact
4⅓ × 1¾
estimate exact
E True or false?
2½ × 1⅓ = 2⅙
Every mixed number can be written as an improper fraction.
To multiply mixed numbers, multiply the wholes and the parts separately.
3 = 3/1
★ The challenge
? × ? = 4
Find two different pairs of mixed numbers whose product is exactly 4.
Show the improper form that proves it.
In one sentence, explain why 2½ × 1⅓ is not 2⅙.
Answer key — screen only, not printed. A1 · 1½ × 2¼ → pieces 1×2 = 2, ½×2 = 1, 1×¼ = ¼, ½×¼ = ⅛
· total 3⅜ (3/2 × 9/4 = 27/8) A2 · 2⅓ × 1½ → pieces 2×1 = 2, ⅓×1 = ⅓, 2×½ = 1, ⅓×½ = ⅙
· total 3½ (7/3 × 3/2 = 21/6) B · 11/4 · 3⅖ · 2⅚ · 23/4 · 15/8 |
C · 5/2×4/3 = 20/6 → 3⅓ · 3/2×2/3 = 6/6 → 1 · 4/1×7/4 = 28/4 → 7 ·
9/4×6/5 = 54/20 → 2 7/10 · 5/3×12/5 = 60/15 → 4 D · 1. estimate 4 × 2 = 8, exact 8 15/64 ·
2. estimate 4 × 2 = 8, exact 7 7/12 |
E · false · true · false · true ★ · 1. any two of 2½×1⅗, 1½×2⅔, 3⅓×1⅕, 2⅖×1⅔ ·
2. any wording carrying "it leaves out two of the four pieces". Item ★2 is the diagnostic. A learner can complete everything above it by rule and
still believe the part-by-part method works. Read the sentences first. Watch D2. The estimate is 8 but the exact answer is 7 7/12 — below the
estimate, because both factors rounded up. A learner who "corrects" their exact answer to
match the estimate has misunderstood what an estimate is for. Watch for erasers.