Cogito
Grade 5 Math · Chapter 6 · Lesson 1
A Fraction of a Fraction
Cut it, then cut the piece again.
10 problems · about 16 minutes · 5.NF.B.4
What this lesson teaches
The child multiplies a fraction by a fraction and explains the result with an area model.
- "Of" means multiply.
- Multiply the top numbers, then the bottom numbers.
- A piece of a piece is smaller than either.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Line Plots and Fraction Data: 5 beakers at 2/8 litre. How many eighths in all?
Answer 10
Why 10/8 litres.
Review — Judging an Answer with Benchmarks: About how much is 8/9 + 1/10? Nearest whole number.
Answer 1
Why About 1.
Warm Up
Straightforward practice. Get the method working first.
4 problems3/4 × 2/5. What is the bottom number?
Answer 20
Why 6/20, which tidies to 3/10.
What does "of" mean in "1/2 of 1/3"?
Answer Multiply.
Why "Of" is a multiplication.
1/2 × 1/4. What is the bottom number?
Answer 8
Why 2 × 4.
2/3 × 1/5. What is the top number?
Answer 2
Why 2 × 1.
Build It Up
The same ideas with more to keep track of.
2 problems2/3 × 1/5. What is the bottom number?
Answer 15
Why 3 × 5.
Is 1/2 × 1/3 bigger or smaller than 1/3?
Answer Smaller.
Why A piece of a piece.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsHalf of a Third: 1/2 × 1/3. What is the bottom number of the answer?
Answer 6
Why 1/6.
The Cake: 1/4 of 2/3. What is the top number of the answer, before tidying?
Answer 2
Why 2/12, which is 1/6.