Cogito
Grade 5 Math · Chapter 6 · Lesson 3
Area with Fractional Sides
A rectangle that is part of a unit wide.
10 problems · about 15 minutes · 5.NF.B.4
What this lesson teaches
The child finds the area of a rectangle with fractional side lengths.
- Area is length × width, fractions included.
- Multiply the tops, then the bottoms.
- A rectangle with sides under 1 has an area under both.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Multiplying as Scaling: What is 3/5 × 25?
Answer 15
Why 15.
Review — A Fraction of a Fraction: 3/4 × 2/5. What is the bottom number?
Answer 20
Why 6/20, which tidies to 3/10.
Warm Up
Straightforward practice. Get the method working first.
4 problems1/2 by 2/5. What is the bottom number of the area?
Answer 10
Why 2/10, which is 1/5.
How do you find the area of a rectangle?
Answer Length × width.
Why Area is always length × width.
1/3 by 1/5. What is the bottom number of the area?
Answer 15
Why 3 × 5.
2/3 by 1/2. What is the top number of the area?
Answer 2
Why 2 × 1.
Build It Up
The same ideas with more to keep track of.
2 problems3/5 by 2/3. What is the bottom number of the area?
Answer 15
Why 5 × 3.
Does the area formula change for fractional sides?
Answer No. It is still length × width.
Why Nothing about area changed.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Small Tile: A rectangle 1/2 by 1/4. What is the bottom number of its area?
Answer 8
Why 1/8 of a square unit.
The Garden Patch: A patch 3/4 m by 2/5 m. What is the bottom number of its area?
Answer 20
Why 6/20, which is 3/10 of a square metre.