Cogito
Grade 6 Math · Chapter 8 · Lesson 1
Volume When the Edges Are Fractions
The formula does not change.
10 problems · about 18 minutes · 6.G.A.2
What this lesson teaches
The child finds the volume of a right rectangular prism with fractional edge lengths.
- Volume is length × width × height, fractions included.
- A box can be filled with smaller cubes and counted.
- The count and the formula always agree.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Breaking a Shape Apart: A 7 by 4 rectangle with a 3 by 2 piece removed. Area left?
Answer 22
Why 22 square units.
Review — Area of a Trapezoid: Parallel sides 5 and 11, height 4. Area?
Answer 32
Why 32 square units.
Warm Up
Straightforward practice. Get the method working first.
4 problemsA box 8 by 3 by 1/2. Volume?
Answer 12
Why 12 cubic units.
Does the volume formula change for fractional edges?
Answer No. It is still length × width × height.
Why The formula is the same.
A box 2 by 2 by 1/2. Volume?
Answer 2
Why 4 × 1/2.
A box 6 by 2 by 1/2. Volume?
Answer 6
Why 12 × 1/2.
Build It Up
The same ideas with more to keep track of.
2 problemsHow many cubes of side 1/3 fit inside one unit cube?
Answer 27
Why 3 along each edge.
A box 5 by 4 by 2. Volume?
Answer 40
Why 20 × 2.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Small Cube: How many cubes of side 1/2 fit inside one unit cube?
Answer 8
Why 8.
The Box: A box 4 by 3 by 1/2. What is its volume?
Answer 6 cubic units
Why 6 cubic units.