Cogito
Grade 6 Math · Chapter 8 · Lesson 2
Packing with Fraction Cubes
Counting the little cubes that fit.
10 problems · about 18 minutes · 6.G.A.2
What this lesson teaches
The child finds the volume of a prism with fractional edges by counting unit-fraction cubes.
- A box with fractional edges can be packed with unit-fraction cubes.
- Eight half-unit cubes fill one unit cube; twenty-seven third-unit cubes do.
- Counting cubes and multiplying edges give the same volume.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Volume When the Edges Are Fractions: A box 8 by 3 by 1/2. Volume?
Answer 12
Why 12 cubic units.
Review — 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.
3 problems32 half-unit cubes. Volume in cubic units?
Answer 4
Why 4 cubic units.
4 by 2 by 2 small cubes. How many cubes?
Answer 16
Why 4 × 2 × 2.
16 half-unit cubes. Volume in cubic units?
Answer 2
Why 16 ÷ 8.
Build It Up
The same ideas with more to keep track of.
2 problemsHow many third-unit cubes fill one unit cube?
Answer 27
Why 3 × 3 × 3.
A box 2 by 3 by 4 units. Volume?
Answer 24
Why Multiply the three edges.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Small Cubes: How many cubes with half-unit edges fill one whole unit cube?
Answer 8
Why 8.
The Packed Box: A box holds 24 half-unit cubes. What is its volume in cubic units?
Answer 3
Why 3 cubic units.