Cogito
Grade 5 Math · Chapter 8 · Lesson 1
Measuring Volume by Counting Cubes
How many unit cubes fit inside?
10 problems · about 15 minutes · 5.MD.C.3, 5.MD.C.4
What this lesson teaches
The child measures the volume of a solid by counting unit cubes.
- Volume is how much space a solid fills.
- The unit is a cube 1 unit on every side.
- Counting the cubes gives the volume.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Dividing a Unit Fraction by a Whole Number: 1/3 ÷ 4. What is the bottom number?
Answer 12
Why 1/12.
Review — Dividing a Whole Number by a Unit Fraction: 6 ÷ 1/3 = ?
Answer 18
Why 18 thirds fit into 6.
Warm Up
Straightforward practice. Get the method working first.
4 problemsA box 4 by 4 by 2. How many cubes?
Answer 32
Why 32 cubic units.
Why is volume measured in cubic units?
Answer Because what is counted is cubes.
Why The unit being counted is a cube, so the answer is in cubic units.
A box 2 by 2 by 2. How many cubes?
Answer 8
Why 4 per layer, 2 layers.
A box 3 by 3 by 3. How many cubes?
Answer 27
Why 9 per layer, 3 layers.
Build It Up
The same ideas with more to keep track of.
2 problemsA box 6 by 2 by 3. How many cubes?
Answer 36
Why 12 per layer, 3 layers.
What is the volume of one unit cube?
Answer 1
Why One cubic unit.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Small Box: A box 3 by 2 by 4 cubes. How many cubes in all?
Answer 24 cubes
Why 24 cubic units.
The Layer: A box 5 by 4 cubes at the base. How many cubes in one layer?
Answer 20 cubes
Why 20 cubes per layer.