Cogito
Grade 5 Math · Chapter 8 · Lesson 2
The Volume Formula
A shortcut for the count you can already do.
10 problems · about 15 minutes · 5.MD.C.5
What this lesson teaches
The child relates volume to multiplication and applies V = l × w × h and base area × height.
- Volume is length × width × height.
- It is also base area × height.
- Volumes of separate solids add together.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
1 problemReview — Measuring Volume by Counting Cubes: A box 4 by 4 by 2. How many cubes?
Answer 32
Why 32 cubic units.
Warm Up
Straightforward practice. Get the method working first.
4 problemsVolume of a 7 by 3 by 2 box?
Answer 42
Why 42 cubic units.
What does base area × height give?
Answer The volume.
Why One layer times how many layers gives the volume.
Volume of a 6 by 3 by 2 box?
Answer 36
Why 18 per layer.
Volume of a 5 by 5 by 4 box?
Answer 100
Why 25 per layer.
Build It Up
The same ideas with more to keep track of.
2 problemsVolume 48, base 4 by 2. What is the height?
Answer 6
Why 48 ÷ 8.
A base area of 15 and a height of 4. What is the volume?
Answer 60
Why 15 × 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsThe Crate: A crate 5 by 4 by 3. What is its volume?
Answer 60 cubic units
Why 60 cubic units.
The Missing Height: Volume 72, base 4 by 3. What is the height?
Answer 6
Why The height is 6.
The Two Boxes: Two boxes side by side, one 24 cubic units and one 18. What is the total volume?
Answer 42 cubic units
Why 42 cubic units.