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Count Unit Cubes to Measure Volume

Students measure the volume of solid figures by counting the total number of unit cubes (cubic cm, cubic in, cubic ft, or improvised units) used to fill them. They practice counting cubes in organized layers to find total volume.

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Count Unit Cubes to Measure Volume

Grade 5 · Measuring Volume · question 1 of 3

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20 rungs. A star at the top.

What is the volume of the case in cubic inches?

Count the cubes.

How it is taught

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Volume is how many unit cubes fill a solid.

Counting by layers finds the cubic units inside.

Read it: Measuring volume in cubic units

To measure volume, count unit cubes: cubic centimeters, cubic inches or cubic feet. This box is 3 by 2 by 3: 6 cubes in a layer and 3 layers, so 18 cubes. Its volume is 18 cubic units.

  1. Count the bottom layer: 3 rows of 2 cubes is 6.
  2. Count the layers: the box is 3 cubes tall.
  3. Multiply: 6 × 3 = 18 cubes, in the unit each cube measures.

A cube 1 centimeter on each edge is 1 cubic centimeter, and a cube 1 inch on each edge is 1 cubic inch.

Every layer of a packed box holds the same number of cubes.

So 3 layers of 6 cubes is 6 × 3 = 18 cubes.

Volume is the cubes in one layer times the number of layers, in cubic units.

Counting the cubes on the faces you can see, and stopping there.

Count a whole layer, 3 × 2 = 6, then the layers: 6 × 3 = 18 cubes.

A box is 6 by 4 by 5. Its volume is ___ cubic units. — 120. The base is 6 × 4 = 24, and 5 layers: 24 × 5 = 120.

3 × 2 × 2 cube tower = 12 cubic cm

How much space does this little box take up? We can find out by counting the cubes inside it.

Grade 5 · Counting one-centimeter cubes layer by layer

Here's a box built from small unit cubes, all the same size.

Each tiny cube is one cubic centimeter — that's our unit of volume.

Let's count layer by layer. Start with the bottom layer.

Three cubes across, two cubes deep — that's six cubes on the bottom.

Now the top layer, sitting right on top of the first one.

Same shape: another six cubes.

Two layers of six. Six plus six equals twelve.

The volume of the box is twelve cubic centimeters. Nice counting!

Now you try. Count every cube that fills this box. What is the volume?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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