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Count Unit Cubes in Layered Structures

Students extend their cube-counting skills to structured rectangular prisms by counting cubes layer by layer. They use the layer structure to develop an efficient counting strategy that bridges to multiplication.

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Count Unit Cubes in Layered Structures

Grade 5 · Measuring Volume · question 1 of 3

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20 rungs. A star at the top.

The block is built solid from cubes. Count them.

Count the cubes.

How it is taught

0:00 of 3:08

Volume can be counted layer by layer.

Each identical layer has the same cube count.

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 5 by 3. Its volume is ___ cubic units. — 90. The base is 6 × 5 = 30, and 3 layers: 30 × 3 = 90.

Counting a 4 × 3 × 2 prism layer by layer

Let's count the unit cubes inside this rectangular prism — but the smart way, layer by layer.

Here's our shape, made of small unit cubes. Notice it's built from two equal layers stacked on top of each other.

Look at the bottom layer first. It's a flat slab of cubes, four across and three back.

Grade 5 · Counting cubes layer by layer

Each row in this layer has four cubes.

And there are three rows in the layer.

So one layer holds four times three — that's twelve cubes.

The top layer looks exactly the same. Same shape, same twelve cubes.

Two equal layers means twelve times two.

Twelve times two is twenty-four. Our prism has twenty-four unit cubes in all!

Now you try. Count the unit cubes in this solid. How many unit cubes?

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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