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Understand Unit Cubes and Cubic Units

Students learn that a unit cube has side lengths of 1 unit and a volume of 1 cubic unit. They understand that cubic units (cubic cm, cubic in, cubic ft) are the standard units used to measure volume.

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Understand Unit Cubes and Cubic Units

Grade 5 · Understanding Volume · question 1 of 3

0 of 20

20 rungs. A star at the top.

Count the inch cubes in the case for its volume.

Count the cubes.

How it is taught

0:00 of 3:18

A unit cube has edges of 1 unit.

Its volume is 1 cubic unit.

Read it: Volume: cubes that fill a box

Volume is how much space a solid takes up, counted in unit cubes. This box is packed 3 by 2 by 4: 6 cubes in a layer and 4 layers, so 24 cubes. Its volume is 24 cubic units.

  1. Count the cubes in the bottom layer: 3 rows of 2 is 6.
  2. Count the layers: the box is 4 cubes tall.
  3. Multiply: 6 cubes in a layer × 4 layers = 24 unit cubes.

A unit cube is 1 unit long, 1 unit wide and 1 unit tall: 1 cubic unit.

A box packed with no gaps and no overlaps holds the same number of cubes in every layer.

So the volume is the cubes in a layer times the layers: 6 × 4 = 24 cubic units.

Volume is the number of unit cubes that fill a solid, with no gaps and no overlaps.

Counting only the cubes on the front, and missing the ones hidden behind them.

Count a whole layer, 3 × 2 = 6, then every layer: 6 × 4 = 24, the hidden cubes too.

A box is 4 by 5 by 6. Its volume is ___ cubic units. — 120. The base is 4 × 5 = 20, and 6 layers: 20 × 6 = 120.

What is a unit cube?

How do we measure the space inside a box? We use a special tool — the unit cube!

A unit cube is a small cube where every side is exactly one unit long.

Grade 5 · Measuring volume with unit cubes

This side is one unit long.

This side is also one unit.

And the depth going back — also one unit.

Because every side is one unit, this cube has a volume of one cubic unit.

If we measure in centimeters, it's one cubic centimeter. We can also use cubic inches or cubic feet.

Now here's a bigger cube. How many unit cubes fit inside it?

Count with me — one, two, three, four in front, and four more hiding behind. Eight unit cubes!

So this cube has a volume of eight cubic units. Volume tells us how many unit cubes fit inside!

Now you try. Count the cubes. Type how much space is inside. 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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