Recognize Volume as an Attribute of Solid Figures

Students learn that volume is a measurable attribute of three-dimensional (solid) figures, just as area is an attribute of two-dimensional figures. They distinguish volume from area and perimeter and identify when volume is the appropriate measure.

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Grade 5 · Understanding Volume · question 1 of 3

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20 rungs. A star at the top.

How many cubes make up the block? Add them row by row.

Your answer:

How it is taught

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Volume is how much space a solid fills.

It is counted in cubic units.

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.

Count the cubes in the bottom layer: 3 rows of 2 is 6.
Count the layers: the box is 4 cubes tall.
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 2 by 3 by 6. Its volume is ___ cubic units. — 36. The base is 2 × 3 = 6, and 6 layers: 6 × 6 = 36.

Volume of a 2 × 2 × 2 box

Today we'll learn about volume. Volume tells us how much space fills the inside of a solid shape.

First, here's a flat rectangle. We measure flat shapes with AREA — by counting square units.

But this box is SOLID. It has length, width, AND height — so we measure the space inside it with VOLUME.

Grade 5 · Volume is the space inside a solid shape

Volume is measured in cubic units. One tiny cube like this — one across, one tall, one deep — is ONE cubic unit.

Look at the bottom layer of our box. It holds four cubic units.

Now stack another layer on top — that's four more cubic units.

Four plus four is eight. Eight cubic units fill the whole box.

Volume tells us the space inside a solid shape — here, eight cubic units. Great work!

Now you try. Find how much space fills this solid. 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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