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Common Core Math5th GradeMeasurement & Data

5.MD.4: Measure Volume by Counting Cubes

Also written as 5.MD.C.4 and CCSS.MATH.CONTENT.5.MD.C.4 · Cluster: Geometric measurement: understand concepts of volume.

Make 5.MD.4 Graph PaperAll 26 5th Grade Math Standards

The Official Wording

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Common Core State Standards, Grade 5, Measurement & Data · Read it at the source · Checked October 14, 2026

What 5.MD.4 Means in Plain English

Fifth graders find volume by counting. They fill a shoebox with inch cubes, or count the centimeter cubes in a drawn stack, or pack a bin with identical blocks and report the volume in those blocks. The unit is named every time: 36 cubic inches, or 15 blocks.

Counting is slow on purpose. Once students see that every layer of a box holds the same number of cubes, they are ready for the formula (5.MD.5). An L-shaped stack is counted in parts, the additive idea 5.MD.5c makes official. Fractional edges arrive in 6th grade (6.G.2).

5.MD.4 I Can Statements

  • I can count unit cubes to find the volume of a solid.
  • I can report volume in cubic centimeters, cubic inches or cubic feet.
  • I can measure volume with an improvised unit, like sugar cubes.

5.MD.4 Worked Example

An L-shaped stack of centimeter cubes: the kind of solid where counting carefully beats guessing.

Problem

A solid is built from centimeter cubes. The bottom layer is 5 cubes long and 2 cubes wide. On top of one end sits a second layer 2 cubes long and 2 cubes wide. What is the volume?

Counting cubes in an L-shaped stack
  1. Name the unit before counting: each cube is 1 cm on every edge, so each one is 1 cubic centimeter.1 cube = 1 cm³
  2. Count the bottom layer. It is a rectangle 5 cubes long and 2 wide, so count by rows of 5.Bottom layer: 5 + 5 = 10 cubes
  3. Count the top layer. It covers only one end: 2 cubes long and 2 wide.Top layer: 2 + 2 = 4 cubes
  4. Every cube is counted once and none is hidden, so add the layers.10 + 4 = 14 cubes
Answer14 cubic centimeters

Check it: Count by columns instead: 6 columns are 1 cube tall (6 cubes) and 4 columns are 2 cubes tall (8 cubes). 6 + 8 = 14, the same total.

Common Mistakes with 5.MD.4

Counting faces instead of cubes

Counting every visible square on the drawing and calling that the volume

Try this: Hand out real cubes and rebuild the drawing. One cube shows up to three faces, so counting squares overcounts badly.

Forgetting the cubes underneath

“The top layer has 4 cubes, plus the ones I can see in front”

Try this: Count layer by layer from the bottom, saying each total out loud: 10 in the bottom layer, then 4 more on top.

Dropping the unit

“The volume is 14”

Try this: Require the unit in every answer. 14 cubic centimeters and 14 cubic inches are very different boxes, and 14 alone is a count.

Where 5.MD.4 Fits

Comes Before5.MD.3Know what a unit cube is and what packing without gaps means.3.MD.6Measure area by counting unit squares.
Alongside5.MD.5Replace the counting with length × width × height, and add parts for L-shapes.
Comes Next6.G.2Find volume with fractional edge lengths by packing with fractional cubes.6.G.4Use nets to find surface area, the other measure of a box.

Practice 5.MD.4

Graph Paper GeneratorFree ToolCentimeter grid paper for drawing each layer of a stack to scale and counting the squares that become cubes.1 cm squaresLetterPrint
Make Graph Paper
Word Problem GeneratorFree ToolCounting stories: layers of cubes in a box, blocks in a bin, with the unit named in every answer.MeasurementVolumeGrade 5
Make Word Problems

Quick Check

  1. A box is packed with 3 layers of 12 inch cubes. What is its volume?
  2. A stack has a bottom layer of 8 centimeter cubes and a top layer of 3. What is its volume?
  3. A bin is filled with 20 identical blocks with no gaps. What is its volume, and in what unit?

5.MD.4: Other Names

5.MD.45.MD.C.4CCSS.MATH.CONTENT.5.MD.C.4

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.