Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Measuring volume starts with counting. Students fill or build solids with cubes and count them, recording the result in cubic centimeters, cubic inches, cubic feet or an improvised unit such as a sugar cube. The unit must match the size of the cube used: centimeter cubes give cubic centimeters, and inch cubes give cubic inches.
Counting becomes smarter as students notice structure. Rather than counting every cube one by one, they count the cubes in one layer and then the number of layers, or count rows within a layer. This organized counting is what later becomes multiplying length, width and height. Using improvised units also teaches an important lesson about measurement: the same box can hold 60 small cubes or 8 large ones, so a volume is meaningless without its unit, and smaller units give larger counts. Choosing a sensible unit for the object, cubic feet for a closet but cubic centimeters for a jewelry box, is part of the skill too.
A student who says a box holds 8 cubes and another who says 64 may both be right if they used different cubes. The unit must always be stated.
When counting by faces, cubes on edges and corners can be counted twice. Counting by layers avoids this.
60 cubic centimeters is much smaller than 8 cubic feet. Comparing volumes requires the same unit.
In drawings, students sometimes count the cubes they can see on top and stop. Every layer must be included.
A box is filled with centimeter cubes. The bottom layer has 5 rows of 6 cubes and the box is 4 layers tall. What is the volume?
Answer: The volume is 120 cubic centimeters.
Provide open boxes and a mix of centimeter and inch cubes. Groups measure the same box with both and compare their counts, which leads naturally to a discussion about units. Then move to pictures where students must reason about hidden cubes.
Tests show cube figures or partly filled boxes and ask how many cubes fill them, or ask which unit was used given two different counts for the same box.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 36 (also accepted: 36 cubic inches)
One layer has 3 × 3 = 9 cubes. Four layers have 9 × 4 = 36 cubes, so the volume is 36 cubic inches.
Answer: C) Cubic feet
A classroom is large, so cubic feet give a manageable number. Square feet measure floor area, not volume.
Answer: D) The large cubes are bigger units, so fewer fit
The box's volume is the same; the units differ. Bigger units mean fewer of them fit.
Answer: 42 (also accepted: 42 cubes)
One layer holds 2 × 7 = 14 cubes and there are 3 layers, so 14 × 3 = 42 cubes fill the box.
Answer: 9 (also accepted: 9 cubic centimeters)
Each cube is 1 cubic centimeter and there are 9 of them.
A full lesson with slides, activities and an exit ticket on measuring volume by counting cubes, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.MD.C.4 with an answer key, ready in about a minute.
Make a worksheet →Turn measuring volume by counting cubes into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Any non-standard cube used for counting volume, such as small wooden blocks. They help students understand that volume depends on the unit chosen.
Counting by layers (cubes in one layer times number of layers) is the same as multiplying base area by height, which 5.MD.C.5 formalizes.