Volume by packing cubes: 5th grade math lesson

What this lesson shows

A box packed layer by layer: 6 rows of 4, 6 layers, 144 cubic units.

The worked example

The lesson works this one step by step: 4 × 6 × 6. Then your kid tries one like it on paper.

The steps

Count one layer
Count the layers
Multiply for the volume

Helping at home

Count the cubes in the bottom layer first: rows times cubes in a row. Then multiply by the number of layers. The count is the volume, in cubic units.

If your kid gets stuck

Count one layer, then the layers.

Watch it with Lux

With Lux, this lesson is a narrated video and a printed page your kid works on. Then Lux helps with the same math on their own worksheet, one question at a time.

See how Lux works

Standards

Common Core 5.MD.C.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Common Core 5.MD.C.5a
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

Matches a standard in all 50 states and DCSee each state's code

Alabama MA19.5.18a, MA19.5.19a
Alaska 5.MD.5.c, 5.MD.6, 5.MD.7.a
Arizona 5.MD.C.4, 5.MD.C.5.a
Arkansas 5.GM.3
California 5.MD.C.4, 5.MD.C.5
Colorado 5.MD.C.4, 5.MD.C.5.a
Connecticut 5.MD.C.4, 5.MD.C.5
Delaware 5.MD.C.4, 5.MD.C.5
District of Columbia 5.MD.C.4, 5.MD.C.5
Florida MA.5.GR.3.1
Georgia 5.GSR.8.3
Hawaii 5.MD.C.4, 5.MD.C.5
Idaho 5.MD.C.4, 5.MD.C.5.a
Illinois 5.MD.C.4, 5.MD.C.5
Indiana 5.M.4
Iowa 5.MD.C.4, 5.MD.C.5.a
Kansas 5.MD.4, 5.MD.5.a
Kentucky KY.5.MD.4, KY.5.MD.5.a
Louisiana 5.MD.C.4, 5.MD.C.5.a
Maine 5.MD.C.4, 5.MD.C.5a
Maryland 5.GR.C.4, 5.GR.C.5.a
Massachusetts 5.MD.C.4, 5.MD.C.5.a
Michigan 5.MD.C.4, 5.MD.C.5
Minnesota 5.3.2.2, 5.3.2.3
Mississippi 5.MD.4, 5.MD.5.a
Missouri 5.GM.B.4.b
Montana MT.5.MD.4, 5.D3.5, MT.5.MD.5.a
Nebraska 5.G.1.b, 5.G.4.c, 5.G.4.d
Nevada 5.MD.C.4, 5.MD.C.5
New Hampshire 5.MD.C.4, 5.MD.C.5
New Jersey 5.M.B.3, 5.M.B.4a
New Mexico 5.MD.C.4, 5.MD.C.5
New York NY-5.MD.4, NY-5.MD.5.a
North Carolina NC.5.MD.4, NC.5.MD.5.a
North Dakota 5.GM.M.3
Ohio 5.MD.4, 5.MD.5.a
Oklahoma 3.GM.1.2, 3.GM.2.3, 4.GM.2.3, 5.GM.2.1
Oregon 5.GM.D.5, 5.GM.D.6, 5.GM.D.7
Pennsylvania CC.2.4.5.A.5
Rhode Island 5.MD.C.4, 5.MD.C.5.a
South Carolina 5.MGSR.1.2
South Dakota 5.MD.C.4, 5.MD.C.5.a, 5.MD.C.5.b
Tennessee 5.MD.C.4, 5.MD.C.5.a
Texas 111.7.b.6.B, 111.7.b.4.G
Utah 5.MD.4, 5.MD.5.a
Vermont 5.MD.C.4, 5.MD.C.5
Virginia 5.MG.2c, 5.MG.2d
Washington 5.MD.C.4, 5.MD.C.5
West Virginia M.5.20, M.5.21, M.5.22
Wisconsin M.5.MD.C.4, M.5.MD.C.3, M.5.MD.C.5
Wyoming 5.MD.5a, 5.MDP.5.A

Volume by packing cubes