5.MD.5: Volume by Multiplying and Adding
Also written as 5.MD.C.5 and CCSS.MATH.CONTENT.5.MD.C.5 · Cluster: Geometric measurement: understand concepts of volume.
The Official Wording
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Common Core State Standards, Grade 5, Measurement & Data · Read it at the source · Checked October 14, 2026
What 5.MD.5 Means in Plain English
Fifth graders stop counting cubes one by one. A 6 by 4 by 3 box has 24 cubes per layer and 3 layers, so V = 6 × 4 × 3 = 72 cubic units. An L-shape is split into two boxes and the volumes added.
Parts a and b are the formulas V = l × w × h and V = b × h, where b is the area of the base, the bottom layer counted in 5.MD.4. Part c makes volume additive. In 6th grade the edges turn fractional (6.G.2).
5.MD.5 I Can Statements
- I can find a box’s volume with V = l × w × h.
- I can explain why the formula matches counting the cubes.
- I can split an L-shaped solid into two boxes and add.
5.MD.5 Worked Example
An L-shaped storage unit: two boxes, two formulas, one sum. Every part of the standard in one problem.
A storage unit is shaped like an L. The main part is 8 ft long, 3 ft wide and 4 ft tall. At one end, a 3 ft by 3 ft by 4 ft section sticks out sideways to make the L. What is the total volume?
- Two boxes with no overlap. Draw the line where they meet and label each box with its three edges.Box A: 8 × 3 × 4, Box B: 3 × 3 × 4
- Box A: the base is 8 by 3, so 24 square feet, which means 24 cubes in each layer. It is 4 layers tall.V = b × h = 24 × 4 = 96 ft³
- Box B with the full formula.V = l × w × h = 3 × 3 × 4 = 36 ft³
- Volume is additive: the whole L holds what the two parts hold.96 + 36 = 132 ft³
Check it: Picture the full 8 by 6 by 4 box the L would fit inside: 192 cubic feet. The missing corner is 5 by 3 by 4, which is 60. 192 − 60 = 132, the same answer.
Common Mistakes with 5.MD.5
Adding the edges instead of multiplying
8 + 3 + 4 = 15 cubic feet
Try this: Go back to one layer: 8 by 3 is 24 cubes, not 11. Then stack 4 layers. Addition only joins separate boxes.
Multiplying every number in sight
8 × 3 × 4 × 3 × 3 × 4 = 3,456
Try this: Separate the boxes with a drawn line first. Each box gets exactly three edges and its own formula, and the two results are added.
Measuring the shared wall twice
Box A as 8 × 3 × 4 and box B as 6 × 3 × 4 because “it reaches across”
Try this: Shade the two parts in different colors on the drawing. Every cube belongs to one color only, so no edge is measured twice.
Where 5.MD.5 Fits
Practice 5.MD.5
Quick Check
- A box is 7 cm long, 5 cm wide and 3 cm tall. What is its volume?
- A prism has a base area of 18 square inches and a height of 4 inches. What is its volume?
- An L-shaped figure is made of a 5 × 2 × 2 box and a 3 × 2 × 2 box with no overlap. What is its volume?