CCSS.Math.Content.5.MD.C.5b
The Standard
Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the volume of rectangular prisms with whole-number dimensions. They multiply length, width, and height, or multiply the base area by the height, in word problems.
What Mastery Looks Like
- Students choose the needed dimensions, multiply accurately, and label answers in cubic units. They can use either the three edge lengths or the area of the base and the height.
Common Misconceptions
- Students may add the dimensions instead of multiplying them. They may treat the base value as one edge length rather than the area of a face, or label volume with square units.
How to Assess It
- Give this exit ticket: “A rectangular box is 8 cm long, 3 cm wide, and 5 cm high. Find its volume and show your calculation.”
Lesson moves
Ways to Teach It
Build a 3-by-4-by-2 prism with unit cubes, count the cubes, then verify the volume by multiplication.
Write an explanation for why multiplying the base area by the number of layers gives a prism’s volume.
Play a matching game with cards showing prism dimensions, base areas, calculations, and volumes.
Compare two shipping boxes with labeled whole-number dimensions and decide which holds more, showing both volume calculations.
Free download
Printable 5.MD.C.5b Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.5.MD.C.5b, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.5.MD.C.5a
Packing cubes and relating layers to l × w × h supports using volume formulas accurately in problem situations.
- CCSS.Math.Content.3.MD.C.7b
Volume formulas for rectangular prisms use the rectangle’s length times width as base area, then multiply by height.
- CCSS.Math.Content.4.NBT.B.5
Multi-digit multiplication and area models support calculating prism volumes and seeing volume as repeated layers of rectangular area.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.5.MD.C.5c
Students must calculate each rectangular prism’s volume before adding the non-overlapping parts of a composite solid.
- CCSS.Math.Content.6.G.A.2
Students extend prism volume formulas and base-area reasoning from whole-number edges to fractional edge lengths and unit-fraction cubes.
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