NY Next Generation Math NY-5.MD.5.a
The Standard
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.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students pack right rectangular prisms with unit cubes and connect the cube count to multiplying whole-number edge lengths. They also connect layers to multiplying the base area by the height.
What Mastery Looks Like
- A student packs a 5-by-3-by-4 prism and explains that each layer has 15 cubes and there are four layers. The student verifies 15 times 4 and 5 times 3 times 4 both equal 60 cubic units.
Common Misconceptions
- Students may count only cubes along the edges or leave gaps inside a model. They may multiply the base perimeter by the height instead of the base area.
How to Assess It
- Give students unit cubes and a 4-by-3-by-2 prism frame. Ask them to pack it and show why the cube count equals both edge-length multiplication and base-area times height.
Lesson moves
Ways to Teach It
Pack a transparent rectangular-prism container in complete cube layers and record cubes per layer, layer count, and total volume.
Ask students why multiplying base area by height counts every unit cube exactly once.
Play model-formula match with packed prisms, edge lengths, base areas, heights, and cubic-unit volumes.
Determine how many unit-cube packages fill a whole-number rectangular storage box.
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Printable NY-5.MD.5.a Worksheet
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- NY-5.MD.5.b
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 ...
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