5.MD.C.5.B
*This standard is part of a major cluster
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.
Unpacked
From 5.MD.C.5.B students learned to determine the volumes of several right rectangular prisms, using
cubic centimeters, cubic inches, and cubic feet. They learned to increasingly apply multiplicative reasoning
to determine volumes, looking for and making use of structure. That is, they understand that multiplying
the length times the width of a right rectangular prism can be viewed as determining how many cubes
would be in each layer if the prism were packed with or built up from unit cubes. They also learn that the
height of the prism tells how many layers would fit in the prism.
This standard calls for students to draw on the conceptual understanding built from 5.MD.3, 5.MD.4, and
5.MD.C.5.A standards to learn the formulas V= l x w x h and V= b x h for right rectangular prisms (b
represents the area of the base) as efficient methods for computing the number of unit cutes that pack a
right rectangular prism. They use these competencies to find the volumes of right rectangular prisms with
edges whole lengths are whole numbers and solve real-world and mathematical problems involving such
prisms.
* Students should have ample experiences to describe and reason about why the formula is true.
Specifically, that they are covering the bottom of a right rectangular prism (length x width) with multiple
layers (height). Therefore, the formula (l x w x h) is an extension of the formula for the area of a rectangle.
Students might describe the effectiveness of the formula
with this type of model.
Questions to check for understanding and increase rigor:
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How can you measure the volume of a container that is 5 ½ units x 2 ⅓ units x 1 ¾ units? What is
the approximate volume of this container? Explain your strategy with both numbers and a model.
A cereal box has a volume of 128.8 cubic centimeters. What could the dimensions be?
Looking at the dimensions of two different boxes with identical volumes, what do you notice
about multiples and factors?
8 in x 2 in x 2 in
4 in x 2 in x 4 in
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Can you use the relationship from the previous question to find a container with the same volume,
but different dimensions? For example, one prism has the dimensions of 6 x 8 x 2 with a volume
of 96 cubic units. Will halving and doubling of factors help you find a container with a volume of
96 cubic units, but different dimensions?
A box 2 centimeters high, 3 centimeters wide, and 5 centimeters long can hold 40 grams of clay. A
second box has twice the height, three times the width, and the same length as the first box. How
many grams of clay can it hold? (volume increases 6 times, so second box should hold 40 x 6 =
240 grams of clay)