In This Unit of Study…

The concept of volume extends from an understanding of area; the number of unit cubes covering the bottom layer are built up by adding layers on top until the solid is filled. Students reason that volume is the number of unit cubes needed to fill a solid figure without gaps or overlaps. As students develop their understanding of volume, they recognize that volume is measured in cubic units, represented by using an exponent of 3. Students use concrete objects, such as unit cubes, to measure volume. Through repeated practice, students come to see that the number of unit cubes needed to fill a right rectangular prism is equal to the product of its three edge lengths (length, width, and height) and also equal to the product of the area of the base and the height. Students describe and reason about why volume formulas work, and they apply these formulas as an efficient and accurate means of determining volume. When presented with a problem where one of the side lengths is unknown, students use the formula that includes a variable to represent the unknown value. To solve, students use the mathematical concept that division is the inverse operation of multiplication to reason that the cubic volume of a right rectangular prism can be divided by the product of the known values to arrive at the unknown value.

B.E.S.T. Benchmarks:

• MA.5.GR.3.1 Explore volume as an attribute of three-dimensional figures by packing them with unit cubes without gaps. Find the volume of a right rectangular prism with whole-number side lengths by counting unit cubes.
• MA.5.GR.3.2 Find the volume of a right rectangular prism with whole-number side lengths using a visual model and a formula.
• MA.5.GR.3.3 Solve real-world problems involving the volume of right rectangular prisms, including problems with an unknown edge length, with whole-number edge lengths using a visual model or a formula. Write an equation with a variable for the unknown to represent the problem.

Key Concepts:

• I can reason that volume is the number of unit cubes needed to fill a solid figure without gaps or overlaps.
• I can use concrete objects to measure volume.
• I can use unit cubes (with a length, width, and height of 1 unit) to measure volume.
• I can select appropriate-sized units for measuring volumes of varying sizes
• I can determine the volume of a rectangular prism.
• I can use a visual model and a formula for finding the volume of a rectangular prism.
• I can solve real-world problems involving the volume of right rectangular prisms.
• I can write an equation with a variable for the unknown to represent a problem with volume.