MA.5.GR.3 Geometric Reasoning
Solve problems involving the volume of right rectangular prisms.
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.
Clarification 1: Instruction emphasizes the conceptual understanding that volume is an attribute that can be measured for a three-dimensional figure. The measurement unit for volume is the volume of a unit cube, which is a cube with edge length of 1 unit.
Purpose and Instructional Strategies
This benchmark introduces volume to students. Their prior experiences with volume were restricted to liquid volume (also called capacity). The concept of volume should be extended from the understanding of area starting in Grade 3 (MA.3.GR.2.1), with the idea that a layer (such as the bottom of cube) can be built up by adding more layers of unit cubes. In Grade 6, (MA.6.GR.2.3) students solve volume problems involving rectangular prisms with fraction and decimal side lengths.
As students develop their understanding of volume, they recognize that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. This cube has a length of 1 unit, a width of 1 unit and a height of 1 unit and is called a cubic unit. This cubic unit is written with an exponent of 3 (e.g., in3, m3). Students connect this notation to their understanding of powers of 10 in our place value system (K12.MTR.5.1).
Common Misconceptions or Errors
Students may incorrectly fill figures to find volume with cubes. Students need to ensure there is no empty space included and that unit cubes are equally-sized and packed tightly in without overlaps.
Instructional Task 1
Molly is putting her cube-shaped blocks into their storage container after she finishes playing with her sister. The storage container is shaped like a right rectangular prism and she has a total of 120 blocks. The bottom layer of her storage container holds exactly 6 rows of 4 blocks each with no gaps or overlaps. The storage container holds exactly 6 layers of blocks with no gaps or overlaps.
Part A. Will all of Molly’s blocks fit in the storage container? Explain how you know using drawings and equations.
Part B. If there is enough room, determine how many more blocks Molly could fit in the storage container. If there is not enough room, determine how many blocks will not fit be able to fit in the storage container. Instructional Items
Instructional Item 1
What is the volume of the right rectangular prism?