In this Grade 6 lesson from Big Ideas Math Course 1, students learn how to find the volume of rectangular prisms with fractional edge lengths using the formulas V = Bh and V = ℓwh. Through hands-on activities, they explore how unit cubes can be subdivided to reason about fractional dimensions, then apply multiplication of fractions to calculate volumes. The lesson also introduces the formula V = s³ for cubes and connects volume concepts to real-world problems.
Section 1
Volume
We use cubic units to measure the volume or amount of space inside a three-dimensional object. For a box with dimensions length , width , and height , the volume is found by multiplying the three dimensions.
Section 2
Volume with Fractional Edge Lengths
To find the volume of a real-world object shaped like a rectangular prism, multiply its length, width, and height. The dimensions can be whole numbers, fractions, or mixed numbers.
Section 3
Finding a Missing Dimension
When the volume and two dimensions of a rectangular prism are known, the missing dimension can be found by rearranging the volume formula: .
Solve for the unknown dimension by dividing the volume by the product of the known dimensions.
Expand to review the lesson summary and core properties.
Section 1
Volume
We use cubic units to measure the volume or amount of space inside a three-dimensional object. For a box with dimensions length , width , and height , the volume is found by multiplying the three dimensions.
Section 2
Volume with Fractional Edge Lengths
To find the volume of a real-world object shaped like a rectangular prism, multiply its length, width, and height. The dimensions can be whole numbers, fractions, or mixed numbers.
Section 3
Finding a Missing Dimension
When the volume and two dimensions of a rectangular prism are known, the missing dimension can be found by rearranging the volume formula: .
Solve for the unknown dimension by dividing the volume by the product of the known dimensions.