In this lesson, students complete their understanding of why the method of multiplying the edge lengths works for finding the volume of a prism with fractional edge lengths, just as it did for prisms with whole-number edge lengths. They use this understanding to find the volume of rectangular prisms given the edge lengths, and to find unknown edge lengths given the volume and other edge lengths.
Problems about rectangles and triangles in the previous two lessons involved three quantities: length, width, and area; or base, height, and area. Problems in this lesson involve four quantities: length, width, height, and volume. So finding an unknown quantity might involve an extra step, for example, multiplying two known lengths first and then dividing the volume by this product, or dividing the volume twice, once by each known length.
In tackling problems with increasing complexity and less scaffolding, students must make sense of problems and persevere in solving them (MP1).
- Apply dividing by fractions to calculate one edge length of a rectangular prism, given its volume and the other two edge lengths.
- Explain (orally, in writing, and using other representations) how to solve a problem involving the volume of a rectangular prism with fractional edge lengths.
- Generalize that it takes more smaller cubes or fewer larger cubes to fill the same volume.
Let’s look at the volume of prisms that have fractional measurements.
- I can solve volume problems that involve fractions.