Lesson objective: Find the dimensions and volumes of all unique prisms possible built with a given number of half-unit cubes.

This lesson helps to build the procedural skill of finding the dimensions and volumes of rectangular prisms built with fractional edge-length cubes. Half-inch cubes placed along rulers are used in this lesson because the image supports the conversion between a prism’s cube edge lengths with its measured edge lengths. This work develops students' understanding that the formula for volume of a rectangular prism is connected to filling the prism with unit cubes.

Students engage in Mathematical Practice 5 (Use Appropriate Tools Strategically) as they use formulas and unit cubes to help them find volume. Students will use cm cubes to represent ‘half inch’ cubes to determine the edge lengths of the prisms and then choose to use those edge lengths or the number of half-inch cubes to find the volume of the prism.

**Key vocabulary:**

- cubic units
- edge lengths
- half-inch cube
- rectangular prism
- volume

**Special materials needed:**

- cm cubes or unit cubes from Base Ten Blocks to represent ‘half-inch’ cubes (enough for each student/pair/group to have 60 cubes each)