Lesson objective: Recognize that rectangular prisms can be built with unit cubes with fractional edge lengths which then can be used to determine the prisms' dimensions and volume.

Students bring prior knowledge of packing prisms with unit cubes to find the volume from CCSS 5.MD.C.3.b. This prior knowledge is extended to unit cubes with fractional edges as students build prisms with half-inch cubes. A conceptual challenge students may encounter is thinking that a half-inch cube has a volume of 1/2 cubic inch rather than 1/8 cubic inch.

The concept is developed through clues given about various prisms built with half-inch cubes, which students can recreate at their desks with cm cubes or unit cubes from Base Ten Blocks. These clues and models help students realize that edge lengths of prisms are not always whole-unit measures but the prisms can still be filled with unit cubes.

This work helps students deepen their understanding of equivalence because prisms can be packed with whole-unit or fractional-unit cubes to find the volume, or we can use a volume formula. They are all means of arriving at the same answer. This work also helps students deepen their understanding of operations because students will use multiplication of whole numbers and fractions to find the volume of rectangular prisms.

Students engage in Mathematical Practice 4 (Model with Mathematics) as they use unit cubes that represent 'half-inch' cubes to model prisms with different attributes. The models show the mathematical relationships between the volumes and dimensions of the prisms.

Students also engage in Mathematical Practice 7 (Look for and Make use of Structure) as they use unit cubes to visualize why eight half-inch cubes have a volume of one cubic inch.

**Key vocabulary:**

- cubic units
- height
- length
- volume
- width

**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 64 cubes each)