**Task Narrative**

Students generate dimensions of rectangular prisms with volume 60 ft^3. They make a model with linker cubes and then create the footprint of the actual prism on the floor of the classroom and hold up ropes to illustrate the height. The mathematical purpose of this task is to realize that different prisms can have the same volume and to deepen the understanding of volume as the number of unit cubes that fill a 3-d space. As students work, take note of groups that use different dimensions.

**Launch**

Have linker cubes or other cubes available for students to make a plan for how to stack the boxes in a rectangular prism. Other materials needed: painter’s tape to mark the outline on the floor and rope to illustrate the height.

**Task Statement**

The library is getting painted over the summer and they need to store 60 (50?) boxes that are 1 ft3 in our classroom. We need to figure out where to put them. The overall configuration has to be a rectangular prism. Use the linker cubes to make a plan for how to stack the boxes. Be prepared to share your reasoning with the class.

**Task Solution**

60 = 10*3*2=10*2*3=2*3*10=3*2*10=2*10*3=3*10*2 (length, width, height - some more practical than others, ceiling might not be 10 ft high)

60 = 5*3*4 (or any permutation)

60 = 6*2*5 (or any permutation)

60 = 60*1*1 (probably not feasible)

60 = 30*2*1 (not feasible?, not efficient)

60 = 15*2*2 (not feasible?, not efficient)

**Synthesis**

After students make their linker cube models, have groups that used different dimensions show their models and demonstrate that it gives the correct volume. Keep track of the different numerical equations on the board.

Some configurations are mathematically possible but would not fit into the classroom. Discuss the pros and cons of different configurations for this particular purpose - too high is hard to stack, too low requires too much floor space. Have students agree on one or two and as a class mark the footprint of the prism on the floor of the classroom using painter’s tape. Have student hold up rope or stand in the corners and illustrate how high the prism would be. Make a point that the entire inside of this prism would be solidly filled with boxes.