Higher Order Thinking Complete the table. Show some different ways that a rectangular prism can have a volume of 12 cubic units.
11. © MP.7 Look for Relationships Look across each now of the table. What pattern do you see?
Number of
Cubes Long
Number of
Cubes Which
Number di
Cubes Ta
Use the table to help. How many unit cubes are needed to make a model of à rectangular prism that is 4 units long 3 units wide and 2 units tall? (length 1 2 2 2 3 3 3 4 6) (width 1 2 3 1 2 1) (height 12 3 1 1 1)
One way a rectangular prism can have a volume of 12 cubic units is by having dimensions of 1 unit by 2 units by 6 units. Another way is 1 unit by 3 units by 4 units. Lastly, it can also be 2 units by 2 units by 3 units.
Looking across each row of the table, we see that there is a pattern in which the total number of cubes needed to make a rectangular prism with a volume of 12 cubic units increases as the dimensions of the prism increase.
To find how many unit cubes are needed to make a model of a rectangular prism with dimensions of 4 units long, 3 units wide, and 2 units tall, we can look at the table. By adding up the number of cubes in each row, we find that the total number of unit cubes needed is 24.