What do you notice? What do you wonder?

Yellow rectangular prism with blue rectangular prism on top. Yellow prism: 10 feet by unknown width by 3 feet. Blue prism: 5 feet by 3 feet by 5 feet. Height of both prisms combined is 8 feet. 

Blue rectangular prism joined on the side with a yellow rectangular prism. Blue prism: 5 feet by 3 feet by 8 feet. Yellow prism: 5 feet by 3 feet by 3 feet. 

1. Write an expression to represent the volume of the figure in unit cubes.

   

   Figure composed of two attached prisms. First prism: 3 cubes by 5 cubes by 5 cubes. Second prism: 2 cubes by 2 cubes by 5 cubes.

2. Compare expressions with your partner.
   1. How are they alike?
   2. How are they different?
3. If they are the same, try to find another way to represent the volume.

1. Find the volume by decomposing the figure in as many ways as you can. Show your thinking. Organize your work so it can be followed by others.

   

   6-sided rectangular prism. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, 10 feet. Right side rises 4 feet, then goes left 6 feet, goes up an unlabeled distance, then goes left an unlabeled distance, then goes down 8 feet. Width shown as 3 feet.  

   

   6-sided rectangular prism. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, 10 feet. Right side rises 4 feet, then goes left 6 feet, goes up an unlabeled distance, then goes left an unlabeled distance, then goes down 8 feet. Width shown as 3 feet.  

2. Write expressions to represent each way that you decompose the figure.

3. Mai used this expression to find the volume of the figure:

   .

   Use the diagram to interpret Mai's expression. Show your thinking. Organize your work so it can be followed by others.

   

   6-sided rectangular prism. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, 10 feet. Right side rises 4 feet, then goes left 6 feet, goes up an unlabeled length, then goes left an unlabeled length, then goes down 8 feet. Width shown as 3 feet.