Now that you are familiar with the problem-solving standard and some of its aspects, we'd like you to apply it. Middle school teacher Ruth Ann Duncan wants to evaluate how well students in her combined seventh- and eighth-grade math class understand how to find the volume of a container.

How does problem solving fit into this picture? First, consider a problem similar to the one Ms. Duncan sets for her students: At home, use one standard sheet of paper (8 1/2" x 11") to make the largest possible closed container. Think about the different types of containers you can make.

Note: You have a set surface area and want to find the maximum volume.

As you work through the problem, keep the following questions in mind:

• Which surface is the base?
• Which is the side?
• Which is the top?

  Explore the solution and consider some reflection questions