In this problem, we engage our students in a consideration of how others might have approached the Pizza Crusts problem, probing them to identify the misconceptions about perimeter and area.

When the students respond to this problem, we heavily focused on the visual, asking students to show us. We say, "Can you show it in a picture? Can you prove it?" We wanted both the answer and for students to connect it to a picture. We wanted them to tell us not only that the answer is 9, but where the 9 comes from. We wanted students to see that the 9 comes from the square units inside the geometric shape. We kept asking, "Can you explain your response?"

I remember when we were planning this lesson, we really wanted the class to focus on proof because it was a geometry lesson, and when they get to high school geometry there is a real emphasis on proof. We wanted them to connect the process and the explanation to prepare them for that.

When the students respond to this problem, we heavily focused on the visual, asking students to show us. We say, "Can you show it in a picture? Can you prove it?" We wanted both the answer and for students to connect it to a picture. We wanted them to tell us not only that the answer is 9, but where the 9 comes from. We wanted students to see that the 9 comes from the square units inside the geometric shape. We kept asking, "Can you explain your response?"

I remember when we were planning this lesson, we really wanted the class to focus on proof because it was a geometry lesson, and when they get to high school geometry there is a real emphasis on proof. We wanted them to connect the process and the explanation to prepare them for that.