Pizza Cutting
How it works
Imagine that you're cutting a pizza. There are three rules for cutting:
Each cut must be a straight line.
Cuts must go crust to crust.
Cuts can cross each other but can't go exactly on top of each other.
However, cuts don't have to go through the center of the pizza, and pieces can be different sizes and shapes.
Given these rules, what are the different numbers of pieces you can make with 3 cuts? What about with 4 cuts? What is the maximum number of pieces you can make with 5 cuts? What about with 10 cuts?
In this activity, students first try to find all the different numbers of pieces they can make with 3 and 4 cuts. Then they try to figure out the maximum number of pieces they can make with 5 cuts and see if they can predict the maximum possible number of pieces with 10 cuts.
Why we like this activity
It’s fun! Students enjoy exploring the different ways to cut the pizza and making different numbers of pieces.
It helps students to develop spatial reasoning.
It helps students to develop algorithmic reasoning.
It requires students to engage in mathematical habits of mind:
- Finding and using strategies to make specific numbers of pieces with a given number of cuts
- Looking for patterns and making and testing predictions when exploring the maximum possible numbers of pieces with different numbers of cuts
It has a low floor and a high ceiling: Students can start exploring by trial and error, but finding all the different numbers of pieces (and, in particular, finding the maximum number of pieces) for a given number of cuts requires more careful strategizing, especially as the number of cuts increases.
