Pizza Cutting
How it works
Imagine that you're cutting a pizza. There are two rules for cutting:
Each cut must be a straight line.
Cuts can't start or stop in the middle of the pizza.
But cuts don't have to go through the center of the pizza, and pieces can be different sizes and shapes.
What are the different numbers of pieces you can make with 3 cuts? What is the maximum number of pieces you can make with 3 cuts? What about with 4 cuts? 5 cuts? 10 cuts?
In this activity, students explore making different numbers of pieces with different numbers of cuts. They strategize to make specific numbers of pieces, in particular the maximum number of pieces, and they explore the relationship between the number of cuts and the maximum number of pieces.
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 the maximum number 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 cutting pizzas by trial and error, but as the number of cuts increases, making the maximum number of pieces requires more careful strategizing.
