Brownie Points

How it works

Imagine that you have a brownie that you want to share with other people. To make sure everyone is happy with their piece, you want to cut the brownie into pieces that are the same size.

To help with this, imagine that there are grid lines like on the brownie below:

The goal then is to cut along the grid lines so that each piece has the same number of grid squares.

Is it possible to cut this brownie into 2 pieces so each piece has the same number of grid squares? 3 pieces? 4 pieces? 5 pieces? What if the brownie is 3 x 5 instead of 3 x 4?

Now imagine that you have a brownie with chocolate chips like the one below:

Now the goal is to cut the brownie into pieces so that each piece has the same number of squares AND the same number of chocolate chips.

Which numbers of pieces can you cut this brownie into?

In this activity, students start by trying to cut brownies into pieces that are the same size. They start with a 3 x 4 brownie before exploring other brownies that are different sizes. Then students explore brownies with chocolate chips, with the goal of cutting them into pieces so that each piece is the same size and has the same number of chocolate chips. This is a bit trickier!

Equal Size Pieces handout

Chocolate Chip Challenges handout 1

Chocolate Chip Challenges handout 2

Chocolate Chip Challenges handout 3

Why we like this activity

  • It’s fun! Students enjoy trying to figure out how to cut the brownies into different numbers of pieces.

  • It helps students to develop numerical reasoning.

  • It helps students to develop geometric reasoning.

  • It requires students to engage in mathematical habits of mind:

    • Using logic and finding and using strategies when trying to cut the brownies into different numbers of pieces

    • Using logic and understanding and explaining when trying to determine whether or not it is possible to cut a brownie into a given number of pieces

  • It has a low floor and a high ceiling: Students can get started making cuts by trial and error, but as the challenges get more complex, more careful strategizing is required!

 
 

This activity was adapted from the Julia Robinson Mathematics Festival's activity Yin-Yang.