Activity icon (image only) - Cup Stacking.png
 
 

Cup Stacking

How it works

Imagine that we have a bunch of upside-down cups arranged in a line. Our goal is to stack the cups on top of each other so they end up in a single stack.

There are some rules we have to follow when stacking cups on top of each other:

  • The number of spaces a stack of cups can jump is equal to the number of cups in the stack. For example: A single cup jumps 1 space to the left or right; a stack of 2 cups jumps 2 spaces to the left or right; a stack of 3 cups jumps 3 spaces to the left or right; etc.

  • Cups in a stack always jump together.

  • Cups can only jump onto other cups — they can't jump to an empty position.

In this activity, students start by trying to figure out how to get 5 cups into a single stack. When they can do this, they try to get larger numbers of cups into a single stack. Next, they try to get different numbers of cups into a single stack in specific positions, and then in rainbow order (the cups are colored in rainbow order from left to right). After they've explored all of this, they explore similar challenges with cups arranged in a 2D grid instead of a line.

Why we like this activity

  • It’s fun! Students enjoy stacking the cups and attempting the different challenges.
  • It helps to develop algorithmic reasoning.

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

    • Finding and using strategies to get all the cups into a single stack without getting stuck.
    • Making and testing predictions about whether you'll be able to get all the cups into a single stack in different positions.
    • Making and testing predictions about whether you'll be able to get all the cups into rainbow order with different numbers of cups.
  • It has a low floor and a high ceiling: Students can start stacking cups by trial and error, but figuring out how get all the cups into a single stack (especially with different constraints) is challenging!
 
 

This activity was developed in collaboration with the Julia Robinson Mathematics Festival and is based on an activity from MathPickle.