Staircases
How it works
A staircase is a collection of squares where the number of squares in each level increases by exactly 1 as you go down. (The top level can have any number of squares.) Imagine you want to build staircases with different numbers of squares and levels. For which numbers of squares and levels will it be possible, and for which will it be impossible?
In this activity, students start by building different staircases. Next, they try to build staircases with specific numbers of squares and levels (or to show that it's impossible). Ultimately, they try to predict when it will be possible or impossible to build staircases with given numbers of squares and levels (without actually trying to build the staircases).
Why we like this activity
- It’s fun! Students enjoy trying to build different types of staircases.
- It helps students to develop spatial reasoning.
- It helps students to develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
Finding and using strategies to build staircases with specific numbers of squares and levels.
Making observations / comparing and contrasting / looking for patterns / making and testing predictions / understanding and explaining when trying to predict which staircases will be possible / impossible to build.
- It has a low floor and a high ceiling: It's easy for students to start building staircases, but predicting which staircases are possible or impossible to build is more challenging.
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.