Doodles & Doors
How it works
You probably know how to draw a 5-pointed star without lifting your pencil or retracing any lines. Is it possible to draw a 6-pointed star without lifting your pencil or retracing any lines? Are there doodles that it's impossible to draw without lifting your pencil or retracing lines? Is there a general rule you can use to help you determine which images you can and can't draw without lifting your pencil or retracing lines?
In this activity, students attempt to draw a variety of different doodles without lifting their pencil or retracing lines. They find that it's possible to draw some of these doodles without breaking the rules, but some are impossible.
Next, students explore a variety of door puzzles: Each of these puzzles consists of a set of rooms, with doors between different rooms. The goal is to trace a path that goes through each doorway exactly once.
Doodle Start & End Challenges handout
Door Start & End Challenges handout
Why we like this activity
- It’s fun! Students enjoy trying to draw the different doodles without lifting their pencil or retracing lines.
- It helps students develop algorithmic reasoning.
It requires students to engage in mathematical habits of mind:
Using logic / looking for patterns / making and testing predictions / understanding and explaining when exploring which doodles you can draw without lifting your pencil or retracing lines and which ones you can't.
Finding and using strategies to draw doodles without lifting your pencil or retracing lines.
- It has a low floor and a high ceiling: It’s possible to start drawing doodles by trial and error, but as the doodles get more complex, it’s helpful to think more strategically, and there is a lot to discover about which doodles can be drawn without lifting your pencil or retracing lines and which ones can’t.
