Bridge Crossings

How it works

Given a set of bridges, is it possible to cross each bridge exactly once? Given a doodle, is it possible to draw the doodle without lifting your pencil or retracing any lines?

In this activity, students explore both of these types of challenges, as well as the connections between them.

Bridges of Konigsberg Handout
Bridge Crossing Problems
Doodle Tracing Handouts
Create Your Own Doodles Handouts

Why we like this activity:

• It’s fun! Students enjoy trying to solve the bridge-crossing challenges and trying to draw the doodles.

• It helps to develop algorithmic reasoning.

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

  • Finding and using strategies to solve bridge-crossing challenges and draw doodles.

  • Making observations / looking for patterns / finding similarities and differences / understanding and explaining when exploring which challenges have solutions and which don’t.

• It has a low floor and high ceiling: Students can get started solving bridge-crossing challenges and drawing doodles by trial and error, but more difficult challenges require more advanced strategies.

To find out more about our approach to math and math education, click here.