Crossing Every Bridge Exactly Once (aka Eulerian Paths)
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Objective
Students will try to find a path across this city which crosses each bridge exactly once.
Steps
- First, students will cross five bridges exactly once.
- Next, they'll try to cross seven bridges one time each. ⚠️ Note: This is impossible.
- They come up with three more layouts using seven bridges. At least one should work.
- Students count how many bridges come out of the cities. They're looking for patterns to determine whether a map will work.
- Finally, they try four other maps and learn about Euler and the Seven Bridges of Königsberg!
Resources
- Worksheet Part 1 (PDF) (Half sheets)
- Worksheet Part 1 (Google Slides)
- Worksheet Part 2 (PDF) (Half sheets)
- Worksheet Part 2 (Google Slides)
- Worksheet Parts 3 and 4 (PDF)
- Worksheet Parts 3 and 4 (Google Slides)
- Worksheet Part 5 (PDF)
- Worksheet Part 5 (Google Slides)
- Worksheet Part 5 - Solutions (PDF) For teacher's eyes only!
