2. Pre-Lesson thinking…

3. Any root with -ology?

5. Topology

7. What is a NETWORK? A network is a collection of points (vertices) and a collection of line segments (arcs), connecting these points (vertices).

8. What is a TRACEABLE network? A network is traceable if it can be drawn by tracing each arc exactly once by beginning at some point and not lifting your pencil from the paper.

9. Challenge #1 Traceable Networks You need a writing utensil, a way to erase, a place to write, and a partner to verify your work.

10. Try to make these shapes without lifting your pencil or retracing a line.

15. Have you ever wondered what makes a shape traceable?

16. What makes a network traceable? Today, you will explore this important idea in TOPOLOGY:

17. Your instructor will give you a set of networks to explore.

18. Task #1: 1. Try to trace each network without lifting your pencil or retracing a line.

19. Task #2: 2. If a network is traceable, demonstrate for your partner. He/she should initial your paper.

20. Task #3: 3. Count and record the number of even vertices and odd vertices in each network.

21. 1 3 2 odd 1 2 3 4 even

22. oddeven odd even Count all the even and odd vertices on this network! 3 even 2 odd

23. Task #4: Make a conjecture about the relationship between even/odd vertices and traceable networks.

24. Best wishes on this topological exploration!!!