2. Pre-Lesson thinking…

3. Any
root with
-ology?

4. Teachers, let students play around with this a bit
Teachers, let students play around with this a bit! “-ology” is the study of…”tops” are what we are studying…

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.

11. Wait about clicking on solution…let students show their way to trace this.

12. If students were able to trace the first one, they should be able to trace this one without much difficulty.

13. This one takes some advanced planning…again, be sure that students have a chance to share their ideas. There are multiple solutions.

14. Let students struggle with this one
Let students struggle with this one! Remember that when we are not successful, our brain is growing! They should wrestle with this one before realizing that it is not traceable.

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

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

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.
The next slide explains even and odd vertices.

21. even 1 1 2 2 3 3 4
odd
Make certain students understand how to determine even & odd vertices.

22. Count all the even and odd vertices on this network!
Let the students practice on this network!
odd
even

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

24. Best wishes on this topological exploration!!!