6th Grade Math Textbook, Progress

Networks

4 paths (even vertex)

3 paths (odd vertex)

2 paths (even vertex)

vertex

path

traversable network

Use the networks below.

ABCD

EFG

not traversable network

1. How many even vertices are in each network? odd vertices?


2. Trace each network. Which are traversable?


3. Look for a pattern for traversable networks in the number of odd vertices.
   How many odd vertices are in a traversable network?


4. Use the pattern to draw three traversable networks.


5. Use the same pattern to draw three more networks that are not traversable.

A network is a set of points connected by segments or arcs, called paths. If it is

possible to draw or trace each segment or arc exactly once without lifting a pencil

from paper, then the network is traversable. A point at which the segments or arcs

intersect is called a vertex (plural: vertices), or a corner.

A vertex is even if there are an even number of paths at a vertex.

A vertex is odd if there are an odd number of paths at a vertex.

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