Introductory focus

Vertex edge graphs can represent real-life problems and help us solve them.

*Example 7: Minimum number of paved paths in “Muddy City”*

Below you see the map of Muddy City. Each vertex represent a point of interest that all those who live in the city need to get to, like: home, shop, school, recreation center etc. Your task is to find a path that will go through all of the vertices, but requires least number of edges. City wants to save money on pavements. Fewest # of roads need to be paved.

*Example 8: Finding the optimum path from home to school*

In this example, you need to find an optimum path from home to school. Each vertex means a turn on the road. Each edge represents a piece of a road. Distances are in meters. Edges are not be in proportion. Calculate and draw the shortest path. Use different colors to represent different routes and their total lengths.

Wholeness Vertex-edge graphs consists of vertices (nodes i.e. dots) and edges (lines or arches) that allow us to represent and solve real-life problems graphically.

Motivation step Example(s), questions, video

**2. Explore**

- Divide into pre-assigned groups of 4.
- Assign team members (use printed title tags)
- Facilitator to make sure team works and achieves its goal
- Scribe i.e. Summarizer to summarize and write down the results
- Presenter to present the results
- Critic to make sure questions from the audience are considered when preparing the task
- Assign one task per team:
- Pet shop problems Handout 2a Vertex-edge graphs
- Willow forest food chain Handout 2b Vertex-edge graphs
- Circle of friends Handout 2c Vertex-edge graphs
- Alternate advanced ones: home->school, maps, underground
- Give tools to use
- Paper and pen
- Vertex-edge graph technology http://illuminations.nctm.org/ActivityDetail.aspx?ID=20
- maps.google.com
- Google London underground map and attractions.
- …

**3. Summarize**

- Presentations from all teams, times 2 minutes per team.
- Turn in worksheets
- Summary questions

**Exit card / Homework**

**Image sources**

- http://dimacs.rutgers.edu/nj_math_coalition/framework/ch14/ch14_03-04.html
- http://en.wikipedia.org/wiki/Path_(graph_theory)
- http://en.wikipedia.org/wiki/Path_graph
- http://www.patricktaylor.com/1933-underground-map
- http://architectureboston.wordpress.com/2009/11/09/points-of-view/image5/
- http://www.utm.edu/departments/math/graph/glossary.html
- maps.google.com
- youtube.com
- http://www.glencoe.com/sites/common_assets/support_pages/MC_Course2/Networks.pdf
- http://jwilson.coe.uga.edu/EMAT6680Fa09/KimS/EMAT6690/3rd%20Write%20up/vertex-edge%20connection/vertexedge.html
- http://www.amphimath.com/Materials/Vertex-Edge%20HW%20Grade%203%20%28Part%202%29%20V1.pdf