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.
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
- 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
- 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
- Paper and pen
- Vertex-edge graph technology http://illuminations.nctm.org/ActivityDetail.aspx?ID=20
- Google London underground map and attractions.
- Presentations from all teams, times 2 minutes per team.
- Turn in worksheets
- Summary questions