Vertex-edge graphs part 2

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

  1. Divide into pre-assigned groups of 4.
  2. 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
  3. Assign one task per team:
  4. 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