Title
Picking Up The Pieces (Liz Sansone)
Goals
Students will explore the concept of graph theory as it relates to scheduling, desired critical paths, and earliest-start time(EST).
Abstract
Students are asked to form groups, study the given task table, illustrate it as a graph and then find the desired critical path. Each group is then asked to present and explain their method to the class.
Problem Statement
Discuss with your students that we have all been in situations when we are pressed for time and we must find the shortest way to get everything accomplishes. This activity will allow students to explore a graph theory situation and employ discrete mathematics by devising a method that will locate the critical path so a time frame for a job can be estimated. ..
Instructor Suggestions
1) Discuss "Problem Statement" from above with your students.
2) Decide on a method to have students form small groups
3) Distribute "Picking Up The Pieces" activity sheet, also distribute a transparency and a marker to each group, one person needs to illustrate the groups' approach..
4) When the small groups are finished, have a spokesperson for each group share their method using the transparency that they prepared.
5) Discuss the students' work as it relates to group theory
Materials
"Picking Up The Pieces" activity sheet, transparencies, markers.
Time
Introduction (5 min.) small group work (20 min.), presentation of small group work and large group discussion (20 min.).
Mathematics Concepts
Discrete Mathematics Concepts
Group Theory, critical paths, EST, prerequisites, Liz SansoneT.
Related Mathematics Concepts
Edges, vertices, adjacency, prerequisites
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Math.
Colorado Model Content Standards Addressed
Collecting and Analyzing Data (3), Geometric Techniques (4), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be integrated into a traditional or Integrated Algebra and/or Geometry class as the topics of modeling, vertices, edges, paths, graphs, circuits
Further Investigation
Expand the problem by changing a task's time and see how this does or doesn't affect the minimum project time.
Variations/Comments
Give the students the names of the tasks, or give them the graph and have them design a task table..
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W.H. Freeman and Company.