Title
Thanksgiving Dinner (Kim Kendrick)
Goals
(1) Students will examine the concept to graph theory as it applies to organizing data and setting up schedules.
(2) Students will use communication skills and graph theory vocabulary when solving a real-world problem.
Abstract
Planning for and executing a large project takes time and careful planning. We will map out a plan for preparing a Thanksgiving Dinner so that all of the items are fully cooked, hot and ready to be served at the same time. We will evaluate the most scientific way to arrive at the minimal solution while taking into consideration the prerequisite tasks required to complete every item on our list. Students will be using introductory graph theory to solve this problem.
Problem Statement
Many people think that planning for and organizing a large get together is simple. What people sometimes fail to realize is that simply throwing it all together at the last minute is not the best way to insure that all of the requirements of a project are met and the individual components are completed by the deadline. We will be examining the planning necessary to cook a large meal. You and your friends have decided to cook a traditional Thanksgiving meal. You want to spend as little time as possible on the task. We will decide as a class the individual tasks required and the menu we plan to serve. Keep in mind that some items on our list will require the completion of a previous task while others will not. Our time constraints will be in hours. We want to know how many hours we will have to spend to prepare a meal fit for a king (or our beloved family).
Instructor Suggestions
(1) Set the stage by discussing the "Problem Statement" (see above) with the class.
(2) Distribute the "Thanksgiving Dinner" activity sheet (see attachment) and allow the students to individually read the first part of the activity.
(3) When all of the students are finished reading, have the class formulate a list of tasks necessary to prepare for and cook the meal. (Be sure to include time for shopping, thawing, preparing, and cooking the meal).
(4) Have the students form small groups (3-4 students) to develop the minimum time plan for preparing the dinner. (Use hours)
(5) When the small-groups are finished, have a spokesperson for each group share their plan and explain their method and reasoning involved in arriving at their solution.
(6) Discuss the students' work as it relates to modeling projects and graph theory.
Materials
"Thanksgiving Dinner" activity sheet, chalk board, overhead transparencies
Time
Introduction of problem statement (5 minutes), Individual work (5 minutes), Large group work (10 minutes), Small group work (20 minutes), Presentation of small-group work (15 minutes), Large group discussion (15 minutes)
Mathematics Concepts
Discrete Mathematics Concepts:
Project modeling, introduction to graph theory.
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections (within mathematics and across disciplines), Algebra, Geometry, Discrete Mathematics.
Colorado Model Content Standards Addressed
Algebraic Techniques (2), Data Collection and Analysis (3), Problem Solving Techniques (5)
Curriculum Integration
This activity will be used in the first year of the Integrated Math Program as a separate module in graph theory. It could also be used in a traditional Algebra I class when the focus is on developing organizational techniques and applications of scientific methods to solve simple, real-world problems.
Further Investigation
This lesson could be extended to include budget constraints as well as planning for the task with differing amount of people participating in the preparation. How would this change the outcome of the original solution?
Variations/Comments
Students may be given more complex tasks to solve - such as planning more elaborate functions using data and information of a more formal setting. This could include organizing the plans for a city or the work schedule for 20 or more people while maintaining a minimum staffing and meeting budget constraints.
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete Mathematics Through Applications. New York: W.H. Freeman and Company.