Title
School Population (Kim Kendrick)
Goals
(1) Students will explore the concept of recursion theory.
(2) Students will work individually to interpret data and represent the information in table form.
(3) Students will write a general recurrence relation and calculate finite differences for the table.
(4) Students will choose a representative to present the information to the rest of the class, and they will be able to explain and justify their solution.
Abstract
This activity presents students with a population problem relating to supply and demand of space in a school as growth continues. They should be familiar with the concept of basic recursion theory and finite differences and the vocabulary relating to this topic.
Problem Statement
The population of the world has been growing at a (somewhat) constant rate. On a smaller, yet similar scale, the population of our school district and enrollment in our public schools has also been increasing. You will examine the dilemma almost all schools are facing - Is there enough room in our present school to accommodate the students enrolled? As the population grows, plans must be made which address concerns about adding on or build new facilities. We are going to examine this type of situation.
Instructor Suggestions
(1) Set the stage by discussing the "Problem Statement" (see above) with the class.
(2) Distribute the "School Population" activity sheet (see attachment) and allow the students to individually read and complete the first part of the activity.
(3) Allow students to form small groups to check over their solutions.
(4) Ask for students to volunteer their plans and solutions in a large group setting.
Materials
"School Population" activity sheet, chalk board, Calculators
Time
Introduction of problem statement (5 minutes), Individual work (30 minutes), Small group work (10 minutes) , Present the information, explain and justify their solution (10 minutes)
Mathematics Concepts
Discrete Mathematics Concepts:
recursion theory, finite differences
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), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity will be used in the first year of the Integrated Math Program as a separate module to introduce concepts of recursion in the unit/module covering discrete mathematics. It could also be used in a traditional Algebra I class when discussing patterns and data tables.
Further Investigation
This project could be extended by having the students create a plan for building the new addition or facility. This could refer back to the unit which covered graph theory.
Variations/Comments
Students may need help setting up the table or writing the correct recursion formula. Be sure that they have had adequate preparation in these areas before attempting this activity.
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete Mathematics Through Applications. New York: W.H. Freeman and Company.