Title
Digging Deep to Snowboard (Liz Sansone)
Goals
Students will explore the concept of mixed recurrence relation as it relates to iteration and recursion. Students will generalize number patterns and produce a recurrence expression. . This activity explores a recurrence relation that has both a geometric and an arithmetic component. This activity could also introduce a discussion of explicit relations.
Abstract
Students are asked to form groups and devise a method that would predict the price of snowboarding in years to come.. Each group is then asked to present and explain their method to the class.
Problem Statement
Discuss with your students that as we all know, the cost for most sports events and entertainment continually increase. This activity will allow students to explore a recurrence relation to employ discrete mathematics in devising a method that estimates the cost of snowboarding in N years from now.
Instructor Suggestions
1) Discuss "Problem Statement" from above with your students.
2) Decide on a method to have students form small groups
3) Distribute Digging Deep to Snowboard 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 a recurrence relationship, and discuss their data organization.
Materials
Digging Deep to Snowboard 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
recursion
Related Mathematics Concepts
patterns, sequences, arithmetic mean, geometric mean
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Math.
Colorado Model Content Standards Addressed
Data Collection and Analysis (3), 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 patterns, recursion, conjecturing in Geometry .
Further Investigation
Extend the problem by having the price depend on the percentage of snowboarders and then lead them into finding an explicit relationship instead of recursive.
Variations/Comments
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (199410. Discrete mathematics through applications. New York: W.H. Freeman and Company.