Title
Eeek, Cobwebs! (Liz Sansone)
Goals
Students will explore the concept of recursion and display the expressions as a cobweb diagram.
Abstract
Students are asked to work in small groups, design a cobweb graph and present what happens when one alters the geometric and algebraic mean in a recursion..
Problem Statement
Discuss with your students that graphs are another form of data representation and cobweb diagrams help visualize what happens when successive terms are calculated. They are to come up with three conjectures about these recursive relationships based on the diagrams.
Instructor Suggestions
1) Discuss "Problem Statement" from above with your students.
2)Have students get together in small groups to graph and discuss the effect of changing some numbers around..
3) Distribute "Eeek, Cobwebs!" 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 and discuss what happened when they changed one number in the expression .
Materials
"Eeek, Cobwebs!" activity sheet, transparencies, markers.
Time
Introduction (5 min.) small group work (15 min.), presentation of small group work and large group discussion (15 min.).
Mathematics Concepts
Discrete Mathematics Concepts
Iteration, recursion, cobweb diagrams
Related Mathematics Concepts
graphing equations
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Math.
Colorado Model Content Standards Addressed
Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be integrated into a traditional or Integrated Algebra 1 class as the topic of recursion is introduced, graphing is a pre-requisite.
Further Investigation
Variations/Comments
Give the students a cobweb diagram and have them write the recurrence relation.
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (199410. Discrete mathematics through applications. New York: W.H. Freeman and Company.