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10-001-TilingHallway-ModelingScenario

Author(s): Robert Krueger1, Eric Stachura2

1. Concordia University, St. Paul MN USA 2. Kennesaw State University, Marietta GA USA

Keywords: Geometry iteration tiling recurrence shift operator patterns closed form analytic solution

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Abstract

Resource Image Students investigate difference equations through tiling hallways. They observe patterns in the tiling which lead to a difference equation. Solutions will be calculated by iteration. and the shift operator.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

In this exercise, you will explore difference equations in the context of tiling hallways. You will calculate solutions to your difference equation by iteration and become familiar with a helpful tool known as the shift operator.

Work has been slow for Kyle the Tile Guy lately.  With all the new wood and laminate flooring options, Kyle is not in demand. To pass the time, Kyle, a double major in math and construction engineering was reading one of his old math textbooks and ran across the following problem:

How many ways can the floor of a hallway that is  units long and  units wide be tiled with tiles, each of which is 2 units by 1 unit?  Tiles can be placed vertically or horizontally. Kyle was intrigued…how about you?

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Authors

Author(s): Robert Krueger1, Eric Stachura2

1. Concordia University, St. Paul MN USA 2. Kennesaw State University, Marietta GA USA

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