Explore Linear Patterns adapted from PBS MATHLINE Mark Jankowski Asheville City Schools Kenan Fellows Class of 2012
Major Cluster Addressed • Expressions and Equations Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations. • Functions Define, evaluate, and compare functions. Use functions to model relationships between quantities.
Prerequisites • Review linear patterns • Have students practice solving linear equations
Materials • Graphing calculators • 31 pennies for each group • Set of algebra tiles for each group
The Yo-Yo Problem Andy wants to buy a very special yo-yo. He is hoping to be able to save enough money to buy it in time to take a class in which he will learn how to do many fancy tricks. The 5 -ounce aluminum yo-yo costs $89. 99 plus 6% sales tax. Andy has already saved $17. 25, and he is earning $7. 20 a week by doing odd jobs and chores. How many weeks will it take him to save enough money for the yo-yo?
The Yo-Yo Problem
Penny Pattern Exploration • The first stage should have one penny surrounded by six pennies. • Each successive stage should add six pennies to outer layer. • Continue to make stages until you run out of pennies.
Penny Pattern Exploration • Create a table of values using n for the stage number and p for the number of pennies used. • Determine an algebraic rule representing the relationship between the stage number and the number of pennies used.
Algebra Tiles •
Algebra Tiles •
Solve Equations Using the Graphing Calculator •
Back to the Yo-Yo Problem Try to use a different method to determine the solution (writing a symbolic equation and solving it, using trial and error method, use simple arithmetic, etc. )
Extensions & Adaptations • Have students write problems similar to the Yo-Yo problem. Give as classwork, homework, or display on bulletin board. • Have students write equations, draw graphs, and make a table of values for the relationship in the penny and yo-yo problems. Then have them compare three representations.
Discussion Questions • What different methods did students in this class use to solve linear equations? Which methods do your students use most often? How can a teacher encourage multiple approaches to solving problems?
Discussion Questions • The Penny pattern activity could have been done by simply drawing the patterns rather than actually physically handling the pennies. Discuss the pros and cons of actually using pennies.
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