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 the 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.