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Mathematics Grade 6
Strand: EXPRESSIONS AND EQUATIONS (6.EE) Standard 6.EE.2
This activity gives a fun introduction to two-step equations.
Algebra Tiles for the Overhead Projector, by Hilde Howden; ISBN 0-914040-42-1
Solving two-step algebraic equations is a concept used throughout all of algebra. In order to be successful, students must understand equality and variables (which may be taught using the Pyramid Equality lesson), as well as the order of operations. They should be able to add and subtract integers, as well as understand the concept of zero pairs of tiles. This occurs when a negative x tile and a positive x tile are together, which create a sum of zero. For example, -2 + 2 = 0. Similarly, they should understand that addition and subtraction are the inverse operations of each other, just as multiplication and division are the inverse operations of one another.
Students must also understand exponents. The expression x^2 means x squared, or x times x.
Algebra tiles provide a useful way to introduce algebra operations to students of all ages. Students use the tiles as numbers to replace the variables, which provides a visual image of the equations. This will make the transition to paper and pencil much easier to understand. Using the manipulatives will also aid in retention of the concepts.
Invitation to Learn
Write the following question on the board: If tickets to a high school football game cost $4 per person, explain in words, numbers, or pictures how you can calculate how much money it will cost your family to go to the game?
Give students a few minutes to work alone, and then pair them up to share their strategies. Discuss as a class. (Students should realize that the number of people per family would cause the cost of the tickets to vary.
Day 1: Introduction to Algebra Tiles
Solving Two-Step Equations with Algebra Tiles
Day 2: Solving Two-Step Equations with Paper and Pencil
Step One: Add or subtract the inverse operation on each side of the equation.
2x 4 + 4 = 10 + 4. (After simplifying, 2x = 14.)
Step Two: Take the inverse (divide) from both sides of the equation. This will affect the number directly beside the variable.
2x / 2 = 14/2. (After simplifying, x = 7.)
Leitze, A.R., & Kitt, N. A. (2000 September). Using homemade algebra tiles to develop algebra and prealgebra concepts. Mathematics Teacher, 93, 462-466, 520.
Algebra for all is possible by using algebra tiles as concrete models in the classroom. This article describes how to use homemade tiles to reach a broader group of students for successful algebra thinking. Provides concepts appropriate for this approach.
Leinenbach, M., & Raymond, A.M. (1996). A two-year collaborative action research study on the effects of a hands-on approach to learning algebra. ERIC Source (ERIC ED398081). Retrieved November 30, 2006, from http://www.eric.ed.gov
A hands-on approach to algebra enhances students confidence, interest in, and ability to solve and retain understanding of algebraic equations. This article describes a two-year research project focused on two phases and data collection.