**ERIC Number:**EJ1044543

**Record Type:**Journal

**Publication Date:**2014-Feb

**Pages:**6

**Abstractor:**ERIC

**Reference Count:**4

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

Successfully Transitioning to Linear Equations

Colton, Connie; Smith, Wendy M.

Mathematics Teacher, v107 n6 p452-457 Feb 2014

The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to generate and compare the relationship between two patterns, such as those formed by x + 3 and x + 6. The standard goes on to ask students to graph ordered pairs on a coordinate plane to support their investigation. Students in sixth grade are asked to evaluate expressions as well as write and solve equations derived from real-world contexts. These early expectations lay the foundation for meeting multiple standards outlined in the Common Core standard for high school algebra. However, for many students, progressing from modeling situations with equations such as 3x + 10 = 25 to equations such as 3x + 10 = y creates a seemingly insurmountable problem. The transition from one-variable equations with a single solution to linear equations with two variables and infinitely many solutions presents many challenges. One specific obstacle to making this transition lies in students' misunderstanding of the equals sign. For many students, the equals sign indicates an operation rather than a relationship (Ronda 2009). Once the concept of relational equality is sufficiently developed, students can begin the task of making sense of two-variable equations. Knowledge construction for understanding linear equations occurs in various stages. Ronda (2009) suggests four clearly defined stages of conceptual development, which range from the most elementary level--being able to evaluate variables for specific values--to the most complex level--being able to view the function holistically. This article describes a series of activities that comprises a single, multiphase lesson which incorporates Rhonda's stages and guides students students from single-variable equations to linear relationships.

Descriptors: Equations (Mathematics), Mathematics Instruction, Algebra, Word Problems (Mathematics), Teaching Methods, Learning Activities, Secondary School Mathematics, Problem Solving, Elementary School Mathematics

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Secondary Education; Elementary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A