Algebra is the language of mathematics and science, a gateway to mathematical and scientific thinking. Algebra generalizes and builds on arithmetic and its properties. In algebra we consider not just individual calculations but whole collections of calculations all at once. We can reason about collections of calculations to determine which specific ones are especially interesting or useful. Using algebra, we can work with quantities that change and we can relate quantities that change together.
In the domain of Operations and Algebraic Thinking (Kindergarten through Grade 5), students formulate and solve equations to solve problems. They write and interpret expressions that record calculations. They observe, describe, and analyze patterns. In the domain of Expressions and Equations (Grades 6 through 8), students use variables in expressions and equations. They begin to treat expressions as entities in their own right and they consider how expressions are broken into component parts. They represent and analyze quantitative relationships, leading to the study of functions. Students learn to solve equations by viewing equation-solving as a process of determining which values make the equation true. They solve equations to solve real-world problems.
Opportunities to engage in all eight of the Standards for Mathematical Practice described in the CCSSM occur throughout the study of algebra, although the following standards may be especially appropriate for emphasis:
• 2 Reason abstractly and quantitatively. Students engage in this practice when they seek to understand variables, expressions, equations, and functions in terms of a context and when they use contexts to help make sense of how we work with variables, expressions, equations, and functions.
• 4 Model with mathematics. Students engage in this practice when they define variables and formulate expressions and equations for quantities of interest and when they define, represent, and reason about functions.
• 7 Look for and make use of structure. Students engage in this practice when they look for the structure of expressions to determine which values are possible or to guide strategic choices in solving equations.
• 8 Look for an express regularity in repeated reasoning. Students engage in this practice when they recognize that repeated calculations could be described by a “recipe” and when they recognize and use expressions as “calculation recipes.”
(From Common Core Standards for Mathematical Practice. Published by Common Core Standards Initiative.)