Content Framework For Algebra
Students in Algebra I fully master linear equations and linear functions, especially the algebra-geometry interplay regarding slope and graphs. Students also work intensively to master quadratic functions, both from an algebraic and formal perspective as well as in the context of modeling. The work that students do with quadratic functions is connected with and reinforces their work in quadratic equations, polynomial arithmetic and seeing structure in expressions. From an applications perspective, quadratic functions provide opportunities for solving problems involving maxima and minima, an important aspect of modeling. Working intensively with linear and quadratic expressions, equations and functions in Algebra I enables students to focus and master this material.
At the same time, however, students in Algebra I encounter general principles and techniques that apply much more generally than in the linear or quadratic case — for example, learning that the graph of an equation in two variables often forms a curve, which could be a line (A-REI.10). Thus, although most of Algebra I focuses on linear and quadratic equations and functions, the course does include concepts that apply more generally and therefore need to be illustrated beyond the linear and quadratic case. Exponential functions may be discussed in this context but studied in depth later in Algebra II.
Within the domain of Statistics and Probability, Algebra I students work with data on a single count or measurement variable as well as data on two categorical and quantitative variables. Connecting their statistical work with their work in algebra and functions, they also interpret linear models.
To summarize, the critical areas in Algebra I include mastery of linear equations and inequalities, formalization and extension of function concepts (including function notation, domain and range, and exploration of many types of functions, including sequences), linear regression models, quadratic and exponential expressions (including rational exponents), and quadratic functions.
The Standards for Mathematical Practice apply throughout the Algebra I course and, when connected meaningfully with the content standards, allow for students to experience mathematics as a coherent, useful and logical subject. Details about the content and practice standards follow in this analysis.