Algebra 1R/A

(in 8th grade)

Key Advances from K-8

Having already extended arithmetic from whole numbers to fractions (grades 4-6) and from fractions to rational numbers (grade 7), students in Algebra 1 (Middle School) will encounter particular irrational numbers such as 5 and . In Algebra 1, students will begin to understand the real number system. For more on the extension of number systems.

Students in middle grades worked with measurement units, including units obtained by multiplying and dividing quantities. In Algebra 1, students apply these skills in a more sophisticated fashion to solve problems in which reasoning about units adds insight (N-Q).

Themes beginning in middle school algebra continue and deepen during high school. As early as grades 6 and 7, students began to use the properties of operations to generate equivalent expressions (6.EE.3, 7.EE.1). By grade 7, they began to recognize that rewriting expressions in different forms could be useful in problem solving (7.EE.2). In Algebra 1, these aspects of algebra carry forward as students continue to use properties of operations to rewrite expressions, gaining fluency and engaging in what has been called “mindful manipulation.”

Students in this course will extend their prior understanding of proportional relationships to begin working with functions, with an emphasis on linear functions. In Algebra 1, students will master linear and quadratic functions. Students encounter other kinds of functions to ensure that general principles are perceived in generality, as well as to enrich the range of quantitative relationships considered in problems.

Students in this course will connect their knowledge about proportional relationships, lines, and linear equations (8.EE.5, 6). In Algebra 1, students solidify their understanding of the analytic geometry of lines. They understand that in the Cartesian coordinate plane:

The graph of any linear equation in two variables is a line.
Any line is the graph of a linear equation in two variables.

As students acquire mathematical tools from their study of algebra and functions, they apply these tools in statistical contexts (e.g., S-ID.6). In a modeling context, they might informally fit a quadratic function to a set of data, graphing the data and the model function on the same coordinate axes. They also draw on skills they first learned in middle school to apply basic statistics and simple probability in a modeling context. For example, they might estimate a measure of center or variation and use it as an input for a rough calculation.

Algebra 1 techniques open a huge variety of word problems that can be solved that were previously inaccessible or very complex in grades K-8. This expands problem solving from grades K-8 dramatically.

Fluency Expectations

Algebra 1A students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given a point and a slope. Such fluency can support them in solving less routine mathematical problems involving linearity, as well as in modeling linear phenomena (including modeling using systems of linear inequalities in two variables).
Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in algebra, as well as in their symbolic work with functions. Manipulation can be more mindful when it is fluent.
Fluency in transforming expressions and chunking (seeing parts of an expression as a single object) is essential in factoring, completing the square, and other mindful algebraic calculations.

Algebra 1 Overview

Students in Algebra 1 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 1 enable students to focus and master this material.
At the same time, however, students in Algebra 1 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 1R 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 2.
Within the domain of Statistics and Probability, Algebra 1 students work with data on a single count of 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 1 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 1 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 document.

What's the Difference between Algebra 1R and Algebra 1A?

The Algebra 1R (MS) and Algebra 1A (MS) curricula share many core topics but differ in pacing, depth, and the long-term math pathways available to students. Algebra 1A ultimately covers more content at a faster pace, including additional topics such as inverse functions, advanced transformations, and more complex applications of algebraic concepts.
The "A" pathway is ultimately designed to prepare students for AP Calculus BC in their senior year, a course that covers both Calculus 1 and Calculus 2 in a single year, similar to a college-level sequence taught over two semesters.
The "R" pathway is designed to prepare students for AP Calculus AB in their senior year, which covers college Calculus 1 over a full year, or one of our concurrent enrollment Calculus 1 courses.
To explore these pathways further, please visit our Acceleration & Electives webpage HERE.

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