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Course Descriptions

The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, called modules, deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. 

Algebra 1A (Year 1) 

In Module 1, students build off their prior knowledge from middle school mathematics as it relates to building expressions given a real-world context and their understanding of the relationship between rational and irrational numbers. Students will also begin to examine polynomials and how they are classified. Additionally, students will use the knowledge they gained from integer exponent rules and applying them to rational exponents. Students will expand their knowledge of radical expressions to knowing how to add and subtract these expressions and simplify.

In Module 2, students continue to build off prior knowledge gained in the middle school mathematics courses. Students continue to solve equations and inequalities but now have to justify and/or explain their process. Additionally, students examine compound inequalities and solving absolute value equations and inequalities.

In Module 3, students will begin to grow their understanding of functions. They will see how the domain and range are related to the independent and dependent variables. The process of graphing piecewise function is introduced along with composition of functions. In terms of graphing, students will be see how to identify features of a graph and how transformation effect a parent function. Students will also expand their knowledge of polynomials by understanding how polynomials are closed under the operations of addition, subtraction, and multiplication.

In Module 4, students will build on their knowledge of rate of change, slope-intercept form, and systems of equation from Pre-Algebra. Additionally, students will discover systems of linear inequalities and how the solutions of these systems are a set of solutions. Furthermore, students will see how arithmetic sequences are related to linear functions.

In Module 5, students will begin to expand their knowledge of functions to that of quadratics. Students will use key features of parabolas in context of a real world situation. Additionally, students will explore different ways of solving a quadratic equation and understand what the roots (zeros) of the function is. Furthermore, the idea of how the quadratic formula is derived and how the discriminant is used to decide how many solutions there are for a quadratic will be explored.

Algebra 1B (Year 2) 

In Module 1a, students will be reviewing the concepts that they learned in Algebra 1-A, in particular, linear functions.  In Module 1b, students will begin to expand their knowledge of functions to that of quadratics. Students will use key features of parabolas in thecontext of a real world situation. Additionally, students will explore different ways of solving a quadratic equation and understand what the roots (zeros) of the function are. Furthermore, the idea of how the quadratic formula is derived and how the discriminant is used to decide how many solutions there are for a quadratic will be explored.Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. 

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Module 2 allows students to explore nonlinear functions that exhibit some linear characteristics. This module explores different situations that can be modeled with exponential functions and equations. This module continues to reinforce the work with creating and representing equations and with connecting the structure of expressions to contexts. Additionally, students’ understanding of functions and their notation will deepen. Students will investigate key features, domains, and ranges of exponential functions; write exponential functions to model relationships between two quantities. Students will use technology to explore simple transformations of exponential functions as described and compare their properties.

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In Module 3, students will explore the graphs of polynomial functions. They will identify the zeros and end behavior to sketch the graph. Students will see how looking at the leading coefficient and the degree of the polynomial helps determine the end behavior and the possible number of zeros that a polynomial function could have.

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Module 4 reviews the univariate data representations and then introduces statistical models for bivariate categorical and quantitative data. Students have already addressed in previous modules many of the standards in the module, and they should now be able to apply their understandings from that previous work in the new work with the statistics standards in this module. This module provides opportunities to reinforce students’ work from the previous unit with representing linear functions symbolically and graphically. Instruction should always require students to reason about the mathematics, model and apply the mathematics and justify their thinking.