# Algebra II

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### Course Summary

**What is Algebra 2 all about? **

Algebra 2 develops students’ conceptual understanding, fluency, and ability to apply advanced functions. Students draw connections between function types. In particular, students apply skills learned early in the year with linear, quadratic, and polynomial functions to inform their understanding later in the year when they study rational, radical, and trigonometric functions. Students choose appropriate functions and restrictions, based in solid understanding of the features of the functions, to build functions that model contextual situations. Fluency is an important part of Algebra 2, as the ability to perform procedures quickly and easily allows students to more deeply understand concepts.

**How did we order the units? **

In **Unit 1, Linear Functions and Applications**,** **students review the features of functions through the study of inverse functions, modeling contextual situations, and operating with functions, systems of functions, and piecewise functions. Students will increase their fluency in identifying and analyzing features of linear functions through algebraic, graphic, contextual, and tabular representations. Students will use these features to effectively model and draw conclusions about contextual situations. The skills students develop in this unit will be applied and extended to other function types throughout the year, including quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions.

In **Unit 2, Quadratics**, students will revisit concepts learned in Algebra 1, such as features of quadratic equations, transformation of quadratic functions, systems of quadratic functions, and moving from one equation form to another (e.g., vertex form to standard form, standard form to intercept form). Increased fluency with quadratic equations and functions provides a strong base for studying polynomials, rational functions, and trigonometric identities. In this unit, students will also be introduced to a new type of number system, the imaginary numbers, and will identify and operate with imaginary solutions. As with Unit 1, students will apply quadratic equations to contextual situations, to systems of functions, and when translating between representations. Graphing calculators are introduced heavily in this unit and will be used for the remainder of the year.

In **Unit 3, Polynomials**, students will apply skills from the first two units to develop an understanding of the features of polynomial functions. Analysis of polynomial functions for degree, end behavior, and number and type of solutions builds on the work done in Unit 2; these are advanced topics that will be applied to future function types. Students will write polynomial functions to reveal features of the functions, find solutions to systems, and apply transformations, building from Units 1 and 2. Students will be introduced to the idea of an “identity” in this unit as well as operate with polynomials. Division of polynomials is introduced in this unit and will be explored through the concepts of remainder theorem as well as a prerequisite to rational functions.

In **Unit 4, Rational and Radical Functions**, students will extend their understanding of inverse functions to functions with a degree higher than 1. Alongside this concept, students will factor and simplify rational expressions and functions to reveal domain restrictions and asymptotes. Students will become fluent in operating with rational and radical expressions and use the structure to model contextual situations. In this unit, students will also revisit the concept of an extraneous solution, first introduced in Unit 1, through the solution of radical and rational equations.

In **Unit 5, Exponential Modeling and Logarithms**, students will model with exponential growth and decay, including use of the continuous compounding base, *e*, to solve contextual problems in finance, biology, and other situations. Students will learn that logarithms are the inverse of exponentials and operate with and graph logarithms fluently. Students will discover the strength of logarithms to identify solutions, features, and patterns in functions. Students will use exponential functions and logarithmic functions as part of a system of functions in modeling contexts.

In **Unit 6, Trigonometric Functions and Identities**, students will review geometric trigonometry as an introduction to trigonometric functions. Students will use sketches of the trigonometric functions of sine and cosine to develop understanding of the reciprocal trig functions, inverse trig functions, and transformational identities of trig functions. Features of trigonometric functions represented graphically will be translated to algebraic representations, and the features unique to trig functions will be explored and used in mathematical and application problems. Students will be introduced to the unit circle and will be expected to derive this easily. The Pythagorean identity will be used heavily in this unit, and students will be expected to know this identity and derive other forms of the identity for use in problems. This unit concludes the formal study of transformation, inverse, systems, features of functions, and using different functions to model contexts that began in Unit 1.

In **Unit 7, Descriptive Statistics**, students will build on their understanding of shape center and spread developed in middle school and Algebra 1 to use the mean and standard deviation to estimate population percentages. Students will synthesize their understanding of descriptive statistics with univariate and bivariate data through identification of strength and weakness of “evidence” from the analysis of statistical models to prepare them for the next unit.

In **Unit 8, Inferential Statistics**, students will become critical consumers of statistical information. Students will use their understanding of descriptive statistics, developed in Unit 7, as well as their understanding of probability, developed in Geometry, to make inferences about population parameters. Students will look critically at methodology in collecting data, citing procedures and practices that lead to reliable statistical models. In this unit, students will use technology to run simulations, using sound practices in probability concepts to make decisions and predictions.

This course follows the 2017 Massachusetts Curriculum Frameworks and incorporates foundational material from Algebra 1 where it is supportive of the current standards.

### How to Use This Course

### Mathematics at Match

The goals of Match Education’s math program are intrinsically tied to our school’s mission of providing our students with the skills and knowledge they will need to succeed in college and beyond. At Match, we seek to inspire our scholars to pursue advanced math courses, and we provide them with the foundations they will need to be successful in these courses.

Our math curriculum is designed around several core beliefs about how to best achieve our ambitious goals. These beliefs drive the decisions we make about what to teach and how to teach it.

**Content-rich Tasks:**We believe that students learn best when asked to solve problems that spark their curiosity, require them to make novel connections between concepts, and may offer more than one avenue to the solution.**Practice and Feedback:**We believe that practice and feedback are essential to developing students’ conceptual understanding and fluency.**Productive Struggle:**We believe that students develop essential strategies for tackling complex problems, and build non-cognitive skills such as grit and resilience, through productive struggle.**Procedural Fluency Combined with Conceptual Understanding:**We believe that knowing “how” to solve a problem is not enough; students must also know “why” mathematical procedures and concepts exist.**Communicating Mathematical Understanding:**We believe that the process of communicating their mathematical thinking helps students solidify their learning and helps teachers assess student understanding.

*For more information, view our full Mathematics Program Overview.*

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