# Mathematics

*Use this chart in conjunction with the specific course descriptions and prerequisites, and note that the typical pathways shown do not reflect every possible scenario for student progression through the curriculum.*

Central to the philosophy of the mathematics department is the belief that all students are capable of, and can profit from, learning significant mathematical concepts, skills and techniques. As described below, one level of Algebra I, two levels of Geometry, and three levels of Algebra II are offered. In general, the sequence of courses in mathematics moves from Algebra I to Geometry to Algebra II. Students then enter a variety of advanced and elective courses to continue their study of mathematics through Grade 12.

The ASL math curriculum is aligned to the Common Core State Standards (CCSS) and develops the math practices that are an essential part of those standards throughout each course. At every level, students are asked to not only find answers to problems, but to give detailed and thoughtful solutions that demonstrate the learning process and deep understanding of the fundamental concepts. Students learn how to express their solutions mathematically, and also how to explain their understanding through written reflection.

Throughout an ASL high school student's mathematics career, the department endeavors to provide learning experiences that utilize appropriate technology. The graphing calculator equips students with opportunities to explore concepts and topics in depth. Learning to use a graphing calculator effectively and efficiently is, therefore, an integral part of the mathematics curriculum, and students in the High School are expected to have a Texas Instruments brand TI-84, TI-84 Plus, or TI-NSpire graphing calculator for use in math courses.

The mathematics department sponsors the Math Club, which provides motivated students with an opportunity to work on problems that require them to think laterally and creatively and to explore methods outside the curriculum. Students work individually and in small groups in preparation for various math competitions. Participation in contests, including ISMTF mathematics competitions and the UKMT and other mathematical challenges, is open to all students willing to undertake extra work in mathematics.

### Accelerated program

In order to provide a challenging and rigorous mathematics curriculum for exceptionally able ASL students, accelerated courses are offered in Algebra II with Trigonometry, Precalculus with Calculus, AP Statistics, AP Calculus AB, AP Calculus BC and Advanced Math Seminar. These courses are designed for students with advanced conceptual skills, who are capable of applying ideas in new circumstances, and who are adept at mathematical and algebraic manipulation. All units are studied at an accelerated rate and in substantial depth, with more emphasis on theory and a higher degree of difficulty in problem solving. Strong emphasis is placed on investigation, analysis, discovery and independent thinking.

A student may take courses in the accelerated program provided s/he has demonstrated in previous mathematics courses the characteristics described above and been recommended by the department. For a student new to ASL, approval is granted by the mathematics department upon review of the student's mathematics record from a previous school and his/her ASL placement test.

- Algebra I
- Geometry with Algebra
- Geometry with Proof
- Algebra II Foundations
- Algebra II
- Algebra II with Trigonometry
- Precalculus with Statistics
- Precalculus with Analysis
- Precalculus with Calculus
- Calculus
- AP Calculus AB
- AP Calculus BC
- Financial Mathematics I
- Financial Mathematics II
- AP Statistics
- Advanced Math Seminar

## Algebra I

**1 credit; full year**

Prerequisite: Math 8 or Pre-algebra

Prerequisite: Math 8 or Pre-algebra

This is a first-year algebra course organized around essential families of functions, aligned with the Common Core State Standards for Mathematics. The focus is on linear, quadratic and exponential functions, with algebraic and computer science skills merged together to allow students to interpret and manipulate these functions in multiple ways. Further applications include the study of systems of equations and inequalities, polynomials and factoring, and radicals. The emphasis of the class is on problem-solving, reasoning, algorithmic thinking, and communication; students learn through game development and the use of a graphing software. Students enhance their abstract reasoning skills by developing games using the Scheme programming language.

## Geometry with Algebra

**1 credit; full year**

**Prerequisite: Algebra I**

This course introduces students to plane geometry, the angles and relationships between parallel and perpendicular lines, triangles, quadrilaterals, similarity and congruence, polygons, area and volume, polyhedra and right-triangle trigonometry. The CCSS set the geometry standards that students need to master, but an emphasis is placed throughout the course on reviewing and strengthening algebra skills within the realm of geometry.

## Geometry with Proof

**1 credit; full year**

**Prerequisite: Algebra I**

This is a robust geometry course that begins each unit by working towards mastery of the CCSS, and then delves into rich and challenging applications of those standards. It features reasoning and proof, the angles and relationships between parallel and perpendicular lines, triangle congruence, relationships within triangles, similarity, right-triangle trigonometry, quadrilaterals, properties of transformations, properties of circles, area and perimeter, polyhedra, surface area and volume. Strong algebra skills are required, as many geometric situations require application of material from Algebra I. Reasoning with analytic proofs is at the forefront of every unit studied.

## Algebra II Foundations

**1 credit; full year**

**Prerequisite: Algebra I and Geometry with Algebra**

This course serves as a foundational course in algebraic skills and ideas to help students develop greater understanding of topics that may have been challenging in Algebra I. Students study the topics of linear equations and functions, systems of linear equations, inequalities and absolute value, quadratic equations and functions, exponents**, polynomials and factoring. The class aligns to the first part of the higher-level standards in the CCSS math strands, emphasizing application and reasoning with the goal of preparing students for the multiple approaches to problems that are essential for standardized exams and further study in math.**

## Algebra II

**1 credit; full year**

**Prerequisite: Algebra I and either Geometry with Proof or Geometry with Algebra, along with departmental recommendation**

This course is designed as the first part of a two-year sequence that completes all of the higher-level strands of the CCSS. It deepens students’ understanding of linear systems through a study of matrices, focuses heavily on quadratic functions and equations, exploring complex numbers and many graphing concepts through that. Polynomial functions and radicals allow students to deepen their understanding, before rational, exponential, and logarithmic functions show the breadth of functions that create complexity in higher-level math. A unit on probability and combinatorics continues the statistics strand of the CCSS, introducing more theory and building on applications learned in Algebra I.

## Algebra II with Trigonometry

**1 credit; full year**

**Prerequisite: Algebra I, Geometry with Proof and departmental recommendation **

This rigorous course is designed for exceptionally able math students and covers all of Algebra II as well as a comprehensive unit on trigonometry. The topics of the course and the focus are similar to what is listed for Algebra II, but each unit moves from the initial standards to rich problem solving at a much quicker pace. The emphasis is on mastery of the higher-level concepts and problems. Creative problem solving is a core value of the course, and the units are synthesized into challenging problems that require and build these creative skills.

## Precalculus with Statistics

**1 credit; full year**

**Prerequisite: Algebra II Foundations or Algebra II**

This course strengthens and deepens students' knowledge of material first encountered in Geometry and Algebra II courses. Topics introduced include descriptive statistics, algebraic problem solving, functions and graphs (including linear, quadratic, root, power, logarithmic and exponential), transformations of functions and data, tr**igonometry, probability, and binomial and normal distributions. The focus is to ensure that students complete the primary elements of the CCSS before the end of high school, while finding real-world applications that help show students where their knowledge can be applied in other fields.**

## Precalculus with Analysis

**1 credit; full year**

**Prerequisite: Algebra II and departmental recommendation**

This course is the second part of the two-year sequence that completes the higher-level CCSS strands. The focus is on trigonometry and its applications and creating a deeper understanding of functions. Polynomial, exponential, and logarithmic functions are explored in depth, along with applications to analytical geometry and analytical **trigonometry. Sequences and series build another component of the knowledge related to combinatorics and inductive proof. Students finish the course prepared to enter AP Calculus AB or a first-semester college calculus course the following year.**

## Precalculus with Calculus

**1 credit; full year**

**Prerequisite: Algebra II with Trigonometry**

This rigorous course finishes the two-year sequence that began with Algebra II with Trigonometry, continuing to stress depth of knowledge and an ability to move from initial standards to higher-level ones at a fast pace. In addition to the topics covered in Precalculus with Analysis, students explore conic sections, vectors, polar and parametric equations, probability and combinatorics. The class concludes with a study of limits and differential calculus, in preparation for the AP Calculus BC course the following year.

## Calculus

**1 credit; full year**

**Prerequisite: Precalculus with Statistics or Precalculus with Analysis**

This course features the study of differential calculus along with its standard applications to the theory of graphs and related rates. This is followed by study of integral calculus, the fundamental theorems, and applications to motion, area and volume. The idea of the course is to introduce students to the topics of calculus along with some of the problem solving involved in dealing with constantly changing functions. Applications to real-world situations and collaborative thinking allow students to grapple with these difficult ideas and see their interconnectedness before going into the higher-level problems that are a part of college calculus courses.

## AP Calculus AB

**1 credit; full year**

**Prerequisite: Precalculus with Analysis and departmental recommendation**

This is a challenging, college-level calculus course, basing itself on the standards from the AP Calculus AB curriculum, but building depth of problem solving in each unit beyond that. Students learn to interpret the concepts of calculus through a variety of examples of problem solving, which are based around the two major themes of differential and integral calculus. A thorough study of limits begins the year, followed by both the theory and application of derivatives and integrals, including optimization, related rates, volumes of revolution, and interpretation of graphs. All students take the AP Calculus AB exam in May.

## AP Calculus BC

**1 credit; full year**

**Prerequisite: Precalculus with Calculus or AP Calculus AB and departmental recommendation**

This rigorous calculus course begins at the point of differential calculus where students have already mastered the basics and can begin to apply their understanding at a high level. It covers all of the topics in AP Calculus AB with more depth of problem solving, along with units on differential equations, additional techniques and applications of the definite and indefinite integral, sequences and series including the power and Taylor series, and the calculus of polar and parametric functions. All students take the AP Calculus BC exam in May.

## Financial Mathematics I

###### ½ credit; semester I

Prerequisite: Algebra II or Algebra II Foundations

This course will begin with a discussion of financial goal-setting and planning for the future. Students learn about compound interest in order to understand future and present values of a lump sum and an annuity. This leads into a discussion of how to save for retirement, how to distribute an annuity over a certain time period, and how to understand the value of a salary package. Students will also investigate the various types of bank accounts a commercial institution might offer. Threaded throughout the course will be discussions around the psychology of spending and lifestyle choices, inflationary pressures, and how to use credit wisely.

## Financial Mathematics II

###### ½ credit; semester II

Prerequisite: Financial Mathematics I, or permission from the department

Students continue to study credit and borrowing, including discussions on how to finance large purchases, such as a car or a boat. This leads to an investigation of how to plan for the purchase of a house, and what types of legal and economic issues can influence the choice of payment options. Students discuss the consequences of excessive debt and bankruptcy, carefully consider the psychological component of risk and investment, and understand how stocks are traded and valued. Throughout, students consider ethics and how best to make informed choices.

## AP Statistics

###### 1 credit; full year

Prerequisite: Algebra II and departmental recommendation, or Precalculus

This course is a college-level introduction to the major themes of statistics, building upon the foundations of statistics and probability taught throughout the ASL math curriculum. It focuses on four broad conceptual themes: exploring data, planning a study, probability as it relates to distribution of data, and inferential reasoning. The rigor of the course comes in the detailed focus on inferential reasoning that dominates the second semester. Students learn how to investigate research questions and how to use data to know what they can generalize about a population. All students take the AP Statistics exam in May.

## Advanced Math Seminar

###### 1 credit; full year

Prerequisite: Completion of AP Calculus AB or completion of/concurrent enrollment in AP Calculus BC

This is a college seminar-style math course that explores a variety of advanced mathematical topics. These vary from year to year, and are tailored to the background of the group of students who take the class. Possible topics include polar and parametric functions, complex analysis, advanced geometry, further topics in calculus, number theory, vectors and space curves. An emphasis is placed on creative and complex problem solving and presenting work to the class with regularity.