# Upper School Mathematics

Mathematics education should give all individuals the power of problem solving, the ability to participate intelligently in civic affairs, the skills needed to pursue educational and career choices, and an appreciation of the richness and beauty of mathematics along with its importance in our culture. All classes provide opportunities for students to organize their thinking, reason logically, choose critically from different problem-solving strategies, learn and apply various technologies, express their ideas both orally and in writing, and work cooperatively with their peers.

##### Sequence of Courses

Thirty credits in mathematics are required for graduation, including one year each of Algebra I, Algebra II, and Geometry and one semester of Introduction to Statistics. Typically, students complete these required courses in the following sequence: Algebra I (one year); Geometry A (fall) and Algebra IIA (spring); and Algebra IIB (fall) and Geometry B (spring), Introduction to Statistics (fall). Students may choose to take more classes upon completing these courses, including Pre-calculus, Calculus, Advanced Statistics and other elective offerings.

## Semester Required Courses

- Algebra I
- Geometry A: Foundations of Plane Geometry
- Algebra IIA: Introduction to Functions
- Algebra IIB: Functions
- Geometry B: Logic and Proof
- Introduction to Statistics

## Algebra I

*Full year, seventh, eighth, or ninth grade*

Students develop skills and concepts so as to learn how to solve problems using variables. Learning occurs through discussion, exploration, and group work, with the teacher acting as a guide. Topics include real, rational, and irrational numbers; solving linear and quadratic equations; graphing linear and quadratic equations; systems of linear equations; factoring polynomials; properties of exponents; properties of radicals; and simplifying rational expressions. There is an emphasis on solving problems algebraically, as well as through other methods including modeling and graphing. Developing communication skills is essential to the progression of the students’ mathematical competence.

## Geometry A: Foundations of Plane Geometry

*First semester, eighth, ninth, or tenth grade*

Students use an inferential approach to problem solving to build a foundation in Euclidean geometry. Through investigations of parallel lines, triangles, quadrilaterals, and circles, students make conjectures about the nature of these shapes and search out evidence to support their ideas. Students use both physical representations of diagrams and dynamic geometric software to explore the relationships present in geometric figures. The distinction between conjecture and proof and the limitations of inferential reasoning are given particular emphasis. Other course topics include conditional logic, right triangle trigonometry, and the extension of geometric relationships to three-dimensional figures. *Prerequisite: *successful completion of Algebra I (or equivalent).

## Algebra IIA: Introduction to Functions

*Second semester, eighth, ninth, or tenth grade*

The first semester of second-year algebra emphasizes the role of algebra as the foundation for further mathematics study. It stresses the structure of algebra, the development of algebraic problem-solving skills, and the use of functions as models of real-world situations. This course concentrates on the application of linear equations through matrices, counting and probability methods, an introduction to functions, and rational expressions. A TI-83, TI-83 Plus, TI-84, or TI-84 Plus is required. *Prerequisite*: successful completion of Algebra I (or equivalent). A grade of C or better is recommended.

## Algebra IIB: Functions

*First or second semesterNinth, tenth, or eleventh grade*

The second semester of second-year algebra emphasizes the role of algebra as the foundation for further mathematics study. It stresses the structure of algebra, the development of algebraic problem-solving skills, and the use of functions as models of real world situations. By studying functions and their graphs, students explore the characteristics of polynomial, rational, exponential and logarithmic functions including an introduction to complex numbers. A TI-83, TI-83 Plus, TI-84, or TI-84 Plus is required. *Prerequisite:* successful completion of Algebra IIA. A grade of C or better is recommended.

## Geometry B: Logic and Proof

*Second semester or first intensive**Ninth, tenth or eleventh grade*

This course is an introduction to formal reasoning, logic, and proof. Students examine how Euclid’s postulates are the basis of an axiomatic structure for plane geometry. Various methods for illustrating deductive reasoning are used, including two-column proof, proof by contradiction, and derivation. While the emphasis for this course is on geometric reasoning, students extend their studies with investigations of algebraic reasoning and proof. Throughout the course, students construct proofs for important mathematical concepts such as the Pythagorean Theorem, the laws of sines and cosines, and the quadratic formula. *Prerequisites:* successful completion of Geometry A and Algebra IIA (or equivalents). Grades of C or better recommended.

## Introduction to Statistics

*First semester or first intensiveTenth, eleventh, or twelfth grade*

Collecting, representing, analyzing and interpreting data are activities of major importance in contemporary society. This statistics course emphasizes that learning to interpret data correctly is a means to developing increased awareness of social, political, and scientific issues. Students learn to create unbiased surveys and experiments; describe data objectively with graphs, tables, and numerical statistics; determine correlation between variables and understand the concept of a statistically significant result. A TI-83, TI-83 Plus, TI-84, or TI-84 Plus graphing calculator is required. *Prerequisite:* successful completion of Algebra IIB (or equivalent).

## Semester Elective Courses

- Pre-Calculus with Trigonometry
- Applied Calculus
- Calculus I
- Calculus II
- Advanced Statistics
- Big Data and Analytics
- Mathematical Finance
- Individualized Program in Mathematics

## Pre-Calculus with Trigonometry

*Second semesterTenth, eleventh, or twelfth grade*

This semester course begins with a significant emphasis on trigonometry. Students explore concepts and applications from a circular function approach and then proceed to graphing trigonometric functions, using identities to transform expressions, and using trigonometric functions as mathematical models. Properties of elementary functions are reviewed, expanded upon, and applied to data analysis. In addition to trigonometry, the course provides an introduction to vectors and three-dimensional graphing, matrices, and conic sections. A TI-83, TI-83 Plus, TI-84, or TI-84 Plus graphing calculator is required. *Prerequisites: *successful completion of Algebra IIB and Geometry B (or equivalents). Grades of C or better recommended.

## Applied Calculus

*Full year, twelfth grade*

This year-long course develops and applies the concepts of differential and integral calculus. Concepts related to limits, derivatives and integrals are explored and understood through contextualized application and analysis. This is often accomplished by first starting with the application of a concept in a real-world situation such as Business Calculus or Physics. These concepts are then used in a variety of applications, such as optimization, related rates of change, and volumes of revolution. Students interpret, analyze and apply single-variable calculus concepts graphically, numerically, algebraically, and analytically. A TI-83, TI-83 Plus, Ti-84, or TI-84 Plus is required. *Prerequisite:* successful completion of Pre-Calculus (or equivalent).

## Calculus I

*Full year; eleventh or twelfth grade*

This year-long course develops and applies the concepts of differential and integral calculus. An in-depth exploration of the underlying concepts is used to develop a foundation and understanding of limits, derivatives, and integrals. These concepts are then used in a variety of applications, such as optimization, related rates of change, and volumes of revolution. Students learn to interpret the calculus concepts from several frames of reference: graphically, numerically, algebraically, and verbally. Clear communication of ideas and process is emphasized. Material in this course is a subset of the material on the AB Calculus AP exam. A TI-83, TI-83 Plus, Ti-84, or TI-84 Plus is required. *Prerequisite: *successful completion of Pre-Calculus (or equivalent). A grade of B- or better is recommended.

## Calculus II

*Full year; twelfth grade*

This year-long course initially revisits the fundamental concepts of calculus, emphasizing rigorous analysis. It continues with a dual approach: exercising the application of course topics and visiting their logical, conceptual basis. The application side may consist of short exercises and more involved projects. The logical, conceptual side introduces and explores the idea of rigorous derivation and proof. In both approaches, students look at the derivative and the integral as they relate to the following topics: infinite series, non-Cartesian coordinate systems, differential equations, vector-valued functions, and multivariable functions. A TI-83, TI-83 Plus, TI-84, or TI-84 Plus graphing calculator is required. *Prerequisite:* successful completion of Calculus I (or equivalent). A grade of B- or better is recommended.

## Advanced Statistics

*Elective, second semesterEleventh or twelfth grade*

A continuation of Introduction to Statistics, this course concentrates on statistical inference procedures. In the first half of this semester course, students analyze and interpret data. Topics include confidence intervals, tests of significance, and power and errors analysis associated with tests of significance. In the second half of the course, students design and implement a data collection method for a project of their choosing. Students then analyze and interpret the collected data and present their processes and findings. A TI-83, TI-83 Plus, TI-84, or TI-84 Plus graphing calculator is required. *Prerequisite: *successful completion of Introduction to Statistics (or equivalent).

## Big Data and Analytics

*Elective, first semester*

Have you ever wondered how websites like Netflix and Amazon know which products to suggest to you next? Or how the NBA uses past performance to inform recommendations for athletes? This course explores questions such as these by using programming and statistics concepts to understand big data and analytics. Topics include data visualization, program efficiency, probability and randomness, artificial intelligence, and data structures. This course uses Python as a programming language to access the extensive graphing and statistical tools of the Pylab library. In addition to programming assignments, students also complete short math, reading, and writing assignments relating to data science concepts. This course is cross-listed in both Mathematics and General Studies subject areas. *Prerequisite*: Computer Science I or permission of instructor.

## Mathematical Finance

*Elective, first semester*

Students use mathematical thinking and skills to build an understanding of personal finance as well as broader knowledge of the financial world. Students learn about saving for short- and long-term goals of college, homes, and retirement and about investing in stocks, bonds, and funds. Students study, from a mathematical perspective, taxes and the differences between progressive and regressive taxation. Each student develops and works on a mock financial portfolio for the semester and stays current on financial news and developments through blogging and online discussion. *Prerequisite: *Algebra IIB (may take concurrently).

## Individualized Program in Mathematics

*Semester or full year*

This course meets the needs of those students whose previous math experiences do not fall neatly into our traditional sequence. Students work on an individually designed course of study. The student’s course of study is contracted with the teacher for either a semester or a year, and the student works with the teacher in a one-on-one relationship. Students interested in this course must speak with the department head before registration.

## Intensive Courses

## Geometry B: Logic and Proof

*Second semester or first intensive**Ninth, tenth or eleventh grade*

This course is an introduction to formal reasoning, logic, and proof. Students examine how Euclid’s postulates are the basis of an axiomatic structure for plane geometry. Various methods for illustrating deductive reasoning are used, including two-column proof, proof by contradiction, and derivation. While the emphasis for this course is on geometric reasoning, students extend their studies with investigations of algebraic reasoning and proof. Throughout the course, students construct proofs for important mathematical concepts such as the Pythagorean Theorem, the laws of sines and cosines, and the quadratic formula. *Prerequisites:* successful completion of Geometry A and Algebra IIA (or equivalents). Grades of C or better recommended.

## Introduction to Statistics

*First intensiveTenth, eleventh, or twelfth grade*

Intro to Statistics develops students’ potential to quantify and interpret what they observe; collecting, representing, analyzing, and modeling with data are activities of major importance in contemporary society. This statistics course emphasizes that learning to interpret data correctly is a means to developing increased awareness of social, political, and scientific issues. Students learn to create unbiased surveys and experiments, detect bias in other surveys, describe data objectively with graphs table, and numerical statistics; determine correlation between variables and understand the concept of a statistically significant result.

In the intensive model of Intro to Statistics, students look outside the Statistics textbook and inside the city of Seattle (and beyond) to learn how to become a generator, user, and interpreter of information from a statistical perspective.