# Math

A broad spectrum of Mathematics classes, from Algebra to Advanced Calculus, helps prepare students to be mathematically literate, critical thinkers, skilled in reasoning and logic.

Students have the opportunity to participate in many local and national mathematics competitions and activities throughout the year, including the Northwest Math Championships, World Math Day, the American Mathematics Contest and many more. Students also have the opportunity to join the Northwest School Math Club. Club members meet weekly, having fun with mathematics as well as offering free tutoring to the student body.

## Habits of Mind

- Account for how your brain works. Be intentionally open to learning.
- Establish a process for solving problems.
- Use multiple approaches and ways to solve problems. For example, visualize problems and solutions, draw a picture.
- Look for connections….ask and apply.
- Look for patterns….ask and apply.
- Find mathematical equivalence.
- Ask why of yourself and others.
- Represent mathematical ideas in a variety of ways.
- Communicate your thinking both verbally and in writing.
- Attend to precision and check your accuracy.
- Persevere. Tinker, try stuff, be willing to make mistakes and don’t erase them. Take a risk.

## 9th Grade

Students are placed in math classes according to their past experience and accomplishment. In making placement decisions, the Department considers the skills students have acquired, the habits of mind they’ve developed, and the concepts they’ve studied, but also the depth of their experience and the degree of mastery they’ve achieved. We use a holistic approach, considering records of past performance (e.g., grades), teacher recommendations, syllabi/textbook review, and proficiency exams.

Algebra I with Geometry

This course is designed for 9th graders who have not completed an Algebra I course. Students will develop their skills and understanding of linear equations and functions and their graphs, and begin the study of a variety of basic functions including quadratics. Students will develop skills in working with polynomials, exponents, radicals, and rational expressions in algebraic terms. Basic ideas of geometry will also be part of the course.

Geometry

Geometry focuses on visual and spatial skills of students while working with geometric shapes in two and three dimensions. We study geometric principles, including congruence, proofs, similarity, the Pythagorean Theorem, and trigonometry with an emphasis on developing logical problem-solving skills and reasoning. This course will combine the study of the theoretical ideas of geometry along with their applications.

Algebra II

Algebra II extends the many ways in which mathematics can model the world. Students explore how to represent patterns with mathematics, including what it means to find the best fit line to represent the pattern. Then students take an in-depth look at the major properties of polynomials as well as how to manipulate polynomials in order to better represent the world. Then other modeling techniques are explored, including matrices, exponential functions, and logarithmic functions. During these investigations, complex numbers are also explored as a necessary way in which to accurately model the world.

Pre-Calculus

Pre-Calculus is an in-depth study of functions with an emphasis on thinking about change in preparation for calculus. We study linear, exponential, logarithmic, trigonometric, polynomial and rational functions. We learn to move fluently between verbal, numeric, graphic and formulaic representations, and we learn the sorts of real-world phenomena that each kind of function models. We study compositions of functions, inverses and transformations, in each case considering what the changes mean in terms of the function’s graph and the sorts of situations it models. In the course of these investigations, we work in new ways with topics students are familiar with (e.g., the family of quadratic functions) and we use algebraic skills the students will need in calculus. The course includes a significant amount of trigonometry and an introduction to the concept of limits.

## 10th Grade

Students are placed in math classes according to their past experience and accomplishment. In making placement decisions, the Department considers the skills students have acquired, the habits of mind they’ve developed, and the concepts they’ve studied, but also the depth of their experience and the degree of mastery they’ve achieved. We use a holistic approach, considering records of past performance (e.g., grades), teacher recommendations, syllabi/textbook review, and proficiency exams.

Algebra II

Algebra II extends the many ways in which mathematics can model the world. Students explore how to represent patterns with mathematics, including what it means to find the best fit line to represent the pattern. Then students take an in-depth look at the major properties of polynomials as well as how to manipulate polynomials in order to better represent the world. Then other modeling techniques are explored, including matrices, exponential functions, and logarithmic functions. During these investigations, complex numbers are also explored as a necessary way in which to accurately model the world.

Pre-Calculus

Pre-Calculus is an in-depth study of functions with an emphasis on thinking about change in preparation for calculus. We study linear, exponential, logarithmic, trigonometric, polynomial and rational functions. We learn to move fluently between verbal, numeric, graphic and formulaic representations, and we learn the sorts of real-world phenomena that each kind of function models. We study compositions of functions, inverses and transformations, in each case considering what the changes mean in terms of the function’s graph and the sorts of situations it models. In the course of these investigations, we work in new ways with topics students are familiar with (e.g., the family of quadratic functions) and we use algebraic skills the students will need in calculus. The course includes a significant amount of trigonometry and an introduction to the concept of limits.

Calculus

Calculus, the mathematics of motion and change, includes the study of the major concepts of limits, derivatives, and integrals. An understanding of the concepts and their connections with each other is emphasized. Students will develop facility with calculating limits, derivatives, and integrals and will work with using these ideas in a variety of applications.

## 11th Grade

Students are placed in math classes according to their past experience and accomplishment. In making placement decisions, the Department considers the skills students have acquired, the habits of mind they’ve developed, and the concepts they’ve studied, but also the depth of their experience and the degree of mastery they’ve achieved. We use a holistic approach, considering records of past performance (e.g., grades), teacher recommendations, syllabi/textbook review, and proficiency exams.

Math Analysis

This course is for students who want to work at their own pace and/or fill in gaps from prior learning experiences in math. Students propose their own topics of study in algebra and geometry, working with the teacher and their peers and using textbooks and online resources to study their topics of focus. One day per week, the class applies their knowledge to collaboratively analyze data from the news and other sources. As a part of each trimester, the class engages in alternative forms of visually representing mathematical thinking. In addition, once per week, students pose questions to each other in an open forum of math conversation. This course is not designed to prepare students for calculus, but rather to develop a strong basic understanding of advanced algebra and geometry.

Pre-Calculus

Pre-calculus is an in-depth study of functions with an emphasis on thinking about change in preparation for calculus. We study linear, exponential, logarithmic, trigonometric, polynomial and rational functions. We learn to move fluently between verbal, numeric, graphic and formulaic representations, and we learn the sorts of real-world phenomena that each kind of function models. We study compositions of functions, inverses and transformations, in each case considering what the changes mean in terms of the function’s graph and the sorts of situations it models. In the course of these investigations, we work in new ways with topics students are familiar with (e.g., the family of quadratic functions) and we use algebraic skills the students will need in calculus. The course includes a significant amount of trigonometry and an introduction to the concept of limits.

Calculus

Calculus, the mathematics of motion and change, includes the study of the major concepts of limits, derivatives, and integrals. An understanding of the concepts and their connections with each other is emphasized. Students will develop facility with calculating limits, derivatives, and integrals and will work with using these ideas in a variety of applications.

Advanced Calculus

This is a second-year calculus course. We begin with an in-depth study of Taylor polynomial approximations of transcendental functions. We study the origins and the many practical uses of polynomial expansions, and we learn the convergence tests for infinite series. We go into further depth with techniques and applications of integrals, including partial fractions and improper integrals. We spend roughly half the year studying multivariable calculus, beginning with partial fractions and their applications and working through double integrals in both rectangular and polar coordinates and triple integrals. We use these skills to explore applications in physics that involve functions of multiple variables.

## 12th Grade

Statistics

It is often noted that we live in a data-driven society. A more accurate description is that we live in an “interpretation of data”-driven society. This course is all about how we interpret, process, and visualize the data we confront in our daily lives. You will read, discuss, and write about the use and misuse of statistics in media and politics. You will also design and conduct observational studies and experiments to answer questions of interest to you. There are a wide variety of disciplines that require an understanding of statistics. Examples include, but are not limited to, the social sciences (i.e., psychology or sociology), biostatistics, criminology, political science, business, economics, and law.

Pre-Calculus

Pre-calculus is an in-depth study of functions with an emphasis on thinking about change in preparation for calculus. We study linear, exponential, logarithmic, trigonometric, polynomial and rational functions. We learn to move fluently between verbal, numeric, graphic and formulaic representations, and we learn the sorts of real-world phenomena that each kind of function models. We study compositions of functions, inverses and transformations, in each case considering what the changes mean in terms of the function’s graph and the sorts of situations it models. In the course of these investigations, we work in new ways with topics students are familiar with (e.g., the family of quadratic functions) and we use algebraic skills the students will need in calculus. The course includes a significant amount of trigonometry and an introduction to the concept of limits.

Calculus

Calculus, the mathematics of motion and change, includes the study of the major concepts of limits, derivatives, and integrals. An understanding of the concepts and their connections with each other is emphasized. Students will develop facility with calculating limits, derivatives, and integrals and will work with using these ideas in a variety of applications. One section will move at a slower pace than the others.

Advanced Calculus

This is a second-year calculus course. We begin with an in-depth study of Taylor polynomial approximations of transcendental functions. We study the origins and the many practical uses of polynomial expansions, and we learn the convergence tests for infinite series. We go into further depth with techniques and applications of integrals, including partial fractions and improper integrals. We spend roughly half the year studying multivariable calculus, beginning with partial fractions and their applications and working through double integrals in both rectangular and polar coordinates and triple integrals. We use these skills to explore applications in physics that involve functions of multiple variables.