Upper School Mathematics
The Mathematics Department offers a sequence of courses by which students can gain an understanding of the style and content of mathematics, become adept in its fundamental skills, develop an understanding of the analytic power of mathematics through problem solving, and begin to explore the subject for the beauty of its abstractions and the variety of its applications. Confidence building and minimization of fears are conscious goals. While technology is used in many situations, students are also asked to do work by hand to ensure a deep understanding; our emphasis is usually on “why,” instead of simply “how.”
Our aim is to develop creative, fresh, innovative, deep-thinking—not rote doing. Lessons center around multidimensional, open, visual, contextualized, and compelling tasks that encourage student exploration, creativity, questioning, pondering, and discussion. We believe mistakes are valuable, that everyone can learn math to the highest levels, and provide regular feedback to inform learning and emphasize individual growth.
Requirements
Three years of math courses—30 credits—are required for graduation but students are encouraged to take Calculus before graduating. Most students also explore other branches of mathematics through the range of one-term electives that are offered. A student may elect to do an independent study in an area of particular interest where a course is not offered.
Honors
Honors placements by Departmental recommendation only.
Math FAQs
Rather than solely focusing on one element of math (i.e., algebra, geometry, etc.) in a given year, elements of all the math disciplines are integrated at each grade level. This also means we are able to incorporate data science into the curriculum.
Integrated Math courses can be defined by themes and applications, putting focus on context and critical thinking.
Integrating our courses provides even more opportunities for:
- Authentic learning and assessment
- Students to see themselves in the curriculum
- Students do the “sense-making” and develop as creators of mathematics
- Students to use authentic mathematics to analyze sociopolitical, cultural, and global issues.
What this looks like in practice:
Ninth-graders are assessed throughout their first 12-week term of math where they are provided with choices for tasks at varying levels of complexity. Teachers gather evidence and conference with students regularly to determine the most appropriate level of math for each student. Separate honors-level sections are offered beginning with the second term in 9th grade.
The Beaver Upper School schedule builds in time for students to work with teachers individually or in small groups during and outside of class. Teachers provide extra support and enrichment during all parts of the day.
Upper School Math Courses
Foundations for Algebraic Reasoning
Foundations for Algebraic Reasoning
This course is designed for students who have not completed Algebra 1 through quadratics in middle school. Students will build a strong foundation in algebraic reasoning and grapple with real-world applications. Work will focus on solving linear equations and systems and the exploration of exponential and quadratic relationships.
Not offered at the Honors level.
… [read more]Integrated Math 2: Algebra, Geometry, and Data Science
Integrated Math 2: Algebra, Geometry, and Data Science
Integrated Math 2 students expand their algebraic reasoning and understanding of mathematical models including quadratic equations and exponential functions. Students also explore probability and build upon their knowledge of transformations, congruence, and similarity while developing logic skills through conjecture, argument, and proof. Investigations in this course build connections between all topics covered.
Prerequisites: Integrated Math 1,
… Algebra 1, or Foundations for Algebraic Reasoning. Offered at the Honors and Standard levels. Honors level requires departmental recommendation. [read more]Integrated Math 3: Algebra, Geometry, and Data Science
Integrated Math 3: Algebra, Geometry, and Data Science
Integrated Math 3 students continue to expand their algebraic reasoning and understanding of mathematical models including complex numbers, exponential equations, and polynomials. Students also explore sampling and build upon their knowledge of solid geometry and circle theorems while building connections between all topics covered.
Prerequisites: Integrated Math 2. Offered at the Honors and Standard levels. Honors
… level requires departmental recommendation. [read more]PreCalculus – Functions
PreCalculus – Functions
In this course, students will take a deeper look at various families of functions: rational, radical, exponential, logarithmic, and polynomial. Students will learn about the ways in which domain, range, continuity, inverses, composition and transformation apply to those functions. Students will also have opportunities to analyze real-world data and generate predictive models. Topics from data science
… are often included in this course, as well.Prerequisites: Integrated Math 2 and Integrated Math 3. Offered at the Honors and Standard levels. Honors level requires departmental recommendation.
[read more]PreCalculus – Trigonometry
PreCalculus – Trigonometry
Students in this course will learn about angle measurement, periodic behavior, and a range of applications related to both right triangle and circular trigonometry. Analytic geometry and polar coordinates are often included in this course, as well. Prerequisites: Algebra II and Geometry. Honors level requires departmental permission.
Prerequisites: Integrated Math 2 and Integrated Math 3. Offered
… at the Honors and Standard levels. Honors level requires departmental recommendation. [read more]Calculus – Derivatives & Integrals
Calculus – Derivatives & Integrals
The Derivatives course includes all of the topics of an introductory Calculus course including limits, derivatives and their applications.
The Integrals course includes all of the topics of an introductory Calculus course including definite integrals, indefinite integrals and their applications.
Prerequisite: Precalculus. Offered at the Honors and Standard levels. Honors level requires departmental recommendation.
… [read more]Advanced Calculus – Derivatives & Integrals (Honors)
Advanced Calculus – Derivatives & Integrals (Honors)
This course covers all of the topics of an introductory Calculus course, exploring concepts in depth with a greater emphasis on both the abstract aspects of calculus and its various applications in the real world. Students will be expected to enter the class with a firm grasp of all concepts covered in previous math courses.
Prerequisite:
… Precalculus and departmental recommendation. Offered at the Honors level only. [read more]Upper School Math Electives
Advanced Topics (Honors)
Advanced Topics (Honors)
In this course, students will be asked to grapple with a range of topics that extend beyond fundamental calculus topics. Topics covered may include but are not limited to l’Hospital’s rule, linear approximations, differentials, Newton’s Method of Approximation, center of mass, arc length, surface area, and differential equations. Students will be asked to think creatively and
… apply their knowledge to complex real-world problems, and extend their knowledge of fundamental calculus topics. Students taking Advanced Calculus or others with a strong interest in pursuing advanced mathematics at the college level are strongly encouraged.Class offered at the Honors level only
Prerequisites: Advanced Calculus or departmental permission
[read more]Financial Algebra
Financial Algebra
Ever wondered, “How do I create a budget?” or “What’s the secret to mastering debt?” Want to unravel the mysteries of taxes and insurance, and discover the keys to paving your way through college expenses? In this course, you will be using skills you have previously learned in Integrated Math 3 (or Algebra II) to deepen
… your knowledge on personal finances. Get ready to transform your understanding of money, making it not just about equations but about owning your financial future with confidence!Students can opt to take this class at the Honors level
Prerequisites: Integrated Math 2 or Algebra 1 [read more]
Probabilities and Matrices
Probabilities and Matrices
Delve into the realms of Probability and Matrix Theory through the fascinating lens of Markov Chains and other applications. After learning the fundamentals of probability and matrix theory, you will work with models of possible event sequences. This course blends theory with applications to explore how matrices are used to understand and calculate probabilistic processes and
Students can opt to take this class at the Honors level
Prerequisites: Integrated Math 2 or Algebra 2
Statistics and Data Science
Statistics and Data Science
This course includes the gathering of data and a variety of sampling techniques, hypothesis testing, frequency distribution, normal distribution, correlation, linear regression, theoretical distributions, and inferential statistics. This course asks students to consider questions such as these: How is data summarized so that it is intelligible? How should statistical data be interpreted? How can we measure
… the inherent uncertainty built into statistical data? Students will be asked to collect, analyze and interpret real data to answer real questions in their areas of interest.Students can opt to take this class at the Honors level.
Prerequisites: Integrated Math 3 or Algebra 2 and Geometry
[read more]Examples from the US Math Classroom

BVR Academics: US math students design public spaces
