Through studying mathematics at Putney, students learn the skills necessary for academic and personal success while building deep conceptual understanding through projects, rich problems, and explorations. Our math courses cover fundamentals for college preparation while encouraging our students to explore the beauty of mathematics and its connection with other subjects.
0.5 Credit
What lies beyond Calculus? Advanced Topics in Mathematics explores areas of math not typically covered in a standard math course progression. In addition to building understanding of new topics, students refine their ability to discuss sophisticated mathematical concepts. This course emphasizes mathematical literacy and writing to prepare students for advanced mathematical studies. Topics vary from year to year based on the interests of the students. In recent years, topics have included group theory, linear algebra, graph theory, and multivariable calculus. Prerequisite: Calculus 2
1.0 Credit
How do we model change using mathematics? Algebra 1 uses collaborative tasks, written explanations, and formal assessments to explore change in the context of linear and exponential functions. The course emphasizes working flexibly with multiple representations of a function (words, tables, equations, and graphs.) Students collaborate in small groups to articulate how and why a mathematical method works, both aloud and in writing. Practical examples range from modeling costs for different orchard apple-picking scenarios to analyzing historical changes in The Putney School’s tuition. Spreadsheets are used to automate repeated calculations and focus on identifying mathematical patterns and trends. Students demonstrate their learning through regular completion of practice work, cumulative review assignments, and formal, in-class assessments.
1.0 Credit
How can we use mathematics to understand and describe patterns found in our world? Algebra 2 investigates this question through the study of algebraic functions and by building mathematical models for input-output relationships that are ubiquitous in everyday life. Students examine projectile motion, suspension bridges, population growth, compound interest, and common logarithmic scales, such as the Richter scale, to learn about different ways that variables are used in linear, quadratic, higher-degree polynomial, exponential, and logarithmic functions. Students demonstrate their understanding through quizzes, written assignments showcasing applied problem-solving strategies, and cumulative unit write-ups of skills and concepts. Prerequisite: Geometry
1.0 Credit
How do we quantify the rate at which something is changing? How do we measure the total change within a system? How can we describe the relationship between these variables? Calculus 1 explores these questions through guided investigations, discussion, algorithmic practice, and writing. Students focus on building full explanations of key calculus concepts that tie together verbal, algebraic, and graphical representations with real world examples and models. Topics include the meaning, calculation, and applications of derivatives and integrals. Students demonstrate their mastery of the analysis of incessant change through quizzes and a course-long writing assignment. Prerequisite: Precalculus
1.0 Credit
How do we transform complicated integrals into simpler, integratable problems? Calculus 2 interrogates this question through an in-depth study of integration techniques, including u-substitution, integration by parts, trigonometric integration, trigonometric substitution, integration of rational functions by partial fractions, and manipulations of the integrand. Activities include applications of Calculus 2 content to science and engineering scenarios to demonstrate utility as well as develop problem-solving skills. Students demonstrate their learning through quizzes and writing assignments (including examples and explanations of what they have learned). Prerequisite: Calculus 1
0.5 Credit
How can we use various programming languages to help us design virtual models and create experiences that bring our ideas to life? Computer Science 1 provides students with the foundations and opportunities to develop computer coding skills in a supportive project-based environment. The opportunities and limits of basic computer programming are tested through the use of p5js, a visual JavaScript library, and Python. Students learn how using loops, binary logic and decision making, arrays, methods, and functions with an object-oriented approach allows for creative program design. Assessments are founded on project-based tasks where students must demonstrate the proficient application of specific assigned skills in creative programs of their own design.
1.0 Credit
How can visual logic and numerical data connect to expand mathematical thinking from the paper into the real world? Geometry explores the use of foundational numeric and algebraic concepts to discover patterns and relationships in dimension and space. This course focuses on practicing an in-depth and intentional approach to creative problem solving. In-class collaborative tasks ask students to discover, explain, and prove concepts and formulas including the Pythagorean Theorem, Triangle Sum Theorem, area formulas, and trigonometric ratios. Students demonstrate their learning through in-class assessments and a written portfolio reporting on the logic and methods used to solve complex problems. Prerequisite: Algebra 1
0.5 Credit
What is debt? What is equity? How do individual investors plan for the cost of an education or prepare for retirement? Under what circumstances might businesses’ need for funds create opportunities for investors to save for personal financial goals? Investment and Finance addresses these questions through real-world data analysis, guided reading on investing topics, vocabulary work to demystify technical jargon, and conversations with outside visitors from the business world. Students read financial statements from publicly traded companies, analyze historical patterns in stock and bond prices, compute effective income tax rates for different income levels, and model the impact of different savings rates on when people can retire. This course uses spreadsheets extensively, but previous experience with spreadsheets is not required. Prerequisite: Algebra 2
1.0 Credit
How do we transform mathematical functions to model specific patterns found in real-world data? Precalculus students discover ways to answer this question by expanding their earlier understanding of functions to model a more complex set of situations. The class examines the growth of greenhouse gasses in our atmosphere, the properties of a snowflake, and many examples of circular motion, ranging from Ferris wheels to bike wheels. Through the patterns in these phenomena, students are introduced to exponential and logarithmic change, sinusoidal functions, sequences and series, and parametric equations. Students learn how to calibrate mathematical models to given data sets, deepening their understanding of functions and the ways they can be transformed. Students demonstrate their understanding through quizzes, tests, and cumulative unit write-ups of skills and concepts. Prerequisite: Algebra 2
0.5 Credit
How can one make defensible inferences from data? Statistics is a one-trimester course focusing on exploratory data analysis through lectures, discussions, and learning the statistical programming language R and RStudio user interface. Topics include an introduction to data, experimental design, graphical presentations, linear regression, confidence intervals, and hypothesis testing. Prerequisite: Algebra 2