Mathematics

Our Mathematics Department offers a sequence of rigorous courses that prepare students for anything they choose to do next. At the same time, we recognize that all students do not acquire mathematical skills at the same rate or develop the ability for abstract thinking at the same age. There is no 9th grade mathematics course, for instance; rather, our offerings provide a variety of placement options at a given grade level. The goal of placement decisions is to offer each student a course that challenges them and allows them to take risks, but at the same time provides them with a reasonable opportunity to experience the satisfaction of success.

*Honors Distinction for Algebra 1 and Geometry (9th and 10th grade students only)

Algebra I begins with a study of the real number system. We will take a close look at the operations and properties of real numbers, signed numbers, and fractions. We will spend the majority of the year studying the topics associated with equations, inequalities, and systems in one and two variables. This includes simplifying, solving, and graphing. The curriculum also includes an in-depth study of exponents, polynomials, and factoring. We will close out the year with radicals and quadratic equations. Students will need to take concepts they have learned and apply them to real world applications. TI-84 Graphing Calculator is required. An honors distinction is available for 9th and 10th grade students through the completion of additional in-depth work.

This introductory course in geometry integrates coordinates and transformations with a traditional approach to 2-dimensional and 3-dimensional Euclidean geometry. We approach and solve problems from different perspectives to gain an appreciation of the interconnectivity among concepts in mathematics. Writing will be used to help students develop their understanding of geometry by applying concepts to their own experiences and constructing meaning for mathematical symbols, procedures and concepts. Technology will be incorporated regularly to strengthen and explore geometric properties. An honors distinction is available for 9th and 10th grade students through the completion of additional in-depth work. Prerequisite: Successful completion of Algebra 1

*Honors Distinction for Algebra 1 and Geometry (9th and 10th grade students only)

This course reviews and extends the concepts and methods covered in Algebra I while introducing the concept of a function. The course reviews and enhances student skills and understanding of solving equations, inequalities, and systems of inequalities. New topics include the study of quadratic, logarithmic, polynomial, exponential, radical, and rational functions. The course builds strong skills in working with exponents, radical expressions, complex numbers. Students are instructed in the use of the TI-84 Plus graphing calculator, a tool they use to explore and investigate concepts, to learn about the behavior of the different families of functions in addition to modeling and data analysis. Prerequisite: Successful completion of Algebra 1 and Geometry

This second-year algebra course consists of a thorough and fast-paced study of algebra and an introduction to the topic of trigonometry. Its emphasis is on the structure of mathematical systems and their underlying concepts. The focus is on the representation of problems algebraically and graphically. Topics include a study of functions (linear, quadratic, polynomial, and rational), systems of equations in two and three variables, inequalities and complex numbers, variation, exponential and logarithmic functions, and trigonometric functions. Applications include an introduction to data analysis and modeling through the introduction of regression analysis. Strong algebraic skills are presumed. The ability to absorb and master large amounts of material quickly and with little review is essential for success. Prerequisite: Successful completion of Algebra 1 and Geometry.

This course is for students who are in need of a deeper understanding of algebra and trigonometry in order to be prepared for more advanced math courses like precalculus. Topics include properties of functions, matrices, sequences and series, logarithms, trigonometry, and probability, as well as a review of elementary algebra as dictated by the needs of the students in the class. For the various functions, students will gain a deep understanding of domain and range through studying parent functions, transformed functions, algebraic properties, and graphs. Regression will be used throughout the year as it applies to a variety of functions including linear, quadratic, and exponential. Prerequisite: Completion of  Geometry and Algebra 2;  Division Head approval required.

Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will observe patterns and departures from patterns, decide what and how to measure, produce models using probability and simulation, and confirm models. Appropriate technology, including TI-84 graphing calculators and spreadsheets will be used regularly for instruction and assessment. Students will become fluent in basic probability, measures of central tendency and the normal distribution. In addition, students will also study important and timely real-world mathematical skills. These skills—basic accounting, the behavior of the stock market, and financial analysis performed in the business world—will be developed and learned through using statistically based data analysis and technology. A key goal of the course is to focus on students’ development of critical thinking skill. Prerequisite: Senior or PG standing, and completion of Algebra 2. Juniors may elect Statistics and be concurrently enrolled in another math course.

This course introduces students to new concepts needed for the study of calculus and strengthens understanding of topics in algebra and geometry. Students study functions with particular attention to linear, quadratic, trigonometric, polynomial rational, exponential, and logarithmic functions. Students learn to work with functions numerically, visually, algebraically, and verbally. In addition, students study sequences and series. Graphing technology is utilized throughout the course to enhance student understanding of mathematical concepts. The frequent use of real-world applications illustrates and reinforces mathematical ideas. Prerequisite: Successful completion of Algebra 2 and Geometry. Students must demonstrate strong knowledge of the content of Algebra 2 and Geometry; and strong problem solving ability.

This course includes an extensive study of trigonometric, exponential, and logarithmic functions. Particular attention is paid to the properties of their graphs. Other topics include polynomials, analytic geometry, matrices and determinants, sequences and series, the binomial theorem, polar coordinates, and probability. During the fourth quarter, students will begin to see the connections between the mathematics they have studied and the idea of calculus. Graphing technology is utilized throughout the course to enhance student understanding of mathematical concepts. The frequent use of real-world applications illustrates and reinforces mathematical ideas. The ability to absorb and master large amounts of material quickly and with little review of Geometry and Algebra 2 and Trigonometry is essential. Prerequisite:  Successful completion of Algebra 2 and Geometry. Students must demonstrate outstanding knowledge of the content of both Algebra 2 and Geometry, and strong critical thinking and problem solving ability.

This course provides students with an intuitive approach to the fundamentals of differential calculus and integral calculus. The language of calculus will play an important role in developing the definitions of derivatives and integrals. Focusing on algebraic functions, students explore limits, leading to the definition of derivative. The concepts of average and instantaneous rate of change are investigated. We develop the rules of differentiation, including the chain rule and implicit differentiation, and apply them to problems in optimization, related rates, and curve sketching. We will introduce the concepts of finding area under a curve, the integral regarded as the anti-derivative, and the Fundamental Theorem of Calculus. Applications of integration are also included. Generally, the content of this course is not as broad or as deep as the content of Calculus AB and will take the time to review algebra topics as needed.  Prerequisite: Successful completion of a Precalculus course.

This course is a study of the basic concepts, methods and applications of differential and integral calculus. Students learn through a multi-representational approach with concepts, results, and problems being expressed geometrically, analytically, and verbally. This is a college level course as determined by the College Board. Topics covered include limits, rates of change, the chain rule, implicit differentiation, related rate problems, movement of a particle, optimization, Riemann Sums, fundamental theorem of calculus, area between curves, volume of solids of revolution, differentiation and integration of polynomial, trigonometric, exponential and logarithmic functions, and L’Hopital’s Rule. Students may earn one semester of college credit in calculus. They need a TI-84 graphing calculator and must take the College Board AB Calculus exam. Prerequisite: Completion of Introduction to Calculus or Precalculus Accelerated or Precalculus with permission of the department.

This course is an extension of AB Calculus, not an enhancement. It covers all topics of AB Calculus, as well as analysis of planar curves, differential equations, slope fields, derivatives of parametric, polar and vector functions, the convergence and divergence of sequences and series, as well as Taylor and Maclaurin polynomials. A student may earn two semesters of college credit in calculus. Students must have a TI-84 graphing calculator and must take the College Board BC Calculus exam at the end of the year. Prerequisite: Completion of AB Calculus and permission of the department.

The course follows the syllabus for the Advanced Placement examination in Statistics. Students study the tools for collecting, organizing, and displaying data. They learn about planning and conducting surveys and experiments and drawing conclusions from their results. The course includes probability, the properties of the normal distribution, and statistical inference. Students must have a TI-84 (or better) graphing calculator and are required to take the College Board AP Statistics exam. Prerequisite: Completion of math through precalculus or outstanding achievement in Statistics, and recommendation of both the English and Math Department.

 

When entering Tilton School, students are placed into classes that correspond to their background, ability, and interests. After the first year of algebra, all students study Geometry followed by Algebra 2 and Trigonometry. Goals for students throughout the sequence include mastery of fundamental operations along with development of calculator and problem solving skills and an appreciation for the structure and applications of mathematics. Students are required to have a TI-84 Plus graphing calculator beginning in Algebra 1.

The Mathematics Department recognizes the importance of having students work with data throughout the curriculum. In many courses, including Algebra 2, Trigonometry, and Precalculus, students are given the opportunity to learn about the modeling of functions by using data taken from real-world situations. Students will learn how to apply “continuous mathematics” to data taken from disciplines including science, politics, and current events.

Although any student’s greatest resource is themselves, they will, at Tilton, learn that even more can be accomplished through working with their classmates and teachers. Individual conversations and one-to-one help sessions between a student and their mathematics teacher are an integral part of their learning experience.

We strongly encourage students to study mathematics for each of their years at Tilton School and explore the wide array of course offerings that expand their knowledge and critical thinking skills.