Mathematics - St. John's Preparatory School

Let's Run the Numbers

MATHEMATICS

The ability to comprehend, develop, and utilize mathematical concepts is invaluable throughout life; all global citizens need strong fluency in this area. Achieving this ability is best done by learning to draw reasonable conclusions from information found in various sources. Whether from observation, words, data, or graphs, students use the tools of mathematics to analyze information and become adept at problem solving. Students are encouraged to welcome new challenges, question and justify their conjectures and solutions, test the reasonableness of those solutions, develop facility with and understanding of mathematical operations and procedures, and use them appropriately to make sense of the world.

Middle School Requirements

The Middle School math program is unleveled in the sixth grade. One day a week is designated for extension or review, individualized for the students. Seventh and eighth grade math classes will be leveled; levels will be determined by student demonstration of knowledge and teacher recommendation. Students have the opportunity to complete two full years of algebra.

High School Requirements

The High School mathematics requirement is four full years of math. Students also have the opportunity to take more than one math course when their schedule allows for it. The mathematics curriculum encompasses the traditional high school courses of Algebra 1 through AP Calculus AB and BC, with additional courses in statistics and advanced level calculus.

Course Descriptions

Middle School Mathematics Courses

Grade 6 Math

In the problem-centered math 6 curriculum, students employ the inquiry approach to learn new concepts. The purpose of this format is to begin the exploration of rigorous math in a real world context. Students become contributors to what is learned in class by posing and exploring their own questions. They are encouraged to think critically and share their results and conjectures as they collaborate with their classmates. They develop the ability to ask effective questions, assess their own work, and learn communication and presentation skills. These skills become the foundation of their future development in all levels of mathematics.

This course develops students’ mathematical reasoning as they explore problems dealing with factors and multiples; the distributive property; comparisons with ratios, rates, and percentages; arithmetic operations with fractions; the basics of perimeter and area, extending to surface area and volume using triangles and parallelograms; and computations and operations involving decimals and percentages.

Grade 7 Pre-Algebra

This course continues building essential pre-algebra skills with a deep dive into topics introduced in the 6th grade that lay the groundwork for a beginning study of algebra in grade 8. Students in pre-algebra 7 extend knowledge of the real number system with an aim to master operations with integers, rational numbers and the properties of these real number operations. Ratios, rates, unit rates, and proportionality are examined in detail. Students gain depth of understanding on percents, percent proportions, percent equations, percent change, and simple interest. Students conjecture about chance, test with experimental probability, and make decisions based on theoretical probability in the fundamental exploration of statistics and probability. Variable expressions are introduced and students begin simplifying algebraic expressions and solving one and two-step linear equations and inequalities. Students round out their focus through a grade level examination of geometric shapes and angles, including surface area and volume.

Grade 7 Algebra 1A

Algebra is the foundation of all of the subsequent mathematics courses. It is a problem-solving tool for modeling real world occurrences, both symbolically and graphically. “Owning” algebra is the key to successful understanding and navigation of future courses like geometry, trigonometry, calculus and higher math, and thus lays the groundwork for study in science, economics, medicine, computers, and many other fields, including those which have yet to be imagined. Students develop conceptual understanding and technical facility with algebraic procedures to support their continued study of mathematics.

This course begins the study of algebra—the abstract modeling of the real world. In this course, students build the foundation for higher math through the following work: reviewing operations of real numbers, expressions and variables; solving equations and inequalities; understanding ratios, rates, percentages, proportions, and similar figures while solving problems; working with sets, unions and intersections; recognizing patterns and understanding the concept of functions; studying, modeling and graphing linear functions and developing trend lines; and solving systems of linear functions and inequalities.

Grade 8 Intro to Algebra

This course begins the study of algebra—the abstract modeling of the real world. Students are introduced to the language and structure of algebra. Topics of development include: solving simple and multi-step equations, graphing and writing linear equations, solving systems of linear equations, an introduction to functions and the language and representation of functions, properties of exponents and scientific notation, rational and irrational numbers and the Pythagorean Theorem, and other exploratory topics. Grade-level geometry includes a study of: transformations in the coordinate plane; angles, triangles and similarity; and an in-depth examination of surface area and volume through an algebraic lens. Real world data is modeled and analyzed with scatter plots and trendlines. Students who complete this course move on to take a comprehensive Algebra I course at the CP, Accelerated, or Honors level in the ninth grade.

Grade 8 Algebra 1B

This course continues the study of algebra. Students review real numbers, functions, linear functions, and solving equations. They develop facility by delving deep into the following skills: working with integral, zero, negative and rational exponents, and exponential functions; solving problems involving exponential growth and decay; operating with polynomials and factoring; recognizing and graphing quadratic functions and solving quadratic equations by factoring, completing the square, and the quadratic formula; solving systems of linear and quadratic functions; simplifying radicals and operations with radical expressions, graphing square root functions, and solving radical equations; simplifying rational expressions and solving rational equations; solving problems involving direct and inverse variation; organizing and analyzing data using matrices, statistical graphs, measures of central tendency and dispersion; and exploring probability, permutations and combinations. Students who complete the Algebra IA—Algebra IB sequence move on to take a CP, Accelerated, or Honors Geometry course in the ninth grade.

High School Mathematics Courses

Algebra 1

Geometry

Geometry teaches students to represent situations with geometric models and apply properties of figures, to classify figures in terms of congruence and similarity and apply these relationships to deduce properties of and relationships of axioms. Algebra skills will be applied and reinforced throughout this course.

*offered at the College Prep, Accelerated, & Honors Levels [1 credit]

Algebra 2/Trigonometry

Precalculus

Calculus

Statistics

Financial Algebra

The purpose of this course is to provide students with an opportunity to learn and use algebra on real world problems with a financial focus. The course is designed for students to explore algebraic thinking patterns and functions in a financial context, and to apply these skills to relevant research topics of interest. Topics covered in the course will include function analysis and systems of equations, graphing, statistics, variables, and modeling. Financial applications will be a primary emphasis of the course and will include loans, investments, credit, insurance, taxes, and budgeting.

*offered at the Accelerated & Honors Levels [1 credit]

AP Precalculus

AP Calculus AB

AP Calculus AB includes methods of finding and applying the derivative and integral as a limit, studying the calculus of polynomial, trigonometric, exponential, logarithmic and inverse functions and applying it to problems involving analytic geometry, science and economics. The syllabus is determined by the AP College Board, and necessitates a rigorous and challenging pace. Preparation for the Advanced Placement Calculus AB Exam is extensive.

[1 credit]

AP Calculus BC

AP Calculus BC is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions.

[1 credit]

AP Statistics

Advanced Placement statistics is equivalent to a first year college statistics course. The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Topics will include measures of central tendency and variation, probability, binomial distributions, the central limit theorem, linear regression, chi-square tests, and an introduction to calculus. Emphasis will be on applied problems in business, psychology, biology and the social sciences. Course content will include preparation for the Advanced Placement Statistics exam.

[1 credit]

Multivariable Calculus & Differential Equations

During the first semester after covering some preliminary topics on trigonometric substitutions, areas of surfaces of revolution, center of mass, work, fluid pressure, and the binomial series, the main topics are vector algebra, vector calculus, partial derivatives, multiple integrals, line integrals, and surface integrals as well as applications of these concepts. The second semester is a course on ordinary differential equations beginning with the complex exponential function, homogeneous and non-homogeneous linear differential equations and systems of those, including applications to various types of harmonic motion and electric circuits. Separable, Bernoulli, exact, and Euler differential equations with some applications are covered as well as graphical solutions of autonomous equations, series solutions, and numerical methods employing a graphing calculator. If time permits, the Laplace transform is introduced.