# St. Anselm’s Abbey School

A Catholic, Benedictine School for Boys Grades 6 - 12

75 years of rigorous, classical education

# Mathematics

Mathematics is taught at St. Anselm's in the traditional way, building strong foundations in Algebra, Geometry, and Calculus which give our students the tools needed to make predictive analyses of their world.

## Department Overview

Every student has math class every day, and all students take an Advanced Placement Mathematics course their senior year with ninety-five percent taking AP Calculus. Technology is implemented to augment, but not replace, the classical formalism of Mathematics.

## Curriculum Sequence

 Form A Fundamentals of Math Form I Pre-Algebra Form II Algebra Form III Algebra II & Trigonometry Form IV Geometry Form V AB Pre-Calculus or BC Pre-Calculus and AP Calculus I BC Form VI AB Pre-Calculus students: AP AB Calculus or AP StatisticsBC Pre-Calculus students: AP BC Calculus II; Calculus III (Multivariable)**Instructor permission needed

## Fundamentals of Math

The introductory course in the St. Anselm's mathematics sequence. Over the year, students will build confidence in understanding and applying the fundamentals of advanced arithmetic and basic geometry. Topics to be studied include: Fractions, decimals, rational and irrational numbers, probability, combinations and permutations, areas, and volumes.

Course Length: All Year

Registration Policy: Required for Form A

## Pre-Algebra

This course finalizes students’ foundation in arithmetic and provides an introduction to Algebra. Topics covered include: introduction to signed numbers, arithmetic operations, introduction to variables, simple one-variable equations, simple geometric figures and their measurements, ratio, percent and probability.

Course Length: All Year
Registration Policy: Required for Form I

## Algebra I

This course, which covers the full Algebra I textbook, will help students to become comfortable with symbol manipulation and the idea of a quantity without a fixed value. Topics covered over the year include: variables, fundamental and distributive properties, exponents, adding, subtracting, multiplying and dividing polynomials, factoring, linear and quadratic equations, word problems, inequalities, and systems.

Course Length: All Year

Registration Policy: Required for Form II

## Algebra II & Trigonometry

A continuation of the students' study of algebra which begins to explore higher-order equations and the concept of complex numbers. Topics covered over the year include: division of polynomials, factoring to solve third-degree and higher polynomials, irrational and complex numbers, algebraic fractions, trigonometric functions, exponential and logarithmic functions, sequences and series, statistics and probability.

Course Length: All Year

Registration Policy: Required for Form III

## Geometry

This course exposes students to the principles and applications of common geometric operations in two and three dimensions. Students embrace an intuitive and axiomatic approach to the material, studying truth tables and symbolic and syllogistic arguments. The focus of the course will be on traditional Euclidean geometry, including theorems on lines and planes, angles, constructions, areas and volumes, coordinate geometry and trigonometry. The course concludes with a section in preparation for pre-calculus, including sequences and series, matrix algebra, probability theory, and analytic geometry.

Course Length: All Year
Registration Policy: Required for Form IV

## Pre-Calculus (AB)

This is a course in algebra designed to introduce and develop those topics that are used in higher math and includes limits, the analysis of rational and polynomial functions, transcendental functions including the exponential, logarithmic, trigonometric and complex. Considerable attention will be placed on the trigonometric functions including the derivation of the laws of sines and cosines and an introduction to vectors. Systems of equations will be studied including both equalities and inequalities. Matrix methods will be developed for the solution of the systems. Finally, there will be an introduction to sequences, series and probability.

Course Length: All Year
Registration Policy: Mathematics option for Form V

## Pre-Calculus (BC)

This course is identical to the (AB) course except that it will be taught in one semester. In the second semester, students will take the first-year college course in differential calculus.

Course Length: Fall Semester
Registration Policy: Mathematics option for Form V

## AP Calculus (AB)

This course covers the material found in the first year of college calculus. It includes the theory of the derivative and its uses in finding the maximum and minimum of functions, the tangents to curves, how the change of one function is related to the change in another function and includes application to the sciences. In the second semester, the integral is developed and is applied to the problems of finding areas, length of curves, volumes and surface areas.

Course Length: All Year
Registration Policy: Mathematics option for Form VI

## AP Calculus (BC) I

A second-semester follow-up to the students' course in Pre-Calculus (BC). In this fast-paced course, students will become fluent in the vocabulary, principles, and procedures of introductory calculus. Topics to be covered include: Limits, continuity, derivatives, mean value theorem, related rates, min-max, inflection points, derivative tests, introduction of the integral.

Course Length: Spring Semester
Registration Policy: Prerequisite: Pre-calculus (BC); Mathematics option for Form V

## AP Calculus (BC) II

This is a continuation of the Calculus (BC) I which was begun in the second semester of Form V. The theory of the integral and its use to calculate averages of continuous functions, areas, length of curves, volumes, and surface areas are discussed. Methods of integration are studied and integration over two dimensions is introduced. Topics developed include separable and first order differential equations as well as Taylor series expansions.

Course Length: All Year
Registration Policy: Prerequisite: AP Calculus I (BC); Mathematics option for Form VI

## AP Statistics

This is an introduction to Statistics and is equivalent to the first-year college course, although it is more conceptual in nature and less focused on software and formulas than many introductory courses. The basic techniques of hypothesis testing are covered, and the conceptual framework is built slowly and emphasized. The course is not as mathematically rigorous as the calculus; it places greater demands on communication skills so that the students can explain the concept of data analysis, form conclusions, support these conclusions with statistical facts and explain what these conclusions mean to others to make them better consumers of statistical information.

Course Length: All Year
Registration Policy: Mathematics option for Form VI

## Multi-Variable Calculus

This is the material covered in the third semester of college calculus. The emphasis is on the vector approach to three dimensional systems and the calculus that applies to them.

Course Length: All Year
Registration Policy: Prerequisite: AP Calculus II (BC) with Departmental Permission; Mathematics option for Form VI

## Creative Origami and 3-D Design (Non-Departmental)

This course will teach students about the art of origami. We will begin with the basics by folding Japanese traditional models and learn how to follow diagrams. More complex models will follow, including birds, mammals, dinosaurs, dragons, insects, and geometric shapes such as stars and polyhedra. Students will learn techniques for folding a variety of papers including thicker paper for wet-folding that allows for exhibit-quality work. Students will also learn to design their own origami through folding techniques, patterns, math, and spatial relationships and will develop a final project. There is flexibility as students learn at their own pace and can choose from a wide variety of subjects. Models will be exhibited.

Mathematics Faculty
Mr. John Corrigan, '83, Department Chair
Algebra I; Pre-Calculus (BC); AP Calculus (BC) I & II
B.S., Physics, University of Maryland
jcorrigan@saintanselms.org
Mr. Chris Battle
Mathematics
B.A., Biology, Johns Hopkins University
cbattle@saintanselms.org
Mr. Paul Commins
Algebra II/Trigonometry; AP Statistics
M.S., Statistics, University of Minnesota
B.A., Mathematics, Grinnell College
pcommins@saintanselms.org
Mr. Bill Crittenberger
Pre-Calculus AB, AP Calculus (AB)
M.S., Education, Johns Hopkins University
M.A., History, Yale University
B.A., Journalism, George Washington University
bcrittenberger@saintanselms.org

Dr. Michael Manglitz, '00
Pre-Algebra
Ph.D. English Language and Literature, The Catholic University of America
M.Ed. Reading Instruction, Goucher CollegeM.A. English Literature, The Catholic University of America B.A.
English Literature & Secondary Education, Goucher College
mmanglitz@saintanselms.org

Mr. John Montroll
Geometry, AP Calculus (AB)
M.A., Applied Mathematics, University of Maryland
M.A., Electrical Engineering, University of Michigan
B.A., Mathematics, University of Rochester
jmontroll@saintanselms.org
Dr. Herbert T. Wood
Multi-Variable Calculus
Ph.D., Physical Chemistry, University of Wisconsin, Madison
B.Ch.E., Chemical Engineering, Catholic University of America
hwood@saintanselms.org