MATHEMATICS PHILOSOPHY
The MacDuffie mathematics curriculum is a program in which students can develop an understanding of the meaning of mathematical concepts and gain proficiency with the mechanics of mathematics. The curriculum provides experiences designed to help students move along the continuum from concrete to abstract mathematical representations. These experiences include continued development of arithmetic, algebra, geometry, and advanced concepts with a further goal of training students in the “language” of mathematics, thus preparing them for future work in math and science. MacDuffie’s math program treats problem-solving as an ongoing process, designed to help students bridge the gap between the theory of mathematics and its applications in the real world. Problems are presented in a manner which requires students to use their knowledge and understanding to resolve new situations. The introduction of historical references is designed to show students that mathematics is a human endeavor and to lead them towards a greater appreciation of the power of pure mathematical thinking. All math classes at MacDuffie encourage independent thinking and the willingness to take academic risks.
Although the school encourages students to study mathematics during all of their UpperSchoolyears, all candidates for graduation from MacDuffie must take at least three math courses in grades 9 – 12. The three courses must include the equivalent of Algebra I, Geometry, and Algebra II. If the required distributional courses are completed before a student has taken three courses in grades 9 – 12, he or she must continue to advanced math courses. Honors courses are offered as options for Algebra I, Algebra II, Geometry and Pre-calculus to provide capable students with opportunities for more in-depth work at each level. Those students who are ready to take a college-level calculus course may take AP Calculus. Students must have a year grade of at least C- to advance to the next level of mathematics. Students enrolled in Algebra I Honors and in other math courses from Algebra II on, are required to have a TI-83 or TI-84 graphing calculator.
Note on math placement: Students entering MacDuffie are tested for math proficiency. Math placement is based on the test results and previous math achievement.
MIDDLE SCHOOL
1300 – Math 6
Grade 6
This course is designed to promote an understanding of the decimal numeration system along with mastery of the basic operations with whole numbers, fractions and decimals. The course also introduces integers, percents and statistical analysis. The use of variables combined with the creation and solution of simple equations sets the foundation for abstract thinking. Various problem-solving techniques are introduced and utilized in all aspects of the course.
1302 – Math 7
Grade 7
This course is designed so that students can gain mastery of the basic operations of integers and rational numbers. More emphasis is placed on abstract thinking. The students learn to create and solve two-step equations and inequalities along with how to represent linear functions graphically on a coordinate system. Percents are presented through ratios and proportions as well as equations. In addition to basic problems, various applications of percents are studied. Students continue to do statistical analysis. Geometry skills include measurement and the development and use of formulas for calculating perimeter, circumference, area and volume. Problem-solving techniques continue to be developed and reinforced.
1312 – Algebra 1
Grades 8 – 10
This course analyzes the basic arithmetic concepts in an abstract way. The content includes integers and rational numbers, solving equations, operations with polynomials, graphing, systems of equations, ratios and proportions, factoring, quadratic equations, rational expressions, and radicals. The course introduces the students to the language of mathematics and teaches them how to translate from words to symbols. Continued emphasis is given to problem-solving and critical thinking. This course is normally followed by Geometry.
1314 – Algebra 1 (Honors)
Grades 7 – 8
Department Approval Only
This is an Algebra 1 course designed for Middle School students who have solid arithmetic skills and whose pre-algebra introduction included manipulation of integers as well as positive and negative rational numbers. The content covers traditional first-year algebra material in greater depth. It also introduces students to topics from an
Algebra II curriculum. Emphasis is on developing analytical skills through the use of problem-solving, proof and mathematical readings.
UPPER SCHOOL
1330 -Geometry
Grades 9 – 11
Geometry allows students to analyze their physical world mathematically as they are introduced to the language and symbolism pertaining to the subject. The content includes parallel and perpendicular lines, polygons, congruent triangles, ratios and proportions, Pythagorean Theorem, circles and arcs, as well as perimeters, areas and volumes. The mastery of these geometric concepts provides an excellent opportunity for utilizing algebraic skills. This course is normally followed by Algebra II.
1332 – Geometry (Honors)
Grades 8 – 11
Department Approval Only
The content for the honors level Geometry is similar to that of regular geometry but goes more in-depth and has a greater emphasis on the theoretical. Students learn to use inductive and deductive reasoning to develop logical chains of thought and to construct paragraph and two-column proofs. This course is normally followed by Algebra II with Trigonometry (Honors Level).
1316 – Algebra II
Grades 10 – 12
This course includes a study of the real number system and its properties, the complex number system, linear equations and inequalities, relations and functions, polynomials, rational expressions, and quadratic functions. Students are also introduced to exponential and logarithmic functions, and trigonometric functions, identities, and graphs. Practice in analyzing and solving word problems is given throughout the course. This course is normally followed by Pre-calculus or Introductory Statistics.
1318 – Algebra II & Trigonometry (Honors)
Grades 10 – 12
Department Approval Only
This course is designed for students who show mathematical aptitude and interest and would benefit from a faster paced curriculum. In addition to the regular content of a second-year algebra course, students do more in-depth work in trigonometry. The development of analytical skills is a continuous process with emphasis on problem-solving and the communication of mathematical ideas. Successful completion of the course may allow students to take Pre-AP Calculus.
1360 – Pre-Calculus
Grades 11 – 12
The content and skills of this course are designed to prepare students for the study of calculus and advanced mathematics. Students also gain an appreciation for the use of mathematics in such areas as business and the social and biological sciences. Topics include trigonometry, functions (including exponential and logarithmic), analytic geometry, sequences and series, and an introduction to calculus. The purpose of this course is to gain an understanding of the development of mathematical concepts and theorems as well as the ability to interpret real-life situations using the symbolic and graphic languages of mathematics. Emphasis is placed on the skills of analysis and synthesis of mathematical ideas. Students learn to draw on a variety of past experiences as a means of creating mathematical models.
1364 – Pre-AP Calculus (Honors)
Grades 11 – 12
Department Approval Only
This course is designed to prepare students for the AP Calculus course. Emphasis is on functions and graphing. Topics include polynomial and rational functions, trigonometric functions, exponential and logarithmic functions and analytic geometry. Students in this course focus on the development of mathematical concepts and theorems. The curriculum is rigorous and provides students with a broad, but in-depth, foundation for advanced study in mathematics. The final quarter of the year will be spent on an introduction to calculus, including limits and derivatives.
1366 – Calculus (Honors)
Grades 11 – 12
Department Approval Only
Students who have successfully completed Pre-Calculus may opt to take this introductory Calculus course. Students in this course learn to find derivatives and study definite and indefinite integrals. Emphasis is on how basic calculus concepts can be applied to business, economics, the life sciences, and other fields.
1368 – Advanced Placement Calculus AB (AP)
Grades 11 – 12
Department Approval Only
Following the recommendations from the “Advanced Placement Course Description” published by the College Board, this course includes: differentiation of polynomials, exponential and logarithmic functions, explicit and implicit differentiation, applications of the derivative including curve sketching, maxima-minima problems, motion problems, and related rates.
The Fundamental Theorem of Calculus and techniques of integration are covered as well as applications of the definite integral including area under the curve, volume, and differential equations.
Students are required to take the AP exam at the conclusion of the course.
1370 – BC and Multivariable Calculus – (AP) (Full year course)
Grades 11 – 12
(Prerequisite: AP Calculus)
Department Approval Only
This AP level course will cover topics from the BC AP Calculus syllabus: parametrized curves, polar and vector functions, Euler’s Method for solutions of differential equations and L’Hospital’s Rule. Applications of integrals will be included, as well as polynomial approximations and series, most notably the Taylor Series. The course will continue with an introduction to Multivariable Calculus: partial derivatives, multiple integrals, and ultimately vector calculus.
Students are required to take the AP exam at the conclusion of the course.
1380 – Introductory Statistics
Grades 11 – 12
(Prerequisite: Algebra II)
Statistical ideas and statistical reasoning and their relevance in our world today are the focus of this course. Students learn to collect, organize, and display data; to use appropriate statistical methods to analyze that data; and to develop and evaluate inferences and predictions that are based on the data.
1382 – Advanced Placement Statistics (AP)
Grades 11 – 12
Department Approval Only
This course follows the syllabus recommendations published by the College Board. The course is divided into four major units: Organizing Data, Producing Data, Probability, and Statistical Inference. The first unit, Organizing Data, covers graphing and data presentation along with descriptive statistics, correlation, and regression. The unit on Producing Data delves into the processes involved in sampling, surveys, experiments, and simulation. The Probability unit discusses the rules of general probability and randomness, and how these apply to the most common types of variable distributions. The last unit, Statistical Inference, ties all these ideas together by showing how to make conclusions with confidence based on available data.
Students are required to take the AP exam at the conclusion of the course.
