Over the past eight years, 50% of our seniors (on average) have successfully completed AP Calculus before graduating from MPH. At MPH math classes are multi-age, allowing every student to complete the required three-year sequence of college preparatory mathematics while providing the flexibility for gifted students to progress at a different pace. (Over 80 % of our students complete five years of Math.) Whenever possible, we utilize a five-point approach to presenting material: numerically, algebraically, graphically, verbally (descriptively) and concretely (through an activity or with a picture).
Most students also pursue a variety of elective courses, including advanced mathematics, such as Calculus III, AP Calculus and AP Statistics, and/or independent studies with faculty. Our pre-calculus curriculum is associated with Dr. Helen Doerr at Syracuse University, whose program/research MPH helped pilot a number of years ago.
Teachers blend the best of traditional pedagogy with proven contemporary teaching practices, including frequent collaborative projects and open-ended investigative activities. Faculty members encourage students to take intellectual risks by raising questions and formulating conjectures using mathematical argument. Interactive computer software, graphing calculators, and the Calculator-Based Lab (CBL) are used in courses when appropriate. As part of the School's "Writing for Life" initiative, students are required to express mathematical concepts in clear, coherent prose in their math courses.
MPH students actually enjoy participating in math, and chose to spend their free time testing and sharpening the math skills they have acquired. Our math league team is a popular extracurricular activity and consistently places first among similarly sized schools in Onondaga County. This year, over 80 students signed-up to take the Upper School American Competition Exam (AMC), even though it was not required and had no bearing on their class grade.
Accounting
This is an introductory course in the basics of financial accounting. Students learn the rules for debit and credit as well as the structure and preparation of a General Journal and of a General Ledger. The content of the course includes the preparation of a worksheet from which the students write a business’s financial statements. Students study cash controls, the maintenance of a checking account, and various special journals to make the recording of repetitive transactions more efficient. At a more advanced level, students prepare year-end adjustments, they write the financial statements of a corporation, and they complete the process of closing the books at the end of a fiscal period. A final topic of payroll accounting is introduced if time permits. The course includes the use of spreadsheet software, an essential tool used in accounting and business today. Students complete three major practical exercises in accounting during the course. Prerequisite: Successful completion of Math II. May not be taken in place of Math III.
Advanced Placement CalculusAB (1 academic credit) Calculus is a branch of mathematics that deals with two kinds of problems: the determination of the rate of variable change (differential calculus) and the derivation of functions from known rates of change (integral calculus). The AP Calculus course is designed to be an introduction to differential and integral calculus which covers all topics specified by the College Board committee in its Advanced Placement Mathematics AB course description. The course style is that of a freshman college course with open‑ended assignments, independent study, and class periods evenly divided between lectures and problem solving sessions. The development of the course is less rigorous than AP Calculus BC since a number of concepts require sophisticated mathematical concepts for complete proof—concepts that the students are not expected to grasp at this level. AP Calculus stresses problem solving, manipulative skills, and theory. The course ends with a comprehensive review in preparation for the May Advanced Placement examination. Text: Calculus and Analytical Geometry by Sherman K. Stein, Anthony Marcellos. Published: McGraw Hill 5th ed., 1992
Advanced Placement CalculusBC with Applications (1 academic credit) The second year of calculus covers topics unique to the Advanced Placement BC Calculus curriculum and numerous applications of calculus. Topics include vector and parametric functions and their derivatives, polar coordinates, rigorous definitions of limits, advanced integration techniques with improper integrals, and an extensive treatment of sequences and series. Applications include length of a path, areas bounded by polar curves and work. Various applications from economics and physics are also treated. The course includes a thorough preparation for the Calculus BC examination, including a demanding review of CalculusAB from an advanced view.
Text: Calculus and Analytical Geometry by Sherman K. Stein, Anthony Marcellos. Published: McGraw Hill 5th ed., 1992 Prerequisite: AP Calculus AB
The study of Statistics at MPH is a full year course that follows the suggested course content specified by the College Board in order to prepare students for the Advanced Placement exam in Statistics.
Requirements for the AP Designation:
Students who wish to qualify for the “AP” designation on their MPH transcripts must meetthe following conditions:
1) They must earn at least a B- (80%) in the course.
2) They and their parents must sign the AP contract.
3) They must take the AP exam on the scheduled day in May.
Students who do not meet these requirements will have the course title “Statistics” on their transcripts.
The course in Statistics begins by focusing on the analysis of data with an emphasis on observing patterns in data and the departures from those patterns. Students plan a study of data, deciding what to measure and how to measure it. Students calculate the more familiar statistical indicators, such as the mean, median, and mode, as well as more complex statistical measures, such as the standard deviation.
Students produce models of data using regression analysis, probability and simulation in order to be able to anticipate patterns beyond the measured data, to predict the patterns that random events might make. They observe the normal distribution and learn how to mathematically describe the variations from the norm.
Students study the process of sampling and sampling distributions to produce a confidence interval and to make an inference about a population based on the sample. The binomial and normal distributions provide good models for inference. Students analyze the relationship between a statistical model and the raw data used to create the model. Using the model and the laws of probability, they state how confident one can be about an inference from a given model. Students use several tests of significance to make inferences from a sample, including the "z," "t," and Chi-Square tests.
It is recommended that students take the AP exam in Statistics to measure their progress against the national norms. Prerequisite: Grade of “B” in Math IIIAC or equivalent.
Functions (1 academic credit) This course offers a bridge between Math IIIAC and Precalculus AC for those students who would like further practice with algebraic manipulations and the study of functions. It also serves as an additional course for those who are interested in continuing with math after Math IV CP. Topics include a review of algebraic manipulations, linear and quadratic equations and inequalities, characteristics of functions and manipulations with polynomial, rational, exponential and logarithmic functions. The unit circle, right triangles, graphs and applications of trigonometry are also studied. The calculator plays an integral role in discovering mathematical concepts. Text: Contemporary College Algebra & Trigonometry, A Graphing Approach, 2nd edition, Thomas W. Hungerford, Saunders College Publishing, 2005.
Mathematics IAC (1 academic credit)
This course is offered to accelerated seventh, eighth and ninth graders with exceptional achievement and aptitude. This course is for students who are capable of a challenge and who enjoy delving into how and why mathematical concepts work. Students pursue traditional topics of algebra: solving equations and inequalities, linear functions and graphing, systems of linear functions and inequalities, operations with polynomials, quadratic equations, and rational and irrational numbers. The course pays special attention to problem solving skills, written communication of ideas, and the use of the graphing calculator.
Text: Algebra I, McDougal Littell 2001.
Mathematics ICP (1 academic credit) This course is offered to ninth graders who have successfully completed Math 8. Students pursue traditional topics of algebra: solving equations and inequalities, linear functions and graphing, systems of linear functions and inequalities, operations with polynomials, quadratic equations, and rational and irrational numbers. The course pays special attention to algebraic manipulation skills, communication of ideas, and the basic use of the graphing calculator.
Mathematics IIAC (1 academic credit) The second course in the AC mathematics sequence is offered to students who have successfully completed Math IAC. This course is for students who wish to be challenged and who enjoy delving into how and why mathematical concepts work. Students examine topics in plane and coordinate geometry using algebra as a foundation for each unit. Math II introduces Euclidean geometry as an axiomatic mathematical model founded on postulates, and students experience its development as theorems and properties are explored. Students are also introduced to indirect, paragraph, and two-columnproofs for plane geometry, and algebraic proofs that are used particularly in analytic geometry and the coordinate plane. The graphing calculator is used to explore linear equations. Activities are used to explore the properties of geometric shapes using interactive geometric software and the ancient tools of construction, the compass and straight edge.
Text: Unified Mathematics, Book II, Houghton-Mifflin,1985.
Prerequisite: Successful completion of Math IAC.
Mathematics IICP (1 academic credit) The second course in the CP mathematics sequence introduces the student to geometric concepts. Students examine topics in plane geometry using algebra as a foundation for each unit. Math II introduces Euclidean geometry as an axiomatic mathematical model founded on postulates and theorems. Students experience its development as rules are explored. Each theorem and definition is used in a variety of situations. Algebraic equations that are used to solve the problems are justified by the theorems, postulates and definitions. Activities are used to explore the properties of geometric shapes using hands on explorations with measurement tools (ruler and protractor), interactive geometric software and the ancient tools of construction- the compass and straight edge.
Text: Unified Mathematics, Book II, Houghton-Mifflin, 1985.
Prerequisite: Successful completion of Math I.
Mathematics IIIAC (1 academic credit) The third course in the AC mathematics sequence is offered to students who have successfully completed Math IIAC. It stresses algebraic techniques, problem solving, and exploring rational, radical and quadratic equations. Students continue their study of algebraic structures, including the real and complex number systems. The course begins to develop function theory. Trigonometric functions are introduced from the viewpoint of the unit circle and students explore their graphs, and applications. Exponential and logarithmic functions are introduced, as well as practical applications. The graphing calculator is used to explore and solve equations, discover the properties of trigonometric, logarithmic, and exponential functions, and to simplify calculations involving complex functions. Material from this class is now included on the SAT.
Text: Algebra 2: Application, Equations and Graphs, McDougall Littell, 2003.
Prerequisite: Successful completion of Math IAC and IIAC.
Mathematics IIICP (1 academic credit) The third course in the CP mathematics sequence is offered to students who have successfully completed Math II. It stresses algebraic manipulations and problem solving, exploring rational, radical and quadratic equations. Students continue their study of algebraic structures, including the real number system. The course begins the development of function theory. Algebraic manipulations involving whole number, integral and fractional exponents are examined. Trigonometric functions are introduced from the viewpoint of the unit circle and students explore their graphs and applications. The graphing calculator is used to explore and solve equations, to check solutions, to discover properties, and to simplify calculations. Material from this class is now included on the SAT.
Text: Algebra 2: Application, Equations and Graphs, McDougall Littell, 2003
Prerequisite: Successful completion of Math II. Mathematics IVCP(1 academic credit)
Mathematics IV CP (1 academic credit) The fourth course in the CP mathematics sequence is offered to students who have successfully completed Math III. This course is for students who wish to sharpen the mathematical skills learned in previous courses. It reinforces and extends the algebraic skills taught in Math I, II and III. Math IV reviews and extends the topic of circular and trigonometric functions, including problem-solving and graphing. The manipulative algebra skills mastered in the first part of the year are applied to trigonometric problems. A variety of topics, including linear algebra and matrices, probability, exponential and logarithmic functions are surveyed throughout the year.
Text: Understanding Intermediate Algebra, Hirsch and Goodman, 2002.
Precalculus AC (1 academic credit) The Precalculus AC course builds on the skills developed in the accelerated UpperSchool mathematics sequence. Precalculus AC places a strong emphasis on problem solving. Sound manipulative algebra skills are necessary. Students analyze the relationships between numeric, algebraic and graphic representations of linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions, along with the special characteristics of each function. The graphing calculator, Calculator Based Laboratory (CBL), various probes and programs, and computer software and applications provide a variety of ways to explore and create mathematics. Algebraic proofs are discussed to provide a greater appreciation for the "how and why" of our mathematical system. One to three essays, lab reports or projects are due each quarter to increase the student’s ability to communicate mathematical knowledge. Text: Pre-calculus Lab Activities, Doerr, 2001; Pre-calculus: A Graphing Approach, Demana, Wait et al., Addison Wesley, 1987.
Prerequisite: Successful completion of Math III AC and a B+ test average in Math III AC, or successful completion of Functions.