Math Department

The goal of the HPA Math Department is to offer a curriculum that is student centered. Each class is steeped in the essential skills and nurtures the growth of problem solving strategies. The curriculum is heavily laced with the inquiry and discovery methods.

* Please be aware that a student must take three years of math in high school, which must include algebra II/ trig. 

Department Philosophy

Teachers in the Math Department incorporate a variety of instructional practices to engage students with different learning styles. From beginning to college level courses, the faculty in this department strive to demonstrate the importance of mathematics in the real world to each student.

Possible careers in the field of Mathematics:

• Aircraft Pilot
• Actuary
• Architect
• Astronomer
• Banker
• Biologist
• Business
• Certified Public Accountant
• Computer Engineer
• Data Processor
• Dentist
• Economist
• Electronics Technician
• Engineer
• Environmental Analyst
• Lawyer
• Mathematician
• Natural Science Manager
• Navigator
• Pharmacist
• Physician
• Physician’s Assistant
• Psychologist
• Real Estate Broker
• Statistician
• Systems Analyst
• Teacher

_________

Algebra I

Term: 2 Semesters

Credit: 1.0

Prerequisites: Pre-Algebra and teacher recommendation

Algebra I is a comprehensive course that includes topics such as recognizing and using patterns, operations in the real number system, solving equations and inequalities, proportional reasoning and statistics, linear functions, absolute value functions, solving system of equations, laws of exponents and exponential equations, polynomials and factoring, quadratic functions, rational functions, square-root functions, trigonometry, probability and set theory, and transformations of functions. Algebraic thinking skills are developed through a variety of classroom activities, including group and individual investigations, hands-on manipulatives, real-world problem solving, projects, class discussions, note taking, and utilizing technology.

Algebra IB

Term: 2 Semesters

Credit: 1.0

Prerequisites: Algebra IA* and teacher recommendation

This course focuses on providing a foundation for all future math courses. Upon completion, students will have reviewed the same material covered in Algebra I. Many real-life problems are modeled to stimulate interest and provide a stronger foundation for greater understanding. Topics covered include: solving system of equations, laws of exponents, exponential equations, polynomials and factoring, quadratic functions, rational functions, square-root functions, trigonometry, probability and set theory, and transformations of functions. Algebraic thinking skills are developed through a variety of classroom activities, including group and individual investigations, hands-on manipulatives, real-world problem solving, projects, class discussions, note taking, and using technology.

Algebra I Honors

Term: 2 Semesters

Credit: 1.0

Prerequisites: Pre-Algebra and teacher recommendation.

Algebra I Honors is organized around families of functions, with special emphasis on linear and quadratic functions. Students learn about each family of functions and represent them in multiple ways—as verbal descriptions tables, and graphs. Students also learn to model real-world situations using functions to solve problems arising from those situations. 

Algebra II Trigonometry

Term: 2 Semesters

Credit: 1.0

Prerequisites: Algebra I and Geometry

This course follows the mathematics curriculum delineated by the National Council of Teachers of Mathematics. Increased emphasis is placed on reading comprehension, problem solving, and the use of functions as tools for modeling real-world situations. Some of the topics in this course include: linear and quadratic functions, polynomial equations, exponential and logarithmic functions, trigonometric functions, matrices, and systems of equations.

Algebra II Trigonometry Honors

Term: 2 Semesters

Credit: 1.0

Prerequisites: Algebra 1, Geometry, and teacher recommendation

This course presents the topics of a college freshman course covering Algebra and Trigonometry and provides students with a solid preparation and firm foundation of concepts, techniques, and applications for more advanced college-level mathematics. Topics presented include: equations, inequalities, mathematical modeling, functions and their graphs, polynomial functions, rations functions with conics, logarithmic functions, basic trigonometry, analytic trigonometry, systems of equations, and matrices. Accelerated algebraic thinking skills are developed through a variety of classroom activities, including group and individual investigations, real-world problem solving, class discussions, note taking, and utilizing technology.

AP Calculus AB

Term: 2 Semesters

Credit: 1.0

Prerequisites: Honors Calculus and teacher recommendation

Advanced Placement Calculus AB presents the topics of a college freshman course in differential and integral calculus that include: limits and continuity, derivatives, applications of derivatives, the definite integral, differential equations and mathematical modeling, applications of definite integrals. Upper School students who complete the course and earn satisfactory grades on the AP exam (given in May) may be awarded credit at the college they will attend.

AP Calculus BC

Term: 2 Semesters

Credit: 1.0

Prerequisites: Honors Calculus, AP Calculus AB and teacher recommendation

Advanced Placement Calculus BC presents the topics of a college freshman course in differential and integral calculus. Material covered includes: limits and continuity, derivatives, applications of derivatives, the definite integral, differential equations and mathematical modeling, applications of definite integrals, sequences, L’Hopital’s Rule and improper integrals, infinite series, parametric, vector, and polar functions. Upper School students who complete this course and earn satisfactory grades on the AP BC exam (given in May) may be awarded credit at the college they will attend and receive both AB and BC scores.

AP Statistics

2 Semesters

Credit: 1.0

Prerequisites: Algebra II Trigonometry

This course, which follows the College Board AP Statistics Course requirements, introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students learn to conduct statistical analyses, reflect on what these concepts and techniques mean, and identify how they were derived. Students are challenged to develop their critical thinking and general analytical skills.

Geometry

Term: 2 Semesters

Credit: 1.0

Prerequisites: Algebra IB or Algebra I

Students actively engage in a process of self-discovery, constructing meaning, and making connections to geometric concepts with greater depth of understanding and retention. Some of the topics in this course include: reasoning in geometry, using tools of geometry, discovering and proving triangle properties, discovering and proving polygon properties, discovering and proving circle properties, transformations and tessellations, area, the Pythagorean Theorem, volume, similarity, and trigonometry.

Calculus Honors

Term: 2 Semesters

Credit: 1.0

Prerequisites: Algebra II Trigonometry Honors, Pre-Calculus or teacher recommendation

The major topics of study in the first semester are functions, limits and derivatives, while the second semester is devoted to extending these topics to include more complex families of functions and to introducing the integral calculus. The goals of this course are to: (a) support and strengthen the student‘s understanding of the fundamental concepts underlying calculus, (b) develop the student‘s problem-solving skills, and (c) provide students with a solid conceptual introduction to calculus. This course is designed to prepare students for an introductory college-level calculus course or an Advanced Placement calculus course.

Math Topics

Term: 1 Semester

Credit: 0.5

Prerequisites: None

This course is offered to students who wish to improve their scores on the SAT and to review selected math concepts and appropriate problem-solving strategies. The course is designed to meet the following objectives: (1) improve student success with College Board aptitude and achievement tests, (2) develop and extend the skills necessary to complete distribution requirements in college, and (3) enrich student experiences in mathematics. Typically, interested students take this course in the fall of senior year or spring of junior year.

Pre-Calculus

Term: 2 Semesters

Credit: 1.0

Prerequisites: Algebra II Trigonometry

Pre-Calculus is designed for students seeking an in-depth review and enrichment experience in preparation for the College Board examinations. The course provides solid preparation and a firm foundation of concepts and techniques that build on familiar topics from algebra and geometry and extend to a pre-calculus level of understanding. Topics covered include an extension of some Algebra II topics: polynomial functions, inequalities, functions, exponents and logarithms, analytic geometry, trigonometry, vectors and determinants, introduction to combinatorics.

Probability and Statistics

Term: 1 Semester

Credit: 0.5

Prerequisites: Algebra II Trigonometry and teacher recommendation

This course provides an understanding of the kinds of regularity that occur in random functions and also provides experiences in associating probabilistic mathematical models with phenomena in the real world. Topics include averages, measures of variation, frequency distributions, and probability functions associated with random variables, binomial distributions, sampling, the normal curve, and statistical methods available for decision-making.