Mathematics

Mathematics is offered in the Academy at three levels: Honors (H), Regular, and Basic College Prep (BCP). The level of study for each student is determined by his/her past performance in mathematics courses. The Honors courses are for those students who have done very well in mathematics. Students must be highly motivated and able to quickly understand and easily apply new concepts. The Regular courses provide a thorough study of Algebra, Geometry, and Pre-Calculus. The Basic College Prep courses are for students who find the regular level of mathematics too challenging. The BCP curriculum covers all the basic material in Algebra, Geometry, and Pre-Calculus with topics and a pace suitable for the needs of the students.

All levels of mathematics require students to reinforce the work done in class so they will acquire the skills necessary to progress through a sequential course of study. Homework is assigned at each class meeting and tests are given regularly. Semester examinations are given at the end of both semesters in most of the core courses, except AP courses, which do not have a second semester exam. The elective courses provide enrichment topics. The material covered in the electives requires students to use the skills developed in the core courses. The offerings include Elements of Design, Money Management, and Computer Science. Advanced Placement (AP) courses are offered in Calculus AB, Calculus BC, Statistics, and Computer Science. A student enrolled in an AP course is required to take the AP examination in that subject in May. The exam is written, administered, and assessed by the College Board.

The faculty in the Mathematics Department uses technology, when appropriate, to deepen understanding and enhance productivity. Computers are routinely used in Elements of Design, AP Statistics, and Computer Science classes. All classrooms have Smart Boards and all students in Algebra 2/Trigonometry and subsequent courses are required to own a graphing calculator. Students may purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended.

Graduation Requirements

Three years of study in the core courses are required for graduation. Typically a student will study Algebra 1, Geometry, and Algebra 2/Trigonometry; or Geometry, Algebra 2/Trigonometry, and Pre-Calculus as the minimum for their graduation requirements. Almost all students choose to study four years of mathematics.

A student may take only one summer school course in mathematics. It is recommended that students who wish to accelerate in their study of mathematics take Geometry in the summer between Algebra 1 and Algebra 2/Trigonometry. Students must receive a grade of B+ or better in both semesters of the prerequisite course to be eligible to take a summer school course for acceleration.

Progression by Grade Level 

 

 


Course Offerings

Algebra 1 Basic College Prep

This first-year algebra course is for students who have experienced difficulties with mathematics. Class size is somewhat reduced to allow for more individual instruction, and shorter class presentations leave time in class for extra drill and one-on-one help with homework. Students may purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended. A graphing calculator is required and can be used throughout the BCP courses.

Quarter grades are based on test results, quizzes and homework grades.

Open to Grades 9, 10. Prerequisites: Eighth grade mathematics and teacher recommendation. Year course. One credit. Satisfies Mathematics graduation requirement.

Algebra 1

This course presents two semesters of elementary algebra. Topics include: number systems and sets; operations with irrational numbers; an introduction to functions and function notation; graphing and solving linear and quadratic equations and systems of linear equations and inequalities. Problem solving and applications of these topics are integral parts of the course.

Each cycle, students attend class four times plus a testing session. Homework is assigned daily and is used not only for practice, but also to evaluate a student’s progress in the course. At the end of the semester, students take a 90-minute exam which counts as 20% of their semester grade. Students completing Algebra 1 gain a firm basis for understanding material in higher level math courses.

Open to Grades 9, 10. Prerequisite: Eighth grade mathematics at Punahou or recommendation of department. Year course. One credit. Satisfies Mathematics graduation requirement.

Algebra 1X (Algebra I)

Algebra 1X is a variation of the regular Algebra 1 course. It is especially designed for students new to Punahou, allowing them, in the first semester, one more hour of class time per cycle. The material covered is identical to that covered in the regular Algebra 1 course. At the end of the first semester, students will be scheduled into Algebra 1 classes.

Each cycle, students attend class five times, plus attend a testing session. Homework is assigned daily and is used not only for practice, but also to evaluate a student’s progress in the course. The sixth meeting in the cycle is a testing session. At the end of the semester, students take a 90-minute exam which counts as 20% of their semester grade.

Open to Grade 9. Prerequisites: Eighth grade mathematics and recommendation of department. Year course. One credit. Satisfies Mathematics graduation requirement.

Geometry Basic College Prep

This geometry course is for students who have experienced difficulties in mathematics, but is rigorous enough to include the traditional geometric topics: congruence, similarity, areas, volumes and proofs.

Test grades and homework are included in the computation of the quarter grade. A 90-minute semester exam counts as 20% of the semester grade. Students may purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended. A graphing calculator is required and can be used throughout the BCP courses.

Open to Grades 9, 10, 11. Prerequisites: Algebra 1 or Algebra 1 (BCP) and teacher recommendation. Year course. One credit. Satisfies Mathematics graduation requirement.

Geometry

This course transitions students from a visual to an abstract understanding of both plane and solid geometry concepts. It stresses both inductive and deductive reasoning. Algebra and right triangle trigonometry problems are integrated into the course.

Students work together as they discover and apply geometric relationships and concepts to a large range of routine as well as non-routine problems. Lab experiences incorporate manipulatives and hands-on activities to offer students different opportunities to gain a solid understanding of the material. Communication and collaboration skills, both at the small and large group levels, are strengthened daily through student presentations and discussions. Active and engaged participation is an expectation for all students. Homework is assigned for each class meeting. Test grades, class participation and homework are included in the computation of the quarter grade.

Open to Grades 9, 10, 11. Prerequisites: Algebra 1. Year course. One credit. Satisfies Mathematics graduation requirement.

Geometry Honors

This course is designed for accelerated students and includes units on solid and coordinate geometry in addition to an introduction to right triangle trigonometry. There is a much greater emphasis on proof and applications of concepts throughout the course.

Students attend five classes per cycle.

Open to Grades 9, 10. Prerequisites: Eighth grade Algebra 1 Honors and teacher recommendation. Year course. One credit. Satisfies Mathematics graduation requirement.

Algebra 2/Trigonometry Basic College Prep

This course is the third in the Basic College Prep (BCP) sequence and currently uses the University of Chicago School Mathematics Project (UCSMP) curriculum. The concept of function provides the organization for the course. New topics include matrices, logarithms and trigonometry. Graphing calculators are used to reinforce concepts and introduce mathematical modeling.

Each cycle, students attend class four times, plus a testing session. Students may purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended. A graphing calculator is required and can be used throughout the BCP courses. This course does not satisfy the prerequisite for Pre-Calculus or Advanced Pre-Calculus.

Open to Grades 10, 11, 12. Prerequisites: Geometry or Geometry (BCP) and teacher recommendation. Year course. One credit. Satisfies Mathematics graduation requirement.

Algebra 2/Trigonometry

Algebra 2/Trigonometry includes the further development and blending of algebraic and geometric concepts. Topics studied from both algebraic and geometric viewpoints include linear, quadratic, exponential, logarithmic, and trigonometric functions and the complex number system. Permutations, combinations, sequences and series are also introduced.

Each cycle, students attend class four times, plus a testing session. Students are required to purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended.

Open to Grades 10, 11, 12. Prerequisite: Geometry. Year course. One credit. Satisfies Mathematics graduation requirement.

Algebra 2/Trigonometry Honors

Designed for accelerated students, this Honors Algebra 2/Trigonometry course covers all of the material introduced in the regular Algebra 2/Trigonometry course but in greater depth than is possible in the regular course. Also, many Pre-Calculus topics are studied.

Students are required to purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended.

Open to Grades 10, 11. Prerequisites: Geometry Honors with B or better and teacher recommendation. Year course. One credit. Satisfies Mathematics graduation requirement.

Pre-Calculus Basic College Prep

This course is the fourth year in the BCP sequence of mathematics and was developed to expand students’ understanding of functions, statistics, and trigonometry. Pre-Calculus (BCP) integrates the ideas of functions and trigonometry with the statistics necessary to collect and analyze data, and to hypothesize and draw conclusions from this data. A graphing calculator with a statistics package is required and is one means of engaging students in extended learning. Reading mathematics and problem solving real life situations promote students as independent learners. Pace, workload, and more individual help distinguish this course from courses in the regular track.

The course uses a University of Chicago School Mathematics Project text. Each cycle, students attend class four times, plus attend a testing session. Evaluation is based on individual math projects, a math homework folder, quizzes, chapter tests, and semester exams.

Students may purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended. A graphing calculator is required and can be used throughout the BCP courses.

Open to Grades 11, 12. Prerequisites: Algebra 2/Trigonometry or Algebra 2/Trigonometry (BCP) and teacher recommendation. Year course. One credit. Satisfies Mathematics graduation requirement.

Pre-Calculus

Designed for students who have completed Algebra 2/Trigonometry and who wish to continue with a Pre-Calculus program, this course provides a less demanding alternative to Advanced Pre-Calculus but covers similar material. Pre-Calculus is recommended for students with a grade of B or lower in Algebra 2/Trigonometry. This course does not satisfy the prerequisite for AP Calculus.

Students are required to purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended.

Open to Grades 11, 12. Prerequisites: Algebra 2/Trigonometry and teacher recommendation. Year course. One credit. Satisfies Mathematics graduation requirement.

Advanced Pre-Calculus

This is the fourth course in the sequence that begins with Algebra 1, Geometry and Algebra 2/Trigonometry. It blends and extends topics from the previous courses. In addition to learning specific mathematical skills, students also develop their ability to make significant connections between topics as they enhance their ability to solve non-routine problems. Focused study and attention to detail are a significant requirement of the course. During the first semester, topics include polynomial, exponential, logarithmic and trigonometric functions. In the second semester, students study vectors, polar coordinates, complex numbers, matrices, sequences, series, combinatorics and probability. The course also introduces basic calculus concepts including limits and derivatives. Students completing Advanced Pre-Calculus will be prepared to take Calculus.

Students are required to purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended.

Open to Grades 11, 12. Prerequisites: Algebra 2/Trigonometry with B or better and teacher recommendation. Year course. One credit. Satisfies Mathematics graduation requirement.

Advanced Pre-Calculus Honors

This course is designed for the student who enjoys studying mathematics at a deeper level and welcomes the challenge that comes with solving difficult problems. The topics covered include the traditional pre-calculus ones (functions, trigonometry, probability, statistics, vectors, analytic geometry, matrices) as well as elementary calculus operations normally found in a first semester college calculus course.

The course meets five times a cycle.

Students are required to purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended.

Open to Grades 11, 12. Prerequisites: Algebra 2/Trigonometry Honors with B or better and teacher recommendation. Year course. One credit. Satisfies Mathematics graduation requirement.

Differential Calculus

This course is designed for students who have the motivation to begin their study of Calculus in high school, but who do not have a strong enough background to enroll in Advanced Placement Calculus. This course includes a review of functions from pre-calculus. Limits are explored algebraically, graphically and numerically, leading to the definition of derivative. Techniques of differentiation with special emphasis on the chain rule and implicit differentiation develop the students’ skills. Applications of the derivative to graphing, related rates and optimization enrich the students’ understanding of applications of the derivative. Basic integrals are introduced.

The course does not cover enough material to prepare the students to take the Advanced Placement Calculus Exam. The course meets five times a cycle. A TI-83 Plus, TI-84 Plus, TI-84 Plus Silver Edition or TI-84 Plus C Silver Edition graphing calculator is required.

Open to Grades 11, 12. Prerequisite: Pre-Calculus with B- or better or Advanced Pre-Calculus with teacher recommendation. Year course. One credit. Satisfies Mathematics graduation requirement.

Advanced Placement Calculus AB and BC

These courses are part of a national program in Advanced Placement. All students who enroll in these courses are required to take the AP Exam in May. Appropriate credit and placement are granted by colleges in accordance with their policies. The content of Calculus BC is designed to qualify the student for advanced placement and/or credit beyond that which is granted for Calculus AB.

Calculus AB is the equivalent of a college-level calculus course, including differential and integral calculus with applications.

Calculus BC is an extension, rather than an enhancement, of Calculus AB. Common topics require the same depth of understanding and BC students receive an AB subscore with their AP results in July.

Calculus BC also includes study of infinite series and calculus of polar, parametric and vector functions. Calculus BC is the preferred course for students enrolled in the AP Physics C course.

The courses meet five times each cycle. Students are required to purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended.

Open to Grades 11, 12. Prerequisites: Advanced Pre-Calculus with B+ or better or Advanced Pre-Calculus Honors and teacher recommendation. Year course. One credit. Advanced Placement courses must be taken for a letter grade. Satisfies Mathematics graduation requirement.

Advanced Placement Statistics

This course is part of a national program in Advanced Placement. All students who enroll are required to take the AP Exam in May. Appropriate placement and credit are granted by colleges in accordance with their policies.

The purpose of AP Statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, planning a study, anticipating patterns, and statistical inference.

This class meets for 1 hour three times per cycle and 1 1/2 hours once a cycle. Students are required to purchase any TI-83 Plus or TI-84 Plus graphing calculator, but a TI-84 Plus CE graphing calculator is recommended.

Open to Grades 10, 11, 12. Prerequisite: Any level of Algebra 2/Trigonometry or concurrent enrollment. Year course. One credit. Advanced Placement courses must be taken for a letter grade. Satisfies general elective credit.

Introduction to Computer Science

This course provides a hands-on introduction to programming through the lens of game design. The class explores the history of games and methods of visual expression and representation. Students use block-based coding languages, interactive fiction and storytelling tools, and create games for the Meggy, a handheld video game simulator, using Arduino C.

Previous programming experience is not required.

This class meets for 1 1/2 hours three times a cycle.

Open to Grades 10, 11, 12. No prerequisite. Semester course. One-half credit. Satisfies general elective credit.

Advanced Placement Computer Science

This course is an introduction to the intellectual enterprises of computer science and the art of programming. The problem sets are based on forensics, biology, finance, game design and cybersecurity topics, and students must find the appropriate solutions through rigorous testing and iterative design. The course also involves an independent programming project of the student’s choice. The course covers the fundamentals of programming such as abstraction, encapsulation, data structures, security and software engineering, and provides an excellent foundation for any of the other computer science courses at Punahou.

Previous programming experience is not required. However, willingness to work hard, collaborate with others, and ask for help when necessary will greatly help students to succeed in this course.

This class meets for 1 1/2 hours three times a cycle. Students must take the AP Exam in May.

Open to Grades 10, 11, 12. Prerequisite: B or better in previous math course (Algebra 1, Geometry, Geometry Honors, Algebra 2, Algebra 2 Honors, Advanced Pre-Calculus, Advanced Pre-Calculus Honors). Year course. One credit. Advanced Placement courses must be taken for a letter grade. Satisfies general elective credit.

Computer Science Independent Study: iOS App Development

This is an opportunity for students who have previously taken a Computer Science course to further their understanding by applying their knowledge and skills in a real world situation. By working with the AP Computer Science Instructor, independent study students build apps for the iPod, iPhone and iPad using Xcode and Swift, and publish them in the App Store. Working much like a small startup, students collaborate as a team, share code and learn to communicate with each other. This is an intensive project-based course that requires students to be resourceful in learning the skills they will need to complete their work. The instructor will provide debugging support and advice to students during lab periods, as well as guidance and support for design and UX/UI.

This class meets for 1 1/2 hours three times a cycle.

Open to Grades 11, 12. Prerequisites: Introduction to Computer Science, AP Computer Science or consent of instructor. Semester course. One-half credit. Satisfies general elective credit.

Advanced Topics in Computer Science

This course focuses on Java programming. The course covers topics such as problem solving, design strategies and methodologies, organization of data (data structures), approaches to processing data (algorithms), analysis of potential solutions, and the ethical and social implications of computing. The course emphasizes both object-oriented and imperative problem solving and design. Although it is not an AP course, students may choose to take the AP Computer Science A exam in May.

Open to Grades 10, 11, 12. Prerequisite: Advanced Placement Computer Science.

Elements of Design

This is a design course focusing on graphic and oral communication. Topics include graphic design, product design, set design, perspective drawing, architectural design, and computer graphics with illustrator, iMovie and SketchUp. The course is modeled after an introductory college design course. Students learn about the process of design, hone presentation skills, both visual and oral, and practice objective critical analysis.

Assignments and grading are on a contract system, with point values and a pre-set grading scale. There are no semester exams; grades are determined primarily from assignments and projects, some of which involve design for the community. Students spend two hours in lecture and two hours in lab per cycle. Course activities include field trips to several architecture offices, a landscape architect’s office, building construction sites and a theater site. Extra credit projects are encouraged.

A high school course in design is preferred by some colleges’ architecture and engineering programs.

Open to Grades 9, 10, 11, 12. No prerequisite. Year course. One credit. Satisfies general elective credit.

Money Management

In this course students are introduced to the value of thrift, budgeting, saving and investing. Students learn how to set up a budget and the importance of living within their means. The subject of debt is also addressed in this course. Students learn the importance of establishing and maintaining good credit. Through a survey of banking practices and institutions, students learn the role that savings plays in wealth accumulation and in budgetary maintenance. Students first learn the importance of the time component in investing and then undertake a detailed examination of several investment options including, but not limited to, stocks including options, mutual funds, ETFs and SPIDERS, bonds, real estate and various commodities. Students will have an opportunity to trade securities and to actively manage an investment portfolio. There is also a section on taxation both as an obligation and the role it plays in maximizing return on investment.

This class meets four times a cycle for one hour. Grading is by semester and based on performance on tests, class participation and project work. There is no final exam.

Open to Grades 11, 12. Prerequisite: Any level of Algebra 2/Trigonometry or concurrent enrollment. Semester course. One-half credit. Satisfies general elective credit.