The following table shows the most common pathways students follow through our mathematics curriculum.  Just the same, these are not all the possible paths.  In the past we've offer an Accelerated Precalculus Program for exceptional math students to skip Precalculus and move directly from Algebra 2 to AP Calculus.  (Note: The status of this program in Spring 2021 is uncertain due to closed school buildings.)  In very special circumstances, it is possible for a student to skip* a course by studying the content independently and passing a final exam.  Please reach out to the math department teacher leader (Mr. Zak) with questions about these very special situations.

 *Note, students do not receive credit or a grade for a skipped course.  They simply move more quickly through our curriculum.

Why do we have both honors and standard courses?

The word “honors” in math honors is perhaps a misleading term.  An honor is a kind of recognition of excellent achievement.  We honor those who are uniquely good or excellent with regard to important human endeavors.

In truth, there are likely reasons to honor every student at Central High School.  In this sense it would seem every student deserves to be honored and therefore “deserves” to be in a math honors course.  However, this is not what we mean when we talk about “math honors.”  It is not in itself an honor to be in a math honors course.  Similarly, it is not a dishonor to be in a standard course!  

We have honors and standard courses in order to provide two unique class experiences that enable students to flourish in their math learning.  We recognize that students are different -- they learn at different paces, they have different levels of preparedness, and different kinds of interests to say the least!  We hold “honors” courses to create a more rigorous experience for students ready and eager to move more quickly and deeply in their math learning than the majority of students.  

How are math honors courses and standard courses similar?

Both honors and standard courses cover the same course topics overall.  For example, the core curriculum for Precalculus and Precalculus Honors is essentially the same.

How are math honors courses and standard courses different?

There are five main differences that make an honors course different than a standard course: 

1. Topics treated in greater depth

2. Types of questions are significantly more challenging

3. Significantly increased pace

4. Higher expectation of student independence

5. Higher expectation of the amount of time devoted to the course outside class

What is the difference between honors and AP courses?

Everything we stated about honors courses is also true of AP courses.  In addition, the curriculum and expectations of AP courses are developed by Collegeboard and are designed to give high school students a college-level course experience before graduation.  All math AP courses reflect an equivalent one- or two-semester college course in the same subject.  AP teachers must receive special training and approval through Collegeboard to offer the course at a school.  All students enrolled in an AP course must take the AP exam offered in May.  The majority of colleges will grant students with excellent scores (at least 3 out of a maximum score of 5) college credit in recognition of their performance and mastery of the content.  

How can a student apply to take a math honors or AP course?

• Students complete an online application via a Google form with basic information about previous coursework.

• Students complete a placement exam (most likely in March).

• Teachers complete a short recommendation based on student attendance and other characteristics not easily captured by a student’s grade or performance on an exam.

• Based on all three, the department makes a recommendation of either an honors or standard course.  The recommendation is the student’s default course placement.

• If a student or parent disagrees with the department’s recommendation they can still request math honors via a Google Form; the math department teacher leader (Mr. Zak) will follow-up with parents individually.  

What does “double-up” mean?

At Central High School, second-year students have room for one elective course, i.e. students can “elect” to take one course of their choosing.  All sophomore students take Geometry / Geometry Honors.  In addition students can take Algebra 2 / Algebra 2 Honors as their elective course.  Therefore, to “double-up” in math typically means that students will take both Geometry / Geometry Honors and Algebra 2 / Algebra 2 Honors during their sophomore year.  [Note: in some cases, students test out of Algebra 1 and into Algebra 2 during their freshman year.  These students can also double-up in both Geometry Honors and Pre-Calculus Honors; however, their reasons for doing so will be different than for a student taking Algebra 1 during their first year.]

Why should I “double-up” in math?

There is really only one good reason to double-up in mathematics during the second-year: to take Calculus by your senior year.  If a student begins with Algebra 1 during year one, it is impossible* to take Calculus by the senior year without “doubling-up.”  (See the Mathematics Career Pathways chart above.) 

* In very special circumstances there are still alternative pathways you can consider with the math teacher leader.

Why shouldn't I double-up” in math?

Reason #1: “I already struggle in math.”  

If you currently are earning a C or lower in Algebra 1, then you probably should not double up in math.  Sometimes even a student who is earning a B but only through extreme effort should think twice about doubling up in math.  In addition to Geometry, second-year students also take Physics, a math heavy course.  Students who struggle in math and double-up with Algebra 2 in addition often find themselves overwhelmed.

Reason #2: “I like math, but I really like other subjects much more.”

There are plenty of awesome elective options for students, including AP courses such as AP Computer Science Principles and AP European History.  If you are really passionate about another subject, you can elect to take that course during the second year – just know that it means it's not possible to take Calculus.

Reason #3: “I don’t really like math and I only want to double-up to get done with math more quickly.”

This is generally a very bad reason for doubling-up.  As stated above, there is already a lot of math during the second year.  Students who don’t like math will typically struggle with so much math during the sophomore year, which experience shows is already a formative, challenging time in the life of most students.  If you don’t particularly like math, take one of the other awesome electives and just take math one year at a time.

Algebra I/ Algebra I Honors

This course lays the foundation needed for the study of all later mathematics courses. Some topics studied are the following; solving equations and inequalities, working with polynomials and rational expressions, graphing of functions, the quadratic equations and radical expressions. Interspersed throughout are many and varied word problems that provide opportunities to apply the material studied.  The course also works to improve student’s basic number sense and ability to work confidently with rational numbers and fractional expressions.

Honors Eligibility:  Incoming 9th grade students will be recommended for this course based on their performance on a placement examination given in the spring or summer.

Geometry/ Geometry Honors

This is the first mathematics course in which the student sees a mathematical system, developed from simple definitions and fundamental axioms grow into a full and useful body of knowledge. This logical development is a prime reason for the study of geometry. Topics studied include proofs of theorems about circles, triangles and quadrilaterals, as well as areas and volumes.  An introduction to practical trigonometry is also included, including the laws of sines and cosines.

Algebra II / Algebra II Honors

Extending first year algebra, students explore the transformation of functions, complex numbers, the theory of polynomial equations and functions, exponential equations and functions, logarithmic equations and functions, linear and quadratic systems of three variables, matrices, conic sections, and probability.

Pre-Calculus/ Pre-Calculus Honors  

Pre-Calculus introduces topics necessary for success in calculus as well as formally treating topics in discrete areas of mathematics not typically encountered in previous courses, such as sequences and series, combinatorics, the binomial theorem, and probability.  Significant course time is devoted to circular angles and analytic approaches to trigonometry necessary for calculus and real applications in physics and engineering.  If time permits, students will define the polar coordinate system and polar representation of complex numbers, vectors, and the concept of limits.

Calculus 

This course is designed to introduce the students to the fundamental principles of differential and integral calculus.  Topics covered include detailed study of limits, the derivatives of polynomial, algebraic, exponential, logarithmic, and trigonometric functions with applications to curve-tracing, maxima-minima related-rate problems, and the antiderivative.  Students will also develop basic integration and its applications, including volumes of revolution.

AP Mathematics Courses

AP Calculus AB / AP Calculus BC 

AP Calculus includes two courses, AP Calculus AB and AP Calculus BC, which were developed in collaboration with college faculty. The curriculum for AP Calculus AB is equivalent to that of a first-semester college calculus course, while AP Calculus BC is equivalent to the first two semester college calculus courses.

Both courses cover topics in differential and integral calculus, including concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus.  BC additionally includes parametric, polar, vector functions, and series.  Each course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations.  Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions.

AP Statistics

The AP Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics.  The course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data.  The course emphasizes understanding and analyzing statistical studies and the development of an intuitive understanding of statistics and probability.  There are four themes in the AP Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding.

AP Computer Science Courses

AP Computer Science A

AP Computer Science A is equivalent to a first-semester, college-level course in computer science. The course introduces students to computer science with fundamental topics that include 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 using Java language. These techniques represent proven approaches for developing solutions that can scale up from small, simple problems to large, complex problems. The AP Computer Science A course curriculum is compatible with many CS1 courses in colleges and universities.

AP Computer Science Principles

AP Computer Science Principles offers a multidisciplinary approach to teaching the underlying principles of computation. The course will introduce students to the creative aspects of programming, abstractions, algorithms, large data sets, the Internet, cyber security concerns, and computing impacts. AP Computer Science Principles also gives students the opportunity to use current technologies to create computational artifacts for both self-expression and problem solving. Together, these aspects of the course make up a rigorous and rich curriculum that aims to broaden participation in computer science.

*** A vs. Principles: What is the difference?

The AP Computer Science A course and exam focus on computing skills related to programming in JAVA.  The new AP Computer Science Principles course complements AP Computer Science A and focuses on the fundamentals of computing, including problem solving, large-scale data, the Internet, and cyber-security. 

As of 2019, a passing score on the AP Computer Science A exam typically gives students credit for a first semester computer programming course, while a passing score on the AP Computer Science Principles exam typically gives students credit for a one semester elective.

IB Mathematics Courses

There is some content that is common with the Mathematics: Applications and Interpretations course but the Mathematics: Analysis and Approaches has a greater emphasis on calculus, numerical  and algebraic approaches.

Mathematics: Applications and Interpretations SL

This one-year course emphasizes the applied nature of the subject and is designed for students who wish to understand how mathematics relates to the real world and to other subjects. This course is suitable for students who may go on to further study in subjects that utilize mathematics in this way such as social sciences, natural sciences, statistics, business, psychology or design.

The five topics below are covered during the SL course – each of these topics has sub-topics: Number and Algebra, Functions, Geometry and Trigonometry, Probability and Statistics, and Calculus.

In addition to this the course contains investigative and inquiry-based learning, supporting the students in their internally assessed exploration task.

Mathematics: Analysis and Approaches SL

This one-year course is designed for students who wish to study mathematics as a subject in its own right or to pursue their interests in areas related to mathematics. It will appeal to students who are interested in exploring real and abstract applications of mathematical concepts. They will enjoy problem solving and generalization. This course is suitable for students who may go on to further study in subjects that have a significant level of mathematics content, for example mathematics itself, engineering, physical sciences or economics.

The five topics below are covered during the SL course – each of these topics has sub-topics: Number and Algebra, Functions, Geometry and Trigonometry, Probability and Statistics, and Calculus.

In addition to this the course contains investigative and inquiry-based learning, supporting the students in their internally assessed exploration task.

Mathematics: Analysis and Approaches HL

This two-year course is designed for students who wish to study mathematics as a subject in its own right or to pursue their interests in areas related to mathematics. It will appeal to students who are interested in exploring real and abstract applications of mathematical concepts. They will enjoy problem solving and generalization. This course is suitable for students who may go on to further study in subjects that have a significant level of mathematics content, for example mathematics itself, engineering, physical sciences or economics.

The five topics below are covered during the SL and HL courses. Each of these topics has sub-topics with HL students covering some additional sub-topics or the same sub-topics at greater depth.  Number and Algebra, Functions, Geometry and Trigonometry, Probability and Statistics, and Calculus.

In addition to this the course contains investigative and inquiry-based learning, supporting the students in their internally assessed exploration task.

Other Elective Courses

Computer Science

This half-year (half-credit) course will introduce you to the field of computer science and the fundamentals of computer programming.  Computer Science is specifically designed for students with no prior programming experience.  Students will be introduced to the processing and JavaScript languages, along with logic, computer hardware and software, multimedia, computer security, web economics, and game design.

Statistics

This course is an introductory, non-calculus based statistics course that emphasizes understanding and analyzing statistical studies.  Participants develop skills in sampling procedures, analyzing data, designing and analyzing surveys and experiments, as well as hypothesis testing. The course emphasizes the development of an intuitive understanding of statistics and probability.  Students gain a sense of the importance/relevance of statistics in the real world and are able to evaluate the use and misuse of statistics.