# Math

Understanding not just the how, but the why.

Critical thinking, deep understanding, and communication are the cornerstones of our mathematics program. We work hard to help our students feel positive about themselves and their relationship with mathematics, and we strive to develop persistent, confident, and creative problem solvers who see and appreciate both the beauty and the utility in mathematics.

"With help from the Penn Charter Math Center and supportive teachers, I was able to gain confidence in math and become an overall stronger student. This specific curriculum has helped me think outside of the box in mathematics and has pushed me to think deeply about each part of the material."* David Garnick, Class of 2019*

## Key Characteristics

- A personalized approach, helping each student experience challenges and success through extra help, the math center, and a wide range of courses to choose from
- An appropriate level of both intellectual challenge and success for every student
- Group work that encourages persistence, communication and collaboration
- The use of appropriate tools and technology

## Curricular Highlights

**The Math Center.** The Math Center is staffed throughout the day by math faculty. Help is available to all students, regardless of grade or course level, in addition to the extra help already provided by their teachers.

**Cutting-edge courses. **In addition to the traditional courses leading to calculus, students have the opportunity to experience courses in the use of data and statistics and the mathematics of finance (applying mathematics to fields other than just engineering and science).

**Robust participation.** In the 2017-18 school year, all but two seniors took a full year of math, and 25% of the senior class doubled up, taking two or more math classes in their final year.

"We see struggle as a positive force in learning. Students are able to think more deeply and make connections when they are given the time and opportunity to wrestle with challenging problems."* Beth Menzie, department chair*

## Graduation Requirements

- The minimum requirements in mathematics are as follows: Students must satisfactorily complete Algebra I, Geometry, Algebra II and Precalculus or Integrated Mathematics.
- Beginning in the 9th grade, students must take at least 7 semesters of mathematics, including a full year of Precalculus or Integrated Mathematics. It is expected that these 7 semesters will be taken consecutively.

The Penn Charter Mathematics Department attempts to provide each and every student with an appropriate level of both intellectual challenge and success. As student needs evolve, the department strives to meet these needs by adding new courses and experiences.

## Advanced Math Courses

## Read about the process for placement

Penn Charter’s math program strives to provide an appropriately challenging math experience for each and every student. **Rigor is present in every math course, regardless of its level.**

**We also recognize that there are students who crave even greater mathematical challenges** and who possess the ability and drive to succeed at a higher level. For these students, we offer advanced level courses. Placement in these courses is based on a number of factors:

- grades earned in the current year;
- teacher recommendations;
- strength in executive functioning and self-regulation; and most importantly
**a student’s demonstrated love and enthusiasm for math.**

Our advanced courses move at a faster pace, explore concepts more deeply, and demand a level of academic maturity above and beyond that of our regular courses, and, for all of these reasons, our teachers give a great deal of thought to their recommendations.

**Students will have multiple conversations with their math teacher and their advisor in the spring**, in order to select the appropriate level of math for the following year. We encourage parents to take part in these discussions as well. The final determination of course level will be made by the math department at the very end of the school year, after year-long grades have been calculated, so that the entirety of a student’s body of work can be considered.

- Typically, students moving into an advanced course have earned grades in the A range in their traditional-level course, including an A on the final exam, and have demonstrated all of the qualities cited in the bullet points above.
- Students currently in an advanced course must demonstrate mastery and retention of the skills taught over the course of the year; they should have earned a final year grade of at least a B and a final exam grade of B in order to continue at the advanced level.

**Students new to Penn Charter take a placement test.** Consideration will be given to a student’s performance on it, as well as to their standardized test scores, previous grades, teacher recommendations, and conversations with the parents and the child when placing the child.

## Course List

### All Year

- Algebra I
- Geometry, Advanced Geometry
- Algebra II
- Advanced Algebra II
- Integrated Mathematics
- Precalculus
- Advanced Precalculus (A)
- Advanced Precalculus (AA)
- AP Statistics
- AP Calculus (AB)
- AP Calculus (BC)
- Multivariable Calculus

## Algebra I

**M110**

**ALGEBRA I**

**(2 UNITS) ALL YEAR**

This course is focused on the basic concepts of algebra. Particular emphasis is placed on, but not limited to, factoring, solving linear and quadratic equations, solving systems of equations and inequalities, and graphing equations. The course also explores, in an elementary fashion, functions. (9th grade)

## Geometry, Advanced Geometry

**M120, M120A**

**GEOMETRY, ADVANCED GEOMETRY**

**(2 UNITS) ALL YEAR**

These courses, which focus on Euclidean geometry, emphasize, encourage and challenge students to discover geometric ideas through investigative activities and technology. Topics include the foundations of geometry definitions, inductive and deductive reasoning, the nature and development of a mathematical system using axioms, theorems, and proof, the close study of a wide variety of geometric figures, right triangle geometry, basic isometries, area and volume. A dynamic software package is used in this class. *Prerequisite for M120: Algebra 1; for M120A: grade of A in Algebra I and departmental approval. (9th, 10th grades)*

## Algebra II

**M330**

**ALGEBRA II**

**(2 UNITS) ALL YEAR**

This course further explores the concepts that were introduced in Algebra I. Students examine a variety of different functions, such as linear, quadratic, polynomial, exponential and logarithmic functions. Multiple approaches to problem solving will be employed, including the use of technologies such as a graphing calculator and Desmos. *Prerequisites: successful completion of Algebra I and Geometry*. (10th, 11th grades)

## Advanced Algebra II

**M330A**

**ADVANCED ALGEBRA II**

**(2 UNITS) ALL YEAR**

This course furthers the study of algebra by looking at classes of functions. Students will examine linear, quadratic, polynomial and exponential functions algebraically, numerically and geometrically. A graphing calculator and technologies such as Desmos, will be used to support the algebraic manipulation and allow the students to see and explore the mathematics. Advanced Algebra II moves at a rapid pace and requires students to be independent and to make conjectures on their own. *Prerequisites: **grades of A in Algebra I and Geometry and departmental approval, or a grade of B or better in Advanced Geometry. (10th grade)*

## Integrated Mathematics

**M670**

**INTEGRATED MATHEMATICS**

**(2 UNITS) ALL YEAR**

Integrated Mathematics reinforces and builds upon the topics studied in Algebra 1, Geometry, and Algebra II, with an emphasis on collaboration and communication, both written and verbal. Students will apply their algebraic and geometric skills, as well as technology, to support and enhance their overall understanding of high school mathematics, including selected topics from Precalculus. *Prerequisites: successful completion of Algebra I, Geometry and Algebra II, and departmental approval*. (11th, 12th grades)

## Precalculus

**M570**

**PRECALCULUS**

**(2 UNITS) ALL YEAR**

Precalculus prepares students for the study of calculus by building on the topics studied in Algebra II. Students will apply their algebraic skills, as well as technology, to support and enhance their overall understanding of functions and statistics. The course will include trigonometric, exponential, logarithmic and polynomial functions.* Prerequisites: successful completion of Algebra I, Geometry and Algebra II.* *(11th, 12th grades)*

## Advanced Precalculus (A)

**M570A**

**ADVANCED PRECALCULUS**

**(2 UNITS) ALL YEAR**

This course continues to build on the concepts studied in Advanced Algebra II. Students will explore a variety of functions, including trigonometric, polynomial, exponential and logarithmic functions. The course requires students to think independently and to make conjectures on their own, preparing them to begin the study of AP Calculus AB in the spring.* Prerequisites: grades of B or better in Advanced Algebra II and Advanced Geometry, or grades of A in Algebra II and Geometry, and departmental approval. (11th grade)*

## Advanced Precalculus (AA)

**M570AA**

**ADVANCED PRECALCULUS**

**(2 UNITS) ALL YEAR**

This rapidly moving and intense course prepares students for AP Calculus BC. The properties and transformations of functions, including linear, quadratic, polynomial, rational, exponential and logarithmic functions are examined algebraically, numerically and geometrically. Mathematical models are created to solve real-life applications. The pace of this course is particularly fast because students begin the AP Calculus curriculum, including learning to differentiate using numerical methods, the limit definition and the differentiation rules. *Prerequisites: grade of A in the advanced sections of Algebra II and Geometry, and departmental approval*. (11th grade)

## AP Statistics

**M660**

**AP STATISTICS**

**(2 UNITS) ALL YEAR**

AP Statistics introduces students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to exploring data, sampling and experimentation, exploring random phenomena using probability and simulation, and statistical inference. This course provides students with the opportunity to earn Advanced Placement credit in college. *Prerequisites: Algebra 2 and departmental approval. (11th and 12th grade)*

## AP Calculus (AB)

**M790A**

**AP CALCULUS (AB)**

**(2 UNITS) ALL YEAR**

This is a full-year calculus course designed to provide students with the opportunity to earn Advanced Placement credit in college. The course provides a study of differential and integral calculus.* Prerequisites: grade of B or higher in Advanced Precalculus and departmental approval*. (12th grade)

## AP Calculus (BC)

**M790AA**

**AP CALCULUS (BC)**

**(2 UNITS) ALL YEAR**

This course is similar to AP Calculus (AB) but covers additional material such as sequences and series and also provides students with the opportunity to earn Advanced Placement credit in college. The TI-Nspire CAS is used in this class. *Prerequisites: grade of B or higher in Advanced Precalculus AA and departmental approval*. (12th grade)

## Multivariable Calculus

**M890AA **

**MULTIVARIABLE CALCULUS
(2 UNITS) ALL YEAR**

This course covers a typical college-level Calculus III curriculum, including vectors and vector-valued functions, curves and surfaces in space, partial derivatives and gradients, multiple integration, and line and surface integrals. In the course’s final unit, students learn how to identify and solve various kinds of differential equations, including exact first-order equations, second-order homogeneous and nonhomogeneous linear equations, partial differential equations, and applications to various scientific fields. Built on a foundation of sophisticated problem solving, the course also features discussions and exploratory activities that will help students develop their advanced math skills in collaborative and creative ways. *Prerequisites: grade of B or higher in AP Calculus BC and departmental approval. *(11th and 12th grades)

### One Semester

## Introduction to Statistics

**M664**

**INTRODUCTION TO STATISTICS**

**(1 UNIT) SEMESTER 2**

This course, intended for juniors and seniors, will focus on the study of real data and gives students a significant introduction to several core topics of statistics. These include displaying and describing distributions, measures of center, measures of spread, comparing distributions of both categorical and quantitative variables, graphical displays of data, normal distributions and the correlation coefficient. Emphasis is placed on the development of effective verbal and written explanations, and technology will be utilized. *Prerequisites: Algebra II*. (11th, 12th grades)

## Calculus

**M791, M792**

**CALCULUS**

**(1 UNIT) SEMESTER 1, SEMESTER 2**

These calculus courses are sequential classes. M791 (Semester 1) introduces students to the concepts of calculus and includes the study of limits and derivatives. M792 (Semester 2) continues with the study of derivatives and adds the study of integrals. If taken all year, these courses cover a full-year course in differential and integral calculus. Students may not enroll in M792, without having taken M791. If a student has not maintained an average of B or higher at the end of semester 1 in M791, Calculus Part I, that student will need departmental approval in order to continue in M792 Calculus, Part II. *Prerequisites: Precalculus and departmental approval. (12th grade)*

## Mathematics of Finance

**M795, M796**

**MATHEMATICS OF FINANCE
(**

**1 UNIT) SEMESTER 1, SEMESTER 2**

In this senior elective course, the students acquire the knowledge and skills required to make sound financial decisions and to manage their own personal finances. The lessons engage students in critical thinking, problem solving, and decision-making. Topics covered include budgeting, saving and investing, mortgages, credit and interest, insurance, and taxes. *Prerequisites: Algebra II*. (12th grade)