# Mathematics

## Introduction

### Mathematics

The mathematics program should ensure that all students have an opportunity to become mathematically literate, are capable of extending their learning, have an equal opportunity to learn, and become informed citizens capable of understanding issues in a technological society. Knowledge of mathematics is an essential element in the development of the whole person.

All students should be provided access to the full range of mathematical topics. Knowledge of patterns, relations, and functions; of geometry and measurement; of probability and statistics; and of increasingly important topics in discrete mathematics is a necessary foundation for all students. Because students' interests, goals and achievements change as they mature and advance through high school, the mathematics program should be designed to keep options open. While recognizing that individuals have different career objectives, and may well pursue careers as yet undefined, we further recognize that all students have the right to learn significant mathematics and to develop power over mathematical ideas.

The goals of the mathematics program are that all students:

- Learn to value mathematics

- Gain confidence in their ability to do mathematics

- Become mathematical problem-solvers

- Learn to communicate mathematically

- Learn to reason mathematically

- Use technology as a tool to solve problems

Hand-held graphing calculators are playing an integral part in the learning and comprehension of mathematics. It is the Mathematics Department’s policy that all students are required to have their own graphing calculator, which is needed for classwork and homework assignments. Thus, it is necessary for students to purchase a graphing calculator. Special arrangements may be available to students who are unable to purchase one.

Please Note: The courses and grade levels below represent typical programming tracks. Shaker Heights High School's counseling staff can help direct students and their families to the courses that best fit a student's academic needs.

### Academic Planning Suggestions for Students Entering Grade 9

Grade 9

AP Sequence: 9 HONORS MATH H

IB Sequence: 9 HONORS MATH H

Grade 10

AP Sequence: 10 HONORS MATH H

IB Sequence: 10 HONORS MATH H

Grade 11

AP Sequence: 11 ADVANCED MATH D

IB Sequence: MATHEMATICS:ANALYSIS & APPR. I HL

Grade 12

AP Sequence: BC CALCULUS AP and/or STATISTICS AP

IB Sequence: MATHEMATICS: ANALYSIS & APPR. II HL and MATHEMATICS: ANALYSIS & APPR. III HL

Students completing ALGEBRA I with a grade of B should consider the following four-year program for high school mathematics:

Grade 9

AP Sequence: GEOMETRY

IB Sequence: GEOMETRY

Grade 10

AP Sequence: ALGEBRA II

IB Sequence: ALGEBRA II

Grade 11

AP Sequence: PRECALCULUS

IB Sequence: MATHEMATICS: ANALYSIS & APPR. I SL

Grade 12

AP Sequence: AP CALCULUS AB and/or AP STATISTICS

IB Sequence: MATHEMATICS: ANALYSIS & APPR. II SL

Students completing ALGEBRA I with a grade of C should consider the following four-year program for high school mathematics:

Grade 9

AP SEQUENCE: GEOMETRY IB SEQUENCE: GEOMETRY

Grade 10

AP SEQUENCE: ALGEBRA II or Mathematical Modeling & Reasoning

IB SEQUENCE: ALGEBRA II or Mathematical Modeling & Reasoning

Grade 11

AP SEQUENCE: PRECALCULUS or STATISTICS

IB SEQUENCE: MATHEMATICS:ANALYSIS & APPR. I, SL

Grade 12

AP PATHWAY: AP CALCULUS AB or AP STATISTICS

IB PATHWAY: MATHEMATICS: ANALYSIS & APPR. II SL

Students completing Algebra I with a D or F should consider the following four-year program for high school mathematics:

Grade 9

ALGEBRA I

Grade 10

GEOMETRY

Grade 11

ALGEBRA II or Mathematical Modeling & Reasoning

Grade 12

PRECALCULUS or STATISTICS or FINANCIAL ALGEBRA

(A graphing calculator is required for all courses.)

### Suggestions for Students Earning Less Than C Grades in Math

Students who are earning less than C grades during the first semester of a full-year mathematics course should schedule conferences with their teachers and school counselor to discuss options.

Students earning grades less than C during the second semester of a full-year mathematics course should plan to exercise one of the following options before attempting the next sequential mathematics course:

- Repeat the course on a remedial basis in summer school or through online/blended instruction at the student’s expense.
- Repeat the course on a private tutoring basis at the student’s expense.

### Suggestions for Students Planning to Attend College

Students planning to attend college for a science education (Mathematics, Economics, Medicine, Engineering, Physical or Social Science, etc.) should complete four years of mathematics in high school including at least Algebra I, Geometry, Algebra II and Pre-Calculus.

### Guidelines for Students Who Fail First Semester of a Math Course

Semester 1 Course Failure | Indicated Course for 1 Unit of Credit |

Calculus 3 | Calculus 3 |

BC Calculus | AB Calculus |

AB Calculus | Intro to Calculus |

Intro to Calculus | Intro to Calculus |

11 Advanced Math | Precalculus |

Precalculus | Precalculus |

Discrete Math/Computer Sci. | Discrete Math/Computer Sci. |

Math: Analysis & Appr. I & II HL | Math: Analysis & Appr. I & II SL |

Math: Analysis & Appr. I & II SL | Math: Analysis & Appr. I & II SL |

10 Honors Math | Algebra II |

Algebra II | Algebra II |

Math. Modeling & Reasoning | Math. Modeling & Reasoning |

9 Honors Math | Geometry |

Geometry | Geometry |

Algebra I | Algebra I |

### Calculators

### Graphic Calculators

The Shaker Heights High School Math Department is experienced in the use of Texas Instruments graphing calculators and uses Texas Instruments calculators for classroom demonstrations. We recommend that students purchase a TI-84 Plus, unless the student plans on taking AP Calculus AB or BC his/her senior year, in which case we recommend a TI-89 Titanium graphing calculator. Do NOT purchase TI-81, TI-82, TI-85 or TI-86 calculators because they are obsolete. Do NOT purchase a TI-92, which is not permitted on standardized tests.

## Courses

### Algebra I

Full Year – 1 Unit

Unit Topics: Equation Solving, Graphing Functions, Polynomial and Quadratic Expressions, Linear Functions, Exponential Functions, and Descriptive Statistics. A graphing calculator is required. A TI-84 Plus is recommended.

### Geometry

Full Year – 1 Unit

Unit Topics: Basics of Geometry, Segments and Angles, Parallel and Perpendicular Lines, Triangle Relationships, Transformations, Congruent Triangles, Quadrilaterals, Similarity, Polygons and Area, Surface Area and Volume, Right Triangles and Trigonometry, and Circles. A graphing calculator is required. A TI-84 Plus is recommended.

Recommended Prerequisite: Algebra I

### 9 Honors Math

Full Year – 1 Unit

9 Honors Math is intended for students who completed Algebra 1 in middle school with an A or B. Unit Topics: Congruence, Proof, and Constructions; Similarity, Proof and Trigonometry; Extending to Three Dimensions; Connecting Algebra and Geometry through Coordinates; Circles with and without Coordinates; Applications of Probability; and Foundations of Intermediate Algebra. A graphing calculator is required. A TI-89 Titanium graphing calculator is recommended for students who plan on taking AP Calculus AB or BC as seniors. Otherwise, a TI-84 Plus is acceptable.

Recommended Prerequisite: Algebra I

### 10 Honors Math

Full Year – 1 Unit

10 Honors Math is intended for students in grade 10 who completed 9 Honors Math with an A, B or C. Topics: Linear, quadratic, polynomial, rational, exponential, and logarithmic functions, quadratic relations, conics, sequences, series, probability, functions, limits, curve sketching, max/min problems and other topics as time permits. A graphing calculator is required. A TI-89 Titanium calculator is recommended.

Recommended Prerequisite: 9 Honors Math

### Mathematical Modeling & Reasoning

Full Year – 1 Unit

This course is designed to promote reasoning, problem-solving and modeling through thematic units focused on mathematical practices while reinforcing and extending content in Number and Quantity, Algebra, Functions, Statistics and Probability, and Geometry. This is an Algebra 2 equivalent course and could provide a 3rd or 4th year mathematics credit. It is a yearlong course taught using student-centered pedagogy. Students could take a variety of courses after this one such as Algebra 2, Statistics or AP Statistics.

Recommended Prerequisite: Geometry

### Algebra II

Full Year – 1 Unit

Algebra II is intended for students who completed Geometry. In addition, students who completed both Algebra I and Geometry should attempt Algebra II. Unit Topics: Quadratic Functions, Polynomials and Polynomial Functions, Rational Exponents and Radical Functions, Exponential and Logarithmic Functions, Sequences and Series, Trigonometry, Rational Functions, Probability, Data Analysis and Statistics. A graphing calculator is required. A TI-89 Titanium calculator is recommended for students who plan on taking AP Calculus AB as seniors. A TI-84 Plus is recommended for future AP Statistics or IB Diploma Program students.

Recommended Prerequisite: Geometry & Algebra I

### Discrete Math/Computer science

Full Year – 1 Unit

Discrete Math/Computer Science (DMCS) will explore a variety of discrete math topics through a mix of hands-on classroom activities, traditional mathematical/logical reasoning and interactive computer science activities designed for students with no prior coding experience. Topics include Computational Thinking, Computer Logic, Game Theory, Counting/Combinatorics, Probability, Connectivity, Iteration and Recursion, and Cryptography. All topics emphasize logical reasoning, proof, and communication with precise mathematical and computer science language.

Recommended: Algebra 2

### Mathematics: Applications & Interpretations I SL

### Mathematics: Analysis & Approaches I and II SL

Full Year – 2 Units

Mathematics: Analysis and Approaches I and II SL offer a two-year experience for 11th and 12th graders. The courses will have an emphasis on students appreciating mathematics as a body of knowledge that has important applications across various disciplines and in an international context. Topics: (Math SL I) algebra, functions and equations, circular functions and trigonometry, (Math SL II) limits, statistics and probability, and calculus.

During these two years, the students will be required to complete an internal assessment and an external assessment (the IB Math SL examination) taken in May of the senior year. The internal assessment is 20% and the external assessment is 80% of a student’s IB score. A graphing calculator is required. A TI-84 Plus is recommended. To receive International Baccalaureate credit on a Shaker Heights High School transcript, the student must complete IB Internal and External Assessments.

Recommended Prerequisite: Algebra II or 10 Honors Math

### Mathematics: Analysis & Approaches I HL/11 Advanced Math

Full Year – 1 Unit

Mathematics: Analysis and Approaches I HL/11 Advanced Math is intended for students who completed 10 Honors Math. Topics: Circular functions, trigonometric functions, vectors, polar coordinates, complex numbers, formal limits, continuity, derivatives, antiderivatives and differential calculus. A graphing calculator is required. A TI-89 Titanium calculator is recommended. To receive International Baccalaureate credit on a Shaker Heights High School transcript, the student must complete IB Internal and External Assessments.

Recommended Prerequisite: 10 Honors Math

### Precalculus

Full Year – 1 Unit

Precalculus is intended for students who completed Algebra II. Topics: Circular functions, trigonometric functions, complex numbers, vectors, sequences, series, exponential and logarithmic functions, limits, continuity and derivatives. A graphing calculator is required. A TI-84 Plus is recommended, except for juniors who will be taking AB Calculus next year. In that case a TI-89 is recommended.

Recommended Prerequisite: Algebra II

### Introduction to Calculus

Full Year – 1 Unit

Introduction to Calculus is intended for students who completed Precalculus with an A, B or C. Introduction to Calculus is not intended to prepare students for the Advanced Placement Examination. Topics: Functions, limits, and an inductive treatment of differential and integral calculus. A graphing calculator is required. A TI-89 Titanium is recommended.

Recommended Prerequisite: Precalculus

### AP Calculus AB

Full Year – 1 Unit

AP Calculus AB is intended for students who completed Precalculus or 11 Advanced Math. The Advanced Placement Examination (Calculus AB) is a course requirement. Students are responsible for meeting registration deadlines and paying fees. A limited amount of financial aid is available. Topics: Functions, limits, differential calculus and integral calculus. A graphing calculator is required. A TI-89 Titanium calculator is recommended. To receive Advanced Placement Credit on a Shaker Heights High School transcript, the student must take the Advanced Placement Exam.

Recommended Prerequisite: Precalculus or Introduction to Calculus

### College Algebra and College Trigonometry, Tri-C/CCP

2 Semesters – 2 Units

College Algebra and College Trigonometry is a Tri-C course series offered through College Credit Plus. Designed for the calculus-bound student or a student planning to continue the study of mathematics in college, these courses present a study of advanced algebra topics and analytic geometry, along with an exploration of various functions, including polynomial, rational, exponential, logarithmic and trigonometric models. Polar and parametric equations, mathematical induction, and the binomial theorem will be studied as well. These topics will be explored using modern technology and graphical analysis along with the more traditional approaches. Acceptance to Tri-C’s College Credit Plus program is required for enrollment in College Algebra/College Trigonometry. Upon completing course requirements, qualifying students will earn 1 high school unit per semester, and 3 hours of college credit per semester from Cuyahoga Community College, through College Credit Plus.

Required: Meet the established standards for admission and course placement of the college/university

### Statistics

Full Year – 1 Unit

Statistics is intended for students who are not planning to study calculus in college or at a university. Topics: Interpreting categorical and quantitative data, making inferences and justifying conclusions, conditional probability and the rules of probability, and using probability to make decisions. A graphing calculator is required. A TI-84 Plus is recommended.

Recommended Prerequisite: Mathematical Modeling & Reasoning, or Algebra II, or Precalculus, or Mathematics: Analysis & Approaches II HL/AP Calculus BC

### AP Statistics

Full Year – 1 Unit

AP Statistics is intended for students in grades 11 or 12 who completed 10 Honors Math and Precalculus or Algebra II or Mathematical Modeling & Reasoning. Eleventh graders who elect to take Statistics should be enrolled in 11 Advanced Math or Precalculus. The Advanced Placement Statistics Examination is a course requirement. Topics: Data analysis using graphical and numerical techniques, designing samples and experiments, probability and simulation, and statistical inference. A graphing calculator is required. A TI-84 Plus graphing calculator is recommended. To receive Advanced Placement Credit on a Shaker Heights High School transcript, the student must take the Advanced Placement Exam.

Recommended Prerequisite: Algebra II, 10 Honors Math, or Precalculus, or Mathematical Modeling & Reasoning

### AP Calculus BC

Full Year - 1 Unit

AP Calculus BC is intended for students who completed 11 Advanced Math. The Advanced Placement Examination (Calculus BC) is a course requirement. Students are responsible for meeting registration deadlines and paying fees. A limited amount of financial aid is available. Topics: Differential calculus, integral calculus, sequences and series. A graphing calculator is required. A TI-89 Titanium calculator is recommended. To receive Advanced Placement Credit on a Shaker Heights High School transcript, the student must take the Advanced Placement Exam. To receive International Baccalaureate credit on a Shaker Heights High School transcript, the student must complete the IB Internal and External Assessments. The AP Calculus BC exam is optional for IB students.

Recommended Prerequisite: Mathematics HL I (or equivalent) or 11 Advanced Math

### Mathematics: Analysis & Approaches II HL/AP Calculus BC

*To receive Advanced Placement Credit on a Shaker Heights High School transcript, the student must take the Advanced Placement Exam. To receive International Baccalaureate credit on a Shaker Heights High School transcript, the student must complete the IB Internal and External Assessments.*The AP Calculus BC exam is optional for IB students.

### Mathematics: Analysis & Approaches III HL (concurrent enrollment)

Full Year – 2 Units

Mathematics HL II and HL III may be taken concurrently. When taken concurrently, students will be scheduled for two periods of math. One period will be for the IB topics that are not addressed in the AP Calculus BC course, and the other period will be for Calculus BC. Topics for Calculus BC: Differential calculus, integral calculus and series. Topics for HL: Probability and statistics, series and differential equations. The IB students will complete an Internal Assessment and an External Assessment (the IB Math HL examination) taken in May of the senior year. The Internal Assessment is 20% and the External Assessment is 80% of a student’s IB score. A TI-84 graphing calculator is required. To receive International Baccalaureate credit on a Shaker Heights High School transcript, the student must complete IB Internal and External Assessments. The AP Calculus BC exam is optional for IB students.

Recommended Prerequisite: Mathematics HL I (or equivalent)

### Financial Algebra

Full Year – 1 Unit

The Financial Algebra course provides students with a motivating student-centered curriculum that provides a financial context for understanding and applying mathematics they are guaranteed to use in the future. This course empowers students to think analytically about the important financial decisions that they will have to make in life. Financial Algebra connects the mathematics of piecewise functions, regression, limits, exponential functions, linear/quadratic systems, and more to financial decisions that one has to make in daily life. Unit Topics: The Stock Market, Modeling a Business, Banking Services, Consumer Credit, Automobile Ownership, Employment Basics, Income Taxes, Independent Living, Planning for Retirement, and Prepare a Budget. A graphing calculator is required. A TI-84 Plus is recommended.

Recommended Prerequisite: Algebra II or Statistics or Mathematical Modeling & Reasoning