# Math Department Curriculum

Given the variability in curriculum across our many feeder schools, we feel we can best meet the needs of our students by testing all students in math. All students that enroll at Presentation High School are required to take a math proficiency test in order to ensure proper placement.

All current students receive an individualized course recommendation from their math teacher prior to course selection. As part of the recommendation process, math teachers also reflect on the attributes necessary to succeed as they advance to more complex content. Thus, course recommendations are not based solely on grades but are used to help students/parents open conversations between themselves, with their math teachers, and with their counselors as they decide what course is best for them.

## Core Math Courses

## Algebra Readiness

**Algebra Readiness**

**Grade:** 9

**Credits:** 10

**College Prep: **UC/CSU “c” Mathematics

Due to the learning loss during the COVID-19 pandemic, we began offering this unique course to close the gap for some students. Algebra Readiness is a course designed to prepare students for a rigorous college preparatory high school mathematics course. Each class, students in Algebra Readiness use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Under teacher guidance, students learn in collaboration with others while sharing information, expertise, and ideas. The course helps students to develop multiple strategies to solve problems and to recognize the connections between concepts. The lessons in the course meet all of the content standards and embed the “Mathematical Practices” of the Common Core State Standards released in June 2010.

## Algebra I

**Algebra I**

**Grade:** 9

**Credits: **10

**College Prep: **UC/CSU “c” Mathematics

This is a standard course in algebra designed to develop an understanding of a mathematical system, the algebra of real numbers. It focuses on the properties of real numbers, solving linear and quadratic functions in a coordinate plane, solving linear systems of equations, factoring, applications of algebra in problem solving, functions and relations, polynomials, factoring, simplifying rational expressions, solving rational equations, solving systems of equations, radical expressions, applications with rational numbers, graphing and solving quadratics.

## Geometry

**Geometry**

**Grade:** 9, 10, 11

**Credits: **10

**Prerequisite: **Passing grade in each semester of Algebra I

**College Prep: **UC/CSU “c” Mathematics

This course includes all of the basic concepts and constructions of plane and solid geometry. Emphasis is placed on the development of logic, beginning with a set of axioms and postulates which are then used in the proofs of theorems and in solving problems. The course emphasizes exploration and testing of mathematical ideas by using manipulatives and open-ended questioning to lead to concepts. This course also includes an introduction to the trigonometry of right triangles and provides a continuing review of the skills developed in Algebra I.

## Honors Geometry

**Honors Geometry**

**Grade:** 9, 10

**Credits: **10

**Prerequisite:** B+ in each semester of Algebra I. Students currently enrolled in the Daily Algebra course are not eligible for Honors Geometry.

**College Prep: **UC/CSU “c” Mathematics

Honors Geometry covers the topics in the Geometry curriculum at a faster pace and with an emphasis on developing abstract reasoning skills. It is designed to provide a challenge for students who are strong in math and to move them toward a more theoretical approach to the subject matter. Students will study postulates and theorems about both plane and solid figures of geometry (2-D & 3-D shapes). Topics include, but are not limited to: points, lines, and planes, congruence and similarity, circles, lines cut by a transversal, trig ratios, area, surface area and volume, as well as coordinate geometry. This course will help students to develop their critical thinking skills through many hands-on activities designed to guide students to discovery of geometrical relationships. Problem sets, which stretch their critical thinking skills and encourage methodical problem solving, will be employed. Logical reasoning will be emphasized through the development of theorems/proofs, problem solving, and geometric constructions. Students will be expected to use their algebra skills (factoring quadratics and solving systems of equations) for solving problems in a geometry context.

## Algebra II

**Algebra II**

**Grade:** 10, 11, 12

**Credits: **10

**Prerequisite: **Passing grade in each semester of Geometry or Honors Geometry; summer Geometry student with B in each summer session

**College Prep**: UC/CSU “c” Mathematics

The Algebra II course is the 3rd in the standard sequence of math for college preparatory programs. Completion of the course with a passing grade will enable the students to go on to Pre-Calculus or Statistics. This course continues the development of algebraic structures begun in Algebra I in areas such as linear systems, quadratic functions, polynomial functions, and graphing in the coordinate plane. New topics include quadratic systems, complex numbers, conic sections, exponential functions and logarithms, radical equations, and matrices. Students will also work in cooperative settings on problem solving, and become familiar with scientific and graphing calculators, as well as using the iPad and apps for mathematical applications. This course, together with Algebra I and Geometry, satisfies the requirements of many colleges for three years of college preparatory mathematics.

## Honors Algebra II

**Honors Algebra II**

**Grade: **9, 10, 11

**Credits: **10

**Prerequisite:** B+ unweighted Math GPA AND B+ in each semester of Geometry or B in each semester of Honors Geometry; summer Geometry student with A- in each summer session

**College Prep:** UC/CSU “c” Mathematics

This course continues the development of algebraic structures begun in Algebra I with the study of functions, irrational and complex numbers, quadratic functions, systems of equations, conic sections and exponential and logarithmic functions. These topics are the same as regular Algebra II, but will be covered in greater depth. Additionally, it will include the topics of series and sequences, probability, combinatorics, binomial expansion/Binomial Theorem, logic and proof techniques. A graphing calculator will be used on a regular basis to assist the concepts. This course, together with Algebra I and Geometry (or Honors Geometry), satisfies the requirement for three years of college preparatory mathematics. Due to the fast pace and depth of topics, it is recommended for STRONG math students only.

## Math: Elective Courses (after completion of core coursework)

- Statistics I
- Statistics II
- AP Statistics
- Precalculus
- AP Precalculus
- Calculus I
- AP Calculus AB
- AP Calculus BC
- Honors Multi-Variable Calculus
- Introduction to Computer Science
- AP Computer Science A

## Statistics I

**Statistics I**

**Grade: **11-12

**Credits:** 5

**Prerequisite:** Passing grade in each semester of Algebra II or Honors Algebra II

**College Prep: **UC/CSU “c” Mathematics

Statistics I is an introductory course in statistics designed for students with a wide variety of vocational interests and applications are taken from many fields. This course introduces the fundamental ideas of observational/experimental design, displaying and summarizing data in both graphical and numerical forms, linear regression, probability, and discrete distributions. Connections to the fields of medicine, psychology, business, economics, the sciences, and much more will be made. A graphing calculator will be used daily to assist in the work. This course is ideal for students who intend to major in non-math/science fields in college.

## Statistics II

**Statistics II**

**Grade: **11-12

**Credits:** 5

**Prerequisite: **Passing grade in Statistics I

**College Prep: **UC/CSU “c” Mathematics

This course is a continuation of Statistics I and introduces the fundamental ideas of statistical inference including Confidence Intervals and Hypothesis Testing. Topics include the normal distribution, sampling distributions, one and two sample confidence intervals and hypothesis testing for means and proportions, and Chi-Squared testing. It is a graphing-calculator based course and will allow students to analyze data that was collected in class. The course is designed for students with a wide variety of vocational interests, and applications are taken from many fields and is encouraged for students who intend to major in non-math/science fields in college.

## AP Statistics

**AP Statistics**

**Grades: **11, 12

**Credits: **10

**Prerequisite:** B+ in each semester of Algebra II or C+ in each semester of Honors Algebra II

**College Prep:** UC/CSU “c” Mathematics

The purpose of the AP® Statistics course is to introduce major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four broad conceptual themes:

- Exploring Data: Describing patterns and departures from patterns
- Sampling and Experimentation: Planning and conducting a study
- Anticipating Patterns: Exploring random phenomena using probability and simulation
- Statistical Inference: Estimating population parameters and hypotheses testing

Students who successfully complete the course and pass the AP® exam may be eligible to receive college credit for a one-semester introductory college statistics course.

## Precalculus

**Precalculus**

**Grades:** 11, 12

**Credits:** 10

**Prerequisite: ** B- in each semester of Algebra II or C in each semester of Honors Algebra II

**College Prep: **UC/CSU “c” Mathematics

This course includes the study of trigonometry, analysis of functions with graphing including linear, absolute value, rational, irrational, quadratic and higher powers, log, an introduction to vectors, polar, and parametric functions and graphing. The course concludes with an introduction to calculus covering limits, continuity and basic derivatives.

## AP Precalculus

**AP Precalculus**

**Grade:** 10, 11, 12

**Credits: **10

**Prerequisite:** A in each semester of Algebra II with teacher recommendation or B- in each semester of Honors Algebra II

**Note: **This new Advanced Placement (AP) course is replacing Honors Precalculus and Honors PreCalculus/Calculus A for the 2023-2024 school year.

**College Prep: **UC/CSU “c” Mathematics

AP PreCalculus is a rigorous college level course. It provides a comprehensive study of trigonometry, including circle trigonometry, triangle trigonometry, trigonometric identities and formulas, graphing trigonometric functions, inverse trigonometric functions, solving trigonometric equations, polar coordinates, and two and three dimensional vectors. It also covers parametric equations, rotation of conic sections, and polar equations in parametric form. Some concepts to prepare the student for AP Calculus AB will be introduced including the concept of limits, continuity of functions, and a brief introduction to derivatives.

## Calculus I

**Calculus I**

**Grade:** 11, 12

**Credits: **10

**Prerequisite: **B- in each semester of Precalculus or C in each semester of Honors Precalculus

**College Prep: **UC/CSU “c” Mathematics

This year-long course is for students who wish to take a beginning Calculus course, without the rigor of the AP Calculus courses and without the full range of AP Calculus topics. This class will move more slowly and provide more assistance and practice time than the AP Calculus courses. This class will provide a solid foundation for students wishing to take Calculus in college. This course includes a study of functions and graphing, limits, continuity, Differential Calculus and its applications, and integral Calculus and its applications.

## AP Calculus AB

**AP Calculus AB**

**Grade: **10-12

**Credits: **10

**Prerequisite: **B- in each semester of Honors Precalculus or A in each semester of Precalculus with teacher recommendation

**College Prep: **UC/CSU “c” Mathematics

This course will review and build on derivatives and their applications and introduce the concept of integration, its techniques and applications. The course will cover the range of topics on the AP Calculus AB test with some review of the AP Calculus AB test offered. Strong honors math students with a B+ or better in Honors PreCalculus are encouraged to bypass AB and enroll in AP Calculus BC. Passing the College Board AP Calculus AB exam may give the student credit for ONE semester of college calculus. If credit is awarded depends on the admissions policies at the student’s intended college/university.

## AP Calculus BC

**AP Calculus BC **

**Grade: **10-12

**Credits:** 10

**Prerequisite: **B- in each semester of AP Calculus AB

**College Prep: **UC/CSU “c” Mathematics

The first semester will introduce the concept of integration and its techniques. It will cover applications of integral calculus, such as solids and surfaces of revolution, and the range of topics on the AP Calculus AB test. The second semester will continue with advanced techniques of integration and applications of integration, such as average value of a function and arc length. It will also cover differential equations, slope fields, sequences and infinite series, parametric equations, polar coordinates, vectors and vector functions, and the range of topics on the AP Calculus BC test with some review of the AP Calculus AB and BC test offered. Passing the College Board AP Calculus BC exam may give the student credit for TWO semesters of college calculus. If credit is awarded depends on the admissions policies at the student’s intended college/university.

## Honors Multi-Variable Calculus

**Honors Multi-Variable Calculus**

**Grade:** 11-12

**Credits: **10

**Prerequisite: **B- in each semester of AP Calculus BC

**College Prep: **UC/CSU “c” Mathematics

This year-long course is designed to provide students who have completed AP Calculus BC with the opportunity to take a third year or fourth year of math and prepare them for further studies of mathematics. It will offer rigorous preparation for college level math and deepen their understanding of what they have learned in previous math classes. Students will study vectors and geometry of space, vector functions, partial derivatives, multiple integrals, vector calculus, and second-order differential equations. They will also use maple software to assist them with visualizing objects in 3-Ds, computing problems and checking their answers, doing projects and independent exploration.

## Introduction to Computer Science

**Introduction to Computer Science **

**Grade:** 9, 10, 11, 12

**Credits:** 5

**College Prep: **UC/CSU “g” College-Preparatory Elective

Computer science isn't as mysterious or difficult as many people believe. Find out the truth with this semester-long introductory course in computer science, for students who want to dip their toes into this increasingly important field of knowledge, or for students who want a head start for the AP Computer Science A course. You will be learning by doing, with hands-on, guided lessons where you will write, analyze, and improve upon programming code. We will focus on practical applications of coding for the creation of applets, websites and more, with an eye toward beautiful and functional design. No prior experience is required, as we work in an increasingly popular coding language with tight integration to our iPads. Topics include data types, data structures, control flow, and interface design. Come crack the code of coding.

## AP Computer Science A

**AP Computer Science A**

**Grade:** 10, 11, 12

**Credits: **10

**Prerequisite: **B in each semester of Algebra II or C in each semester of Honors Algebra II

**College Prep: **UC/CSU“c” Mathematics (third year only)

The AP Computer Science A course is an introductory course in computer science. Because the design and implementation of computer programs to solve problems involve skills that are fundamental to the study of computer science, a large part of the course is built around the development of computer programs that correctly solve a given problem. These programs should be understandable, adaptable, and, when appropriate, reusable. At the same time, the design and implementation of computer programs is used as a context for introducing other important aspects of computer science, including the development and analysis of algorithms, the development and use of fundamental data structures, the study of standard algorithms and typical applications, and the use of logic and formal methods. In addition, the responsible use of these systems is an integral part of the course.

## Contact

Heidi Olson

Department Chair

(408) 264-1664

holson@presentationhs.org