High School Math Classes
The main purpose of Algebra I is to develop the students’ fluency with linear, exponential, and quadratic function. The course formalizes and extends the mathematics learned in middle grades. This student-centered and standards-based course uses the CME Project Algebra I textbook. Within each chapter are several investigations (which are clusters of related lessons), section reflections, and embedded mid-chapter and end-of-chapter assessments. The text takes an investigative approach, encouraging students to develop strategies to solve various types of challenging problems. Students will investigate, conjecture, validate, generalize, extend, connect, communicate and reflect upon mathematical ideas. Implementing the “Habits of Mind” is prevalent throughout the book, thus focusing on the students’ use of the Mathematical Practices. PREREQUISITE: None.
The fundamental purpose of the Geometry course is to introduce students to formal geometric proof and the study of plane figures, culminating in the study of right triangle trigonometry and circles. The course formalizes and extends students’ geometric experiences from the middle grades. Students begin to prove results about the geometry of the plane by using previously defined terms and notions. Similarity is explored in greater detail, with an emphasis on discovering trigonometric relationships and solving problems with right triangles. This course uses the Big Ideas Math Geometry textbook. Each lesson begins with an Essential Question and is followed by Explorations. Students will investigate, conjecture, validate, generalize, extend, connect, communicate and reflect upon mathematical ideas. A key difference in this course and the historical approach to teaching geometry is the emphasis on transformations. The Standards for Mathematical Practice complement the content standards so that students increasingly engage with the subject matter as they grow in mathematical maturity and expertise throughout their years at the secondary level. In Geometry, instructional time should focus on six critical areas: (1) establish criteria for congruence of triangles based on rigid motions; (2) establish criteria for similarity of triangles based on dilations and proportional reasoning; (3) informally develop explanations of circumference, area, and volume formulas; (4) apply the Pythagorean Theorem to the coordinate plane; (5) prove basic geometric theorems; and (6) extend work with probability. PREREQUISITE: Grade of C or better in Algebra IP.
Units of study in Honors Geometry are the same as described in Geometry P. The Honors Geometry course expects a high level of understanding of mathematical concepts with an emphasis on applying algebraic expressions and the incorporation of non-routine problems. PREREQUISITE: Grade of A in Algebra I.
The fundamental purpose of the Algebra II course is to extend students’ understanding of functions and the real numbers, and to incase the tools students have for modeling the real world. Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include logarithmic, polynomial, rational, and radical functions. This course uses the Big Ideas Math Algebra 2 textbook. Each lesson begins with an Essential Question and is followed by Explorations. Students work closely with the expressions that define the functions, competently manipulate algebraic expressions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms. Standards that were limited in Algebra I no longer have those restrictions in Algebra II. In Algebra II, instructional time should focus on four critical areas: (1) relate arithmetic of rational expressions to arithmetic of rational numbers; (2) expand understandings of functions and graphing to include trigonometric functions – extended to all real numbers, and their graphs and properties are studied; (3) synthesize and generalize functions and extend understanding of exponential functions and their inverses to logarithmic functions; and (4) relate data display and summary statistics to probability and explore a variety of data collection methods. Students’ statistics knowledge is extended to understanding the normal distribution, and they are challenged to make inferences based on sampling, experiments and observational studies. PREREQUISITE: Grade of C or better in Geometry and Algebra I.
Units of study in Honors Algebra II are the same as described in Algebra IIP. Honors Algebra II includes the study of trigonometric identities and conics in preparation for the next course in the progression, Honors PreCalculuc/Calculus A. The Honors Algebra II course expects a high level of understanding of mathematical concepts and incorporates non-routine problems. TI84 PLUS or like graphing calculator recommended. PREREQUISITE: Grade of A in Geometry or B or better in Honors Geometry with teacher recommendation.
In Precalculus, students extend their work with complex numbers begun in Algebra II to see that the complex numbers can be represented in the Cartesian plane and that understanding of trigonometry and the geometry of the plane to express complex numbers in polar form. Students begin working with vectors, representing them geometrically and performing operations with them. They connect the notion of vectors to complex numbers. Students also work with matrices, their operations, and find inverse matrices. They see the connection between matrices and transformations of the plane. Students use matrices to represent and solve linear systems. Students extend their work with trigonometric functions, investigating the reciprocal functions secant, cosecant, and cotangent and their graphs and properties. They find inverse trigonometric functions by appropriately restricting the domains of the standard trigonometric functions and use them to solve problems that arise in modeling contexts. Although students have worked previously with parabolas and circles, they now work with ellipses and hyperbolas. They also work with polar coordinates and curves defined parametrically and connect these to their other work with trigonometry and complex numbers. Finally, students work with more complicated rational functions, graphing them and determining zeros, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points. TI84 PLUS or like graphing calculator recommended. PREREQUISITE: Grade of C or better in Algebra II.
Pre-Calculus/Calculus A HP
Students will complete the course material as described in the second semester of the PreCalculus course. During the second semester of this course, the Calculus A portion, the content includes limits, continuity, and differentiation techniques of both algebraic and transcendental functions, curve sketching, and the relationships among position, velocity, and acceleration. Antidifferentiation and the Fundamental Theorem of Calculus are introduced in this Pre-Calculus/Calculus A HP course. The course also incorporates non-routine problems. A high level of proficiency with polynomials, linear systems, exponential/logarithmic and rational functions in Algebra II HP is expected in the fast paced course with minimal prior course review since it begins the study of calculus in second semester. TI84 PLUS or like graphing calculator recommended. PREREQUISITE: Grade of B or better in Algebra II HP or Algebra II with an A and teacher recommendation.
AP Calculus AB
This course is designed to prepare students for the Advanced Placement examination in Calculus AB and teaches the curriculum typical of the first semester of a college level Calculus course. Students who are enrolled in AP Calculus AB are expected to work with functions represented in multiple ways: graphical, numerical, analytical, or verbal, and understand the connections among these representations. They will examine the meaning of the derivative interims of a rate of change and local linear approximation and use derivatives to solve problems, accumulation of change and use integrals to solve problems. They will develop an understanding of the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus. TI84 PLUS or like graphing calculator recommended. PREREQUISITE: Grade of B or better in Trigonometry/Pre-Calculus.
AP Calculus BC
This course is designed to prepare student for the Advanced Placement examination in Calculus BC and teaches the curriculum typical of two semesters of college level Calculus. This course builds from and extends all content described in Calculus AB, plus additional content including sequences and series, vectors, improper integrals, and functions in polar and parametric form are part of this course. A high level of proficiency in Pre-Calculus/Calculus AP HP is a must for this course due to its building from Calculus AB and incorporation of non-routine problems. TI84 PLUS or like graphing calculator recommended. PREREQUISITE: Grade of B or better in Calculus AB or Calculus A.
Students extend their work in Statistics and probability by applying Statistics ideas to real-world situations. They link classroom mathematics and statistics to everyday life, work, and decision-making, by applying these standards in modeling situations. They choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students in Statistics and Probability take their understanding of probability further by studying expected values, interpreting them as long-term relative means of a random variable. They use this understanding to make decisions about both probability games and real-life examples using empirical probabilities. With depth over breadth in mind, the course offers the opportunity to delve deeper into those repeated Statistics and Probability standards while addressing new ones. PREREQUISITE: Grade of C or better in Algebra II.
This course is designed to prepare students for the Advanced Placement Examination in Statistics and covers the curriculum typical of the first semester of a college level Statistics course. The course is divided into four skill categories: selecting statistical methods, data analysis, using probability and simulation, and statistical argumentation. In the selecting statistical methods category, students will select methods for collecting and/or analyzing data for statistical inference. In the data analysis category, students will describe patterns, trends, associations, and relationships in data. In the using probability and simulation category, students will explore random phenomena. In the statistical argumentation category, students will develop an explanation or justify a conclusion using evidence from data, definitions, or statistical inference. PREREQUISITE: A or B in Algebra II HP.
Multi-Variable Calculus corresponds to the university level calculus course that follows the courses in Calculus of a Single Variable. This course is designed for high school students who have successfully completed Advanced Placement Calculus BC. The content of the course consists of the differential and integral calculus of several variables as well as the calculus of vector-valued functions. A graphing calculator is required and is used to enhance the teaching and learning of calculus. PREREQUISITE: Grade C or better in Calculus BC