C. Mathematics (3 courses required, 4 courses recommended)
Three units (equivalent to three years) of college-preparatory mathematics (four units are strongly recommended), including or integrating topics covered in elementary algebra, advanced algebra, and two-and three-dimensional geometry.
CALCULUS HONORS [549CALC]
In this course, students will develop develop understanding about the topics of differential and integral calculus. Emphasis is placed on conceptual and computational knowledge of limits, continuity, derivatives and integrals of algebraic and transcendental functions of a single variable. Upon completion, students should be able to select and use appropriate models and techniques for finding solutions to derivative- and integral- related problems with and without technology.
INTEGRATED MATH I [549MATHI]
The Integrated Math I concentration is on manipulation of algebraic expressions, representing situations with equations, the solutions of these equations, graphing linear equations with a focus on the representation of linear statistical data, the solution of systems of equations and inequalities graphically and algebraically, the use of function notation to represent and analyze linear and exponential data, the application of rigid geometric transformations to include their application in coordinate geometry and their effects on linear equations, and the use of coordinate geometry to examine the geometric properties of basic geometric shapes. The Mathematical Practice Standards apply throughout each unit and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Students will communicate their thinking both orally and in writing and will explore how algebra, geometry, probability, and statistics are used in a variety of real-life scenarios. Though the course will increase students’ theoretical knowledge, it will do so in a way that leads to understanding as opposed to memorization. This course aligns perfectly with the five goals of the UC Mathematics requirement. The students learn mathematical sense making, make and test conjectures and justify conclusions, use mathematical models to represent real-world data, be able to provide clear and concise answers, and have computational and symbolic fluency. [Click Here for the Complete Syllabus]
INTEGRATED MATH II [549IMII]
Students will meet the California Common Core State Standards for Integrated Mathematics II. The math strands that will be explored and enriched include: Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability.
Emphasis will be placed on principles of logical reasoning and proof to understand properties of congruence and similarity and the deepening of understanding of a variety of functions (quadratic, absolute value, and cubic). Specific topics will include: theorems involving angles, lines, and planes, similar and congruent triangles, parallelograms. Circles are studied and used to develop deductive reasoning skills. Other topics will include perimeter, area and volume, coordinate transformational geometry, trigonometry, and an introduction to statistics and probability through compound events. Students will communicate their thinking both orally and in writing and will explore how algebra, geometry, probability, and statistics are used in a variety of real-life scenarios.
Emphasis will also be placed on manipulation of equations and number sense in order to understand the underlying important of algebraic expressions and their relationships with their representations: tables, graphs, and functions. This course will develop a strong understanding of quadratics and how it is an extension of algebra and its study of linear equations, sequences, and functions.
In this course, students will continue their study of higher math topics and delve deeper into those studied in Integrated Math I. Students will understand mathematical concepts in a variety of ways: graphically, numerically, and algebraically. They will learn to clearly and concisely communicate their mathematical thinking, both verbally and in writing. Though the course will increase students' theoretical knowledge, it will do so in a way that leads to understanding as opposed to memorization. Students will also experience math as a tool for modeling the world around them, allowing them to better understand and analyze it and solve problems in a variety of contexts. Students who successfully complete this course will be prepared to take Integrated Mathematics III.
INTEGRATED MATH III [549IMIII]
Integrated Math 3 will focus heavily on building the students’ foundation on functions and extending that knowledge into inverses, logarithm, polynomials, rational expressions, and trigonometric functions. Furthermore, students will learn to demonstrate their knowledge of functions through modeling these various types of functions so that they can understand the relationship among the functions and how they interact. The course will focus heavily on solving and interpreting functions in its different forms and modelling them. [Click Here for the Complete Syllabus]
PRECALCULUS HONORS [549PreCal]
The purpose of this course is to provide students with the tools they will need for college mathematics courses, particularly calculus. The course is structured around investigations and problem solving. Students will explore concepts and develop mathematical relationships through observation, application, and both formal and informal proof. Lessons are designed to facilitate teamwork and encourage students to pose conjectures, justify solutions, and defend their thinking.
STATISTICS HONORS [549Stats]
In this course, students will gain an understanding about the field of Statistics through real-world scenarios. Specifically, students will make connections between mathematics and other subject areas and within math itself.
Students will learn how to display and interpret data in a variety of contexts. Specific topics include: measures of central tendency, measures of spread, locating data points within normal distributions, designing samples and experiments, sampling distribution, and the chi-square test. The course will culminate with a final project in which students will explore a topic of their choice through the statistical lens. Individually or in groups, students will develop and conduct a survey for a specific sample population, collect and analyze data, and draw conclusions from their research study. In addition to writing a research paper, students will communicate the results of their study to a real-world audience through infographics and/or presentations.
In this course, students will develop develop understanding about the topics of differential and integral calculus. Emphasis is placed on conceptual and computational knowledge of limits, continuity, derivatives and integrals of algebraic and transcendental functions of a single variable. Upon completion, students should be able to select and use appropriate models and techniques for finding solutions to derivative- and integral- related problems with and without technology.
INTEGRATED MATH I [549MATHI]
The Integrated Math I concentration is on manipulation of algebraic expressions, representing situations with equations, the solutions of these equations, graphing linear equations with a focus on the representation of linear statistical data, the solution of systems of equations and inequalities graphically and algebraically, the use of function notation to represent and analyze linear and exponential data, the application of rigid geometric transformations to include their application in coordinate geometry and their effects on linear equations, and the use of coordinate geometry to examine the geometric properties of basic geometric shapes. The Mathematical Practice Standards apply throughout each unit and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Students will communicate their thinking both orally and in writing and will explore how algebra, geometry, probability, and statistics are used in a variety of real-life scenarios. Though the course will increase students’ theoretical knowledge, it will do so in a way that leads to understanding as opposed to memorization. This course aligns perfectly with the five goals of the UC Mathematics requirement. The students learn mathematical sense making, make and test conjectures and justify conclusions, use mathematical models to represent real-world data, be able to provide clear and concise answers, and have computational and symbolic fluency. [Click Here for the Complete Syllabus]
INTEGRATED MATH II [549IMII]
Students will meet the California Common Core State Standards for Integrated Mathematics II. The math strands that will be explored and enriched include: Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability.
Emphasis will be placed on principles of logical reasoning and proof to understand properties of congruence and similarity and the deepening of understanding of a variety of functions (quadratic, absolute value, and cubic). Specific topics will include: theorems involving angles, lines, and planes, similar and congruent triangles, parallelograms. Circles are studied and used to develop deductive reasoning skills. Other topics will include perimeter, area and volume, coordinate transformational geometry, trigonometry, and an introduction to statistics and probability through compound events. Students will communicate their thinking both orally and in writing and will explore how algebra, geometry, probability, and statistics are used in a variety of real-life scenarios.
Emphasis will also be placed on manipulation of equations and number sense in order to understand the underlying important of algebraic expressions and their relationships with their representations: tables, graphs, and functions. This course will develop a strong understanding of quadratics and how it is an extension of algebra and its study of linear equations, sequences, and functions.
In this course, students will continue their study of higher math topics and delve deeper into those studied in Integrated Math I. Students will understand mathematical concepts in a variety of ways: graphically, numerically, and algebraically. They will learn to clearly and concisely communicate their mathematical thinking, both verbally and in writing. Though the course will increase students' theoretical knowledge, it will do so in a way that leads to understanding as opposed to memorization. Students will also experience math as a tool for modeling the world around them, allowing them to better understand and analyze it and solve problems in a variety of contexts. Students who successfully complete this course will be prepared to take Integrated Mathematics III.
INTEGRATED MATH III [549IMIII]
Integrated Math 3 will focus heavily on building the students’ foundation on functions and extending that knowledge into inverses, logarithm, polynomials, rational expressions, and trigonometric functions. Furthermore, students will learn to demonstrate their knowledge of functions through modeling these various types of functions so that they can understand the relationship among the functions and how they interact. The course will focus heavily on solving and interpreting functions in its different forms and modelling them. [Click Here for the Complete Syllabus]
PRECALCULUS HONORS [549PreCal]
The purpose of this course is to provide students with the tools they will need for college mathematics courses, particularly calculus. The course is structured around investigations and problem solving. Students will explore concepts and develop mathematical relationships through observation, application, and both formal and informal proof. Lessons are designed to facilitate teamwork and encourage students to pose conjectures, justify solutions, and defend their thinking.
STATISTICS HONORS [549Stats]
In this course, students will gain an understanding about the field of Statistics through real-world scenarios. Specifically, students will make connections between mathematics and other subject areas and within math itself.
Students will learn how to display and interpret data in a variety of contexts. Specific topics include: measures of central tendency, measures of spread, locating data points within normal distributions, designing samples and experiments, sampling distribution, and the chi-square test. The course will culminate with a final project in which students will explore a topic of their choice through the statistical lens. Individually or in groups, students will develop and conduct a survey for a specific sample population, collect and analyze data, and draw conclusions from their research study. In addition to writing a research paper, students will communicate the results of their study to a real-world audience through infographics and/or presentations.