# C. Mathematics

### *COMMON CORE ALGEBRA 1

Annual Course – Grade 9 or 10

Prerequisite: Common Core Mathematics 8 AB

310341 CC Algebra 1

310342 CC Algebra 1 (10 credits)

COURSE DESCRIPTION The purpose of Algebra I is for students to use reasoning about structure to define and make sense of rational exponents and explore the algebraic structure of the rational and real number systems.  They understand that numbers in real world applications often have units attached to them, that is, they are considered quantities. Students explore the structure of algebraic expressions and polynomials.  They see that certain properties must persist when working with expressions that are meant to represent numbers, now written in an abstract form involving variables.  When two expressions with overlapping domains are set equal to each other, resulting in an equation, there is an implied solution set (be it empty or non-empty), and students not only refine their techniques for solving equations and finding the solution set, but they can clearly explain the algebraic steps they used to do so.

In Algebra I, students extend this knowledge to working with absolute value equations, linear inequalities, and systems of linear equations.  After learning a more precise definition of function in this course, students examine this new idea in the familiar context of linear equations (for example, by seeing the solution of a linear equation as solving for two linear functions  and ).  Students continue building their understanding of functions beyond linear ones by investigating tables, graphs, and equations that build on previous understandings of numbers and expressions.  They make connections between different representations of the same function.  They learn to build functions in a modeling context, and solve problems related to the resulting functions.  Note that the focus in Algebra I is on linear, simple exponential, and quadratic equations.

This course is offered to students who demonstrate a thorough understanding of Pre-algebra concepts. The intent of the course is to develop skill and understanding of the language of algebra, functions, number operations, solving and graphing equations and inequalities involving real-world concepts, ratios, quadratic functions, factoring terms, completing the square, using the quadratic formula, monomial and polynomial expressions, exponents and rational expressions, and problem solving.  Through the study and use of Algebra, the learner develops an understanding of the symbolic language of mathematics and the sciences. Algebra 1 develops the skills and concepts to help solve a wide variety of problems. Goals: A) To help students own and command the language of Algebra; B) To prepare students for the study of higher mathematics and for those who are college bound, to provide a basic understanding of the symbolic nature of algebra; C) To focus on the big ideas of Algebra1.

Finally, students extend their prior experiences with data, using more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.

### *COMMON CORE GEOMETRY AB

Annual Course – Grade 9 or 10

Prerequisite: Common Core Algebra 1

310423 CC GEOMETRY A

310424 CC GEOMETRY B

The essential purpose of this Geometry course is to introduce students to formal geometric proofs and the study of plane figures, with an emphasis on plane Euclidean geometry—both synthetically and analytically.  Furthermore, transformations of rigid motion are the foundations of proof for congruency and similarity.  Concepts included in this course are geometric transformations, proving geometric theorems, congruence and similarity, analytic geometry, right triangle trigonometry, and probability and statistics.  Students are expected to model real world situations and make decisions using these ideas.

### COMMON CORE ALGEBRA 2AB

Annual Course – Grade 10 or 11

Prerequisite: Common Core Algebra 1 and Common Core Geometry AB

310343 CC ALGEBRA 2A

310344 CC ALGEBRA 2B

Course Description: In this course, students expand understanding of expressions including rewriting, interpreting and examining rational, radical, polynomial expressions and deriving the formula of the sums of finite geometric series. Students continue expanding their knowledge of rational, polynomial, radical, exponential and logarithmic functions; they learn to represent functions algebraically, graphically, in numerical tables and by verbal descriptions. Students expand their knowledge of the real numbers to model/ solve a variety of equations/ inequalities and the systems of equations with two or more variables. Students practice creating equations for real world situations, learn how to solve them, interpret the solutions and explain the reasoning. Students learn about complex numbers and explore real /complex roots of polynomial functions using the Fundamental Theorem of Algebra. Students explore/ apply the Remainder Theorem and the Binomial Theorem with the polynomial expressions and equations.   Students explore the relationship between the exponential functions and their inverses, the logarithmic functions.

Students explore all conic sections and learn how to express geometric properties with equations. Students extend their trigonometry knowledge: they learn how to interpret the radian measure of angles in the unit circle, graph all six trigonometric functions, model the periodic phenomena of the graphs, and prove/apply trigonometric identities.

Finally, students continue expanding their knowledge of statistics by summarizing, representing, and interpreting data using the normal distribution. Moreover, students make inferences and justify conclusions based on sampling, experiments and observational studies.

The standards in this Algebra 2 course cover the following conceptual categories: Modeling, Functions, Number and Quantity, Algebra, and Statistics and Probability. The standards are developed to help educators implement mathematical practices of reasoning abstractly/ quantitatively, constructing viable arguments, modeling with mathematics, analyzing the structure of algebraic problems and persevering in solving them. This course content provides the rich instructional experiences for students and helps them to succeed beyond the high school and compete in the 21st century job market.

Annual Course – Grade 10 or 11

Prerequisite: CC Algebra 1 and CC Geometry AB

Honors Advanced Mathematics is accelerated, covering all topics in the regular Pre-calculus course, and advancing through introductory concepts of Limit, instantaneous rate of change including differentiation, and definite integral. Students will develop the ability to apply the knowledge gained to real-world application of these ideas.  In this course also, students are provided more thorough practice with basic sequences, series such as Taylor’s series and Mclauren series, and summation notation.  To receive Honors designation and credit, Students will be asked to design a project that would help to solve problems in the district or in the city

such as water conservation project or a system to minimize electric consumption at their school sites as well as participate as peer tutors on campus.  This course is intended for students who wish to advance directly to AP Calculus BC the following academic year, or for any student who wishes to undertake a higher level course than the regular Pre-calculus.

In the Honors Advanced Mathematics course, students connect the addition of complex numbers to addition of vectors. Students learn complex numbers and explore real and complex roots of polynomial functions using the Fundamental Theorem of Algebra. They also investigate the geometric interpretation of multiplying polar coordinates using polar representation. They perform operations on matrices and use matrices in applications. In this course also, students expand their understanding of interpretation and examination of complex rational, radical, and polynomial expressions as well as derive the sums of finite geometric series formula. They continue to expand their knowledge of rational, polynomial, radical, exponential and logarithmic functions; and explore the relationship between the exponential functions and their inverses. They also explore and apply the Remainder Theorem and the Binomial Theorem with the polynomial expressions and equations.

Students explore all conic sections and learn how to express geometric properties with equations. They extend their trigonometry knowledge: they learn how to interpret the radian measure of angles in the unit circle, graph all six trigonometric functions, model the periodic phenomena of the graphs, and prove and apply trigonometric identities. The Standards for Mathematical Practice would be embedded throughout the course. The Mathematical Practices describe varieties of expertise that teachers of this course should seek to develop in their students by the end of the course. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. Therefore, students will reason abstractly/ quantitatively, construct viable arguments and critique the reasoning of others, model with mathematics, analyze the structure of algebraic problems and persevering in solving them. They also solve problems with mathematical precision, look for and make use of structures, look for and express regularity in repeated reasoning, and use appropriate tools strategically. (Common Core State Standards, Mathematics (2010). This course content provides the rich instructional experiences for students and helps them to succeed beyond the high school and compete in the 21st century job market.

### PRE-CALCULUS AB

Annual Course – Grade 10, 11, or 12

Prerequisite: CC Algebra 2AB

310711 PRECALC A

310712 PRECALC B

The focus of the course will be on problem solving using mathematical models to represent real world situations. Students enrolled in Honors Precalculus will gain the confidence and skills necessary to be successful in Advanced Placement Calculus and math related curriculum in college. Students will build upon and further explore expressions, equations and functions learned in earlier math courses to develop patterns, make or test conjectures and try multiple representations. Students will also learn about inverse functions and how restricting the domain of a function that is not always increasing or decreasing allows its inverse to be constructed.

Students are introduced to vectors in the complex plane and gain fluency transferring between rectangular and polar forms. Students will explore the properties of matrices as they apply matrix operations to solve systems of equations and gain the understanding of how matrices help solve real world problems quickly and algorithmically. Students will apply their knowledge of trigonometry as they explore the unit circle and model periodic phenomena with trigonometric functions. Students will solve the real world problems involving the Laws of Sines and Cosines. Students will derive equations for conic sections from the definition of foci and by completing the square.

The standards in this Honors Precalculus course cover the following conceptual categories: Functions, Number and Quantity, Algebra and Geometry. The standards assure the implementation of the eight mathematical practices including reasoning abstractly/ quantitatively, constructing viable arguments, modeling with mathematics, analyzing the structure of algebraic problems, and persevering in solving them. This course content provides rich instructional experiences for students and helps them to succeed beyond high school and compete in the 21st century job market.

### PROBABILITY & STATISTICS AB

Annual Course – Grade 11 or 12

Prerequisite: CC Algebra 2AB

310607 PROB & STAT A

310608 PROB & STAT B

This discipline is an introduction to the study of probability, interpretation of data, and fundamental statistical problem solving. Mastery of this academic content will provide students with a solid foundation in probability and facility in processing statistical information.

### TRANSITION TO COLLEGE MATH AND STATISTICS AB

Annual Course – Grade 11 or 12

Prerequisite: CC Algebra 2AB

310311 TC MATH STAT A

310312 TC MATH STAT B

Course Description: The Transition to College Mathematics and Statistics (TCMS) course provides an effective way of addressing the need in many schools for a fourth year high school mathematics course beyond algebra II and geometry. It also helps schools meet the Common Core State Standards (CCSS), particularly the Mathematical Practices standards. It is anticipated that the TCMS course content, with its realistic problems, projects, relevant applications, and appropriate use of technology tools, will stimulate more college-intending students to elect a fourth year of mathematics.

The TMCS course at LAUSD is designed as a capstone course for high school mathematics

programs. Students who complete three high school mathematics courses together with the

proposed TCMS course will be well-prepared for two-year or four-year college programs and

also for training programs leading to career-level jobs.

The mathematical concepts that will be deepened and applied in this course correlate well with

the CSU's college readiness exam in mathematics, the Entry Level Math test (ELM). This test is

taken in the spring of 1 i 11 grade, and will act as one summative data point in our assessment of

the course. As a formative assessment, students will use an adaptive online mathematics resource

(ALEKS) throughout the year to measure their level of preparation for the ELM. The ALEKS

module employed is identical to that used by CSU Northridge (CSUN) to place students into or

out of developmental mathematics. This steady stream of formative assessments will guide

instructors and course coordinators as they progress through the TCMS topics. (For details see

Assessment Plan below.) Moreover, students enroll in a dual enrollment CSU course that

provides students with an opportunity beyond the ELM to place out of developmental

mathematics at participating CSU campuses. This evaluation is based on students receiving a C

or better in the TCMS course as well as 80% or better on a proctored final assessment on the

ALEKS system.

Annual Course – Grade 11 or 12

Prerequisite: Algebra 2AB or Honors Advanced Math AB

310609 AP STATS A

310610 AP STATS B

The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:

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

Annual Course – Grade 11 or 12

Prerequisite: Precalculus AB or Honors Advanced Math AB

310701 AP CALC A

310702 AP CALC B

Before studying calculus, all students should complete four years of secondary mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defined functions. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions at the numbers  and their multiples.

Course Description: Calculus AB is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The courses emphasize a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations also are important.

Prerequisite: Pre-Calculus AB OR Honors Advanced Math AB OR AP Calculus AB

310705 AP CALC B

310706 AP CALC C

Before studying calculus, all students should complete four years of secondary mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defined functions. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions at the numbers  and their multiples.

Course Description: Calculus AB is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The courses emphasize a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations also are important. Calculus BC is an extension rather than an enhancement of Calculus AB; common topics require a similar depth of understanding.

### ADVANCED PLACEMENT COMPUTER SCIENCE AB

Prerequisite: Exploring Computer Science AB (recommended) OR AP Comp Sci Prin AB (recommended)

180227 AP COMP SC A A

180228 AP COMP SC A B

Course Description: AP Computer Science A is equivalent to a first-semester, college-level course in computer science. The course introduces students to computer science with fundamental topics that include problem solving, design strategies and methodologies, organization of data (data structures), approaches to processing data (algorithms), analysis of potential solutions, and the ethical and social implications of computing. The course emphasizes both object-oriented and imperative problem solving and design using Java language. These techniques represent proven approaches for developing solutions that can scale up from small, simple problems to large, complex problems. The AP Computer Science A course curriculum is compatible with many CS1 courses in colleges and universities.

*Honors sections are available.