Mathematics

JUNIOR HIGH MATH

COURSE: MATH 7
COURSE NUMBER: 2007
A-G: Not for UC Acceptance, 7th grade course
COURSE PREREQUISITE: None
COURSE DESCRIPTION:  This course serves as a precursor to Algebra 1.  Various hands on activities are provided to stimulate interest and to facilitate the introduction of math concepts including whole numbers, properties and rules of operations, number theory, rational numbers, ratio, proportion, percentage, measurement, statistics, probability, real numbers, and graphing.  Students will also study basic algebra principles such as algebraic expressions, polynomials, equations, and factoring.

Curriculum will use a variety of resources.  Encore’s primary resource for this class is the state approved online curriculum, Cyber High.

CORE CURRICULUM:
Pre Algebra – Full Course, Cyber High

COURSE: MATH 8 (HS Algebra)
COURSE NUMBER: 2008
A-G: 10 credits, Mathematics
PREREQUISITE: Math 7, Pre Algebra Recommended
DESCRIPTION: This course shows how algebraic skills are applied in a wide variety of problem-solving situations and, in seeing the larger picture and in understanding the underlying concepts, students will be in a better position to apply their knowledge to new situations and problems.  Students review Pre-Algebra skills (including variables, expressions, order of operations, and equations) and the fundamentals of the language of mathematics. As students progress through the course, they will study concepts like sequences and their graphs, independent and dependent relationships, how to simplify and solve equations and functions, monomials and polynomials, factorization, exponential graphs and functions, transformations, slope, how to solve systems, square roots, quadratic equations, inequalities, absolute value, statistics, etc. Much of the course covers abstract relationships and their manipulations, but it also involves algebraic thinking and the application of these skills to word problems and real life situations. Problems are designed to engage higher order thinking processes in a collaborative environment and provide opportunities for practical applications of the concepts developed within the course.  Students have the opportunity to develop and utilize analytical skills, think critically, develop logical thought processes, and make valid inferences.  The plan of instruction includes demonstration, modeling, guided practice, and independence which will lead students to broaden their scope of the problem-solving process. Questions, activities, and performance-based learning tasks are designed to engage higher order thinking processes and provide opportunities for practical applications of the concepts developed within the course.

COURSE: MATH 8 HONORS (HS HONORS ALGEBRA 1)
COURSE NUMBER: 15
A-G: 10 Units, 5.0 Grading Scale Mathematics
PREREQUISITE: Grade “A” in the four prior quarters of Math 7
DESCRIPTION: In conjunction with Algebra B, this course shows how algebraic skills are applied in a wide variety of problem-solving situations and, in seeing the larger picture and in understanding the underlying concepts, students will be in a better position to apply their knowledge to new situations and problems.  Students review Pre-Algebra skills (including variables, expressions, order of operations, and equations) and the fundamentals of the language of mathematics. As students progress through the course, they will study concepts like sequences and their graphs, independent and dependent relationships, how to simplify and solve equations and functions, monomials and polynomials, factorization, exponential graphs and functions, transformations, slope, how to solve systems, square roots, quadratic equations, inequalities, absolute value, statistics, etc. Much of the course covers abstract relationships and their manipulations, but it also involves algebraic thinking and the application of these skills to word problems and real life situations. Problems are designed to engage higher order thinking processes in a collaborative environment and provide opportunities for practical applications of the concepts developed within the course.  Students have the opportunity to develop and utilize analytical skills, think critically, develop logical thought processes, and make valid inferences.  The plan of instruction includes demonstration, modeling, guided practice, and independence which will lead students to broaden their scope of the problem-solving process. Questions, activities, and performance-based learning tasks are designed to engage higher order thinking processes and provide opportunities for practical applications of the concepts developed within the course.

HIGH SCHOOL MATH

COURSE: INTEGRATED MATH I
COURSE NUMBER: 2001
A-G: 10 units
PREREQUISITE: Math 8
DESCRIPTION: Topics include recognizing and developing patterns using tables, graphs, and equations. Mathematical modeling is stressed as methodology for approaching the solution to problems. Exploration of algebraic expressions, problem solving using equations, and investigating linear relationships are also covered. Geometry is part of Integrated Math I including area, perimeter, Pythagorean theorem, and geometric proportions. Mathematical probability is provided to reinforce use of fractions and numeric modeling. Technology is used to introduce and expand the areas of study.

COURSE: INTEGRATED MATH I HONORS
COURSE NUMBER: 20011
A-G: 10 units, 5.0 scale
COURSE PREREQUISITE: Grade “A” in the four prior quarters of Math 8 or at least a “B” grade in the four prior quarters of Math 8 Honors
COURSE DESCRIPTION: Building from the curriculum from Integrated Math I, students take a more in depth look at Integrated Math. This course includes additional practice for concepts and include an annual project with EAS.

COURSE: INTEGRATED MATH II
COURSE NUMBER: 2002
A-G: 10 units
PREREQUISITE: Math I
DESCRIPTION: This course includes an analytical approach to geometry concepts. Topics include patterns using tables, graphs, and equations. How to predict a formula with proof and geometric properties of both two and three dimensions as they apply to points, levels, planes, circles, and polygons. Focus on transformations and right triangle trigonometry through investigative and explorative activities is covered using explorative activities.

COURSE: INTEGRATED MATH II / III HONORS
COURSE NUMBER: 20021 / 20031
A-G: 20 units, 5.0 scale
PREREQUISITE: Grade “A” in the four prior quarters of Math I or at least a “B” grade in the four prior quarters of Math I Honors
DESCRIPTION: Building from the curriculum concepts from Integrated Math II, this course offers more in depth critical thinking with additional practice.  Students enrolled in this course will complete 2 years of math instruction in one year.  There is an extensive summer assignment in Math II that must be completed before the first class meeting.  At the successful conclusion of the Math II/III Honors course, students will earn 10 credits toward Math II Honors and 10 credits toward Math III Honors.  Students wishing to take the AP exam for advanced math should enroll in this course and sign up for the AP study team.

COURSE: INTEGRATED MATH III
COURSE NUMBER: 2003
A-G: 10 units
PREREQUISITE: Math II
DESCRIPTION: Expands on the concepts covered in Integrated Math I and Integrated Math II. Algebraic solutions as used in systems of quadratic equations, logarithms, exponential functions, statistics, and trigonomic functions are covered.

COURSE: MATH III / PRE-CALCULUS HONORS
COURSE NUMBER: 20031 / 241
A-G: 20 units, 5.0 scale
PREREQUISITE: At least a “B” grade in either Math II or “C” in Math II Honors
DESCRIPTION: Students develop reasoning and problem solving skills as they study functions, graphs, trigonometry, polar coordinates, conic exponential functions, logarithmic functions, discrete math, and the introduction of calculus.  Students in this course will complete 2 years of math in 1 year of instruction.  At the successful conclusion of Math III / Pre-Calculus Honors, students earn 10 credits toward Math III Honors and 10 credits toward Pre-Calculus Honors. Students enrolled in this course are required to complete an intense summer project that is based on Math III curriculum before the first day of classes.

COURSE: CALCULUS HONORS
COURSE NUMBER: 2071
A-G: 10 units, 5.0 scale
PREREQUISITE: At least a “C” in Pre-Calculus Honors
DESCRIPTION: Calculus is a transition course to upper-division mathematics and computer science courses. Students will extend their experience with functions as they study the fundamental concepts of calculus: limiting behaviors, difference quotients and the derivative, Riemann sums and the definite integral, antiderivatives and indefinite integrals, and the Fundamental Theorem of Calculus. Students review and extend their knowledge of trigonometry and basic analytic geometry. Important objectives of the calculus sequence are to develop and strengthen the students’ problem-solving skills and to teach them to read, write, speak, and think in the language of mathematics. In particular, students learn how to apply the tools of calculus to a variety of problem situations.

COURSE: STATISTICS HONORS
COURSE NUMBER:1111
A-G: 10 units, 5.0 scale
PREREQUISITE: At least a “C” Math III
DESCRIPTION: Statistics and Probability offers students an alternative to Precalculus as a fourth high school mathematics course. In the Statistics and Probability course, students continue to develop a more formal and precise understanding of statistical inference, which requires a deeper understanding of probability. Students learn that formal inference procedures are designed for studies in which the sampling or assignment of treatments was random, and these procedures may be less applicable to non-randomized observational studies. Probability is still viewed as long-run relative frequency, but the emphasis now shifts to conditional probability and independence, and basic rules for calculating probabilities of compound events. In the plus (+) standards are the Multiplication Rule, probability distributions, and their expected values. Probability is presented as an essential tool for decision making in a world of uncertainty.

COURSE: STRATEGIC MATHEMATICS
COURSE NUMBER: 20181 (HS) 20182 (JR)
A-G: None
PREREQUISITE: None
DESCRIPTION: This course is intended to create strategic mathematical learners from underprepared mathematics students. The basic understandings will stimulate students to think about their approach to mathematical learning. These basic understandings will include identifying errors in the teaching and learning process, input errors, physiological concerns, and key cognitive skills. The essential knowledge and skills will foster a deeper understanding of the task of learning mathematical concepts.

COURSE: ALGEBRA I CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4777
A-G: 10 units
PREREQUISITE: Pre Algebra CH or equivalent
DESCRIPTION: In conjunction with Algebra B, this course shows how algebraic skills are applied in a wide variety of problem-solving situations and, in seeing the larger picture and in understanding the underlying concepts, students will be in a better position to apply their knowledge to new situations and problems. Students review Pre-Algebra skills (including variables, expressions, order of operations, and equations) and the fundamentals of the language of mathematics. As students progress through the course, they will study concepts like sequences and their graphs, independent and dependent relationships, how to simplify and solve equations and functions, monomials and polynomials, factorization, exponential graphs and functions, transformations, slope, how to solve systems, square roots, quadratic equations, inequalities, absolute value, statistics, etc. Much of the course covers abstract relationships and their manipulations, but it also involves algebraic thinking and the application of these skills to word problems and real life situations. Students have the opportunity to develop and utilize analytical skills, think critically, develop logical thought processes, and make valid inferences. The plan of instruction includes demonstration, modeling, guided practice, and independence which will lead students to broaden their scope of the problem-solving process. Questions, activities, and performance-based learning tasks are designed to engage higher order thinking processes and provide opportunities for practical applications of the concepts developed within the course.

COURSE: ALGEBRA II CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4778
A-G: 10 units
PREREQUISITE: Algebra I CH or equivalent
DESCRIPTION: In Algebra 2A and 2B, students build on mathematical concepts learned in Algebra and Geometry by extending their knowledge through the study of functions (polynomial, rational, radical, quadratic, exponential, and logarithmic), systems of equations and inequalities, modeling (linear, quadratic, and exponential), trigonometric functions, and probability and statistics. Problems are designed to engage higher order thinking processes in a collaborative environment and provide opportunities for practical applications of the concepts developed within the course. Students work with the concepts in various applications including practice exercises, solving word problems, and working with real-world situations, and they have the opportunity to develop and utilize analytical skills, think critically, develop logical thought processes, and make valid inferences. The plan of instruction includes demonstration, modeling, guided practice, and independent application which will lead students to broaden their scope of the problem-solving process. Activities and performance-based learning tasks are designed to engage higher order thinking processes and provide opportunities for practical applications of the concepts developed within the course.

COURSE: APPLICATIONS MATH CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4779
A-G: None
PREREQUISITE: None
DESCRIPTION: PART A: Application Math A is a California State and Common Core standards-based course that helps students develop mathematical computational and procedural skills. Concepts covered in the course include: operations with whole numbers, fractions, and decimals; using proportion, ratio, and percent; measurements in both U.S. and metric systems; and using mathematical reasoning to solve various types of word problems and applications. PART B: Application Math B is a standards-based course that continues to build on concepts presented in Application Math A. This course helps students develop mathematical computational and procedural skills. Concepts covered in the course include: statistics and probability, algebraic equations, geometry fundamentals, and using mathematical reasoning to solve various types of problems.

COURSE: BASIC MATH CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4780
A-G: None
PREREQUISITE: None
DESCRIPTION: Essential math skills, including the numeration system, addition, subtraction, multiplication, and division and their application in daily life situations are covered. Basic Math is designed to teach students basic mathematical concepts including fractions, mixed numbers, decimals, ratio, proportion, percent, and measurement. Concepts presented address foundational skills for future mathematical studies. This course helps students develop a concrete understanding of the mathematical concepts necessary to prepare for the math portion of testing.

COURSE: CONSUMER MATH CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4781
A-G: None
PREREQUISITE: None
DESCRIPTION: The course is designed to address and build upon basic mathematical concepts that are applicable to real-world consumer situations such as banking, finance, investments, housing, insurance, budgeting, employment, compensation, taxes, and starting and operating a small business. Upon completion, students will be familiar with consumerism, their role as consumers in today’s economy, and fundamental principles of economics related to personal and household finances.

COURSE: CONSUMER MATH CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4781
A-G: None
PREREQUISITE: None
DESCRIPTION: The course is designed to address and build upon basic mathematical concepts that are applicable to real-world consumer situations such as banking, finance, investments, housing, insurance, budgeting, employment, compensation, taxes, and starting and operating a small business. Upon completion, students will be familiar with consumerism, their role as consumers in today’s economy, and fundamental principles of economics related to personal and household finances.

COURSE: GEOMETRY CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4782
A-G: 10 units
PREREQUISITE: Algebra I
DESCRIPTION: In Geometry A and B, geometric skills are applied to a wide variety of problem-solving situations and, in seeing the larger picture and in understanding the underlying concepts, students will be in a better position to apply their knowledge to new situations and problems. Students begin by studying the basic essentials of geometry including points, lines, planes, angles, segments, geometric figures, patterns, logic, and reasoning. As students progress through the course, they will study concepts like parallel and perpendicular properties, coordinate geometry, translations and constructions, triangles, congruency and similarity, reflections and symmetry, ratios and proportions, trigonometry, sine and cosine, polygons, proofs, circles, perimeter, area, volume, etc. Students also cover a variety of statistical concepts and applications. Problems are designed to engage higher order thinking processes in a collaborative environment and provide opportunities for practical applications of the concepts developed within the course. Students have the opportunity to develop and utilize analytical skills, think critically, develop logical thought processes, and make valid inferences. The plan of instruction includes demonstration, modeling, guided practice, and independent application which will lead students to broaden their scope of the problem-solving process. Questions, activities, and performance-based learning tasks are designed to engage higher order thinking processes and provide opportunities for practical applications of the concepts developed within the course.

COURSE: INTEGRATED MATH I CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4783
A-G: 10 units
PREREQUISITE: None
DESCRIPTION: Both semesters of Integrated Math 1 introduce concepts related to: function families, graphing linear and nonlinear functions, and exponential functions; simplifying, evaluating, and solving equations and systems; algebraic properties; and geometric concepts like angle measures, triangles, circles, constructions, congruency, similarity, the Pythagorean Theorem, etc.; and the fundamentals of the language of mathematics. Students will engage in the content through reading of material, a plethora of examples and opportunities for practice, and utilize technology and online resources successfully and strategically and demonstrate their understanding through problem solving practice, project-based/performance task analysis, writing assignments, interactive activities, and a variety of self and summative assessments. They also utilize technology and online resources successfully and strategically so they can produce written and digital texts that demonstrate their understanding of the concepts presented in the course.

COURSE: INTEGRATED MATH II CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4784
A-G: 10 units
PREREQUISITE: Integrated Math I CH
DESCRIPTION: In both semesters of Integrated Math 2, students will gain experience with geometric and algebraic solutions to problems in various content areas including: properties of polygons, trigonometry, circles, area and perimeter, proofs, dilations, similarity, ratios, surface area and volume, polynomials, quadratic functions, and radicals, as well as statistical concepts related to probability, data distribution, linear regression, and the fundamentals of the language of mathematics. Students will engage in the content through reading material, a plethora of examples and opportunities for practice, and the utilization of technology and online resources successfully and strategically. Students demonstrate their understanding through problem solving practice, project-based/performance task analysis, writing assignments, interactive activities, and a variety of self and summative assessments.

COURSE: INTEGRATED MATH III CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4785
A-G: 10 units
PREREQUISITE: Integrated Math II CH
DESCRIPTION: Integrated Math 3, students build on mathematical concepts learned in Integrated Math 1 and 2 by extending their knowledge through the study of functions and graphs, systems of equations and inequalities, polynomial functions, rational expressions and equations, radical functions, and imaginary and complex numbers. Problems are designed to engage higher order thinking processes and provide opportunities for practical applications of the concepts developed within the course. Students work with the concepts in various ways including practice exercises, word problems, and performance tasks, and they have the opportunity to develop and utilize analytical skills, to think critically, to develop logical thought processes, to use technology and online resources strategically, and to make valid inferences. The plan of instruction includes demonstration, modeling, guided practice, and independent application which will lead students to broaden their scope of the problem-solving process.

COURSE: MATH SKILLS CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4786
A-G: None
PREREQUISITE: None
DESCRIPTION: This course is aligned with the California State Mathematics Standards and Frameworks and the five strands adopted by the State Board of Education: Statistics and Data Analysis, Number Sense, Algebra and Functions, Mathematical Reasoning and Measurement, and Geometry. Proficiency in the California Mathematics Standards covered in the course will help students acquire rudimentary math skills and sharpen critical thinking skills.

COURSE: PRE ALGEBRA CH(INDEPENDENT STUDY COURSE)
COURSE NUMBER: 4786
A-G: None
PREREQUISITE: None
DESCRIPTION: This course serves as a precursor to Algebra A. Calculator activities are provided to stimulate student interest and to facilitate the introduction of math concepts including whole numbers, properties and rules of operations, number theory, rational numbers, ratio, proportion, percentage, measurement, statistics and probability, real numbers, and graphing. Students will also study basic algebra principles such as algebraic expressions, polynomials, equations, and factoring.

While all courses are offered each year, if student interest does not warrant, courses may be cancelled.