## Course Descriptions & Outlines

### Elementary School Mathematics - Course Descriptions and Outlines

#### Kindergarten

In Kindergarten, instructional time should focus on two critical areas: (1) representing and comparing whole numbers, initially with sets of objects, and (2) describing shapes and space. More learning time in kindergarten should be devoted to numbers rather than to other topics.
(CCSSO, 2010, Common Core State Standards Grade Level Introduction)

In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of and composing and decomposing geometric shapes.
(CCSSO, 2010, Common Core State Standards Grade Level Introduction)

In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.
(CCSSO, 2010, Common Core State Standards Grade Level Introduction)

In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.
(CCSSO, 2010, Common Core State Standards Grade Level Introduction)

In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
(CCSSO, 2010, Common Core State Standards Grade Level Introduction)

In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.
(CCSSO, 2010, Common Core State Standards Grade Level Introduction)

### Middle School Mathematics - Course Descriptions and Outlines

#### Math 6

In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.
(CCSSO, 2010, Common Core State Standards Grade Level Introduction)

#### Math 6 ACC

Math 6 Accelerated compacts all of the grade 6 Common Core State Standards and half of the grade 7 Common Core State Standards into a one-year course. Students who successfully complete Math 6 Accelerated will take Math 7 Accelerated in the seventh grade, and Algebra 1 in the eighth grade.

The sixth grade mathematics standards are about (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking. (CCSSO, 2010, Common Core State Standards Grade Level Introduction)

The seventh grade mathematics is about (1) developing understanding of and applying proportional relationships; and (2) developing understanding of operations with rational numbers and working with expressions and linear equations. (CCSSO, 2010, Common Core State Standards Grade Level Introduction)

#### Math 7

In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.
(CCSSO, 2010, Common Core State Standards Grade Level Introduction)

#### Math 7 ACC

Math 7 Accelerated compacts half of the grade 7 Common Core State Standards and all of the grade 8 Common Core State Standards into a one-year course. Students who successfully complete Math 7 Accelerated will take Algebra 1 in the eighth grade.

The seventh grade mathematics standards are about (1) developing understanding of and applying proportional relationships; (2) working with expressions and linear equations; (3) working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples. (CCSSO, 2010, Common Core State Standards Grade Level Introduction)

The eighth grade mathematics standards are about (1) formulating and reasoning about expressions and equations and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. (CCSSO, 2010, Common Core State Standards Grade Level Introduction)

#### Math 8

In Grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.
(CCSSO, 2010, Common Core State Standards Grade Level Introduction)

#### Algebra 1

The fundamental purpose of the Algebra 1 course is to formalize and extend the mathematics that students learned in the middle grades. This course includes standards from the conceptual categories of Number and Quantity, Algebra, Functions, and Statistics and Probability. Some standards are repeated in multiple higher mathematics courses; therefore instructional notes, which appear in brackets, indicate what is appropriate for study in this particular course. For example, the scope of Algebra 1 is limited to linear, quadratic, and exponential expressions and functions as well as some work with absolute value, step, and functions that are piecewise-defined. Therefore, although a standard may include references to logarithms or trigonometry, those functions are not to be included in course work for Algebra 1; they will be addressed later in Algebra 2. Successful completion of Algebra 1, or an equivalent sequence, is a graduation requirement.

For the Algebra 1 course, instructional time should focus on four critical areas: (1) deepen and extend understanding of linear and exponential relationships; (2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions; (3) extend the laws of exponents to square and cube roots; and (4) apply linear models to data that exhibit a linear trend. (CA Mathematics Framework, 2013, Course Introduction)

### High School Mathematics - Course Descriptions and Outlines

#### Algebra 1

The fundamental purpose of the Algebra 1 course is to formalize and extend the mathematics that students learned in the middle grades. This course includes standards from the conceptual categories of Number and Quantity, Algebra, Functions, and Statistics and Probability. Some standards are repeated in multiple higher mathematics courses; therefore instructional notes, which appear in brackets, indicate what is appropriate for study in this particular course. For example, the scope of Algebra 1 is limited to linear, quadratic, and exponential expressions and functions as well as some work with absolute value, step, and functions that are piecewise-defined. Therefore, although a standard may include references to logarithms or trigonometry, those functions are not to be included in course work for Algebra 1; they will be addressed later in Algebra 2. Successful completion of Algebra 1, or an equivalent sequence, is a graduation requirement.

For the Algebra 1 course, instructional time should focus on four critical areas: (1) deepen and extend understanding of linear and exponential relationships; (2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions; (3) extend the laws of exponents to square and cube roots; and (4) apply linear models to data that exhibit a linear trend. (CA Mathematics Framework, 2013, Course Introduction)

#### Algebra Lab

This course is an elective course designed to provide intensive support to high school students identified for strategic intervention concurrently enrolled in Algebra 1-2. This course will help students build their conceptual understanding of algebra content while practicing necessary fundamental skills. This course will reinforce what is taught in their core Algebra 1-2 class described above. Since Algebra is required for graduation from high school, students enrolled in Algebra Lab should have a strong interest in success in Algebra 1-2.

#### Algebra AB SDC

The fundamental purpose of the Algebra AB SDC course is to formalize and extend the mathematics that students learned in the middle grades. Algebra AB SDC mathematics is designed specifically to address the needs of students with disabilities who are enrolled in a Special Day Class (SDC). This is the first of a two-year sequence of courses that, combined, will be equivalent to a traditional Algebra 1 course. The instructional pacing has been altered to provide the opportunity to allow for depth versus breadth of the content standards including standards from the conceptual categories of Number and Quantity, Algebra, Functions, and Statistics and Probability. Some standards are repeated in multiple higher mathematics courses; therefore instructional notes, which appear in brackets, indicate what is appropriate for study in this particular course. For example, the scope of Algebra 1 is limited to linear, quadratic, and exponential expressions and functions as well as some work with absolute value, step, and functions that are piecewise-defined. Therefore, although a standard may include references to logarithms or trigonometry, those functions are not to be included in course work for Algebra AB/CD.

For the Algebra AB SDC course, instructional time should focus on four critical areas: (1) deepen and extend understanding of linear and exponential relationships; (2) contrast linear and exponential relationships with each other; (3) extend the laws of exponents to square and cube roots; and (4) apply linear models to data that exhibit a linear trend. (CA Mathematics Framework, 2013, Course Introduction)

• Algebra AB SDC Course Outline

#### Algebra CD SDC

The fundamental purpose of the Algebra CD SDC course is to formalize and extend the mathematics that students learned in the middle grades and continue the development of algebraic skills emphasized in Algebra AB SDC. This is the second of a two-year sequence of courses that, combined, will be equivalent to a traditional Algebra 1 course. The mathematics in Algebra CD SDC is designed specifically to address the needs of students with disabilities who are enrolled in a Special Day Class (SDC). The instructional pacing has been altered to provide the opportunity to allow for depth versus breadth of the content standards including standards from the conceptual categories of Number and Quantity, Algebra, Functions, and Statistics and Probability. Some standards are repeated in multiple higher mathematics courses; therefore instructional notes, which appear in brackets, indicate what is appropriate for study in this particular course. For example, the scope of Algebra CD SDC is limited to linear, quadratic, and exponential expressions and functions as well as some work with absolute value, step, and functions that are piecewise-defined. Therefore, although a standard may include references to logarithms or trigonometry, those functions are not to be included in course work for Algebra AB/CD SDC.

For the Algebra CD SDC course, instructional time should focus on four critical areas: (1) deepen and extend understanding of linear and exponential relationships; (2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions; (3) extend the laws of exponents to square and cube roots; and (4) apply linear models to data that exhibit a linear trend. (CA Mathematics Framework, 2013, Course Introduction)

#### Geometry

The fundamental purpose of the Geometry course is to formalize and extend students’ geometric experiences from the middle grades. This course includes standards from the Geometry conceptual category. Some standards are repeated in multiple higher mathematics courses; therefore instructional notes, which appear in brackets, indicate what is appropriate for study in this particular course.

In this Geometry course, students explore more complex geometric situations and deepen their explanations of geometric relationships, presenting and hearing formal mathematical arguments. Important differences exist between this course and the historical approach taken in geometry classes. For example, transformations are emphasized in this course.

For the Geometry course, instructional time should focus on five critical areas: (1) establish criteria for congruence of triangles based on rigid motions; (2) establish criteria for similarity of triangles based on dilation and proportional reasoning; (3) informally develop explanations of circumference, area, and volume formulas; (4) apply the Pythagorean Theorem to the coordinate plan; and (5) prove basic geometric theorems. (CA Mathematics Framework, 2013, Course Introduction)

#### Algebra 2

Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include logarithmic, polynomial, rational, and radical functions in the Algebra 2 course. This course includes standards from the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Some standards are repeated in multiple higher mathematics courses; therefore instructional notes, which appear in brackets, indicate what is appropriate for study in this particular course. Standards that were limited in Algebra 1 no longer have those restrictions in Algebra 2. 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.

For the Algebra 2 course, 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; (3) synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions; and (4) relate data display and summary statistics to probability and explore a variety of data collection methods. (CA Mathematics Framework, 2013, Course Introduction)

#### Pre Calculus

Precalculus combines the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus, and strengthens students’ conceptual understanding of problems and mathematical reasoning in solving problems. Facility with these topics is especially important for students intending to study calculus, physics, and other sciences, and/or engineering in college. Because the standards for this course are (+) standards, students selecting Precalculus should have met the college and career ready standards.

For Precalculus, instructional time should focus on four critical areas: (1) extend work with complex numbers; (2) expand understanding of logarithms and exponential functions; (3) use characteristics of polynomial and rational functions to sketch graphs of those functions; and (4) perform operations with vectors. (CA Mathematics Framework, 2013, Course Introduction)

#### Finite Math

This course is a one year program in advanced mathematics. It is comparable to the Finite Mathematics courses taught at the college level. The course is designed for students as a senior level mathematics course. It is recommended for students who plan to pursue a college major that does not require calculus and the higher levels of mathematics.

#### Career Math

Career Math is designed to help students extend their knowledge of mathematics and develop appropriate consumer and career mathematical skills. Course content will cover such topics as basic operations, ratio, percent, algebra and geometry concepts, probability, measurement, and many consumer topics. Technology will be integrated.

#### Introduction to Applied Math

The Introduction to Applied Math course will prepare students to enter the work force or to attend college with an understanding of the mathematics in the real world. The course will help students develop quantitative literacy as a habit of mind and an approach to problems that employs and enhances both statistics and mathematics.  The main goal of the course is for students to see that mathematics is a powerful tool for living, as they develop confidence with mathematics, habits of inquiry and logical thinking, and the ability to use mathematics to make decisions in everyday life.  Topics address the math used to run our country's households, businesses, and governments, such as the mathematics of consumption, inflation, depreciation, borrowing, saving, and taxation, as well as the mathematics of logic, likelihood, statistics, and sports.