## Middle School Courses

**MS Math 7**

In grade seven instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships, including percentages; (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. Students also work towards fluently solving multi-step equations with rational coefficients.

**MS Math 8**

In grade eight, 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. Students also work towards fluency with solving simple sets of two equations with two unknowns by inspection.

**MS Enhanced Math 7/8**

This course differs from the standard Math 7 and Math 8 courses above in that it contains content from both courses. This course is intended for the student who is able to move through the mathematics quickly and still master the full range of mathematical practices, content and skills. Instructional time in the Math 7/8 course focuses on the following grade 7 critical areas: (1) developing understanding of and applying proportional relationships, including percentages; (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. In addition, the following critical areas from Grade 8 will be included: (1) formulating and reasoning about expressions and equations; (2) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence.

**MS Enhanced Math I**

In Enhanced Math I, students continue their work with expressions and modeling and analyzing situations at an accelerated pace. Students will informally define, evaluate, and compare functions, and use them to model relationships between quantities. (critical area from Grade 8 Math) Students will learn function notation and develop the concepts of domain and range. They move beyond viewing functions as processes that take inputs and yield outputs and start viewing functions as objects that can be combined with operations. They explore many examples of functions, including sequences. They interpret functions represented graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that, depending upon the context these representations are likely to be approximate and incomplete. Their work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions. In Enhanced Math I, students build on their prior experiences with data, developing 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. In Enhanced Math I, students will understand and apply the Pythagorean Theorem and will establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work. Finally, building on their work with the Pythagorean Theorem in the grade eight standards to find distances, students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines.

## High School Course Description for Integrated Math

**Math I**

The fundamental purpose of Mathematics I is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, organized into units, deepen and extend understanding of linear relationships, in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Mathematics I uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades. The final unit in the course ties together the algebraic and geometric ideas studied. The Mathematical Practice Standards apply throughout each course 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.

**Math II**

The focus of Mathematics II is on quadratic expressions, equations, and functions; comparing their characteristics and behavior to those of linear and exponential relationships from Mathematics I. The need for extending the set of rational numbers arises and real and complex numbers are introduced so that all quadratic equations can be solved. The link between probability and data is explored through conditional probability and counting methods, including their use in making and evaluating decisions. The study of similarity leads to an understanding of right triangle trigonometry and connects to quadratics through Pythagorean relationships and circles, with their quadratic algebraic representations, round out the course. The Mathematical Practice Standards apply throughout each course 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.

**Math III**

Math III is the third course in the college preparatory math sequence. Instructional time will focus on four critical areas: applying methods from probability and statistics to draw inferences and conclusions from data; expanding understanding of functions to include polynomial, rational, and radical functions; expanding right triangle trigonometry to include general triangles and trigonometric functions; and consolidate functions and geometry to create models and solve contextual problems. This course is aligned with the California Common Core State Standards.

**Enhanced Math II **

Enhanced Math II is an accelerated and challenging course designed for students who excel in math. Students entering from Math I should easily grasp higher level concepts, embrace rigorous curriculum and master all Math I standards. In Enhanced Math II, students will go deeper into Math II standards, including those (+) standards as defined in the CA Mathematics Framework, as well as several Math III and Pre-Calculus standards. Student assignments contain more critical thinking and higher depth of knowledge.

**Enhanced Math III (Honors)**

Enhanced Math III is the second course in the rigorous accelerated sequence of high school math courses. Instructional time will focus on five critical areas: expanding understanding of functions to include polynomial, rational, and radical functions; extending their work with complex numbers; extending trigonometry to general triangles, trigonometric functions, reciprocal functions, and inverse functions; working with parametric and polar curves; and consolidating functions and geometry to create models and solve contextual problems. In addition, students will deepen and extend their understanding in each of these areas through study of advanced related topics and application to more complex problem solving situations, in order to prepare students for advanced mathematics at an accelerated pace. This course is aligned with the California Common Core State Standards.

**Math I AB and Math I CD**

This two-year Math I course will build on and extend skills learned in middle school while developing mastery and understanding of fundamental algebraic and geometric concepts, properties and skills. Students will explore the content of Math I over a two-year period with a focus on conceptual understanding and symbolic reasoning. The Mathematical Practice Standards apply throughout the two-year course 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.

## Additional Links for Course Descriptions for Traditional Math

- Irvine High School Course Catalog
- Northwood High School Course Catalog
- University High School Course Catalog
- Woodbridge High School Course Catalog