# Math Overview

**Core Classes**

**Algebra I**

The fundamental purpose of the Algebra I 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. For example, the scope of Algebra I 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 I; they will be addressed later in Algebra II. Instructional time will 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.

Unit 1: Linear Equations and Inequalities

Unit 2: Patterns and Functions

Unit 3: Linear Functions

Unit 4: Sequences and Functions

Unit 5: Exponential Functions

Unit 6: One-Variable Statistics and Bivariate Categorical Data

Unit 7: Systems of Linear Equations

Unit 8: Modeling Linear Data

Unit 9: Quadratic Functions

Unit 10: Seeing Structure in Expressions and Functions

**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 conceptual categories of Geometry and Statistics and Probability. 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. Instructional time will focus on six critical areas: (1) establish criteria for congruence of triangles based on rigid motions; (2) establish criteria for similarity of triangles based on dilations and proportional reasoning; (3) informally develop explanations of circumference, area, and volume formulas; (4) apply the Pythagorean Theorem to the coordinate plane; (5) prove basic geometric theorems; and (6) extend work with probability.

Unit 1: Constructions and Defining Terms

Unit 2: Transformations in a Plane and Rigid Motion

Unit 3: Geometric Relationships and Properties (Lines and Quadrilaterals)

Unit 4: Triangles and Congruence

Unit 5: Dilations and Similarity

Unit 6: Right Triangle Trigonometry

Unit 7: Circles and Conics

Unit 8: Geometric Measurement and Modelling (Areas and Volumes)

Unit 9: Probability

**Algebra II**

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 II course. This course includes standards from the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Standards that were limited in Algebra I no longer have those restrictions in Algebra II. 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. 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.

Unit 1: Transformations of Functions

Unit 2: Trigonometry

Unit 3: Quadratic Functions

Unit 4: Polynomial Functions

Unit 5: Exponential Functions & Series

Unit 6: Logarithmic Functions

Unit 7: Statistics

Unit 8: Radical and Rational Functions