# Math 3 Course Description

• In Math 3, students extend their study of algebra and functions to new families of functions including logarithmic, polynomial, rational, and trigonometric functions.  Math 3 also includes a geometric emphasis on modeling as well as circles and their properties. Probability rules learned in previous courses are extended to the statistics of making inferences and justifying conclusions.  Each topic within the algebra and functions strands will be experienced as an integration of concepts, procedures, and applications. Variable, equivalence and procedures such as solving equations and inequalities are equally important.

## Unit 1 - More Functions, More Features

Students develop and use piecewise defined and absolute value functions to model mathematics.  Students develop properties and use of inverse functions. They use knowledge of features of functions to identify features and to create functions given features.

## Unit 2 - Inverse and Exponential Functions

Students develop and extend the concept of inverse functions using tables, graphs, equations, and written descriptions of functions. Students evaluate and compare logarithmic expressions. They model with exponential functions and equations to solve problems.

## Unit 3 - Polynomial Functions

Students compare graphs, growth rates, and end behavior of polynomial functions and expressions to other known functions.  They use graphical representations of arithmetic operations on polynomial functions to build other polynomial functions.  Students apply the Fundamental Theorem of Algebra and Remainder Theorem to factor and solve polynomial functions and equations.

## Unit 4 - Rational Expressions and Functions

Students explore rational expressions and functions through connections to rational numbers and improper fractions.  They model with rational functions and equations. Students analyze characteristics of various families of functions to identify characteristics of rational functions.  They identify the end behavior of rational functions. Students graph rational functions using their features. Students solve rational equations.

## Unit 5 - Modeling with Geometry

Students solve problems using geometric modeling.  They visualize two dimensional cross sections of three-dimensional objects and solids of revolution.  Students approximate volumes of solids of revolution.

## Unit 6 - Geometric Figures and Proof

Students learn the structures and reasoning of formal proofs through theorems about triangle angle sum, lines and angles, triangles and parallelograms.  They prove properties of triangles and parallelograms. Students examine parallelism from a transformational perspective.

## Unit 7 - Circles

Students develop and justify formulas for perimeter, area, circumference.  They use proportional reasoning to calculate arc length and area of sectors and other circular relationships.  Students develop concept of radian as ratio of arc length to radius. Students develop understanding of circles as conic sections. They use both standard and general forms of the equations of circles to solve problems.

## Unit 8 - Modeling Periodic Behavior

Students develop understanding of circular trigonometry by using angles of rotation, reference angles, right angle trigonometry, unit circle and the proportionality and symmetry of a circle to extend to radian measure, arc length and trigonometric functions.  Students graph trigonometric functions, identify horizontal transformations and other graphical characteristics, and use them to model periodic behavior.

## Unit 9 - Statistics

Students compare and contrast methods of sampling, surveys, observational studies, and experiments.  Students use data from a sample to estimate a population mean or proportion. They use simulations to develop a concept of a margin of error and decide if differences between parameters are significant .  Students use data from a randomized experiment to compare treatments.

• ## Student Math Practices

Practice 1: Make sense of problems and persevere in solving them.
Practice 2: Reason abstractly and quantitatively.
Practice 3: Construct viable arguments and critique the reasoning of others.
Practice 4: Model with mathematics.
Practice 5: Use appropriate tools strategically.
Practice 6: Attend to precision.
Practice 7: Look for and make use of structure.
Practice 8: Look for and express regularity in repeated reasoning. 