Given an experimental situation, the student will write linear functions that provide a reasonable fit to data to estimate the solutions and make predictions.

Given a pictorial or tabular representation of a pattern and the value of several of their terms, the student will write a formula for the nth term of a sequences.

Given a verbal and symbolic representations of a function, the student will find specific function values.

Given verbal and symbolic representations of polynomial expressions, the student will simplify the expression.
 

Given verbal and symbolic representations in the form of equations or inequalities, the student will transform and solve the equations or inequalities.

The student will use a variety of methods to solve problems by factoring including models, guess and check, grouping, and special cases.

Given algebraic, tabular, graphical, or verbal representations of linear functions in problem situations, the student will determine the meaning of slope and intercepts as they relate to the situations.

Given algebraic, graphical, or verbal representations of linear functions, the student will determine the effects on the graph of the parent function f(x) = x.

Given two points, the slope and a point, or the slope and the y-intercept, the student will write linear equations in two variables.

Given data in the form of an equation, the student will use the equation to interpret solutions to problems.

Given a real-world situation that can be modeled by a linear function or a graph of a linear function, the student will determine and represent the reasonable domain and range of the linear function using inequalities.

.

.

.

In this topic, students explore a variety of different functions. The intent is merely to introduce these new functions, providing an overview but not a deep understanding at this point. The topic is designed to help students recognize that different function families have different key characteristics. In later study in this course, they will formalize their understanding of the defining characteristics of each type of function.

In this topic, students explore sequences represented as lists of numbers, in tables of values, by equations, and as graphs on the coordinate plane. Students move from an intuitive understanding of patterns to a more formal approach of representing sequences as functions. In the final lesson of the topic, students are introduced to the modeling process. Defined in four steps—Notice and Wonder, Organize and Mathematize, Predict and Analyze, and Test and Interpret—the modeling process gives students a structure for approaching real-world mathematical problems.

In this topic, students focus on the patterns that are evident in certain data sets and use linear functions to model those patterns. Using the informal knowledge of lines of best fit that was built in previous grades, students advance their statistical methods to make predictions about real-world phenomena. They differentiate between correlation and causation, recognizing that a correlation between two quantities does not necessarily mean that there is also a causal relationship. At the end of this topic, students will synthesize what they have learned to decide whether a linear model is appropriate.