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Writing Verbal Descriptions of Functional Relationships

Given a problem situation containing a functional relationship, the student will verbally describe the functional relationship that exists.

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Writing Inequalities to Describe Relationships (Graph → Symbolic)

Given the graph of an inequality, students will write the symbolic representation of the inequality.

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Writing Inequalities to Describe Relationships (Symbolic → Graph)

Describe functional relationships for given problem situations, and write equations or inequalities to answer questions arising from the situations.

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Connecting Multiple Representations of Functions

The student will consider multiple representations of linear functions, including tables, mapping diagrams, graphs, and verbal descriptions.

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Writing the Symbolic Representation of a Function (Graph → Symbolic)

Given the graph of a linear or quadratic function, the student will write the symbolic representation of the function.

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Determining Reasonable Domains and Ranges (Verbal/Graph)

Given a graph and/or verbal description of a situation (both continuous and discrete), the student will identify mathematical domains and ranges and determine reasonable domain and range values for the given situations.

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Interpreting Graphs

Given a graph, the student will analyze, interpret, and communcate the mathematical relationship represented and its characteristics.

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Making Predictions and Critical Judgments (Table/Verbal)

Given verbal descriptions and tables that represent problem situations, the student will make predictions for real-world problems.

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Collecting Data and Making Predictions

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

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Writing Expressions to Model Patterns (Table/Pictorial → Symbolic)

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.

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Analyzing the Effects of the Changes in m and b on the Graph of y = mx + b

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*.

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Writing Equations of Lines

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

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Investigating Methods for Solving Linear Equations and Inequalities

Given linear equations and inequalities, the student will investigate methods for solving the equations or inequalities.

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Selecting a Method to Solve Equations or Inequalities

Given an equation or inequality, the student will select a method (algebraically, graphically, or calculator) to solve the equation or inequality.

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Determining Intercepts and Zeros of Linear Functions

Given algebraic, tabular, or graphical representations of linear functions, the student will determine the intercepts of the graphs and the zeros of the function.

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Solving Systems of Equations with Graphs

Given verbal and/or algebraic descriptions of situations involving systems of linear equations, the student will solve the system of equations using graphs.

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Determining the Domain and Range for Quadratic Functions

Given a situation that can be modeled by a quadratic function or the graph of a quadratic function, the student will determine the domain and range of the function.

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Determining the Domain and Range for Quadratic Functions: Restricted Domain/Range

Given a situation that can be modeled by a quadratic function or the graph of a quadratic function, the student will determine restrictions as necessary on the domain and range of the function.

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Analyzing the Effects of the Changes in "a" on the Graph y = ax^2 + c

Given verbal, graphical, or symbolic descriptions of the graph of* y = ax^2 + c*, the student will investigate, describe, and predict the effects on the graph when *a* is changed.

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Solving Quadratic Equations Using Concrete Models

Given a quadratic equation, the student will use tiles to factor and solve the equation.