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Equations in the Real World

**Students will create and solve equations with variables on one side before comparing the equation with another to determine at what rate they will be equal. **

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Four Representations of Linear Relationships

Given one representation of a linear relationship, students will create a poster displaying the other three representations of linear relationships.

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Rise Over Run! Let’s Have Fun!

Students will collaboratively practice identifying and graphing slope and y-intercept.

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Generating Different Representations of Relationships

Given problems that include data, the student will generate different representations, such as a table, graph, equation, or verbal description.

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Interpreting Scatterplots

Given scatterplots that represent problem situations, the student will determine if the data has strong vs weak correlation as well as positive, negative, or no correlation.

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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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Finding Specific Function Values (Verbal/Symbolic)

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

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Simplifying Polynomial Expressions

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

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Solving Equations and Inequalities

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

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Quadratics: Connecting Roots, Zeros, and x-Intercepts

Given a quadratic equation, the student will make connections among the solutions (roots) of the quadratic equation, the zeros of their related functions, and the horizontal intercepts (*x*-intercepts) of the graph of the function.

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Applying the Laws of Exponents: Verbal/Symbolic

Given verbal and symbolic descriptions of problems involving exponents, the student will simplify the expressions using the laws of exponents.

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Using the Laws of Exponents to Solve Problems

Given problem situations involving exponents, the student will use the laws of exponents to solve the problems.

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Formulating Systems of Equations (Verbal → Symbolic)

Given verbal descriptions of situations involving systems of linear equations the student will analyze the situations and formulate systems of equations in two unknowns to solve problems.

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Solving Quadratic Equations Using Graphs

Given a quadratic equation, the student will use graphical methods to solve the equation.

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Writing Equations to Describe Functional Relationships (Verbal → Equation)

Given a problem situation represented in verbal form, students will write an equation that can be used to represent the situation.

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Writing Inequalities to Describe Relationships (Verbal → Symbolic)

Given a problem situation represented in verbal form, students will write an inequality that can be used to represent the situation.

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Solving One-Variable Inequalities

Students will solve one-variable inequalities using a variety of representations, including tables, graphs, and symbolic representations.

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Determining the Meaning of Intercepts

Given algebraic, tabular, and graphical representations of linear functions, the student will determine the intercepts of the function and interpret the meaning of intercepts within the context of the situation.