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Working with Literal Equations

The lesson will provide a conceptual basis for illustrating the parallelism between solving multi-step equations and translating literal equations into solutions for specified variables.

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Product and Quotient Properties of Exponents

This lesson helps students understand two foundational exponential properties: The Product and Quotient Properties of Exponents. Students will collaborate to formulate a rule for these properties. Ultimately, students should conclude that when the same bases are being multiplied, exponents will be added; and when the same bases are being divided, exponents will be subtracted. As the lesson progresses, students will apply these rules to simplify expressions of various difficulties.

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6 OnTRACK Algebra I: Properties and Attributes of Functions

Students will learn how to use the properties and attributes of functions.

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Linear Inequalities

This activity provides an opportunity for students to examine how to find solutions to linear inequalities.

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Linear Transformations

This activity provides an opportunity for students to examine transformations of linear equations.

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Solving Quadratic Equations Using Algebraic Methods

Given a quadratic equation, the student will solve the equation by factoring, completing the square, or by using the quadratic formula.

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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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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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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.

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Predicting the Effects of Changing y-Intercepts in Problem Situations

Given verbal, symbolic, numerical, or graphical representations of problem situations, the student will interpret and predict the effects of changing the *y*-intercept in the context of the situations.

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Solving Linear Inequalities

The student will represent linear inequalities using equations, tables, and graphs. The student will solve linear inequalities using graphs or properties of equality, and determine whether or not a given point is a solution to a linear inequality.

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Predicting the Effects of Changing Slope in Problem Situations

Given verbal, symbolic, numerical, or graphical representations of problem situations, the student will interpret and predict the effects of changing the slope in the context of the situations.

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Direct Variation and Proportional Change

The student will use a variety of methods inculding tables, equations and graphs to find the constant of variation and missing values when given a relationship that varies directly.

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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.