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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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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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Using Linear Equations to Count Pecans

**Students will write linear equations in point-slope form given two points via a verbal description.**

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Kid2Kid: Determining the Meaning of Slope and Intercepts

Kid2Kid videos on determining the meaning of slope and intercepts in English and Spanish

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No Interest If Paid in Full: How Much Do I Owe?

Students will write a linear equation from a real-world situation, identify the components of the equation, and interpret their meanings in the problem’s context.

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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 Parent Functions (Verbal/Graph)

Given a graph or verbal description of a function, the student will determine the parent 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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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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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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Determining the Domain and Range for Linear Functions

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.