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Using Logical Reasoning to Prove Conjectures about Circles

Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

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Generalizing Geometric Properties of Ratios in Similar Figures

Students will investigate patterns to make conjectures about geometric relationships and apply the definition of similarity, in terms of a dilation, to identify similar figures and their proportional sides and congruent corresponding angles.

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Determining Area: Sectors of Circles

Students will use proportional reasoning to develop formulas to determine the area of sectors of circles. Students will then solve problems involving the area of sectors of circles.

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Making Conjectures About Circles and Segments

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties and relationships among the resulting segments.

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Determining Area: Regular Polygons and Circles

The student will apply the formula for the area of regular polygons to solve problems.

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Making Conjectures About Circles and Angles

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties of and relationships among the resulting angles.

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Solving Problems With Similar Figures

Given problem situations involving similar figures, the student will use ratios to solve the problems.

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Writing Equations to Describe Functional Relationships (Table → Equation)

Given a problem situation represented in verbal or symbolic form, the student will identify functions.

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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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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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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.