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Solving Rational Equations

Students will discuss and formulate an equation to solve an engaging real-world problem. They will use manipulatives to describe how to find the common denominator they need to solve the equation. They will break up into groups and solve for a more complicated problem.

**Texas Essential Knowledge and Skills (TEKS) Vertical Alignment**

Click below to learn about the TEKS related to the unit and Research Lesson. The highlighted student expectation(s) is the chosen focus for the Research Lesson.

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Vertical Alignment Charts for Revised Mathematics TEKS

This resource provides vertical alignment charts for the revised mathematics TEKS.

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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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Domain and Range: Numerical Representations

Given a function in the form of a table, mapping diagram, and/or set of ordered pairs, the student will identify the domain and range using set notation, interval notation, or a verbal description as appropriate.

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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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Transformations of Square Root and Rational Functions

Given a square root function or a rational function, the student will determine the effect on the graph when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values.

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Transformations of Exponential and Logarithmic Functions

Given an exponential or logarithmic function, the student will describe the effects of parameter changes.

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Solving Square Root Equations Using Tables and Graphs

Given a square root equation, the student will solve the equation using tables or graphs - connecting the two methods of solution.

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Functions and their Inverses

Given a functional relationship in a variety of representations (table, graph, mapping diagram, equation, or verbal form), the student will determine the inverse of the function.

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Rational Functions: Predicting the Effects of Parameter Changes

Given parameter changes for rational functions, students will be able to predict the resulting changes on important attributes of the function, including domain and range and asymptotic behavior.

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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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Connecting Multiple Representations of Functions

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