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A2-A-1-3

Page history last edited by Brenda Butz 6 years, 3 months ago

A2.A.1.3 Solve one-variable rational equations and check for extraneous solutions.

In a Nutshell

Students will use previous knowledge of rational expressions and solving equations to solve rational equations, and they will check all solutions to eliminate the possibility of extraneous solutions.

Student Actions	Teacher Actions
Students will develop accurate and appropriate procedural fluency for procedures for solving rational equations. Students will develop a deep conceptual understanding of how extraneous solutions occur and use their knowledge of evaluating expressions to check for extraneous solutions. Students will develop strategies for solving rational equations and identify an entry point to begin the search for a solution.	Provide students with opportunities to build procedural fluency on a foundation of conceptual understanding, so that students become skillful in using procedures for solving rational equations, as they solve contextual and mathematical problems. Ask students why the procedure they chose is effective in solving the equation. Facilitate meaningful discourse among students as they solve and discuss tasks that require students to solve rational equations with extraneous solutions. Implement mathematical tasks that provide students multiple entry points. Allow students the opportunity to decide if a variety of rational equations can be solved as a proportion or with methods involving the least common denominator.
Key Understandings	Misconceptions
Understand that a rational equation’ solution may not always work within the context of the original problem creating extraneous solutions which need to be excluded. Know how to find the least common denominator in a rational equation in order to either add or subtract the rational parts before solving the equation, or multiply the entire equation by the LCD before solving the equation.	Procedural: Students use incorrect procedures when solving rational equations, forgetting rules for adding, subtracting, multiplying and dividing rational expressions. When multiplying rational expressions, students try to cross multiply. If a rational expression has more than one term, students forget to use the distributive property to multiply expressions by the LCD or to obtain an LCD . Conceptual: Students forget to check all solutions to eliminate or find the existence of extraneous solutions and to eliminate them as solutions.