# Math - Algebra II: Rational Expressions and Equations Complete Unit Plan

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Resource Type Activity, Assessment, Handout, Presentation
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Common Core State Standards

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The unit plan is appropriate for students in grade 11 who have passed Algebra I and Geometry. This topic is Rational Expressions & Equations and is part of a unit in Algebra II. The unit contains five lessons and it takes 10 hours of teaching. Rational expressions can be used in solving many problems involving mixtures, photography, electricity, medicine, and travel. The learning objective of the unit is for students to learn how to:

• Simplify rational expressions.
• Multiply and divide rational expressions
• Determine the LCM of polynomials.
• Add and subtract rational expressions.
• Simplify complex rational expressions
• Solve rational equations
• Solving real-world problems.
• Solve rational inequalities.
• Graphing rational functions using a calculator.
• Determine the vertical asymptotes and the point discontinuity for the graphs of rational functions.
• Graph rational functions.

The daily lesson plan will start with a warm-up to review the previous lessons. The learning objectives will be stated using PowerPoint.  A sample PowerPoint is created and you may modify it to your liking. Students will be encouraged to share any information they already know about the topic and the lesson will start by stating examples of the usage of the specific math concept in real-life. This will tap into students’ background knowledge and students will be able to know the reason they need to learn the topic. Furthermore, the lesson will have many examples and students will be engaged. In the end, the objective of the lesson will be reviewed and an exit ticket for each lesson will identify how and what students have learned. The exit-ticket is in the form of a journal. The file for the quiz, test, homework, warm-ups, how to make the journal, and a rubric for the journal are included. Since the unit will cover five lessons, student’s performance will be assessed using formative assessments and after the third lesson, a quiz can be taken and a unit test can be administered at the end of the fifth lesson.

At the end of the unit, students will be able to define, understand, and apply terms such as rational equation, rational expression, rational function, rational inequality, complex fraction, asymptote, continuity, and point of discontinuity.

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### Standards

Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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