Lesson Plan

Operations with Rational Expressions


Grade Levels

Related Academic Standards

Assessment Anchors

Eligible Content

Big Ideas




In this lesson, students will perform operations with rational expressions. Students will:

·         find the sum of rational expressions.

·         find the difference of rational expressions.

·         find the product of rational expressions.

·         find the quotient of rational expressions.

·         solve applied problems involving operations with rational expressions.

Essential Questions

·         How can we extend arithmetic properties and processes to algebraic expressions and processes and how can we use these properties and processes to solve problems?


·         Polynomial: An algebraic expression that contains one or more polynomials. [IS.1 - Struggling Learners] [IS.2 - Struggling Learners]

·         Least common denominator (LCD): The least common multiple of the denominators in two or more fractions.

·         Expression: A variable, or any combination of numbers, variables, and symbols that represent a mathematical relationship (e.g., 24 × 2 + 5 or 4a – 9).

·         Rational expression: An expression that is the ratio, or quotient, of two polynomials.

·         Rational function: A rational expression that is written in function form, or expressed as a function, i.e., f(x) = 2 / ( x – 3).

·         Rational number: A number that can be expressed as a ratio of two integers. A rational number can be expressed in the form a/b, where a and b are integers and b is not equal to zero.


200–270 minutes/3–4 class periods [IS.3 - All Students]

Prerequisite Skills


·         copies of Multiplying Rationals Stations Problem Set (M-A2-5-1_Multiplying Rationals Stations Problem Set.doc)

·         copies of Stations Activity Records Sheet (M-A2-5-1_Stations Activity Records Sheet.doc)

·         copies of Level Up Problem Set (M-A2-5-1_Level Up Problem Set and KEY.doc)

·         copies of Multiplying Rationals IP (M-A2-5-1_Multiplying Rationals IP and KEY.doc)

·         copies of Operations Guided Notes (M-A2-5-1_Operations Guided Notes.doc)

·         copies of Common Denominators (M-A2-5-1_Common Denominators and KEY.doc)

·         copies of Adding Subtracting IP (M-A2-5-1_Adding Subtracting IP and KEY.doc)

Related Unit and Lesson Plans

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

·         Video–Simplifying Rational Expressions http://www.youtube.com/watch?v=B4bVlDgHF5I

·         Video Multiplying Rational Expressions http://www.youtube.com/watch?v=-aZ0a7aMiPE&feature=channel

·         Video–Dividing Rational Expressions http://www.youtube.com/watch?v=Fdie6CqInyg&NR=1

·         Video–Adding Rational Expressions http://www.youtube.com/watch?v=omv7Di2o8-Y&feature=channel

·         Video–Subtracting Rational Expressions http://www.youtube.com/watch?v=gv8h9Ivs__Y&feature=channel

Formative Assessment


Suggested Instructional Supports


Instructional Procedures


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