Multiplying and Dividing Rational Expressions

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Students will be to multiply and divide rational expressions.

Big Idea

Extend and analyze an area model with rational expressions.

Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogenous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Multiplying and Dividing Rational Expressions which asks students to determine whether a rational expression as been properly simplified.

I also use this time to correct and record the previous day's Homework.  

Modeling Multiplication and Division of Rational Expressions

15 minutes

This lesson begins with an area application of multiplying and dividing rational expressions  (Math Practice 4). 

Advertisements can be purchased in the year book.  You want to buy one where your image has one side that is three inches longer than the other. 

The students begin by finding the area of this advertisement.  I then tell them that this advertisement turned out to be much too expensive so the image is going to be shrunk to where each side is half the original.  I will give this problem to the students and then walk around and pick students to put their solutions on the board.  This can be found both visually and algebraically. 

Finally, I ask them if the costs of the advertisements are based on the area, what portion of the original cost will the new advertisement be?  I also ask them to prove it algebraically (Math Practice 2).  This is the key to the task as it provides them their first experience dividing rational expressions. 

Multiplying and Dividing Rational Expressions Guided Practice

23 minutes

The remainder of this lesson is a Guided Practice on multiplying and dividing Rational Expressions.  Students can use their graphing calculator to graphically simplify in any way that works for them if they choose and I will ask students to share these.  Please see the PowerPoint for specifics.  

Exit Ticket

2 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

Today's Exit Ticket asks students to divide two rational expressions.


This short assignment begins with several practice problems to reaffirm the students' skills.  The final problem asks them to find the mistake in a simplified expression and explain how to fix it (Math Practice 3).  This error is the most common error that I have seen when dealing with rational expressions.  

This assignment was created with Kuta Software, an amazing resource for secondary mathematics teachers.