Complex Rational Expressions

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Students will be to simplify complex rational expressions.

Big Idea

Perseverance is the key to this lesson on complex fractions.

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 homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up- Complex Rational Expressions asks students to explain how to split 3/4 of a pizza between 3 people.

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

Initial Activity

15 minutes

My goal for this Initial Activity of this PowerPoint is to give the students an opportunity to practice perseverance ( Math Practice 1).  At this point, the students have the skills they need to simplify complex fractions; however, they have not put them together in this particular way.  I present them with a challenging complex fraction, and let them know they have all the skills they need to simplify this expression.  There will probably be a wide range of attempts from completion to very little effort depending on their skills and comfort level.  As they work, I walk around providing some support for those who need it.  It is fine if all groups don’t complete this as we will be building/refining this process during the remainder of the lesson.

Once all of the groups have made some decent process and several groups have finished, we will simplify the expression together.  

Guided Practice

23 minutes

The remainder of this lesson consists of a Guided Practice of Complex Rational Expressions.  I may skip some of these problems depending on the performance of the class during the initial activity.  

Please see the PowerPoint for detailed presentation notes.

Exit Ticket

3 minutes

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

Today's Exit Ticket, I ask the students to simplify a rational expression.


This Assignment provides students with an opportunity to simplify complex rational expressions.  The last expression is an extension problem.  One scaffolding measure would be to ask the students to simplify either the first four or the final three expressions.  The final problem asks students to write a list of steps that one could use to simplify a rational expression (Math Practice 3).

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