Adding and Subtraction Rational Expressions

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Students will be to add and subtract rational expressions.

Big Idea

Compare and connect the graphic and algebraic representations of the sums and differences of 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 homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Adding and Subtracting 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 Addition and Subtraction of Rational Expressions

15 minutes

Here's the scenario I used in this section of the lesson:

Ian and his brother are painting houses as a summer job.  Ian can get one room done in 6 hours.  His brother can get one done in 4 hours. 

This work problem is both an introduction to adding rational expressions and a preview of the rational equations which we will be doing in a couple of lessons (Math Practice 4).  I use the Note Card strategy here as I think there will be some really great mistakes made.   The next couple of tasks deal exclusively in rational numbers.   The final question of x hours which will probably be a stretch as it extends these problems into rational expressions (Math Practice 1). 

Please see the PowerPoint which includes detailed presentation notes.

Addition and Subtraction of Rational Expressions Guided Practice

23 minutes

The remainder of the lesson will be spent on Guided Practice with a twist.  We begin by adding several fractions and then several rational expressions of increasing difficulty.  The final three problems relate this lesson back to graphing rational functions which the students saw several lessons ago (Math Practice 7).  They simplify each problem and then I pull up a graph with each expression graphed separately.  I ask them to predict what the sum of each graph will look like.  The first one consists of three linear expressions as the denominators have numbers rather than variables.  The second has to rational expressions with the same asymptotes while the final problem has different asymptotes.  

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 add two rational expressions.


This assignment begins with 6 practice problems of varying difficulty.  These are important to help students develop and solidify this skill.  The final question asks students to describe the graphs of the sum or difference of three problems.  This helps them connect the algebraic manipulation to the graphical version (Math Practice 7).