# Simplify Rational Number Expressions Using the Distributive Property

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## Objective

SWBAT simplify algebraic expressions containing fractions using the distributive property

#### Big Idea

This is a fluency lesson using the distributive property with fractional coefficients and constants.

## Introduction

5 minutes

This is another brief direct instruction lesson.  This is a lesson designed to help students gain fluency with simplifying the types of expressions included within - this brings to mind mathematical practice 8.  The steps provided and the use of properties to justify steps is an example of mathematical practice 3.

The example using the area model.  I will draw a rectangle and label the sides with the given values.  I will split the length into two sections - one whose length is x inches and the other whose length is 3 inches.  This is the tie in to area or array model and the distributive property.

We know area of a rectangle is length times width (or vice versa) so I will write:

3 2/5 (x + 3)

17/5 (x + 3) <--- rewrite using an improper fraction

17/5x + 51/5 <--- distributive property

## Guided Problem Solving

10 minutes

Students have 4 problems to solve here.  The first is similar to the example.  The others require students to use the distributive property and combine like terms.  Students will be expected to justify their steps during this section in a manner similar to the example.

I may pair students to work together.  One student will read each step and watch his/her partner execute the problems step by step.  Then they will switch roles for the next problem.

Students may still make errors when it comes to simplifying expressions.  They will be reminded that they will likely have to find common denominators before adding like terms.

## Independent Problem Solving

15 minutes

Students will work on this problem set independently.  The first 4 problems mirror the guided problem solving problems.  The last problem in the set is a multiple choice problem; students still must show work!  I expect most students will use each multiple choice answer and multiply it by (x+2) until they find the given area of 3/4x + 1 1/2.  Students may try to multiply the given terms in the problems - (x + 2) times (3/4x + 1 1/2).  Of course that would be a mistake; plus they haven't learned FOIL yet!

I will mostly monitor work without given much input or help.  After a few minutes of work, I may begin to help.  For students to be eligible for help, they will need work down.  The first three steps should be doable.

## Exit Ticket

5 minutes

Before beginning the exit ticket, we will review the steps to simplifying expressions using the distributive property.  This could be as simple as having a student read the list of steps.

There are only 3 problems on the exit ticket.  I will take off points if a student does not simplify a fraction in their simplified answer.  So in problem 2, 3/12b + 6/3 is as good a 1/4b + 2.

Two out of three correct answers is a sign that a student will have this objective mastered soon.