Simplifying Linear Expressions by Combining Like Terms

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Objective

SWBAT simplify linear expressions by combining like terms

Big Idea

Students add 5 apples and 3 bananas to 6 apples and 2 bananas algebraically.

Introduction

10 minutes

I will begin with the essential question:  How can we use addition to simplify algebraic expression?  Students will need to be familiar with two vocabulary terms:  like terms and constant.  These will be defined with examples.  It might be helpful to present several problems and ask students to identify the like terms.  For example:

8m + 3 - 5m + 25

7b + 3x - 5b + 21x

8 - 15 + 12x + 7

etc.

As a hook I will will play this video from 2:30 - 3:10.  It relates adding like terms to totaling two different baskets of two types of fruit.

This is a direct instruction lesson so I have presented 3 steps for students to follow as a reference.  

I will then present each example.  Students are to watch my work on the board.  Then, they will do the "You try!" problem.  The "You try!" problem is a check for understanding.   

 As I modeled identifying like terms I will use different colors to circle or underline the like terms.  I will provide my students with markers so that they can visually see the terms that belong to each other.  If you do not want to use different colors you may circle the like terms with different shapes - perhaps using a circle for variables and triangles for consonants.

 

Guided Problem Solving

15 minutes

Students will solve these by working with their partner(s).  I will be looking for common errors.  Students will sometimes ignore the like terms.  For example on GP1 students my simplfy 6x + 2 + x + 7 as 15x or 16x.  

I will emphasize integers but have included fractions and decimals to make sure all rational number coefficients are being addressed. 

 

GP7) Is a "real-world" problem.  For this (and all problems), I will ask:  "How can we make sure our answers are correct?"  I want students to realize they could assign a value to the variable(s) and evaluate the given expression and the simplified expression.  Each expression should have the same value.  This speaks to MP1 where students ask "Does this make sense?".  

 

 

Independent Problem Solving

20 minutes

Students now work independently on 8 problems.  The first 6 are virtually identical to the guided problem solving problems.  If students are stuck, I will ask them to refer to the guided problem solving section first.  GP1 corresponds to problem 1, GP2 corresponds to problem 2, and so on.  

 

Problem 7 may cause some problems.  Students may only add 5x + 8 and 3x + 5.  However to find the perimeter, each of these values should be added twice.  Note:  I do not expect students to use the distributive property to solve (i.e. 2(5x + 8) + 2(3x + 5).  This will come later in the unit.  However, in future years this could be expected as 6th grade student will use the distributive property to evaluate expressions.

The last question calls on MP3.  Students will be asked to explain which expressions are equivalent.  Three of the four expressions are equivalent.  I want to remind students of the relationship between addition and subtraction and how the commutative property can be used. 

Exit Ticket

5 minutes

Before we begin the exit ticket we'll discuss how to identify and annotate like terms.  I will purposely use the term "annotate" because it is a word they here often from their ELA and Science teachers.  They are used to annotating reading.  

Students will then take the exit ticket.  A successful exit ticket will be at least 3 correct answers.