# Linear Expressions and Word Problems

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## Objective

SWBAT write and match linear expressions to word problems

#### Big Idea

Students analyze and match algebraic expressions to word problems. Students then write some algebraic expressions to represent word problems.

## Introduction

15 minutes

I will begin with a question:  "What does the term algebraic expression bring to mind?"  I will have a simple word web organizer drawn on the SmartBoard.  As students contribute answers, I will draw in the connections on the word web.  Hopefully students come up with answers like:  they involve variables, numbers, operations, represent word problems, etc...

This is not only to assess prior knowledge but to also have students show see how much they already know about expressions.  I will try (emphasis on "try") to make every relevant response a correct answer so that students feel free to contribute their thoughts.  Almost every time I do this, I am pleased with how much useful information students are able to contribute.

Then I will present four simple statements in the resource.  We will work together to match the statement to the expression.  For each expression, we will discuss what the variable means in context to the verbal statement.

Note that a couple of the statements may have more than one matching expression depending on the perspective you take in the problem.

All of this is a simple exercise to prepare students for the work ahead in the next section.  This is also an exercise in MP1  - specifically connecting the relationship between verbal descriptions and expressions.

## Gallery Walk and Discussion

20 minutes

Logistics:

Before the lesson:

I'll place the 6 verbal statements throughout the room.

I'll divide the class into 6 groups based.  (These may be mixed ability groups)

I'll need enough sticky notes for each student to have 6.

During the lesson:

I'll have students copy the 6 algebraic expressions onto their sticky notes - one expression per sticky note.

I'll explain that they will rotate with their groups to the statements around the room.  They are to pick the expression that they think best matches the statement.  They should place their sticky note on that expression.

I will set the timer for about 1-2 minutes before rotating.  Of course, I'll judge whether or not it appears they need more or less time and adjust accordingly.

Once all of the statements have been placed we will discuss the responses.

I purposely did not include a question with the statements, so that for each I can ask:  What question could the expression answer?  For each expression we will discuss what each part (coefficient, constant, variable, operations, etc) represents.

I expect for there to be some disagreement over several of these since they all use 10, 15 and x.  Students will often confuse 10x + 15 with 15x + 10 or even 10x + 15x.  This activity should bring about all of the misconceptions.

## Writing Expressions

15 minutes

Now students will have a chance to write algebraic expression to represent some word problems.  I'll have students work for the first several minutes by themselves before they will be allowed to check in with a neighbor.  The first 4 problems are 1-step expressions.  The last two are 2-step expressions which is right where the common core expects 7th grade students to be.  We will briefly discuss answers before beginning the exit ticket.

## Exit Ticket

5 minutes

There are 4 question on the exit ticket.  Two are multiple choice to represent the matching algebraic expressions to statements part of the objective.  The other two are open ended to match the writing algebraic expressions to statements part of the objective. The first two problems are one-step expressions and the last two are two-step expressions.

A successful exit ticket will be measured as at least 3 correct responses out of 4.