Variables and Expressions

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SWBAT evaluate an expression containing one variable to find possible solutions.

Big Idea

Expressions can be evaluated by replacing the variable with a number then calculate.


5 minutes

In today's lesson, the students learn to evaluate expressions containing one variable to find possible problem solutions.  This aligns with 4.OA.A3 because the students are representing  these problems using equations with a letter standing for the unknown quantity.

To get the students started, I pose a scenario to get them thinking about our lesson for today.  "Imagine that you wanted to invite friends over for a party.  Your mom wants to buy cupcakes for your party.  She asks you for the number of friends that you are inviting.  You look blank because you haven't decided.  You tell your mom that it will either be 6, 7, 8, or 9.  How can your mom figure out the cost of the cupcakes?"  I give the students a few minutes to think about the question.  I take a few student responses. One student responds, "Buy more than 9 cupcakes." I redirect that student to let him know that he did not answer the question that was asked.  I always tell my students that they must answer what is asked of them.  Another student responds, "Add all of the numbers up, then multiply by 3."   From their responses, I know that this is a skill that is really needed.  I tell the students, "Let us find our how mom can find the cost of the cupcakes when there are more than one possible solution."

Whole Class Discussion

10 minutes

I call the students to the carpet as we prepare for a whole class discussion.  The power point is already up on the Smart board.  I like for my students to be near so that I can have their full attention while I'm at the Smart board.  

I begin by going over important vocabulary for this lesson.  The students will have to know these terms to understand the lesson.


Variables – A symbol that stands for a number.

Algebraic expression – A mathematical phrase containing numbers or variables and at least one operation.

I go back to the scenario that I posed earlier for the students about the cupcakes.  

"Imagine that you wanted to invite friends over for a party.  Your mom wants to buy cupcakes for your party.  She asks you for the number of friends you are inviting.  You look blank because you haven't decided.  You tell your mom that it will either be 6, 7, 8, or 9.  How can you mom figure out the cost of the cupcakes?"
Let’s find out.
We can use a table to set up the problem. 
Because we do not know how many students are coming to the party, mom does not know how many cupcakes to buy.  We need a variable to represent the number of cupcakes. Let “c” represent the cupcakes.  Mom does know that each cupcake will cost $3.00.











Now that we have our variable, we can now write an expression to represent the cost of the cupcakes. We have learned that if a number is repeat, it is a multiplication problem.  

 c x 3 = ?

Replace the number for “c” in the expression.

This is called evaluating the expression.

6 x 3 = 18

7 x 3 = 21

8 x 3 = 24

9 x 3 = 27

Therefore, these are the amounts mom will spend if 6, 7, 8, or 9 people attend the party.

Group or Partner Activity

20 minutes

I give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others (MP3).

For this activity, I put the students in pairs.  I give each group a Group Activity Sheet Variables and Expressions. The students must decontextualize the problem and represent them symbolically (MP2).  The students must work together to write the expressions and solve them. They must look for a pattern (MP7).  They must communicate precisely to others within their groups (MP6). They must use clear definitions and terminology as they precisely discuss this problem (MP1). 

The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.  The students communicate with each other and must agree upon the answer to the problem.  Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students (MP3).  From the Video of Students, you can hear the students discuss the problem and agree upon the answer to the problem.  As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6).  As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.  

As they work, I monitor and assess their progression of understanding through questioning. 

1.  What does the variable represent?

2. What numbers did you substitute for the variable?  Why?

3.  How do you find the answer?

As I walked around the classroom, I heard the students communicate with each other about the assignment.  From the video, you can hear the classroom chatter and constant discussion among the students.  Before Common Core, I thought that a quiet class working out of the book was the ideal class.  Now, I am amazed at some of the conversation going on in the classroom between the students.  As I walked past one group, I heard a student say, "This is a subtraction problem because it said how many will she give away."  I always tell my students that they must justify their answer by referring back to the problem.  

There were a few students who struggled with finding the correct operation for the problem.  From this sample of student work Incorrect Solution - Student Work, you can see that for problem number 1 on the Group Activity Sheet Variables and Expressions, this pair thought that it was a multiplication problem.  I question students as I walk around to guide them to the correct answer.  With that being said, I still like to pull students for small group to reinforce the skill the next day.  This pair of students will work with me first thing the next day to make sure they can read a word problem and know which operation to use.    

Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing.


15 minutes

To close the lesson, I have one or two students share their answers.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples, as well as work that may have incorrect information.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.