Writing and Evaluating Expressions

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SWBAT use variables to write and evaluate expressions when solving a real-world problem

Big Idea

The value of an algebraic expression can be found by replacing the variables with a known value and following the order of operations

Think About It

7 minutes

Students work independently on the Think About It problem. 

After 2 -3 minutes of work time, I ask students for the expression they've written.  I ask what the variable stands for, what the coefficient is, and what it means.  I ask how they used the expression to find how fast Luis was driving.   

I frame the lesson by letting students know that we're going to be putting together 3 major skills - writing complex equations, substituting, and evaluating using the order of operations.

Guided Practice

15 minutes

In this section, I ask students to write and solve a multi-step expression when given a word problem with a known value for a variable. I want my students to follow the order of operations when simplifying expressions. Because this lesson combines all of the skills learned so far in this lesson, there is not an introduction to new material section.  Rather, there are Guided Practice problems that we complete as a class.

The first example is a verbal expression that students translate and then evaluate for a given value. The process students should use to write and evaluate the expression can be seen and heard here. The second problem presents students with a real-world example.  Students must define the variable before writing and evaluating the expression.

Partner Practice

15 minutes

Students work in pairs on the Partner Practice problem set.  As students work, I circulate around the room.  I am looking for:

  • Are students correctly identifying the variable?
  • Are students correctly identifying the constant?
  • Are students correctly identifying the coefficient?
  • Are students correctly translating the verbal expression into an algebraic expression? Are students using substitution and their expression correctly to solve the problem?

I am asking:

  • How did you know what the variable was?
  • How did you know what the constant was?
  • How did you know what the coefficient was?
  • How did you know what operations to use?
  • How did you know the value of the variable?
  • Why does the expression you wrote help you solve the problem?
  • Use the steps above as questions if more are needed.

After 10 minutes of partner work time, I bring the class back together for a discussion.  I use Problem 2 to drive our conversation.  I pull a popscicle stick to cold call on a student for work to display on the document camera.   The class gives positive and critical feedback on the displayed work. 

Students complete the Check for Understanding independently.  

Independent Practice

15 minutes

Students work on the Independent Practice problem set.  

The first four problems require students to evaluate when n is a decimal.  As I am circulating, I am checking to be sure that students are careful with their arithmetic when they are evaluating. 

Throughout this section, I am praising students for their organization.  Students must annotate the problems, define their variables, and keep their work space neat and orderly.  

Problem 8 can be difficult for students, in that students have to find half of a quantity.  Students can use 1/2 as a coefficient, or divide by 2.  I check to be sure that students are not dividing by 1/2.  

Closing and Exit Ticket

8 minutes

After independent work time, I bring the class together.  I display work for Problem 7.  I intentionally display the incorrect expression, using 4 - 2c.  I have students turn and talk about my expression.  I then ask for a student to share out the mistake I've made in my work.  Finally, I ask for a student volunteer to share out the correct expression.

Students work on the Exit Ticket independently to close the lesson.