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# Writing Two Variable Equations

Lesson 11 of 11

## Objective: SWBAT write an equation to express the dependent variable in terms of the independent variable

## Big Idea: When two values vary in relation to each other, there exists a single equation that relates the two variables.

*73 minutes*

#### Think About It

*10 min*

Students work independently on the Think About It problem. This problem asks students to interpret the meaning of each piece of the two equations. My students are usually able to answer the questions fairly quickly. We discuss which variables are independent and which are dependent. In this unit, I don't use the word 'intercept,' but students are starting to internalize what the y-intercept in an equation represents, and how it impacts the graph and values of an equation.

Later in this lesson, students will be writing equations given real life situations using what we know about identifying 2 variables and how they are related.

#### Resources

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#### Intro to New Material

*25 min*

To start the Intro to New Material section, I ask students what the first example is asking us to do. Students identify the information that is given, identify the variables, and then also the relationship between the variables. At this point it can be helpful to construct an input/output table, so that students can see the relationship between the two variables.

In the second example, students will need to construct the equation on their own. The equation has an initial value, which can be tricky for students. I have students brainstorm other instances where there might be a starting amount. After they do so, we talk through the pieces of the equation. It's useful to have students test the equation we create. I ask them how much Daisy has after 2 months in her account. We then substitute 2 into the equation and make sure that we get $280 as our value.

I have students complete the check for understanding problem. Normally, I have students work in partners *before *completing a written CFU. However, I use this problem to determine if students are ready to move on to partner practice or if I should guide them through more examples.

#### Resources

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#### Partner Practice

*15 min*

Students work in pairs on the Partner Practice problem set. A partner practice sample is here. As students are working, I circulate around the room and check in with each group. I am looking for:

- Are students identifying the correct variables?
- Are students defining their variables with precise language?
- Are students writing the correct equations?
- Are students checking their equations, using substitution?

I am asking:

- How did you know these were the correct variables?
- How did you know which operation(s) to use?
- How can you check to be sure that your equation is correct?

After 10 minutes of partner practice time, students complete the Check for Understanding problem independently. I put a student response on the document camera and the class gives feedback on the work that is displayed.

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#### Independent Practice

*15 min*

Students work on the Independent Practice problem set. If students are having trouble, I have them continue to create input/output tables, as it helps them to make sense of the relationship between the variables.

The student work sample here showed me that I needed to work with students to be more precise in how they defined their variables. This particular student was not being precise enough.

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#### Closing and Exit Ticket

*8 min*

After independent work time, I have students share out anything that was difficult for them. They can ask for help or clarification from their peers. My role in this discussion is as facilitator - I keep the conversation moving, if needed, but I want students to drive the discussion.

After a few students have the opportunity to get clarification from the class, I then ask students to help me create an exemplar definition for the variables in problem 4. I want to drive home that defining a variable as m = money is not precise enough. We work together to craft strong definitions for the variables.

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

#### Resources

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- UNIT 1: Number Sense
- UNIT 2: Division with Fractions
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Coordinate Plane
- UNIT 5: Rates and Ratios
- UNIT 6: Unit Rate Applications and Percents
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- UNIT 9: Inequalities
- UNIT 10: Area of Two Dimensional Figures
- UNIT 11: Analyzing Data

- LESSON 1: Determining Solutions
- LESSON 2: Solving One-Step Equations Using Reasoning
- LESSON 3: Solving Equations Using Reasoning, Part 2
- LESSON 4: Writing Simple Algebraic Equations
- LESSON 5: Writing Algebraic Equations to Represent Real-World Scenarios (One-Step)
- LESSON 6: Solving Real-World Problems with Algebra (Addition & Subtraction)
- LESSON 7: Solving Real-World Problems with Algebra (Multiplication & Division)
- LESSON 8: Two Unknowns in Real-World Context
- LESSON 9: Using Graphs and Tables to Determine Relationships
- LESSON 10: Solving for Independent and Dependent Variables
- LESSON 11: Writing Two Variable Equations