Two Unknowns in Real-World Context

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SWBAT identify, define and explain independent and dependent relationships in real-world and mathematical contexts.

Big Idea

In situations where there are two unknowns, we can determine which variable causes a change in the other unknown.

Think About It

7 minutes

As class begins, I ask students to work independently on the Think About It problem.

After a few minutes, I ask students to clap out their answers for the first problem.  I then ask a student to explain why C is the best answer choice.  I expect my students may talk about the context of the problem, or, they may eliminate other answer choices with their reasoning. Either approach is okay.

I then ask a student for the answer for Problem 2.  Once we determine that the answer is choice A, I have students explain why B and C cannot be the correct equation. In this instance, I hope that my students will talk about the relationship between the two variables representing the ages of Tyree and Monica. 

Intro to New Material

20 minutes

In this lesson, students are not writing and solving equations.  Instead, they are determining the relationship between the variables in each scenario.  Throughout this lesson, students will use the sentence "A change in (the independent variable) causes a change in the (dependent variable)."

After filing in the notes at the start of the Intro to New Material section, I guide students through 3 examples.  In the first example, I discuss the scenario as though it were our class.  If I decided to take our class on a field trip, we'd need one bus.  If we took all of the 6th grade classes, we'd need more buses.  I ask the class to imagine that I'm taking only them - they are the only ones with permission slips for the trip.  What would happen if 5 buses showed up? We'd still be the only ones on the trip.  Students record the independent and dependent variable and describe the relationship between the variables as "A change in the number of students going on the trip causes a change in the number of buses needed."

In examples 2 and 3, we need to define the variables and then describe the relationships.

Partner Practice

15 minutes

Students work in pairs on the Partner Practice problem set.  A student work sample is included here.  As students work, I circulate around the classroom, checking in with each group.  I am looking for:

  • Are students explaining their thinking to their partner?
  • Are students identifying the correct variables and explaining their meaning within the context of the problem?
  • Are students explaining the relationship between the two variables, using the sentence frame?

I am asking:

  • (when appropriate) How did you know what the variables are?
  • Which variable is independent?  Why?  
  • Which variable is dependent?  Why?
  • What is the relationship between the variables?
  • What would happen if the independent variable increased?  Decreased?


For problem 2 in this set, I needed to give students some help with unfamiliar vocabulary.  Before partner work time, I quickly tell students about bushels of wheat and plots of land.  

After partner time, students solve the Check For Understanding problem independently.  I circulate as students work, to check their responses.  The class has a quick conversation about the problem.  First, I ask what each variable stands for.  I then ask them what the 5 represents (in this unit, students are not introduced to the idea of slope/rate of change, but getting them to understand the meaning of the coefficient here will help them to make sense of linear functions in higher level math).  


Independent Practice

20 minutes

Students work on the Independent Practice problem set.

Problem 3 can be difficult for students, particularly the sentence describing the relationship.  A change in Leeann's age doesn't literally cause a change in Gabriel's age, and that can be difficult for students to grasp.

In this lesson, students are working independently for 20 minutes.  I am able to circulate around the room and check in with each individual student multiple times.  I'm looking to see that students are correctly identifying the independent and dependent variables, and also that they are correctly describing the relationship between the variables.  

Closing and Exit Ticket

8 minutes

Because I've had the opportunity to check in with each student multiple times during Independent Practice, students move in to completing the Exit Ticket after independent work time.  A exit ticket sample is included here.

After 5 minutes of work time, I have students share the answers to the first and second problems with their partners.  I then cold call on students to share the answers with the class.  

To end the lesson, I let students know that in the next lesson, we will continue to look at independent and dependent variables, using tables, graphs, and equations.