Stacking Cups: Systems of Equations Real World Application

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SWBAT apply their knowledge of systems of equations to model a real world scenario.

Big Idea

Students use data to create equations describing a concrete scenario. Students analyze the equations as a system to solve a problem.


10 minutes

Students will complete today's Do Now in 5 minutes.  I will then ask three students to come up to the board to show their answers to the class. I will ask that each student solve the system using a different method. After they finish, I will ask the class to analyze their work to see if the students arrived at the same answer.

Next, I will ask a student will read the objective, "SWBAT apply their knowledge of systems of equations to model a real world scenario."

Before moving forward, I will return the graded Exit Cards to students from our last class. We will review the responses as a whole group.


5 minutes

Today's investigation is one of my favorite activities in the Systems of Equations Unit.  This lesson is adapted from the website 101 Questions. 101 Questions is a great resource for discovery-based lessons, as it provides users with intriguing videos and photos that intend to spark student's natural curiosity. 

After the Do-Now I will tell students that they will be completing an investigation, but I will be careful to not give them too much information since each group will be developing their own procedures. I will show the class the Stacking Cups Video Clip 2-3 times and ask them to make careful observations and notes about what they see.

I will ask students to share the questions that they immediately thought of when watching the Stacking Cups video. I will record the questions on the board.


35 minutes

Instructor Note: Students should be pre-sorted into homogeneous ability pairs. Each group will need a ruler, yard stick, graphing calculator, paper, 2 styrofoam cups, and 2 red/blue plastic cups.

After we summarize our discussion of the students' question about the video, I will tell the class that their task is for each group to figure out the point at which the both stacks of cups are level, and, what the height of the cup-stack will be.

The initial guidance that I give students is:

  • You will only be given two of each cup. You will also have a ruler and a yard stick.
  • You will have to prove your answer using multiple methods.
  • You must be able to present your findings with different representations (table, graph, equation etc.)
  • If you and your partner are stuck, you can request a hint card, but you may only request one card every 5 minutes.

At this point I will release students to begin the investigation. I will circulate around the class during this activity asking students questions to guide their own reasoning as they work. 

Some pairs will be able to start immediately, while I expect others will need more guidance. This activity differentiates itself with the use of the hint cards. Depending on the ability level of the students in a group, I distribute particular hint cards strategically. I did not distribute the hint cards in sequential order; rather I distribute them based on where a given pair is in the progression of the activity. For students that I want to challenge, I provided a stated limit of how many hint cards they can request.

After about 20 minutes, we will reconvene as a whole group to share our data and to hear the ideas that students have developed. I will ask 3 students to come up to the front of the room to demonstrate their methods: system of equations, table, and graph.

After viewing all three group's models, we will physically test their solutions with the cups to see if they are correct. I will also show students this picture and the Act Three Video on the 101 Questions website.

Partner Practice

25 minutes

After the investigation students will complete this handout with the same partner from the Stacking Cups activity. This activity is not related to the Stacking Cups activity, but also requires students to use systems of equations to solve a real-world scenario involving moving truck rentals.

After 20 minutes will will share out responses as a whole group. I will ask students to make a connection between the Truck Rental and Stacking Cups activities, and to elaborate further about the importance of Systems of Equations in math.

End of Unit Reflection + Goal Setting

5 minutes

By the time my classes reach today's lesson, it is close to the end of the third marking period. Nonetheless, a large majority of my 9th grade students remain unfamiliar with high school grading policies and GPA calculations. I have informally spoken with students about these topics, but will use this assignment to help students set an attainable goal for themselves for the conclusion of the school year.

We will complete both sides of the reflection together as a whole group. I will ask students to review what they have written with someone at home, and to return it back signed to me for a homework grade.

Sample Assessment Questions

My students will take an interim assessment that is created by my school district (DCPS). I have attached some sample questions from the assessment that show the level of rigor and reasoning required for students to demonstrate mastery of the standards covered in this unit.