This MEA deals with creating a business plan for a movie theater, based on provided data. Students will first determine the best film to show, and then based on that decision, will create a model of ideal sales. Students will need to create equations and graph them to visually represent relationships.
General Information
Lesson Content

Lesson Plan Template:
Model Eliciting Activity (MEA) 
Formative Assessment
To successfully complete this lesson, it is important for students to have already been introduced to the concepts of equations/functions, and understand how to interpret a symbolic function as a graph, and vice versa. Before the lesson begins, the teacher should assess students’ familiarity with the content by providing problems dealing with graphing given functions and representing given data as a function. Students should know that “f(x) =” is the same “as y =” and be able to label axes appropriately. If the teacher believes that the class needs more experience/familiarity with these concepts, they should give a lesson in preparation for the activity.
The teacher may provide students with a review worksheet:
Movies__Review_Worksheet.docx
Questions a teacher can use to assess students’ familiarity with the content might include:
“What is a function?”
“Are functions and equations the same, or are the different? Explain your reasoning.”
“If I wanted to model a situation in which the cost of a bus is shared equally amongst all passengers, what would the graph look like, if x was the number of people, and y was the cost per passenger? Explain your reasoning.”
If it is determined that students require additional instruction/preparation for this MEA, one suggested resource dealing with Mathematical Modeling can be found at
In addition, Readiness Questions can be used as formative assessment (for questions, see the Readiness questions section). Readiness questions will indicate whether the students understand the problem and the problem context. The readiness questions are asked of students after they read the client letters (see Reading Passage 1 & 2). The teacher can ask the class to respond to these questions and ensure understanding before students begin working with the data.

Feedback to Students
Students should receive feedback about their performance throughout the MEA. The teacher should walk around the classroom, listening to group discussions about the presented problem, and ask students to explain their thought processes and problemsolving strategies. If students should run into roadblocks in the activity, it is important for the teacher not to simply suggest the correct answer or strategy. Rather, the teacher should ask students to clarify what outcome they are trying to achieve, and ask questions that will guide them towards that desired outcome. Students can then use this feedback to evaluate their thought processes and make adjustment where necessary to improve their performance.

Summative Assessment
At the end of this activity, students should understand that math can be used to model realworld problems (such as creating a business plan). The degree of this achievement will be evident in the written responses students create during the activity. If students are able to interpret the data provided to them in an organized manner that makes sense, create a mathematical model that represents relationships in the data, and provide clear explanations of their thought processes, the students will have reached the learning targets for this resource.
Student responses exhibiting achievement could include:
 A wellformulated explanation of their method
 An organized set of data
 An accurate graphical representation of the data they collect
 If students choose to revise their method, they should provide a clear explanation of why their original method needed to be improved or changed, as well as describe their revision process.

Learning Objectives
Students will:
 Recommend a solution and solution method clearly to the client.
 Create equations in two or more variables.
 Formulate an explicit expression from the data.
 Present information, findings, and supportive evidence in a clear, logical manner.
 Maintain a formal style and objective tone while addressing the problem.

Prior Knowledge
Before completing this MEA, students should know:
 How to solve a twostep equation
 How to graph linear functions
 The definitions of these terms: slope, intercept, xaxis, yaxis, f(x), m, b

Instructional Suggestions
The following steps are recommended when implementing this activity:
Individual Component
The individual component allows students to get settled, get oriented to the task and context of the problem, and begin thinking of possible solutions on their own.
 Day 1: Ensure that students have the required prior knowledge; review any concepts as needed. To ensure that students have the knowledgebase to successfully complete this activity (see list of Prior Knowledge), it may be necessary to assess students’ abilities in relation to functions and math modeling. This can be accomplished formatively through class discussion and observation, or diagnostically through preassessment (either in class or assigned as homework). A possible source of assessment is listed in the Formative Assessment section.
 Provide students with the background reading (found in the Supplemental Reading section). Students may read the information individually or it can be displayed on the projector and read through as a class.
 In addition to checking for prior knowledge, it is strongly suggested that the students are given the supplemental reading. This will provide background information on the topic of the MEA, and help them understand the relevancy of the activity to the real world, and usefulness of the mathematics behind it. After students have completed the readings (either as homework or as a class, if more control is desired by the teacher), guide a class discussion addressing questions regarding the readings.
 Distribute the first letter to the students and the first data set (reading passage 1 and data set 1).
 Allow students time to individually read the letter and the information in the data set.
 Use the Readiness Questions with the class to ensure students understand the task. If the students are not very familiar with MEA’s, it may be advantageous to read through Reading Passage 1 as a class, and discuss the Readiness Questions together to make sure all students are in agreement regarding the goals of the activity.
 Go over any new or confusing terminology with students. Explain to students the importance of clearly communicating in their letters to the client when describing their decisionmaking process and providing evidence for their decisions.
 Have the students work individually to brainstorm about the different ways they can address the client's needs. Each student needs to come up with one solution to the problem that they can share with their team.
Individual to Team Work Transition
When students come together in their groups, they will begin the process of building consensus, including using/understanding key terminology, concepts, and the task (i.e., understanding the client’s needs and using evidence rather than basing their decisions on personal preference).
 Assign the students to work in groups of 3 to 4 to share ideas, come up with a process, and work collaboratively on their solution.
 If students are new to working in groups, you may choose to provide a group work rubric, establish norms, and assign roles.
 In their groups, students will share the solution that they chose individually. As a group, they must then decide which components of each student’s solution to use as their group solution.
 The teacher will facilitate each group’s sharing of ideas, coming up with a process to solve the client’s problem, and working collaboratively on their solution.
 Ensure that each team develops a procedure (e.g., their stepbystep method of how they arrived at their solution). The students must include an explanation/justification for each decision. The students must explain and show the work for any math they used.
 Walk around the classroom and observe how the students are working on the assignment.
 Use the Guiding/Reflective Questions and provide any necessary feedback.
 As students collaborate on the MEA, it is important for the teacher to monitor their progress and thought processes, not only to ensure they stay on task, but to encourage higherlevel problemsolving strategies. A teacher can encourage such thought processes by asking the groups questions that require them to explain or rationalize an idea or method. Potential teacher questions are listed in the Guiding/Reflective Questions section. Also, when students are creating and comparing models, it may be helpful to supply them with graph paper.
 Once the students are ready they need to write a letter back to the client including a detailed explanation of the selection process they designed and supporting reasons/documentation. You may choose to have students write a group letter, or each student can individually write a letter back to the client to explain the procedure and solution that their team developed. Having students individually write the letter is useful for assigning a grade for the writing standard.
 Day 2: Students finish writing their letters as needed.
 Students receive the second letter with the additional data set which applies a twist to the original problem.
 Again, allow students to brainstorm individually before they get back into their groups to share their ideas.
 Teams test, evaluate, and revise their first procedure to make the adjustments necessary to proceed with the second part of the task.
 Walk around the classroom and observe how the students are working on the assignment. Use the Guiding/Reflective Questions and Reflection Questions 2 and provide any necessary feedback.
 Students write a second letter back to the client explaining whether their solution is different or remained the same as the first one and why. They should also explain their new process and provide supporting documentation/reason.
 After the MEA has been completed, it is suggested that each student group presents their work to their classmates. In doing so, students may gain additional insight into alternative problemsolving techniques. These presentations create the opportunity for class discussion on the validity of different groups’ methods, and can serve as a meaningful wrapup to the MEA.
 For further assessment see the Summative Assessment section.

Supplemental Reading
**These sites contain ads. For the first article, the teacher should click on the "print this" link to display the information or print it out for students adfree. For the second article, the teacher should copy/paste the text into a word document for printing or display.
Informational Text 1
Lexile: 1120L
Why does that popcorn cost so much?
http://money.cnn.com/2002/03/08/smbusiness/q_movies/
Citation: Lobb, Annelena (2002, March). Why does that popcorn cost so much? CNN Money: Small Business. Retrieved online from: http://money.cnn.com/2002/03/08/smbusiness/q_movies/
Summary: The cost of running a movie theater involves the price of the building (either building it or leasing a preexisting structure), utilities, film technology/equipment and maintenance, the cost of leasing films to show, and of course employees’ salaries. All of these expenses impact the cost of how much movie goers pay for the movie theater experience – this includes ticket and concession prices.
Discussion Questions: What factors might be important to think about when managing a movie theater? What can theater owners do to make up for having to pay so much to film studios? The article contains the quote, “If you didn’t have concessions at a movie theater, there would be no movie theater.” Do you agree with this statement? Explain why or why not. Is there a reason why snacks at movie theaters are so expensive? Explain.
Informational Text 2
Lexile: 1150L
The Economics of Movie Theaters
http://onwardstate.com/2011/02/04/theeconomicsofmovietheaters/
Citation: Johnson, Nick (2011, February). The Economics of Movie Theaters. Onward State. Retrieved online from: http://onwardstate.com/2011/02/04/theeconomicsofmovietheaters/
Summary: In a college town of about 40,000 students, a movie theater has been forced to close its doors due to lack of profit. Even though adolescents and young adults are the biggest target in the movie market, the lack of concession sales ultimately led to the demise of the theater. The hesitancy in building a new theater shows skepticism in how successful it will be.
Discussion Questions: What is to prevent this new theater from meeting the same fate as its predecessor? If concessions are the main source of profit for the movie theaters, but the prices of the snacks are the bane of movie patrons, how is repetition of this cycle to be avoided? Do you think the new movie theater will be successful? Why or why not? Explain what it would take for the business to make enough profit. Why did the original movie theater have to close?

Guiding/reflective Questions
 Do you think this graph accurately models the data? What information does the model not take into account?
 How could you improve this model? Why do you think so?
 Did your initial prediction prove to be true? Why or why not? What changes must you make?
 Do you agree with this groups’ model? Why or why not?
 Why do you think that?
 How do you know if you have an answer to the problem?
 Would your solution work in a different situation?
 What are the most important things to consider in your procedure?
 What are the strengths and weaknesses of each?

Reading Passage 1

Readiness Questions
 Who is the client in this problem? (Deja View)
 Why does the client need help with? (determining a ranking system for selecting the best movie)
 What does the client want to know? (which movie they should select for a theater)
 What do you think will be difficult about solving this problem for the client? (answers may vary)

Data Set 1

Letter Template 1
The activity sheet can be used to get students started in figuring out which categories to prioritize.
The letter template should only be used as a writing accommodation as needed.
Movie_theater__Letter_Template_1.docx

Comprehension/readiness questions
These questions can be posed during and after students work on the problem.
 What part(s) of the data table do you believe are the most important when considering potential profit? Why do you think so?
 What part(s) of the data table do you believe are the least important when considering potential profit? Why do you think so?
 Are you noticing any patterns between any of the table values? If so, what are they? (Cost of production/budget of the film and studio/theater ticket profits?)
 Do any of the table values surprise you? Why did you expect that? Can you think of any realworld explanations?
 Which movie does your group think will bring the theater the greatest profit? What factors led to your decision?
 Which movie do you think will bring the theater the lowest profit? What factors make you think so?
 How will you go about creating an equation/model for the data? What variables will you use?
 If the studio gets a higher percentage of ticket profits, how will this impact concessions sales?

Reading Passage 2

Data Set 2

Letter Template 2
Movie_theater__Letter_Template_2.docx
Letter templates should be used only as accommodations as needed.

Reflection question 2
Did your procedure change after the new data? Why or why not?
Assessment
 Feedback to Students:
Students should receive feedback about their performance throughout the MEA. The teacher should walk around the classroom, listening to group discussions about the presented problem, and ask students to explain their thought processes and problemsolving strategies. If students should run into roadblocks in the activity, it is important for the teacher not to simply suggest the correct answer or strategy. Rather, the teacher should ask students to clarify what outcome they are trying to achieve, and ask questions that will guide them towards that desired outcome. Students can then use this feedback to evaluate their thought processes and make adjustment where necessary to improve their performance.  Summative Assessment:
At the end of this activity, students should understand that math can be used to model realworld problems (such as creating a business plan). The degree of this achievement will be evident in the written responses students create during the activity. If students are able to interpret the data provided to them in an organized manner that makes sense, create a mathematical model that represents relationships in the data, and provide clear explanations of their thought processes, the students will have reached the learning targets for this resource.Student responses exhibiting achievement could include:
 A wellformulated explanation of their method
 An organized set of data
 An accurate graphical representation of the data they collect
 If students choose to revise their method, they should provide a clear explanation of why their original method needed to be improved or changed, as well as describe their revision process.
Accommodations & Recommendations
Accommodations:
 Letter templates can be used as writing accommodations.
 Parts of the MEA can be completed together as a whole class activity.
Extensions:
 A possible extension for this lesson would be discussing how to choose the best way to model a set of data (exponentially, linearly, logarithmically, as a polynomial, or a power).
 Another possible extension would be compositions of functions, if the function of decrease of studio profit on tickets were given.

Suggested Technology: Basic Calculators, Microsoft Office Special Materials Needed:
Excel may be a helpful tool in checking correctness of models.
Additional Information/Instructions
By Author/SubmitterMAFS.K12.MP.1 Make sense of problems and persevere in solving them.
MAFS.K12.MP.3 Construct viable arguments and critique the reasoning of others.
MAFS.K12.MP.4 Model with mathematics.
Source and Access Information
Aligned Standards
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