
Lesson Plan Template:
Model Eliciting Activity (MEA)

Formative Assessment
Formative assessment questions to assess students' prior knowledge (these questions should be asked in combination with the comprehension/readiness questions after the data set 1 is presented to the students)
 What is the definition of rate? It is the ratio between two different units of measurement; for example 145m/3h (which is read as 145 miles traveled in 3 hours)
 What is the definition of unit rate? It is a rate in which the denominator is equal to one; for example $3.99/gallon (which means that you will pay $3.99 for a gallon of milk or gas depending on the content of the problem).
 Give an example in which you can use a unit rate to solve a problem. How many gallons of milk can I buy if I have only $20? How many miles can you travel in 4 hours if your speed is 45m/h?
 When knowing the rate, how can you find the unit rate? Remember that a rate is a fraction and a unit rate is a fraction that has 1 as a denominator so to find the unit rate you need to divide the numerator and the denominator by the denominator. Using the first example, 145m/3h then divide 145 by 3 and 3 by 3 so the answer will be around 27.6m/h (unit rate).
 What is a conversion factor? It is a rate or unit rate that you use to convert from a given unit of measurement to another, for example the following conversion factor 0.3048m/ft can help you convert length from the metric system to the English system and viceversa).
Formative assessment questions to assess students' understanding (these questions should be asked in combination with the comprehension/readiness questions after the data set 1 is presented to the students).
 Do you need to use a conversion factor? How could that information help you to solve the problem? Yes, and I can use that to convert the square meters to square feet to find how many people can cover that area.
 Give an example of unit rate that you can find in this problem. How would that be used to solve the problem? $54/day is an example of unit rate and using that information I can calculate the salary expense.

Feedback to Students
Teacher's observation will be crucial in this activity since the purpose is to let the students work by themselves and arrive at their own decisions. As recommended by experts, during a model eliciting activity, teachers will be facilitators. They will intervene when students are not applying the mathematical concepts taught in class or when the process used cannot be justified using logical reasoning. Questions will be answered using other questions that can drive students to think out of the box and place them into the "uncomfortable zone". The main objective of this activity is to "disturb" students so that they can apply their critical thinking abilities and skills.
Examples of feedback questions to redirect students' reasoning
 Look at the answer one more time. Now if you multiply a decimal bigger than one by another smaller than one, what would be a reasonable answer? The answer always will be a decimal smaller than the biggest one for example 14.25 x 0.75, the answer will be a number smaller than 14.25.
 Can you find the number of persons that can cover the area of the design? How? Yes, by knowing the area a person can cover.
 The area a person can cover, what is that called? Why? It is called a unit rate because the denominator is one.
 Analyze what you have done: is that the unit measurement that you are looking for? No, I need square feet and the area is in square meters.

Summative Assessment
A rubric will be used to evaluate students' reports or letters and oral presentations.
Rubric for letter 2. Lilys Cola TV Commercial.xls
Rubric oral presentation. Lilys Cola TV Commercial.xls

Learning Objectives
Students will be able to:
 Analyze informational documentation and look for relevant details.
 Apply the definition of rates and unit rates to solve real world problems.
 Develop a model to solve a realistic problem and test its application to similar problems.
 Create a written explanation of the model using an example to show how it works.

Prior Knowledge
Students should know:
 How to add, subtract, multiply, and divide decimals without using technology.
 How to round decimals to the hundredth place.
 What the definitions of rate and unit rate are.

Instructional Suggestions
 Give students 5 to 10 minutes (depending on their reading levels: you can anticipate that by looking at the data from the district) to read the supplemental article and answer the text dependent questions.
 Discuss the answers with the students and use the content as a preamble to introduce the activity (if it is the first time the teacher is implementing this design, explain expectations clearly).
 Divide the class in groups of three (arrange the groups taking into account students' strengths and weakness as well as any data collected from the school district) and pass around the first letter.
 Analyze the first letter together with your students (teachers can read it or choose a student to read it) using the readiness questions to make sure students understand the assignment. (*show the illustration so that students can have an idea of what the customer is looking for)
 Walk around the classroom to observe how students are working on the assignment
 Implement the reflection questions to redirect students' logical reasoning and application of mathematical concepts (only if teachers realize students are struggling with the material learned in class before)
 Create a set of disturbing questions related to the reading that can prompt students to think out of the box (make them feel uncomfortable and test their critical thinking skills) *Also can be used for feedback and formative assessment.
 It is the teacher's decision to let students use calculator (*In my case, I did not allow the calculators because I want them to practice the addition, subtraction, multiplication, and division of decimals)
 If computers are available, make students fill in the letter template and save it for the oral presentation. If computers are not available, just give students the letter template to complete it and recreate the same template on the board so they can fill that out during the oral presentation (the oral presentation can be used as a summative assessment)
 After the oral presentations, congratulate students for their hard work and introduce the second letter (twist)
 Follow the same procedure, but this time without the oral presentation.
 Collect the response to the second letter (make sure students have written their names and team number. Teachers can use this as a summative assessment)
* Teachers can select the response letter with the higher scores and display them on the "Well Done" board or around the classroom.

Supplemental Reading
Title : Innovation in Advertising. Cocacola marketer of the year
Summary : In this article marketing and advertising strategies implemented by Cocacola company are discussed and analyzed.
Link to text: Innovation In Advertising  CocaCola  Marketer Of The Year
Lexile level: 11080 L
Citation: DeVault, Gigi. Innovation in Advertising. Coca Coal marketer of the year.
Text dependent questions
 Why do you think that CocaCola company won the Marketer of the year award?
 What were the causes for the overhaul of the marketing and advertising strategies?
 According to the text, what does the word innovative mean?

Guiding/reflective Questions
 Does a bigger area mean a better design? What are other factors you should take into consideration?
 According to your background information, what are the consequences of hiring union extras?
 What are the disadvantages of having a preconceived design before considering the number of extras? How would you change that situation?

Reading Passage 1
Letter 1 Lilys cola TV commercial.docx
Illustration_to_be_used_with_letter_1__Lilys_Cola_TV_Commercial.docx
Dear Client :
Our company is launching a new and innovative advertising campaign. As you may know many of our commercials involve the opening of a can or bottle of soda and we would like to keep that idea because that reflects the spirit of the company. However, this time we want to do something different, remarkable, and BIG. We want to simulate the filling of a glass with our new flavor of soda. But this time we want to use people to represent the liquid going from the bottle to the glass.
The commercial will be shoot from the air so that is why we need a design big enough to be seen from above . In addition, we need to hire people for this project and the number of people required is unknown. Your job is to find the maximum number of people we can employ for this commercial keeping in mind that we only have $45000 to spend in salaries. Furthermore, you will select the design that would be used for the commercial. To communicate your decision, you will write a letter back to us showing:
 The design you have selected with supporting details explaining why that is the one and no other
 The type of extra we need to hire. Remember to justify your selection
 The number of extras we will need for the commercial as well as the amount of money we will expend in salaries. (our budget is only $45000)
If any calculation or computation is needed for your decision, disclose all of them clearly. Be precise and accurate when reporting the final numbers (round decimals to the hundredth place) and keep in mind that the presentation of the project is very important because we need the approbation of the Board of Directors. Also, I would like you to send me the process that you follow to solve this problem. Step by step instructions will work perfectly since I am not very good at solving math problems. Thank you in advance for your help.
Sincerely,
Toni Vazquez
Advertising and Marketing Director
PS: Attached to this letter you can find an illustration that can give you a hint of the area we want to cover with people during the commercial.

Readiness Questions
 What do you need to do?
 According to the first paragraph, what would be the ideal design?
 What are the limitations you have in this problem?
 Do you have enough information to solve the problem? What additional information is needed?

Data Set 1
Data set 1 Lilys cola TV commercial.docx

Letter Template 1
Letter template 1 Lilys Cola TV Commercial.docx
Dear Mr. Vazquez:
After a careful analysis of the data you sent us, we have arrived at the following decision. The design that fits your requirements is ___________________ with an area equal to ________ . We selected that design because:
In addition, below you can find a table with the information you requested from us :
Type of extra 
Number of extras 
Salary expense (*show all calculations) 



Sincerely,
Team #:
Names: _____________________________

Comprehension/readiness questions
 According to the data given, what is the ideal design? Why?
 Do you have enough information to solve the problem?
 How can you find the number of people required for the commercial?

Reading Passage 2
Letter 2 Lilys cola TV commercial.docx
Dear Client:
The board of directors congratulates you for the excellent work and dedication. Your letter was clearly written, so everyone in the audience was able to understand all the steps you follow to arrive at the final decision. However, we have another problem. Yesterday, while the commercial crew was working on your recommended design, I received a call from the human resource department. Our budget did not include the rental expense for the helicopter that is going to be used for the commercial . I was in despair and made some calls to fix this situation, but it was in vain. The company does not have the extra money we need. Consequently, you may need to change your original procedure to select the design and the number of people required for the commercial. Your help in this matter would be greatly appreciated. One more time, I am very sorry for this inconvenience and I hope to hear from you soon.
Sincerely,
Toni Vazquez
Advertising and Marketing Director
PS: helicopter daily rental rate = $ 1000/day

Data Set 2
Students will use data set 1; however, a helicopter daily rental rate will be introduced.

Letter Template 2
Same as letter template 1

Additional Instructions or Materials
 paper, pencils, and erasers
 markers of different colors for the oral presentation (in case computers are not available)
 Calculator (if teachers decide to use it)
 Highlighters (students can use them to analyze their data)
 envelops (if teachers decide to collect the second letter for a grade, envelops can be used to avoid losing them. Highly recommended to ask students to write the team number outside the envelops)

Reflection question 2
 What is the main problem?
 Is your prior decision still viable?
 What are the factor(s) that you will analyze?