Model-Eliciting Activities (MEAs) - The UTeach Institute

Adem Ekmekci & Gladys Krause 

UTeach Institute - NMSI Annual Conference 

Austin, TX / May 24 – 26, 2011 

Model-Eliciting Activities (MEAs) 

5 th Annual UTeach Institute-NMSI Conference 

Thursday, May 26, 2011 

Adem Ekmekci 

Science & Mathematics Education/ 

The UTeach Institute 

The University of Texas at Austin 

ekmekci@mail.utexas.edu 

& 

Gladys Krause 

Science and Mathematics Education 


gladyshrueda@gmail.com 

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Austin, TX / May 24 – 26, 2011 


Agenda 

• Group Work: Solve an MEA in Groups 

• What are MEAs? 

• Designing MEAs 

• Questions and Comments 

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Austin, TX / May 24 – 26, 2011 


Group Work 

• Toolbox! 

• In groups of 3-4 

• Solve the problem ~30 min. 

• Present solutions and discuss ~10-15 min. 

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Austin, TX / May 24 – 26, 2011 

The Team Ranking 

Problem 

Summer Jobs Problem 

Carmona & Greenstein (2010). 

Investigating the Relationship 

Between the Problem and the 

Solver: Who Decides What Math 

Gets Used? In R. Lesh et al. (eds.), 

Modeling Students’ Mathematical 

Modeling Competencies. 

Case Studies for Kids 

Purdue University 

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Austin, TX / May 24 – 26, 2011 


What are MEAs? 

• Thought-revealing activities that elicit students’ 

mathematical and scientific knowledge (Lesh, 1999; 

Lesh & Doerr, 2003; and others), 

• Complex problem solving situation for students that 

incorporate the development of a mathematical or 

scientific model to describe a real-life situation, 

• Encourages students to describe, revise, and refine 

their mathematical and/or scientific ideas, 

• Encourages the use of representational media to 

explain and document students’ conceptual systems, 

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Austin, TX / May 24 – 26, 2011 



• Designed for small groups (3-4 people), 

• Similar to a Case Study version for Kids, 

• Introduce a problem related to a real life situation, 

- The context can be given in an introductory 

newspaper article - 

• Their solution is a model describing a mathematical 

or scientific situation, 

• They allow for multiple solutions. 

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Austin, TX / May 24 – 26, 2011 


MEAs are designed to be: 

• Purposeful 

• Meaningful 


And… 

• Elicit knowledge (models) 

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Austin, TX / May 24 – 26, 2011 



• Students’ different approaches to solving the problem 

are valued and recognized 

• Extending the notion of what it means to do 

mathematics and science extends the number of 

students who are capable of doing math and science 

• The group becomes greater than the sum of its parts 

• Diversity is seen as an asset that engages and 

promotes learning 

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Austin, TX / May 24 – 26, 2011 

Designing MEAs 

6 Principles 

The Reality Principle 

The Simple Prototype Principle 

The Model Construction Principle 

The Model-Documentation Principle 

The Model Generalizibility Principle 

The Self-Evaluation Principle 

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Austin, TX / May 24 – 26, 2011 


The Reality Principle 

(Personal Meaningful Principle ) 

• Could this really happen in a “real life” situation? 

• Will students be encouraged to make sense of the situation 

based on extensions of their own personal knowledge and 

experiences? 

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Austin, TX / May 24 – 26, 2011 


The Simple Prototype 

Principle 

• Is the situation as simple as possible, while still 

creating the need for a significant model? 

• Will the solution provide a useful prototype (or 

metaphor) for interpreting a variety of other 

structurally similar situations? 

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Austin, TX / May 24 – 26, 2011 


The Model Construction 

Principle 

• Does the task create the need for a model to be 

constructed, modified, extended, or redefined? 

• Does the task involve constructing, explaining, 

manipulating, predicting or controlling a structurally 

interesting system? 

• Is attention focused on underlying patterns & 

regularities rather than on surface-level 

characteristics? 

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Austin, TX / May 24 – 26, 2011 


The Model Documentation 

Principle 

• Will the response require students to explicitly reveal 

how they are thinking about the situation (givens, 

goals, possible solution paths)? 

• What kind of system (mathematical objects, relations, 

operations, patterns, regularities) are they thinking 

about? 

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Austin, TX / May 24 – 26, 2011 


The Model Generalization 

Principle 

• How shareable and reusable is the model developed 

by the students? Does it only apply to the particular 

problem, or can it be reused in other situations? 

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Austin, TX / May 24 – 26, 2011 


The Self-Evaluation 

Principle 

• Will the students be able to determine the usefulness 

of alternative responses? 

• Will students be able to determine when their 

responses are good enough? 

• Why does the client need the students’ result? For 

what purposes? Under which circumstances? 

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Austin, TX / May 24 – 26, 2011 

Multi-tier Design of thought revealing 

activities that promote research, 

teaching, and learning 

(Based on Lesh & Kelly, 1999) 

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Austin, TX / May 24 – 26, 2011 

Modeling Cycles in MEAs 

Example: Historic Hotels MEA 

Problem: 

There is a client who inherited a historic hotel and does 

not have management skills. He wants to determine the 

rate per room where he was told by the previous owner 

that all of 80 rooms are occupied when the daily rate is 

$60 per room; the rate per room increases by $1 for every 

vacant room; and each occupied room has a $4 cost for 

service and maintenance. 

(Based on Aliprantis & Carmona, 2003) 

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Austin, TX / May 24 – 26, 2011 

Modeling Cycles in MEAs 

Example: Historic Hotels MEA 

These are the most common testing 

-revising cycles emerged from 

students’ solution process of the 

Historic Hotels problem. 

(Based on Ekmekci & Dominguez, 2007) 

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Austin, TX / May 24 – 26, 2011 


• QUESTIONS... 

• COMMENTS... 



gladyshrueda@gmail.com 


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Austin, TX / May 24 – 26, 2011 

References 

Aliprantis, C.D. & Carmona, G. (2003). Introduction to an economic 

problem: A Models and Modeling Perspective. In R. Lesh & H. Doerr 

(Eds.), Beyond constructivism: Models and modeling perspectives on 

mathematics problem solving, learning, and teaching (pp. 255-264). 

Mahwah, NJ: Erlbaum. 

Carmona, G. & Greenstein, S. (2010). Investigating the Relationship 

Between the Problem and the Solver: Who Decides What Math Gets 

Used? In R. Lesh et al. (eds.), Modeling Students’ Mathematical 

Modeling Competencies, DOI 10.1007/978-1-4419-0561-1_21, C 

Springer Science+Business Media, LLC 2010. 

Ekmekci, A. and Dominguez, A. (2007, Oct) "College Level Students’ 

Reasoning of an Optimization Problem: Historic Hotel MEA (Model 

-Eliciting Activity)" Paper presented at the annual meeting of the North 

American Chapter of the International Group for the Psychology of 

Mathematics Education, University of Nevada, Reno, Reno, Nevada 

Retrieved from http://www.allacademic.com/met/p201387_index.html 

Publication Type: Poster 

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Austin, TX / May 24 – 26, 2011 

References 

Lesh, R. & Doerr H. M. (Eds.), 2003. Beyond Constructivism. Manwah, 

NJ: Lawrence Erlbaum Associates. 

Lesh, R., Hoover, M., Hole, B., Kelly, A. E., & Post, T. (2000). Principles 

for developing thought-revealing activities for students and teachers. In 

A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in 

mathematics and science education (pp. 591-646). Mahwah, NJ: 

Lawrence Erlbaum Associates, Inc. 

21

Adem Ekmekci & Gladys Krause HANDOUTS UTeach Institute - NMSI Annual Conference 

Austin, TX / May 24 – 26, 2011 

College Level Students’ Reasoning of an Optimization Problem: 

Historic Hotel MEA (Model-Eliciting Activity) 

Adem Ekmekci 

University of Texas at Austin 


Angeles Domínguez 

Instituto Tecnologico de Estudios 

Superiores de Monterrey 

angeles.dominguez@itesm.mx 

Model-eliciting activities (MEAs) are based on real-life situations where students, 

working in small groups, present a mathematical model as a solution to a client’s need 

(Zawojewski and Carmona, 2001). The problem of Historic Hotels is an MEA in which 

students are asked to develop a mathematical model to maximize profit that can be 

calculated with a quadratic equation. In the problem, there is a client who inherited a 

historic hotel and does not have management skills. He wants to determine the rate per 

room where he was told by the previous owner that all of 80 rooms are occupied when 

the daily rate is $60 per room; the rate per room increases by $1 for every vacant room; 

and each occupied room has a $4 cost for service and maintenance. The problem can be 

solved by using quadratic formulas, 1 st and 2 nd derivative method, or simply looking at 

the profit for each value. In this study, college level students are asked to solve this 

optimization problem to see possible their ways of solution to the problem. Two groups 

of students were given this non-traditional problem. The first group was a calculus class 

where the majority of students were engineering major and the second one was an 

education course required for teaching certification where students were either science or 

math major. There were 23 groups of 3 in calculus class and 11 groups of 3 in the other. 

After the problem was solved in groups, students were asked to present their 

models to their class-mates. Discussions about different solutions were done after each 

presentation. Authors and their colleagues observed students and took field notes while 

students were working on the problem and discussing their results afterwards. This 

particular type of MEA made students’ thinking about optimization as a mathematical 

concept visible to both their peers and teachers. Formative assessment (Black & William, 

1998) cycles that students went through appeared in the problem solving process. 

Students’ final works are analyzed in terms of the function they used, variables and their 

definitions, graphical representations, and generalizations. 

Analysis of solutions of both groups to the problem and observations by authors 

and their colleagues will be reported in the poster. In addition, math major students’ and 

pre-service teachers’ ways of thinking will be discussed. Following questions will also be 

touched upon in the poster: 

- How much calculus knowledge do college level students associate with solving an 

optimization problem? 

- In what ways, did college level students model the maximization of profit in the 

given context? 

- What symbols and tool did students use in solving the problem? 

- Were there any differences in the method used between calculus students and 

students in teacher certification program? 

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Austin, TX / May 24 – 26, 2011 

References 

Aliprantis, C.D. & Carmona, G. (2003). Introduction to an economic problem: A Models 

and Modeling Perspective. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models 

and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 

255-264). Mahwah, NJ: Erlbaum. 

Black, P. & Wiliam, D. (1998). Inside the black box: raising standards through classroom 

assessment. Phi Delta Kappan, October 1998, 139-148. 

Dominguez, A. (2007). Single solution, multiple perspectives. Proceedings of thirteenth 

annual meeting of The International Community of Teachers of Mathematical Modeling 

and Applications (ICTMA). Bloomington, IN. 

Lesh, R., Hoover, M., Hole, B., Kelly, E., & Post, T. (2000). Principles for developing 

thought revealing activities for students and teachers. In A. E. Kelly & R. A. Lesh (Eds.), 

Handbook of research design in mathematics and science education (pp. 591-645). 

Mahaway, NJ: Lawrence Erlbaum. 

Zawojewski, J., & Carmona, G. (2001). A developmental and social perspective on 

problem solving strategies. In R. Speiser & C. Walter (Eds.), Proceedings of the twentythird 

annual meeting of the north American chapter of the international group for the 

psychology of mathematicseducation. 

Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental 

Education. 

Citation for this proceeding: 

Ekmekci, A. and Dominguez, A. (2007, Oct) "College Level Students’ Reasoning of an 

Optimization Problem: Historic Hotel MEA (Model-Eliciting Activity)" Paper presented at the 

annual meeting of the North American Chapter of the International Group for the Psychology of 

Mathematics Education, University of Nevada, Reno, Reno, Nevada Online Retrieved 

2008-09-04 from http://www.allacademic.com/meta/p201387_index.html 

Publication Type: Poster 

2

  


  

  

College Students’ Reasoning in an  

Optimization Problem  

INTRODUCTION 

Model-eliciting activities (MEAs) present a problem based on 

real-life situations to be solved by students in small groups (Lesh et. 

al., 2000; Zawojewski & Carmona, 2001). The activity used in this 

study, the Historic Hotel Problem designed by Aliprantis and 

Carmona (2003), is a model-eliciting activity with single numerical 

answer with multiple solutions (Dominguez, 2007). Through MEAs 

students’ ways of thinking, as they work on the problem, become 

visible to the teacher as well as to their peers (Lesh et. al., 2000). In 

that sense, MEAs are thought-revealing activities in which students 

express their initial ideas and revise them according to feedback they 

get from their peers. 

SIGNIFICANCE 

Classroom practices play a crucial role in efforts to improve 

student learning. One of the most important steps for teachers to 

accomplish this goal is to know what their students know. Black & 

William (1998) defined classroom assessment as the activities 

undertaken by teachers and students to provide information about 

how students think and what they know. MEAs can be used and be 

very beneficial as a non-traditional way of classroom assessment. 

MEAs usually start with a newspaper article that warms student to 

problem statement. Readiness questions related to the article make 

us sure that all students are ready to the problem. Finally, problem 

statement emphasizes the need of a model rather than just a numeric 

answer. As the output of MEAs, attention should be paid to the 

model students develop rather than the numerical answer. That is, 

descriptions, explanations, constructions, and the math student use 

(Lesh et. al., 2000) in their models are more important than their 

single-numerical answer to the problem. 

PARTICIPANTS & THE ACTIVITY 

This study is an extended version of an earlier study conducted by 

Dominguez (2007) with an addition of 30 pre-service science and 

math teachers (10 groups of 3) to 94 calculus students (23 groups of 

4 or 5) at a university in central Texas. The activity was done in two 

episodes, 50-60 minutes each. In the first episode, students read the 

newspaper article and answered the readiness questions as a class. 

Then, they worked on the problem in groups. 

In the second episode, students completed their letters and each 

group presented their models to other groups and discussed their 

ways of solving. 

PROBLEM STATEMENT 

Mr. Frank Graham has just inherited a historic hotel with 80 

rooms. He is told that all of the rooms were occupied when the 

daily rate was $60 per room and, for every dollar increase in the 

daily rate, one less room is rented (if the daily rate was $61, 79 

rooms would be occupied). Each occupied room has a $4 cost for 

service and maintenance per day. Mr. Graham would like to know 

how much he should charge per room in order to maximize his 

profit, what his profit would be at that rate, and a procedure for 

finding the daily rate that would maximize his profit in the future 

even if the hotel prices and the maintenance costs change. 

THE PURPOSE OF THE STUDY 

We focused on the following questions: 

• What different models and optimization strategies were there? 

• How many college level students incorporated calculus 

knowledge and at what level? 

• Were there any difference in solution ways of calculus 

students and pre-service math and science teachers? 

• Were there any particular testing and revising cycles students 

went through? 

DATA COLLECTION 

All of students’ written work was analyzed and field notes were 

taken by researchers during the solution process. 

Strategy  

SINGLE ANSWER – MULTIPLE 

PERSPECTIVES 

Calculus groups  

(n=23)  

Adem Ekmekci  

Department of Science & Mathematics Education  

University of Texas at Austin  

Pre‐service Teacher  

Groups (n=10)  

Derivative  24  5  

Table  1  1  

Graph  1  1  

Vertex formula  1  1  

Historic Hotel MEA (Model‐Eliciting Activity)  

Total  27*  8**  

*3 groups gave 2 solutions and 1 group used a different strategy to verify. 

**The optimization strategy of 2 groups could not be identified. 

All calculus groups used derivative strategy, whereas 5 out of 8 

of pre-service teacher groups favored that method. 

n  

x  

y  

r  

&  

Austin, TX / May 24 – 26, 2011 

Angeles Domínguez  

Instituto Tecnologico de Estudios  

Superiores de Monterrey  

Functions and Variables in Students’ Solutions 

Definition of    

variables  

Modeling Function  

# of vacant    P(n) = (80 ‐ n)(56 + n)  

rooms    P(r) = (80 ‐ r)(56 + r)  

# of occupied    P = x y ‐ 4 x  &  y = 140 ‐ x  

rooms    P(x) = x (140 ‐ x) ‐ 4 x  

Daily rate     P = x y ‐ 4 x & x = 140 ‐ y  

per room    P(y) = y (140 ‐ y) ‐ 4 (140 ‐ y)  

Amount raise     P(y) = (80 ‐ (y ‐ 60)) (y – 4)  

in daily rate     P(y) = (y – 4) (140 ‐ y)  

Calculus  

Students  

  

Pre‐service  

Teachers  

20  5  

2  4  

2  2  

2  0  

      Total  26*  11**  

*Three teams gave two solutions  

** One team gave two solutions  

  

Test-Revise Cycles 

These are the most common testingrevising 

cycles emerged from students’ 

solution process of the problem. The most 

common pattern was I – II – III. A few 

groups went through all cycles and very 

few groups did not use III at all: they went 

through I – II – IV. These were all preservice 

teachers 

CONCLUSIONS 

Although it seems like there is one single-numerical answer to the 

Historic Hotel Problem, students used 4 different strategies for 

optimization. Moreover, the modeling functions students developed can 

be classified into four groups. From students’ written work, it was 

possible to see that there are multiple pathways to find a singlenumerical 

answer. Observing students during the modeling process 

made it possible to see how they went through various modeling cycles 

(Lesh et. al., 2000) to develop their models. Calculus students were 

more likely to use derivative strategy than pre-service teachers, as 

expected. 

REFERENCES: 

Aliprantis, C.D. & Carmona, G. (2003). Introduction to an economic problem: A Models and Modeling Perspective. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 255-264). Mahwah, NJ: Erlbaum. 

Black, P. & Wiliam, D. (1998). Inside the black box: raising standards through classroom assessment. Phi Delta Kappan, October 1998, 139-148. 

Dominguez, A. (2007). Single solution, multiple perspectives. Proceedings of thirteenth annual meeting of The International Community of Teachers of Mathematical Modeling and Applications (ICTMA). Bloomington, IN. 

Lesh, R., Hoover, M., Hole, B., Kelly, E., & Post, T. (2000). Principles for developing thought revealing activities for students and teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591-645). Mahaway, NJ: Lawrence Erlbaum. 

Zawojewski, J., & Carmona, G. (2001). A developmental and social perspective on problem solving strategies. In R. Speiser & C. Walter (Eds.), Proceedings of the twenty-third annual meeting of the north American chapter of the international group for the psychology of mathematicseducation. 

Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education. 

3


Austin, TX / May 24 – 26, 2011 

Summer Jobs Case Study 1 

Newspaper Article: Heat Is on for Summertime Jobs. 

Saturday is the Meers Middle School’s annual job fair, organized by the Youth Action 

Club. The fair gives students an early start to plan how they will earn money during the 

summer. 

It also honors innovative work efforts. This year’s Earnest Earner award went to 

seventh-grader Tyrone Wakes. His Kids on the Run service provided mail pickup, errand 

running, and pet walking for residents in his apartment complex. 

“Summer jobs are big business,” claims Randy Tye, President of Youth Action. “Our 

fair gives ideas about the kinds of jobs kids can get and the money they can earn. We 

will hand out information on pay rates for different jobs and advice on ‘talking money’ 

with employers.” 

The fair will show how to track down hard-to-get jobs. Student Greg Maby reports, 

“The basic idea is to go after the jobs. Don’t wait for them to come to you. It’s up to 

kids to show what they can do. We’ll give money-making tips, like how to win babysitting 

jobs by getting to know young children in the neighborhood.” 

Students Jack Elliot drums up yard work by mowing his own lawn early on Saturday 

mornings. “Wake up and smell the grass clippings! Is my motto. When people see the 

job I do on my parents’ lawn, they often ask me to do theirs.” Showing off your skills is 

a good way to attract business. 

Visitors to the fair can take a lesson on washing cars for fun and profit. Prices for 

commercial car washes are high enough hat young people can compete for the business. 

Tye says, “Most adults don’t care who washes their car. If you provide services as good 

as others but at a better price, you’ll get the job.” 

A profit-making venture often overlooked is services for the elderly. As life 

expectancy increases, people live longer, and they can use different kinds of help. Senior 

citizens often need help shopping, clearning hourse, or doing yard work. Households 

with infirm elderly may need someone to visit with then, so that family members can take 

a break. 

Jenny Crisp says, “Believe it or not, my baby-sitting job is with my next-door 

neighbor’s grandmother. She has Alzheimer’s disease. We read stories together. 

Sometimes I play my flute. We have a good time and I also get paid. I’m going into 

medical research when I grow up. I’d like to find a cure for Alzheimer’s.” 

Today’s students use brochures to get summer jobs. Teacher Helen Soleski says, “Our 

computer lab has software for designing flyers that advertise job skills and experience. 

Some students design resumes giving potential employers information about their 

training and previous work experience.” 

Eighth-grader Justin Shar says, “My resume tells about the baby-sitting I’ve done in 

the past, my class in first aid, and my advanced swimmer’s certificate. I listed references 

with names and phone numbers of people I worked for. They gave me such good 

recommendations that I got five job offers.” 

Sixth-grader Marsha Turi advises, “Don’t give up. Last year I made flyers, went doorto-door, 

and advertised on bulletin boards. I must have asked a hundred people for work. 

I got ninety-nine no’s and one very good job that lasted all summer. By September, I had 

put $350 in the bank. I did such a good job that I expect to get the job again next 

summer.” 

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Austin, TX / May 24 – 26, 2011 


Typical Pay for Student Summer Jobs 

Washing Cars 

Own Parents 

Others 

$2/car MEDIAN $4/car 

$2 to $5 LOW/HIGH $3 to $6 

Lawn Mowing 

Own Parents 

Others 

$5/lawn MEDIAN $10/car 

$3 to $10 LOW/HIGH $5 to $15 

Paper Routes 

MEDIAN 

$12.50/week 

LOW/HIGH $7 to $25 

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Austin, TX / May 24 – 26, 2011 


READINESS QUESTIONS 

1. About how much money might a student earn mowing his or her parent's lawn 

once a week for a month? Be sure to show your calculations below. 

2. About how much might a student earn mowing 10 average-size lawns once a 

week for a month? Show your calculations below. 

3. About how much might a student earn in a month mowing 5 small-size lawns 

once a week and 5 average-size lawns once every two weeks? Show your 

calculations below. 

4. Next summer Jack Elliot wants to do more than just yard work. He plans to mow 

10 yards, get a newspaper route, and wash cars on Saturdays. Jack wants to know 

about how much money he can realistically expect to make during the summer, 

but this depends on many things, such as how often he mows a lawn or how big 

the lawn is. 

Estimate what his earnings might be and list the assumptions you make. Give at 

least 5 of your assumptions. 

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Austin, TX / May 24 – 26, 2011 


Last summer Maya started a concession business at Wild Days Amusement Park. Her 

vendors carry popcorn and drinks around the park, selling wherever they can find 

customers. Maya needs your help deciding which workers to rehire next summer. 

Last year Maya had nine vendors. This summer, she can have only six – three full-time 

and three half-time. She wants to rehire the vendors who will make the most money for 

her. She doesn’t know how to compare them because they worked different numbers of 

hours. Also, when they worked makes a big difference. After all, it is easier to sell more 

on a crowded Friday night than a rainy afternoon. 

Maya reviewed her records from last year. For each vendor, she totaled the number of 

hours worked and the money collected – when business in the park was busy (high 

attendance), steady (medium attendance), and slow (low attendance). (See the tables.) 

Please evaluate how well the different vendors did last year for the business and decide 

which three she should rehire full-time and which three she should rehire half-time. 

Write a letter to Maya giving your results. In your letter describe how you evaluated the 

vendors. Give details so Maya can check your work, and give a clear explanation so she 

can decide whether your method is a good one for her to use. 

7


Austin, TX / May 24 – 26, 2011 


HOURS WORKED LAST SUMMER 

June July August 

Busy Steady Slow Busy Steady Slow Busy Steady Slow 

MARIA 12.5 15 9 10 14 17.5 12.5 33.5 35 

KIM 5.5 22 15.5 53.5 40 15.5 50 14 23.5 

TERRY 12 17 14.5 20 25 21.5 19.5 20.5 24.5 

JOSE 19.5 30.5 34 20 31 14 22 19.5 36 

CHAD 19.5 26 0 36 15.5 27 30 24 4.5 

CHERI 13 4.5 12 33.5 37.5 6.5 16 24 16.5 

ROBIN 26.5 43.5 27 67 26 3 41.5 58 5.5 

TONY 7.5 16 25 16 45.5 51 7.5 42 84 

WILLY 0 3 4.5 38 17.5 39 37 22 12 

MONEY COLLECTED LAST SUMMER 

June July August 

Busy Steady Slow Busy Steady Slow Busy Steady Slow 

MARIA 690 780 452 699 758 835 788 1732 1462 

KIM 474 874 406 4612 2032 477 4500 834 712 

TERRY 1047 667 284 1389 804 450 1062 806 491 

JOSE 1263 1188 765 1584 1668 449 1822 1276 1358 

CHAD 1264 1172 0 2477 681 548 1923 1130 89 

CHERI 1115 278 574 2972 2399 231 1322 1594 577 

ROBIN 2253 1702 610 4470 993 75 2754 2327 87 

TONY 550 903 928 1296 2360 2610 615 2184 2518 

WILLY 0 125 64 3073 767 768 3005 1253 253 

Figures are given for times when park attendance was high (busy), medium (steady), and low (slow). 

8


Austin, TX / May 24 – 26, 2011 

THE TEAM RANKING PROBLEM 

Each point in the figure below represents the win-loss record of 

each of the twelve elementary school soccer teams in Flat Mountain 

School District. 

READINESS QUESTIONS 

1. Which team(s) won the most games? How do you know? 

2. Which team(s) lost the most games? How do you know? 

3. Did all teams play the same number of games? How do you know? 

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Austin, TX / May 24 – 26, 2011 

THE PROBLEM 

Your task is to develop a method for determining which of the 

twelve teams wins the first, second, third, fourth, and fifth place trophies. 

Make sure you explain very clearly why the teams should be ranked this 

way, so that the kids on all the teams will understand that your system is 

fair. 

There are twelve teams in the Flat Mountain School District, but 

many, many more in the whole state! At the end of the season, the state 

soccer officials will need to find the top five teams for the state. Write 

a letter to the soccer officials where you explain how your system works 

and why it is fair. Make sure the officials will understand how to use your 

ranking system for any number of teams. 

10


Austin, TX / May 24 – 26, 2011 

11


Austin, TX / May 24 – 26, 2011 

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Austin, TX / May 24 – 26, 2011 

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Austin, TX / May 24 – 26, 2011 

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Austin, TX / May 24 – 26, 2011 

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Austin, TX / May 24 – 26, 2011 

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Model-Eliciting Activities (MEAs) - The UTeach Institute

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