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Mathematics Projects that Foster a Critical Look at our World
Using real-life investigations, this seventh grade teacher motivates her students to critically examine the world around them, helping them become quantitatively literate or "numerate."
by Fanny Sosenke, Mathematics Teacher, Indianapolis, Indiana
As a middle school math teacher, I believe my job goes beyond teaching the mathematics skills and concepts that will prepare my students for the next math class. I want to make sure that the curriculum my students are exposed to: "represents significant, powerful mathematics for all students; emphasizes topics that are relevant to students' present and future needs; and emphasizes the full use of such tools as calculators, computers, ... for making sense of and doing mathematics." (Lappan, 1999).
Ultimately, I hope my students will use the math they learn in my class to better understand the world in which they live and work. I designed the following open-ended projects to help attain this goal. In each of them, students need to use mathematics, technology, and critical thinking in real-world situations to analyze data and make decisions.
Students must have some basic spreadsheet skills and know how to navigate the World Wide Web to complete these projects. Some projects require local or toll-free telephone research. I often expand the technology requirements of these projects by sending the assignments to the students in email messages. To evaluate the students' work, I create a rubric for each project; often I ask students to evaluate their own work or the work of their peers. An evaluation sheet for project 1 is included below.
References
Dudley, U. (September/October 1998). Numerology: Comes the Revolution. Skeptical Inquirer 29-31, 59.
Lappan, G. (November 1999). Revitalizing and Refocusing Our Efforts. Journal for Research in Mathematics Education 30, 568-78.
PROJECT 1: Cost of Living Comparisons
Information for this project, listed below, includes a link to the Big Mac Index, Cost of Living Comparisons, and an evaluation rubric.
Your current salary in Indianapolis is $30,000 a year. You are planning to move to a city in another country of your choice. What would your salary have to be in your chosen country to equal $30,000 in US currency? How do the salaries in each country compare with the cost of a newspaper in the respective countries? How do the salaries in each country compare with the cost of a Big Mac? (See The Big Mac Index below.) Can you analyze the differences? What would your salary have to be in your chosen country for you to maintain your current standard of living?
Steps:
- Choose two foreign countries to investigate; you will also need to do research on the United States for comparisons.
- Find out equivalent salaries in the countries using this web site: The Salary Calculator from Homefair.com (www.homefair.com/homefair/cmr/salcalc.html)
- Find out the cost of a newspaper and the cost of a Big Mac in the countries. (While you may have sources to help students find this information on their own, I have compiled data on these costs for several countries. See the Cost of Living Table below.)
- Determine the currency exchange rates for the chosen countries at either of these web sites: www.oanda.com/converter/classic or www.x-rates.com/tables/USD.html
- Create a spreadsheet:
INPUT:
- Country
- Salaries (Note: the web site has the salaries in dollars.)
- Exchange rate
- Price of a newspaper in local currency
- Price of a Big Mac in local currency
OUTPUT:
- Price of a newspaper in dollars for each country.
- Price of a Big Mac in dollars for each country.
- Ratio of your salary in the foreign country to your U.S. salary.
- Ratio of the price of a newspaper in a foreign country to the price of a newspaper in the U.S.
- Ratio of the price of a Big Mac in a foreign country to the price of a Big Mac in the U.S.
- Write a half-page to one-page conclusion based on your results. In the report you will state your opinion on the relationship between salaries and the cost of a newspaper and a Big Mac. Some questions you should answer in your report (but not the only questions you should answer) include:
- Do you think it's cheaper to live in your chosen countries than in the United States?
- Are there differences between the salary, newspaper, and Big Mac ratios?
- Why are there differences between the ratios?
- Does the price of a Big Mac say something about the cost of living in a country? What about the price of a newspaper?
The Big Mac Index
 The Economist has published the Big Mac Index for 13 years. They use the price of a Big Mac around the world to analyze the purchasing power of local currencies and to predict, in a light-hearted way, where particular currencies may be headed. You may wish to do some reading to help students discuss this issue critically. See the articles at www.economist.com/editorial/freeforall/focus/big_mac_index.html
Data for Project 1:
Cost of Living Comparisons
Prices are in the country's currency.
| Country |
Sunday Paper |
Daily Paper |
Big Mac |
| Ireland |
1 |
0.3 |
2.81 |
| England |
1 |
0.3 |
2.43 |
| Costa Rica |
150 |
80 |
600 |
| Spain |
275 |
125 |
375 |
| Canada |
2.01 |
0.66 |
2.99 |
| Thailand |
8 |
8 |
52 |
| Ecuador |
40000 |
40000 |
35860 |
| Germany |
2.5 |
1.3 |
4.95 |
| Israel |
7.8 |
3.6 |
13.9 |
| Australia |
1.7 |
1 |
2.65 |
| Italy |
2500 |
1700 |
4500 |
| Uruguay |
25 |
17 |
40 |
| China |
3.5 |
3.5 |
9.9 |
| France |
6 |
5 |
17.5 |
| U.S.A. |
1.75 |
0.35 |
2.43 |
| Hong Kong |
7 |
7 |
10.2 |
| Mexico |
5 |
10 |
19.9 |
| Japan |
160 |
160 |
294 |
| Chile |
300 |
500 |
1,250 |
| South Africa |
4.9 |
2.3 |
8.6 |
| Netherlands |
- |
2.5 |
5.45 |
| Brazil |
2.5 |
1.25 |
2.9 |
(Data collected by Fanny Sosenke, 1999.)
Evaluation Sheet
Cost of Living Project
Name ____________________________
| Spreadsheet: |
| Spreadsheet includes all required information |
___/10 points |
Data:
Correct data for exchange rates
Correct data for newspaper price in local currency
Correct data for Big Mac price in local currency
Correct data for salaries
|
___/10 points
|
Used correct formulas:
Formula to get newspaper price in dollars
Formula to get Big Mac price in dollars
Ratio of salaries
Ratio of prices of newspaper
Ratio of prices of Big Macs
|
___/20 points |
| Presentation |
___/5 points |
| |
|
Graph: |
| Graphed correct data |
___/10 points |
| Graph presentation |
___/10 points |
| |
| Report: |
| Report draws thoughtful conclusions based on the details
found in the spreadsheet or graph |
___/25 points |
| Report presentation |
___/10 points |
| |
| Total: |
___/100 points |
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PROJECT 2: Choosing a Long-Distance Service
 You just moved to the United States from another country of your choice. You need to get a telephone account with long distance service. Since you miss your family and friends back home, you want to call them often. Your project is to select a long-distance service to go along with your regular local telephone account. The class will need to determine as a whole how often immigrants will be calling home and for how long they will speak each time.
Steps:
- Decide which country you are from.
- Find out how much it costs to have a telephone in Indianapolis for local calls.
- Choose the company that will give you the best deal for long distance calls to your home country. You should conduct research with at least three companies before making your decision.
- Given how often you will be calling home and how long you will be talking, estimate how much money you will be spending on international calls every month.
- Finally, estimate the total cost of having a telephone for a year.
You need to submit:
- A spreadsheet summarizing your results
- A dated log of your research activities in completing this project
- A summary and conclusion based on your findings
- An evaluation of your work.
NOTE: Any decision will be accepted as long as you have a reasonable justification for making that decision.
PROJECT 3: Vacation Planning
 For both parts of this assignment you should present your research results on a spreadsheet.
Part I:
Your family is planning a two-week vacation for a year from now. You may choose among the following destinations: Orlando, Florida; Washington, DC; and San Francisco, California. You will get to your destination by car. Your parents have asked you to estimate the total cost of the trip.
Steps:
- Choose your vacation destination from the three choices.
- Find the distance between Indianapolis and your city (from www.danagateway.com/mall/travel/drive).
- Estimate how much money you should budget for highway tolls on a round trip to that city. Explain how you arrived at that estimate. A road atlas will be helpful for these estimates.
- Your family car can travel about 28 miles on a gallon of gas. About how much gas do you think you will need on a round trip to the city you chose? About how much will that gasoline cost? Explain how you arrived at that estimate.
- Determine other major expenses for a two-week trip to your chosen destination. Factors to consider: Where will you stay? What will your activities be? Will you be going to amusement parks, museums, national parks? What types of meals will you eat?
- Estimate the total cost of a trip for a family of four to your vacation city. Show separate estimates for all major expenses. Be sure to show how you arrived at each estimate.
- Your parents plan to put aside some money for the vacation each month for the next year. What amount do you think this should be? Explain.
Part II:
Your family of four is taking a two-week vacation by car. Your budget is $2,500. Where can you go and what can you do? Choose a city from the three named above that you want to visit-do not use the same one you researched for the first part of this project. You have to spend all your money! Keep in mind all of the factors that you budgeted for in Part I. At the end, your spreadsheet should show all major expenses and how they fit into your budget.
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PROJECT 4: Choosing a Pizza Restaurant
 For this project you will work with a partner. Your task is to research local pizza restaurants to make an informed decision regarding which pizza to buy. Students who receive an A in this project will participate in a pizza lunch!
Steps:
- Research prices and dimensions of plain cheese pizzas by calling at least five local restaurants that serve pizza.
- Make a decision regarding which pizza to order. You should take into account the factors that are most important to you--some factors to consider include best buy, quality, and how much you plan to eat. You will need to decide and explain how you define quality and best buy!
- Make a spreadsheet to present the information you collect.
- Write a business letter to your teacher that describes the results of your research and convinces her or him what pizza to order for the pizza lunch. Include your own definition of pizza quality and best buy in your letter, as well as any other information you decide is important. Your letter has to be typewritten, and use business letter format.
PROJECT 5: Facts and Numbers Fun
 Did you know that if you look hard enough you can often find interesting facts connected to certain numbers? The mathematics of probability will tell you that amazing things can happen at random.
For this project, you will work in a group, and your group will pick a number and a theme and find unusual instances of the number's occurrence. Be creative--your ingenious minds will find all sorts of amazing connections. Hand in a short report with your number and the facts you have found--you don't have to find more than a few facts connected to your number. Have fun!
Example: Arthur Finnessey (Dudley, 1998) compiled the following interesting facts about the appearance of the number 57 in the American Revolution:
- Four of the first six US Presidents were inaugurated at age 57.
- On a presidential data chart in a particular encyclopedia those four 57-year-old presidents are listed at the top of their columns and surprisingly there is not another age 57 in the remainder of the long list.
- The number of chests of tea that were thrown into the harbor at the Boston Tea party is 6 times 57.
- A few weeks after Lafayette's 57th birthday, Francis Scott Key wrote the Star Spangled Banner.
- When Lafayette died, the Declaration of Independence was 57 years old.
- Princeton and Yorktown, Washington's two victories over Cornwallis, were 57 months apart.
- The fateful year of Yorktown began with two battles 57 days apart.
- In June 1781, 57 Americans died in the assault on the British Fort 96 in South Carolina.
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 Fanny Sosenke teaches seventh grade math at Park Tudor School in Indianapolis; she also teaches math teaching methods and elementary mathematics courses for preservice teachers at Indiana University-Purdue University at Indianapolis. She has given workshops and presentations on mathematics education and technology at various conferences, including workshops in Uruguay, her country of origin. Sosenke received the 1997 Presidential Award for Excellence in Science and Math Teaching.
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