Example Lesson #2: The Field Trip
Example Lesson #2: The Field Trip
The Jefferson High School History Club wants to raise enough funds to help pay for 17 of its seniors to take a week-long trip to the Smithsonian Institution in Washington, D.C. They have decided to sell specially printed t-shirts at school to raise money for their trip. All of the profits will be used to cover costs of the trip. The club's goal is to raise at least $6000 over the next two months to pay for transportation, lodging, and meals.
This problem involves data gathered from T-Shirts 4 You, a local t-shirt store in a popular shopping mall. Mr. Callahan, the owner of T-Shirts 4 You, provides important information on t-shirt sales. This information, along with data gathered from a student survey, will be used for "what if" questions as the students use the spreadsheet. Based on the results of Callahan's information, the student survey, and spreadsheet analyses of different options, the students will write a memo to their vice principal and History Club advisor about the best way to sell t-shirts to accomplish their goal.
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Math Objective |
Applied problem solving in mathematics and a written memo |
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Skills/Outcomes |
Clarify a problem Collect data on the problem Compute sums, averages, percentages Convert decimals to percents
Spreadsheet Skills Entering data Applying functions Charting data
Word-processing Skills Formatting and writing a memo |
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Materials |
(see below) |
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Files to Use |
gridport.doc gridland.doc guides.doc example2.xls |
Step 1: Problem Identification and Clarification
This problem was identified and clarified in the following manner. The teacher introduced the problem of a student group that wants to send 17 seniors in the History Club on a one-week field trip to the Smithsonian in Washington, D.C. This will be an expensive trip, but a great opportunity for the students who have been members of the club for 3 or 4 years. The school has said that it would allow the students the opportunity to sell something during school as a way of raising money for the field trip.
One way to raise money is to sell a popular, but modestly priced item. Food is always popular, but there's not a lot of profit in it. Clothing is much more profitable, and after some thinking about costs, the teacher notes that there is a considerable mark-up on clothes. One student suggests t-shirts. Another student recommends that the best way to make sure that the t-shirts sell is to use designs that are popular with students.
The teacher uses the chalkboard when identifying the different dimensions of the problem: there are no funds, the school will approve some kind of sale, the trip will be expensive if all 17 students go for one week. A potential solution to the problem is also represented on the board: Find items that are modestly priced, that have a good mark-up, and that are popular with the students.
The teacher then prods students to be more specific about each aspect of the problem. Students need to be more precise about the costs of the trip in order to determine how much money they will need to raise. They will also need to find out more about the t-shirt business. What do t-shirts cost at the wholesale level? How much more do designs cost? What is the typical mark-up? Finally, they need to find out what will be popular with students. Also, how many different kinds of t-shirts will they need to make and how many do they think will sell? After all, there are only about 1700 students at Jefferson High. They might be able to sell more if they get permission to sell t-shirts at Marcus Middle School, which is next to Jefferson. There are about 700 students at Marcus.
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Teacher Note: You can simulate portions of the steps above. Students could actually check into the price of t-shirts at retail stores or wholesale distributors. They could also find out sales trends (e.g., are trends seasonal, do people mainly buy 2 or 3 popular t-shirts, etc.). Data for this problem can be found in example2.xls. |
The teacher represented the problem on the chalkboard as it developed, used brainstorming techniques, examined specific dimensions of the problem, and scaffolded student observations and questions to elaborate on all of the issues mentioned above. The teacher made sure to model and make explicit how s/he reasoned about the problem. The teacher also spent time talking about why some issues came up (e.g., "What if we make too many t-shirts?") and how to think about the problem rather than rushing to finish it and move on. Once the students and the teacher felt that they were done analyzing the problem, they brainstormed the next steps. These included forming subgroups that would complete specific tasks:
Step 2: Analysis of the Information or Data
Students use think sheets from guides.doc to collect and organize information for this problem. In this case, four different sets of think sheets are used. Examples of how students filled them in can be seen below. One set of sheets addressed the goal-how much the trip will cost. The second set involved an analysis of the t-shirt sales data from the store, T-Shirts 4 You. The third set of think sheets presents the results of the student survey data. The final set of sheets directs the students to use all of the above data to determine which option is best for selling t-shirts and meeting the goal in the fastest period of time. The different data analyses can be found in the file example2.xls.
This step in the process will require a considerable amount of teacher guidance. Students will need assistance in organizing the data, particularly if they are working in different teams or groups. They will also need help in planning how to analyze the data before they work on it in the lab. The Data Organization, Analysis, and Summary Sheets all help in this process.
title: Cost of the Trip
Main Questions To Answer:
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How much will it cost to send 17 seniors to Washington, D.C. for a week? |
Relevant Data:
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Find out the price of air fare, hotel costs, transportation in Washington, D.C., and food. Be sure to allow for some extra, unexpected expenses. |
DATA ANALYSIS SHEET #1
title: Cost of the Trip
1. What data or information am I going to analyze?
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Data on transportation, lodging, and food costs. |
2. What are some of the important parts of the data that I want to look at?
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How much each type of expense costs and ways to reduce that cost. |
3. How do I want to use math to analyze the data?
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Multiply the cost of each item such as air fare times 17. Also, I want to add a miscellaneous to the total for unexpected expenses. |
DATA ORGANIZATION SHEET #2
title: T-Shirts 4 You Information
Main Questions To Answer:
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What are some of the important things to know about the t-shirt business? How many t-shirts per month do you sell? Are some more popular than others? What do t-shirts cost? What is the mark-up or profit on them? |
Relevant Data:
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Ask Bob Callahan at T-Shirts 4 You about the t-shirt business. Put information on one month's sales in a spreadsheet file (example2.xls). The file tells how many t-shirts he sold, what kind, how much it cost him, how much he charged. It also tells the profit for the month. Ask Mr. Callahan about how well different t-shirts sell. |
DATA ANALYSIS SHEET #2
title: T-Shirts 4 You Information
1. What data or information am I going to analyze?
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The monthly t-shirt sales at T-Shirts 4 You. |
2. What are some of the important parts of the data that I want to look at?
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Which t-shirts sell and which ones don't sell. How many t-shirts are sold in one month. How much profit you make on 1 shirt. |
3. How do I want to use math to analyze the data?
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Total the different columns of numbers for each t-shirt. Also, subtract the wholesale cost of t-shirts from the sale price to figure out the profit. |
DATA ORGANIZATION SHEET #3
title: The Student Survey
Main Questions To Answer:
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What kind of t-shirts will be most popular at Jefferson High School and Marcus Middle School. |
Relevant Data:
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We will do a survey of 100 students at each school. We will begin by asking about 10 students to think of designs that they would like and then make up some choices. We will have 8 choices that we will ask the 100 students in each school about in our survey. We will choose the top 4 t-shirt choices. |
DATA ANALYSIS SHEET #3
title: The Student Survey
1. What data or information am I going to analyze?
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The top 4 choices. |
2. What are some of the important parts of the data that I want to look at?
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(left blank-no need to fill in) |
3. How do I want to use math to analyze the data?
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(left blank-no need to fill in) |
DATA ORGANIZATION SHEET #4
title: Reaching the Goal
Main Questions To Answer:
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How long will it take us to reach our goal? |
Relevant Data:
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Use the difference between the wholesale price per t-shirt and what we can sell it for to determine the profit. Also decide if we need to sell all 4 kinds or if we should just sell the most popular 2 kinds of t-shirts. |
DATA ANALYSIS SHEET #4
title: Reaching the Goal
1. What data or information am I going to analyze?
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Information on the cost of making t-shirts with popular student designs and what we can sell the shirts for at school. |
2. What are some of the important parts of the data that I want to look at?
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If we should sell all 4 kinds of t-shirts or if we should sell fewer t-shirts as a faster way to reach our goal. |
3. How do I want to use math to analyze the data?
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Make up one spreadsheet that has the costs for all 4 t-shirts. Use the spreadsheet to figure out the best way to sell all 4 kinds of shirts and still take advantage of the discounts on buying and printing shirts in units of 100. |
SUMMARY SHEET FOR ANSWERS TO ALL OF THE MAIN QUESTIONS
Question: How much will the Smithsonian trip cost?
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Answer: About $6000 |
Question: How much does Callahan make per month at T-Shirts 4 You?
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Answer: He makes about $4,700 per month, but he says that we should be careful about using his numbers. He buys t-shirts that are already printed, and he can buy them cheaper because he owns a store. If we want to have our own t-shirts printed, it will cost us a lot more. Also, it is cheaper to buy t-shirts in boxes of 100 and have them printed in groups of 100. He also says that there is a big difference between how well the 2 most popular t-shirts sell and how well the rest of his shirts sell. Callahan says that if you were just selling 4 shirts, about 70 percent of the sales would be from the 2 most popular t-shirts. He also said that only about 1/3 of the students would buy shirts in the school. This last fact is important because there is a trade-off in selling shirts. If you just sell 2 kinds of shirts, you can buy more of them in packs of 100 and it is cheaper. But, you won't sell as many t-shirts overall because there are just 2 choices. If you have 4 choices, you will sell more t-shirts, but you won't make as much money on the less popular shirts because you have to buy them in packages of less than 100. You also have to work this out to make sure that you don't have a lot of t-shirts left over. This means that you have to look at what you are going to do very carefully so that you don't make a big mistake. |
Question: What did the student survey show?
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Answer: Students said that they would like these 4 designs the best. They are in order of what they liked the most: 1) School logo with an athlete 2) School logo with mountains and mascot 3) Rock band and school name 4) Athlete and school name |
Question: What was the cost of t-shirts?
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Answer: Plain white t-shirts were $3.95 apiece in boxes of 100. They were $5.25 each for boxes of less than 100. It cost $2.15 per shirt for a multi-colored design. The price for the design went down to $1.75 per shirt for printings in groups of 100 of the same design. |
Question: What is the best way to reach our goal?
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Answer: We looked at the problem on the spreadsheet. We first worked out how much money we would make if we sold the t-shirts for $12.95 and we sold the exact amounts of each t-shirt (70% for the 2 most popular and 30% for the other 2 kinds of shirts). We came up short so we decided to do two things. We ordered more of the most popular so that we can buy the shirts and print them at a lower price. We also raised the sales price of each shirt until we reached our goal of $6000. |
Question: How long will it take to reach our goal?
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Answer: We will hold t-shirt sales for 2 mornings each week and at sporting events until we sell all of the shirts. We expect that students will buy most of the shirts in the first two weeks. It may take 6 weeks to sell all of the shirts. |
Students will need help transforming findings above into a text structure. This will be critical before students start the memo-writing process found in the next step. The Findings-Recommendation guide helps students summarize all of their data in a useful text structure. The key words serve as a basis for structuring different statements that will be used in the memo.
Key Words: Found, Should, Recommend, Suggest, If, Then, Encourage, Propose, Approve
What is Being Explained?
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How we will sell enough t-shirts to send our History Club on a field trip to the Smithsonian. |
Findings:
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We estimate that it will cost $6000 for the trip. |
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About 1/3 of the students at both schools will buy t-shirts. We will need to have sales at the high school and middle school to reach our goal. |
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It makes a difference if you buy shirts in boxes of 100 and do the printing in quantities of 100. You have to pay more for quantities of less than 100. |
Recommendations:
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We propose to buy more of the most popular shirts and order exactly 300 of the most popular shirt so that we can save on discounts. There is no advantage to doing this on the less popular shirts. |
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We propose to raise the price of the shirts from $12.95 to $13.50 in order to reach our goal. |
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We think it will probably take 6 weeks to sell all of the shirts, and we may have to sell some of the final shirts at a sale price. |
Step 3: Clear Communication of the Results
Once students have collected, analyzed, and summarized all of the relevant information, they need to communication their findings and recommendations to an authentic audience in a clear and concise manner. This means that some information-even important information-will be left out in the final summary. The guides that follow show how students work from the Think Sheets above to a more concise summary. This process will take several iterations, and a memo checklist (see guides.doc) will be helpful in determining the quality of the final product. We recommend that you follow typical process writing procedures as a way of helping students through their various drafts.
MEMO PLANNING SHEET
Main Idea/ Topic Sentence:
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We believe that we can make enough money to send 17 seniors from the History Club on a one-week trip to the Smithsonian. |
Major Ideas/ Supportive Information:
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Mr. Callahan at T-Shirts 4 You has given us important information on the t-shirt business and how we can be successful. If we sell more of the 2 most popular shirts we can save money on discounts and meet our goal. Also, if we sell the shirts at $13.50 we should also reach our goal. |
Closing Statement:
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We expect to run the sale for about 6 weeks at both schools, and we may have to discount the last few shirts in order to make sure that none are left over. |
Sample Memo
MEMORANDUM
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DATE: |
November 18, 1997 |
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TO: |
Ms. Gabriela Hale, Vice Principal |
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FROM: |
History Club |
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RE: |
T-shirt Sales |
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CC: |
Ms. Connie Martinez, History Club Advisor |
We would like to send 17 seniors in the History Club to the Smithsonian Institute for one week in June. We will need to raise $6000 for the trip. We think we can do that if we get permission to sell t-shirts in the morning before school and at sporting events. We would also like to sell the shirts at Marcus Middle School. We have talked with Mr. Bob Callahan who runs T-Shirts 4 You in the mall. He gave us excellent advise on how to buy and print the right kinds of t-shirts so that we make the most money.
We propose to sell 4 kinds of shirts. We expect that 2 of the shirts will be much more popular than the other 2, so we will make more of these shirts. We plan to sell the shirts for $13.50 each in order to reach our goal. We anticipate that it may take 6 weeks to reach our goal. We may also have to discount the last few shirts in order to make sure that none are left over. If we sell all of the shirts, we should make approximately $6,000.