Example Lesson #1: Donut Sales
Example Lesson #1: Donut Sales
This example problem is built around a donut sale scenario. A volunteer group of students wants to sell donuts to their classmates on Wednesday and Friday mornings before school. The purpose of the donut sale is to raise money for school soccer equipment. In this scenario, the students got the idea from Johnson High School, another school in the district. These students interviewed students at the other school who were in charge of the donut sales about their business-What are the group's financial goals? What is their timeline? What kind of donuts are they selling? Do they have any data on the weekly sales?
There is a key difference between the students' school, McNamara High School, and Johnson High. McNamara has 1050 students, while Johnson High has a student body of 1856. This difference will have to be taken into account when McNamara students estimate how many donuts to buy for their sale.
Some of the student activities in this lesson are: 1) determining the cost of the soccer equipment in order to determine the goal; 2) using Johnson High School data to project total sales for a month; 3) calculating how much profit will be made, on average, every month; 4) calculating how long it will take to reach the goal of buying enough soccer equipment; and 5) writing a memorandum to the McNamara High School vice principal explaining the proposed donut sale.
This problem can be simulated. That is, you do not need to arrange a donut sale to do the problem. You simply need to pose the problem as if a hypothetical group of students had a donut sale based on data from another high school. Your job is to work the students through the steps needed to solve the problem. You can decide whether you want to use the data provided in example1.xls or have students create their own data.
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Math Outcome |
Applied problem solving in mathematics and a written memo |
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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 example1.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 buy new equipment for the soccer team. There are no funds in the activities budget for new equipment, so it's up to the students to raise enough money to buy it. The school has said that it would allow the students the opportunity to sell something during school as a way of raising money.
When the teacher elicits background knowledge from the class, one student mentions that Johnson High School sells donuts every Wednesday and Friday morning as a fund raiser. Her friend at Johnson says that they make a lot of money doing it because the club buys the donuts by the dozen from a grocery store and then sells each one for a profit. As a teacher, you can simulate this kind of discussion by bringing up donut sales as one way to raise money.
The teacher uses the chalkboard when identifying both the problem and a potential solution. The problem-no money for equipment-and the solution-a donut sale-are starting points for all of the major issues associated with each.
The teacher then prods students to be more specific about each aspect of the problem. Exactly what is the goal, how will students know when they reach it, etc.? Students will also need to determine exactly what equipment is necessary and how much it costs. Finally, they will need to know what kind of donuts students prefer, how much they will cost , and an estimation of how much the group thinks they should buy. This information can be acquired in a number of ways, including interviews with students at Johnson. Someone also needs to be in charge of finding out from a grocery store how much donuts cost by the dozen and it they can get a discount for large volumes. Also, another group of students may want to develop a survey of what kind of donuts would sell the best. Finally, it would be very helpful if they could get some data from Johnson on monthly sales-how many donuts were purchased for the sale each day, how many sold, cost per donut, profits, and what the students did with the extra donuts.
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Teacher Note: You can simulate portions of the steps above. Students could actually check into the price of donuts by the dozen at different grocery stores or bakeries as a way of finding the best price. You could also create a hypothetical month's sale or use the data found in example1.xls. |
The teacher represented the problem on the chalkboard as it developed, used brainstorming techniques, examining 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 buy the wrong kind of donuts?") 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 addresses the goal-how much the equipment will cost. The second set involves an analysis of the Johnson High data. The third set of think sheets presents an analysis of the student survey data. The final set shows how long they estimate it will take to reach the goal. The different data analyses can be found in the file example1.xls.
This step in the process will require a great deal of teacher guidance. Students will need a considerable amount of assistance in organizing the data, particularly if they are working in different teams or groups. They will also need help 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.
DATA ORGANIZATION SHEET #1
title: The Soccer Equipment
Main Questions To Answer:
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How much will our soccer equipment cost if we want to have enough for 30 students? |
Relevant Data:
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Check with school price lists for jerseys, shoes, socks, balls, and 2 nets. Be sure to include sales tax. |
title: The Soccer Equipment
1. What data or information am I going to analyze?
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Soccer equipment data using the school sheet. I'm also going to check on tax. |
2. What are some of the important parts of the data that I want to look at?
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How much each item costs. |
3. How do I want to use math to analyze the data?
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Multiply the number of pieces of equipment that I need by the cost of each item. Also, I want to figure tax on the total. |
title: The Johnson High Data
Main Questions To Answer:
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What were the Johnson High School sales for February? What kind of donuts did they buy and how many? How much did they charge per donut? What was their profit for the month? |
Relevant Data:
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We got records from Johnson for February. We put them in a spreadsheet file (example1.xls). The file tells how many donuts they sold, what kind, how much it cost, how much they charged, and how many they had left over. It also tells the profit for the month. |
title: The Johnson Data
1. What data or information am I going to analyze?
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The donut sales per day and per month. |
2. What are some of the important parts of the data that I want to look at?
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What it cost to buy the donuts and what they sold them for. We also need to find out if any were left over. |
3. How do I want to use math to analyze the data?
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Multiply the number of donuts by the cost per donut. Subtract the cost from the sales price. Also, subtract the cost of the donuts left over from the profit. Add up all of the numbers. Figure out the percent of each kind of donut that they bought. |
DATA ORGANIZATION SHEET #3
title: The Student Survey
Main Questions To Answer:
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What kind of donuts should we buy and how many? How much should we charge per donut? How much can we buy the donuts for at a store? How do we make sure that we don't buy too many donuts (Johnson High is much bigger than our school)? |
Relevant Data:
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We will do a survey of 50 students in the cafeteria on Wednesday to find out their top 3 donuts. We will need to compare Johnson High, which has 1865 students, with McNamara, which has 1050 students. We will need to use student survey results to figure out how many donuts we are going to buy. We need to call some stores to find out the cheapest price for donuts. |
title: The Johnson Data
1. What data or information am I going to analyze?
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The student survey and the survey of different stores for the price of donuts. |
2. What are some of the important parts of the data that I want to look at?
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The top 3 choices and the percent of students who liked those donuts. Figure the percent of students in McNamara compared to Johnson. Also, how many of each kind of donut we should buy based on the smaller number of students at McNamara. |
3. How do I want to use math to analyze the data?
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Figure out percent of top 3 choices based on 50 students. That means divide number of students who chose the donut by 50. Also, figure the percent of students at McNamara compared to Johnson (divide McNamara by Johnson). Figure the number of donuts we should buy (multiply total daily donuts at Johnson by the percent). Then figure how much of each kind we should buy. |
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 price per donut from the store survey and the cost of the equipment to figure out how long it will take to reach the goal. |
title: Reaching the Goal
1. What data or information am I going to analyze?
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Soccer equipment data and the store survey on the cost of the donuts. |
2. What are some of the important parts of the data that I want to look at?
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How much money we expect to make each day and how many days it will take to reach the goal. |
3. How do I want to use math to analyze the data?
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Multiply the number of donuts bought by the cost per donut. Then do the same for the sales price. Subtract the cost from the sales price to get the profit. Divide one day's profit into the total amount we need to reach our goal. |
SUMMARY SHEET FOR ANSWERS TO ALL OF THE MAIN QUESTIONS
Question: How much will the soccer equipment cost?
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Answer: $2464.75 |
Question: How much did Johnson buy and what was the daily profit?
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Answer: They bought 525 donuts for each day's sale and they averaged $142 profit per day. |
Question: What did the student survey show?
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Answer: Students liked glazed, chocolate covered, and cinnamon twist. We figured out the percent of students who liked each kind of donut and used this to figure out how many of each donut we should buy. We figured that McNamara is 57% as big as Johnson, so we should buy only 57% of the donuts they bought each day so that we will have just enough donuts. That means that we should buy only 300 donuts. |
Question: What was the best price per donut if we buy them by the dozen at a store?
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Answer: 18 cents per donut was the best price at Save Rite Foods. |
Question: How long will it take to reach our goal?
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Answer: We figured that it would take 23 days if we sold all of our donuts each day (no leftovers). That probably won't happen, so it may take 25 days. That means that we need to sell 2 times per week for just over 3 months. |
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 be able to sell enough donuts to buy the soccer equipment that we need for our team. |
Findings:
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We found that soccer equipment will cost $2464.75. |
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Johnson High has donut sales and makes an average of $142 per day on their sales. |
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Students at our school like 3 kinds of donuts and would pay 55 cents each for a donut before school. |
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We can buy donuts at 18 cents each (per dozen) at Save Rite Foods. |
Recommendations:
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We propose to charge students 55 cents for donuts and buy 300 donuts total. |
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Run the donut sale 2 times per week for about 25 days in order to reach the goal. This will allow for donuts that do not get sold. Be sure to keep track of daily sales and buy more or less donuts depending on how well each kind of donut sells. |
Step 3: Clear Communication of the Results
Once students have collected, analyzed, and summarized all of the relevant information, they need to communicate 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.
Main Idea/ Topic Sentence:
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We believe that we can have a donut sale at McNamara to make enough money for soccer equipment. |
Major Ideas/ Supportive Information:
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Johnson High makes a profit on its donut sales. Our survey of students shows that they would buy donuts. We expect to make a daily profit of $111. |
Closing Statement:
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We expect to run the sale for about 25 days (just over 3 months) as a way of buying the soccer equipment. We will keep track of daily sales to get to the goal as fast as possible. |
Sample Memo
MEMORANDUM
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DATE: |
March 20, 1998 |
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TO: |
Ms. Linda Elhurst, Vice Principal |
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FROM: |
Soccer Club |
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RE: |
Donut Sales |
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CC: |
Mr. Leroy Jackson, Soccer Coach |
We would like to have permission to sell donuts before school two times a week in order to raise money for soccer equipment. We have done some research on this and found out that we can successfully raise the money we need in about 3 months. We asked students at Johnson High about their donut sales and found that they make a profit of $142 a day. We surveyed students at our school and found out that they would be willing to buy donuts before school. McNamara is smaller than Johnson, so we expect to make a daily profit of $111.
We recommend that the soccer club sell donuts every Wednesday and Friday morning before school from 7:00 to 7:45. We propose to sell 3 different kinds of donuts at 55 cents each. If we sell all of our donuts, then we should reach our goal in 25 days of sales or about 3 months. We will keep track of daily sales and make changes in the number of donuts we buy and the different kinds so that we reach our goal as quickly as possible.