The French Fries Problem

This lesson connects a very simple problem in the immediate world of students to a very big problem in the world of food services-fast food restaurants, ice cream chains, and coffee shops. All of these services depend on a high level of quality control to make money. Each item sold is carefully measured so that products are not accidentally or casually given away. For example, an ice cream store can lose as much as $5,000 in a summer by adding a small, extra portion of a scoop to the ice cream that goes on a cone or into a sundae.

It is possible that your school cafeteria serves french fries or some other kind of fast food during lunch. This set of lessons enables students to study the variations in servings and ultimately, their implications for the fast food industry. These lessons will help students understand how a standard serving can be developed. It will also help them measure how much variation in weight or quantity can be found in their school lunches.

In Lesson 1 students measure french fries, record the data, prepare a spreadsheet, and calculate basic statistics. Students in Lesson 2 build a frequency table and make a chart. Lesson 3 shifts the focus from individual to class data and organizes it around a standard. Students then create their spreadsheet and make charts from the class data from each serving of fries.

Math Objective

Students will learn how to model a problem using the spreadsheet. This will entail data collection, analysis, and asking "what if" questions.

Skills/Outcomes
  • Collect, organize, graph, and interpret data from real-life situations, and apply results in solving problems
  • Summarize data using mean, median, mode, and range
  • Make tables
  • Make inferences, support arguments, and make decisions based on statistical evidence

Spreadsheet Skills

  • organize data on a spreadsheet
  • save a block of data with a name
  • find a mean, median, mode
  • make a line chart

 

What To Do

Materials

french fries

scales

rulers

recording sheets

computer lab

Files to Use

Download Info/Instructions

fries.doc (student worksheet)

Basic Line Chart (math concepts lesson)

Optional Resources
data from local fast food restaurants about serving size

 

Lesson 1

Lesson 2

Lesson 3

 

Teacher Note: This file contains 3 lessons generated from the french fry data. Each lesson may take more than one day. Lesson 1 gets students to record data on containers of french fries. Lesson 2 allows students to calculate basic statistics and makes charts using the spreadsheet. Lesson 3 helps students see relationships in the data by looking at variations across the different sets of data. These lessons work the best when students are arranged in small groups.

 

Lesson 1 - Collecting Data on Fries

 

Classroom Discussion and Activities (Whole Group or Teams)

 
This activity is best done in teams. Student lab sheet for collecting data is provided in fries.doc. Develop your best method for obtaining french fries servings from your school cafeteria or another source. The only criteria is that they are all labeled the same serving size (large or small servings).
 
 
Use rulers or have students draw a ruler on paper with 1/4" marks, eliminating the 1/8" marks. Measure each fry, rounding it to the nearest quarter inch, and record the length on data collection lab sheet (see fries.doc). Weigh the container of french fries and record results.

 

Lesson 2 - Analyzing the Fries Data and Making Charts

 

Computer Lab Activities

 
Students can enter the data they have collected on their fries.doc sheet into a spreadsheet file. Another option is for you to enter the data or have an instructional aide do it. This will reduce logistical problems and give you more time for data analysis and charting activities in the lab.
 
See stats1.doc for help with basic statistics. This file explains how to enter formulas for basic statistics such as mean, median, mode, and range. It also explains how to make a basic chart from the data.
 
Use two columns for your data. Put Length as a label at the top of the first column and Number at the top of the second column. (Skip the Tally Marks column from your fries.doc data sheet.) Create labels for the different lengths of the french fries (e.g., 1/4", 1/2", etc.). and have the students enter the number of fries for each length in the Number column. After you have entered all of the lengths of french fries and associated numbers, set up the spreadsheet so that it looks like this at the bottom of the file:

 

These terms will be labels for appropriate calculations. Use the appropriate formulas to calculate the statistics for the data in the number column (e.g., =sum for Total, =average for Mean). Students can also look back over the data to see which length had the greatest number of fries (Most or =max) or the least (Least or =min).

Teacher Note: Be sure to discuss the statistics once they have been calculated. Ask students about the range (most and least), why there are relatively few numbers of fries at the extremes, etc. By Lesson 3, students will be able to see a pattern-the more shorter fries, the more fries in the basket or container. This is also an opportunity to review basic statistical concepts such as mean and range.

 

 
Have students create either a bar chart or line chart using their two columns of data. See linechrt.doc or barchrt.doc for instructions on making different charts. These charts should reinforce the discussion above. In most cases, the greater number of fries can be found away from the extremes.

 

Lesson 3 - Using Class Data as a Whole and Comparing Data to the Grand Mean

 

Classroom Discussion and Activities

The main purpose of this lesson is to get students to see relationships in the data. Without using the term correlation, students can use line charts in the spreadsheet to see correlations. However, you probably want to stay away from this term and just talk about relationships in the data.

You can prepare students for this exercise by reviewing the decimal terms for the common fractions that we have been using. Remind them that 1/4 is the same as .25, 1/2 = .5, and 3/4 = .75. They will need to know this to convert their Tally Mark data into decimals as they enter it in the spreadsheet.

 

Computer Lab Activities

 
Begin with a column label for Column A. You could use the word Length for length of the french fry. Work from the fries.doc data sheet. Start with the smallest fry. For each tally, have the student enter the length in one cell of the column. For example, if there are 4 tally marks in 1/4" row on the data sheet, the spreadsheet should look like this.

 

Teacher Note: At this point, you can do one of two things. You can have students save a copy of their data and then combine all of the different sets of data into one large spreadsheet file. This will mean that all of the lengths of the french fries for the entire class will be in one spreadsheet file (and one long column of data). You can then calculate the number of fries, averages, and other statistics in this large file.

A faster option is to have the students each report their averages on their data. You can then average these individual averages to get a grand average or mean.

 

Once you have calculated the grand mean, have students use it to determine how many of their fries are equal to or less than this grand mean. For example, if the grand mean is 3.5 inches, have the students count all of the fries equal to or less than 3.5 inches. They can do this by hand, or they can use the COUNT function on the spreadsheet.
 
 
Have students report key data from their different groups. Your combined spreadsheet should look something like this.

 

 
Ask the students how the different baskets compared to the grand mean. Which ones had more than the mean? Which ones had less? How did these findings relate to the total number of fries? What is the average (mean) number of fries that make quality control? Did anyone in our data group get a good deal? Did anyone in our data group get cheated?

 

 
Copy different columns to make different line charts. Start with these two columns: Equal or Shorter and Total Number. These two columns of data should show that the greater the number of fries below the grand mean, the more the total number of fries. The opposite should be generally true when you compare the Longer and Total Number columns. Finally, there should be no relation between the weight of the baskets and the number (or the other columns).

 

Extended Activities 

Compare your weight findings with data from fast food chains. Most of them have published nutrition sheets which include the weight of different serving sizes.