Time 1 session

Overview: Students explore how to chose random samples as they map Journey North data.

Teacher Background
Teachers may feel overwhelmed by the volume of data as Journey North migration reports flow in from observers. One option is to reduce the number of data points students plot on their maps.
But how to decide which reports to use?

This is a great opportunity to introduce the mathematical idea of choosing random samples, which gives each item or subject (reported data, in this case) the same chance of being selected as any other. It is a "fair" (unbiased) way to select data to represent the whole.

Laying the Groundwork
Hold up a candy bar or other treat and ask students, What would be a fair way for me to choose one student to give this treat to? For instance, would it be fair for me to give it to the student who raises his or her hand the highest?

 How do you decide in a fair way? Draw straws? Pick a number? Draw from a hat?

Students might suggest pulling names out of a hat, turning your back on the class and throwing it overhead, and so on. Discuss which suggestions seem most fair and why. (For instance, tossing the candy bar into the crowd isn’t fair because it might favor taller students with big hands.)

Explain that scientists and mathematicians think that to make something like this fair, everyone would have to have an equal chance of being chosen. Before moving on to selecting samples from Journey North data, have the class decide on the fairest method for distributing the candy bar and then use it!

Exploration

 How Many to Choose? There is no right answer to the question of how many samples to choose. Explain that sometimes time or money constraints, or a huge volume of data, prevents scientists from studying an entire group of subjects or data. Help students come to the idea that a large sample size will give them more certainty about what their maps “tell” them than a small one will. They can, however, choose a number in between.
1. Show students the current week’s data for the Journey North project you’re following. Discuss the idea of selecting a smaller sample of the data so it will be easier to post sightings on individual or classroom maps. Ask, How many reports do you think we should choose, and why? If we used data from just three sites versus 30 sites, how do you think the big picture and our interpretation could change?

As a class, decide how many reports from that week you think would give you a reasonable sense of what’s happening with the migration.

2. Ask, How should we decide which reports to choose? Document students’ responses and/or throw out these two fairly biased methods: a.) Going down the list of reports and choosing the first 10 we come to. (Hint: The reports are listed in order of date received.); b.) Choosing reports from the states closest to us.

Next ask, What would be the pluses and minuses of using each method?

3. If students didn't come up with this approach, suggest it now:
Give a number to each report starting with 1 and going through to the last report. Next, write the same numbers on pieces of paper and pick them out of a hat one at a time. Match each number to one of the reports until you have the total number of reports you decided to use.

Ask, Is that more or less fair than the other suggestions? Remind them that, to be fair, each report should have to have an equal chance of being chosen. So, for instance, pulling numbers from a hat would be more fair than choosing the first X reports that came in.

Digging Deeper (Younger Students)
Tell students that some computer programs are set up to come up with random numbers. It’s like picking numbers out of a hat, but the computer does it for you. Invite them to choose random numbers using this kid-friendly Web site: Random Numbers Between 0 and 30.

Digging Deeper: Using a Random Numbers Table (Older Students)
Explain that mathematicians and scientists also use tables of random numbers to choose samples. Have them follow the procedure below to select samples of reported data to use on their maps.

 Decide on the number of reports you want to use. Go straight down the list of reports and assign numbers in order. Go to this Random Number Table. Close your eyes and put a finger on the table. Open your eyes without moving your finger. The set of numbers closest to your finger is the starting point. If your total number (from step 2) is two-digit (that is, above 9), use the two digits on the right side of the set of numbers. Example: Starting point on table = 698433. So the first report you’ll choose is #33. Continue down the column to the next set of numbers that fits a number on your list of reports. (If you come to one that doesn’t, just skip it.) When you get to the bottom of a column, move to the top of the next. Continue until you have picked the total number of data samples you decided to use on your maps.

Making Connections — Discussion and Journaling Questions

• In what other situations might you need to select a sample of something from a large number? (See how scientist Dr. Bill Calvert uses random numbers to help him choose the location of quandrants from which to sample butterflies in The Effect of Snow on Monarchs.)
• What factors other than the size of your data sample can affect the reliability of your data (e.g., the observers' skills). See You're the Scientist: Verifying Data Collected by Peers.
• Why do you think being “fair” (unbiased) is important to science research?

Assessment
As students discuss and practice selecting random samples, they should improve in their ability to distinguish between more and less biased methods.

National Education Standards

National Science Education Standards
Use math in all aspects of scientific inquiry. (5-8)

NCTM Math Standards
Students will collect, organize, and interpret data using the methods of exploratory data analysis.