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.
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.
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?
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.
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.)
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.