Class 2:
Learning
objective: children should understand the need to normalize distributions in
order to compare them, and should be able to perform the normalization and make
the comparison using an “absolute difference” metric.
Materials needed:
Class 1, Class 4, and Class 5 broccoli distributions.
Teacher: remember
the other day we were talking about distributions and how we could compare
them. We learned that we could take two bar charts and come up with a
quantitative measure of the difference between two distributions.
In our work the
other day, each of the three classes had 25 students in them. Remember that
Class 1 had the following distribution:
Class 1: 5 liked broccoli, 15 hated broccoli, 5 didn’t care
Now suppose that
we surveyed two other classes—Class 4 and Class 5—and got the
following distribution:
Class 4: 9 liked broccoli, 15 hated broccoli, 6 didn’t care
Class 5: 10 liked broccoli, 30 hated broccoli, 10 didn’t care
Adding up all the
different groups, we see that there were 30 kids in Class 4 and 50 kids in
Class 5. So here’s the question: who likes broccoli better, class 1, 4,
or 5?
Expected answers:
Class 5, because 10 liked broccoli. Should lead to an argument over fairness.
Discussion should lead to the conclusion (prompted if necessary) that
distributions 1 and 5 are “the same.”
Okay, so when we
compare the distributions of two classes of different sizes, we can’t
just rely on the numbers to see if they’re the same or different. But
last time we also figured out a way to compare two distributions numerically.
If we used the method we figured out last time, what would be the difference
between Class 1 and Class 5? (answer=25). Is this right? You said that they
were the same!
How could we fix
our method so that the difference came out to be zero when two classes are the
same in terms of percentages? I’m going to let the groups work on this
problem. Can you figure out the differences between classes 1, 4, and 5? (We
will hand them a sheet with the numbers on them).
Kids work for a while
in small groups, then come back together to report their findings and make sure
each group has an algorithm for doing this.
Okay, now
let’s talk about the Field that you guys explored a few weeks ago in
Virtual Reality. That Field was part of a special project by the U.S.
Department of Agriculture to see how well different kinds of plants grew as
global warming got worse and worse. Each year they go out and count the actual
numbers of different kinds of plants, and they compare the results with previous
years. However, the budget for this project has been significantly reduced for
next year, so the Department of Agriculture is looking for a way to save some
money, while still being able to make comparisons with the results from the
past.
(Show transparency
of overhead view of the Field). The field you were in looks like this from
above. It is divided into nine regions, like a checkerboard. One idea going
around the Department of Agriculture is to just count one of the nine regions
next year; the problem is, they would like to have the region which is the most
representative of the whole Field. In other words, they want to choose the
region whose distribution of plants is most like the distribution of plants in
the whole Field.
How could we find
this out? (hopefully, kids will cite the work they’ve just done as a way
to do this; if not, teacher reminds them…)
Okay, so we could
figure out the distributions of each individual region, and then compare them
with the distribution of the whole field. But how will we get these
distributions? (Expected response: we have to count them).
Okay, we want to
save some time and money here, and we want to be fair, so how can we take
advantage of all this people power to do this job?
Okay, so
we’ll divide into teams, and each team will count one region. How will we
know the distribution of the WHOLE field? (Answer: we’ll add up the
numbers for each of the region distributions)
When each
individual group is in their region, exactly what work will they do?
Okay, we’re
ready to go…