Where Does My Stuff Come From? Part 3: Two Way Frequency Tables

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SWBAT use a two-way frequency table to organize categorical data in two categories.

Big Idea

Sometimes, we have to get our hands dirty if we want to learn to use a new tool. Today, students dig into their data in order to come up with a neat two-way frequency table.

Opener: Mental Math and Percentages

5 minutes

Today's opener consists of a dozen simple percentage problems.  As students continue to brush up on their percentage skills, the main purpose of these problems is to show them that it's not always best to rush to use a calculator - or at least to rush to use the percentage algorithm.  When we're finding a percentage of a multiple of 100, it's best just to think of it as a multiplication problem.  When we're finding 10%, 50% or 25% of a number, it can save time to just divide by 10, 2 or 4.  

In a message aimed particularly at students who have already done well on Percentage Practice #1, but want to get faster in order to accomplish more, I say that this will help.

"Where Does My Stuff Come From?" Part 3

30 minutes

Here is Part 3 of the "Where Does My Stuff Come From?" Project.  As I describe in this narrative video, students work in groups to disaggregate their data by using a two-way frequency table, which will allow them to see associations between the countries that make the stuff we buy, and kinds of stuff produced by each of those countries.

This analysis may turn out to be a little messy, but that's part of the experience that I want my students to have.  To spend two days poring over the numbers, trying to figure out what's going on within the data gives students a feel for why more efficient tools have been invented.  In particular, I'm talking about statistical and algebraic structures that allow us to organize and generalize information, and about the computing tools that make it easier to gather and analyze data.  I will refer back to this work frequently as the year proceeds.

There are two particular reactions that my students may have about this work.  Some students are relieved to have such a conceptually straightforward task to complete - for the second consecutive day, this is essentially a counting exercise.  This is an opportunity for such students to be successful and to gain confidence in this class moving forward.  A subset of these students do benefit from the applied practice on simple arithmetic.  I try to question such students in ways that will get them to think a little more deeply about the data with which they're working.

Other students see this as a rather tedious assignment and ask why we didn't just skip over Part 2, and straight to this part of the project.  Indeed, when I've done this project with older students, that's exactly what I do, and I might consider ways to allow my more advance 9th grade students to skip from Part 1 to Part 3 in the future.  But on the other hand, I do feel that the attention to detail, the group collaboration, and the practice with percentages offered by the sequence is worth the two class periods that it takes.  These students have a point, and they deserve that acknowledgement.  I tell them that this part won't take too long, that I'm glad they got the practice, and that this is probably as close as I'll come to giving them busy work this year.

Class Data Collection & Rolling Debrief

8 minutes

To close today's class, I join in on the data collection and summarizing.  As each group completes their work on the front of Part 3 of the project, they see that on the back, the task is to gather the results of this project for the entire class.  "Don't worry," I tell them, "you've done a lot of the work so far - now you get to hand it off to me to finish up."

Projected on the front board, I have an Excel spreadsheet ready to go with columns for country names, each of the four categories, and the total, and I ask for a volunteer from each group to read their data aloud as soon as the group is done.  As they do, I record it publicly.  Once a group shares their own data with me, they're naturally invested in seeing what other groups have to share.  Group by group, the data goes up, and as that happens we engage in impromptu conversations about the similarities, differences, what surprised us, and what does not about the data.  We might have a little geography lesson, when students ask where a certain country is.  We might begin to speculate about the reasons that the data looks like it does.  We might wonder how accurate this data is on a larger scale.  I love these unstructured moments that follow work on a task, in which we can just see where the conversation goes.  It gives me the chance to get to my students better as they express their natural curiosity.

Additionally, Excel is brand new to many of my students.  They're going to use it for themselves later in this course, but in order to introduce them to the program, I take this opportunity just to navigate the program for all to see, so it's not completely foreign when it becomes their turn to use the software.  As we go, I'll demonstrate how to sum rows and columns, and this is always enough to convince the kids that this is probably a tool worth knowing how to use, especially after the nitty-gritty work in which they were just engaged.

Here is an example of the results for a whole class.  There are all sorts of reasons that we might question the validity of this data, but it is our data, and as we look at together, I express some awe and I make that point to students.  In this course, we're not delving too deeply into statistical methods, but in the next part of the project, we will get to compare what we've done here to some world trade data.