When students arrive today, their scores from yesterday's Game of Greed are on the board (there is a different slide for each group in this Greed Scores and Box Plots document). I want to make sure that everyone has this data in their notes. I've posted the task that students completed at the end of most classes yesterday: to find the mean, median, and mode of this data. For most students, this is already done. I circulate and ask everyone to find this data in their notes. If it's missing, or if they're not done finding these measures, I coach students to catch up quickly. "In just a few minutes," I tell everyone, "we'll make a box plot of this data."
After a few minutes of making sure that everyone is with me, I review today's agenda, and we get started on making a box plot.
I've prepared the side white board with these notes about box plots. The notes begin with the learning target:
2.1: I can represent data with plots on the real number line. This means that I can create dot plots, box plots, and histograms that accurately represent a data set. (CCS S-ID.1)
Following that are three steps for creating a box plot. I tell students to take a minute or two to copy these notes. Then we'll work through each step.
The first step is to construct a number line that will fit the data. I remind students that we spent a lot of time working with number lines in Unit 1, and that I hope that work will pay off now. The range of the data is different for each class, so that will inform what we require of our number lines. Whatever the data says, we'll talk about the minimum and maximum values as starting and ending points for our number lines, then we can count by something reasonable: 10's, 25's, 50's or even 100's might work. I usually stick to 25's or 50's, but I'll follow whatever lead the class wants me to follow. I give students another few minutes to construct their number lines in their notes, with the hint that everyone will want to leave a little space above their number line, because that's where the box plot will go. I take a quick trip around the room to see how everyone is doing, then we move on to step two.
The next step is to find the minimum, maximum, median, first quartile, and third quartile of the Greed data. "The great news here," I say, "is the we've already done a lot of this! Yesterday, we found the median of the data, and when we created our number lines, we looked for the minimum and maximum. Now, we just have to talk about quartiles."
"Before we do that," I continue, "let's talk a little bit about the median." I ask what the median is, and almost everyone is comfortable with the idea that it's the middle of the list. A great many of my students have been trained in the "crossing-off" method of finding the median, however, and I'd like to build a little more conceptual understanding here. "What does the median do to a list of data?" I ask, in an effort to get at the idea that the median splits a list in half. In order to emphasize this, I either circle the median (if the data count is odd) or draw a line in the middle of the data, where the median goes, and emphasize the idea that the median splits the data in half. Then, I write a "bottom half" list on the left side of the board, and a "top half" list on the right. These lists will allow us to see both what quartiles are, and what they do to a data set.
"When you look at the word quartile, what word to you see?" I ask. When students throw out the word quartile, I ask them how they think of quarters. I wait a beat, and say, "I think of quarters as halves of halves. So I know that 25 cents is half of a half of a dollar." Again, I wait just to let this sink in, and I scan the room for understanding. "How long is a quarter of an hour?" I ask, and this gets us at the idea that 15 minutes is half of a half-hour. "So quartiles split the list into quarters," I say. "Or, we can say that they're the medians of each half of the list." I point to the bottom-half-list. "What is the median of these numbers?" I ask, and students are quick to answer. "So that will be the first quartile." We repeat the drill to find the third quartile, which is the median of the top half of our data.
I remove the data slide from the board, leaving behind our half-lists, which gives me room to draw the number line that we'd discussed previously across the middle of the board. Then we're onto step three, which simply says to draw the box plot. "Once you have number line and these five data points," I say, "it's not too difficult to make the box plot." I demonstrate how I draw each of the five points above the number line, and then how to connect them into a box plot. Here's an example of the resulting notes. If we've been moving quickly and I see that students are with me, I'll spend a few minutes beginning to show students how to interpret a box plot, but I don't worry too much about this now; digging a little deeper here is for an upcoming lesson.
I circulate to make sure that everyone has the notes, then it's time for a practice task.
To frame this practice task, I say that box plots can be used in business to predict future performance. In many fields, the business won't generate the same amount of revenue every week, month, or season, and it's important to be able to figure out what the business can expect. "Here is an example of that for a small business," I say, as I post the practice task.
Of course, box plots become especially useful when one can be compared to another. Sometimes a student will ask a question that allows me to preview this idea, and other times it's best just to practice on this one example now. We're moving toward comparing two or more data sets, but first we need some data. That's what we're going to begin to generate at the end of today's class.