The Game of Greed

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Objective

SWBAT collect and organize the first data set of the semester by playing a game; they will see how to construct a box plot from this data.

Big Idea

Sticky notes make this data set a manipulative that can be rearranged as student understandings of statistical representations evolve.

Opening Problem

5 minutes

As students enter on the first day of class, I project the second slide of today's Prezi on the screen. The first instruction is to "Sit in a group where you'll be able to have good conversations."  This simple instruction indicates to students that they'll need to work in groups and that I expect them to talk to each other; it also indicates that I'm not going to dictate their seating arrangement and that it's up to them to make the most of this course.  As the semester continues, there will be structures for getting students to talk to each other beyond their chosen groups, but as we begin, I think it's fine to let everyone be where they're comfortable.

I start with a Problem right away, to begin setting the expectation that here, we'll be solving problems all the time.  The traditional way to solve this problem is by using a Venn Diagram, but I have no prescribed method in mind.  If students bring up the Venn Diagram method on their own, I'll coach them through it, but if they don't, I'll follow their thinking whatever direction it takes.

The key thing I want to note to my students is that this is a counting problem, and that counting is part of what we're going to learn how to do in this class.  I love saying this line, because it's provocative: "We already know how to count!" is what I can count on students telling me.  Of course, I add, we'll get pretty deep into counting, and it's going to be an exciting semester.

 

URL for the PREZI: (accessed Sept 14 2014)

http://prezi.com/-7bxp4ylobuf/?utm_campaign=share&utm_medium=copy&rc=ex0share

The Game of Greed

15 minutes

After beginning with a quick counting problem, I continue to set the tone for this class by introducing a game.  The game is called "Greed," and it will generate our first data set of the semester.  The data will initially be collected on sticky notes, and we will continue to use this data for the next few classes. 

How to Play

Please take a look at slide #'s 3 through 5 of today's Prezi, and at my Game of Greed video for an overview of the game.

Collecting Data

After we play, as students are tabulating their final scores, I distribute two different colored sticky notes: one color for the girls, and one for the guys.  When we look at this data, I'll introduce the idea of correlation by asking if there's any evidence that one gender's scores are higher than the other's.  There is unlikely to be too much of a correlation, but I am ready to have a sense of humor if kids try to see one.  "If you can see a correlation between gender and greed scores," I ask, "does it really mean anything?  Would this always happen?  Would it happen if we played again right now?"  It's fun to start these conversations, and, as we continue with our study of stats, to watch as students question their initial ideas. 

This game also serves as a first-day formative assessment, because it's interesting to observe how each student reacts to playing this game.  You'll catch a glimpse of who your risk-takers and risk-averse students might be.  

After we play, I present students with the task of finding the mean and median of our data set. The data is in the form of a bunch of sticky notes stuck the board at the front of the room.  I leave it to students to see how they'll get this data from the "primary source" (sticky notes) to their notebooks.  If they ask, I say that of course they can rearrange the notes and try to organize them.  If a student or two want to read the numbers to the class so everyone else can write them down, that works too.  See what happens.  

Over the next few classes, we'll continue to use this data to learn about dot plots, box plots, and histograms.  Look at how this could lead to a histogram, by arranging these in buckets.  These sticky notes become an initial data set and a manipulative that we can return to as we engage in this work.

 

Mini-Lesson: About this Stats Class and Box Plots

30 minutes

Syllabus and Introduction to this Class

After we solve a problem, play a game, and take a peek at our first data set, I spend a few minutes introducing the class.  I distribute the syllabus and briefly read through it with the class.  At each section of the syllabus, I pause to allow for student questions.  I tell students that we'll return to the syllabus as a check-in throughout the semester, and that they should hold on to these, becuase all of the learning targets for which they are responsible are right here.  Please take a look at my strategy notes on Mastery-Based Grading for an overview of how I use learning targets to assess my students.

Guiding Question and Student Learning Target

On slides 6 and 7 of today's Prezi are the first guiding question and the first Student Learning Target (SLT) for this course.  I post the learning target on the screen:

SLT 1.1: I can represent data with dot plots, histograms, and box plots on the real number line.  (CCS HSS-ID.A.1)

Here's how I introduce a new learning target: I ask for a student volunteer to read the SLT aloud, then I ask students to identify the key words in this SLT.  By doing this, we generate a working vocabulary list that we'll be able to revisit as a check-in on our progress.

How to Construct a Box Plot

Among other vocabulary words are the first three data representations we'll study in this class: dot plots, histograms, and box plots.  I tell the class that we're going to start by looking at box plots.  I change to slide #8 and add that we've already started this work, by finding the median.  In order to make a box plot, we need five data points.  One of them is the median.  Then we'll need the minimum and the maximum.  I look around the class to gauge understanding, and I expect to be able to say how that part was easy enough, and that now we just need to find the quartiles.

I know that many of my students have seen box plots and quartiles before, but I treat it like it's new, just to make sure that everyone is on board.  There are a few connections I make to the word quartiles.  First, I ask students what other words they know that looks like this one, and I'm fishing for the word "quarter."  This allows us to talk about a quarter as one-fourth or 25% of a whole, and I'll throw in references to money and to basketball games here.  I also make the point that a quarter is "half of a half," and I say this a few times, to make sure my students can think of it this way.  I like to watch how my students engage with this definition of a quarter, and it's always neat to see their satisfaction as they make sense of that.

With that in mind, I say that we can think of a "quartile" as the "median of one half of the data set".  I ask the class why this is the case, and I'm looking for students to have the idea that the median is the half-way point in an ordered list, so we might informally define quartile as the "median of the median" or the "median of half the list."  I try not to say too much, but to quickly pose the task of find the quartiles of our scores from the Game of Greed.  This way, I can circulate to check for understanding.

After students have a few minutes to try this, we can work together to solve this problem by arranging and annotating the sticky notes on the board.  Of course, the arrangement of the stickies depends on whether there is an odd or even number of data points (both in the whole set and in each half of the list).  A combination of easily-movable stickies and some chalk (or dry-erase) annotations can really help students make sense of what they're seeing.

Scaling the Number Line

"By simply dividing our data set into four parts, we can see the values in each part of the set," I say.  "But here's the other great thing about a box plot: it can help us see how spread out the values in our data set might be."

This is how I frame the next part of our task: to construct a scaled number line that we can use to make our plot.  Do not underestimate this part of the lesson.  As this class begins, I really want to make sure to get it right, circulate, ask questions, make sure students are making reasonable decisions.  The key elements of our number line will be its minimum, its maximum, and its scale. If the Greed scores range from 0 to 300, for example, I'll help students define scale by asking them what they'd want to count by if they were counting from 0 to 300.  I follow up by asking how many numbers they'd say if they counted by 10, or 25, or 50, or 100, and by saying that this is how many evenly-spaced marks they'll need on the number line.  I show students where to find the rulers, and I give them time to make these number lines.

Finally, when the number lines are complete, I show them how to mark each of the 5 data points and then how to draw the box plot itself.  One interesting thing that will happen is that a student will choose to count by 100's, but then have trouble figuring out exactly where to put the point for a number in-between.  I show the class that you can always add more marks in-between to allow for greater precision.  

Optional Extension

Here's a great question to ask: 

What would happen to the shape of this box plot if the "losing number" was 7?  12?

I generally try to save this question for an upcoming class, but it may come in handy here.  

 

First Day Survey

15 minutes

With about 20 minutes left in class, it's time for the First Day Survey (I'm presenting this here as an example - you'll probably want to make your own. One of the questions I ask, for example, is for the age of everyone's favorite teacher.  Kids find this question really funny.  You should replace Mr. Cyrus' name with someone else.) Because I have access to a laptop cart, I use a Google Form for the survey, but I think this would work just as well on paper.  This method makes it slightly easier for me to go through the responses, and the use of laptops on the first day of class is another way I am able to show students some of the structures they can expect in the class.

This survey serves two purposes:

  1. It gives me some background about each of the students in my class
  2. Some of these questions will generate data sets that I'll use in the first homework problem set, which you can find in the next lesson.

Homework: Find an Article

10 minutes