The Game of Greed and an Intro to Statistics

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Objective

SWBAT collect qualitative and quantitative data, and explain the difference between the two. They will also review the measures of central tendency on a data set that we create today.

Big Idea

To the extent possible, students will generate their own data during this five-week statistics unit.

Opener: What are you going to roll?

3 minutes

As class opens today, so do our second marking period and the Statistics unit.  My goals for the Statistics unit are twofold:

  • To help students develop an understanding some statistical tools and how they're used
  • To lay some scaffolding for students to gain traction with conceptual understanding of the upcoming units on equations, graphs, and function representations that comprise most of the Algebra 1 curriculum

With an eye on both goals, I want students to use as much real data as possible over the next few weeks.  Today, we'll start producing data immediately, and we'll use this data a few times.  

With that in mind, today's opener is informal, and meant simply to get kids thinking.  With a note that today is a transition point, the opener says, "Sit with a partner who can help you work hard." It's enough to get students to think about where they're sitting and who with, and it once again invokes that idea of hard work as one that's central to success in this class.

The question that follows gets kids thinking about probabilities.  I don't try to answer this question during the first three minutes of today's class, but I'll ponder it with anyone who wants to.  After a few minutes of this, I say that we're going to play a game, and that's where class goes next.

Generating Data: Playing Greed

10 minutes

On the second slide of today's class notes are the rules of the game.  I explain the game, and we play.  Students record their scores, and just like that, we have our first data set.  Check out my video narrative for a description of the game, and some of my thinking behind it.

Framing the Class and Analyzing Greed Data

25 minutes

Gathering Data

When we've played through the fifth round of Greed, I tell students to find the sum of their five scores, and I distribute the Statistics Unit Syllabus.  This document has the Student Learning Targets for the Unit on one side.  On the other is a "Data Collection Sheet," which is a place for students to record a variety of their own data over the next few weeks.  I ask students to find where the Greed data goes, and to total things up there.  While this happens, I make another trip around the room and give everyone a sticky note.  "Once you have your total Greed score, please write it on your sticky note.  Then place your sticky note on the poster at the front of the room." The result looks like this.

The Idea of Qualitative vs. Quantitative Data

On today's agenda, I've written the words "qualitative and quantitative" data.  Moving forward, I'd like for students to be able to make this distinction, so before we begin to analyze the Greed data, I point to the words on the board.  I follow the popular approach of asking students to identify the words they see within qualitative and quantitative, then I ask what "a quality" is and what "a quantity" might be.  We get to the point of discussing personal characteristics that fit each description.  Students realize that their height, weight, age, and shoe size are examples of quantitative data, while hair color, eye color, and personal demeanor are qualities.

"So what if I wanted to collect qualitative data about this class?" I ask.  "I would like to try to answer this question: Is there evidence that this class is working hard?  If I was looking for an answer to that question, what would I need?  What does it look like to work hard?"  I loosely and informally follow the think-pair-share protocol, by asking students to write a few ideas of their own, then to discuss their answers and record a favorite idea or two from their partner.  Then I project this document on the board (the side that says "Data Collection Sheet"), and elicit a few answers from students, which gives us this qualitative data.  With a few of my classes that need a little motivational boost, I'll collect data on these traits in Class Dojo.  We'll then be able to compare this data to achievement on some SLTs later in the marking period.  For other classes, these are just examples, but we'll be able to reference these qualities in conversations that continue throughout the year. 

After this, we briefly run through the syllabus.  I show students that there are two background learning targets and five Unit 2 SLTs on the syllabus, and that the Mathematical Practices are still in play.  I ask students if the grading system is making more sense, and for the most part they're fully bought in by now.  Seeing how the learning targets change for the new unit makes it a bit more clear how this all works, and I watch as students consider these learning targets and look ahead at how they'll meet each one.

Mean, Median, and Mode

Now it's time to practice the first background target: calculating the mean, median, and mode for a data set.  We'll use the Greed Data that's up on the board.  I simply post the task of finding these measures.  Students quickly notice that they can't quite see the data set from their seats, a small problem that requires a solution.  Usually, someone volunteers to read the data to the class; if that doesn't happen I'll suggest it.  As the volunteer begins to read, however, we also notice that it would help for this data to be a little better organized.  It happens quite naturally that the class decides to order the stickies from least to greatest, and now the organized stickies look like this.  Now, when someone reads the data aloud, students recording it will have an easier time making sense of it.  

Now students can get to the task of finding these three measures of central tendency.

If Time Allows

For most classes, time runs out as students finish the previous task, but if things have moved quickly today, or if it's an extended period, the next step is to review 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.

We then make a quick box plot representing this data.  This is the primary focus of tomorrow's class.

Return Exams, Mastery Session, Homework

5 minutes

With a little more than five minutes left in class, usually as students are finishing up and checking their measures of center on the Greed data, I return the Unit 1 Exam that students took last time we met.  I have a little time to answer a question or two about the exam, but for the most part my focus is practical: I want to help students understand that their grades on this exam consist of separate grades for each Student Learning Target.  I ask students to think about whether or not these grades are a fair representation of what they've learned and done so far.

Then, I explain that for anyone who wants to improve their grade from the first marking period, I would love to help.  "The way to improve your grade is to work on one learning target at a time," I say.  Then I tell everyone that there will a series of after-school "mastery sessions" in the coming weeks.  This is what is made possible by mastery-based grading.  Anyone who wants to come can.  To build scarcity, I put a sign up sheet on my wall.  It usually fills up by the end of the day, so then my job is to make sure that everyone who signs up comes.  I'll do these once or twice each week, each time focusing on a different SLT.  The sessions consist of working on exam problems, going back and completing previous work that we've done on the SLT, and then students solving a few "mastery problems" that, if students can solve them, give me reason to change student mastery grades.