James Dunseith NORTH HIGH, WORCESTER, MA
12th Grade Math : Unit #2 - Statistics: Bivariate Data : Lesson #2

Where Does My Stuff Come From? Part 2

Objective: SWBAT create two-way frequency tables to organize the data that they have collected, both individually and as a group.
Standards: HSS-ID.B.5 MP3 MP5 MP7
Subject(s): Math
60 minutes
1 Opener - 10 minutes

Today's opener in on slide 2 of today's Powerpoint presentation.  I instruct students to look at what they've completed on Stuff Part 1 Gathering Data, which was their homework from the previous class, and to answer the opening questions in their notebooks.  "Later in the class," I say, "we're going to use these values to check our work."

As they work on the opener, I take a quick lap of the room, and record the number of items each student has on Part 1.  I'll sum these numbers to see the total amount of data for the entire class, and I'll reference this number later when we combine all the data for the class.

Whether they have one piece of data or 20+ on Part 1, students can answer these questions.  If any students did not complete Part 1, I'll have a word with them about how they must finish this in order to complete the rest of the project, and as I outline later in the lesson, I'll have tasks to assign to any students with no data on Part 1.

After students complete the opener as stated, I ask them to find some sums as a check.  I ask them to add up the totals for each "category of stuff," and make sure that it adds up to the total number of items.  Next, I ask them to do the same with their "number of items from each country".  This is a preview of how we'll add up the marginal frequencies on the two-way tables that they'll produce in just a few minutes.

When this is complete, I say, "Great!  Now we're going to dig a little deeper into this data, and see what else we can see!"

2 Learning Target Review - 5 minutes

Today, our focus is the first learning target of Unit 2:

  • 2.1: I can use a two-way frequency table to summarize categorical data in two variables.

This SLT is taken from S-ID.B.5:

  • Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 

The next SLT for Unit 2 addresses relative frequency.  I've split this standard into two parts to make it a little clearer for students.

I post slide #3 of today's Powerpoint, and as always, I ask a student to read the new SLT, then open it up for students to point out key vocabulary.

When this is complete, I tell students that Part 2 of the "Where Does My Stuff Come From?" Project is all about this learning target, and that there will be a few more vocabulary words related to this target later in the class.

 

3 Part 2 - Individual Two-Way Frequency Tables - 20 minutes
4 Part 2 - Groups and Whole Class Tables - 30 minutes

Group Totals

On the back of Part 2 is another two-way frequency table on which students will record the totals of all the data for their group.  I make sure that every group has at least four students (with a maximum of six students) who have completed Part 1 and have filled in their table on the front of Part 2.

I leave it to students to figure out how they'll want to go about this task, and I expect to learn a bit about how they work together in organizing themselves to get this done accurately and efficiently.  What will happen is this: students will automatically want to talk about similarities and differences in their data.  I don't use a formal protocol to structure this conversation.  Instead, I just let it happen.  But when it starts to happen, I cultivate it, and I say that everyone should write their thoughts about similarities and differences between individual data sets in their notebooks.

If there is a case where students are having a hard time getting started on the group table, I suggest that they start by following the same process from the first side of the handout: they should make a list of all the countries named by every person in their group, then go country-by-country through the list, recording a sum for each category.

If their list of countries is too long, I have legal-sized paper available, and I tell students that they can reproduce this two-way table on separate sheet.

Class Totals

When the group tables are complete, it's time to summarize all the data for the class in one big two-way table.  The best way to do this is to use Excel.  I project the table (Class TwoWay Table (blank)) on the Smartboard, and follow the procedure from the front of Part 2.  Going group by group, I ask students to name all the countries they have in their group tables.  This will take a little time with the first group, so as that first group recites their list, I tell other groups to check off the countries that have already been named.  Then, when I get to each successive group, they'll only have to name the countries that have not been previously identified.  

If there was a student who was completely unprepared because they didn't complete Part 1, I will have previously asked that student to collect names of countries from each group, and to type them into this Excel sheet.  If that happened, it saves me time on this end.

Once the list of countries is ready to go, I use Excel's alphabetize function to order the list from A to Z, and I go country by country and category by category asking students to tell me the joint frequency that should go in each cell of this table.  It actually moves pretty quickly.  I have tried breaking this part of the action up by letting each group take a few countries on the list, but I find that collecting the data this way ensures accuracy, and it's nice to give students a little time to just watch and think once in a while.

If you don't have access to Excel and a big screen in your classroom, a poster paper version of this chart will suffice.  It might have to be long - at least as long as the list of countries produced by 500 or so data points.

During the next class, we'll use our recently-polished percentage skills and all that we've produced today to dig into relative frequencies.

5 Problem Set 4 - 5 minutes

In addition to the parts of the "Stuff" Project that they'll be working on at home, here is this week's problem set.  Now that we're falling into the rhythm of the class, I distribute this without much fanfare and say that it's due in a week.

At this point, Problem Sets begin to serve the purposes of review prior topics, introducing background knowledge (from prior years) that we'll use in upcoming units, and giving kids a chance to work on current topics.  

Sometimes Problem Sets are more coherent than this one; this one is really more of a mixed bag.  As students work through it, they'll be uploading some important ideas into their working memory.  Also, I like to occasionally give them the task of working on a variety of problems, because that's a skill they'll need for standardized exams like the SAT and the Regents.

6 New Record Sheets and First Prompt: Any Surprises? - 5 minutes

We begin new Record Sheets for the "Where Does My Stuff Come From?" project.  The purpose of these record sheets is to give students a place to record their thoughts, and to serve as a pre-writing activity for paper students will write at the end of this project.  When a record sheet is done right, it should later be a great resource to kids.

Today's Prompt:

When you look at the two-way frequency tables that you and your group produced today, are you surprised by any of the data you see?  Why or why not?

I encourage students to include specific examples and to write as much as they want.