Class period 1.

 

Goal: understanding of the concept of a categorical distribution, representations of categorical distributions, qualitative and quantitative comparisons of distributions of the same size.

 

Materials needed:

 

  1. transparencies for teacher: Poll results, Class 1 table, Class 1 pie chart, Class 1 bar graph, Class 1 line graph (one copy of each)
  2. transparencies for class: Class 1 bar graph, Class 2 bar graph, Class 3 bar graph (one copy for each group: say 10 copies of each)

 

 

Sample bar graph

 

 

15

15                                                                                                     Total = 25

 

 

10

 

                                     5                                                                       5

  5

 

 

 

 

 


                               love  broccolli           hate broccoli                don’t care

 

Script:

 

Teacher: President Bush’s father, the former President Bush, once got into a lot of trouble by telling everybody that he hated broccoli. How many of you like broccoli? How many of you hate broccoli? How many of you can take it or leave it?

 

Let’s imagine that there was a school with three sixth grade classes, each of which had 25 kids in them, and that they took a survey in each class to see who liked broccoli.

 

Show poll results on overhead transparency:

 

Class 1: 5 liked broccoli, 15 hated broccoli, 5 didn’t care

Class 2: 12 liked broccoli, 3 hated broccoli, 10 didn’t care

Class 3: 3 liked broccoli, 16 hated broccoli, 6 didn’t care

 

Teacher: How many kids are in each class? OH, they’re all the same size: 25 kids.

Let’s think about Class 1 for a minute; here is a table (class 1 transparency table) which shows how Class 1 responded. Remember that little math quiz Mr. Moher gave you a few weeks ago? How could we draw a picture to represent what Class 1 thought about broccoli?

 

Expected kid responses: bar graph, pie chart, line graph. As kids say them, teacher puts appropriate transparency up on the overhead.

 

Teacher: Okay, there are all perfectly good pictures of what Class 1 thought about broccoli. We call these things “distributions,” and the different pictures are different “representations” of these distributions. We’re going to be using bar graphs.

 

Teacher: Now which of these classes would you say liked broccoli the most? How could you tell? Which of them liked broccoli the least? All of these classes were different from each other, but were two of them more alike each other, and one different? Which two classes were “similar” to each other? Which was different? Why?

 

Okay, we seem to be able to tell that there’s a difference, that somehow Class 1 and Class 3 are more alike, and Class 2 is different. But scientists like measure things with numbers. What we’re going to do for the rest of this class period is to have each group (clusters of tables around the room) try to invent a way to measure the difference between these Classes. We’re going to give each group transparencies showing the different class distributions, let them invent a formula, and then the groups will report back on the measuring technique that they invented. Next week, we’re going to use your measuring techniques to compare distributions of data that we collect in the Field in VR.

 

Teacher distributes transparencies. Students work in small groups for about 10-15 minutes.

 

Come back to whole-class orientation.

 

Teacher selects groups to present their measurement technique.

 

Expected responses:

 

Desired response: sum of absolute differences of each bar

 

Then comparing Class 1 to Class 2:

 

 

 

Class 1

Class2

Difference

Liked broccoli

5

12

7

Hated broccoli

15

3

12

Didn’t care

5

10

5

 

 

 

24

 

 

Then comparing Class 1 to Class 3:

 

 

 

Class 1

Class 3

Difference

Liked broccoli

5

3

2

Hated broccoli

15

16

1

Didn’t care

5

6

1

 

 

 

4

 

 

Then comparing Class 2 to Class 3:

 

 

 

Class 2

Class 3

Difference

Liked broccoli

12

3

9

Hated broccoli

3

16

13

Didn’t care

10

6

6

 

 

 

28

 

 

So: most alike are classes 1 and 3. Most different are classes 2 and 3.

 

 

Alternative response: signed difference.

 

Consider comparing class 2 to class 3, though:

 

 

 

Class 2

Class 3

Difference

Liked broccoli

12

3

9

Hated broccoli

3

16

-13

Didn’t care

10

6

4

 

 

 

0

 

That would say there was NO difference between Class 2 and Class 3.

 

Summary comments:

 

  1. Vocabulary: distribution, representation, quantitative comparison, absolute difference
  2. Concepts: metric for comparing distributions of equal sizes.