1. MATH 7174: Statistics & Modeling for Teachers June 11, 2014

2. Agenda
HW Discussion
Big ideas
What Fits? #1
What Fits? #2

3. Warm-Up Find someone with whom you did not work last week.
Spend 5 minutes discussing the following with your partner. Be prepared to summarize your discussion for the larger group:
Which of the concepts included in Big Idea 3 and 5 do your students seem to understand well?
Which of the concepts included in Big Idea 3 and 5 are more of a challenge for your students?

4. What Fits?
Question: What is the relationship between the drop height of a golf ball and the height of its first bounce?
What is the population of interest?
What are the two variables of interest?
Which variable is the explanatory variable? Why?
Do you expect there to be a strong association between these two variables? Why?
What form do you expect the relationship to follow (i.e., what function family would be used to model this relationship?)? Why?
What direction do you expect the association to take? Why?
Do you expect a golf ball to bounce back up to its drop height? Lower than its drop height? Higher than its drop height?

5. Data Collection
Get into the following groups. Drop your ball from the given heights and measure the height of the bounce. Record in the table.
The given height are:
11 cm, 18cm, 26 cm, 38cm, 50cm, 52cm
Create a visual display of the data. Explain why you choose the particular display.

6. What Fits? Compare the scatterplot to our predictions.
Positive or negative association?
Strength of association?
Form of the relationship?
Determine where you think the line of best fit should be placed on the scatterplot by manipulating a piece of spaghetti. Draw your line on the scatterplot once you have determined its best placement.
Compare your lines with others at your table. How did you determine where to put your line?

7. What Fits?
What did you consider when determining the line’s placement?
Does the line match the relationship you predicted prior to data collection?
What are some reasons why the data are not perfectly linear?
Work in groups on Part Two of the activity.

8. What Fits?: Teacher “Hat”
What would you hope your students would say in response to the Summary Questions (p. 15)?
Some of the learning targets for this lesson include:
SWBT informally fit a straight line.
SWBT informally assess the model’s fit by judging the closeness of the data points to the line.
Why might it be valuable for students to begin this topic with these “informal” approaches?

9. What Fits #2

10. For Next Week HW 6: Coffee & Crime Work individually on the task.
Keep in mind that your work will be scored and returned to you. So, please write out complete answers. In other words, answer the questions in the manner that you would hope your students would. 