Unit 6, Lesson 8
Using the Correlation Coefficient
Integrated Math 1
8.1
Warm-up
Instructional Routines
NoneMaterials
NoneActivity Narrative
The mathematical purpose of this activity is for students to match bivariate data with its context. Students should think about whether they expect a strong correlation and whether the relationship has a positive or negative correlation. Monitor for students who discuss linear relationships or variability in the data.
Launch
Arrange students in groups of 2 to 4. For the Warm-up, provide access to the scatter plots and contexts.
Activity
NoneMatch the variables to the scatter plot you think they best fit. Be prepared to explain your reasoning.
| -variable | -variable | |
|---|---|---|
| 1. | low temperature in Celsius for Denver, CO, on a given day | boxes of cereal in stock at a grocery store in Miami, FL, on a given day |
| 2. | number of free throws shot in a game | basketball team score in a game |
| 3. | measured student height in feet | measured student height in inches |
| 4. | number of minutes spent in a waiting room | hospital satisfaction rating given by patient |
AScatterplot, origin O. Horizontal from 0 to 8, by 1’s. Vertical from 0 to 80, by 10’s. 13 points that represent the data, clustered in the upper middle portion of the graph and trend linearly upward and to the right. First data point approximately begins at 4 point 8 comma 58 and last is approximately at 6 point 3 comma 74.
BScatterplot, origin O. Horizontal from 0 to 33, by 3’s. Vertical from 0 to 130, by 10’s. 20 points that represent the data, clustered in the upper middle portion of the graph and trend mostly upward and to the right. First data point approximately begins at 13 comma 80 and last is approximately at 25 comma 95. Highest point is approximately at 22 comma 120.
CScatterplot, origin O. Horizontal from 0 to 33, by 3’s. Vertical from 0 to 130, by 10’s. 21 points that represent the data, clustered together in the upper middle portion of the graph. A few data points in the center of the cluster are approximately 16 comma 95, 19 comma 105, and 21 comma 97.
DScatterplot, origin O. Horizontal from 0 to 135, by 15’s. Vertical from 0 to 10, by 1’s. 21 points that represent the data, clustered at the top left first and then widely spread, trend downward and to the right. First data point approximately begins at 7 point 5 comma 8 and last is approximately at 128 comma 5.
Student Response
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Building on Student Thinking
Students may struggle with matching the pairs of variables with a scatter plot. Encourage students to think about how related the variables are and how the -variable may change as the -variable increases.
Activity Synthesis
The goal of this discussion is for students to discuss how the characteristics of the scatter plots allowed them to determine the context. For each context, select groups to share their match and reasoning. Select groups who used linear models and variability in their small-group discussions.
Here are some questions for discussion.
- “How did the concept of linear relationships help you to make a match?” (For the height in inches and the height in feet, I knew that the data would be very linear. I chose scatter plot A because it was the only one that appeared linear. I did wonder why scatter plot A was not perfectly linear. Maybe it had to do with rounding or measurement error.)
- “How did you use the concept of linearity to help you to make a match?” (First, I expected the temperature and cereal context relationship to be totally random rather than linear, so that led me to choose scatter plot C. Second, I knew that the third set of variables matched with scatter plot A because I knew it should be almost perfectly linear. For a given height in feet, there is only one height in inches.)
- “Which matches were the most difficult? What helped you figure them out?” (It was hardest to find the matches for scatter plots B and D because they were pretty scattered. I noticed that the data in scatter plot D displayed a negative relationship, so I looked for a context that would have a negative relationship. It makes sense that customer satisfaction decreases as wait time increases.)