Observing More Patterns in Scatter Plots
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to elicit the idea that some variables can be associated in a way that is not linear, which will be useful when students work with non-linear data in a later activity. While students may notice and wonder many things about these data, the association and non-linearity are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Arrange students in groups of 2. Display the scatter plot for all to see. Tell students that oil production and price are shown. Production is measured in “thousands of tons,” so a point on the left side of this graph represents 250,000 thousand tons (or 250,000,000 tons). Price is measured in “dollars per barrel.” One barrel of oil is equivalent to 42 gallons. The prices in this chart are for crude oil which would still need to be processed to be made useful for gasoline, plastics, or other oil-based materials.
Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner.
Student Task
What do you notice? What do you wonder?
Sample Response
Things students may notice:
- The points don’t all lie near a line like they have in previous scatter plots.
- As production increases, the price decreases.
Things students may wonder:
- What does “oil production” or “import price” mean?
- Is it okay to model this relationship using a line?
- Why does it seem to level out at the end?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the scatter plot. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If the idea that the data show an association, but are not linear does not come up during the conversation, ask students to discuss this idea.
Tell students that, even when a linear association seems to be present, it may only fit the data very close to the data that is present. For example, if we cover up the scatter plot to the right of 300,000 thousand tons, there may appear to be a linear association that would fit the data, but it would not apply to the data on the right side of the scatter plot. Additionally, in this particular situation, a linear model does not make sense in the long term, since a linear model would eventually have a value of 0 and then become negative, something that would probably not happen to the price of oil.
Standards
- 8.SP.1·Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
- 8.SP.A.1·Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
20 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Observing More Patterns in Scatter Plots
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to elicit the idea that some variables can be associated in a way that is not linear, which will be useful when students work with non-linear data in a later activity. While students may notice and wonder many things about these data, the association and non-linearity are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Arrange students in groups of 2. Display the scatter plot for all to see. Tell students that oil production and price are shown. Production is measured in “thousands of tons,” so a point on the left side of this graph represents 250,000 thousand tons (or 250,000,000 tons). Price is measured in “dollars per barrel.” One barrel of oil is equivalent to 42 gallons. The prices in this chart are for crude oil which would still need to be processed to be made useful for gasoline, plastics, or other oil-based materials.
Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner.
Student Task
What do you notice? What do you wonder?
Sample Response
Things students may notice:
- The points don’t all lie near a line like they have in previous scatter plots.
- As production increases, the price decreases.
Things students may wonder:
- What does “oil production” or “import price” mean?
- Is it okay to model this relationship using a line?
- Why does it seem to level out at the end?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the scatter plot. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If the idea that the data show an association, but are not linear does not come up during the conversation, ask students to discuss this idea.
Tell students that, even when a linear association seems to be present, it may only fit the data very close to the data that is present. For example, if we cover up the scatter plot to the right of 300,000 thousand tons, there may appear to be a linear association that would fit the data, but it would not apply to the data on the right side of the scatter plot. Additionally, in this particular situation, a linear model does not make sense in the long term, since a linear model would eventually have a value of 0 and then become negative, something that would probably not happen to the price of oil.
Standards
- 8.SP.1·Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
- 8.SP.A.1·Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.