Fitting a Line to Data
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students are asked to think about a point in the context of the entire data set. They compare two different possible predictions for the dependent variable, given a value for the independent variable. This sets them up to understand and interpret a linear model for the relationship between independent and dependent variables. They use the potential location of a point not included in the scatter plot to answer a question about the context, based on the visual structure of the scatter plot (MP7, MP2).
Launch
Arrange students in groups of 2. Give 1 minute of quiet work time followed by 1 minute to check their solution with their partner. Follow with a whole-class discussion.
Student Task
Here is a scatter plot that shows weights and fuel efficiencies of 20 different types of cars.
If a car weighs 1,750 kg, would you expect its fuel efficiency to be closer to 22 mpg or to 28 mpg? Explain your reasoning.
Sample Response
We expect the fuel efficiency to be closer to 22 mpg. There are several cars close to that weight, and their fuel efficiency is between 18 and 22 mpg. The cars that have a fuel efficiency close to 28 mpg have a weight less than 1,250 kg, although there is one car that has a weight greater than 1,500 kg and a fuel efficiency of 26 mpg. But that one has a higher fuel efficiency than any other car with a weight between 1,500 and 1,750 kg.
Activity Synthesis (Teacher Notes)
Display the graph for all to see. Poll the class to see if they think the fuel efficiency is closer to 22 mpg or 28 mpg. If they are all in agreement that the answer is closer to 22 mpg, ask a few students to share their reasoning. If there is disagreement, ask students to share their reasoning and come to an agreement. If it does not come up in the discussion, ask students to look at cars whose fuel efficiency is close to 28 mpg and note that their weights are quite a bit less. Then look at cars with a weight close to 1,750 kg, and note that their fuel efficiency is between 18 and 22 mpg. As a whole class, decide where to plot both potential points, and point out that 1 is close to the other nearby values and 1 is very far away.
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.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Fitting a Line to Data
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students are asked to think about a point in the context of the entire data set. They compare two different possible predictions for the dependent variable, given a value for the independent variable. This sets them up to understand and interpret a linear model for the relationship between independent and dependent variables. They use the potential location of a point not included in the scatter plot to answer a question about the context, based on the visual structure of the scatter plot (MP7, MP2).
Launch
Arrange students in groups of 2. Give 1 minute of quiet work time followed by 1 minute to check their solution with their partner. Follow with a whole-class discussion.
Student Task
Here is a scatter plot that shows weights and fuel efficiencies of 20 different types of cars.
If a car weighs 1,750 kg, would you expect its fuel efficiency to be closer to 22 mpg or to 28 mpg? Explain your reasoning.
Sample Response
We expect the fuel efficiency to be closer to 22 mpg. There are several cars close to that weight, and their fuel efficiency is between 18 and 22 mpg. The cars that have a fuel efficiency close to 28 mpg have a weight less than 1,250 kg, although there is one car that has a weight greater than 1,500 kg and a fuel efficiency of 26 mpg. But that one has a higher fuel efficiency than any other car with a weight between 1,500 and 1,750 kg.
Activity Synthesis (Teacher Notes)
Display the graph for all to see. Poll the class to see if they think the fuel efficiency is closer to 22 mpg or 28 mpg. If they are all in agreement that the answer is closer to 22 mpg, ask a few students to share their reasoning. If there is disagreement, ask students to share their reasoning and come to an agreement. If it does not come up in the discussion, ask students to look at cars whose fuel efficiency is close to 28 mpg and note that their weights are quite a bit less. Then look at cars with a weight close to 1,750 kg, and note that their fuel efficiency is between 18 and 22 mpg. As a whole class, decide where to plot both potential points, and point out that 1 is close to the other nearby values and 1 is very far away.
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.