Linear Models
5 min
Narrative
The purpose of this Warm-up is to help students recall information about scatter plots, which will be useful when students expand their understanding in a later activity.
While students may notice and wonder many things about these images, the relationship between the number of people and the maximum noise level, the interpretation of the line of best fit, and the general idea of a scatter plot 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.
Monitor for students who use mathematically precise terminology in their responses. In particular, the terms "scatter plot," "linear model," "slope," and "intercept" are important to review during this Warm-up.
Launch
Arrange students in groups of 2. Display the graph for all to see. 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 with their partner the things they notice and wonder.
Student Task
What do you notice? What do you wonder?
y=1.5x+22.7
Sample Response
Students may notice:
- More fans generally means more noise.
- At around 65,000 fans, there are three different noise levels.
- The equation of the line is given.
Students may wonder:
- Where is the origin?
- Why are all the points not on the line?
- What can we do with this?
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 graph. 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 students do not use these terms in their responses, prompt them to recall the vocabulary from grade 8 math:
- "scatter plot"
- "linear model"
- "slope"
- "intercept"
Anticipated Misconceptions
The vertical intercept appears to be approximately 105 decibels, but the origin is not shown on the graph.
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.
- HSS-ID.B.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- S-ID.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- S-ID.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- S-ID.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- HSS-ID.C.7·Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- S-ID.7·Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- S-ID.7·Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- S-ID.7·Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
15 min
5 min
10 min
Knowledge Components
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Linear Models
5 min
Narrative
The purpose of this Warm-up is to help students recall information about scatter plots, which will be useful when students expand their understanding in a later activity.
While students may notice and wonder many things about these images, the relationship between the number of people and the maximum noise level, the interpretation of the line of best fit, and the general idea of a scatter plot 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.
Monitor for students who use mathematically precise terminology in their responses. In particular, the terms "scatter plot," "linear model," "slope," and "intercept" are important to review during this Warm-up.
Launch
Arrange students in groups of 2. Display the graph for all to see. 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 with their partner the things they notice and wonder.
Student Task
What do you notice? What do you wonder?
y=1.5x+22.7
Sample Response
Students may notice:
- More fans generally means more noise.
- At around 65,000 fans, there are three different noise levels.
- The equation of the line is given.
Students may wonder:
- Where is the origin?
- Why are all the points not on the line?
- What can we do with this?
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 graph. 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 students do not use these terms in their responses, prompt them to recall the vocabulary from grade 8 math:
- "scatter plot"
- "linear model"
- "slope"
- "intercept"
Anticipated Misconceptions
The vertical intercept appears to be approximately 105 decibels, but the origin is not shown on the graph.
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.
- HSS-ID.B.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- S-ID.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- S-ID.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- S-ID.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- HSS-ID.C.7·Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- S-ID.7·Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- S-ID.7·Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- S-ID.7·Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.