options: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

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.

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
problem_activity: Optional activity
In the previous activity, students drew a line that best fit the latitude-temperature data and found the equation of this line. The line is a mathematical model of the situation. In this lesson, they use their model to make predictions about temperatures in cities that were not included in the original data set. In the next activity, they also interpret the slope of the line and the intercepts in the context of this situation. This leads to a discussion of the limitations of the mathematical model they developed.
Launch
Students in same groups of 3–4. If available, tell the students the latitude and average high temperature in September in their city.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to support students who benefit from support with organizational skills in problem solving. For example, present one question at a time and monitor students to ensure they are making progress throughout the activity.
Supports accessibility for: Organization; Attention
Student Facing
In the previous activity, you found the equation of a line to represent the association between latitude and temperature. This is a
mathematical model
.
Use your model to predict the average high temperature in September at the following cities that were not included in the original data set:
Detroit (Lat: 42.14)
Albuquerque (Lat: 35.2)
Nome (Lat: 64.5)
Your own city (if available)
Draw points that represent the predicted temperatures for each city on the scatter plot.
The actual average high temperature in September in these cities were:
Detroit:
\(74^\circ\text{F}\)
Albuquerque:
\(82^\circ\text{F}\)
Nome:
\(49^\circ\text{F}\)
Your own city (if available):
How well does your model predict the temperature? Compare the predicted and actual temperatures.
If you added the actual temperatures for these four cities to the scatter plot, would you move your line?
Are there any outliers in the data? What might be the explanation?
Student Response
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Activity Synthesis
Invite some groups to share their results and compare predictions for the different cities. Ask if students think that the line is a good mathematical model to predict the temperature in a location if you know the latitude.
Representing, Speaking, Listening: MLR2 Collect and Display.
Use this routine to collect verbal and written ideas about students’ mathematical models and the limitations of them that they see. During the synthesis discussion, chart key ideas that students share out about the slope, intercept, and differences in their predictions. Remind students that we call this a “mathematical model” (i.e., the line they drew). It is one way to look at data. Ask students, “What are the limitations of this model in making predictions?” Add their language to your chart. Reference this chart in the following lesson and make revisions as needed with student input.
Design Principle(s): Support sense-making; Maximize meta-awareness


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