options: Interpret linear models.

Understand independence and conditional probability and use them to interpret data.

Investigate patterns of association in bivariate data.

Summarize, represent, and interpret data on a single count or measurement variable.

Investigate chance processes and develop, use, and evaluate probability models.

Draw informal comparative inferences about two populations.

Summarize and describe distributions.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Develop understanding of statistical variability.

Use probability to evaluate outcomes of decisions.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Use random sampling to draw inferences about a population.

Calculate expected values and use them to solve problems.

Understand and evaluate random processes underlying statistical experiments.

Summarize, represent, and interpret data on two categorical and quantitative variables.
problem_activity: Optional activity
Students interpret the slope and intercepts in the context of the situation. They also discuss limitations of the mathematical model.
This activity can be extended by having students investigate if temperature on other continents or across continents fits the same pattern that we found for North America.
Launch
Keep students in same groups of 3–4.
Student Facing
Refer to your equation for the line that models the association between latitude and temperature of the cities.
What does the slope mean in the context of this situation?
Find the vertical and horizontal intercepts and interpret them in the context of the situation.
Can you think of a city or a location that could not be represented using this same model? Explain your thinking.
Student Response
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Anticipated Misconceptions
Students may want to say “For every one unit increase in
\(x\)
,
\(y\)
decreases by 1.07 units.” Ask them to use the specific units and quantities in the model, latitude in degrees north and temperature in degrees Fahrenheit.
Activity Synthesis
Invite students to share their responses. Discuss the limitations and uses of the model. Consider asking the following questions:
“What are some limitations of the model?”
“Do limitations mean that the model is not good?” (No, it just means that we have to be aware of when we can use it and when we can’t use it. Our model is pretty good for latitudes between 25 and 65 degrees north, and for locations in North America.)
“What questions do you have about predicting temperature?”
“How could you extend your investigation of predicting temperature or the weather?”
Engagement: Develop Effort and Persistence.
Break the class into small discussion groups and then invite a representative from each group to report back to the whole class.
Supports accessibility for: Language; Social-emotional skills; Attention


correct_option_index: 2