Linear Functions w/ Scatterplots

Warm-Up (10 minutes):

1. Briefly review the concept of linear functions (y = mx + b) and how they represent straight lines on a graph.
2. Present a real-world scenario where two variables might be related. (Ex: As the price of gasoline increases, does the number of miles driven per week decrease?)

Activity 1: Unveiling the Patterns - Scatter Plots (20 minutes):

1. Divide students into pairs.
2. Distribute the handouts (linked in the resources tab).
3. Instruct students to:
   • Identify the independent and dependent variables for each data set.
   • Hypothesize and justify correlations.
   • Label the axes with appropriate units.
4. Facilitate a class discussion:
   • Ask students to describe the "shape" of their scatter plots for each data set.
   • Encourage them to use terms like "positive association," "negative association," or "no apparent association."
   • Discuss what these associations might represent in the real-world context of the data.

Activity 2: The Line of Best Fit (20 minutes):

1. Briefly introduce the concept of a line of best fit as a line that minimizes the distances between the data points and the line itself.
2. Ask students to estimate a line of best fit for each scatter plot on their graphs. (This can be done visually or using calculators with linear regression functions.)
3. Facilitate another class discussion:
   • Ask students to explain their reasoning for choosing the line of best fit.
   • Discuss the limitations of a line of best fit – it won't perfectly capture every data point.

Wrap-Up (10 minutes):

1. Briefly review the key points:
   • Scatter plots help visualize relationships between two variables.
   • The "shape" of the scatter plot indicates a positive, negative, or no linear association.
   • A line of best fit can be an approximate representation of the trend in the data.
2. Exit Ticket:
   • Briefly describe a real-world scenario where a scatter plot might be useful.
   • Explain what kind of association you might expect to see in the data.

differentiation: for struggling students, provide partially completed scatter plots or prompts to guide their analysis.

extension: for advanced students, introduce the concept of correlation coefficient to quantify the strength of the linear association.

Observe student participation in discussions and activities. Collect and review the completed scatter plots and explanations for lines of best fit. Evaluate worksheets to gauge student understanding.