This lesson uses the data from the video of orange weights from the activity Orange You Glad We’re Boxing Fruit. The mathematical purpose of this activity is to introduce the concept of residuals, and to have students plot and analyze the residuals to informally assess the fit of a function. In this activity, students also fit a function to data, and use the function to solve problems. Students learn that a residual is the difference between the actual -value for a point and the expected -value for the point on the linear model with the same associated -value.

Compare student answers to the question about the point that the line estimates best to the answer for the question about the residual closest to zero.

Show a graph of the residuals.

Ask students:

• “What does it mean for the residual to be positive? Negative?” (The residual is positive when the actual data value is greater than what the model estimates for that value and negative when the actual data value is less than the estimate.)
• “What does it mean when a residual is on or close to the horizontal axis?” (It means that the line of best fit passes through or comes close to passing through that point in the graph.)
• “Find the residual that has the furthest vertical distance from the horizontal axis. What does this mean in the context of the scatter plot and the line of best fit?” (The residual that is furthest from the horizontal axis has the same -coordinate as the point that is the greatest vertical distance away from the line of best fit in the scatter plot.)

Students may not understand how to determine if the linear model estimates the weight of oranges well or poorly. Ask them to determine the weight that the model estimates, then ask how close that estimate is to the actual weight.