Florida B.E.S.T. MA.912.DP.2.5
The Standard
Given a scatter plot that represents bivariate numerical data, assess the fit of a given linear function by plotting and analyzing residuals.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use a linear equation to find predicted values, then subtract predicted values from observed values. They plot those residuals and decide whether the pattern supports a linear model.
What Mastery Looks Like
- A student correctly computes each residual as observed value minus predicted value and plots it against the explanatory variable. The student uses spread and visible patterns around zero to make and support a fit decision.
Common Misconceptions
- Students may subtract in the wrong order, using predicted minus observed instead of observed minus predicted. They may judge fit only by small residuals and ignore curved patterns, clusters, or residuals mostly above or below zero.
How to Assess It
- Exit ticket: Plot (1,4), (2,4), (3,8), and (4,8), then test y = 2x + 1. Calculate and plot each residual, then explain whether the model fits.
Lesson moves
Ways to Teach It
Give pairs graph paper, six data points, and a candidate line; students calculate residuals and place sticky dots on a residual plot.
Show two residual plots and ask, "Which linear model fits better, and what pattern supports your choice?"
Play Residual Match: students match scatter plots, linear equations, and residual plots, then check each set with a calculator.
Use temperature and electricity-use data to test whether a proposed linear model predicts usage without a systematic residual pattern.
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