Scatterplots and Fit Lines
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalA scatterplot tells two stories: what each subject actually did, and what the trend line expects. The points leak when the stories swap, a plotted observation answering a what-does-the-line-predict question, in the parameters, the slope and intercept trading jobs or a prediction dropping one of them, and at the end, in the gap: the actual or predicted value reported when their difference was asked.
These patterns aren't really about whether you can substitute into an equation. They're about whether predictions came from the line and observations from the points, whether the slope kept its per-unit meaning and the intercept its at-zero meaning, and whether the number you reported is the gap itself or just one of its ingredients.
The work
4 ways in · any order
Lesson
Scatterplots and Fit Lines
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Predict with the line of best fit, read observations from the plotted points, give the slope and intercept their own jobs, and compute the actual-minus-predicted gap as its own quantity. The lesson works the method and the three patterns that derail it, and it saves the trap for last: an ingredient reported in place of the gap.
Diagnostic
10-item topic check
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Ten items across the three patterns: reading a point when the line was asked, misinterpreting slope or intercept, and reporting a value when the difference was asked. A mix of predictions, interpretations, slopes from two points, and residual gaps. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
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About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.