CCSS.Math.Content.HSS-ID.B.6a
The standard
Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
Common Core State Standards for Mathematics · Summarize, represent, and interpret data on two categorical and quantitative variables
What this standard means
Students need to look at paired data, choose a reasonable model, and use it to answer questions. They should know when a line, parabola, or exponential curve makes sense from the pattern or context, then write or use an equation that fits the data.
Mastery looks like explaining why a model fits, using it for interpolation or prediction, and keeping answers tied to the situation. Students often get stuck choosing a model from the graph, trusting a poor fit, mixing up exponential and quadratic growth, or making predictions far outside the data range.
Ways to teach it
- Give pairs a scatterplot card set and have them sort graphs into linear, quadratic, exponential, or poor fit, then justify two choices.
- Ask students to write: What does your model predict, and why should we trust or question that prediction in this context?
- Show a small data table and three possible equations, then have students pick the best model and predict one missing value.
- Use phone battery drain, falling object height, or savings with interest data to build a model and answer a practical question.
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Related standards
- CCSS.Math.Content.HSF-IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
- CCSS.Math.Content.HSS-ID.C.8
Compute (using technology) and interpret the correlation coefficient of a linear fit.
- CCSS.Math.Content.HSS-ID.B.6b
Informally assess the fit of a function by plotting and analyzing residuals.
- CCSS.Math.Content.8.F.A
Define, evaluate, and compare functions.