Unpacked Content
Knowledge
Students know:
- Techniques for creating a scatter plot.
- Techniques for fitting a linear function to a scatter plot.
- Methods to find the slope and intercept of a linear function.
- Techniques for fitting various functions (linear, quadratic, exponential) to data.
- Methods for using residuals to judge the closeness of the fit of the function to the original data.
Skills
Students are able to:
- Accurately create a scatter plot of data.
- Correctly choose a function to fit the scatter plot.
- Make reasonable assessments on the fit of the function to the data by examining residuals.
- Accurately fit a linear function to data when there is evidence of a linear association.
- Accurately fit linear functions to scatter plots.
- Correctly find the slope and intercept of linear functions.
- Justify and explain the relevant connections slope and intercept of the linear function to the data.
Understanding
Students understand that:
- Functions are used to create equations representative of ordered pairs of data.
- Residuals may be examined to analyze how well a function fits the data.
- When a linear association is suggested, a linear function can be fit to the scatter plot to aid in modeling the relationship.
- Linear functions are used to model data that have a relationship that closely resembles a linear relationship.
- The slope and intercept of a linear function may be interpreted as the rate of change and the zero point (starting point).
Vocabulary
- Quantitative variables
- Scatter plot
- Residuals
- Slope
- Rate of change
- Intercepts
- Constant
- Ordered pairs
- Horizontal lines
- Vertical lines
