At the end of this lesson, students will be able to:
- Collect and organize data.
- Interpolate using an equation.
- Extrapolate using an equation.
- Predict using an equation.
Terms introduced in this lesson:
most accurate method
Teaching Strategies and Tips
Use the introduction to motivate data collection and organization.
- Data are gathered from surveys and experimental measurements.
- Data are organized via tables and scatterplots, where it is easier to spot trends and patterns.
In Example 1:
- Point out that two data sets are being displayed simultaneously in the scatterplot. This is a common practice when two data sets are being compared.
- The two variables are Median Age of Males and Females At First Marriage by Year.
- Discuss with students whether the scatterplot is approximately linear and whether using a line of best fit to predict future values is appropriate. Do the same for Example 2.
Use Examples 3 and 4 to motivate linear interpolation.
- Ask students how they would go about estimating a value where there is no data point available.
- Possible discussion questions: Assume the data are linear. How would the line of best fit help? Should only a subset of the data be used? All of the data? How does the above considerations change for non-linear data?
Use Example 5 to motivate linear extrapolation.
- Point out that the last data point is an outlier and therefore influences the extrapolation heavily.
- Work through the extrapolation a second time using a linear regression. Have students compare answers from the two models.
- Emphasize that extrapolation is not useful when used to predict values far into the future (or far into the past).
For additional data sets, visit:
General Tip: On the TI graphing calculators, students should be using LinReg(ax+b) or LinReg(a+bx) to perform linear regressions and not LnReg.
General Tip: Students can neglect to consider the accuracy of a prediction or estimate. Some estimates will not be good because the desired value is far removed from the rest of the data set.