The mathematical purpose of this activity is for student to informally assess the fit of various lines to data, to use technology to find the line of best fit, and to interpret the slope and vertical intercept of the linear model. The work connects to previous work because students created scatter plots and created linear models for the data. The work connects to upcoming work because students will use the correlation coefficient to describe the strength of the linear relationship. When students sort scatter plots into linear and nonlinear categories, and when they organize lines of best fit by the goodness of fit, they look for and make use of structure (MP7), because they are analyzing representations and structures closely, and making connections. Students are reasoning abstractly and quantitatively (MP2) when they interpret the meaning of the slope and vertical intercept in context.
- Determine which linear model is a better fit for a given data set.
- Interpret (orally and in writing) the rate of change and vertical intercept for a linear model in everyday language.
- Use technology to generate the line of best fit, and use the equation representing the linear model to predict (extrapolate) and estimate (interpolate) values not given in the data set.
- Let’s find the best linear model for some data.
Print and cut up slips for the card sort. One copy of the blackline master for every group of 2 students. To find best fit lines, students will need access to technology that will compute the least-squares regression lines for a set of data.
Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)
- I can describe the rate of change and $y$-intercept for a linear model in everyday language.
- I can use technology to find the line of best fit.