In Module 6, Topic C, students use linear and nonlinear models to answer questions in context (8.SP.A.1, 8.SP.A.2). They interpret the rate of change and the initial value in context (8.SP.A.3). They use the equation of a linear function and its graph to make predictions. Students also examine graphs of nonlinear functions and use nonlinear functions to model relationships that are nonlinear. Students gain experience with the mathematical practice of “modeling with mathematics” (MP.4).

Content Standard(s):

Mathematics MA2015 (2016) Grade: 8

25 ) Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8-SP1]

NAEP Framework

NAEP Statement:: 8DASP1b: For a given set of data, complete a graph and then solve a problem using the data in the graph (histograms, line graphs, scatterplots, circle graphs, and bar graphs).

NAEP Statement:: 8DASP2c: Identify outliers and determine their effect on mean, median, mode, or range.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.8.25- Given a simple scatter plot of points in a straight line, identify a pattern.

Mathematics MA2015 (2016) Grade: 8

26 ) Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8-SP2]

NAEP Framework

NAEP Statement:: 8DASP1b: For a given set of data, complete a graph and then solve a problem using the data in the graph (histograms, line graphs, scatterplots, circle graphs, and bar graphs).

NAEP Statement:: 8DASP2e: Visually choose the line that best fits given a scatterplot and informally explain the meaning of the line. Use the line to make predictions.

Mathematics MA2015 (2016) Grade: 8

27 ) Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8-SP3]

Example: In a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

NAEP Framework

NAEP Statement:: 8DASP1b: For a given set of data, complete a graph and then solve a problem using the data in the graph (histograms, line graphs, scatterplots, circle graphs, and bar graphs).