High School Statistics and Probability Assignment

High school students simulate measurement data and use it to find an appropriate mathematical model for a real-world situation—calculating a murder suspect’s height based on blood spatter data—and then answer questions about the situation and the math involved. The assignment is strongly aligned to the standard because it requires students to fit a function to data, assess the fit of the function by analyzing residuals, and solve problems in the context of the data.

Focus
In eighth grade, students first work with bivariate data (measurement data on two related variables). They create scatter plots, find linear equations that best fit the data, and use their equations to answer real-world questions. These concepts are extended in high school when students work with bivariate data that might have a non-linear relationship. This assignment allows students to work with bivariate data in a manner appropriate for high school: students use graphing technology to test multiple function types, analyze the corresponding residual plots to assess the fit of each function model, and select the one that most closely models the data at hand.

Rigor
The assignment appropriately allows students to build their conceptual understanding by asking them to use functions fitted to data to solve problems in the context of the data, informally assess the fit of a function, and analyze residuals (all aligned with standard HSS.ID.B.6). The assignment also allows students to use the appropriate procedural skills of fitting a function to data and plotting residuals.

Practice Standards
The assignment gives students a strong opportunity to engage with Mathematical Practice Standard #4 (“Model with mathematics”), which suggests that students “apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.” By creating data and working with it in the same way a criminal investigator would, students see several mathematical concepts (such as measurement, data collection, and fitting a function to data) coming together in an authentic, if simulated, context. The assignment also allows students to engage with Mathematical Practice Standard #5 (“Use appropriate tools strategically”) by asking them to fit multiple functions to the data, analyze the residuals for each model, and use that analysis to select the function that most closely models the data, all of which require the use of a graphing calculator or other statistical software.