November 11, 2016

This is a two-week instructional unit for Grades 9-12 on data analysis. Students use real-life data to interpret the slope and y-intercept of least squares regression lines in the context of everyday situations. Lessons include travel distances, bathtub water levels, and automobile age vs. mileage. In each activity, students interpret the meaning of slope and y-intercept, calculate correlation coefficients, and fit the data by estimating parameters. Individual lessons can be easily parsed out to create a shorter unit.

- Mathematics > General

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Write arguments focused on discipline-specific content.

Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.

Reason abstractly and quantitatively.

Interpret functions that arise in applications in terms of the context

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.?

Analyze functions using different representations

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.?

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Summarize, represent, and interpret data on a single count or measurement variable

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Summarize, represent, and interpret data on two categorical and quantitative variables

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Informally assess the fit of a function by plotting and analyzing residuals.

Interpret linear models

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Compute (using technology) and interpret the correlation coefficient of a linear fit.

Understand and evaluate random processes underlying statistical experiments

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Calculate expected values and use them to solve problems

(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

Use probability to evaluate outcomes of decisions

(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).