From a statistics standpoint, students should be able to analyze patterns, trends, and relationships between variables in the data. This is accomplished through discussions about associations between variables, and by the end of the unit students should have a strong understanding that correlation is a precise term describing the strength and direction of the linear relationship between quantitative variables, and understand the difference between correlation and causation.
Specifically, by the end of the unit, students should be able to
-
Interpret the slope of the best-fit line in the context of the data.
-
Distinguish between scatter plots that show a linear relationship and those where the relationship is not linear.
-
Create a residual plot given a set of data and the equation of the best-fit line.
-
Use residuals to investigate whether a line is an appropriate description of the relationship between numerical variables.
This fits in perfectly with a unit on hydrology. By teaching statistics through the lens of the watershed, I hope to facilitate more active, engaged learners who understand how math can be usefully applied to various contexts in the world around us while gaining a deeper appreciation for the water resources on earth. Students will be able to examine the hydrological cycle and water budgets, and apply their knowledge of statistics to examine annual timescales within the watershed, and compare them against different watersheds. They can also mathematically explore the relationship between annual precipitation and annual discharge, annual evapotranspiration, and temperature over time. Creating these graphs will allow students to examine scatter plots that have a clear linear relationship and create linear regressions which model these situations. This will also create opportunities for students to examine correlation versus causation within a scientific context.
After exploring the watershed in various areas through the use of modeling and statistics, I hope to branch out to larger conversations surrounding the importance of the water budget and water availability, as well as human demands on the water budget and the impacts that it has environmentally.
Statistics is also an important element of the redesigned SAT, and is it imperative students are exposed to the mathematics that are on the test as well as interpretation and analysis of graphs, as these are crucial skills needed for students to do well.
I plan to teach this unit by first introducing the basic statistic concepts in the context of hydrology- not only looking at “what are we doing”, but “what does this mean”. As a class, we can examine a local data set, create a regression, and discuss the real world context of the various parts of the graph. As a culminating project, students can break up into groups and examine data sets from watersheds across the world, and examine how the graph reflects changes in temperature and precipitation between watersheds across the globe. Students will be responsible for presenting this data to their peers.
In terms of incorporating SAT practice, there will be opportunities for SAT strategies and practice during warm ups on a daily basis (questions specifically related to hydrology), as well as a unit culmination of SAT style questions based on interpreting the graphs that the students created throughout the unit.