Students learn the relevant equations for refraction (index of refraction, Snell's law) and how to use them to predict the behavior of light waves in specified scenarios. After a brief review of the concept of refraction (as learned in the previous lesson), the equations along with their units and variable definitions, are introduced. Student groups work through a few example conceptual and mathematical problems and receive feedback on their work. Then students conduct the associated activity during which they practice using the equations in a problem set, examine data from a porous film like those used in biosensors, and apply the equations they learned to a hypothetical scenario involving biosensors.

Students use their understanding of projectile physics and fluid dynamics to find the water pressure in water guns. By measuring the range of the water jets, they are able to calculate the theoretical pressure. Students create graphs to analyze how the predicted pressure relates to the number of times they pump the water gun before shooting.

Students are introduced to static equilibrium by learning how forces and torques are balanced in a well-designed engineering structure. A tower crane is presented as a simplified two-dimensional case. Using Popsicle sticks and hot glue, student teams design, build and test a simple tower crane model according to these principles, ending with a team competition.

An interactive applet and associated web page that show the definition of a vertical line in coordinate geometry. The applet has two points that the user can drag which define a line. The line flagged when it is vertical (slope=undefined). The grid, details and coordinates can be turned on and off. The applet can be printed exactly as it appears on the screen to make handouts. The web page has a discussion on how to test for vertical and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Prepared with pre-algebra or algebra 1 classes in mind, this module leads students through the process of graphing data and finding a line of best fit while exploring the characteristics of linear equations in algebraic and graphic formats. Then, these topics are connected to real-world experiences in which people use linear functions. During the module, students use these scientific concepts to solve the following hypothetical challenge: You are a new researcher in a lab, and your boss has just given you your first task to analyze a set of data. It being your first assignment, you ask an undergraduate student working in your lab to help you figure it out. She responds that you must determine what the data represents and then find an equation that models the data. You believe that you will be able to determine what the data represents on your own, but you ask for further help modeling the data. In response, she says she is not completely sure how to do it, but gives a list of equations that may fit the data. This module is built around the legacy cycle, a format that incorporates educational research feindings on how people best learn.

Students learn about the water cycle and its key components. First, they learn about the concept of a watershed and why it is important in the context of engineering hydrology. Then they learn how we can use the theory of conservation of mass to estimate the amount of water that enters a watershed (precipitation, groundwater flowing in) and exits a watershed (evaporation, runoff, groundwater out). Finally, students learn about runoff and how we visualize runoff in the form of hydrographs.

In the first half of this two-part activity, students practice solving problems involving refraction using the index of refraction and Snell's law equations; they mathematically solve for precise angles and speeds caused by refraction. In the second half of the activity, a hands-on lab, they apply the analytical skills required by the problem set to reflectance measurements of porous silicon thin films, including how reflectance measurements would change if various aspects of the film were altered. Students predict the data output in the form of reflectance measurements when samples are altered, which connects to the idea of being able to make predictions about the data output of a biosensing thin film that couples with a target molecule.