In a spin-off to studying about angular momentum, students use basic methods of comparative mythology to consider why spinning and weaving are common motifs in creation of myths and folktales. Note: The literacy activities for the Mechanics unit are based on physical themes that have broad application to our experience in the world — concepts of rhythm, balance, spin, gravity, levity, inertia, momentum, friction, stress and tension.

Refreshed with an understanding of the six simple machines; screw, wedge, pully, incline plane, wheel and axle, and lever, student groups receive materials and an allotted amount of time to act as mechanical engineers to design and create machines that can complete specified tasks. For the competition, they choose from pre-determined goal options such as: 1) dumping goldfish into a bowl, 2) popping a balloon, or 3) dropping mint candies into soda pop (creating a fizzy reaction). Students demonstrate their functioning contraptions to the class, earning points for using all six simple machines, successful transitions from one chain reaction to the next, and completion of the end goal.

In this lesson, students will explore the causes of water pollution and its effects on the environment through the use of models and scientific investigation. In the accompanying activities, they will investigate filtration and aeration processes as they are used for removing pollutants from water. Lastly, they will learn about the role of engineers in water treatment systems.

Students see how potential energy (stored energy) can be converted into kinetic energy (motion). Acting as if they were engineers designing vehicles, they use rubber bands, pencils and spools to explore how elastic potential energy from twisted rubber bands can roll the spools. They brainstorm, prototype, modify, test and redesign variations to the basic spool racer design in order to meet different design criteria, ultimately facing off in a race competition. These simple-to-make devices store potential energy in twisted rubber bands and then convert the potential energy to kinetic energy upon release.

This lab demonstrates Hooke's Law with the use of springs and masses. Students attempt to determine the proportionality constant, or k-value, for a spring. They do this by calculating the change in length of the spring as different masses are added to it. The concept of a spring's elastic limit is also introduced, and the students test to makes sure the spring's elastic limit has not been reached during their lab tests. After compiling their data, they attempt to find an average value of the spring's k-value by measuring the slopes between each of their data points. Then they apply what they've learned about springs to how engineers might use that knowledge in the design of a toy that enables kids to jump 2-3 feet in the air.

Through hands-on group projects, students learn about the force of compression and how it acts on structural components. Using everyday materials, such as paper, toothpicks and tape, they construct structures designed to (hopefully) support the weight of a cinder block for 30 seconds.

Students design and build structures to support the weight of books for 15 seconds.

Students analyze and begin to design a pyramid. Working in engineering teams, they perform calculations to determine the area of the pyramid base, stone block volumes, and the number of blocks required for their pyramid base. They make a scaled drawing of the pyramid using graph paper.

To get a better understanding of complex networks, students create their own, real social network example by interacting with their peers in the classroom and documenting the interactions. They represent the interaction data as a graph, calculate two mathematical quantities associated with the graph—the degree of each node and the degree distribution of the graph—and analyze how these quantities can be used to infer properties of the social network at hand.

To navigate, you must know roughly where you stand relative to your designation, so you can head in the right direction. In locations where landmarks are not available to help navigate (in deserts, on seas), objects in the sky are the only reference points. While celestial objects move fairly predictably, and rough longitude is not too difficult to find, it is not a simple matter to determine latitude and precise positions. In this activity, students investigate the uses and advantages of modern GPS for navigation.

Students act as chemical engineers and use LEGO® MINDSTORMS® NXT robotics to record temperatures and learn about the three states of matter. Properties of matter can be measured in various ways, including volume, mass, density and temperature. Students measure the temperature of water in its solid state (ice) as it is melted and then evaporated.

This hands-on activity explores the concept of static electricity. Students attract an O-shaped piece of cereal to a charged comb and watch the cereal jump away when it touches the comb. Students also observe Styrofoam pellets pulling towards a charged comb, then leaping back to the table.

Student groups rotate through four stations to examine light energy behavior: refraction, magnification, prisms and polarization. They see how a beam of light is refracted (bent) through various transparent mediums. While learning how a magnifying glass works, students see how the orientation of an image changes with the distance of the lens from its focal point. They also discover how a prism works by refracting light and making rainbows. And, students investigate the polar nature of light using sunglasses and polarized light film.

Students are introduced to the technology of flexible circuits, some applications and the photolithography fabrication process. They are challenged to determine if the fabrication process results in a change in the circuit dimensions since, as circuits get smaller and smaller (nano-circuits), this could become very problematic. The lesson prepares students to conduct the associated activity in which they perform statistical analysis (using Excel® and GeoGebra) to determine if the circuit dimension sizes before and after fabrication are in fact statistically different. A PowerPoint® presentation and post-quiz are provided. This lesson and its associated activity are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.

Students apply pre-requisite statistics knowledge and concepts learned in an associated lesson to a real-world state-of-the-art research problem that asks them to quantitatively analyze the effectiveness of different cracked steel repair methods. As if they are civil engineers, students statistically analyze and compare 12 sets of experimental data from seven research centers around the world using measurements of central tendency, five-number summaries, box-and-whisker plots and bar graphs. The data consists of the results from carbon-fiber-reinforced polymer patched and unpatched cracked steel specimens tested under the same stress conditions. Based on their findings, students determine the most effective cracked steel repair method, create a report, and present their results, conclusions and recommended methods to the class as if they were presenting to the mayor and city council. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.

Students learn that math is important in navigation and engineering. They learn about triangles and how they can help determine distances. Ancient land and sea navigators started with the most basic of navigation equations (speed x time = distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts — basic geometry and trigonometry — that have been used for thousands of years.

Students learn about the strength of bones and methods of helping to mend fractured bones. During a class demonstration, a chicken bone is broken by applying a load until it reaches a point of failure (fracture). Then, working as biomedical engineers, students teams design their own splint or cast to help repair a fractured bone, learning about the strength of materials used.

In this activity, students act as engineers to determine which type of insulation would conserve the most energy.

Students learn about composite materials, tension as a force and how they act on structural components through the design and testing of strips of plastic chair webbing.

Students work through an online tutorial on MIT's App Inventor to learn how to create Android applications. Using those skills, they create their own applications and use them to collect data from an Android device accelerometer and store that data to databases. NOTE: Teachers and students must have a working knowledge of basic programming and App Inventor to complete this lesson. This lesson is not an introduction to MIT's App Inventor and is not recommended for use without prior knowledge of App Inventor to produce an end product. This lesson is an application for App Inventor that allows for the storage of persistent data (data that remains in memory even if an app is closed). This required prior knowledge can come from other experiences with the App Inventor. Also, many additional resources are available, such as tutorials from MIT. This lesson could also be used as an enrichment project for students who are self-motivated to learn the App Inventor software.