The task is intended to address standards regarding sample space, independence, probability distributions and permutations/combinations.

Many of today's popular sports are based around the use of balls, yet none of the balls are completely alike. In fact, they are all designed with specific characteristics in mind and are quite varied. Students investigate different balls' abilities to bounce and represent the data they collect graphically.

Student pairs reverse engineer objects of their choice, learning what it takes to be an engineer. Groups each make a proposal, create a team work contract, use tools to disassemble a device, and sketch and document their full understanding of how it works. They compile what they learned into a manual and write-up that summarizes the object's purpose, bill of materials and operation procedure with orthographic and isometric sketches. Then they apply some of the steps of the engineering design process to come up with ideas for how the product or device could be improved for the benefit of the end user, manufacturer and/or environment. They describe and sketch their ideas for re-imagined designs (no prototyping or testing is done). To conclude, teams compile full reports and then recap their reverse engineering projects and investigation discoveries in brief class presentations. A PowerPoint(TM) presentation, written report and oral presentation rubrics, and peer evaluation form are provided.

In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable.

Students write a biographical sketch of an artist or athlete who lives on the edge, riding the gravity wave, to better understand how these artists and athletes work with gravity and manage risk. 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.

Through this lesson students learn how AM radios work through basic concepts about waves and magnetic fields. Waves are first introduced by establishing the difference between transverse and longitudinal waves, as well as identifying the amplitude and frequency of a given waveform. Students then learn general concepts about magnetic fields, leading into how radio waves are created and transmitted. Several demonstrations can be performed in order to help students better understand these concepts. The goal of this lesson is for students to understand how the AM radios built during the associated activity function.

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle: the fact that these triangles are always right triangles is often referred to as Thales' theorem. It does not have a lot of formal prerequisites, just the knowledge that the sum of the three angles in a triangle is 180 degrees.

The result here complements the fact, presented in the task ``Right triangles inscribed in circles I,'' that any triangle inscribed in a circle with one side being a diameter of the circle is a right triangle. A second common proof of this result rotates the triangle by 180 degrees about M and then shows that the quadrilateral, obtained by taking the union of these two triangles, is a rectangle.

Students experience the engineering design process as they design and build accurate and precise catapults using common materials. They use their catapults to participate in a game in which they launch Ping-Pong balls to attempt to hit various targets.

Students learn the concept of angular momentum and its correlation to mass, velocity and radius. They experiment with rotation and an object's mass distribution. In an associated literacy activity, students use basic methods of comparative mythology to consider why spinning and weaving are common motifs in creation myths and folktales.

The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills.

Students build on their understanding and feel for flow rates, as gained from the associated Faucet Flow Rate activity, to estimate the flow rate of a local river. The objective is to be able to relate laboratory experiment results to the environment. They use the U.S. Geological Survey website (http://waterdata.usgs.gov/nwis/rt) to determine the actual flow rate data for their river, and compare their estimates to the actual flow rate. For this activity to be successful, choose a nearby river and take a field trip or show a video so students gain a visual feel for the flow of the nearby river.

Students learn how water is used to generate electricity. They investigate water's potential-to-kinetic energy transformation in hands-on activities about falling water and waterwheels. During the activities, they take measurements, calculate averages and graph results. Students also learn the history of the waterwheel and how engineers use water turbines in hydroelectric power plants today. They discover the advantages and disadvantages of hydroelectric power. In a literacy activity, students learn and write about an innovative new hydro-electrical power generation technology.

Students learn various topics associated with the circle through studying a clock. Topics include reading analog time, understanding the concept of rotation (clockwise vs. counter-clockwise), and identifying right angles and straight angles within circles. Many young students have difficulty telling time in analog format, especially with fewer analog clocks in use (compared to digital clocks). This includes the ability to convert time written in words to a number format, for example, making the connection between "quarter of an hour" to 15 minutes. Students also find it difficult to convert "quarter of an hour" to the number of degrees in a circle. This activity incorporates a LEGO® MINDSTORMS® NXT robot to help students distinguish and visualize the differences in clockwise vs. counter-clockwise rotation and right vs. straight angles, while learning how to tell time on an analog clock. To promote team learning and increase engagement, students work in teams to program and control the robot.

Students continue to build a rigorous background in human sensors and their engineering equivalents by learning about electronic touch, light, sound and ultrasonic sensors that measure physical quantities somewhat like eyes, ears and skin. Specifically, they learn about microphones as one example of sound sensors, how sounds differ (intensity, pitch) and the components of sound waves (wavelength, period, frequency, amplitude). Using microphones connected to computers running (free) Audacity® software, student teams experiment with machine-generated sounds and their own voices and observe the resulting sound waves on the screen, helping them to understand that sounds are waves. Students take pre/post quizzes, complete a worksheet and watch two short online videos about "seeing" sound.

Students learn how two LEGO MINDSTORMS(TM) NXT intelligent bricks can be programmed so that one can remotely control the other. They learn about the components and functionality in the (provided) controller and receiver programs. When its buttons are pressed, the NXT brick assigned as the remote control device uses the controller program to send Bluetooth® messages. When the NXT taskbot/brick assigned as the receiver receives certain Bluetooth messages, it moves, as specified by the receiver program. Students examine how the programs and devices work in tandem, gaining skills as they play "robot soccer." As the concluding activity in this unit, this activity provides a deeper dimension of understanding programming logic compared to previous activities in this unit and introduces the relatively new and growing concept of wireless communication. A PowerPoint® presentation, pre/post quizzes and a worksheet are provided.

Students solidify their understanding of the terms "circumference" and "rotation" through the use of LEGO MINDSTORMS(TM) NXT robotics components. They measure the circumference of robot wheels to determine how far the robot can travel during one rotation of an NXT motor. They sharpen their metric system measurement skills by precisely recording the length of a wheel's circumference in centimeters, as well as fractions of centimeters. Through this activity, students practice brainstorming ways to solve a problem when presented with a given scenario, improve their ability to measure and record lengths to different degrees of precision, and become familiar with common geometric terms (such as perimeter and rotation).

Students groups act as NASA/GM engineers challenged to design, build and test robotic hands, which are tactile feedback systems made from cloth gloves and force sensor circuits. Student groups construct force sensor circuits using electric components and FlexiForce sensors to which resistance changes based on the applied force. They conduct experiments to find the mathematical relationship between the force applied to the sensor and the output voltages of the circuit. They take several measurements force vs. resistance, force vs. voltage and use the data to find the best fit curve models for the sensor. Different weights applied to the sensor are used as a scalable force. Students use traditional methods and current technology (calculators) to plot the collected data and define the curve equations. Students test their gloves and use a line of best fit to determine the minimum force required to crack an egg held between the index finger and thumb. A PowerPoint(TM) file and many student handouts are included.