Students analyze the relationship between wheel radius, linear velocity and angular velocity by using LEGO(TM) MINDSTORMS(TM) NXT robots. Given various robots with different wheel sizes and fixed motor speeds, they predict which has the fastest linear velocity. Then student teams collect and graph data to analyze the relationships between wheel size and linear velocity and find the angular velocity of the robot given its motor speed. Students explore other ways to increase linear velocity by changing motor speeds, and discuss and evaluate the optimal wheel size and desired linear velocities on vehicles.

Posed with a paradigmatic engineering problem, students consider and explore mathematical algorithms and/or geometric concepts to devise possible solutions. The problem: How should a robotic vacuum move in order to best clean a floor of unknown shape and dimensions? They grapple with what could be a complex problem by brainstorming ideas, presenting the best idea for a solution and analyzing all presented solutions, and then are introduced to an elegant solution. Rather than elaborately calculating the most efficient route and keeping track of which tiles the robot has visited, a random number generator determines which direction the robot will take when it hits a barrier. Students are able to visually confirm how an unfamiliar programming concept (a random number generator) can make for a simple and efficient program that causes an NXT robot (that is suitably equipped) to clean a bare floor. Then students think of other uses for random numbers.

A gear is a simple machine that is very useful to increase the speed or torque of a wheel. In this activity, students learn about the trade-off between speed and torque when designing gear ratios. The activity setup includes a LEGO(TM) MINDSTORMS(TM) NXT pulley system with two independent gear sets and motors that spin two pulleys. Each pulley has weights attached by string. In a teacher demonstration, the effect of adding increasing amounts of weight to the pulley systems with different gear ratios is observed as the system's ability to lift the weights is tested. Then student teams are challenged to design a gear set that will lift a given load as quickly as possible. They test and refine their designs to find the ideal gear ratio, one that provides enough torque to lift the weight while still achieving the fastest speed possible.

Vision is the primary sense of many animals and much is known about how vision is processed in the mammalian nervous system. One distinct property of the primary visual cortex is a highly organized pattern of sensitivity to location and orientation of objects in the visual field. But how did we learn this? An important tool is the ability to design experiments to map out the structure and response of a system such as vision. In this activity, students learn about the visual system and then conduct a model experiment to map the visual field response of a Panoptes robot. (In Greek mythology, Argus Panoptes was the "all-seeing" watchman giant with 100 eyes.) A simple activity modification enables a true black box experiment, in which students do not directly observe how the visual system is configured, and must match the input to the output in order to reconstruct the unseen system inside the box.

After a brief history of plastics, students look more closely as some examples from the abundant types of plastics found in our day-to-day lives. They are introduced to the mechanical properties of plastics, including their stress-strain relationships, which determine their suitability for different industrial and product applications. These physical properties enable plastics to be fabricated into a wide range of products. Students learn about the different roles that plastics play in our lives, Young's modulus, and the effects that plastics have on our environment. Then students act as industrial engineers, conducting tests to compare different plastics and performing a cost-benefit analysis to determine which are the most cost-effective for a given application, based on their costs and measured physical properties.

Students learn about contamination and pollution, specifically in reference to soil in and around rivers. To start, groups use light sensors to take light reflection measurements of different colors of sand (dyed with various amounts of a liquid food dye), generating a set of "soil" calibration data. Then, they use a stream table with a simulated a river that has a scattering of "contaminated wells" represented by locations of unknown amounts of dye. They make visual observations and use light sensors again to take reflection measurements and refer to their earlier calibration data to determine the level of "contamination" (color dye) in each well. Acting as engineers, they determine if their measured data is comparable to visual observations. The small-scale simulated flowing river shows how contamination can spread.

Students learn about ultrasound and how it can be used to determine the shapes and contours of unseen objects. Using a one-dimensional ultrasound imaging device (either prepared by the teacher or put together by the students) that incorporates a LEGO(TM) MINDSTORMS(TM) NXT intelligent brick and ultrasonic sensor, they measure and plot the shape of an unknown object covered by a box. Looking at the plotted data, they make inferences about the shape of the object and guess what it is. Students also learn how engineers use high-frequency waves in the design of medical imaging devices, the analysis of materials and oceanographic exploration. Pre/post quizzes, a worksheet and a LEGO rbt program are provided.