In this lesson, students will learn that math is important in navigation and engineering. 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. In this lesson, these basic concepts are discussed and illustrated in the associated activities.

Students expand upon their understanding of simple machines with an introduction to compound machines. A compound machine a combination of two or more simple machines can affect work more than its individual components. Engineers who design compound machines aim to benefit society by lessening the amount of work that people exert for even common household tasks. This lesson encourages students to critically think about machine inventions and their role in our lives.

In this six lesson unit, students recognize and explore the relationships among pennies, nickels, dimes, and quarters. They estimate and count sets of mixed coins, create equivalent sets, write story problems that involve money, and use coins to make patterns. Within the unit there is a link to US Mint. http://www.usmint.gov/kids/teachers/

The study of numbers and operations is the cornerstone of the mathematics curriculum. Learning what numbers mean, how they may be represented, relationships among them, and computations with them is central to developing number sense.

This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis. Assignments require MATLAB programming.

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).

In this extension to the Ohm's Law I activity, students observe just how much time it takes to use up the "juice" in a battery, and if it is better to use batteries in series or parallel. This extension is suitable as a teacher demonstration and may be started before students begin work on the Ohm's Law I activity.

Students work to increase the intensity of a light bulb by testing batteries in series and parallel circuits. They learn about Ohm's law, power, parallel and series circuits, and ways to measure voltage and current.

This interactive Flash game helps students practice counting, subitizing, and grouping by 10s, as they transport Okta the Octopus and his friends to a safe ocean. The goal is to select given numbers of Oktas as quickly as possible before the timer runs out. Then users count the total number of Oktas "saved" and identify that number on a number line. Students choose from three levels of difficulty, which vary according to time limit, range of target numbers, and whether visual target cues appear. These settings are customizable. Users who count incorrectly are given the option of visual help in recounting.

The lesson begins by introducing Olympics as the unit theme. The purpose of this lesson is to introduce students to the techniques of engineering problem solving. Specific techniques covered in the lesson include brainstorming and the engineering design process. The importance of thinking out of the box is also stressed to show that while some tasks seem impossible, they can be done. This introduction includes a discussion of the engineering required to build grand, often complex, Olympic event centers.

Students use three tracks marked on the floor, one in yards, one in feet and one in inches. As they start and stop a robot specific distances on a "runway," they can easily determine the equivalent measurements in other units by looking at the nearby tracks. With this visual and physical representation of the magnitude of the units of feet, yard and inches, students gain an understanding of what is meant by "unit conversion." They also gain a familiarity with different common units of measurement. They use multiplication and division to verify their physical estimated unit conversions. Students also learn about how common and helpful it is to convert from one unit to another in everyday situations and for engineering purposes. This activity helps students make the abstract concept of unit conversion real so they develop mental models of the magnitude of units instead of applying memorized conversion factors by rote.

In this unit, students investigate fractional parts of the whole and use translations, reflections, rotations, and line symmetry to make four-part quilt squares. Students have a practical context for using the mathematical terms associated with divisions of the square, transformations, and symmetries. Suggestions for implementation and extensions are included.

Students act as civil engineers developing safe railways as a way to strengthen their understanding of parallel and intersecting lines. Using pieces of yarn to visually represent line segments, students lay down "train tracks" on a carpeted floor, and make guesses as to whether these segments are arranged in parallel or non-parallel fashion. Students then test their tracks by running two LEGO® MINDSTORMS® NXT robots to observe the consequences of their track designs, and make safety improvements. Robots on intersecting courses face imminent collision, while robots on parallel courses travel safely.

Students are presented with a short lesson on the Coulter principle—an electronic method to detect microscopic particles and determine their concentration in fluid. Depending on the focus of study, students can investigate the industrial and medical applications of particle detection, the physics of fluid flow and electric current through the apparatus, or the chemistry of the electrolytes used in the apparatus.

Students apply concepts of disease transmission to analyze infection data, either provided or created using Bluetooth-enabled Android devices. This data collection may include several cases, such as small static groups (representing historically rural areas), several roaming students (representing world-travelers), or one large, tightly knit group (representing urban populations). To explore the algorithms to a deeper degree, students may also design their own diseases using the App Inventor framework.

This interactive applet lets students create quilting type patterns and explore tessellation possibilities. The applet gives learners a choice of six polygons that can be turned or flipped and fitted together. Suggestions for exploration and five challenge patterns are provided. The tool supports a number of lessons and units including What's So Special About Triangles and Virtual Pattern Blocks (cataloged separately).

Students explore their peripheral vision by reading large letters on index cards. Then they repeat the experiment while looking through camera lenses, first a lens with a smaller focal length and then a lens with a larger focal length. Then they complete a worksheet and explain how the experiment helps them solve the challenge question introduced in lesson 1 of this unit.

Through this lesson and its associated activity, students explore the role of biomedical engineers working for pharmaceutical companies. First, students gain background knowledge about what biomedical engineers do, how to become a biomedical engineer, and the steps of the engineering design process. The goal is to introduce biomedical engineering as medical problem solving as well as highlight the importance of maintaining normal body chemistry. Students participate in the research phase of the design process as it relates to improving the design of a new prescription medication. During the research phase, engineers learn about topics by reading scholarly articles written by others, and students experience this process. Students draw on their research findings to participate in discussion and draw conclusions about the impact of medications on the human body.

This case study investigates the applications of genetics to medicine by exploring one of the first examples of a pharmacogenetic test to enter mainstream clinical practice. Pharmacogenetics examines how genetic variations in an individual correlate with responses to a specific medication in order to develop tailored medical treatments. Through a scenario based on clinical observations, students learn about acute lymphocytic leukemia as well as the wide range of individual responses to the drug used to treat it. Then, students interpret data similar to those initially published in scientific journals in order to construct an understanding of how genetic variation can be used to "tailor" medical care. Lastly, students are asked to apply their understanding of what they have learned in the case by making the appropriate medical recommendation based on a particular individual's genotype.

Physical science is the science of matter and energy and their interactions and examines the physical world around us. Using the methods of the physical sciences, students learn about the composition, structure, properties, and reactions of matter and the relationships between matter and energy. Students are best able to build understanding of the physical sciences through hands-on exploration of the physical world.