In this unit plan, primary learners explore the five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using concrete (links), pictorial, and verbal representations to develop an understanding of symbolic notations. Students also investigate fact families, including those where one addend is 0 and where the addends are alike and also learn that the order (commutative) property) does not hold for subtraction. A brief bibliography of related books for children is provided. Instead of using hands on manipulatives and balances, links to Java applets: Pan Balance-Shapes and Pan Balance-Numbers ( both cataloged separately) are included. Instructional plan, questions for the students, assessment options, extensions,and teacher reflections are given for each lesson as well as links to down load all student resources.

The Mars Climate Orbiter was deployed by NASA as part of a mission to study weather and climate on Mars. It was supposed to enter orbit at an altitude of 140.5-150 km (460,000-500,000 ft) above Mars, but due to an error, the spacecraft dipped as low as 57 km (190,000 ft) and was destroyed. The failure and loss of the Mars Climate Orbiter is examined in this case study, which explores the political, ethical, and economic issues as well as the scientific and technical aspects of the mishap. The case study is designed for use in a freshman-level Introduction to Engineering course.

In this 6-lesson unit students use pasta shapes to explore the take away model of subtraction in several different contexts (counting, sets, number line, balanced equations, and inverse of addition). They decompose numbers, explore the zero property, act out subtraction situations with objects and pictures, record differences with vertical and in horizontal notation, create fact families, find differences with a calculator, and compose and solve problems involving subtraction. The lessons include student activity sheets (pdf), questions for student discussion and teacher reflection, assessment options, and links to online applets.

In this activity about light and perception, learners create pictures in thin air. Using a simple set up of a slide projector, slide, moveable screen or poster board, and a "wand", learners investigate how we see projected images such as those from movies and television. Use this activity to help learners understand concepts associated with light and optics including persistence of vision, reflection, and map projection.

A magical demonstration where a Pyrex tube vanishes in a beaker of mineral oil. Useful demonstration to introduce to concept of refraction (and/or partial reflection).

Students visualize the magnetic field of a strong permanent magnet using a compass. The lesson begins with an analogy to the effect of the Earth's magnetic field on a compass. Students see the connection that the compass simply responds to the Earth's magnetic field since it is the closest, strongest field, and thus the compass responds to the field of the permanent magnets, allowing them the ability to map the field of that magnet in the activity. This information will be important in designing a solution to the grand challenge in activity 4 of the unit.

Students begin working on the grand challenge of the unit by thinking about the nature of metals and quick, cost-effective means of separating different metals, especially steel. They arrive at the idea, with the help of input from relevant sources, to use magnets, but first they must determine if the magnets can indeed isolate only the steel.

In this activity about electricity and magnetism, learners discover how a doorbell works. A coil of wire with current flowing through it forms an electromagnet that acts similar to a bar magnet. The coil will magnetize an iron nail and attract it in a remarkably vigorous way.

Students explore the basic magnetic properties of different substances, particularly aluminum and steel. There is a common misconception that magnets attract all metals, largely due to the ubiquity of steel in metal products. The activity provides students the chance to predict, whether or not a magnet will attract specific items and then test their predictions. Ultimately, students should arrive at the conclusion that iron (and nickel if available) is the only magnetic metal.

Students create large-scale models of microfluidic devices using a process similar to that of the PDMS and plasma bonding that is used in the creation of lab-on-a-chip devices. They use disposable foam plates, plastic bendable straws and gelatin dessert mix. After the molds have hardened overnight, they use plastic syringes to inject their model devices with colored fluid to test various flow rates. From what they learn, students are able to answer the challenge question presented in lesson 1 of this unit by writing individual explanation statements.

In this lesson students find and record addends that sum to ten in three different activities, using ten frames, linking cubes, two-sided counters, and a concentration game. The lesson includes suggestions for assessment and extension, reflection questions for students and teachers, links to related resources, and printable materials (pdf).

Graph theory is a visual way to represent relationships between objects. One of the simplest uses of graph theory is a family tree that shows how different people are related. Another application is social networks like Facebook, where a network of "friends" and their "friends" can be represented using graphs. Students learn and apply concepts and methods of graph theory to analyze data for different relationships such as friendships and physical proximity. They are asked about relationships between people and how those relationships can be illustrated. As part of the lesson, students are challenged to find the social graph of their friends. This prepares students for the associated activity during which they simulate and analyze the spread of disease using graph theory by assuming close proximity to an infected individual causes the disease to spread.

This course gives an overview of engineering management and covers topics such as financial principles, management of innovation, technology strategy, and best management practices. The focus of the course is the development of individual skills and team work. This is carried out through an exposure to management tools.

This lesson will discuss the details for a possible future manned mission to Mars. The human risks are discussed and evaluated to minimize danger to astronauts. A specialized launch schedule is provided and the different professions of the crew are discussed. Once on the surface, the crew's activities and living area will be covered, as well as how they will make enough fuel to make it off the Red Planet and return home.

The storyline of this case study describes a failure of a central system (much like the Internet of today) that occurs in the future, with some degree of mystery as to the cause. Originally designed for a junior level introductory course on microprocessors for computer engineering students, this icebreaker case study illustrates our increasing reliance on technology, particularly highlighting the importance and ubiquity of microprocessors. The discussion involves a number of new technologies and lays the groundwork for future discussions on good system design and integration of secure processors for embedded systems.

This course covers basic topics in autonomous marine vehicles, focusing mainly on software and algorithms for autonomous decision making (autonomy) by underwater vehicles operating in the ocean environments, autonomously adapting to the environment for improved sensing performance. It will introduce students to underwater acoustic communication environment, as well as the various options for undersea navigation, both crucial to the operation of collaborative undersea networks for environmental sensing. Sensors for acoustic, biological and chemical sensing by underwater vehicles and their integration with the autonomy system for environmentally adaptive undersea mapping and observation will be covered. The subject will have a significant lab component, involving the use of the MOOS-IvP autonomy software infrastructure for developing integrated sensing, modeling and control solutions for a variety of ocean observation problems, using simulation environments and a field testbed with small autonomous surface craft and underwater vehicles operated on the Charles River.

In this course the fundamentals of fluid mechanics are developed in the context of naval architecture and ocean science and engineering. The various topics covered are: Transport theorem and conservation principles, Navier-Stokes' equation, dimensional analysis, ideal and potential flows, vorticity and Kelvin's theorem, hydrodynamic forces in potential flow, D'Alembert's paradox, added-mass, slender-body theory, viscous-fluid flow, laminar and turbulent boundary layers, model testing, scaling laws, application of potential theory to surface waves, energy transport, wave/body forces, linearized theory of lifting surfaces, and experimental project in the towing tank or propeller tunnel.

Students learn about slope, determining slope, distance vs. time graphs through a motion-filled activity. Working in teams with calculators and CBL motion detectors, students attempt to match the provided graphs and equations with the output from the detector displayed on their calculators.

Detailed study of the materials with properties that have been optimized for a set of desired applications and their production. Explores atomic structure, crystalline materials, flaws and diffusion, mechanical properties, phase diagrams, specialty materials, and nanotechnology.

As the first engineering design challenge of the unit, students are introduced to the logic for solving a maze. First they observe a blindfolded student volunteer being guided through a classroom maze by the simple verbal instructions of another student. In this demonstration, the blindfolded student represents a robot and the guiding student represents programming commands. Then student groups apply that logic to program LEGO MINDSTORMS(TM) NXT robots to navigate through a maze, first with no sensors, and then with sensors. A PowerPoint® presentation, pre/post quizzes and a worksheet are provided.