This short video and interactive assessment activity is designed to teach third graders about mixed review (numbers up to 100,000).

This short video and interactive assessment activity is designed to teach fifth graders about different unit length comparisons.

This task assumes students are familiar with mixing problems. This approach brings out different issues than simply asking students to solve a mixing problem, which they can often set up using patterns rather than thinking about the meaning of each part of the equations.

In order to solve this problem, students must assume that if you mix a cubic foot of sand with a cubic foot of cement, you will have 2 cubic feet of mix.

The problem deals with a rational expression which is built up from operations arising naturally in a context: adding the volumes of the fertilizer and the water, and dividing the volume of the fertilizer by the resulting sum. Thus it encourages students to see the expression as having meaning in terms of numbers and operations, rather than as an abstract arrangement of symbols.

Students learn about the separation techniques of sedimentation and centrifugation and investigate whether blood is a homogeneous or a heterogeneous mixture. Working in groups as if they are biomedical researchers, they employ the scientific method and make observations about the known characteristics of urine, milk and blood. They probe further by analyzing research on the properties and fractionation modes of blood. As students learn about certain strange characteristics with the fractionation behavior of blood, they formulate hypotheses on the unique nature of blood. Using provided materials —olive oil, tomato juice and petroleum jelly—they design an experiment and construct a blood model. They test their hypotheses by conducting experiments on the blood model, and then propose theories for the nature of blood as a mixture—arriving at the theory of mixture dualism in blood—that blood is a complex mixture system. An activity-guiding handout and PowerPoint® presentation are provided for this student-directed, project-based activity.

As students are learning about substances, mixtures, and solutions, they will participate in several experiments that involve chemical reactions using regular household products. Some experiments will produce gas or create something that will grow. Students will work in groups of 2-3 students to make a car move using the result of a chemical reaction from combining two or more household substances. They will present their project to the class.

Through three lessons and their four associated activities, students are introduced to concepts related to mixtures and solutions. Students consider how mixtures and solutions and atoms and molecules can influence new technologies developed by engineers. To begin, students explore the fundamentals of atoms and their structures. The building blocks of matter (protons, electrons, neutrons) are covered in detail. The next lesson examines the properties of elements and the periodic table one method of organization for the elements. The concepts of physical and chemical properties are also reviewed. Finally, the last lesson introduces the properties of mixtures and solutions. A comparison of different mixtures and solutions, their properties and their separation qualities are explored.

Students learn about life-cycle assessment and how engineers use this technique to determine the environmental impact of everyday products and processes. As they examine what’s involved in making and consuming cupcakes, a snack enjoyed by millions of people every year, students learn about the production, use and disposal phases of an object’s life cycle. With the class organized into six teams, students calculate data for each phase of a cupcake’s life cycle—wet ingredients, dry ingredients, baking materials, oven baking, frosting, liner disposal—and calculate energy usage and greenhouse gases emitted from making one cupcake. They use ratios and fractions, and compare options for some of the life-cycle stages, such as different paper wrapper endings (disposal to landfills or composting) in order to make a life-cycle plan with a lower environmental impact. This activity opens students’ eyes to see the energy use in the cradle-to-grave lives of everyday products. Pre/post-quizzes, worksheets, activity cards, Excel® workbook and visual aids are provided.

The application of engineering principles is explored in the creation of mobiles. As students create their own mobiles, they take into consideration the forces of gravity and convection air currents. They learn how an understanding of balancing forces is important in both art and engineering design.

Modal logic is the logic of necessity and possibility, and by extension of analogously paired notions like validity and consistency, obligation and permission, the known and the not-ruled-out. This a first course in the area. A solid background in first-order logic is essential. Topics to be covered include (some or all of) the main systems of propositional modal logic, Kripkean "possible world" semantics, strict implication, contingent identity, intensional objects, counterpart theory, the logic of actuality, and deontic and / or epistemic logic. The emphasis will be more on technical methods and results than philosophical applications.

An interactive simulation in which students use a model of charged objects to explain how charges interact and construct an understanding of Coulomb's Law. It is concerned with comparing ions and neutral atoms. The model allows the user to investigate the relationships between sign of charge, magnitude of charge, and distance between ions. The model illustrates the operation of three types of electroscopes. Next it visually explores how a static charge can bend the path of a moving electron, and then graphically and numerically explores Coulomb's Law. Lastly a model that illustrates polarization of charge illustrates why a charged balloon is attracted to a neutral wall. The system allows students to enter their multiple choice and written answers throughout the activity and generate a report of their responses at the end even if they are not logged into the system.

Students learn about the advantages and disadvantages of the greenhouse effect. They construct their own miniature greenhouses and explore how their designs take advantage of heat transfer processes to create controlled environments. They record and graph measurements, comparing the greenhouse indoor and outdoor temperatures over time. Students are also introduced to global issues such as greenhouse gas emissions and their relationship to global warming.

Students use provided materials to design and build prototype artificial heart valves. Their functioning is demonstrated using water to simulate the flow of blood through the heart. Upon completion, teams demonstrate their fully functional prototypes to the rest of the class, along with a pamphlet that describes the device and how it works.

Second subject of two-term sequence on modeling, analysis and control of dynamic systems. Kinematics and dynamics of mechanical systems including rigid bodies in plane motion. Linear and angular momentum principles. Impact and collision problems. Linearization about equilibrium. Free and forced vibrations. Sensors and actuators. Control of mechanical systems. Integral and derivative action, lead and lag compensators. Root-locus design methods. Frequency-domain design methods. Applications to case-studies of multi-domain systems.

First of two-term sequence on modeling, analysis and control of dynamic systems. Mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices. Analytical and computational solution of linear differential equations and state-determined systems. Laplace transforms, transfer functions. Frequency response, Bode plots. Vibrations, modal analysis. Open- and closed-loop control, instability. Time-domain controller design, introduction to frequency-domain control design techniques. Case studies of engineering applications.

This course provides an introduction to the study of environmental phenomena that exhibit both organized structure and wide variability - i.e., complexity. Through focused study of a variety of physical, biological, and chemical problems in conjunction with theoretical models, we learn a series of lessons with wide applicability to understanding the structure and organization of the natural world. Students will also learn how to construct minimal mathematical, physical, and computational models that provide informative answers to precise questions.

Mathematics, as we all know, is the language of science, and fluency in algebraic skills has always been necessary for anyone aspiring to disciplines based on calculus. But in the information age, increasingly sophisticated mathematical methods are used in all fields of knowledge, from archaeology to zoology. Consequently, there is a new focus on the courses before calculus. The availability of calculators and computers allows students to tackle complex problems involving real data, but requires more attention to analysis and interpretation of results. All students, not just those headed for science and engineering, should develop a mathematical viewpoint, including critical thinking, problem-solving strategies, and estimation, in addition to computational skills. Modeling, Functions and Graphs employs a variety of applications to motivate mathematical thinking.

Explores the theory and practice of scientific modeling in the context of auditory and speech biophysics. Based principally on seminar-style discussions of the research literature, subject draws on examples from hearing and speech (e.g., cochlear and vocal-fold mechanics) to explore general, meta-theoretical issues that transcend the particular subject matter. Examples include: What is a model? What is the process of model building? What are the different approaches to modeling? What is the relationship between theory and experiment? How are models tested? What constitutes a good model?

Mathematical modeling of complex engineering systems at a level of detail compatible with the design and implementation of modern control systems. Wave-like and diffusive energy transmission systems. Multiport energy storing fields and dissipative fields; consequences of symmetry and asymmetry. Nonlinear mechanics and canonical transformation theory. Examples will include mechanisms, electromechanical transducers, electronic systems, fluid systems, thermal systems, compressible flow processes, chemical processes. This course models multi-domain engineering systems at a level of detail suitable for design and control system implementation. Topics include network representation, state-space models; multi-port energy storage and dissipation, Legendre transforms; nonlinear mechanics, transformation theory, Lagrangian and Hamiltonian forms; and control-relevant properties. Application examples may include electro-mechanical transducers, mechanisms, electronics, fluid and thermal systems, compressible flow, chemical processes, diffusion, and wave transmission.