This course teaches simple reasoning techniques for complex phenomena: divide and conquer, dimensional analysis, extreme cases, continuity, scaling, successive approximation, balancing, cheap calculus, and symmetry. Applications are drawn from the physical and biological sciences, mathematics, and engineering. Examples include bird and machine flight, neuron biophysics, weather, prime numbers, and animal locomotion. Emphasis is on low-cost experiments to test ideas and on fostering curiosity about phenomena in the world.

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

In this book, Sanjoy Mahajan shows us that the way to master complexity is through insight rather than precision. Precision can overwhelm us with information, whereas insight connects seemingly disparate pieces of information into a simple picture. Unlike computers, humans depend on insight. Based on the author's fifteen years of teaching at MIT, Cambridge University, and Olin College, The Art of Insight in Science and Engineering shows us how to build insight and find understanding, giving readers tools to help them solve any problem in science and engineering. (Description courtesy of MIT Press.)

The aim of this video is to introduce high school students to the engineering concept of road construction and to the reasons why problems might arise in road construction. Presentation of this concept is made more accessible to students by comparing road construction to the art of baking a layer cake. This simple comparison can serve to emphasize how important it is to follow proper procedures and to use proper materials for successful road construction. The approach used is highly correlated with the common knowledge of baking layer cakes in Malaysia. Students should be able to relate the procedure of baking a layer cake to the importance of following the correct methods of road construction. An understanding of basic statistics is necessary before starting this lesson. This lesson will take almost 60 minutes to complete. During activity breaks, students are required to answer questions and complete assigned tasks related to the subject.

This article discusses how to use murals as an interdisciplinary, cooperative activity to blend science, art, and math concepts.

Explore some of the wonders of modern engineering in this video from the Sciencenter in Ithaca, New York. Hear a diverse selection of engineers explain how things work.

As teachers it is important to interject real-world applications with science and math whenever possible.  Students often do not connect the principles to the career opportunities.  In our society, advanced manufacturing is creating many exciting careers that incorporate these scientific principles and provide excellent salaries.  This project will require students to determine and design methods that will move a selected product in a designed assembly process.

An exercise assessing the water demand of New York City and population dynamics underlying that demand is provided. Visualization of first order water resource estimates using precipitation data and a known water storage volume are used to draw conclusions about drought risk and the sustainability of NYC water supplies.

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Finding themselves in the middle of the Amazon rainforest after a plane crash, students use map scales, keys, and longitude and latitude coordinates to figure out where they are. Then they work in groups to generate ideas and make plans. They decide where they should go to be rescued, the distance to that location, the route to take, and make calculations to estimate walking travel time.

This article provides an overview of using rubrics as a method of assessment and discusses technological tools that facilitate the creation of rubrics.

In this video segment produced for Teachers' Domain, Andres Berrio, an associate scientist at Biogen Idec, discusses what he has done to succeed in the biotechnology field.

Through this earth science curricular unit, student teams are presented with the scenario that an asteroid will impact the Earth. In response, their challenge is to design the location and size of underground caverns to shelter the people from an uninhabitable Earth for one year. Driven by this adventure scenario, student teams 1) explore general and geological maps of their fictional state called Alabraska, 2) determine the area of their classroom to help determine the necessary cavern size, 3) learn about map scales, 4) test rocks, 5) identify important and not-so-important rock properties for underground caverns, and 6) choose a final location and size.

In this lesson, students learn some basic facts about asteroids in our solar system. The main focus is on the size of asteroids and how that relates to the potential danger of an asteroid colliding with the Earth. Students are briefly introduced to the destruction that would ensue should a large asteroid hit, as it did 65 million years ago.

This article reprints and links to informational text about the adaptations that allow mammals and fish to survive in polar oceans. Versions are available for students in grades K-1, 2-3 and 4-5. Related science and literacy activities are included.

In this activity, students will explore how the Law of Conservation of Energy (the First Law of Thermodynamics) applies to atoms, as well as the implications of heating or cooling a system. This activity focuses on potential energy and kinetic energy as well as energy conservation. The goal is to apply what is learned to both our human scale world and the world of atoms and molecules.

In this lesson, the students will discover the relationship between an object's mass and the amount of space it takes up (its volume). The students will also learn about the concepts of displacement and density.

In this lesson, students are introduced to audio engineers. They discover in what type of an environment audio engineers work and exactly what they do on a day-to-day basis. Students come to realize that audio engineers help produce their favorite music and movies.

This article includes links to expository text for students in grades K-1, 2-3, and 4-5 about the aurora.

This article lists seven art techniques and four poetry types that can be used to depict and describe the aurora.

The engineering design process involves many steps. Not only must an engineer be able to devise a solution to a problem, he or she must also be ready to test and evaluate that solution to reach the best result. To successfully complete the design process, an engineer must be able to identify design flaws and learn from his or her mistakes. In this video segment adapted from ZOOM, learn about the design process as cast members create automatic door openers that enable them to open their bedroom doors while lying on their beds. For grades 3-8.