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The Art of Approximation in Science and Engineering: How to Whip Out Answers Quickly
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CC BY-NC-SA
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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.

Subject:
Algebra
Career and Technical Education
Mathematics
Numbers and Operations
Physical Science
Physics
Technology and Engineering
Material Type:
Lecture
Provider:
MIT Learning International Networks Consortium
Provider Set:
M.I.T. Blossoms
Author:
Stephen M. Hou
Date Added:
10/10/2017
The Art of Approximation in Science and Engineering, Spring 2008
Conditional Remix & Share Permitted
CC BY-NC-SA
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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.

Subject:
Career and Technical Education
Technology and Engineering
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Sanjoy Mahajan
Date Added:
01/01/2008
Ask an Engineer
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Educational Use
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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.

Subject:
Career and Technical Education
Computer Science
Technology and Engineering
Material Type:
Lecture
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media Common Core Collection
Author:
Argosy Foundation
WGBH Educational Foundation
Date Added:
05/09/2006
Assessing the Situation
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Educational Use
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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.

Subject:
Career and Technical Education
Technology and Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Adventure Engineering,
TeachEngineering.org
Date Added:
09/18/2014
Asteroid Impact
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Educational Use
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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.

Subject:
Art and Design
Career and Technical Education
Fine Arts
Technology and Engineering
Material Type:
Full Course
Unit of Study
Provider:
TeachEngineering
Provider Set:
TeachEngineering NGSS Aligned Resources
Author:
Adventure Engineering,
Date Added:
09/18/2014
Asteroids
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Educational Use
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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.

Subject:
Career and Technical Education
Technology and Engineering
Material Type:
Activity/Lab
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Brian Kay
Integrated Teaching and Learning Program ,
Janet Yowell
Karen King
TeachEngineering.org
Date Added:
09/18/2014
Attack of the Raging River
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Educational Use
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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.

Subject:
Career and Technical Education
Physical Science
Physics
Technology and Engineering
Material Type:
Activity/Lab
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering NGSS Aligned Resources
Author:
Adventure Engineering,
Date Added:
09/18/2014
Audio Engineers: Sound Weavers
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Educational Use
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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.

Subject:
Career and Technical Education
Physical Science
Physics
Technology and Engineering
Material Type:
Activity/Lab
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Integrated Teaching and Learning Program,
Janet Yowell
Malinda Schaefer Zarske
Michael Bendewald
TeachEngineering.org
Date Added:
09/18/2014
Bacteria Are Everywhere!
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Educational Use
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Students are introduced to the concept of engineering biological organisms and studying their growth to be able to identify periods of fast and slow growth. They learn that bacteria are found everywhere, including on the surfaces of our hands. Student groups study three different conditions under which bacteria are found and compare the growth of the individual bacteria from each source. In addition to monitoring the quantity of bacteria from differ conditions, they record the growth of bacteria over time, which is an excellent tool to study binary fission and the reproduction of unicellular organisms.

Subject:
Biology
Career and Technical Education
Chemistry
Life Science
Physical Science
Technology and Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
AMPS GK-12 Program,
Janet Yowell
Jasmin Hume
TeachEngineering.org
Date Added:
09/18/2014
The Balancing Act
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Educational Use
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Students visualize and interact with concepts already learned, specifically algebraic equations and solving for unknown variables. They construct a balancing seesaw system (LEGO® Balance Scale) made from LEGO MINDSTORMS® parts and digital components to mimic a balancing scale. They are given example algebraic equation problems to analyze, configure onto the balance scale, and evaluate by manipulating LEGO pieces and gram masses that represent terms of an equation such as unknown variables, coefficients and integers. Digital light sensors, built into the LEGO Balance Scale, detect any balance or imbalances displayed on the balancing scale. The LEGO Balance Scale interactively issues a digital indication of balance or imbalance within the system. If unbalanced, students continue using the LEGO Balance Scale until they are confident in their understanding of solving algebraic equations. The goal is for students to become confident in solving algebraic equations by fundamentally understanding the basics of algebra and real-world algebraic applications.

Subject:
Career and Technical Education
Chemistry
Physical Science
Technology and Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
AMPS GK-12 Program,
Gisselle Cunningham, Russell Holstein, Linderick Outerbridge, Jared Soto, Timothy Li
TeachEngineering.org
Date Added:
09/18/2014
Ball Bounce Experiment
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Educational Use
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Students investigate different balls' abilities to bounce and represent the data they collect graphically.

Subject:
Career and Technical Education
Chemistry
Education
Mathematics
Physical Science
Physics
Technology and Engineering
Material Type:
Activity/Lab
Lesson Plan
Teaching/Learning Strategy
Provider:
TeachEngineering
Author:
Center for Engineering Educational Outreach,
Center for Engineering Educational Outreach, Tufts University
TeachEngineering.org
Tufts University
Date Added:
09/18/2014
Balloons
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Educational Use
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Students follow the steps of the engineering design process as they design and construct balloons for aerial surveillance. After their first attempts to create balloons, they are given the associated Estimating Buoyancy lesson to learn about volume, buoyancy and density to help them iterate more successful balloon designs.Applying their newfound knowledge, the young engineers build and test balloons that fly carrying small flip cameras that capture aerial images of their school. Students use the aerial footage to draw maps and estimate areas.

Subject:
Career and Technical Education
Mathematics
Physical Science
Physics
Technology and Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Integrated Teaching and Learning Program,
Marissa H. Forbes
Mike Soltys
TeachEngineering.org
Date Added:
09/18/2014
Balloons & Buoyancy
Unrestricted Use
CC BY
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Experiment with a helium balloon, a hot air balloon, or a rigid sphere filled with different gases. Discover what makes some balloons float and others sink.

Subject:
Physical Science
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Carl Wieman
Danielle Harlow
Kathy Perkins
PhET Interactive Simulations
Ron LeMaster
Date Added:
11/15/2007
Basically Acidic Ink
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Educational Use
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Students hypothesize whether vinegar and ammonia-based glass cleaner are acids or bases. They create designs on index cards using these substances as invisible inks. After the index cards have dried, they apply red cabbage juice as an indicator to reveal the designs.

Subject:
Career and Technical Education
Chemistry
Physical Science
Technology and Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Christine Hawthorne
Corey Burton
National Science Foundation GK-12 and Research Experience for Teachers (RET) Programs,
Nicole Stewart
Rachel Howser
TeachEngineering.org
Date Added:
09/18/2014
Basically Acids
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Educational Use
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Students learn the basics of acid/base chemistry in a fun, interactive way by studying instances of acid/base chemistry found in popular films such as Harry Potter and the Prisoner of Azkaban and National Treasure. Students learn what acids, bases and indicators are and how they can be used, including invisible ink. They also learn how engineers use acids and bases every day to better our quality of life. Students' interest is piqued by the use of popular culture in the classroom.

Subject:
Career and Technical Education
Chemistry
Physical Science
Technology and Engineering
Material Type:
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Christine Hawthorne
Rachel Howser
TeachEngineering.org
University of Houston,
Date Added:
09/18/2014
Basics of Fluid Mechanics
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Fluid mechanics deals with the study of all fluids under static and dynamic situations. Fluid mechanics is a branch of continuous mechanics which deals with a relationship between forces, motions, and statical conditions in a continuous material. This study area deals with many and diversified problems such as surface tension, fluid statics, flow in enclose bodies, or flow round bodies (solid or otherwise), flow stability, etc. In fact, almost any action a person is doing involves some kind of a fluid mechanics problem. Furthermore, the boundary between the solid mechanics and fluid mechanics is some kind of gray shed and not a sharp distinction (see Figure 1.1 for the complex relationships between the different branches which only part of it should be drawn in the same time.). For example, glass appears as a solid material, but a closer look reveals that the glass is a liquid with a large viscosity. A proof of the glass ``liquidity'' is the change of the glass thickness in high windows in European Churches after hundred years. The bottom part of the glass is thicker than the top part. Materials like sand (some call it quick sand) and grains should be treated as liquids. It is known that these materials have the ability to drown people. Even material such as aluminum just below the mushy zone also behaves as a liquid similarly to butter. Furthermore, material particles that "behaves'' as solid mixed with liquid creates a mixture After it was established that the boundaries of fluid mechanics aren't sharp, most of the discussion in this book is limited to simple and (mostly) Newtonian (sometimes power fluids) fluids which will be defined later.

This book describes the fundamentals fluid mechanics phenomena for engineers and others. It is designed to replace all introductory textbook(s) or instructor's notes for the fluid mechanics in undergraduate classes for engineering/science students but also for technical peoples. It is hoped that the book could be used as a reference book for people who have at least some basics knowledge of science areas such as calculus, physics, etc.

Subject:
Career and Technical Education
Physical Science
Physics
Technology and Engineering
Material Type:
Textbook
Provider:
Potto Project
Author:
Genick Bar–MeirPh. D.
Date Added:
01/01/2011
Battery-Resistor Circuit
Unrestricted Use
CC BY
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Look inside a resistor to see how it works. Increase the battery voltage to make more electrons flow though the resistor. Increase the resistance to block the flow of electrons. Watch the current and resistor temperature change.

Subject:
Physical Science
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Carl Wieman
PhET Interactive Simulations
Reid, Sam
Sam Reid
Wieman, Carl
Date Added:
11/20/2008
Battery Voltage
Unrestricted Use
CC BY
Rating
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Look inside a battery to see how it works. Select the battery voltage and little stick figures move charges from one end of the battery to the other. A voltmeter tells you the resulting battery voltage.

Subject:
Physical Science
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Carl Wieman
PhET Interactive Simulations
Reid, Sam
Sam Reid
Wieman, Carl
Date Added:
11/16/2007
Bending Light
Unrestricted Use
CC BY
Rating
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Explore bending of light between two media with different indices of refraction. See how changing from air to water to glass changes the bending angle. Play with prisms of different shapes and make rainbows.

Subject:
Physical Science
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Emily Moore
Kathy Perkins
Loeblein, Trish
Moore, Emily
Noah Podolefsky
Perkins, Kathy
PhET Interactive Simulations
Podolefsky, Noah
Reid, Sam
Sam Reid
Trish Loeblein
University of Colorado at Boulder
Date Added:
05/09/2011
Beyond Data Collection: Analysis and Identification of Patterns
Conditional Remix & Share Permitted
CC BY-SA
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This article provides a brief discussion of the importance of teaching students to analyze data and representations of data as well as two resources that can help teachers implement these strategies into their instruction.

Subject:
Environmental Science
Life Science
Material Type:
Lesson Plan
Provider:
Ohio State University College of Education and Human Ecology
Provider Set:
Beyond Penguins and Polar Bears: An Online Magazine for K-5 Teachers
Author:
Jessica Fries-Gaither
Date Added:
02/06/2023