Students will learn a sample-variance curve fitting method that can be used …
Students will learn a sample-variance curve fitting method that can be used to determine whether a set of experimental data appears to have been generated by a model. This method is based on minimizing the reduced chi-squared value. This video includes a reminder to inspect normalized residuals before reporting fitted parameters.
The quadrature formula relates the fluctuations of a function to fluctuations in …
The quadrature formula relates the fluctuations of a function to fluctuations in the variables on which the function depends. In this derivation, we approximate a multivariable function using a Taylor expansion, and we assume that fluctuations in the underlying variables are statistically independent, which allows us to apply an identity previously derived in the unit on statistics. Namely, "variances of sums are sums of variances" for variables that fluctuate independently.
In the first video segment, we estimate properties of a parent distribution …
In the first video segment, we estimate properties of a parent distribution (i.e. mean and standard deviation) from a sample of a finite collection of data measurements, and we describe the standard error (SE). In the second segment, we derive the famous square-root of n factor that appears in the SE formula. The third video segment describes the visual comparison of error bars, and the fourth segment warns against a mistake that can generate inappropriate claims of statistical significance during this kind of analysis.
Students learn about Pascal's law, an important concept behind the engineering of …
Students learn about Pascal's law, an important concept behind the engineering of dam and lock systems, such as the one that Thirsty County wants Splash Engineering to design for the Birdseye River (an ongoing hypothetical engineering scenario). Students observe the behavior of water in plastic water bottles spilling through holes punctured at different heights, seeing the distance water spurts from the holes, learning how water at a given depth exerts equal pressure in all directions, and how water at increasing depths is under increasing pressure.
Sixth grade students at Eckstein Middle School use their understanding of electricity …
Sixth grade students at Eckstein Middle School use their understanding of electricity to explore electrical current in a circuit with photovoltaic cells.Using a lamp to model the sun, students work in teams and connect different power sources in series and parallel circuits to determine the effects on light bulbs or small motors. Discussion between students about the differences in voltage and the flow of electrons from negative to positive terminals provide opportunities for students to explain their learning and for the teacher to assess their understanding.Learning is extended beyond the experiment as students use photovoltaic cells to power equipment and offset electrical load in the classroom.
These guides showcase education and public outreach resources from across more than …
These guides showcase education and public outreach resources from across more than 20 NASA astrophysics missions and programs. The twelve guides - one for each month - contain a science topic, an interpretive story, a sky object to view with finding charts, hands-on activities, and connections to NASA science. The guides are modular, so that educators can use the portions that are the most useful for their audiences/events. Following is the theme for each month: January - Betelgeuse, February - Orion Nebula, March - Pleiades, April - Pollux; May - Hubble Deep Field, June - Hercules Cluster, July - Ring Nebula & Veil Nebula, August - The Search for Habitable Worlds, September - Milky Way Galaxy, October - Upsilon Andromedae, November - Andromeda Galaxy, and December - Crab Nebula.
University Physics is a three-volume collection that meets the scope and sequence …
University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result.
University Physics is a three-volume collection that meets the scope and sequence …
University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result.
The airplanes unit begins with a lesson on how airplanes create lift, …
The airplanes unit begins with a lesson on how airplanes create lift, which involves a discussion of air pressure and how wings use Bernoulli's principle to change air pressure. Next, students explore the other three forces acting on airplanes thrust, weight and drag. Following these lessons, students learn how airplanes are controlled and use paper airplanes to demonstrate these principles. The final lessons addresses societal and technological impacts that airplanes have had on our world. Students learn about different kinds of airplanes and then design and build their own balsa wood airplanes based on what they have learned.
In this activity, students build a simple computer model to determine the …
In this activity, students build a simple computer model to determine the black body surface temperature of planets in our solar system: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. Experiments altering the luminosity and distance to the light source will allow students to determine the energy reaching the object and its black body temperature. The activity builds on student outcomes from activity A, "Finding a Mathematical Description of a Physical Relationship." It also supports inquiry into a real-world problem, the effect of urban heat islands and deforestation on climate. Includes a teacher's guide, student worksheets, and an Excel tutorial. This is Activity B of module 3, titled "Using Mathematic Models to Investigate Planetary Habitability," of the resource, Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.
Students explore how mathematical descriptions of the physical environment can be fine-tuned …
Students explore how mathematical descriptions of the physical environment can be fine-tuned through testing using data. In this activity, student teams obtain satellite data measuring the Earth's albedo, and then input this data into a spreadsheet-based radiation balance model, GEEBITT. They validate their results against published the published albedo value of the Earth, and conduct similar comparisons Mercury, Venus and Mars. The resource includes an Excel spreadsheet tutorial, an investigation, student data sheets and a teacher's guide. Students apply their understanding to the real life problem of urban heat islands and deforestation. The activity links builds on student outcomes from activities A and B: "Finding a Mathematical Description of a Physical Relationship," and "Making a Simple Mathematical Model." This is Activity C in module 3, Using Mathematical Models to Investigate Planetary Habitability, of the resource, Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.
This is a lesson about elemental spectra. Learners will compare known elemental …
This is a lesson about elemental spectra. Learners will compare known elemental spectra with spectra of Titan and Saturn‰Ûªs rings from a spectrometer aboard the NASA Cassini spacecraft. They identify the elements visible in the planetary and lunar spectra. The activity is part of Project Spectra, a science and engineering program for middle-high school students, focusing on how light is used to explore the Solar System.
Students use the spectrograph from the "Building a Fancy Spectrograph" activity to …
Students use the spectrograph from the "Building a Fancy Spectrograph" activity to gather data about different light sources. Using the data, they make comparisons between the light sources and make conjectures about the composition of these sources.
This is an activity about vectors and velocity. It outlines the addition …
This is an activity about vectors and velocity. It outlines the addition and subtraction of vectors, and introduces the application of trigonometry to describing vectors. The resource is designed to support student analysis of THEMIS (Time History of Events and Macroscale Interactions during Substorms) Magnetometer line-plot data. Learners will complete worksheets consisting of problem sets that allow them to work with vector data in magnetic fields. This is activity 15 from Exploring Magnetism: Earth's Magnetic Personality.
This is a lesson about the vertical dimension of the atmosphere and …
This is a lesson about the vertical dimension of the atmosphere and includes four activities. Activity 1 Introduces concepts related to distance, including length and height and units of measurement. Students are asked to make comparisons of distances. In activity 2, students learn about the vertical profile of the atmosphere. They work with a graph and plot the heights of objects and the layers of the atmosphere: troposphere, stratosphere, mesosphere, thermosphere, and exosphere. In activity 3, students learn about other forms of visual displays using satellite imagery. They compare images of the same weather feature, a hurricane, using two different images from MODIS and CALIPSO. One image is looking down on the hurricane from space, the other looks through the hurricane to display a profile of the hurricane. Activity 4 reinforces the concept of the vertical nature of the atmosphere. Students will take a CALIPSO satellite image that shows a profile of the atmosphere and use this information to plot mountains and clouds on their own graph of the atmosphere. The recommended order for the activities is to complete the first two activities on day one, and the second two activities on day two. Each day will require approximately 1 to 1.5 hours.
Students are introduced to the concept of viscoelasticity and some of the …
Students are introduced to the concept of viscoelasticity and some of the material behaviors of viscoelastic materials, including strain rate dependence, stress relaxation, creep, hysteresis and preconditioning. Viscoelastic material behavior is compared to elastic solids and viscous fluids. Students learn about materials that have viscoelastic behavior along with the importance of engineers understanding viscoelasticity. To best engage the students, conduct the first half of the associated Creepy Silly Putty activity before conducting this lesson.
Students study the physical properties of different fluids and investigate the relationship …
Students study the physical properties of different fluids and investigate the relationship between the viscosities of liquid and how fast they flow through a confined area. Student groups conduct a brief experiment in which they quantify the flow rate to understand how it relates to a fluid's viscosity and ultimately chemical composition. They explore these properties in milk and cream, which are common fluids whose properties (and even taste!) differ based on fat content. They examine control samples and unknown samples, which they must identify based on how fast they flow. To identify the unknowns requires an understanding of the concept of viscosity. For example, heavy cream flows at a slower rate than skim milk. Ultimately, students gain an understanding of the concept of viscosity and its effect on flow rate.
Students are introduced to the similarities and differences in the behaviors of …
Students are introduced to the similarities and differences in the behaviors of elastic solids and viscous fluids. Several types of fluid behaviors are described Bingham plastic, Newtonian, shear thinning and shear thickening along with their respective shear stress vs. rate of shearing strain diagrams. In addition, fluid material properties such as viscosity are introduced, along with the methods that engineers use to determine those physical properties.
In this lesson, the electromagnetic spectrum is explained and students learn that …
In this lesson, the electromagnetic spectrum is explained and students learn that visible light makes up only a portion of this wide spectrum. Students also learn that engineers use electromagnetic waves for many different applications.
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