Students work as engineers to design and test trebuchets (in this case LEGO® MINDSTORMS® robots) that can launch objects. During the testing stage, they change one variable at a time to study its effect on the outcome of their designs. Specifically, they determine how far objects travel depending on their weights. As students learn about the different components of robot design and the specific function controls, they determine what design features are important for launching objects.

Students work within constraints to construct model trusses and then test them to failure as a way to evaluate the relative strength of different truss configurations and construction styles. Each student group uses Popsicle sticks and hot glue to build a different truss configuration from a provided diagram of truss styles. Within each group, each student builds two exact copies of the team's truss configuration using his/her own construction method, one of which is tested under shear conditions and the other tested under compression conditions. Results are compiled and reviewed as a class to analyze the strength of different types of shapes and construction methods under the two types of loads. Students make and review predictions, and normalize strengths. Teams give brief presentations to recap their decisions, results and analysis.

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 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 (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.

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 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 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.

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 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 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.

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.

Veritasium explores puzzling scientific concepts, discussing them with experts and the public to uncover intriguing ideas.

*Math
*Physics
*Engineering
*Astronomy
*Misconceptions

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 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.

In this demonstration, a plastic soft drink bottle is used to demonstrate properties of gases and liquids with respect to temperature and pressure. Calculations using the formula for the Ideal Gas Law are included. The resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

This lesson was developed to give participants an understanding of Earth's water cycle. In this one-hour long activity, students participate in a webquest to learn about the water cycle, and then build a mini-model of the water cycle to observe how water moves through Earth's four systems. The activity uses the 5E instructional model and is part of the "Survivor Earth" series of one-hour lessons.

This is a hands-on lab activity about the water cycle, specifically evaporation and condensation. Using materials such as clay, ice and a lamp, learners will observe the relationship between temperature and condensation and temperature and evaporation. They will then draw a diagram or a concept map of the water cycle. Background information, common preconceptions, a glossary and more is included. This activity is part of the Aquarius Hands-on Laboratory Activities.

Students learn about the importance of dams by watching a video that presents historical and current information on dams, as well as descriptions of global water resources and the hydrologic cycle. Students also learn about different types of dams, all designed to resist the forces on dams. (If the free, 15-minute "Water and Dams in Today's World" video cannot be obtained in time, the lesson can still be taught. See the Additional Multimedia Support section for how to obtain the DVD or VHS videotape, or a PowerPoint presentation with similar content [also attached].)

This is a series of seven brief activities about Jupiter's atmosphere and weather. Learners will look at Jupiter's distinct banded appearance, violent storms, and clouds of many different colors. The activities are part of Explore! Jupiter's Family Secrets, a series designed to engage children in space and planetary science in libraries and informal learning environments.