National Aeronautics and Space Administration

Problem 316: Counting Craters on the Hubble Space Telescope Students count craters on a piece of the Wide Field Planetary Camera recovered from the Hubble Space Telescope in 2009. They determine the cratering rate and use this to predict how many impacts the solar panels on the International Space Station experiences each day. [Grade: 6-9 | Topics: Counting; Area; density]

Problem 295: Details from an Exploding Star Students work with an image from the Hubble Space Telescope of the Crab Nebula to calculate scales and sizes of various features. [Grade: 6-9 | Topics: Scale; measurement; metric units]

Problem 240: The Eagle Nebula Close-up Students measure a Hubble image of the famous Eagle Nebula 'Pillars of Creation' to determine the sizes of arious features compared to our solar system [Grade: 8-10 | Topics: scale, proportion, angle measure]

Problem 239: Counting Galaxies with the Hubble Space Telescope Students use an image of a small area of the sky to estimate the total number of galaxies in the universe visible from Earth. [Grade: 8-10 | Topics: area, angular measure]

Problem 238: Satellite Drag and the Hubble Space Telescope Satellite experience drag with the atmosphere, which eventually causes them to burn up in the atmosphere. Students study various forecasts of the altitude of the Hubble Space Telescope to estimate its re-entry year. [Grade: 8-10 | Topics: interpreting graphical data; predicting trends]

Problem 197: Hubble Sees a Distant Planet Students study an image of the dust disk around the star Fomalhaut and determine the orbit period and distance of a newly-discoveblack planet orbiting this young star. [Grade: 6-10| Topics: Calculating image scales; Circle circumferences; Unit conversions; distance-speed-time]

Problem 122: XZ Tauri's Super CME! Ordinarily, the SOHO satellite and NASA's STEREO mission spot coronal mass ejections (CMEs) but the Hubble Space Telescope has also spotted a few of its own...on distant stars! Students will examine a sequence of images of the young star XZ Tauri, and measure the average speed and density of this star's CME event between 1955 and 2000. [Grade: 8-10 | Topics:Calculate image scale; speed from distance and time; mass:volume:density]

Problem 49: A Spiral Galaxy Up Close. Astronomers can learn a lot from studying photographs of galaxies. In this activity, students will compute the image scale (light years per millimeter) in a photograph of a nearby spiral galaxy, and explore the sizes of the features found in the image. They will also use the internet or other resources to fill-in the missing background information about this galaxy. [Grade level: 6-8 | Topics: Online research; Finding the scale of an image; metric measurement; decimal math]

Interstellar Boundary Explorer (IBEX)

Problem 274: IBEX Uses Fast-moving Particles to Map the Sky! Students learn about Kinetic Energy and how particle energies and speeds are related to each other in a simple formula, which they use to derive the speed of the particles detected by the IBEX satellite. [Grade: 8-10 | Topics: Algebra I, Scientific notation]

Problem 273: IBEX Creates an Unusual Image of the Sky Students create an image of the sky by using a Bingo-like technique of tallying particles in various sky directions using a simple 5x5 grid. [Grade: 6-8 | Topics: Counting, tallying]

Problem 114: The Heliopause...a question of balance Students will learn about the concept of pressure equilibrium by studying a simple mathematical model for the sun's heliopause located beyond the orbit of Pluto. They will calculate the distance to the heliopause by solving for 'R' and then using an Excel spreadsheet to examine how changes in solar wind density, speed and interstellar gas density relate to the values for R. [Grade: 8-10 | Topics: Formulas with two variables; scientific notation; spreadsheet programming]

Imager for Magnetosphere to Auroral Global Exploration (IMAGE)

Problem 41: Solar Energy in Space Students will calculate the area of a satellite's surface being used for solar cells from an actual photo of the IMAGE satellite. They will calculate the electrical power provided by this one panel. Students will have to calculate the area of an irregular region using nested rectangles. [Grade level: 7-10 | Topics: Area of an irregular polygon; decimal math]

Problem 35: Exploring the Plasmasphere Students use an image of the plasmasphere obtained by the IMAGE satellite to calculate how fast it orbits the Earth. They will use this to determine whether gravity or Earth's magnetic field provides the forces responsible for its movement through space. [Grade: 7 - 9 | Topics: Geometry; ratios; decimal math; time arithmetic]

Problem 25: The Distance to Earth's Magnetopause Students use an algebraic formula and some real data, to calculate the distance from Earth to the magnetopause, where solar wind and magnetosphere pressure are in balance. [Grade: 8 - 10 | Topics: Evaluating a function with two variables; completing tabular entries]

Problem 22: The Auroral Oval Students learn that the aurora are observed as two 'halos' of light encircling the North and South Poles. Students use measurements made from two satellite images of the 'auroral ovals' to determine the diameter of the rings, and their approximate geographic centers - which are not at the geographic poles! [Grade: 5 - 7 | Topics: Finding the scale of an image; measurement; decimal math]

Problem 21: Exploring the Plasmasphere Students learn that the Pythagorean Theorem is more than a geometric concept. Scientists use a photograph taklen by the IMAGE satellite to measure the size of Earth's plasmasphere region using a ruler and protractor. [Grade: 7 - 9 | Topics: Finding the scale of an image; decimal math; measurement]

Problem 15: Radio Plasma Imaging with IMAGE Students use the Distance=VelocityxTime relationship to determine the distances to plasma clouds seen by the IMAGE satellite. [Grade: 6 - 8 | Topics: Polar graphs; time = distance x speed; decimal math]

Problem 13: Plasma Clouds Students use a simple 'square-root' relationship to learn how scientists with the IMAGE satellite measure the density of clouds of plasma in space. [Grade: 7 - 9 | Topics: Square-root; solving for X; evaluating a function]

Problem 12: The Ring Current Students use the formula for a disk to calculate the mass of the ring current surrounding Earth. [Grade: 7 - 9 | Topics: Volume of a disk; scientific notation; mass = density x volume]

InSight Seismographic Station on Mars

Problem 527:Exploring a Possible InSight Landing Area on Mars
Students work with latitude and longitude and scaled images of mars to locate the InSight proposed landing area, and describe the terrain of the landing area. [Grade: 6-8 | Topics: degree measure; latitude and longitude; working with scaled images; metric measure] (PDF)

Problem 526:Comparing the InSight Landing Area to a City Block!
Students use scaled images of a proposed InSIght landing area and a scaled image of an urban neighborhood on Earth to compare the sizes of familiar things with the unfamiliar martian landscape. [Grade: 6-8 | Topics: scale; proportion; metric measurement] (PDF)

Problem 525:Exploring Marsquake Energy with the Moment Magnitude Scale
Students are introduced to the Moment Magnitude marsquake scale which gives a logarithmic index for marsquakes of differing energies. They calculate two examples of marsquakes and meteor impacts and compare their Moment Magnitude. [Grade: 8-10 | Topics: logarithms; scientific notation; algebra ] (PDF)

Problem 524:Exploring Logarithms and the Richter Magnitude Scale
Students work with a logarithmic scale to estimate how much ground movement occurs for earthquakes of different strengths. [Grade: 8-10 | Topics: logarithms; base-ten exponents] (PDF)

Problem 523:The Distance to the Martian Horizon
Students devive a basic equation for the distance to the horizon on a spherical body using the Pythagorean Theorem and a bit of algebra. The estimate the number of cell towers needed to cover Mars. [Grade: 8-10 | Topics: Pythagorean Theorem, Algebra; scientific notation; areas of spheres and circles ] (PDF)

Problem 522:Exploring the Interior of Mars with Spheres and Shells
Students use the volume properties of spheres and shells along with the relationship mass=densityxvolume to create a model of the interior of mars. [Grade: 8-10 | Topics: formula for volume of spheres and spherical shells; mass=densityxvolume; scientific notation ] (PDF)

Problem 521:Exploring the Mass of Mars
Students calculate the mass of mars by using satellite data and Keplers Third Law. [Grade: 8-10 | Topics: Algebra; scientific notation ] (PDF)

Problem 520:Exploring Impacts and Quakes on Mars
Students work with logarithmic scales to explore the relationship between the energy of an marsquake and its logarithmic index, which is similar to the Richter Scale used for earthquakes. [Grade: 8-10 | Topics: Logarithmic scales; scientific notation ] (PDF)

Problem 519:Comparing the Heat Output of Mars and Earth
Students learn about the heat flow formula and use it to explore the properties of Earth and Mars in terms of their crust composition. [Grade: 8-10 | Topics: Algebra; temperature gradients] (PDF)

Problem 518:Exploring Heat Flow and Insulation
Students explore how insulation works to reduce heat flow. They convert a verbal description of a formula expressed in proportions, and use it to calculate why aluminum pots heat faster than steel pots, and how we can determine the properties of martian sooil from heat flow and temperature changes. [Grade: 8-10 | Topics: algebra; rates of change ] (PDF)

Problem 517:Exploring Temperature Change in Earth’s Outer Crust
Students explore the rate of temperature change in the crust of Earth and Mars and learn about units expressed as degrees C/km. They calculate how hot the ground will be at various depths, and how gold miners must deal with extreme heat. [Grade: 6-8 | Topics: fahrenheit and celsius degrees; rates of change] (PDF)

Problem 516:Exploring the InSight Lander Telemetry Data Flow
Students explore how long it takes to transmit digital data using examples from downloading songs from their computer to their ipod. [Grade: 6-8 | Topics: working with kilo, mega and rates of data transfer in bytes/sec. ] (PDF)

Problem 515:Seeing the Martian Surface with IDC
Students learn about the IDC camera and calculate resolution and how many images are needed to map the InSight landing area. [Grade: 6-8 | Topics: ANgular measurfe, degrees and seconds; image scal; tiling an area with overlap. ] (PDF)

Problem 514:Telling Time on Mars - Earth Days and Mars Sols
Students work with two clocks on Earth and Mars and learn about earth and mars time given that a day on Mars is 40 minutes longer than an Earth day. [Grade: 6-8 | Topics: time calculations, hours, minutes, seconds; length of day ] (PDF)

Problem 513:Radio Communications with Earth – The Earth-Sun Angle
The earth-sun angle is given in tabular form in degrees. Students graph the data and find the dates when transmissions to Earth cannot occur. [Grade: 8-10 | Topics: Interpreting tabular data; rates and slopes ] (PDF)

Problem 512:Estimating the Mass of a Martian Dust Devil!
Students estimate the mass of a martian dust devil using the approximation that it is a cylinder with a fixed density of dust. [Grade: 8-10 | Topics: Volume of a cylinder; mass = density x volume ] (PDF)

Problem 511:The Work Area In Front of the Lander
Students estimate the area in front of the InSight lander where experiments will be conducted and instruments moved with a single robotic arm. [Grade: 6-8 | Topics: Area of a circle segment; Area common to two intersecting circles] (PDF)

Problem 510:Scheduling Events in Time for Launch
Students learn about scheduling many events along a timeline (breakfast, packing, driving, etc ) by planning a family trip where the family members have to arrive at the airport for a flight that leaves at a specific date and time. [Grade: 5-7 | Topics: working with time units; creating a timeline] (PDF)

Problem 509:The InSight Seismographic Station Solar Power System
Students explore the properties of decagons to determine the area of the solar panels used on the InSight lander. [Grade: 7-9 | Topics: area of regular polygons; estimating areas of non-square shapes] (PDF)

Problem 508: The InSight Seismographic Station - Wave arrival times
Students work with the circumference of Mars and the speed of shock waves in the martian crust to estimate the arrival times of the waves at the InSight Lander. [Grade: 6-8 | Topics: speed=distance/time; Time calculations; circumference of a circle] (PDF)

Juno to Jupiter

Problem 472: Investigating Juno's Elliptical Transfer Orbit
Students use the Standard Formula for an ellipse to study the elliptical orbit of the Juno spacecraft, and relate specific properties of the ellipse to features of the spacecrafts trajectory such as aphelion, perihelion, and ellipticity. [Grade: 9-12 | Topics: formula for an ellipse; semi-major and minor axis] (PDF)

Problem 471: Investigating the Launch of the Juno Spacecraft
Students use a series of images from a launch video to determine the scale of each image and determine the speed of the rocket as it leaves the gantry. [Grade: 6-8 | Topics: scale models; speed = distance/times] (PDF)

Problem 470: The Launch of the Juno Spacecraft - Ascent to orbit
Students use tabulated altitude and range data following the launch of the Juno mission, to determine the speed of the rocket as it travels to arth orbit. [Grade: 6-8 | Topics: scale models; speed = distance/time] (PDF)

Problem 469: Solar Energy and the Distance of Juno from the Sun
Students use the formula for an ellipse, along with the inverse-square law to create a mathemartical model that predicts the declining solar power produced by Junos solar panels as the spacecraft travels from Earth to Jupiter. [Grade: 9-12 | Topics: algebra; trigonometry; distance formula] (PDF)

Kepler Exoplanet Transit Explorer

Problem 465: Comparing Planets Orbiting other Stars
Students use simple fraction arithmetic to determine the relative sizes of several new planets recently discovered by the Kepler mission, and compare these sizes to that of Jupiter and Earth. [Grade: 3-5 | Topics: scale models; proportions; fractions] (PDF)

Problem 458: Playing Baseball on the Earth-like Planet Kepler-22b!
The recently-confirmed Earth-like planet Kepler-22b by the Kepler Observatory is a massive planet orbiting its star in the temperature zone suitable for liquid water. This problem explores the gravity and mass of this planet, and some implications for playing baseball on its surface! [Grade: 8-10 | Topics: scale models; proportions; scientific notation; metric math; Evaluating equations] (PDF)

Problem 444: Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine - II
Students determine how often the two stars Kepler 16 A and B will line up with Tatooine on the same day of the year. [Grade: 6-8 | Topics: comparing two sequences of numbers; patterns, Least Common Multiple] (PDF)

Problem 443: Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine - I
Students explore the orbit speeds of Tatooine and Kepler-16B and predict how often the two stars line up with the planet to create an 'eclipse'. [Grade: 6-9 | Topics: angle measure; angular speed] (PDF)

Problem 441: Exploring the new planet Kepler 16b called 'Tatooine'
Using the tangent function, students estimate the angular diameter and separation of the two stars in the Kepler 16 binary system as viewed from the planet's surface...if it had one!! [Grade: 8-10 | Topics: angle measure; tangent] (PDF)

Problem 416: Kepler probes the interior of red giant stars Students use the properties of circular arcs to explore sound waves inside stars. [Grade: 8-10 | Topics: geometry of circles and arcs; distance=speed x time] (PDF)

Problem 403: The Goldilocks Planets - Not too hot or cold Students use a table of the planets discovered by the Kepler satellite, and estimate the number of planets in our Milky Way galaxy that are about the same size as Earth and located in their Habitable Zones. They estimate the average temperature of the planets, and study their tabulated properties using histograms. [Grade: 6-8 | Topics: Averaging; histogramming] (PDF)

Problem 402: Kepler- Earth-like planets by the score! II Students use recent Kepler satellite data summarized in tabular form to estimate the number of planets in the Milky Way galaxy that are about the same size as our Earth, and located in their Habitable Zones were liquid water may exist. [Grade: 6-8 | Topics: Percentage; re-scaling sample sizes] (PDF)

Problem 401: Kepler - Earth-like planets by the score! I Students use recent Kepler satellite data to estimate the number of Earth-like planets in the Milky Way galaxy. [Grade: 6-8 | Topics: Percentage; histograms; Re-scaling sample sizes] (PDF)

Problem 400: The Most Distant Objects in the Universe Students use a tabels of the most distant known events and objects in the universe to create a timeline of the universe soon after the Big Bang. [Grade: 6-8 | Topics: Working with millions and billions; elapsed time] (PDF)

Problem 396: Kepler 10b - A matter of gravity Students use the measured properties of the Earth-like planet Kepler 10b to estimate the weight of a human on its surface. [Grade: 8-10 | Topics: Evaluating formulas; mass = density x volume; volume of a sphere; scientific notation] (PDF)

Problem 360: Kepler's First Look at 700 Transiting Planets
A statistical study of the 700 transits seen during the first 43 days of the mission. [Grade: 6-8 | Topics: Percentages; area of circle] (PDF)

Problem 325: Kepler Spies Five New Planets Students count squares on a Bizarro Star to study the transit of a planet, and determine the diameter of the planet. This demonstrates the basic principle used by NASA's Kepler satellite to search for Earth-sized planets orbiting distant stars. [Grade: 4-6 | Topics: Counting; graphing; area of a square]

Problem 225: Areas Under Curves; An astronomical perspective Students work with a bar graph of the number of planet discoveries since 1995 to evaluate the total discoveries, as areas under the graph, for various combinations of time periods. [Grade: 6-8 | Topics: Adding areas in bar graphs.]

Problem 213: Kepler: The hunt for Earth-like planets Students compare the area of a star with the area of a planet to determine how the star's light is dimmed when the planet passes across the star as viewed from Earth. This is the basis for the 'transit' method used by NASA's Kepler satellite to detect new planets. [Grade: 6-8 | Topics: Area of circle; ratios; percents.]

Landsat

Problem 512: New NASA Satellite Takes Pictures of Salton Sea
Students work with image of agricultural area to estimate the percentage of area cultivated and the total rainfall in gallons per year. [Grade: 6-8 | Topics: area of square and rectangle; metric units; unit conversion] (PDF)

Problem 484: Exploring Water Use in Kansas
Students use Landsat imagery from 1972 and 2011 to determine how much additional water is being used for irrigation in a small region of Kansas. [Grade: 6-8 | Topics: Area of a circle; unit conversions ] (PDF)

Lunar Orbiter

Problem 129: How Big is It? - The Moon up close. Students work with an image taken by the Lunar Orbiter III spacecraft to determine image scale, and search for the smallest things seen in a photograph. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 127: How Big is It? - The Moon up close. Students work with an image taken by the Lunar Orbiter IV spacecraft to determine image scale, and search for the smallest things seen in a photograph. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Lunar Reconnissance Orbiter (LRO)

Problem 445: LRO - The relative ages of lunar surfaces
Students examine two Apollo landing areas using images from the LRO spacecraft to estimate the relative ages of the two regions using crater counting. [Grade: 6-8 | Topics: scale; histogramming] (PDF)

Problem 440: LRO explores the Apollo 12 landing area on the moon
Students use a recent image obtained by the LRO spacecraft to estimate how far astronauts walked to get to various points in the landing area. They also estimate how many craters are in this area and the average impact time between crater events. [Grade: 6-8 | Topics: image scale; metric measurement] (PDF)

Problem 378: LRO Makes a Temperature Map of the Lunar South Pole
Students use the published LRO temperature map to study the scale of the south polar region, the sizes of its craters, and estimate the volume of water-ice that may be present in the Shackleton Crater. [Grade: 7-9 | Topics: Volume of a circular disk; scale models] (PDF)

Problem 372: LRO Determines Lunar Cratering History
Students count large craters on an LRO coded image of the lunar surface to estimate whether the impacting asteroids that produced the largest craters were from the same population of asteroids during the two different epocs of impacts. [Grade: 8-10 | Topics: Scaled images; histograming; inference] (PDF)

Problem 321: Lunar Crater Frequency Distributions Students use an image from the LRO satellite of the Apollo-11 landing area, along with a power-law model of cratering, to determine what fraction of the landin garea was safe to land upon. [Grade: 11-12 | Topics: Integral calculus]

Problem 290: The Apollo-11 Landing Area at High Resolution Students use recent images made by the LRO satellite to estimate distances, crater sizes, and how many tons of TNT were needed to create some of the craters by meteor impact. [Grade: 9-12 | Topics: metric measurement; scaling; A = B/C]

Problem 287: LCROSS Sees Water on the Moon Students use information about the plume created by the LCROSS impactor to estimate the (lower-limit) concentration of water in the lunar regolith in a shadowed crater. [Grade: 9-12 | Topics: Geometry; volumes; mass=density x volume]

Problem 262: LRO Explores Lunar Surface Cratering Students count the number of craters in various size ranges from a high-resolution image of the lunar surface. [Grade: 6-8 | Topics: scale, proportion, ratio, area, density]

Problem 261: LRO - Searching for Lunar Boulders Students use a recent image of the Apollo-11 landing area to search for large lunar boulders. [Grade: 6-8 | Topics: scale, ratio, proportion]

Problem 259: Mare Nubium And Las Vegas Students compare two satellite images taken at the same resolution to appreciate how large lunar features ae compared to more familiar objects. [Grade: 8-10 | Topics: scale, proportion, ratio]

Problem 258: LRO's First Image of Mare Nubium Students examine the first image of this lunar region using the high-resolution camera image provided by the Lunar Reconnaissance Orbiter. [Grade: 6-8 | Topics: scale, ratio, proportion]

Problem 257: LRO and the Apollo-11 Landing Site Students examine a map of the Apollo-11 landing area and determine how well various features will be visible to the Lunar Reconnaissance Orbiter high-resolution camera. [Grade: 6-8 | Topics: scale, proportion, ratios]

Problem 236: LRO Sees Apollo-11 on the Moon! Students use the latest image from the Lunar Reconnaissance Orbiter of the Apollo-11 landing site to explore lunar features at 1-meter resolution, and determine the solar elevation angle. [Grade: 6-8 | Topics: scale; ratios; angle measure; right triangles]

Manned Space Programs - Apollo, ISS, Shuttle, Ares, SpaceX

Problem 507: Exploring the Launch of the Falcon 9
Students use data from the launch of the Falcon 9 booster to determine its speed and acceleration. [Grade: 6-8 | Topics: speed=distance/time; Time calculations] (PDF)

Problem 476: SpaceX launches the First Commercial Rocket to the ISS
Students detemine the volume of the Dragon capsule using the volume formula for a cone. [Grade: 9-12 | Topics: Volumes of 3-d objects; cones; evaluating functions] (PDF)

Problem 459: A piece of history - space shuttle thermal tiles
Students explore volume density and mass using the Space Shuttle thermal tiles. Get your own free tile from NASA too! [Grade: 6-8 | Topics: mass = density x volume; metric conversion] (PDF)

Problem 438: The Last Flight of the Space Shuttle Endeavor
Students use tabular data and graphing to determine the launch speed and acceleration of the Space Shuttle from the launch pad. [Grade: 6-8 | Topics: tabular data, graphing, metric measurement, speed=distance/time] (PDF)

Problem 437: Saturn V Rocket Launch Speed and Height
Students tabular data to determine the launch speed of the Saturn V rocket from the launch pad. [Grade: 6-8 | Topics: tabular data, graphing, metric measurement, speed=distance/time] (PDF)

Problem 436: Space Shuttle Challenger Deploys the INSAT-1B Satellite
Students use a sequence of images to determine the launch speed of the satellite from the Space Shuttle cargo bay. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 435: Apollo-17 Launch from Lunar Surface
Students use a sequence of images to determine the speed of ascent of the Apollo-17 capsule from the lunar surface. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 433: Space Shuttle Atlantis - Plume Speed
Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 432: Space Shuttle Atlantis - Exhaust Speed
Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 431: Space Shuttle Atlantis - Launch Speed
Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 430: Space Shuttle Atlantis - Ascent to Orbit
Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 419: The Space Shuttle: Fly me to the moon? Students discuss the popular misconception that the Space Shuttle can travel to the moon by examining the required orbit speed change and the capacity of the Shuttle engines to provide the necessary speed changes. [Grade: 6-8 | Topics: amount = rate x time ] (PDF)

Problem 394: Apollo: Probing the lunar core using seismology Students learn about the geometry needed to determine the diameter of the lunar core using a simplified model. [Grade: 9-10 | Topics: Geometry; Properties of Inscribed Arcs] (PDF)

Problem 346: The International Space Station and a Sunspot: Exploring angular scales
An amateur photograph of the International Space Station crossing in front of the sun is analyzed to determine the scales of sunspots. [Grade: 9-12 | Topics: Similar triangles; angular measure] (PDF)

Problem 282: Exploring the Ares 1-X Launch: The Hard Climb to Orbit Students learn about the energy required to send a payload into orbit by studying the Ares 1-X rocket launch. [Grade: 8-10 | Topics: Algebra II]

Problem 281: Exploring the Ares 1-X Launch: Energy Changes Students learn about kinetic and potential energy while studying the Ares 1-X rocket launch. [Grade: 8-10 | Topics: Algebra II]

Problem 280: Exploring the Ares 1-X Launch: Parametrics Students learn about parametric equations to determine the path of the Ares 1-X rocket. [Grade: 8-10 | Topics: Algebra II; Parametric Equations]

Problem 279: Exploring the Ares 1-X Launch: Downrange Distance Students learn about the path of the Ares 1-X test launch and calculate its downrange landing distance in the Atlantic Ocean. [Grade: 8-10 | Topics: Algebra; Significant Figures; Metric to English Conversion]

Problem 276: Solid Rocket Boosters and Thrust Students learn how solid rocket boosters work, and calculate the SRB Thrust Curve using a simple geometric model and 'counting squares'.. [Grade: 8-10 | Topics: Geometry, Cylindrical volumes and surface areas, Graphing data]

Problem 266: The Ares-V Cargo Rocket Students work with the equations for thrust and fuel loss to determine the acceleration curve of the Ares-v during launch. [Grade: 11-12 | Topics: Algebra II, properties of functions, differential calculus, Excel Spreadsheet]

Problem 245: Solid Rocket Boosters Students learn how SRBs actually create thrust, and study the Ares-V booster to estimate its thrust. [Grade: 8-10 | Topics: volume, area, unit conversions]

Problem 243: ISS - Orbit Altitude Changes Students read an essay describing the increases and decreases in the International Space Station orbit, and calculate the final orbit altitude after all the changes are applied. [Grade: 8-10 | Topics: combining positive and negative mixed numbers; fractions]

Problem 196: Angular Size and velocity Students study a spectacular photo of the ISS passing across the face of the sun, and work out the angular sizes and speeds of the transit to figure out how long the event took in order to photograph it. [Grade: 8-10| Topics: Geometry; Angle measurement]

Problem 185: The International Space Station: Follow that graph! Students use a plot of the orbit altitude of the ISS to pblackict its re-entry year after the peak of the next solar activity cycle. [Grade: 6-8| Topics: extrapolating a simple graph; estimation; forecasting]

Problem 125: How Big is It? - Washington DC up close. Students work with an image taken by ISS astronauts to determine image scale, and search for the smallest things seen in a photograph. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 95: A Study on Astronaut Radiation Dosages in Space Students will examine a graph of the astronaut radiation dosages for Space Shuttle flights, and estimate the total dosages for astronauts working on the International Space Station. [Grade level: 9-11 | Topics:Graph analysis, interpolation, unit conversion]

Problem 36: The Space Station Orbit Decay and Space Weather Students will learn about the continued decay of the orbit of the International Space Station by studying a graph of the Station's altitude versus time. They will calculate the orbit decay rates, and investigate why this might be happening. [Grade: 5 - 8 | Topics: Interpreting graphical data; decimal math]

Magnetosphere Multi-Scale Mission (MMS)

Problem 113: NASA Juggles Four Satellites at Once! Students will learn about NASA's Magnetospheric Multi-Scale (MMS) satellite mission, and how it will use four satellites flying in formation to investigate the mysterious process called Magnetic Reconnection that causes changes in Earth's magnetic field. These changes lead to the production of the Northern and Southern Lights and other phenomena. From the volume formula for a tetrahedron, they will calculate the volume of several satellite configurations and estimate the magnetic energy and travel times for the particles being studied by MMS. [Grade: 8-10 | Topics: Formulas with two variables; scientific notation]

Mars Science Lab and Curiosity Rover

Problem 500: Curiosity Uses X-Ray DIffraction to Identify Minerals on Mars
Students learn about diffraction geometry and then estimate the distance between crystal planes in a mars rock sample. [Grade: 10-12 | Topics: geometry; trigonometry] (PDF)

Problem 491: The Curiosity Rover on the Move.
Students plot the position of the Curiosity Rover on a cartesian grid covering the satellite image of the landing area. They use the 2-point distance formula to determine how far the rover traveled between stops, and determine it speed. [Grade: 6-8 | Topics: Cartseian graphs; ordered pairs and coordinates; distance = speed x time; metric measure ] (PDF)

Problem 485: Curiosity Discovers Ancient Mars River
Students estimate the speed of an ancient mars river using images from the CUriosity rover. [Grade: 9-12 | Topics: Algebra; trigonometry; evaluating functions ] (PDF)

Problem 479: Exploring Gale Crater with the Curiosity Rover
Students explore the Gale Crater landing area and calculate rover distances to various way stations to determine the round trip distance and travel time. [Grade: 9-12 | Topics: Pythagorean Distance Formula; Coordinate geometry ] (PDF)

Problem 457: The Interplanetary Voyage of MSL
Students use the properties of ellipses to determine the formula for the Hohmann Transfer Orbit taking the Mars Science Laboratory to Mars in 2012 [Grade: 10-11 | Topics: time=distance/speed; scale models; metric math; properties of ellipses] (PDF)

Problem 456: The Launch of the Mars Science Laboratory (MSL) in 2011
Students use a sequence of launch images to determine the Atlas V's launch speed and acceleration. By determining the scale of each image, they estimate average speeds during the first 4 seconds after lift-off. [Grade: 8-10 | Topics: time=distance/speed; scale models; metric math] (PDF)

Mars Rovers, Orbiters, etc.

Problem 393: Taking a stroll around a martian crater! Students use a recent photograph of a crater on Mars to estimate its circumference and the time it will take NASAs Opportunity Rover to travel once around its edge. [Grade: 6-8 | Topics: scale model; distance = speedxtime; metric measure] (PDF)

Problem 237: The Martian Dust Devils Students determine the speed and acceleration of a martian dust devil from time laps images and information about the scale of the image. [Grade: 6-8 | Topics: scales; Determining speed from sequential images; V = D/T

Problem 139: How Big Is It? - Mars Students use an image of a crater wall on mars to investigate ancient water gullies discovered in 2008 by the Mars Orbiter. [Grade: 4 - 7 | Topics:image scales; metric measurement; division and multiplication; decimals]

Problem 133: How Big is It? - The Mars Rover. Students work with an image taken by the Mars Orbiter satellite of the Spirit landing site. They determine the image scale, and calculate the sizes of various surface features from the image. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 126: How Big is It? - A Martian Avalanche! Students work with a Mars reconnissance Orbiter image to determine image scale, and search for the smallest things seen in a photograph.This avalanche was caught as it occurred on February 19, 2008! [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 74: A Hot Time on Mars The NASA Mars Radiation Environment (MARIE) experiment has created a map of the surface of mars, and measu black the ground-level radiation background that astronauts would be exposed to. This math problem lets students examine the total radiation dosage that these explorers would receive on a series of 1000 km journeys across the martian surface. The students will compare this dosage to typical background conditions on earth and in the International Space Station to get a sense of perspective [Grade level: 6-8 | Topics: decimals, unit conversion, graphing and analysis ]

Problem 70: Calculating Total Radiation Dosages at Mars This problem uses data from the Mars Radiation Environment Experiment (MARIE) which is orbiting Mars, and measures the daily radiation dosage that an astronaut would experience in orbit around Mars. Students will use actual plotted data to calculate the total dosage by adding up the areas under the data curve. This requires knowledge of the area of a rectangle, and an appreciation of the fact that the product of a rate (rems per day) times the time duration (days) gives a total dose (Rems), much like the product of speed times time gives distance. Both represent the areas under their appropriate curves. Students will calculate the dosages for cosmic radiation and solar proton flares, and decide which component produces the most severe radiation problem. [Grade level: 6-8 | Topics: decimals, area of rectangle, graph analysis]

Mercury Surface, Space Environment, Geochemistry, and Ranging (MESSENGER)

Problem 474: MESSENGER Explores the Interior of Mercury
Students work with a simple spherical core and shell model to determine the interior structure of mercury and the size of its dense iron core. [Grade: 9-12 | Topics: working with volumes of speheres; mass = density x volume] (PDF)

Problem 473: MESSENGER Explores the Mass of Mercury
Students use the orbit of NASA's MESSENGER spacecraft to determine the mass of Mercury. [Grade: 9-12 | Topics: working with equations with integer powers and solving for specified values; scientific notation] (PDF)

Problem 415: Mercury and the Moon - Similar but different Students explore the mass and volume of mercury compared to the moon by using the formula for a sphere and scale changes. [Grade: 8-10 | Topics: scale; volume of a sphere; mass = density x volume] (PDF)

Problem 121: Ice on Mercury? Since the 1990's, radio astronomers have mapped Mercury. An outstanding curiosity is that in the polar regions, some craters appear to have 'anomalous reflectivity' in the shadowed areas of these craters. One interpretation is that this is caused by sub-surface ice. The MESSENGER spacecraft hopes to explore this issue in the next few years. In this activity, students will measure the surface areas of these potential ice deposits an calculate the volume of water that they imply. [Grade: 8-10 | Topics:Area of a circle; volume, density, unit conversion]

Near Earth Asteroid Rendezvous (NEAR)

Problem 143: So..How big is it? - Asteroid Eros surface Students calculate the scale of an image of the surface of the asteroid Eros from the NEAR mission, and determine how big rocks and boulders are on its surface. [Grade: 4 - 7 | Topics: Scaling; multiplication, division; metric measure]

Radiation Belt Storm Probe (RBSP)

Problem 506: A New Belt for the Van Allen Belts
Students use a model of the orbit of the van Allen Belts Probes and simulated data to draw the locations of the three van Allen Belts in space. [Grade: 3-5 | Topics: Interpreting Tabular Data] (PDF)

Problem 489: RBSP and the location of Dawn Chorus - III
The location of the Chorus signal from each of the RBSP spacecraft is given by a linear equation that represents the direction along which the signal is detected by each spacecraft. Students solve the two linear equations for the common intersection point representing the location of the Chorus signal in space. This can be done graphically by plotting each linear equation, or solved algebraically. [Grade: 6-8 | Topics: Linear equations; solving systems of equations; graphical solutions ] (PDF)

Problem 488: RBSP and the Location of Dawn Chorus - II
Students use hypothetical information from the twin RBSP spacecraft to triangulate the location of the Chorus signal near Earth using angle measurements, graphing and protractors to identify the intersection point of the CHorus signals. [Grade: 6-8 | Topics: Angles; graphing; protractors ] (PDF)

Problem 486: RBSP Hears Dawn Chorus - I
Students explore the method of triangulation and how it might be used by the RBSP spacecraft to find the origin of the Chorus signals. [Grade: 6-8 | Topics: Graphing on the Cartesian plane; distances between points. ] (PDF)

Problem 485: - Estimating the total mass of the van Allen Belts Students work with the density and volume of the van Allen Belts to estimate their mass [Grade: 9-12| Topics: mass = density x volume; scientific notation]

Problem 484: - Exploring the donuit-shaped van Allen belts Students determine the volume of the van Allen belts by using the volume formula for a torus. They compare this volume to that of a spherical earth. [Grade: 9-12| Topics: Volume of a sphere and torus; scientific notation]

Problem 483: - How to use the RBSP spacecraft to measure the mass of Earth! Students work with Keplers Third Law to determine the mass of earth by using the orbital data for the RBSP spacecraft. [Grade: 9-12| Topics: Algebra 1; Re-writing equations;scientific notation ]

Problem 482: - Radiation Belt Storm Probes - Telemetry math Students work with units of megabytes and gigabytes to determine how much data will be produced by the RBSP spacecraft. [Grade: 6-8| Topics: giga and mega units; decimal math]

Problem 481: - The RBSP Satellite: Working with octagons Students determine the surface area of the octagonal spacecraft body. [Grade: 6-8| Topics: algebra 1; arease of rectangles and triangles; metric math]

Problem 480: - Working with areas of rectangles and circles Students determine the area of a panel from a spacecraft by subtracting the areas of various holes from the original panel area, and determine the remaining mass of the panel. [Grade: 6-8| Topics: areas of rectangles and circles; mass = density x volume]

Problem 479: - Electricity from sunlight: The RBSP solar panels Students work with a scaled drawing of the RBSP spacecraft to determine the area of its solar panels and how many watts of electricity they can produce. [Grade: 6-8| Topics: area of rectangles; metric math; decimals]

Problem 204: The Mass of the Van Allen Radiation Belts- Students graph some magnetic field lines in polar coordinates, then estimate the volume and mass of the Belts using the formula for a torus. [Grade: 9-12| Topics: Algebra II.]

Problem 93 An Introduction to Radiation Shielding - Students calculate how much shielding a new satellite needs to replace the ISO research satellite. Students use a graph of the wall thickness versus dosage, and determine how thick the walls of a hollow cubical satellite have to be to blackuce the radiation exposure of its electronics. Students calculate the mass of the satellite and the cost savings by using different shielding. [Grade level: 9-11 | Topics: Algebra; Volume of a hollow cube; unit conversion]

Problem 71 Are the Van Allen Belts Really Deadly? - This problem explores the radiation dosages that astronauts would receive as they travel through the van Allen Belts enroute to the Moon. Students will use data to calculate the duration of the trip through the belts, and the total received dosage, and compare this to a lethal dosage to confront a misconception that Apollo astronauts would have instantly died on their trip to the Moon. [Grade level: 8-10 | Topics: decimals, area of rectangle, graph analysis]

Ramaty High Energy Solar Spectroscopic Imager (RHESSI)

Problem 101: Super-Fast Solar Flares!! Students will analyze consecutive images taken of an erupting solar flare, and use the information provided to calculate the speed of the flare. [Grade level: 6-9 | Topics:image scales; time calculations; speed calculations]

Solar and Heliospheric Observatory (SOHO)

Problem 299: Changing Perspectives on the Sun's Diameter Students compare two images of the sun taken by the SOHO satellite to measure the apparent diameter change from different earth obit locations in the winter and summer. [Grade: 6-8 | Topics: measurement; parallax; metric units; percentage change]

Problem 244: Solar Storms - Fractions and Percentages Students create a Venn Diagram to summarize data on a series of solar storms, and determine how often solar flares occur when a solar plasma eruption happens. [Grade: 4-7 | Topics: precentages; Venn Diagramming]

Problem 176: Solar Storms: Sequences and Probabilities I Students continue their study of a stormy week on the sun by working out the probabilities for joint events. [Grade: 4-7| Topics: probability; numerating possible outcomes]

Problem 175: Solar Storms: Sequences and Probabilities II Students work out the probabilities for various combinations of solar storms during a given week. [Grade: 4-7| Topics: probability; numerating possible outcomes]

Problem 117: CME Kinetic Energy and Mass Coronal Mass Ejections (CMEs) are giant clouds of plasma released by the sun at millions of kilometers per hour. In this activity, students calculate the kinetic energy and mass of several CMEs to determine typical mass ranges and speeds. Students will use the formula for kinetic energy to fill-in the missing entries in a table. They will then use the completed table to answer some basic questions about CMEs. [Grade: 8-10 | Topics:time calculation; Evaluating a simple equation; solving for variables]

Problem 94 : Solar Storms: Odds, Fractions and Percentages Students will use actual data on solar storms to learn about the different kinds of storms and how common they are. This is a basic science activity that professionals do in order to look for relationships between different kinds of events that might lead to clues about what causes them. Can your students come up with something new that noone has thought about before? The Venn Diagramming activity is a key element of the activity and is reasonably challenging! [Grade level: 6-8 | Topics: Averaging; fractions; percentages; odds; Arithmetic Operations; Venn Diagrams]

Problem 80 : Data Corruption by High Energy Particles Students will see how solar flares can corrupt satellite data, and create a timeline for a spectacular episode of data loss recorded by the SOHO satellite using images obtained by the satellite. Students will also calculate the speed of the event as particles are ejected from the sun and streak towards earth. [Grade level: 6-8 | Topics: Time and speed calculations; interpreting scientific data ]

Problem 43: An Interplanetary Shock Wave On November 8, 2000 the sun released a coronal mass ejection that traveled to Earth, and its effects were detected on Jupiter and Saturn several weeks later. In this problem, students will use data from this storm to track its speed and acceleration as it traveled across the solar system. [Grade level: 6-10 | Topics: Time calculations; distance = speed x time ]

Problem 7: Solar Flares, CME's and Aurora Some articles about the Northern Lights imply that solar flares cause them. Students will use data to construct a simple Venn Diagram, and answer an important question about whether solar flares cause CME's and Aurora. [Grade: 5 - 7 | Topics: Venn Diagramming]

Problem 5: The November 8, 2004 solar storm Students calculate the speed of a CME, and describe their aurora observations through writing and drawing. [Grade: 6 - 8 | Topics: Time calculations; distance = speed x time]

Solar Dynamics Observatory (SDO)

Problem 505: SDO Sees Coronal Rain - Estimating Plasma Speeds
Students estimate the speed of plasma streamers near the solar surface using images from a Solar Dynamics Observatory. [Grade: 6-8 | Topics: scale models; speed=distance/time; proportions] (PDF)

Problem 467: Estimating Magnetic Field Speeds on the Sun
Students use two images from the Solar Dynamics Observatory to estimate the speed of the X-class solar flare on March 6, 2012. [Grade: 6-8 | Topics: speed=distance/time; scale model; metric measurement] (PDF)

Problem 337: SDO Reveals Details on the Surface of the Sun Students use a spectacular colored image of the Sun to calculate the scale of the image in kilometers per millimeter, and then search for the smallest features relative to the size of Earth. [Grade: 6-8 | Topics: image scales; proportions]

Problem 336: SDO: Measuring the Speed of an Eruptive Prominence Students use recent First Light images of the Sun from SDO to calculate the speed of a prominence using a sequence of scaled images and computing position shift over the time interval of the images. [Grade: 6-8 | Topics: image scales; speed=distane/time ]

Problem 334: Solar Dynamics Observatory: Working with Giga, Tera, Peta and Exabytes The recent launch of SDO will bring 'high definition TV' to the study of the sun's surface details. This also means a HUGE amount of data will have to be processed every day to handle the torrent of information. This activity works with the prefixes giga, tera, peta and exa to familiarize students with how to interpret these quantities in a practical setting. Students already know about 'gigabytes', but the SDO data stream represents terabytes per day, and petabytes per year in data storage demands. [Grade: 8-12 | Topics: powers of ten; time conversion: seconds, minutes, days, years]

Problem 235: Scientific Data: The gift that keeps on giving! Students learn about gigabytes and terrabytes of data and the rates of data generation by NASA missions and how to store it. [Grade: 6-8 | Topics: metric units; rates; money]

Solar Probe Plus

Problem 373: Solar Probe Plus - Having a hot time near the sun!
Students use a simple equation to estimate the temperature reached by the Solar Probe Plus spacecraft as it gets close to the sun. [Grade: 8-10 | Topics: Evaluating a function; square roots and forth roots] (PDF)

Spitzer Space Telescope

Problem 278: Spitzer Studies the Distant Planet Osiris Students learn about the density of the planet HD209458b, also called Osiris, and compare it to that of Jupiter. [Grade: 8-10 | Topics: Spherical volumes; density; Scientific Notation;]

Problem 272: Spitzer Telescope Discovers New Ring of Saturn! Students calculate the volume of the ring and compare it to the volume of Earth to check a news release figure that claims 1 billion Earths could fit inside the new ring. [Grade: 8-9 | Topics: Geometry, Algebra, volumn, scientific notation]

Problem 148 Exploring a Dying Star Students use data from the Spitzer satellite to calculate the mass of a planetary nebula from a dying star. [Grade: 9 - 11 | Topics:Scientific Notation; unit conversions; volume of a sphere ]

Problem 141: Exploring a Dusty Young Star Students use Spitzer satellite data to learn about how dust emits infrared light and calculate the mass of dust grains from a young star in the nebula NGC-7129. [Grade: 4 - 7 | Topics: Algebra I; multiplication, division; scientific notation]

Problem 56: The Sombrero Galaxy Close-up The Sombrero Galaxy in Virgo is a dazzling galaxy through the telescope, and has been observed in detail by both the Hubble Space Telescope and the Spitzer Infrared Observatory. This exercise lets students explore the dimensions of this galaxy as well as its finest details, using simple image scaling calculations. [Grade level: 9-11 | Topics: Finding the scale of an image; measurement; decimal math]

Solar Terrestrial Relations Observatory (STEREO)

Problem 455: The Night Launch of STEREO in 2006
An example of old news seen in a different way! Students use a spectacular time-lapse photo of the launch of the STEREO mission obtained by photographer Dominic Agostini in 2006 to study parabolic curves. [Grade: 8-10 | Topics: time=distance/speed; scale models; metric math; equation of a parabola; curve fitting] (PDF)

Problem 404: STEREO Spacecraft give 360-degree Solar View Students use STEREO satellite images to determine which features can be seen from Earth and which cannot. They learn about the locations and changing positions of the satellites with respect to Earth's orbit. [Grade: 6-8 | Topics: angular measure, extrapolation; distance = speed x time] (PDF)

Problem 298: Seeing Solar Storms in STEREO - II Students explore the geometry of stereo viewing by studying a solar storm viewed from two satellites. [Grade: 10-12 | Topics: Geometry; Trigonometry]

Problem 286: STEREO Watches the Sun Kick Up a Storm Students use images from the STEREO observation of a 'solar tsunami' to estimate its speed and kinetic energy. [Grade: 9-12 | Topics: metric measurement; scaling; Scientific Notation; unit conversion; evaluating a simple 2-variable formula for kinetic energy ]

Problem 248: Seeing Solar Storms in STEREO - I Students work out the details of stereoscopic vision using elementary properties of triangles and the Law of Cosines to determine the distance from earth of a solar storm cloud. [Grade: 8-10 | Topics: geometry, Law of Cosines, V = D/T]

Problem 207: The STEREO Mission: getting the message across Students learn about how the transmission of data is affected by how far away a satellite is for the two satellites in the STEREO constellation. [Grade: 6-8| Topics: multiplication; division; decimal numbers.]

Problem 206: Can You Hear me now? Students learn about how the transmission of data is affected by how far away a satellite is, for a variety of spacecraft in the solar system [Grade: 6-8| Topics: multiplication; division; decimal numbers.]

Problem 118: An Application of the Parallax Effect The STEREO mission views the sun from two different locations in space. By combining this data, the parallax effect can be used to determine how far above the solar surface various active regions are located. Students use the Pythagorean Theorem, a bit of geometry, and some actual STEREO data to estimate the height of Active Region AR-978. [Grade: 8-10 | Topics:Pythagorean Theorem; square-root; solving for variables]

Problem 116: The Comet Encke Tail Disruption Event On April 20, 2007 NASA's STEREO satellite captured a rare impact between a comet and the fast-moving gas in a solar coronal mass ejection. In this problem, students analyze a STEREO satellite image to determine the speed of the tail disruption event. [Grade: 8-10 | Topics:time calculation; finding image scale; calculating speed from distance and time]

Problem 92: A Lunar Transit of the Sun from Space One of the STEREO satellites observed the disk of the moon pass across the sun. Students will use simple geometry to determine how far the satellite was from the moon and Earth at the time the photograph was taken. [Grade level: 9-11 | Topics: Geometry; parallax; arithmetic]

Terra, Landsat, UARS, Earth Observatory

Problem 442: Modeling the Atmospheric Re-entry of UARS
Students graph the altitude of the UARS satellite in the weeks before re-enrty to explore the accelerating effects of atmospheric drag. They create a mathematical model that fits the data, and use this to make their own prediction of the re-entry date. [Grade: 8 - 11 | Topics: graphing data; linear equations; exponential and power functions] (PDF)

Problem 406: Growing Grapes in the Middle of the Desert Students use a dramatic Earth Observatory-1 satellite image of agriculture in Namibia to estimate the total cultivated area and water needs of grape growing under desert conditions [Grade: 6-8 | Topics: areas of irregular regions; unit conversion] (PDF)

Problem 375: Terra Satellite Measures Dangerous Dust
Students determine the number of dust particles inhaled by using a satellite map of the dust concentration and a calculation of the mass of a typical dust grain. [Grade: 8-10 | Topics: unit conversion; scientific notation; mass=densityxvolume] (PDF)

Problem 339: Terra Satellite Spies the Great Gulf Oil Catastrophe of 2010 Students use a Terra satellite image of the oil slick in the Gulf of Mexico to calculate its area, mass and thickness. [Grade: 6-8 | Topics: image scales; area of a circle; metric conversions ]

Time History of Events and Macroscale Interactions during Substorms (THEMIS)

Problem 201: Fly Me To the Moon! Students learn some basic principles and terminology about how spacecraft change their orbits to get to the moon. [Grade: 6-8| Topics: speed = distance/time; Pythagorean Theorem]

Problem 194: A Magnetic Case for 'What Came First?' Students create a timeline for events based on several data plots from the THEMIS program, and use their timeline to answer questions about the causes of magnetic storms. [Grade: 6-8| Topics: Time calculations]

Problem 108: A Problem in Satellite Synchrony The THEMIS program uses five satellites in five different orbits to study Earth's magnetic field and its changes during a storm. This problem asks students to use the periods of the five satellites to figure out when all 5 satellites will be lined-up as seen from Earth. They will do this by finding the Greatest Common Multiple of the five orbit periods, first for the case of 2 or 3 satellites, which can be easily diagrammed with concentric circles, then the case for all five satellites together. [Grade: 5-9 | Topics:multiplication; Greatest Common Multiple]

Problem 3: Magnetic Storms II Students learn about the Kp index using a bar graph. They use the graph to answer simple questions about maxima and time. [Grade: 6 - 8 | Topics: Interpreting bar graphs; time calculations]

Problem 1: Magnetic Storms I Students learn about magnetic storms using real data in the form of a line graph. They answer simple questions about data range, maximum, and minimum. [Grade: 7 - 9 | Topics: Interpreting a graph; time calculations]

Transition Region and Coronal Explorer (TRACE)

Problem 175: Solar Storms: Sequences and Probabilities II - Students work out the probabilities for various combinations of solar storms during a given week. [Grade: 4-7| Topics: probability; numerating possible outcomes]

Problem 104: Loopy Sunspots! Students will analyze data from the Hinode satellite to determine the volume and mass of a magnetic loop above a sunspot. From the calculated volume, based on the formula for the volume of a cylinder, they will use the density of the plasma determined by the Hinode satellite to determine the mass in tons of the magnetically trapped material. [Grade: 9-11 | Topics:image scales; cylinder volume calculation; scientific notation; unit conversions]

Webb Space Telescope

Problem 422: Supercomputers: Getting the job done FAST! Students use a simple counting problem to explore how much faster a supercomputer is compared to as hand-calculation. [Grade: 6-8 | Topics: algebra] (PDF)

Problem 418: Supercomputers: Modeling colliding neutron stars! Students use a series of time-lapse images calculated using a supercomputer to determine the speed of collision of two neutron stars, and whether they will form a black hole afterwards. [Grade: 8-10 | Topics: distance=speed x time; scale model; triangle and circle geometry; circumference] (PDF)

Problem 407: Cryo-testing the Webb Space Telecope ISIM Students explore scaling by creating an enlarged geometric model of the ISIM to better appreciate the small changes due to expansion and contraction [Grade: 6-8 | Topics: scale models; proportions; unit conversion] (PDF)

Problem 381: The Cosmological Redshift - Changing the light from a galaxy.
Students learn about the redshift unit of measurement in astronomy, and solve a simple linear equation to explore how the light from very distant galaxies is reddened compared to nearby galaxies. [Grade: 8-10 | Topics: solving a simple equation for X] (PDF)

Problem 380: Seeing the Distant Universe Clearly
Students calculate the angular sizes and scales of distant objects to study how different sized telescopes see details with varying degrees of clarity. [Grade: 7-9 | Topics: solving a simple equation for X; angular measure; Scientific Notation] (PDF)

Problem 379: Exploring the Cosmos with Supercomputers
Students use two images created by a supercomputer calculation to explore the size and accuracy of computer models of the distanct universe. [Grade: 7-9 | Topics: scale model; proportions; Scientific Notation] (PDF)

Problem 370: 6-fold Symmetry and the Webb Space Telescope Mirror
Students learn about the Webb Space Telescopes segmented mirror and its rotational 6-fold symmetry due to tiling with hexagons. They identify groups of tiles that have identical optical properties [Grade: 8-10 | Topics: Properties of Hexagons; rotation symmetry; counting; tiling] (PDF)

Problem 369: Scaling Up the Webb Space Telescope Mirror
Students learn about the Webb Space Telescopes segmented mirror and determine the area of the mirror along with scaled up versions of this mirror using the formula for the area of a hexagon, and the properties of tiling a surface with hexagons. [Grade: 8-10 | Topics: Properties of Hexagons and triangles; counting; evaluating a formula; tiling] (PDF)

Problem 368: The Hexagonal Tiles in the Webb Space Telescope Mirror
Students learn about the Webb Space Telescopes segmented mirror by studying the geometry of hexagons. [Grade: 8-10 | Topics: Properties of Hexagons and triangles; counting] (PDF)

Problem 331: Webb Space Telescope: Detecting dwarf planets The 'JWST' will be launched some time in 2014. One of its research goals will be to detect new dwarf planets beyond the orbit of Pluto. In this problem, students use three functions to predict how far from the sun a body such as Pluto could be detected, by calculating its temperature and the amount of infrared light it emits. [Grade: 9-12 | Topics: Evaluating square-roots and base-e exponentials]

Wide-Field Infrared Survey Explorer (WISE)