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Use the topic buttons to sort the problems by general topic area - Use the search window to find problems at specific grade levels, for example, enter 'Grade:3' will show all problems at an estimated grade level of 3 in math skills.

Problem 692: Exploring Interplanetary Dust with Solar Probe-Plus
[Grade:8-10 | Topics: rates; areas; proportions; geometry ]
Category: All,Helio
Students examine the impact frequency of dust grains in the vicinity of the Solar Probe orbit around the sun, and estimate how many impact will occur during the mission.
Problem 691: Investigating the Elliptical Orbit of Solar Probe-Plus
[Grade:10 | Topics: Geometry; conic sections; properties of ellipses]
Category: All,Helio, Stars
Students work with the basic algebraic properties of ellipses to determine the orbit of the spacecraft and its period.
Problem 690: Exploring Proton Storms with Solar Probe-Plus
[Grade:8-10 | Topics: proportions; inverse-square law; probability]
Category: All,Helio,Solar System
Students use solar storm data near Earth to estimate how often the spacecraft will encounter solar storms and estimate how much power will be lost from the solar panels due to radiation damage.
Problem 689: Exploring Solar Heating with Solar Probe-Plus
[Grade:8-10 | Topics: algebra; scientific notation]
Category: All,Helio
Students calculate the temperature of the heat shield and how much heat energy the shield has to dissipate to keep the spacecraft from over-heating.
Problem 688: Exploring Solar Energy with Solar Probe-Plus
[Grade:8-10 | Topics: rectangular area; rates; inverse-square law; unit conversions ]
Category: All,Helio
Students examine how solar panels collect energy and estimate how much electrical power the spacecraft will require for operation.
Problem 687: Exploring Equations with Solar Probe-Plus
[Grade:8-10 | Topics: algebraic fractions; solving lineqar equations ]
Category: All,Helio
Students work with the masses of various spacecraft systems expressed as fractions, and create and solve algebraic equations to determine the masses of these systems.
Problem 686: Exploring Orbital Speeds with Solar Probe-Plus!
[Grade:8-10 | Topics: Algebra; evaluating functions; scientific notation]
Category: All,Helio
Students work with an equation for spacecraft speed along its orbit to determine the speed of the Solar Probe Plus spacecraft as it orbits the sun.
Problem 685: Exploring Fractions with Solar Probe-Plus!
[Grade:3-5 | Topics: adding, subtracting, multiplying simple fractions ]
Category: All,Helio
Students use fractions to calculate the mass of various spacecraft systems
Problem 684: Exploring the Pressure of Sunlight with Solar Probe-Plus
[Grade:8-10 | Topics: Unit conversions, area of rectangle; working with F=ma]
Category: All,Helio
Students calculate the light pressure on the heat shield, and use F=ma to calculate acceleration.
Problem 683: Exploring the Solar Probe-Plus Heat Shield
[Grade:6-8 | Topics: volume of a rectangular solid; mass=density x volume ]
Category: All,Helio
Students examine the mass and density of the heat shield by calculating its volume and uding the density formula.
Problem 682:NASA’s Kepler Mission Detects 715 New Planets
[Grade:6-8 | Topics: percentage; histograms; population sampling; scaling and proportion ]
Category: All,Solar System,Universe
Students work with the statistics of the detected candidate planets to estimate the number of planetary systems in the Milky Way and the number of earth-sized planets.
Problem 681:A Practical Application of Vector Dot and Cross Products
[Grade:10-12 | Topics: vectors; dot and cross product; normal vectors; unit conversions ]
Category: All,Helio
Students work with coordinate vectors describing the corners of the roof of a house, calculate the area of the roof using dot products; calculate the normal vector to the roof using cross products; and the amount of sunlight striking the roof using dot products to determine how much solar power could be generated by solar panels on the roof.
Problem 680:A Pulsar Shot Out from a Supernova Explosion!
[Grade:6-8 | Topics: Scientific notation; speed=distance/time; unit conversions; density ]
Category: All,Stars
Students study the speed of a pulsar ejected from a supernova explosion, and describe what would happen if the dense star collided with a star like the sun.
Problem 679:Shipping Cargo to the International Space Station
[Grade:4-6 | Topics: addition, division, multiplication of 3 and 4-digit numbers. ]
Category: All,Rockets
Students work with kilograms and watts to determine the cargo capacity for re-supply missions to the International Space Station.
Problem 678:VAB-Navigating a Magnetic Field with Vector Dot Products!
[Grade:10-12 | Topics: vectors; dot products; vector projections ]
Category: All,Magnetism
Students work with vectors to determine a spacecrafts orientation relative to Earths magnetic field. They compute the expected strength of the magnetic field parallel and perpendicular to the spacecraft motion vector.
Problem 677:VAB-Navigating in a Magnetic Field Using Linear Equations
[Grade:8-10 | Topics: graphing linear equations; equation of line perpendicular to another line; geometry ]
Category: All,Magnetism
Students model spacecraft motion and the local magnetic field direction using two linear equations, then determine the line perpendicular to the spacecraft motion and the angle of motion relative to the magnetic field.
Problem 676:VAB-Navigating in a Magnetic World!
[Grade:7-10 | Topics: coordinate plotting; geometry; graphing data ]
Category: All,Magnetism
Students explore how some satellites navigate in space using Earth's magnetic field and its orientation to the spacecraft.
Problem 675:VAB-Earth’s Magnetic Field and the Van Allen Probes
[Grade:7-10 | Topics: coordinate plotting; properties of right triangles; Pythagorean theorem]
Category: All,Helio,Magnetism
Students explore Earth's magnetic field as seen by spacecraft in their orbit to determine the local 'compass direction' of the magnetic field.
Problem 674:VAB - Exploring the Orbit of the Van Allen Probes
[Grade:7-10 | Topics: coordinate plotting; unit conversion; rates ]
Category: All,Helio,Solar System
Students explore the speed of the spacecraft in their orbit around Earth using coordinate graphing, time differences, pythagorean theorem and unit conversions.
Problem 673:VAB - An Improved Model for Van Allen Belt Radiation Dose
[Grade:9-11 | Topics: Polynomial equations; trigonometric equations; composite functions f(f(x)); estimating areas under curves]
Category: All,Helio
Students use a detailed model of the path of a satellite and the radiation dose rate along the path to calculate the total radiation dose to the spacecraft.
Problem 672:VAB - Modeling the Radiation Dose of the Van Allen Probes
[Grade:11-12 | Topics: Parametric equations;composite functions f(g(x)); integral calculus ]
Category: All,Helio
Students create a simple mathematical model of the radiation exposure to the VABP satellites as they travel through the Van Allen belts.
Problem 671:VAB - The Van Allen Probes and Radiation Dose
[Grade:8-10 | Topics: Unit conversion; rates]
Category: All,Helio
Students study radiation dose units and estimate the exposures for a human living on the gropund; an astronaut in the ISS, and the Van Allen belt environment.
Problem 670:VAB - Exploring the Third Belt with the Van Allen Probes
[Grade:9-12 | Topics: Intersection points of circles and ellipses; graphical and algebraic solutions]
Category: All,Helio
Students use the elliptical equation for the orbit of NASAs Van Allen Probes spaccecraft, and a circle representing the location of the new Van Allen belt, to find where they intersect along the orbit of the spacecraft.
Problem 669:VAB - Exploring the Third Belt with the Van Allen Probes
[Grade:9-12 | Topics: Intersection points of circles and ellipses; graphical and algebraic solutions]
Category: All,Helio
Students use the elliptical equation for the orbit of NASAs Van Allen Probes spaccecraft, and a circle representing the location of the new Van Allen belt, to find where they intersect along the orbit of the spacecraft.
Problem 669: HST - Exploring Two Nearby Stars to the Sun.
[Grade:9-12 | Topics: Working with quadratic equations; intersection points of quadratic functions]
Category: All,Helio,Stars
Students explore two nearby stars Ross 128 and Gliese 445 and determine when they will be the nearest stars to our sun by working with quaddratic equations that model their distances.
Problem 668: Meteor Impacts – How Much Stuff?
[Grade:12 | Topics: Integral calculus]
Category: All,Solar System
Students integrate a powerlaw function to estimate the number of tons of meteoritic debris that Earth collects every year.
Problem 667: Exploring Power-laws: Meteor impacts
[Grade:9-12 | Topics: logarithmic graphs; power laws; linear equations]
Category: All,Solar System
Students estimate a function for logarithmic data that describes the number of meteor impacts on Earth every year.
Problem 666: SAGE - The Ground Track of the International Space Station
[Grade:6-8 | Topics: Working with proportions; time calculations]
Category: All,Rockets
Students determine how many sunrises and sunset the ISS observes every day.
Problem 665: Kepler - Kepler’s Latest Count on Goldilocks Planets
[Grade:6-8 | Topics: percentages, bar graphs, estimation]
Category: All,Helio,Universe
Students examine the statistics of the latest candidate planets beyond our solar system, work with poercentages and a bar graph, and estimate the number of earth-like planets in our Milky Wy.
Problem 664: HST - The Sun’s Nearest Companions…At least for now!
[Grade:6-8 | Topics: Graphical data; finding minimum from a plotted curve]
Category: All,Helio,Stars
Students study a graph that models the distances from the sun of seven nearby stars over a 100,000 year time span. They determine the minimum distances and a timeline of which star will be the suns new closest neighbor in space in the next 80,000 years.
Problem 663: HST - The Hubble Search for the Farthest Galaxy in the Universe
[Grade:6-8 | Topics: working with simple equations; solving for X]
Category: All,Universe
Students learn about the recent discovery of z8_GND_5296 what may be the farthest known galaxy in our visible universe whose light left the galaxy when the universe was only 700 million years old. They use a simple linear equation to estimate the galaxys look-back time, and learn about the cosmological redshift.
Problem 662: SAGE- Measuring Aerosol Concentration in Parts per Million
[Grade:6-8 | Topics: Unit conversion; integer counting]
Category: All,Rockets
Students learn about parts-per-million units by working with percentage and counting squares in different types of grids.
Problem 661: SAGE- Measuring Stratospheric Ozone with SAGE-III
[Grade:6-8 | Topics: Unit conversion; reading a data graph ]
Category: All,Rockets
Students use a data graph to identify the ozone layer from its concentration of ozone, and use parts-per-million to compare ozone concentration to the atmosphere density.
Problem 660: SAGE- Some Basic Properties of the SAGE-III Instrument
[Grade:6-8 | Topics: Unit conversion; proportions ]
Category: All,Rockets
Students examine the mass, data, pointing accuracy and power of the SAGE-III instrument and use unit conversions to translate the units into pounds, watts and degrees.
Problem 659: VAP- Exploring the Outer Atmosphere – Gas Density
[Grade:6-8 | Topics: scientific notation; scale model; number = density x volume; volume = area x length; length=speed x time. ]
Category: All,Helio,Rockets
Students estimate examine the density of gas in the Van Allen belts and use it to estimate how many atoms the Van Allen Probes will encounter.
Problem 658: VAP- Exploring Gas Density in Space
[Grade:6-8 | Topics: geometry; density=number/volume; scale models and proportions; scientific notation ]
Category: All,Rockets
Students explore how gas density is related to the average distances between molecules in the air using a simple geometric mode of a cube with 64 cells.
Problem 657: VAP- Exploring the Density of Gas in the Atmosphere
[Grade:6-8 | Topics: Scientific notation; density ]
Category: All,Rockets
Students examine different ways to represent the density of Earths atmosphere.
Problem 656: VAP- Measuring Earths Magnetic Field in Space
[Grade:9-12 | Topics: minimum and maximum; graphing data; comparing with models of the form 1/r2 and 1/r3 ]
Category: All,Rockets,Magnetism
Students work with satellite data to explore Earths magnetic field through graphing data and comparing it with inverse-square and inverse-cube laws.
Problem 655: VAP- Estimating the Total Mass of the Van Allen Belts
[Grade:9-12 | Topics:Volume of torus; scientific notation; mass = density x volume ]
Category: All,Helio,Rockets
Students estimate the total mass of the Van Allen belts and compare it to the mass of a donut using the formula for a torus.
Problem 654: VAP- Exploring the Donut-shaped Van Allen Belts
[Grade:9-12 | Topics: Scientific notation; volume of spheres and toriods]
Category: All,Helio,Solar System,Rockets
Students estimate the volume of the Van Allen belts in terms of the volume of Earth using a formula for the volume of a torus.
Problem 653: VAP-How to Use the Van Allen Probes Spacecraft to Measure the Mass of Earth!
[Grade:9-12 | Topics: scientific notation; solving formula with integer exponents ]
Category: All,Helio,Solar System
Students use a formula to estimate the mass of Earth from data about the orbit of the Van Allen Probes spacecraft.
Problem 652: VAP- Telemetry Math
[Grade:6-8 | Topics: megabytes; rates in time]
Category: All,Rockets
Students work with data rates for the spacecraft and determine how much data needs to be stored.
Problem 651: VAP- The Van Allen Probes Satellite: Working with Octagons
[Grade:9-12 | Topics: areas of simple figures; algebraic manipulation]
Category: All,Helio,Rockets
Students work with the area formula for squares, rectangles and triangles to find the surface area of an octagonal satellite.
Problem 650: VAP- Working with Areas of Rectangles and Circles
[Grade:3-5 | Topics: area of a rectangle; area of a circle]
Category: All,Rockets
Students use the formulas for simple rectangle and circle areas to determine the areas of the holes in a satellite panel.
Problem 649: VAP- Electricity from Sunlight: The Van Allen Probes Spacecraft Solar Panels
[Grade:3-5 | Topics: area of a rectangle; decimal math; unit conversion]
Category: All,Helio,Rockets
Students work with the area of rectangles to calculate the electrical power produced by solar panels.
Problem 648: SAGE- Using Opacity to Find Aerosol Density
[Grade:6-8 | Topics: solving a system of linear equations; scientific notation]
Category: All,Rockets
Students examine a mathematical model based on the SAGE-III geometry and see how it leads to solving a system of linear equations to determine aerosol concentrations at different altitudes.
Problem 647: SAGE- Investigating Opacity and Extinction
[Grade:9-12 | Topics: exponential functions; exponent math]
Category: All,Rockets
Students work with the properties of filters to prove that the product of exponentials leads to the sum of their exponents.
Problem 646: SAGE- Air Quality Index and Aerosol Density
[Grade:6-8 | Topics: density; scientific notation; volume of a sphere; density]
Category: All,Rockets
Students see how the Air Quality Index is related to the number of aerosols per cubic meter.
Problem 645: SAGE- Exploring the Mass and Density of Aerosol Particles
[Grade:6-8 | Topics: Unit conversions; scientific notation; volume of a sphere; density]
Category: All,Rockets
Students explore the physical sizes of aerosol particles. With unit conversions they convert concentration units of micrograms/m3 to particles/m3.
Problem 644: SAGE- A Scale Model of Aerosol Sizes
[Grade:6-8 | Topics: unit conversion; metric units nano and micro]
Category: All,Rockets
Students work with proportions and scale to create a scale model of aerosol particles.
Problem 643: SAGE- The Sources and Sinks of Carbonyl Sulfide
[Grade:6-8 | Topics: Scientific notation; rates]
Category: All,Rockets
Students explore a molecule important in forming stratospheric aerosols. They calculate total rates of change from a table of sources and sinks, and estimate the change in the number of molecules per year.
Problem 642: SAGE- Three Mathematical Ways to Describe Light Extinction
[Grade:9-12 | Topics: Base-10 and Base-e functions; exponential equations]
Category: All,Rockets
Students explore the three common ways that scientists record extinction using base-10 and base-e functions.
Problem 641: SAGE- A Study of Aerosol Extinction in the Stratosphere
[Grade:6-8 | Topics: slope of a line; linear equations; forecasting]
Category: All,Rockets
Students work with a table of atmospheric extinction at different altitudes and latitudes to graph selected data and draw a straight line thrlough the graphed data to estimate the slope. They create a linear equation from the graph and use it to predict the extinction at a different altitude.
Problem 640: SAGE- Atmospheric Aerosols by Percentage
[Grade:3-5 | Topics: percentages; interpreting tabular data]
Category: All,Solar System,Rockets
Students examine a table that lists the percentages of different aerosol types according to the location on Earth where they are produced.
Problem 639: SAGE- Aerosol Sources in the Stratosphere
[Grade:6-8 | Topics: Rates; percentage; pie graphs]
Category: All,Rockets
Students examine the sources for aerosols in the atmosphere and determine their percentage contributions based upon their individual rates given in megatons/year.
Problem 638: SAGE- Sunset and Sunrise Geometry
[Grade:9-12 | Topics: Pythagorean Theorem; chord lengths]
Category: All,Rockets
Students explore the tangent geometry used by the SAGE-III instrument, and work with chords to determine their lengths using the Pyhtagorean formula.
Problem 637: SAGE- Light Attenuation Using Exponential Functions
[Grade:9-12 | Topics: exponential functions; natural logarithm, e]
Category: All,Rockets
Students work with the extinction formula for light and see how light dimming is an exponetial process.
Problem 636: SAGE- Aerosols and Light Dimming
[Grade:6-8 | Topics: percentage; multiplication ]
Category: All,Rockets
Students explore how light is dimmed as it passes through a series of filters.
Problem 635: SAGE- Exploring Aerosols
[Grade:6-8 | Topics: density; volume; scale ]
Category: All,Rockets
Students compare aerosol sizes to a human hair, calculate volumes and masses from density.
Problem 634: History of Winter - What is a Snowballs Chance on Mars?
[Grade:9-12 | Topics: Graph analysis]
Category: All,Solar System
Students explore the phase diagrams for water and carbon dioxide and discover whether astronauts would be able to create snowballs on mars made from carbon dioxide ice.
Problem 633: History of Winter - Exploring Temperature and States of Matter
[Grade:9-12 | Topics: Rates of Change; Unit conversions; decimal math ]
Category: All,Miscellaneous
Students learn how to read a simple phase diagram and how states of matter are related to temperature and pressure.
Problem 632: History of Winter - Exploring Energy and Temperature
[Grade:9-12 | Topics: Evaluating equations]
Category: All,Miscellaneous
Students learn about the relationship between temperature and the kinetic energy of particles.
Problem 631: History of Winter - Snow Density, Mass and Roof Failure
[Grade:6-8 | Topics: Density = mass/volume; rates of change; proportions]
Category: All,Miscellaneous
Students
Problem 630: History of Winter - Snow Density and Volume
[Grade:6-8 | Topics: Density=mass/volume; metric units; decimal math]
Category: All,Miscellaneous
Students learn how snow density is measured in the field using cylindrical instruments in a snow pit trench.
Problem 629: History of Winter - Snow to Water Ratios
[Grade:6-8 | Topics: Working with tables; decimal math; proportions]
Category: All,Miscellaneous
Students learn how to convert between snow volume and equivalent volumes of liquid water.
Problem 628: History of Winter - Snowflake Growth Rates and Surface Area
[Grade:6-8 | Topics: tabular data; rates of change; decimal math]
Category: All,Miscellaneous
Students study change of scale and dilation by investigating showflake growth.
Problem 627: History of Winter - The Surface Area of a Snowflake
[Grade:6-8 | Topics: geometry; areas of triangles and rectangles; decimal math]
Category: All,Miscellaneous
Students estimate the area of a single snow flake using the areas of triangles and rectangles.
Problem 626: History of Winter - Graphing a Showflake using Symmetry
[Grade:6-8 | Topics: geometry; symmetry; plotting points on a Cartesian graph]
Category: All,Miscellaneous
Students use a simple plotting exercise and reflection symmetry to create a snowflake.
Problem 625: SCOOL-Cloud Droplets and Rain Drops
[Grade:6-8 | Topics: Volume of a sphere; scientific notation ]
Category: All,Miscellaneous
Students
Problem 624: SCOOL-Cloud Cover, Albedo, Transmission and Opacity
[Grade:9-12 | Topics: logarithmic functions; percentage]
Category: All,Miscellaneous
Students explore the concepts of albedo, transmission and opacity for clouds.
Problem 623: SCOOL-Cloud Cover and Solar Radiation
[Grade:6-8 | Topics: Graph analysis; evaluating functions]
Category: All,Helio
Students examine the relationship between percentage cloud cover and the amount of sunlight that reaches the ground.
Problem 622: SCOOL-How Clouds Form - Working with Dew Points and Rates of Change
[Grade:6-8 | Topics: Percentage; rates of change ]
Category: All,Miscellaneous
Students learn about the dew point and how clouds form from humid, cooling air.
Problem 621: SCOOL-Working with Rainfall Rates and Water Volume
[Grade:9-12 | Topics: scientific notation; rates of change ]
Category: All,Miscellaneous
Students learn about rain fall rates and how to convert them into the volume of water that falls.
Problem 620: SCOOL-Estimating the Mass of a Cloud
[Grade:6-8 | Topics: Volume of a sphere; scientific notation; mass = density x volume]
Category: All,Miscellaneous
Students use the relationship between volume and density to estimate the mass of a common cumulus cloud.
Problem 619: SCOOL-Using Proportions to Estimate the Height of a Cloud
[Grade:6-8 | Topics: geometry of right triangles; proportions]
Category: All,Miscellaneous
Students use the method of triangulation to determine the height of a cloud.
Problem 618: Voyager 1 Begins its Interstellar Journey
[Grade:6-8 | Topics: speed=distance/time; time = distance/speed; number = density x volume]
Category: All,Solar System
Students calculate speeds, light travel times and density for the Voyager 1 encounter with the interstellar medium beyond the orbit of Pluto.
Problem 617: The Basic Mathematics of Rocket Engines - I
[Grade:9-12 | Topics: proportions; unit conversions; rates of change]
Category: All,Rockets
Students learn about and calculate specific impulse and thrust.
Problem 616: Adding a Level Gauge to a Conical Tank
[Grade:6-8 | Topics:geometry; volume of a cone ]
Category: All,Miscellaneous
Students work with the formula for the volume of a cone
Problem 615: Radiation Levels on the Surface of Mars
[Grade:6-8 | Topics: unit conversions; graph analysis; rates ]
Category: All,Solar System
Students explore radiation dosages on mars and in interplanetary space
Problem 614: A Simple Gauge in a Tank - II
[Grade:6-8 | Topics: geometry; volume of a cone; tangents ]
Category: All,Miscellaneous
Students work with the formula for the volume of a conical solid to design a gas tank gauge.
Problem 613: Measuring the Speed of Gas Near a Black Hole
[Grade:6-8 | Topics: time; graph analysis]
Category: All,Universe
Students use a graph of intensity and time to estimate thhe orbit period of matter around a black hole.
Problem 612: Exploring Power-laws: Meteor impacts
[Grade:9-12 | Topics: logarithmic functions; power-functions; logarithmic graphs]
Category: All,Miscellaneous
Students work with logarithmic functions, power-laws and explore the mass functiuon of meteors.
Problem 611:Angular Size : The Moon and Stars
[Grade:6-8 | Topics:scale; proportion; angle measure ]
Category: All,Solar System,Stars
Students explore angular size using a simple proportional equation
Problem 610: Calculating the Volume of the J-2x Rocket Engine Bell
[Grade:6-8 | Topics:volume of a conical solid; solving a quadratic equation for a selected value of X]
Category: All,Rockets
Students explore conical volumes by examining the diemnsions of a large rocket engine.
Problem 609: Volumes of Solids - Packing for a trip to the Moon
[Grade:3-5 | Topics: volume of rectangular solids; integers]
Category: All,Solar System
Students calculate volumes of rectangular solids and pack a volume-limited travel kit used by astronauts.
Problem 608: Constellations in 3D
[Grade:6-8 | Topics: geometry; scale]
Category: All,Stars
Students create a 3-d model of the constellation Orion and explore how stars are located in space and how this perspective changes from different vantage points.
Problem 607: The Launch of LADEE to the Moon
[Grade:6-8 | Topics: Graphing tabular data; determining the slope of a line; rates of change]
Category: All,Solar System,Rockets
Students plot the altitude, range and speed of the LADEE rocket launch and investigate rates of change including acceleration by graphing the tabular data and determining the slope of the graph using the definition of the slope of a line between two points.
Problem 606: Global Warming and the Sun’s Evolving Luminosity
[Grade:9-12 | Topics: working with equations; eliminating common variables; functions]
Category: All,Helio,Solar System,Universe
Students work with two functions that relate the brightness of the sun to its age L(t), and the temperature of earth to the suns brightness, T(L) to create a new function that gives the temperature of earth over time T(t).
Problem 605: The Solar System Beyond the Orbit of Neptune
[Grade:9-12 | Topics: volume of a disk; density = number/volume ]
Category: All,Helio,Solar System
Students compute the volume and density of the Kuiper Belt located beyond the orbit of Neptune, and estimate how far apart the objects are located compared to the earth-sun distance.
Problem 603: The Temperature of Earth without Carbon Dioxide
[Grade:9-12 | Topics: evaluating functions; trigonometry; surface area of a sphere ]
Category: All,Solar System
Students study a computer model to determine the temperature of Earth if there were no carbon dioxide in the atmosphere. They also determine the albedo of earth given different amounts of ice cap coverage determined by the computer model.
Problem 602: Transit of Phobos Across the Sun Viewed from Mars
[Grade:6-8 | Topics: proportions; angle measure; similar triangles]
Category: All,Helio,Solar System
Students investigate the geometry of a martian moon passing across the face of the sun using angular measure and proportions.
Problem 601: Gravity and Escape Speed
[Grade:6-8 | Topics: evaluating functions; square-roots ]
Category: All,Miscellaneous
Students calculate the escape speed for various planets using a simple 'square root' equation.
Problem 600: Reading a Speed vs Time Graph - acceleration
[Grade:9-12 | Topics:areas of rectangles and triangles; interpreting graphical data ]
Category: All,Miscellaneous
Students read a graph to determine how speed is related to acceleration as the area under a curve.
Problem 599: Exploring Artificial Gravity
[Grade:9-12 | Topics: evaluating functions]
Category: All,Miscellaneous
Students work with centrifugal forces to calculate the acceleration of County Fair rides; rotating spacecraft and the acceleration of rockets to see if artificial gravity can be created.
Problem 598: Gravity and Energy
[Grade:6-8 | Topics: evaluating functions; unit conversions]
Category: All,Miscellaneous
Students the energy equation E = mgh to expore the energy of falling water near Earths surface to calculate the energy of a water fall.
Problem 597: The Physics of Rock Throwing
[Grade:9-12 | Topics: quadratic equations; parametric equations; parabolas ]
Category: All,Miscellaneous
Students study the motion of a thrown rock to explore the parabolic shape of the rocks motion.
Problem 596: Distance Traveled Under Free Fall by Gravity
[Grade:6-8 | Topics: solving for X; quadratic monomials; square roots]
Category: All,Miscellaneous
Students explore accelerated motion and distance traveled using an equation that related distance to time-squared, and solve the equation under various conditions.
Problem 595: Gravity and Falling Bodies
[Grade:6-8 | Topics:linear equations; solving for x ]
Category: All,Miscellaneous
Students work with simple linear equations to study the speed of falling bodies under gravity.
Problem 594: A Number Puzzle about the Origin of Our Universe
[Grade:6-8 | Topics: distance between two points; slopes; linear equations; dilations; scientific notation]
Category: All,Universe
Students learn about the Big Bang by solving a number puzzle for missing words using solutions to a variety of problems taken from Algebra 1 topics.
Problem 593:A Number Puzzle about Planets Beyond our Solar System
[Grade:6-8 | Topics: quadratic equations; factoring ]
Category: All,Helio
Students solve a puzzle by finding the missing words keyed to solutions for the roots of quadratic equations
Problem 592: Apparent Sizes of Objects from Jupiter’s Moon Europa
[Grade:6-8 | Topics: angle measure; proportions; geometry ]
Category: All,Helio,Solar System
Students explore how the angular sizes of the moons of Jupiter depend on the actual sizes and distances from the observer, and can sometimes allow eclipses of the sun as viewed from Europa.
Problem 591: The Occulting Moons of Mars
[Grade:6-8 | Topics: working with poroportions; angular measure; geometry]
Category: All,Solar System
Students explore the moons of mars and their eclipses during an event seen by the CUriosity rover on August 1, 2013.
Problem 590: Magnetic Storms, Aurora and the Kp Index
[Grade:3-5 | Topics: averaging; percentage; working with tables ]
Category: All,Helio,Magnetism
Students use simple math, percentage and probability to estimate how common intense magnetic storms are by using the magnetic Kp index and its statistics.
Problem 589: Coronal Mass Ejections and Radiation Storms
[Grade:3-5 | Topics: percentage; averaging; probability; working with tables ]
Category: All,Helio
Students explore the frequencies of coronal mass ejections and radiation storms to determine how common both are during sunspot maximum in 2013.
Problem 588: Solar Flares
[Grade:3-5 | Topics: averaging; odds; percentage]
Category: All,Helio
Students explore the frequencies of intense solar flares to determine their average numbers each day during sunspot maximum in 2013.
Problem 587: Comet Encounters after Discovery
[Grade:3-5 | Topics: Averaging, percentages]
Category: All,Solar System
Students examine how often newly discovered comets approach Earth and become a hazard, and how soon after discovery these close passes can occur.
Problem 586: Searching for Comets
[Grade:3-5 | Topics: Percentages]
Category: All,Solar System
Students use tabular data on the detection of new comets since 1999 to explore detection rates over time.
Problem 585: Exploring Comet Orbits
[Grade:6-8 | Topics: speed=distance/time]
Category: All,Solar System
Students explore the elliptical orbit of Halleys Comet and determine its period and the speed of the comet.
Problem 584: Comparing Comets Up Close with NASA Spacecraft
[Grade:3-5 | Topics: percentages; volume of a cube]
Category: All,Solar System
Students compare five comets and determine size ranges and percentages.
Problem 583: Buying a Telescope
[Grade:6-8 | Topics: simple ratio formula; decimal math]
Category: All,Telescopes
Students compare several telescopes and select the one with the best performance and lowest cost.
Problem 582: How do Telescopes Magnify?
[Grade:3-5 | Topics: division of two decimal numbers; evaluating simple ratios. ]
Category: All,Telescopes
Students use a simple ratio formula to calculate the magnification of a telescope.
Problem 581: How Telescopes Work
[Grade:3-5 | Topics: Area of a circle ]
Category: All,Telescopes
Students compare how much light a telescope can gather compared to the human eye.
Problem 580: Measuring Gravity with a Pendulum
[Grade:6-8 | Topics: evaluating square-root equations; scientific notation ]
Category: All,Miscellaneous
Students design pendulum clocks for mars and the moon, and how pendulums can be used for mining on Earth.
Problem 579: The Scale of an Image with a Telescope
[Grade:6-8 | Topics: area; evaluating simple equations; unit conversions]
Category: All,Telescopes
Students design digital cameras for telescopes given information about the image scale of the telescope and the pixel dimensions.
Problem 578: Digital Camera Math
[Grade:6-8 | Topics: integer math; area of a square]
Category: All,Miscellaneous
Students learn about digital cameras and how to interpret formats, megapixels and angular resolution.
Problem 577: Designing a Telescope System
[Grade:6-8 | Topics: graphing inequalities; evaluating simple equations ]
Category: All,Telescopes
Students design two telescopes given information about the desired properties for conducting research.
Problem 576: Telescope Resolution - How much detail can you see?
[Grade:6-8 | Topics: Angular measure; arcseconds; simple equations ]
Category: All,Telescopes
Students determine the resolving power of a telescope and the limit to the finest details that can be see for a telescope of a specific diameter.
Problem 575: Telescope Field of View - How much can you see?
[Grade:6-8 | Topics: Angular measure; degrees]
Category: All,Telescopes
Students calculate the angular field of view for various telescopes using a simple formula of the form: F = A/B
Problem 574: Telescope Light Gathering Ability - Seeing Faint Stars
[Grade:6-8 | Topics: Area of a circle ]
Category: All,Stars,Telescopes
Students calculate the light gathering ability of various telescopes compared to the human eye.
Problem 573: Calculating the Magnification of a Telescope
[Grade:6-8 | Topics: proportions]
Category: All,Telescopes
Students fill in missing numbers in a table using proportions and evaluating a simple equation for magnification.
Problem 572: How Saturns Moon Mimas Created the Cassini Division
[Grade:9-12 | Topics: scientific notation; evaluating a formula for gravity; unit conversions]
Category: All,Solar System
Students calculate the acceleration of gravity in Cassinis Division and estimate the number of years to eject these particles.
Problem 571: Focal Lengths, Apertures and F/numbers
[Grade:6-8 | Topics: fractions; integer division; evaluating simple equations ]
Category: All,Miscellaneous
Students learn about the basic terms that define the performance of a digital camera or a telescope.
Problem 570: Curiosity Heads for Mt Sharp
[Grade:3-5 | Topics: averaging numbers in a table; time = distance/speed]
Category: All,Solar System
Tabular data is used to estimate how long it will take the Curiosity rover to reach the base of Mt Sharp using data from its porevious week travels.
Problem 569: Orbit Speeds and Times for Saturns Rings
[Grade:6-8 | Topics: square root formulae; circumference of circle; speed = distance/time ]
Category: All,Solar System
Students learn about the orbit speeds of ring particles and how orbit periods in the Cassini Division relate to the orbit of the moon Mimas.
Problem 568: Ios Volcanoes and Resurfacing
[Grade:6-8 | Topics: Surface aea of a sphere; rates; scientific notation]
Category: All,Solar System
Students examine how volcanic activity on Jupiters satellite Io can lead to fresurfacing the entire moon in less than a million years covering all new craters.
Problem 567:Exploring Parabolas - The shape of a satellite dish
[Grade:9-12 | Topics: geometry; properties of parabolas]
Category: All,Helio
Students use the equation for a parabola to determine the focus location for a solar cooker and a sound amplifier dish given their diameters and depths.
Problem 566:Exploring Light Brightness and the Inverse Square Law
[Grade:6-8 | Topics: graphing tabular data; surface area of a sphere; ]
Category: All,Miscellaneous
Students collect data and explore the inverse square law using a light meter. They deduce the formula for the brightness of a lamp given its distance and wattage.
Problem 565:Mapping Earth from Space - Swaths and Coverage
[Grade:6-8 | Topics: geometry;scale model; working with square roots ]
Category: All,Solar System
Students explore how satellite observing swaths add up to give full coverage of earths surface.
Problem 564:Exploring the Stars in Orion - Light Year Madness
[Grade:6-8 | Topics: time lines; time interval calculations; time = distance/speed ]
Category: All,Stars
Students explore the light year and its relationship to light travel time for observing events in different parts of space.When would colonists at different locations observe the star Betelgeuse become a supernova?
Problem 563:Comet ISON and its Close Encounter with Mars
[Grade:3-5 | Topics: graphing tabular data]
Category: All,Solar System
Students use tabular data to determine the date and time of closest approach to Mars
Problem 562:Exploring the Orbit of Comet ISON
[Grade:6-8 | Topics: graphing tabular data; scale; measurement; distance between points]
Category: All,Helio,Solar System
Students use tabulated data to estimate when this comet will make its closest approach to the sun in 2013.
Problem 561:Exploring the Evaporating Exoplanet HD189733b
[Grade:6-8 | Topics:mass=densityx volume; rates; volume of a sphere ]
Category: All,Solar System
Students estimate how quickly this planet will lose its atmosphere and evaporate at its present loss rate of 6 million tons/second
Problem 560:The Orbit of Comet ISON
[Grade:3-5 | Topics: Interpreting tabular data; graphing ]
Category: All,Solar System
Students explore how close Comet ISON will get to Mercury, Venus, Earth and Mars during its 2013 passage.
Problem 559:Comet ISON Losing Mass as it Approaches the Sun.
[Grade:6-8 | Topics: volume of a sphere; rates; mass=density x volume]
Category: All,Solar System
Students estimage how much mass the comet will loose at its present rate.
Problem 558:How Quickly are NEOs Being Discovered?
[Grade:6-8 | Topics:bar graphs ]
Category: All,Solar System
Students work with data presented in bar graphs to estimate how many more hazardous Near Earth Objects (NEOS) remein to be found.
Problem 557:The 10000th Near Earth Asteroid 2013 MZ5
[Grade:6-8 | Topics: graphing tabular data; solving a linear equation]
Category: All,Solar System
Students graph tabulated data to determine when this asteroid is closest to Earth and its speed at that time.
Problem 556:IRIS Explores the Solar Transition Region
[Grade:6-8 | Topics: percentage; proportion; scale; scientific notation; volume of a cylinder]
Category: All,Helio
Students use an image from IRIS to examine the sizes and equivalent energy of bright regions in the solar transition region.
Problem 555:Exploring Your Weight Across the Solar System
[Grade:6-8 | Topics: proportions]
Category: All,Helio
Students estimate their weight on different planets, moons and asteroids.
Problem 554:Exploring Volcanoes and Geysers Across the Solar System
[Grade:6-8 | Topics: solving square root equations; ]
Category: All,Helio
Students determine the ejection speed and heights of gasses vented by geysers and volcanoes.
Problem 553:Colliding Galaxies - The future of our Milky Way
[Grade:9-12 | Topics: unit conversions; scientific notation; ballistic equation; solvimg quadratic equations]
Category: All,Universe
Students explore the collision of two galaxies and estimate from their present speed, separation and acceleration how long it will be before they have collided.
Problem 552:Cassini Sees Earth From Space - How Bright is it?
[Grade:9-12 | Topics: logarithms; power laws ]
Category: All,Solar System
Students explore the logarithmic magnitude scale and estimate how bright Earth appears from Saturn as viewed in a recent Cassini image
Problem 551:Giving Particles a Boost in the van Allen Belts
[Grade:6-8 | Topics: equations; scientific notation]
Category: All,Helio
Students examine a ball bouncing down a flight of stairs and compare this to how van Allen particles gain their energy from numerous small boosts.
Problem 550:Comparing the Rings of the Outer Planets
[Grade:6-8 | Topics: scale model; proportions; number line ]
Category: All,Solar System
Students compare the dimensions of the rings of Jupiter, Saturn, Uranus and Neptune to the radius of each planet, and the location of the break up Tidal Limit to test an idea of how the rings may have formed.
Problem 549:Saturns Rings- Shadows from Moons and Ringlets
[Grade: 6-8| Topics: scales; proportions; triangle geometry; angle measurement]
Category: All,Solar System
Students use an image of a ring of Saturn to investigate its thickness using shadows cast by ringlet material kicked up by a passing moon.
Problem 548:Saturns Rings - A close-up study
[Grade:3-5 | Topics: measurement; scales; proportions; metric measure; bar graphs]
Category: All,Solar System
Students use a Cassini image of Saturns rings to calculate the sizes of the smallest rings, and how their thicknesses change with distance from Saturn.
Problem 547:The Rings of Saturn
[Grade:9-12 | Topics: volume of a ring and a sphere; scientific notation]
Category: All,Solar System
Students explore the volume and mass of the rings of saturn to estimate the number of ring particles and their separations, and the radius of the equivalent spherical body.
Problem 546: The Relative Sizes of Planets and other Objects
[Grade:3-5 | Topics:scale; proportion]
Category: All,Helio
Students use proportional information to determine the relative scales of planets and large moons across the solar system.
Problem 545:Measuring Atmospheric Trace Gases Using Parts Per Million
[Grade:6-8 | Topics: percentages; unit conversions ]
Category: All,Miscellaneous
Students convert from percentage units to parts per million and compare trace gases in the atmospheres of various planets.
Problem 544:The Composition of Planetary Atmospheres
[Grade:6-8 | Topics: Pie graphs; percentages; scientific notation]
Category: All,Solar System
Students study the composition of planetary atmospheres and compare the amounts of certain compounds in them
Problem 543:Timeline for Planet Formation
[Grade:3-5 | Topics: time calculations; integers]
Category: All,Solar System
Students calculate time intervals in millions and billions of years from a timeline of events
Problem 542:The Late Heavy Bombardment Era
[Grade:6-8 | Topics: volume of spheres; proportions]
Category: All,Solar System
Students estimate the average arrival time of large asteroids that impacted the moon. They work with the formula for the volume of a sphere to estimate how much additional mass was added to the moon and Earth durung this era.
Problem 541:How to Build a Planet
[Grade:3-5 | Topics: graphing; counting]
Category: All,Solar System
Students study planet growth by using a clay model of planetessimals combining to form a planet by investigating volume addition with spheres.
Problem 540:Travel Times by Spacecraft Around the Solar System
[Grade:6-8 | Topics: time=distance/speed; metric conversion]
Category: All,Helio
Students explore how long it takes our fastest rockets to reach each of the planets.
Problem 539:Visiting the Planets at the Speed of Light
[Grade:6-8 | Topics: Proportions; unit conversions; time = distance/speed; metric units]
Category: All,Miscellaneous
Students learn about the light travel times to the 8 planets by converting the distances in Astronomical Units to travel times at the speed of light.
Problem 538:How Big is Our Solar System?
[Grade:6-8 | Topics: Proportions; unit conversions]
Category: All,Helio
Students work with proportions to convert solar system distances into Astronomical Units for the 8 planets.
Problem 537:A Solar Storm Number Puzzle
[Grade:3-5 | Topics: integer arithmetic; positive and negative numbers]
Category: All,Helio
Students solve 10 problems using positive and negative numbers, addition, subtraction and multiplication to find the missing words in a short essay about solar storms.
Problem 536:Exploring a Possible InSight Landing Area on Mars
[Grade:6-8 | Topics: degree measure; latitude and longitude; working with scaled images; metric measure]
Category: All,Solar System
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.
Problem 535:Comparing the InSight Landing Area to a City Block!
[Grade:6-8 | Topics: scale; proportion; metric measurement]
Category: All,Solar System
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.
Problem 534:Exploring Marsquake Energy with the Moment Magnitude Scale
[Grade:8-10 | Topics: logarithms; scientific notation; algebra ]
Category: All,Solar System
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.
Problem 533:Exploring Logarithms and the Richter Magnitude Scale
[Grade:8-10 | Topics: logarithms; base-ten exponents]
Category: All,Miscellaneous
Students work with a logarithmic scale to estimate how much ground movement occurs for earthquakes of different strengths.
Problem 532:The Distance to the Martian Horizon
[Grade:8-10 | Topics: Pythagorean Theorem, Algebra; scientific notation; areas of spheres and circles ]
Category: All,Solar System
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.
Problem 531:Exploring the Interior of Mars with Spheres and Shells
[Grade:8-10 | Topics: formula for volume of spheres and spherical shells; mass=densityxvolume; scientific notation ]
Category: All,Solar System
Students use the volume properties of spheres and shells along with the relationship mass=densityxvolume to create a model of the interior of mars.
Problem 530:Exploring the Mass of Mars
[Grade:8-10 | Topics: Algebra; scientific notation ]
Category: All,Solar System
Students calculate the mass of mars by using satellite data and Keplers Third Law.
Problem 529:Exploring Impacts and Quakes on Mars
[Grade:8-10 | Topics: Logarithmic scales; scientific notation ]
Category: All,Solar System
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.
Problem 528:Comparing the Heat Output of Mars and Earth
[Grade:8-10 | Topics: Algebra; temperature gradients]
Category: All,Solar System
Students learn about the heat flow formula and use it to explore the properties of Earth and Mars in terms of their crust composition.
Problem 527:Exploring Heat Flow and Insulation
[Grade:8-10 | Topics: algebra; rates of change ]
Category: All,Solar System
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 soil from heat flow and temperature changes.
Problem 526:Exploring Temperature Change in Earth’s Outer Crust
[Grade:6-8 | Topics: fahrenheit and celsius degrees; rates of change]
Category: All,Solar System
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.
Problem 525:Exploring the InSight Lander Telemetry Data Flow
[Grade:6-8 | Topics: working with kilo, mega and rates of data transfer in bytes/sec. ]
Category: All,Solar System
Students explore how long it takes to transmit digital data using examples from downloading songs from their computer to their ipod.
Problem 524:Seeing the Martian Surface with IDC
[Grade:6-8 | Topics: Angular measure, degrees and seconds; image scale; tiling an area with overlap. ]
Category: All,Solar System
Students learn about the IDC camera and calculate resolution and how many images are needed to map the InSight landing area.
Problem 523:Telling Time on Mars - Earth Days and Mars Sols
[Grade:6-8 | Topics: time calculations, hours, minutes, seconds; length of day ]
Category: All,Solar System
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.
Problem 522:Radio Communications with Earth – The Earth-Sun Angle
[Grade:8-10 | Topics: Interpreting tabular data; rates and slopes ]
Category: All,Solar System
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.
Problem 521:Estimating the Mass of a Martian Dust Devil!
[Grade:8-10 | Topics: Volume of a cylinder; mass = density x volume ]
Category: All,Solar System
Students estimate the mass of a martian dust devil using the approximation that it is a cylinder with a fixed density of dust.
Problem 520:The Work Area In Front of the Lander
[Grade:6-8 | Topics: Area of a circle segment; Area common to two intersecting circles]
Category: All,Solar System
Students estimate the area in front of the InSight lander where experiments will be conducted and instruments moved with a single robotic arm.
Problem 519:Scheduling Events in Time for Launch
[Grade:5-7 | Topics: working with time units; creating a timeline]
Category: All,Rockets
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.
Problem 518:The InSight Seismographic Station Solar Power System
[Grade:7-9 | Topics: area of regular polygons; estimating areas of non-square shapes]
Category: All,Helio,Solar System,Rockets
Students explore the properties of decagons to determine the area of the solar panels used on the InSight lander.
Problem 517: A Distant Supernova Remnant Discovered
[Grade:6-8 | Topics: proportions; speed=distance/time]
Category: All,Helio,Stars,Rockets
Students work with proportions and scaling to discover the size of the supernova remnant compared to the distance from the Sun to the nearest star Alpha Centauri. The also work with time and speed calculations to estimate the speed of the supernova compared to the International Space Station.
Problem 516: Hinode Observes a Solar Eclipse from Space
[Grade:3-5 | Topics: Proportions; time intervals; calendar arithmetic]
Category: All,Helio,Solar System
Students work with simple proportions to estimate the diameter of the sun using the Moon and the Moon's distance.
Problem 515: Telling Time on Mars
[Grade:3-5 | Topics: Time intervals; time calculations by addition and subtraction]
Category: All,Solar System
Students work with simple time calculations to explore how the length of a day on Earth and MArs differm and how this affects how scientists navigate the Curiosity Rover on the martian surface.
Problem 514: Solar Flares and the Stormy Sun
[Grade:3-5 | Topics: Averaging integers; rounding]
Category: All,Helio
Students work with simple averaging and explore the latest sunspott cycle to find their averages for 2012 and 2013.
Problem 513: The Remarkable Gamma Ray Burst GRB 130427A
[Grade:8-10 | Topics: surface area of sphere; scientific notation]
Category: All,Stars
Students work with the surface area of a sphere, metric conversions and scientific notation to calculate the total power of this distant supernova event.
Problem 512: New NASA Satellite Takes Pictures of Salton Sea
[Grade:6-8 | Topics: area of square and rectangle; metric units; unit conversion]
Category: All,Miscellaneous
Students work with image of agricultural area to estimate the percentage of area cultivated and the total rainfall in gallons per year.
Problem 511: Giant Gas Cloud in System NGC 6240
[Grade:8-10 | Topics:Volume of a sphere; scientific notation; unit conversion ]
Category: All,Stars
Students use scientific notation and volume of sphere to estimate the density of the gas cloud, and the number of hydrogen atoms per cubic meter.
Problem 510: Planck Mission Sees the Ancient Universe Clearly
[Grade:6-8 | Topics: scale and proportion; angular measure]
Category: All,Universe
Students work with an image of the universe when it was 370,000 years old and determine from simple scaling and proportions the sizes of the features seen in the image compared to the Milky Way.
Problem 509:Grail Spacecraft Creates a New Crater on the Moon
[Grade:6-8 | Topics: scale and proportion; volume of cylinder; mass=DensityxVolume]
Category: All,Solar System
Students work with images of the Grail impact sites to estimate the diameter of the crater created after the spacecraft impacted the moon.
Problem 508: The InSight Seismographic Station - Wave arrival times
[Grade:6-8 | Topics: speed=distance/time; Time calculations; circumference of a circle]
Category: All,Solar System,Rockets
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.
Problem 507: Exploring the Launch of the Falcon 9
[Grade:6-8 | Topics: speed=distance/time; Time calculations]
Category: All,Rockets
Students use data from the launch of the Falcon 9 booster to determine its speed and acceleration.
Problem 506: A New Belt for the Van Allen Belts
[Grade:3-5 | Topics: Interpreting Tabular Data]
Category: All,Helio
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.
Problem 505: SDO Sees Coronal Rain - Estimating Plasma Speeds
[Grade:6-8 | Topics: scale models; speed=distance/time; proportions]
Category: All,Helio
Students estimate the speed of plasma streamers near the solar surface using images from a Solar Dynamics Observatory.
Problem 504: Grail Satellites Create a Gravity Map of the Moon
[Grade:9-12 | Topics: square-roots; evaluating equations]
Category: All,Solar System
Students explore the gravity field of the moon, and the behavior of simple pendulum clocks in places on the moon where the local gravity is slightly different.
Problem 503: The Origin of Cosmic Rays
[Grade:8-10 | Topics: percercentages, scientific notation; volume of a disk]
Category: All,Stars,Universe
Students explore the Fermi Gamma-Ray Observatory's confirmation of the idea that supernova are the sources of cosmic rays in the Milky Way. They use a simple model to estimate how many supernova are needed to account for the current number of cosmic rays in the galaxy.
Problem 502:The Frequency of Large Meteor Impacts
[Grade:6-8 | Topics: percercentages, areas]
Category: All,Solar System
Students examine how often a large meteor should be visible like the one that exploded over Russia on February 14, 2013. This asteroid had a mass of 10,000 tons and injured over 1000 people.
Problem 501: Exploring the Most Distant Galaxies with Hubble
[Grade:11-12 | Topics: polynomials; linearization]
Category: All,Universe
Students use recent Hubble Extreme Deep Field data and a polynomial to determine the light travel time between distant galaxies and Earth.
Problem 500: Curiosity Uses X-Ray DIffraction to Identify Minerals on Mars
[Grade:10-12 | Topics: geometry; trigonometry]
Category: All,Solar System
Students learn about diffraction geometry and then estimate the distance between crystal planes in a mars rock sample.
Problem 499: The Equation of a Magnetic Field Line
[Grade:12 | Topics: differential and integral calculus; slope; parametric equations]
Category: All,Magnetism
Students use calculus to determine the formula for a magnetic field line.
Problem 498: The Slope of a Magnetic Field Line
[Grade:7-8 | Topics: Graphing in the XY plane; midpoint formula; tangent lines to curves]
Category: All,Magnetism
Students graph a magnetic field line in the First Quadrant, then calculate the segment midpoints using the Midpoint Formula, and then draw tangent lines at each midpoint to determine compass direction.
Problem 497: Graphing a Magnetic Field Line
[Grade:6-8 | Topics: graphing in XY plane; reflection symmetry]
Category: All,Magnetism
Students plot points along a magnetic field line in the First Quadrant, then use reflection symmetry to complete the field line shape in all four quadrants.
Problem 496: How to Grow a Planet or a Rain Drop
[Grade:12 | Topics: Solving a simple differential equation.]
Category: All,Solar System
Students use calculus to slove for the growth in mass of a body, and solve the equation for the case of a raindrop and a planet like Earth.
Problem 495: The Volume of a Lunar Impact Crater
[Grade:12 | Topics: Integration involving vollumes of rotation]
Category: All,Solar System
Students use calculus to determine the volume of a crater whose depth is defined by a fourth-order polynomial
Problem 494: The Close Encounter to the Sun of Barnards Star
[Grade:12 | Topics: Derivitives and minimization]
Category: All,Helio,Stars
Students use parametric equations and calculus to determine the linear equation for the path of Barnards Star, and then determine when the minimum distance to the sun occurs
Problem 493: Fun with Gears and Fractions
[Grade:4-7 | Topics: multiplying simple fractions]
Category: All,Miscellaneous
Students learn about how simple fractions are used to describe gears and gear trains that reduce or increase speed.
Problem 492: Alpha Centauri Bb - a nearby extrasolar planet?
[Grade:9-12 | Topics: graphing periodic data; finding periods; evaluating simple formulae ]
Category: All,Solar System
Students plot data for the orbiting planet and determine its orbit period. They use this in a simple formula to determine its distance, then they estimate its surface temperature at this distance.
Problem 491: The Curiosity Rover on the Move.
[Grade:6-8 | Topics: Cartseian graphs; ordered pairs and coordinates; distance = speed x time; metric measure ]
Category: All,Solar System
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.
Problem 490: LL Pegasi - A Perfect Spiral in Space
[Grade:6-8 | Topics: Distance = speed x time; unit conversions; evaluating formulas ]
Category: All,Stars
The star LL Persei is ejecting gas like a sprinkler on a lawn. Every 800 years the gas makes one complete orbit, and over time forms a spiral patteri in space. Students explore the timing of this pattern and estimate the size and age of this gas.
Problem 489: The Van Allen Probes and the location of Dawn Chorus - III
[Grade:6-8 | Topics: Linear equations; solving systems of equations; graphical solutions ]
Category: All,Helio,Rockets
The location of the Chorus signal from each of the Van Allen Probes 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.
Problem 488: The Van Allen Probes and the Location of Dawn Chorus - II
[Grade:6-8 | Topics: Angles; graphing; protractors ]
Category: All,Helio,Solar System,Rockets
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.
Problem 487: The Hubble eXtreme Deep Field
[Grade:6-8 | Topics: Counting, areas, proportions ]
Category: All,Universe
Students use the Hubble XDF to estimate the number of galaxies in the visible universe.
Problem 486: The Van Allen Probes Hear Dawn Chorus - I
[Grade:6-8 | Topics: Graphing on the Cartesian plane; distances between points. ]
Category: All,Helio,Rockets
Students explore the method of triangulation and how it might be used by the Van Allen Probes spacecraft to find the origin of the Chorus signals.
Problem 485: Curiosity Discovers Ancient Mars River
[Grade:9-12 | Topics: Algebra; trigonometry; evaluating functions ]
Category: All,Solar System
Students estimate the speed of an ancient mars river using images from the CUriosity rover.
Problem 484: Exploring Water Use in Kansas
[Grade:6-8 | Topics: Area of a circle; unit conversions ]
Category: All,Miscellaneous
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.
Problem 483: The Radioactive Dating of a Star in the Milky Way!
[Grade:9-12 | Topics: half-life; exponential functions; scientific notation]
Category: All,Stars,Universe
Students explore Cayrel's Star, whose age has been dated to 12 billion years using a radioisotope dating technique involving the decay of uranium-238.
Problem 482: Exploring Density, Mass and Volume Across the Universe
[Grade:9-12 | Topics: Density=mass/volume; scientific notation; unit conversion; metric math ]
Category: All,Universe
Students calculate the density of various astronomical objects and convert them into hydrogen atoms per cubic meter in order to compare how astronomical objects differ enormously in their densities.
Problem 481: Pluto's Fifth Moon
[Grade:9-12 | Topics: Power functions; integer exponents; Scientific Notation; tabular data]
Category: All,Solar System
Students explore Kepler's Third Law and estimate the orbit period of a hypothetical sixth moon using the distance:period law. They also determine the mass of Pluto using the orbit data, including the recently discovered fifth moon (P5) of Pluto by the Hubble Space Telescope.
Problem 480: The Expanding Gas Shell of U Camelopardalis
[Grade:6-8 | Topics: Scientific Notation; distance = speed x time; density=mass/volume ]
Category: All,Miscellaneous
Students explore the expanding U Camelopardalis gas shell imaged by the Hubble Space Telescope, to determine its age and the density of its gas.
Problem 479: Exploring Gale Crater with the Curiosity Rover
[Grade:9-12 | Topics: Pythagorean Distance Formula; Coordinate geometry ]
Category: All,Solar System
Students explore the Gale Crater landing area and calculate rover distances to various way stations to determine the round trip distance and travel time.
Problem 478: The Grail and LRO Encounter in Lunar Orbit
[Grade:9-12 | Topics: formula for an ellipse; semi-major and minor axis]
Category: All,Solar System
Students explore the May 31, 2012 encounter between NASA's Grail and LRO spacecraft in orbit around the moon. Will the Grail/Ebb spacecraft be able to photograph the LRO spacecraft as it passes-by?
Problem 476: SpaceX launches the First Commercial Rocket to the ISS
[Grade:9-12 | Topics: Volumes of 3-d objects; cones; evaluating functions]
Category: All,Rockets
Students detemine the volume of the Dragon capsule using the volume formula for a cone.
Problem 475: Exploring Tidal Forces: Black holes and Saturns rings
[Grade:9-12 | Topics: Evaluating equations; scientific notation]
Category: All,Solar System,Stars
Students use the equation for tidal disruption to explore the stability of a star encountering a black hole, and a satellite of Saturn. Why are there no large satellites of Saturn inside the ring system?
Problem 474: MESSENGER Explores the Interior of Mercury
[Grade:9-12 | Topics: working with volumes of speheres; mass = density x volume]
Category: All,Solar System
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.
Problem 473: MESSENGER Explores the Mass of Mercury
[Grade:9-12 | Topics: working with equations with integer powers and solving for specified values; scientific notation]
Category: All,Solar System
Students use the orbit of NASA's MESSENGER spacecraft to determine the mass of Mercury.
Problem 472: Investigating Juno's Elliptical Transfer Orbit
[Grade:9-12 | Topics: formula for an ellipse; semi-major and minor axis]
Category: All,Rockets
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.
Problem 471: Investigating the Launch of the Juno Spacecraft
[Grade:6-8 | Topics: scale models; speed = distance/times]
Category: All,Rockets
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.
Problem 470: The Launch of the Juno Spacecraft - Ascent to orbit
[Grade:6-8 | Topics: scale models; speed = distance/time]
Category: All,Rockets
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.
Problem 469: Solar Energy and the Distance of Juno from the Sun
[Grade:9-12 | Topics: algebra; trigonometry; distance formula]
Category: All,Helio,Solar System
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.
Problem 468: How Common are X-Class Solar Flares?
[Grade:5-7 | Topics: mean, median, percentage]
Category: All,Helio
Students use simple statistics to determine the solar flare frequency during the last 11-year sunspot cycle to estimate the time between X-class flares during the current sunspot cycle
Problem 467: Estimating Magnetic Field Speeds on the Sun
[Grade:6-8 | Topics: speed=distance/time; scale model; metric measurement]
Category: All,Helio,Magnetism
Students use two images from the Solar Dynamics Observatory to estimate the speed of the X-class solar flare on March 6, 2012.
Problem 466: Exploring the Solar Wind and Coronal Mass Ejections
[Grade:3-5 | Topics: scale models; proportions; fractions]
Category: All,Helio,Solar System
Students use two images of the solar storm during March 2012 to estimate the speed of the solar wind and a coronal mass ejection. They also estimate arrival times for the CME at Earth and Neptune.
Problem 465: Comparing Planets Orbiting other Stars
[Grade:3-5 | Topics: scale models; proportions; fractions]
Category: All,Solar System,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.
Problem 464: Big Moons and Small Planets
[Grade:3-5 | Topics: scale models; proportions; fractions]
Category: All,Helio
Students work with a scaled drawing of 26 large moons in the solar system, and together with an exercise in using simple fractions, explore the relative sizes of the moons compared to Earth.
Problem 463: A Simple Fuel Gauge in a Cylindrical Tank
[Grade:7-9 | Topics: VOlume of cylinder; proportions]
Category: All,Miscellaneous
Rockets use fuel tanks that can be approximated as cylinders. In this simple geometric exercise, students work the formula for the volume of a cylinder to add a fuel gauge at the right level to indicate how much fuel remains.
Problem 462: Using a Gravity Lens to Weigh a Cluster of Galaxies
[Grade:9-12 | Topics: algebra; Scientific Notation]
Category: All,Universe
Students explore how the geometry of a gravity lens can be used to measure the mass of the object producing the gravity.
Problem 461: Cassini Delivers Holiday Treats from Saturn
[Grade:7-9 | Topics: scale models; proportions]
Category: All,Solar System
Students explore proportions and angular size using images of Saturn's moons Titan and Dione
Problem 460: Fermi Explores the High-Energy Universe
[Grade:6-8 | Topics: percentages; pie graphs]
Category: All,Universe
Students work with percentages to explore the identities of the 1873 gamma-ray sources detected by NASAs Fermi Observatory
Problem 459: A piece of history - space shuttle thermal tiles
[Grade:6-8 | Topics: mass = density x volume; metric conversion]
Category: All,Rockets
Students explore volume density and mass using the Space Shuttle thermal tiles. Get your own free tile from NASA too!
Problem 458: Playing Baseball on the Earth-like Planet Kepler-22b!
[Grade:8-10 | Topics: scale models; proportions; scientific notation; metric math; Evaluating equations]
Category: All,Solar System,Stars
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!
Problem 457: The Interplanetary Voyage of MSL
[Grade:10-11 | Topics: Geometry: properties of ellipses]
Category: All,Solar System
Students use the properties of ellipses to determine the formula for the Hohmann Transfer Orbit taking the Mars Science Laboratory to Mars in 2012.
Problem 456: The Launch of the Mars Science Laboratory (MSL) in 2011
[Grade:8-10 | Topics: time=distance/speed; scale models; metric math]
Category: All,Solar System,Rockets
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.
Problem 455: The Night Launch of STEREO in 2006
[Grade:8-10 | Topics: time=distance/speed; scale models; metric math; equation of a parabola; curve fitting]
Category: All,Rockets
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.
Problem 454: The Closest Approach of Asteroid 2005YU55 - III
[Grade:8-10 | Topics: time=distance/speed; scale models; metric math]
Category: All,Solar System
Students work with the equation of a circle and line to find the orbit intersection points, midpoint, and closest distance to earth.
Problem 453: The Closest Approach of Asteroid 2005YU55 - II
[Grade:6-8 | Topics: angular measure; time=distance/speed; scale models; metric math]
Category: All,Solar System
Students work with the properties of circles and angular measure to see where the moon will be at the start of the asteroid encounter.
Problem 452: The Closest Approach of Asteroid 2005YU55 - I
[Grade:6-8 | Topics: time=distance/speed; scale models; metric math]
Category: All,Solar System
Students work with a scaled drawing of the orbit of the moon and the asteroid trajectory to predict where the asteroid will be relative to earth and the orbit of the moon.
Problem 451: The Spectacular Cat's Eye Planetary Nebula
[Grade:6-8 | Topics: time=distance/speed; scale models; metric math]
Category: All,Solar System,Stars
Students measure the diameter of the nebula and use speed information to estimate the age of the nebula
Problem 450: Mapping Dark Matter in a Distant Cluster
[Grade:8-10 | Topics: Volume of a sphere; shells; density]
Category: All,Universe
Students explore the changing density of dark matter within a distant cluster of galaxies to see if the density of dark matter is uniform inside the cluster.
Problem 449: A simple model for the origin of Earth's ocean water
[Grade:8-10 | Topics: volume of a sphere; rates of change]
Category: All,Solar System
Students create a simple model of the arrival of water to Earth using three sizes of cometary bodies and their arrival rates.
Problem 448: The Declining Arctic Ice Cap During September
[Grade:9-11 | Topics: Statistics; Regression; graphing tabular data]
Category: All,Miscellaneous
Students graph the change in Arctic ice surface area, and perform linear and quadratic regressions to model and forecast trends.
Problem 447: The Arctic's Vanishing Ozone Layer
[Grade:9-11 | Topics: Regression; graphing tabular data]
Category: All,Miscellaneous
Students use ozone data for the Arctic region between 1979 and 2011 to graph the tabulated data, perform simple regression analysis, and forecast trends into the future. How much will there be in the year 2030?
Problem 446: Arctic Ozone Hole Continues to Grow in 2011
[Grade:6-8 | Topics: Area of rectangle; volume; percentage]
Category: All,Universe
Students estimate the area of the Arctic ozone hole, and work with the concept of parts-per-million to estimate total ozone volume lost.
Problem 445: LRO - The relative ages of lunar surfaces
[Grade:6-8 | Topics: scale; histogramming]
Category: All,Solar System
Students examine two Apollo landing areas using images from the LRO spacecraft to estimate the relative ages of the two regions using crater counting.
Problem 444: Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine - II
[Grade:6-8 | Topics: comparing two sequences of numbers; patterns, Least Common Multiple]
Category: All,Stars
Students determine how often the two stars Kepler 16 A and B will line up with Tatooine on the same day of the year.
Problem 443: Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine - I
[Grade:6-9 | Topics: angle measure; angular speed]
Category: All,Solar System,Stars
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'.
Problem 442: Modeling the Atmospheric Re-entry of UARS
[Grade:8 - 11 | Topics: graphing data; linear equations; exponential and power functions]
Category: All,Miscellaneous
Students graph the altitude of the UARS satellite in the weeks before re-entry 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.
Problem 441: Exploring the new planet Kepler 16b called 'Tatooine'
[Grade:8-10 | Topics: angle measure; tangent]
Category: All,Solar System,Stars
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!!
Problem 440: LRO explores the Apollo 12 landing area on the moon
[Grade:6-8 | Topics: image scale; metric measurement]
Category: All,Solar System
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.
Problem 439: Chandra Sees a Distant Planet Evaporating
[Grade:6-8 | Topics: Scientific Notation; Rate = Amount/Time]
Category: All,Solar System
The planet CoRot2b is losing mass at a rate of 5 million tons per second. Students estimate how long it will take for the planet to lose its atmosphere
Problem 438: The Last Flight of the Space Shuttle Endeavor
[Grade:6-8 | Topics: tabular data, graphing, metric measurement, speed=distance/time]
Category: All,Rockets
Students use tabular data and graphing to determine the launch speed and acceleration of the Space Shuttle from the launch pad.
Problem 437: Saturn V Rocket Launch Speed and Height
[Grade:6-8 | Topics: tabular data, graphing, metric measurement, speed=distance/time]
Category: All,Solar System,Rockets
Students use tabular data to determine the launch speed of the Saturn V rocket from the launch pad.
Problem 436: Space Shuttle Challenger Deploys the INSAT-1B Satellite
[Grade:6-8 | Topics: scale, metric measurement, speed=distance/time]
Category: All,Rockets
Students use a sequence of images to determine the launch speed of the satellite from the Space Shuttle cargo bay.
Problem 435: Apollo-17 Launch from Lunar Surface
[Grade:6-8 | Topics: scale, metric measurement, speed=distance/time]
Category: All,Solar System,Rockets
Students use a sequence of images to determine the speed of ascent of the Apollo-17 capsule from the lunar surface.
Problem 434: Dawn Spacecraft Sees Asteroid Vesta Up-Close!
[Grade:6-8 | Topics: scale, metric measurement]
Category: All,Solar System,Rockets
Students use an image of the asteroid to determine the diameters of craters and mountains using a millimeter ruler and the scale of the image in meters per millimeter.
Problem 433: Space Shuttle Atlantis - Plume Speed
[Grade:6-8 | Topics: scale, metric measurement, speed=distance/time]
Category: All,Rockets
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.
Problem 432: Space Shuttle Atlantis - Exhaust Speed
[Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time]
Category: All,Rockets
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.
Problem 431: Space Shuttle Atlantis - Launch Speed
[Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time]
Category: All,Rockets
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.
Problem 430: Space Shuttle Atlantis - Ascent to Orbit
[Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time]
Category: All,Rockets
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.
Problem 429: Tracking a Sea Turtle from Space
[Grade: 4-6| Topics: scale, metric measurement, speed=distance/time]
Category: All,Miscellaneous
The latitude, longitude, elapsed time and distance traveled are provided in a table. Students use the data to determine the daily and hourly speed of a leatherback turtle as it travels from New Zealand to California across the Pacific Ocean.
Problem 428: Meteorite Compositions: A matter of density
[Grade:8-10 | Topics: density; mass = density x volume; percentages]
Category: All,Helio
Astronomers collect meteorites to study the formation of the solar system 4.5 billion years ago. In this problem, students study the composition of a meteorite in terms of its density and mass, and the percentage of iron and olivine to determine the volumes occupied by each ingredient.
Problem 427: A Black Hole - Up Close
[Grade:9-12 | Topics: Evaluating an equation with one variable; square roots; metric units; nanometers]
Category: All,Universe
Students explore how the color of a light bulb changes as it gets close to a black hole, demonstrating the principle of the gravitational 'red shift'.
Problem 426: Black Holes - Hot Stuff!
[Grade:9-12 | Topics: Evaluating an equation with one variable; fractional exponents]
Category: All,Universe
Students explore the temperature of matter falling into a black hole using a simple equation to calculate the gas temperature at different distances.
Problem 425: Exploring a Full-sized Black Hole
[Grade:6-8 | Topics: Evaluating an equation with one variable; square roots; speed = distance/time; circumference of a circle]
Category: All,Universe
Students explore how the speed of an orbiting satellite changes if it were near a black hole with five times the mass of our Earth.
Problem 424: Exploring Black Holes
[Grade:3-5 | Topics: working with a compass and metric ruler]
Category: All,Helio
Students compare the sizes of the planets in our solar system if they were actually black holes. They use a compass and metric ruler to create circles that are the actual sizes of the 'black hole' planets.
Problem 423: The Moon as a Black Hole
[Grade:3-5 | Topics: Working with a compass; metric ruler]
Category: All,Solar System,Universe
Students draw a life-sized model of the Earth and Moon as two black holes to explore the actual sizes of these exotic astronomical bodies.
Problem 422: Supercomputers: Getting the job done FAST!
[Grade:6-8 | Topics: algebra]
Category: All,Miscellaneous
Students use a simple counting problem to explore how much faster a supercomputer is compared to as hand-calculation.
Problem 421: The Lense-Thirring Effect Near the Sun and a Neutron Star
[Grade:9-12 | Topics: algebra; scientific notation, angular measure]
Category: All,Helio
Students work with a formula for the Lense-Thirring Effect and estimate how large it will be in orbit around our sun, and in the intense gravitational field of a dense neutron star.
Problem 420: Gravity Probe B: Testing Einstein again!
[Grade:9-12 | Topics: algebra; scientific notation, angular measure]
Category: All,Miscellaneous
Students learn about the Lense-Thirring Effect, and calculate its magnitude near Earth's orbit using an algebraic equation with integer and fractional exponents.
Problem 419: The Space Shuttle: Fly me to the moon?
[Grade:6-8 | Topics: amount = rate x time ]
Category: All,Solar System,Rockets
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.
Problem 418: Supercomputers: Modeling colliding neutron stars!
[Grade:8-10 | Topics: distance=speed x time; scale model; triangle and circle geometry; circumference]
Category: All,Universe
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.
Problem 417: Estimating the Size and Mass of a Black Hole
[Grade:8-10 | Topics: distance=speed x time]
Category: All,Universe
Students use a simple formula to estimate the size of a black hole located 3.8 billion light years from Earth, recently studied by NASA's Chandra and Swift satellites.
Problem 416: Kepler probes the interior of red giant stars
[Grade:8-10 | Topics: geometry of circles and arcs; distance=speed x time]
Category: All,Stars
Students use the properties of circular arcs to explore sound waves inside stars.
Problem 415: Mercury and the Moon - Similar but different
[Grade:8-10 | Topics: scale; volume of a sphere; mass = density x volume]
Category: All,Solar System
Students explore the mass and volume of mercury compared to the moon by using the formula for a sphere and scale changes.
Problem 414: Radiation Dose and Distance
[Grade:9-12 | Topics: unit conversions; amount=rate x time; graphing Log-Log data]
Category: All,Miscellaneous
Students explore the dosimetry from the Japan 2011 Earthquake and graph the decline of the radiation dose rates with distance from the nuclear reactors.
Problem 413: Exploring Nuclear Decay and Radiation Dose
[Grade:9-12 | Topics: unit conversions; amount=rate x time; Solving exponential equations in base-e]
Category: All,Miscellaneous
Students compare the dose rates measured from the same location in Japan on two different days, then determine the half-life of the radioisotope causing the radiation exposure by comparing the derived half-life with those of Cesium-137 and Iodine-131.
Problem 412: Radiation Dose and Dose Rate
[Grade:6-8 | Topics: unit conversions; amount=rate x time]
Category: All,Miscellaneous
Students use radiation measurements across Japan to calculate the total absorbed doses from the 2011 nuclear reactor failures. They also calculate the total dose for passenger trips on jets and the Concorde.
Problem 411: Lifestyles and Radiation Dose
[Grade:6-8 | Topics: unit conversions; amount=rate x time]
Category: All,Miscellaneous
Students see how the kind of lifestyle you lead determines most of your annual absorbed radiation dose. Some factors are under your control, and some are not.
Problem 410:Exploring Radiation in your Life
[Grade:6-8 | Topics: unit conversions; amount=rate x time]
Category: All,Miscellaneous
Students use a pie grap to calculate the total dose and dose rate for various factors that determine your annual radiation exposure while living on Earth.
Problem 409: The 2011 Japan Earthquake Rocks the Earth
[Grade:9-12 | Topics: Algebra; evaluating an equation]
Category: All,Miscellaneous
Using a simple physical model, students explore the principle by which the Japan Earthquake of 2011 caused Earth's rotation to spin up by 1.8 microseconds.
Problem 408: Estimating the Speed of a Tsunami
[Grade:6-8 | Topics: Time arithmetic; time zones; speed = distance/time]
Category: All,Miscellaneous
Students use the tsunami arrival times and earthquake start time for the devastating 2011 Japan Earthquake to estimate the speed of a tsunami as it crosses the Pacific Ocean to make landfall in Hawaii and California.
Problem 407: Cryo-testing the Webb Space Telecope ISIM
[Grade:6-8 | Topics: scale models; proportions; unit conversion]
Category: All,Rockets
Students explore scaling by creating an enlarged geometric model of the ISIM to better appreciate the small changes due to expansion and contraction
Problem 406: Growing Grapes in the Middle of the Desert
[Grade:6-8 | Topics: areas of irregular regions; unit conversion]
Category: All,Solar System
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
Problem 405: Discovering Earth-like Worlds by their Color
[Grade:6-8 | Topics: graphing tabular data; interpreting graphical data]
Category: All,Helio
Students use recent measurements of the reflected light from solar system bodies to graph their colors and to use this in classifying new planets as Earth-like, moon-like or Jupiter-liike
Problem 404: STEREO Spacecraft give 360-degree Solar View
[Grade:6-8 | Topics: angular measure, extrapolation; distance = speed x time]
Category: All,Helio,Solar System,Rockets
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.
Problem 403: The Goldilocks Planets - Not too hot or cold
[Grade:6-8 | Topics: Averaging; histogramming]
Category: All,Solar System,Universe
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.
Problem 402: Kepler- Earth-like planets by the score! II
[Grade:6-8 | Topics: Percentage; re-scaling sample sizes]
Category: All,Universe
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.
Problem 401: Kepler - Earth-like planets by the score! I
[Grade:6-8 | Topics: Percentage; histograms; Re-scaling sample sizes]
Category: All,Universe
Students use recent Kepler satellite data to estimate the number of Earth-like planets in the Milky Way galaxy.
Problem 400: The Most Distant Objects in the Universe
[Grade:6-8 | Topics: Working with millions and billions; elapsed time]
Category: All,Universe
Students use a table of the most distant known events and objects in the universe to create a timeline of the universe soon after the Big Bang.
Problem 399: A Galactic City in the Far Reaches of the Universe
[Grade:6-8 | Topics: Scale; proportion; metric measurement; unit conversion]
Category: All,Universe
Students work with an image of a distant cluster of galaxies to determine its scale compared to nearby galaxies.
Problem 398: The Crab Nebula - Exploring a pulsar up close!
[Grade:6-8 | Topics: Scale drawings; unit conversion; distance = speed x time]
Category: All,Stars
Students work with a photograph to determine its scale and the time taken by light and matter to reach a specified distance from the pulsar.
Problem 397: The Changing Pace of Global Warming
[Grade:8-10 | Topics: Graphing tabular data; linear extrapolation; equation of a line y=mx+b]
Category: All,Solar System,Universe
Students work with a table of global temperatures to forecast the temperature change by 2050 using a linear extrapolation.
Problem 396: Kepler 10b - A matter of gravity
[Grade:8-10 | Topics: Evaluating formulas; mass = density x volume; volume of a sphere; scientific notation]
Category: All,Solar System
Students use the measured properties of the Earth-like planet Kepler 10b to estimate the weight of a human on its surface.
Problem 395: Death Stars
[Grade:6-9 | Topics: Scientific Notation; percentages; rates of change]
Category: All,Stars
Some stars create super-flares that are capable of eliminating life on planets that orbit close to the star. Students learn about these flares on common red-dwarf stars and compare them to flares on our own sun
Problem 394: Probing the lunar core using seismology
[Grade:9-10 | Topics: Geometry; Properties of Inscribed Arcs]
Category: All,Solar System
Students learn about the geometry needed to determine the diameter of the lunar core using a simplified model.
Problem 393: Taking a stroll around a martian crater!
[Grade:6-8 | Topics: scale model; distance = speedxtime; metric measure]
Category: All,Solar System
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.
Problem 392: Exploring the DNA of an organism based upon arsenic.
[Grade:8-10 | Topics: Integer math; percentages]
Category: All,Miscellaneous
Students estimate the increase in the mass of the DNA from an arsenic-loving bacterium in which phosphorus atoms have been replaced with arsenic.
Problem 391: Investigating the atmosphere of Super-Earth GJ-1214b
[Grade:6-8 | Topics: graphing functions; evaluating functions for given values; volume of a sphere; mass = densityxvolume]
Category: All,Miscellaneous
Students investigate a simple model for the interior of an exoplanet to estimate the thickness of its atmosphere given the mass size and density of the planet.
Problem 390: X-rays from hot gases near the black hole SN1979c
[Grade:8-10 | Topics: Functions; substitution; evaluation]
Category: All,Universe
Students use two functions to estimate the size of a black hole from the gas emitting x-rays which is flowing into it.
Problem 389: Estimating the diameter of the SN1979c black hole
[Grade:6-8 | Topics: evaluating linear functions; integer math; metric units]
Category: All,Universe
Students use simple equations to learn about the various definitions for the sizes of black holes in terms of their event horizons, last photon orbit, and last stable particle orbit radii, and apply this to the recently discovered 'baby' black hole in the galaxy M-100
Problem 388: Hubble Detects More Dark Matter
[Grade:8-10 | Topics: evaluating functions; Scientific notation]
Category: All,Universe
Students learn about how astronomers estimate the amount of invisible dark matter in a cluster of galaxies by comparing its visible mass against the speeds of the galaxies to 'weigh' the cluster'
Problem 387: A Mathematical Model of Water Loss from Comet Tempel-1
[Grade:8-10 | Topics: graphing; fitting a parabola to data; evaluating functions]
Category: All,Solar System
Students use data from the Deep Impact spacecraft to create a simple empirical model for predicting the rate of water loss from a comet based on actual data.
Problem 386: Whacky Spacecraft Orbits - They only seem crazy!
[Grade:6-8 | Topics: distance=speedxtime; scientific notation; unit conversion]
Category: All,Solar System
Students investigate the loopy orbit of the THEMIS/Artemis spacecraft as they are being inserted into lunar orbit. To save fuel, their orbits take them on a complicated path in space.
Problem 385: Gamma Ray Bubbles in the Milky Way
[Grade:8-10 | Topics: scale model; scientific notation; unit conversion]
Category: All,Universe
Students use the recent Fermi image of the gamma ray bubbles in the nucleus of the Milky Way to study their sizes and other properties.
Problem 384: Detecting the Most Distant SUpernova in the Universe
[Grade:6-8 | Topics: Analyzing a graph; interpreting mathematical models]
Category: All,Stars,Universe,Rockets,Telescopes
Students use a graph to compare the brightness of supernova produced by three different masses of stars, and predict whether the Webb Space Telescope can see them.
Problem 383: Estimating the mass of Comet Hartley 2 using calculus.
[Grade:12 | Topics: Volume integral using disk method; scale model; scientific notation; unit conversion]
Category: All,Solar System
Students use a recent image of the nucleus of Comet Hartley 2 taken by the Deep Impact/EPOXI camera and a shape function described by a fourth-order polynomial to calculate the volume of the comet's head using integral calculus to estimate the volume of the comets nucleus, and its total mass,
Problem 382: Estimating the mass and volume of Comet Hartley 2.
[Grade:8-10 | Topics: volume of a sphere and cylinder; scale model; scientific notation; unit conversion]
Category: All,Solar System
Students use a recent image of the nucleus of Comet Hartley 2 taken by the Deep Impact/EPOXI camera and a simple geometric 'dumbell' model based on a cylinder and two spheres, to estimate the volume of the comets nucleus, and its total mass.
Problem 381: The Cosmological Redshift - Changing the light from a galaxy.
[Grade:8-10 | Topics: solving a simple equation for X]
Category: All,Universe
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.
Problem 380: Seeing the Distant Universe Clearly
[Grade:7-9 | Topics: solving a simple equation for X; angular measure; Scientific Notation]
Category: All,Universe,Telescopes
Students calculate the angular sizes and scales of distant objects to study how different sized telescopes see details with varying degrees of clarity.
Problem 379: Exploring the Cosmos with Supercomputers
[Grade:7-9 | Topics: scale model; proportions; Scientific Notation]
Category: All,Miscellaneous
Students use two images created by a supercomputer calculation to explore the size and accuracy of computer models of the distanct universe.
Problem 378: LRO Makes a Temperature Map of the Lunar South Pole
[Grade:7-9 | Topics: Volume of a circular disk; scale models]
Category: All,Solar System
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.
Problem 377: Deep Impact: Approaching Comet Hartley-2
[Grade:8-10 | Topics: linear modeling from data; inverse-square law]
Category: All,Solar System
Students use data for the brightness of Comet Hartley-2 measured by the Deep Impact spacecraft to create a linear equation for its approach distance, and use the inverse-square law to estimate its brightness on October 13, 2010.
Problem 376: The Earth-like Planet Gliese 518g
[Grade:3-5 | Topics: scale models; measurement]
Category: All,Solar System
Students use data for the Gliese 581 planetary system to draw a scaled model of the locations and sizes of the discovered planets. They also identify the location and span of the Habitable Zone for this planetary system.
Problem 375: Terra Satellite Measures Dangerous Dust
[Grade:8-10 | Topics: unit conversion; scientific notation; mass=densityxvolume]
Category: All,Miscellaneous
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.
Problem 374: Deep Impact - Closing In on Comet 103P/Hartley 2
[Grade:8-10 | Topics: Scaled images; trigonometry; angle measure]
Category: All,Solar System
Students use the Tangent formula to figure out the angular size of the comet at closest approach, and the scale of the HRI camera image.
Problem 373: Solar Probe Plus - Having a hot time near the sun!
[Grade:8-10 | Topics: Evaluating a function; square roots and forth roots]
Category: All,Helio
Students use a simple equation to estimate the temperature reached by the Solar Probe Plus spacecraft as it gets close to the sun.
Problem 372: LRO Determines Lunar Cratering History
[Grade:6-8 | Topics: Scaled images; probability; percentages]
Category: All,Solar System
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.
Problem 371: Close Encounters of the Asteroid Kind!
[Grade:8-10 | Topics: Evaluating a base-10 power function; graphing; astronomical brightness scale]
Category: All,Solar System,Telescopes
On September 8, 2010 two small asteroids came within 80,000 km of Earth. Their small size of only 15 meters made them very hard to see without telescopes pointed in exactly the right direction at the right time. In this problem, based on a NASA press release, students use a simple formula to calculate the brightness of these asteroids from their distance and size.
Problem 370: 6-fold Symmetry and the Webb Space Telescope Mirror
[Grade:8-10 | Topics: Properties of Hexagons; rotation symmetry; counting; tiling]
Category: All,Rockets,Telescopes
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
Problem 369: Scaling Up the Webb Space Telescope Mirror
[Grade:8-10 | Topics: Properties of Hexagons and triangles; counting; evaluating a formula; tiling]
Category: All,Rockets,Telescopes
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.
Problem 368: The Hexagonal Tiles in the Webb Space Telescope Mirror
[Grade:8-10 | Topics: Properties of Hexagons and triangles; counting]
Category: All,Rockets,Telescopes
Students learn about the Webb Space Telescopes segmented mirror by studying the geometry of hexagons.
Problem 367: Significant Figures...Oh My!
[Grade:8-10 | Topics: Significant figures; rounding; decimal math; scientific notation; evaluating a function]
Category: All,Miscellaneous
Students work with the basic rules of significant figures to evaluate a formula. Exercises also ask students to state the number of SFs in some simple numbers for review.
Problem 366: Solar Probe Plus - Working with angular diameter
[Grade:8-10 | Topics: angular measure; tangent formula; angular size]
Category: All,Helio
Students use the tangent formula to determine the angular diameter of the sun as seen by the Solar Probe Plus spacecraft as it approaches the sun.
Problem 365: Terra Spies a Major Glacier Break-up
[Grade:8-10 | Topics: image scales; speed = distance/time; unit conversions]
Category: All,Miscellaneous
Students use two images from the Terra MODIS instrument to determine the scale of the glacier and the number of cubic kilometers and gallons of fresh water that were 'calved'
Problem 364: The Cometary Planet HD209458b
[Grade:9-12 | Topics: Scientific Notation; volume of a sphere; density; rates]
Category: All,Solar System,Stars,Telescopes
Astronomers using NASA's Hubble Space Telescope have confirmed that this gas giant planet is orbiting so close to its star its heated atmosphere is escaping into space.
Problem 363: Celestial Fireworks Near NGC3603
[Grade:9-12 | Topics: Scientific Notation; evaluating functions; density]
Category: All,Stars
This young star cluster, barely one million years old, is furiously evaporating the clouds of interstellar gas and dust from which it formed.
Problem 362: Hinode Discovers the Origin of White Light Flares
[Grade:9-12 | Topics: Image scale; Algebra; Scientific Notation]
Category: All,Magnetism
A study of the magnetic energy of a flare
Problem 361: The Sky is Falling? Well...not quite!
[Grade:9-12 | Topics: Algebra; Scientific Notation; exponential functions]
Category: All,Miscellaneous
The recent report that the upper atmosphere has collapsed is investigated
Problem 360: Kepler's First Look at 700 Transiting Planets
[Grade:6-8 | Topics: Percentages; area of circle]
Category: All,Miscellaneous
A statistical study of the 700 transits seen during the first 43 days of the mission.
Problem 359: The Most Massive Stars Known
[Grade:9-12 | Topics: Scaling and proportions; Evaluating a function]
Category: All,Stars
A study of the lifespans of the most massive stars known.
Problem 358: A Flyby of Asteroid Lutetia
[Grade:6-8 | Topics: image scale; Pythagorean Theorem; rates]
Category: All,Solar System
The Rosette mission flew by an asteroid. An application of the Pythagorean Theorem and angular size.
Problem 357: The Fastest Sea Level Rise in the United States
[Grade:6-8 | Topics: fitting linear equations to graphical data]
Category: All,Solar System,Universe
Global climate change is causing measurable sea level changes. Which part of the United States is sinking the fastest?
Problem 356: Calculating Molecular Mass
[Grade:6-8 | Topics: Counting; Scientific Notation]
Category: All,Miscellaneous
Students count hydrogen, carbon and oxygen atoms in a molecule of adefovir dipivoxil and calculate its mass and formula.
Problem 355: Astronaut Bone Loss
[Grade:6-8 | Topics: Rates; linear equations]
Category: All,Miscellaneous
From a graph, students predict how much bone loss an astronaut experiences during a long-duration stay in space.
Problem 354: Earth's Polar Wander - The Chandler Wobble
[Grade:6-8 | Topics: Graphing ordered pairs]
Category: All,Miscellaneous
Students plot the circular shape of the track of the North Pole during a 2-year period and estimate the speed of movement.
Problem 353: Dwarf Planets and Kepler's Third Law
[Grade:9-12 | Topics: Fitting functions to data; Evaluating a polynomial]
Category: All,Helio
Students plot the distance versus period relationship for planets and minor bodies in the solar system and fit it to two functions to determine Kepler's Third Law.
Problem 352: Exponential Functions and Atmospheric 'Scale heights'
[Grade:9-12 | Topics: Scientific Notation; evaluating exponential functions; Optional calculus]
Category: All,Miscellaneous
A study of the way a planet's atmosphere changes as its temperature is changed using exponential functions.
Problem 351: Counting Atoms in Molecules
[Grade:3-5 | Topics: Counting; multiplication]
Category: All,Miscellaneous
Students count the number of atoms of various elements in a molecule of inositol nicotinate to deduce the molecule's formula and mass.
Problem 350: Estimating the Temperatures of Exoplanets
[Grade:9-12 | Topics: Equation of ellipse; evaluating functions]
Category: All,Miscellaneous
Students review the basic properties of ellipses by exploring the orbits of newly-discovered planets orbiting other stars. They also use a simple formula to determine the temperatures of the planets from their orbits.
Problem 349: Exoplanet Orbits and the Properties of Ellipses
[Grade:9-12 | Topics: Properties of ellipses]
Category: All,Miscellaneous
Given the formula for the orbits of newly-discovered planets, students determine the basic properties of the elliptical orbits for the planets.
Problem 348: Taking a Log-Log Look at the Universe
[Grade:9-12 | Topics: Base-10 logarithms; graphing logarithmic data]
Category: All,Universe
The size and mass of various astronomical objects is plotted on a Log-Log graph to explore the various physical scales in the universe, and what combinations are excluded.
Problem 347: More Molecular Madness!
[Grade:3-5 | Topics: Counting; multiplication]
Category: All,Miscellaneous
Students count the number of atoms in a molecule of ciprofloaxcin to determine its chemical formula and mass.
Problem 346: The International Space Station and a Sunspot: Exploring angular scales
[Grade:9-12 | Topics: Similar triangles; angular measure]
Category: All,Helio,Rockets
An amateur photograph of the International Space Station crossing in front of the sun is analyzed to determine the scales of sunspots.
Problem 345: How many stars are there?
[Grade:6-8 | Topics: Scaling; unit conversion; angular measure]
Category: All,Stars
A starfield image taken by the 2MASS survey is analyzed to estimate how many stars are in the sky.
Problem 344: Hubble Spies an Asteroid - Yes it does move!
[Grade:6-8 | Topics: Scaling; unit conversion; speed=distance/time]
Category: All,Solar System,Universe
The track of an asteroid in a Hubble image of a cluster of galaxies is analyzed to determine speed of the asteroid.
Problem 343: The Oldest Lunar Rocks
[Grade:3-5 | Topics: Ordering numbers; averaging]
Category: All,Solar System
A list of the ages of the oldest lunar rock samples is grouped into families with about the same average ages to estimate the age of the lunar mare.
Problem 342: The Rate of Oil Leakage in the Gulf Oil Spill of 2010
[Grade:6-8 | Topics: unit conversions; rates; image scale]
Category: All,Miscellaneous
Students use still images from a video of the oil emitted by the leaking British Petrolium oil well in the Gulf of Mexico to estimate the rate of oil leakage in gallons per day.
Problem 341: Recent Events: A Perspective on Carbon Dioxide
[Grade:6-8 | Topics: unit conversions; rates ]
Category: All,Solar System
Students compare the carbon dioxide generated by the 2010 Icelandic volcano and the Gulf Oil Spill to see the relative contributions to the atmosphere of a natural and man-made catastrophe.
Problem 340: Computing the Orbit of a Comet
[Grade:10-12 | Topics: ellipses; solving quadratic systems; fitting ellipse to data points ]
Category: All,Solar System
Students use data from the orbit of Halley's Comet to determine the equation for its elliptical orbit.
Problem 339: Terra Satellite Spies the Great Gulf Oil Catastrophe of 2010
[Grade:6-8 | Topics: image scales; area of a circle; metric conversions ]
Category: All,Miscellaneous
Students use a Terra satellite image of the oil slick in the Gulf of Mexico to calculate its area, mass and thickness.
Problem 338: Asteroids and Ice
[Grade:9-12 | Topics: mass=densityxvolume; volume of a spherical shell]
Category: All,Solar System
Students calculate how much ice may be present on the asteroid 24-Themis based on recent discoveries by NASA
Problem 337: SDO Reveals Details on the Surface of the Sun
[Grade:6-8 | Topics: image scales; proportions]
Category: All,Helio
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.
Problem 336: SDO: Measuring the Speed of an Eruptive Prominence
[Grade:6-8 | Topics: image scales; speed=distane/time ]
Category: All,Helio
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.
Problem 335: Methane Lakes on Titan
[Grade:6-8 | Topics: estimating irregular areas; calculating volume from area x height; scaled images ]
Category: All,Solar System
Students use a recent Cassini radar image of the surface of Titan to estimate how much methane is present in the lakes that fill the image, and compare the volume to that of the fresh water lake, Lake Tahoe.
Problem 334: Solar Dynamics Observatory: Working with Giga, Tera, Peta and Exabytes
[Grade:8-12 | Topics: powers of ten; time conversion: seconds, minutes, days, years]
Category: All,Helio,Rockets
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.
Problem 333: Hubble: Seeing a Dwarf Planet Clearly
[Grade:8-12 | Topics: scales and ratios; volume of sphere; density=mass/volume]
Category: All,Solar System
Based on a recent press release, students use the published photos to determine the sizes of the smallest discernible features and compare them to the sizes of the 48-states in the USA. They also estimate the density of Pluto and compare this to densities of familiar substances to create a 'model' of Pluto's composition. A supplementary Inquiry Problem asks students to model the interior in terms of two components and estimate what fraction of Pluto is composed of rock or ice.
Problem 332: Hubble: The Changing Atmosphere of Pluto
[Grade:10-12 | Topics: properties of ellipses; evaluating an algebraic function ]
Category: All,Solar System
Based on a recent press release, students determine the aphelion and perihelion of Pluto's elliptical orbit using the properties of ellipses, then calculate the temperature of Pluto at these distances to estimate the thickness of Pluto's atmosphere and its changes during its orbit around the sun.
Problem 331: Webb Space Telescope: Detecting dwarf planets
[Grade:9-12 | Topics: Evaluating square-roots and base-e exponentials]
Category: All,Helio,Solar System,Rockets
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.
Problem 330: Fermi Detects Gamma-rays from the Galaxy Messier-82
[Grade:10-12 | Topics: power-laws; log-log graphing; linear regression]
Category: All,Universe
Based on a recent press release, students work with a log-log plot to show that straight lines on this plot represent power-law functions. They use this fact to determine, by interpolation, the strength of the gamma-rays from this galaxy.
Problem 329: WISE and Hubble: Power Functions: A question of magnitude
[Grade:10-12 | Topics: base-10, evaluating power functions ]
Category: All,Stars
Students explore the function F(x) = 10^-ax and learn about the stellar magnitude scale used by astronomers to rank the brightness of stars.
Problem 328: WISE: F(x)G(x): A Tale of Two Functions
[Grade:10-12 | Topics: Power-law functions; domain and range; graphing; areas under curves; integration]
Category: All,Miscellaneous
Students use WISE satellite data to study a practical application of the product of two finctions by graphing them individually, and their product. A calculus-level problem is included for advanced students.
Problem 327: WISE: Exploring Power-law Functions Using WISE Data
[Grade:10-12 | Topics: areas; functions; histograms; unit conversion; power-laws; integration]
Category: All,Stars
Based on a recent press release of the 'First Light' image taken with NASA's new WISE satellite, students explore a practical application of a power law function to count the number of stars in the sky. An additional calculus-level problem is included for advanced students.
Problem 326: Hubble Spies Colliding Asteroids
[Grade:8-12 | Topics: Volume of a thin disk; Algebra 1; Evaluating a definite integral; power-law]
Category: All,Solar System
Based on a recent press release, students calculate how often asteroids collide in the Asteroid belt using a simple formula. Students estimate belt volume, and asteroid speeds to determine the number of years between collisions. They also investigate how the collision time depends on the particular assumptions they made. An 'extra' integration problem is also provided for calculus students.
Problem 325: Kepler Spies Five New Planets
[Grade:4-6 | Topics: Counting; graphing; area of a square]
Category: All,Stars
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.
Problem 324: Deep Impact Comet Flyby
[Grade:9-12 | Topics: Algebra, geometry, differential calculus]
Category: All,Solar System
The Deep Impact spacecraft flew by the Comet Tempel-1 in 2005. Students determine the form of a function that predicts the changing apparent size of the comet as viewed from the spacecraft along its trajectory.
Problem 323: How Many Quasars are There?
[Grade:11-12 | Topics: Piecewise functions; integral calculus]
Category: All,Universe
Students use a piecewise function that estimates how many quasars are found in a given area of the sky. The function is integrated to determine the estimated total number of quasars across the entire sky.
Problem 322: Rotation Velocity of a Galaxy
[Grade:10-12 | Topics: Algebra, limiting form of functions; derivitives]
Category: All,Stars,Universe
Students examine a simple model of the rotation of a galaxy to investigate how fast stars orbit the centers of galaxies in systems such as the Milky Way and Messier-101.
Problem 321: Lunar Crater Frequency Distributions
[Grade:11-12 | Topics: Integral calculus]
Category: All,Solar System
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.
Problem 320: Star Light...Star Bright
[Grade:10-12 | Topics: Algebra II; Polynomials; maxima and minima]
Category: All,Stars
A simple polynomial function is used to determine the temperature of a star from its brightness at two different visible wavelengths.
Problem 319: How Many Stars Are In the Sky?
[Grade:10-12 | Topics: Log Functions; Polynomials]
Category: All,Stars
A simple polynomial is used to determine how many stars are in the sky.
Problem 318: The Internal Density and Mass of the Sun
[Grade:11-12 | Topics: Algebra II; Polynomials; integral calculus]
Category: All,Helio
Students use a simple, spherically symmetric, density profile to determine the mass of the sun using integral calculus.
Problem 317: The Global Warming Debate and the Arctic Ice Cap
[Grade:9-11 | Topics: Modeling data with linear equations; forecasting]
Category: All,Solar System,Universe
Students use graphical data showing the area of the Arctic Polar Cap in September, and compare this to surveys of what people believe about global warming. Simple linear models are used to extrapolate when we will lose half of the Arctic polar cap, and when the belief in climate change will reach zero.
Problem 316: Counting Craters on the Hubble Space Telescope
[Grade:6-9 | Topics: Counting; Area; density]
Category: All,Helio,Solar System,Rockets,Telescopes
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.
Problem 315: The Mysterious Hexagon on Saturn
[Grade:6-9 | Topics: Measuring; Metric Units; speed=distance/time]
Category: All,Helio,Solar System
A curious hexagon formed by the Saturn polar jet stream, and photographed by the Cassini spacecraft, is used to determine wind speed and acceleration.
Problem 314: Chandra Studies an Expanding Supernova Shell
[Grade:6-9 | Topics: Measuring; Metric Units; speed=distance/time]
Category: All,Stars
Using a millimeter ruler and a sequence of images of a gaseous shell between 2000 and 2005, students calculate the speed of the material ejected by Supernova 1987A.
Problem 313: Exploring the Big Bang with the LHC
[Grade:9-12| Topics: ALgebra; Scientific Notation; Unit conversions]
Category: All,Universe
Two simple equations allow students to compute the temperature and energy of matter soon after the Big Bang, and compare these with energies available at the LHC.
Problem 312: Exploring the Large Hadron Collider
[Grade:9-12 | Topics: Scientific Notation]
Category: All,Miscellaneous
The Large Hadron Collider collides protons at very high energy to create new forms of matter. Students explore unit conversions related to energy and mass.
Problem 311: The Volume of a Hypersphere
[Grade:9-12 | Topics: Algebra II; Geometry; recursion relations]
Category: All,Miscellaneous
This problem extends student understanding of volume to include higher-dimensional spheres and their unusual properties. A simple recursion relation is used to calculate the volume formulas for spheres in dimensions 4 through 10.
Problem 310: Energy and Mass - Same things but different!
[Grade:8-10 | Topics: Unit Conversions; Scientific Notation]
Category: All,Miscellaneous
Students use unit conversions to explore the relationship between mass and energy.
Problem 309: The Energy of Empty Space
[Grade:10-12 | Topics: Properties of functions; polynomials; Critical points]
Category: All,Miscellaneous
Students explore the energy of 'empty space' and its relationship to the mass of the Higgs Boson using a simple quartic polynomial.
Problem 308: The Higgs Boson and the Mystery of Mass
[Grade:10-12 | Topics: Properties of functions; polynomials; Critical points]
Category: All,Miscellaneous
The search for the Higgs Boson is underway at the Large Hadron Collider (LHC). In this problem, students explore how the mass of this particle is believed to depend on the energies used to form it by studying a simple quartic polynomial.
Problem 307: The Elementary Particle Masses
[Grade:9-12 | Topics: Scientific Notation; unit conversion]
Category: All,Miscellaneous
Students compare the masses and mass differences between elementary particles using units common to physics such as the electron Volt.
Problem 306: Unit Conversions; Energy, Power and Flux
[Grade:8-11 | Topics: unit conversions with compound units]
Category: All,Miscellaneous
Students work with more complicated unit conversions involving simple powers of quantities and mixed ratios.
Problem 305: From Asteroids to Planets
[Grade:11-12 | Topics: Integral calculus]
Category: All,Solar System,Stars
Students explore how long it takes to form a small planet from a collection of asteroids in a planet-forming disk of matter orbiting a star based on a very simple physical model.
Problem 304: From Dust Balls to Asteroids
[Grade:11-12 | Topics: Integral Calculus]
Category: All,Solar System
Students calculate how long it takes to form an asteroid-sized body using a simple differential equation based on a very simple physical model.
Problem 303: From Dust Grains to Dust Balls
[Grade:11-12 | Topics: Integral Calculus]
Category: All,Solar System
Students create a model of how dust grains grow to centimeter-sized dust balls as part of forming a planet based on a very simple physical model.
Problem 302: How to Build a Planet from the Inside Out
[Grade:9-11 | Topics: Geometry; volume; scientific notation; mass=density x volume]
Category: All,Solar System
Students model a planet using a spherical core and shell with different densities. The goal is to create a planet of the right size, and with the correct mass using common planet building materials.
Problem 301: Planetary Alignments
[Grade:4-8 | Topics: Number series; geometry; Least Common Multiple]
Category: All,Helio,Solar System
Students combine a geometric model with number series to calculate when planets will 'line up' in a simple solar system.
Problem 300: Earth's Rotation Changes and the Length of the Day?
[Grade:4-8 | Topics: Graphing; Finding Slopes; forecasting]
Category: All,Solar System
Students use tabulated data for the number of days in a year from 900 million years ago to the present, to estimate the rate at which an Earth day has changed using a linear model.
Problem 299: Changing Perspectives on the Sun's Diameter
[Grade:6-8 | Topics: measurement; parallax; metric units; percentage change]
Category: All,Helio
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.
Problem 298: Seeing Solar Storms in STEREO - II
[Grade:10-12 | Topics: Geometry; Trigonometry]
Category: All,Helio,Rockets
Students explore the geometry of stereo viewing by studying a solar storm viewed from two satellites.
Problem 297: Atoms - How Sweet They Are!
[Grade:4-8 | Topics: Counting; Ratios; percentage]
Category: All,Miscellaneous
A simple counting activity is based on atoms in a sugar molecule. Students calculate ratios and percentages of various atomic types in the molecule.
Problem 296: Getting an Angle on the Sun and Moon
[Grade:8-10 | Topics: Geometry; angle measure; scale; proportion]
Category: All,Helio,Solar System
Students explore angular size and scale by comparing two images of the sun and moon which have identical angular size, but vastly different scales.
Problem 295: Details from an Exploding Star
[Grade:6-9 | Topics: Scale; measurement; metric units]
Category: All,Stars,Telescopes
Students work with an image from the Hubble Space Telescope of the Crab Nebula to calculate scales and sizes of various features.
Problem 294: Star Cluster Math
[Grade:4-6 | Topics: Counting; percentage; scaling]
Category: All,Stars
A simple counting exercise involving star classes lets students work with percentages and ratios.
Problem 293: Scientists Track the Rising Tide
[Grade:8-10 | Topics: Linear equations and modeling data; forecasting]
Category: All,Miscellaneous
A graph of sea level rise since 1900 provides data for students to fit linear functions and perform simple forecasting for the year 2050 and beyond.
Problem 292: How Hot is That Planet?
[Grade:8-10 | Topics: Algebra II; Evaluating Power functions]
Category: All,Solar System
Students use a simple function to estimate the temperature of a recently discovered planet called CoRot-7b.
Problem 291: Calculating Black Hole Power
[Grade:9-12 | Topics: Scientific Notation; evaluating simple formulas; unit conversion]
Category: All,Stars,Universe
Students use a simple formula to calculate how much power is produced by black holes of various sizes as they absorb matter from nearby stars and gas clouds.
Problem 290: The Apollo-11 Landing Area at High Resolution
[Grade:9-12 | Topics: metric measurement; scaling; A = B/C]
Category: All,Miscellaneous
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.
Problem 289: Chandra Spies the Longest Sound Wave in the Universe
[Grade:6-8 | Topics: metric measurement; scaling; Scientific Notation; exponents]
Category: All,Universe
Students use an image of sound waves produced by a massive black hole to determine wavelength, and comparisons with musical scale to find how many octaves this sound wave is below the wavelength of middle-C.
Problem 288: Fermi Observatory Measures the Lumps in Space
[Grade:9-12 | Topics: Scientific Notation; Evaluating an equation with multiple factors]
Category: All,Miscellaneous
Students use timing data obtained by the Fermi Observatory of a powerful gamma-ray burst 10 billion light years away, to determine how lumpy space is based on travel time delays between the lowest and highest-energy gamma-rays.
Problem 287: LCROSS Sees Water on the Moon
[Grade:9-12 | Topics: Geometry; volumes; mass=density x volume]
Category: All,Solar System
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.
Problem 286: STEREO Watches the Sun Kick Up a Storm
[Grade:9-12 | Topics: metric measurement; scaling; Scientific Notation; unit conversion; evaluating a simple 2-variable formula for kinetic energy ]
Category: All,Helio,Rockets
Students use images from the STEREO observation of a 'solar tsunami' to estimate its speed and kinetic energy.
Problem 285: Chandra Sees the Most Distant Cluster in the Universe
[Grade:9-12 | Topics: Algebra I; Solving for X; Scientific notation]
Category: All,Universe
Students work with kinetic energy and escape velocity to determine the mass of a distant cluster of galaxies by using information about its x-ray light emissions.
Problem 284: Calculating the Thickness of a Neutron Star Atmosphere
[Grade:9-12 | Topics: Algebra I; Exponential functions; graphing; Scientific notation]
Category: All,Stars
Students determine the thickness of the carbon atmosphere of the neutron star Cas-A using Earth's atmosphere and a set of scaling relationships.
Problem 283: Chandra Observatory Sees the Atmosphere of a Neutron Star
[Grade:8-10 | Topics: Volume of spherical shell; mass = density x volume]
Category: All,Stars
Students determine the mass of the carbon atmosphere of the neutron star Cas-A.
Problem 282: Exploring the Ares 1-X Launch: The Hard Climb to Orbit
[Grade:8-10 | Topics: Algebra II]
Category: All,Rockets
Students learn about the energy required to send a payload into orbit by studying the Ares 1-X rocket launch.
Problem 281: Exploring the Ares 1-X Launch: Energy Changes
[Grade:8-10 | Topics: Algebra II]
Category: All,Rockets
Students learn about kinetic and potential energy while studying the Ares 1-X rocket launch.
Problem 280: Exploring the Ares 1-X Launch: Parametrics
[Grade:8-10 | Topics: Algebra II; Parametric Equations]
Category: All,Rockets
Students learn about parametric equations to determine the path of the Ares 1-X rocket.
Problem 279: Exploring the Ares 1-X Launch: Downrange Distance
[Grade:8-10 | Topics: Algebra; Significant Figures; Metric to English Conversion]
Category: All,Rockets
Students learn about the path of the Ares 1-X test launch and calculate its downrange landing distance in the Atlantic Ocean.
Problem 278: Spitzer Studies the Distant Planet Osiris
[Grade:8-10 | Topics: Spherical volumes; density; Scientific Notation;]
Category: All,Solar System
Students learn about the density of the planet HD209458b, also called Osiris, and compare it to that of Jupiter.
Problem 277: Deep Impact Comet Encounter
[Grade:10-12 | Topics: Algebra; Scientific Notation; distance = speedxtime]
Category: All,Solar System
Students learn about the Deep Impact experiment involving Comet Tempel-1, and how the path of an asteroid can be changed by using the Law of Conservation of Momentum.
Problem 276: Solid Rocket Boosters and Thrust
[Grade:8-10 | Topics: Geometry, Cylindrical volumes and surface areas, Graphing data]
Category: All,Rockets
Students learn how solid rocket boosters work, and calculate the SRB Thrust Curve using a simple geometric model and 'counting squares'..
Problem 275: Water on the Moon!
[Grade:8-10 | Topics: Geometry, Spherical volumes and surface areas, Scientific notation]
Category: All,Solar System
Students estimate the amount of water on the moon using data from Deep Impact/EPOXI and NASA's Moon Mineralogy Mapper experiment on the Chandrayaan-1 spacecraft.
Problem 274: IBEX Uses Fast-moving Particles to Map the Sky!
[Grade:8-10 | Topics: Algebra I, Scientific notation]
Category: All,Rockets
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.
Problem 273: IBEX Creates an Unusual Image of the Sky!
[Grade:6-8 | Topics: Counting, tallying]
Category: All,Rockets
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.
Problem 272: Spitzer Telescope Discovers New Ring of Saturn!
[Grade:8-9 | Topics: Geometry, Algebra, volume, scientific notation]
Category: All,Solar System,Telescopes
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.
Problem 271: A Simple Model for Atmospheric Carbon Dioxide
[Grade:10-12 | Topics: Algebra I, rates of change, differential calculus]
Category: All,Solar System
Students work with the known sources of increasing and decreasing carbon dioxide to create a simple model of the rate of change of atmospheric carbon dioxide.
Problem 270: Modeling the Keeling Curve with Excel
[Grade:11-12 | Topics: Algebra II, properties of functions, Excel Spreadsheet]
Category: All,Solar System
Students create a mathematical model of the growth curve of atmospheric carbon dioxide using an Excel Spreadsheet, and create a future forecast for 2050.
Problem 269: Parts Per Hundred (pph)
[Grade:3-5 | Topics: counting, unit conversion]
Category: All,Miscellaneous
Students work with a common unit to describe the number of objects in a population. Other related quantities are the part-per-thousand, part-per-million and part-per-billion.
Problem 268: Planetary Conjunctions
[Grade:3-5 | Topics: geometry, time, patterns]
Category: All,Helio,Solar System
Students study a simple solar system with three planets and work out how often planets will 'line up'.
Problem 267: Identifying Materials by their Reflectivity
[Grade:6-8 | Topics: percentage, interpreting tabular data, area ]
Category: All,Solar System
The reflectivity of a material can be used to identify it. This is important when surveying the lunar surface for minerals, and also in creating 'green' living environments on Earth.
Problem 266: The Ares-V Cargo Rocket
[Grade:11-12 | Topics: Algebra II, properties of functions, differential calculus, Excel Spreadsheet]
Category: All,Rockets
Students work with the equations for thrust and fuel loss to determine the acceleration curve of the Ares-v during launch.
Problem 265: Estimating Maximum Cell Sizes
[Grade:11-12 | Topics: differential calculus, unit conversion]
Category: All,Miscellaneous
Students estimate the maximum size of spherical cells based on the rates with which they create waste and remove it through their cell walls.
Problem 264: Water on Planetary Surfaces
[Grade:8-10 | Topics: unit conversion, rates]
Category: All,Solar System
Students work with watts and Joules to study melting ice.
Problem 263: Ice or Water?
[Grade:8-10 | Topics: unit conversion, scientific notation]
Category: All,Solar System
Whether a planetary surface contains ice or liquid water depends on how much heat is available. Students explore the concepts of specific heat and latent heat of fusion to better understand and quantify the energy required for liquid water to exist under various conditions.
Problem 262: LRO Explores Lunar Surface Cratering
[Grade:6-8 | Topics: scale, proportion, ratio, area, density]
Category: All,Solar System
Students count the number of craters in various size ranges from a high-resolution image of the lunar surface.
Problem 261: LRO - Searching for Lunar Boulders
[Grade:6-8 | Topics: scale, ratio, proportion]
Category: All,Solar System
Students use a recent image of the Apollo-11 landing area to search for large lunar boulders.
Problem 260: Some Famous Unit Conversion Errors
[Grade:6-8 | Topics: unit conversion, metric measure]
Category: All,Miscellaneous
Students examine three famous unit conversion errors that led to catastrophic failures and near-death experiences.
Problem 259: Mare Nubium And Las Vegas
[Grade:8-10 | Topics: scale, proportion, ratio]
Category: All,Solar System
Students compare two satellite images taken at the same resolution to appreciate how large lunar features are compared to more familiar objects.
Problem 258: LRO's First Image of Mare Nubium
[Grade:6-8 | Topics: scale, ratio, proportion]
Category: All,Solar System
Students examine the first image of this lunar region using the high-resolution camera image provided by the Lunar Reconnaissance Orbiter.
Problem 257: LRO and the Apollo-11 Landing Site
[Grade:6-8 | Topics: scale, proportion, ratios]
Category: All,Solar System
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.
Problem 256: A High-resolution Satellite Photo
[Grade:6-8 | Topics: scale, ratios, proportions' angle measure, triangle geometry]
Category: All,Miscellaneous
Students examine a satellite photo of the Tennessee Court House from the GEO-1 satellite and determine the sizes of familiar features in the image.
Problem 255: Tempel-1 - Close-up of a Comet
[Grade:6-8 | Topics: scales, proportions ]
Category: All,Solar System
Students examine an image of the Comet Tempel-1 taken by the Deep Impact spacecraft to determine feature sizes and other details.
Problem 254: Solar Insolation Changes and the Sunspot Cycle
[Grade:8-10 | Topics: graph analysis, correlations, kilowatt, kilowatt-hours]
Category: All,Helio
Students compare changes in the amount of solar energy reaching earth with the 11-year sunspot cycle to predict the impact on designing a photovoltaic system for a home.
Problem 253: NASA 'Sees' Carbon Dioxide
[Grade:6-8 | Topics: interpreting a data image, unit conversion, gigatons ]
Category: All,Solar System
A satellite image of atmospheric carbon dioxide is used to estimate the geographic differences and identify human activity.
Problem 252: Carbon Dioxide Increases
[Grade:6-8 | Topics: graph analysis, slope, rates, unit conversion, parts-per-million, gigatons]
Category: All,Solar System
Students study the Keeling Curve to determine the rates of increase of carbon dioxide in the atmosphere.
Problem 251: Energy at Home
[Grade:6-8 | Topics: unit conversions; use of kilo and mega]
Category: All,Miscellaneous
Students explore watts and kilowatt-hours as measures of energy and energy consumption.
Problem 250: The Most Important Equation in Astronomy
[Grade:8-10 | Topics: geometry, angle measure, scientific notation]
Category: All,Telescopes
Students learn about how an instrument's ability to see details depends on its size and its operating wavelength - the key to designing any telescope or camera.
Problem 249: Spotting an Approaching Asteroid or Comet
[Grade:10-12 | Topics: Algebra 1, logarithms, area, scientific notation]
Category: All,Solar System
Students work with a fundamental equation for determining the brightness of an asteroid from its size and distance from Earth.
Problem 248: Seeing Solar Storms in STEREO - I
[Grade:8-10 | Topics: geometry, Law of Cosines, V = D/T]
Category: All,Helio,Rockets
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.
Problem 247: Space Mobile Puzzle
[Grade:8-10 | Topics: metric measure, algebra 1, geometry]
Category: All,Helio
Students calculate the missing masses and lengths in a mobile using the basic balance equation m1 x r1 = m2 x r2 for a solar system mobile.
Problem 246: Evaluating Secondary Physical Constants
[Grade:10-12 | Topics: Algebra; significant figures, scientific notation]
Category: All,Miscellaneous
Students evaluate complicated algebraic quantities that define important constants in physics with both integer and fractional exponents.
Problem 245: Solid Rocket Boosters
[Grade:8-10 | Topics: volume, area, unit conversions]
Category: All,Rockets
Students learn how SRBs actually create thrust, and study the Ares-V booster to estimate its thrust.
Problem 244: Solar Storms - Fractions and Percentages
[Grade:4-7 | Topics: precentages; Venn Diagramming]
Category: All,Helio
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.
Problem 243: ISS - Orbit Altitude Changes
[Grade:8-10 | Topics: combining positive and negative mixed numbers; fractions]
Category: All,Rockets
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.
Problem 242: Counting Atoms in Molecules
[Grade:3-6 | Topics: integers; counting similar things; fractions; percentages ]
Category: All,Miscellaneous
Students count the number of atoms in a simple molecule and work out some basic fractions, percentages and masses. They also complete the chemical formula for the compound.
Problem 241: Angular Size and Similar Triangles
[Grade:8-10 | Topics: geometry, similar triangles, proportions]
Category: All,Miscellaneous
A critical concept in astronomy is angular size, measured in degrees, minutes or arc-seconds. This is a review of the basic properties of similar triangles for a fixed angle.
Problem 240: The Eagle Nebula Close-up
[Grade:8-10 | Topics: scale, proportion, angle measure]
Category: All,Helio,Stars
Students measure a Hubble image of the famous Eagle Nebula 'Pillars of Creation' to determine the sizes of various features compared to our solar system
Problem 239: Counting Galaxies with the Hubble Space Telescope
[Grade:8-10 | Topics: area, angular measure]
Category: All,Universe,Telescopes
Students use an image of a small area of the sky to estimate the total number of galaxies in the universe visible from Earth.
Problem 238: Satellite Drag and the Hubble Space Telescope
[Grade:8-10 | Topics: interpreting graphical data; predicting trends]
Category: All,Telescopes
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.
Problem 237: The Martian Dust Devils
[Grade:6-8 | Topics: scales; Determining speed from sequential images; V = D/T
Category: All,Solar System
Students determine the speed and acceleration of a Martian dust devil from time laps images and information about the scale of the image.
Problem 236: LRO Sees Apollo-11 on the Moon!
[Grade:6-8 | Topics: scale; ratios; angle measure; right triangles]
Category: All,Helio,Solar System
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.
Problem 235: Scientific Data: The gift that keeps on giving!
[Grade:6-8 | Topics: metric units; rates; money]
Category: All,Miscellaneous
Students learn about gigabytes and terabytes of data and the rates of data generation by NASA missions and how to store it.
Problem 234: The Hand of Chandra
[Grade:6-8 | Topics: Scientific Notation; proportions; angle measure]
Category: All,Miscellaneous
Students use an image from the Chandra Observatory to measure a pulsar ejecting a cloud of gas.
Problem 234: Calculating Arc Lengths of Simple Functions-
[Grade:11-12 | Topics: Calculus; differential; integral, U-substitutions; significant figures.]
Category: All,Miscellaneous
Students work with the differential form of the Pythagorean Theorem to determine the basic integral formula for arc length, then evaluate it for a parabola, logrithmic spiral and normal spiral. They evaluate the length of the spiral track on a CDrom.
Problem 233: The Milky Way: A mere cloud in the cosmos-
[Grade:8-10 | Topics: Volume of disk, density, scientific notation]
Category: All,Universe
Students compare the average density of the Milky Way with the density of the universe.
Problem 232: Star Circles-
[Grade:8-9 | Topics: Lengths of arcs of circles; angular measure.]
Category: All,Stars
Students use a photograph of star trails around the North Star Polaris to determine the duration of the timed exposure based on star arc lengths.
Problem 231: Star Magnitudes and Decimals-
[Grade:5-8 | Topics: Multiplying decimals.]
Category: All,Stars
Students work with the stellar magnitude scale to determine the brightness differences between stars.
Problem 230: Galaxy Distances and Mixed Fractions-
[Grade:3-5 | Topics: Basic fraction math.]
Category: All,Universe
Students use the relative distances to nearby galaxies expressed in mixed numbers to determine distances between selected galaxies.
Problem 229: Atomic Numbers and Multiplying Fractions-
[Grade:3-5 | Topics: Basic fraction math; mixed numbers.]
Category: All,Miscellaneous
Students use a piece of the Periodic Table of the Elements to figure out the identities of atoms based on numerical clues expressed as mixed numbers.
Problem 228: Nuclear Arithmetic-
[Grade:4-6 | Topics: Evaluating a simple equation.]
Category: All,Miscellaneous
Students use the equation N = A - Z to solve for A, Z or N given values for the other two variables.
Problem 227: Working With Rates-
[Grade:6-8 | Topics: Ratios; scientific notation; unit conversion.]
Category: All,Miscellaneous
Students examine mixed rates for a variety of situations and their connections to ratios.
Problem 226: Rates and Slopes: An astronomical perspective-
[Grade:7-9 | Topics: Finding the slope of a linear graph.]
Category: All,Miscellaneous
Students determine the slopes for two linear graphs and make the connection to rates with mixed units.
Problem 225: Areas Under Curves; An astronomical perspective-
[Grade:6-8 | Topics: Adding areas in bar graphs.]
Category: All,Solar System
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.
Problem 224: Perimeters; Which constellation is the longest?-
[Grade:3-5 | Topics: perimeter of a curve; basic fractions; mixed numbers.]
Category: All,Stars
Students use tabulated data for the angular distances between stars in the Big Dipper and Orion to determine which constellation has the longest perimeter, and the average star separations.
Problem 223: Volcanos are a Blast: Working with simple equations-
[Grade:9-11 | Topics: Algebra I; significant figures.]
Category: All,Solar System
Students examine the famous Krakatoa explosion, asteroid impacts on the moon, and geysers on Enceladus using three equations that describe the height of the plume and initial velocity, to answer questions about the speed of the debris and terminal height.
Problem 222: Kelvin Temperatures and Very Cold Things-
[Grade:5-8 | Topics: Evaluating simple linear equations for given values.]
Category: All,Miscellaneous
Students convert from Centigrade to Fahrenheit and to Kelvin using three linear equations.
Problem 221: Pulsars and Simple Equations-
[Grade:6-8 | Topics: Evaluating simple one-variable equations]
Category: All,Miscellaneous
Students work with linear equations describing the rotation period of a pulsar, and evaluate the equations for various conditions. Students use the equations to predict intersection points in time.
Problem 220: The Many Faces of Energy-
[Grade:8-10 | Topics: Scientific notation; unit conversions.]
Category: All,Miscellaneous
Students convert between several different energy units.
Problem 219: Variables and Expressions from Around the Cosmos-
[Grade:6-8 | Topics: Evaluating simple one-variable equations.]
Category: All,Miscellaneous
Students evaluate linear equations describing a variety of astronomical situations.
Problem 218: Craters are a Blast! -
[Grade:8-10 | Topics: Scientific notation; evaluating simple power equations.]
Category: All,Miscellaneous
Students measure crater diameters in a photo of the moon, and determine the energy required to create them using a simple quadratic equation.
Problem 217: Fractions and Chemistry-
[Grade:3-6 | Topics: Basic fraction math; ratios.]
Category: All,Miscellaneous
Students study simple chemical equations by using simple proportions and mixed numbers.
Problem 216: Atomic Fractions-
[Grade:3-6 | Topics: Basic fraction math]
Category: All,Miscellaneous
Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder.
Problem 215: More Atomic Fractions-
[Grade:3-6 | Topics: Basic fraction math.]
Category: All,Miscellaneous
Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder.
Problem 214: Atomic Fractions III-
[Grade:3-6 | Topics: Basic fraction math.]
Category: All,Miscellaneous
Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder.
Problem 213: Kepler: The hunt for Earth-like planets-
[Grade:6-8 | Topics: Area of circle; ratios; percents.]
Category: All,Solar System,Stars
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.
Problem 212: Finding Mass in the Cosmos-
[Grade: 9-12| Topics: Scientific Notation; Algebra II; parametric equations]
Category: All,Universe
Students derive a simple formula, then use it to determine the masses of objects in the universe from the orbit periods and distances of their satellites.
Problem 211: Where Did All the Stars Go?-
[Grade: 6-8| Topics: multiplication; division; decimal numbers.]
Category: All,Stars
Students learn why NASA photos often don't show stars because of the way that cameras take pictures of bright and faint objects.
Problem 210: The Mathematics of Ion Rocket Engines-
[Grade: 9-12| Topics: Scientific Notation; Algebra II; evaluating formulae.]
Category: All,Rockets
Students learn about the basic physics of ion engines, calculating speeds.
Problem 209: How to make faint things stand out in a bright world!-
[Grade: 6-8| Topics: multiplication; division; decimal numbers.]
Category: All,Miscellaneous
Students learn that adding images together often enhances faint things not seen in only one image; the power of averaging data.
Problem 208: Optimization-
[Grade: 9-12| Topics: Calculus; differentiation.]
Category: All,Miscellaneous
Students determine the optimal dimensions of an hexagonal satellite to maximize its surface area given its desired volume.
Problem 207: The STEREO Mission: getting the message across-
[Grade: 6-8| Topics: multiplication; division; decimal numbers.]
Category: All,Rockets
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.
Problem 206: Can You Hear me now? -
[Grade: 6-8| Topics: multiplication; division; decimal numbers.]
Category: All,Helio
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
Problem 205: The Io Plasma Torus-
[Grade: 9-12| Topics: Algebra I - volume of cylinders; calculus - Integrals of volumes.]
Category: All,Miscellaneous
Students approximate the Io radiation belts as a cylinder to determine its volume ,and the mass of the particles within it.
Problem 204: The Mass of the Van Allen Radiation Belts-
[Grade: 9-12| Topics: Algebra II.]
Category: All,Helio,Magnetism
Students graph some magnetic field lines in polar coordinates, then estimate the volume and mass of the Belts using the formula for a torus.
Problem 203: Light Travel Times-
[Grade: 6-8| Topics: Scientific Notation; Multiplication; time = distance/speed.]
Category: All,Miscellaneous
Students determine the time it takes light to reach various objects in space.
Problem 202: The Dawn Mission - Ion Rockets and Spiral Orbits-
[Grade: 9-12| Topics: Calculus - Arc lengths.]
Category: All,Rockets
Students determine the shape of the trajectory taken by a spacecraft using a constant-thrust ion motor using differential and integral calculus for arc lengths.
Problem 201: Fly Me To the Moon!-
[Grade: 6-8| Topics: speed = distance/time; Pythagorean Theorem]
Category: All,Miscellaneous
Students learn some basic principles and terminology about how spacecraft change their orbits to get to the moon.
Problem 200: The Moon's Density - What's Inside?-
[Grade: 9-12| Topics: Volume of a sphere; mass = density x volume.]
Category: All,Miscellaneous
Students develop a simple mathematical model of the moon's interior using two nested spheres with different densities.
Problem 199: Solar Storm Energy and Pie Graphs-
[Grade: 6-8| Topics: Interpreting Pie Graphs.]
Category: All,Helio
Students study two Pie graphs describing solar flares and draw conclusions about percentages and their various forms of energy.
Problem 198: Solar Storm Timeline-
[Grade: 6-8| Topics: Time calculations.]
Category: All,Helio
Students read a narrative about the events involved in a solar storm, create a chronology for the sequence of events, and answer some simple time-related questions.
Problem 197: Hubble Sees a Distant Planet-
[Grade: 6-10| Topics: Calculating image scales; Circle circumferences; Unit conversions; distance-speed-time]
Category: All,Solar System,Stars
Students study an image of the dust disk around the star Fomalhaut and determine the orbit period and distance of a newly-discovered planet orbiting this young star.
Problem 196: Angular Size and velocity-
[Grade: 8-10| Topics: Geometry; Angle measurement]
Category: All,Rockets
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.
Problem 195: Unit Conversions III-
[Grade: 6-10| Topics: unit conversions.]
Category: All,Helio
Students work with more unit conversions and use them to solve a series of practical problems in science and solar energy.
Problem 194: A Magnetic Case for 'What Came First?' -
[Grade: 6-8| Topics: Time calculations]
Category: All,Magnetism,Miscellaneous
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.
Problem 193: Fluid Level in a Spherical Tank -
[Grade: 10-12| Topics: Algebra, differential calculus, related rates]
Category: All,Miscellaneous
Students explore the relationship between volume, and the height of fluid in a spherical tank as fluid is being drained at a constant rate.
Problem 192: The Big Bang - Cosmic Expansion -
[Grade: 10-12| Topics: Algebra, Integral Calculus]
Category: All,Universe
Students explore the expansion of the universe predicted by Big Bang cosmology
Problem 191: Why are hot things red? -
[Grade: 10-12| Topics: Algebra, graphing, differential calculus]
Category: All,Miscellaneous
Students explore the Planck Function using graphing skills, and calculus for experts, to determine the relationship between temperature and peak wavelength.
Problem 190: Modeling a Planetary Nebula -
[Grade: 10-12| Topics: Algebra, Integral calculus]
Category: All,Solar System,Stars
Students use calculus to create a mathematical model of a planetary nebula
Problem 189: Stellar Temperature, Size and Power-
[Grade: 8-10| Topics: Algebra]
Category: All,Stars
Students work with a basic equation to explore the relationship between temperature, surface area and power for a selection of stars.
Problem 188: Cross Sections and Collision Times -
[Grade: 9-11| Topics: Algebra; Area]
Category: All,Miscellaneous
Students explore the relationship between density, speed and size in determining how quickly particles collide in a gas.
Problem 187: Differentiation-
[Grade: 11-12| Topics: differentiation; algebra]
Category: All,Miscellaneous
Students explore partial derivatives by calculating rates of change in simple equations taken from astrophysics.
Problem 186: Collapsing Gas Clouds and Stability-
[Grade: 11-12| Topics: differentiation; finding extrema; partial derivitives]
Category: All,Miscellaneous
Students use the derivative to find an extremum of an equation governing the pressure balance of an interstellar cloud.
Problem 185: The International Space Station: Follow that graph!-
[Grade: 6-8| Topics: extrapolating a simple graph; estimation; forecasting]
Category: All,Helio,Rockets
Students use a plot of the orbit altitude of the ISS to predict its re-entry year after the peak of the next solar activity cycle.
Problem 184: The Ant and the Turntable: Frames of reference -
[Grade: 11-12| Topics: integration; parametric equations; polar coordinates]
Category: All,Miscellaneous
Students predict the motion of an ant crawling from the center of a spinning CDrom to the edge. They also use calculus to estimate the length of the spiral path seen by a stationary observer.
Problem 183: Calculating Arclengths of Simple Functions-
[Grade: 11-12| Topics: calculus; integration; parametric equations]
Category: All,Miscellaneous
Students determine the basic equation for arclength and its integral, and evaluate it for simple polar functions.
Problem 182: Our Neighborhood in the Milky Way-
[Grade: 6-8| Topics: scale models; speed-distance-time]
Category: All,Universe
Students create a scale model of the local Milky Way and estimate distances and travel times for a series of voyages.
Problem 181: Extracting Oxygen from Moon Rocks-
[Grade: 9-11| Topics: ratios; scientific notation; unit conversions]
Category: All,Solar System
Students use a chemical equation to estimate how much oxygen can be liberated from a sample of lunar soil.
Problem 180: Planets, Fractions and Scales-
[Grade: 4-6| Topics: scale models; decimals; fractions]
Category: All,Solar System
Students work with relative planet comparisons to determine the actual sizes of the planets given the diameter of Earth.
Problem 179: Is There a Lunar Meteorite Impact Hazard? -
[Grade: 5-7| Topics: Area; unit conversions; rates]
Category: All,Solar System
Students work with areas, probability and impact rates to estimate whether lunar colonists are in danger of meteorite hazards.
Problem 178: The Mass of the Moon -
[Grade: 8-11| Topics: Algebra]
Category: All,Solar System
Students use the period and altitude of a NASA lunar spacecraft to determine the mass of the moon.
Problem 177: Lunar Cratering: Probability and Odds-
[Grade: 4-7| Topics: Area; probability]
Category: All,Solar System
Students work with crater counting to estimate the area covered by craters and how to convert this into impact probabilities.
Problem 176: Solar Storms: Sequences and Probabilities I -
[Grade: 4-7| Topics: probability; numerating possible outcomes]
Category: All,Helio
Students continue their study of a stormy week on the sun by working out the probabilities for joint events.
Problem 175: Solar Storms: Sequences and Probabilities II -
[Grade: 4-7| Topics: probability; numerating possible outcomes]
Category: All,Helio
Students work out the probabilities for various combinations of solar storms during a given week.
Problem 174: A Matter of Timing -
[Grade: 3-6| Topics: scale model; time calculation; fractions; working with rulers and compasses]
Category: All,Solar System
Students study satellites of Saturn to work out graphically how often they will line up.
Problem 173: Groups, Clusters and Individuals-
[Grade:3-5 | Topics: multiplication]
Category: All,Stars
Students determine the number of individual objects given the number of groups and the number of individuals in an average group for clusters of stars and galaxies.
Problem 172: The Stellar Magnitude Scale-
[Grade: 3-6| Topics: number relationships; decimals; negative and positive numbers]
Category: All,Stars
Students learn about positive and negative numbers using a popular brightness scale used by astronomers.
Problem 171: More Unit Conversions-
[Grade:6-8 | Topics: unit conversions]
Category: All,Miscellaneous
Students work with four unit conversion problems that are a bit tricky!
Problem 170: Measuring Star Temperatures-
[Grade:6-8 | Topics: algebra, graph analysis]
Category: All,Stars
Students use a simple formula to determine the temperatures of stars, and to use a template curve to analyze data for a specific star to estimate its temperature.
Problem 169: The Limiting Behavior of Functions-
[Grade:9-12 | Topics: Algebra II, pre-calculus]
Category: All,Miscellaneous
Students work with two complex formulae to determine their limiting behavior as the independent variables approach infinity and zero.
Problem 168: Fitting Periodic Functions - Distant Planets-
[Grade:9-12 | Topics: trigonometry; functions; algebra]
Category: All,Solar System
Students work with data from a newly-discovered extra-solar planet to determine its orbit period and other parameters of a mathematical model.
Problem 167: Areas and Probabilities-
[Grade:4-6 | Topics: percentages,calculating areas; probability]
Category: All,Miscellaneous
Students work with various means of estimating probabilities using a comparison of areas.
Problem 166: The Dollars and Cents of Research -
[Grade:4-6 | Topics: percentages, decimal math, simple rates (e.g dollars/hour)]
Category: All,Miscellaneous
Students work with dollar amounts, hourly salary rates, percentages to explore various models of the cost of scientific research as seen by the individual scientist.
Problem 165: Fractions in Space -
[Grade: 3-5 | Topics: working with fractions; time calculations]
Category: All,Solar System
Students explore the many ways that simple fractions come up in the study of planetary motion.
Problem 164: Equations with One Variable-
[Grade: 6-8 | Topics: equations in one variable; multiplication; division; decimals]
Category: All,Miscellaneous
Students work with equations like '4.3 = 3.26D' to solve for D in a number of simple astronomical problems involving distances, speed and temperature conversion.
Problem 163: Time Intervals -
[Grade: 3-5 | Topics: Time calculations; unit conversions; decimal math]
Category: All,Miscellaneous
Students calculate time intervals between a number of astronomical events, from milliseconds to years.
Problem 162: Areas and Probabilities-
[Grade: 4-6 | Topics: Working out all possible outcomes for a set of events; fractions and percentages]
Category: All,Miscellaneous
Students explore how area and probability are related in working out meteor impact and 'stormy day' problems.
Problem 161: Earth and Moon to Scale-
[Grade: 4-6| Topics: Decimals; scaling and similarity]
Category: All,Solar System
Students create a scale model of the Earth-Moon system and compare with artistic renditions and actual NASA spacecraft images.
Problem 160: The Relative Sizes of the Sun and Stars-
[Grade:4-6 | Topics: working with fractions; scale models]
Category: All,Helio,Stars
Students work through a series of comparisons of the relative sizes of the sun compared to other stars, to create a scale model of stellar sizes using simple fractional relationships. ( e.g if Star A is 6 times larger than Star B, and Star C is 1/2 the size of Star B, how big is Star C in terms of Star A?)
Problem 159: Galaxies to Scale -
[Grade:4-6 | Topics: working with fractions; scale models]
Category: All,Universe
Students explore the relative sizes of the Milky Way compared to other galaxies to create a scale model of galaxies, similar to the methods in Problem 161.
Problem 158: The Solar Neighborhood within 17 Light Years -
[Grade:6-8 | Topics: Plotting polar coordinates using a ruler and compass; decimal math]
Category: All,Helio
Students create a scale model of the local solar neighborhood and determine the shortest travel distances to several stars.
Problem 157: Space Shuttle Launch Trajectory - I -
[Grade:11-12 | Topics: Algebra; Calculus; Parametric Equations; Differentiation
Category: All,Rockets
Students use the parametric equation for the altitude and range for an actual Shuttle launch to determine the speed and acceleration of the Shuttle during launch and orbit insertion.
Problem 156: Spectral Classification of Stars-
[Grade:5-8 | Topics: Working with patterns in data; simple sorting logic
Category: All,Stars
Students use actual star spectra to classify them into specific spectral types according to a standard ruberic.
Problem 155: Tidal Forces: Let 'er rip! -
[Grade: 7-10| Topics: Algebra; number substitution]
Category: All,Miscellaneous
Students explore tidal forces and how satellites are destroyed by coming too close to their planet.
Problem 154: Pan's Highway and Saturn's Rings -
[Grade:4-6 | Topics:Finding the scale of an image; measurement; unit conversion]
Category: All,Solar System
Students use an image from the Cassini spacecraft to determine how large the satellite Pan is, and the scale of Saturn's rings using a millimeter ruler.
Problem 153: Number Sentence Puzzles -
[Grade:3-4 | Topics: Number Topics and problem solving]
Category: All,Miscellaneous
Students are presented with three number sentences such as 145 + N = 375, and asked to select which 'spacy' word problem they belong to.
Problem 152: The Hubble Law -
[Grade:6-8 | Topics: Plotting data; determining the slope of the data;]
Category: All,Universe
Students plot the speed and distance to 7 galaxies and by deriving the slop of the linear model for the data points, obtain an estimate for the expansion rate of the universe known as Hubble's Constant.
Problem 151: Time Zone Math -
[Grade:3-5 | Topics: time units; addition, subtraction]
Category: All,Miscellaneous
Students learn about time zones and perform simple clock calculations using common United States and European time zones.
Problem 150: Cosmic Bar Graphs -
[Grade:3-5 | Topics: finding maxima and minima; fractions; extrapolating data]
Category: All,Miscellaneous
Students interpret simple bar graphs taken from astronomical data.
Problem 149: Equations with One Variable -
[Grade:3-5 | Topics: addition, subtraction, multiplication, division; solving simple equations]
Category: All,Miscellaneous
Students solve formulas of the form 2001 = 1858 + 11x to find 'X'.
Problem 147: Black hole - fade out
[Grade:9 - 11 | Topics: Scientific Notation; exponential functions]
Category: All,Universe
Students calculate how long it takes light to fade away as an object falls into a black hole.
Problem 146: Black Hole Power
[Grade:9 - 11 | Topics:Scientific Notation; Spherical shells; density; power]
Category: All,Helio,Universe
Students calculate how much power is produced as matter falls into a rotating and a non-rotating black hole including solar and supermassive black holes.
Problem 145: Black Holes - What's Inside?
[Grade:9 - 11 | Topics: Scientific Notation; distance; time calculations; algebra]
Category: All,Miscellaneous
Students work with the Pythagorean Theorem for black holes and investigate what happens to space and time on the other side of an Event Horizon.
Problem 144: Exploring Angular Size
[Grade:7 - 10 | Topics:Scientific Notation; degree measurement; physical size=distance x angular size.]
Category: All,Stars
Students examine the concept of angular size and how it relates to the physical size of an object and its distance. A Chandra Satellite x-ray image of the star cluster NGC-6266 is used, along with its distance, to determine how far apart the stars are based on their angular separations.
Problem 143: So..How big is it? - Asteroid Eros surface
[Grade:4 - 7 | Topics: Scaling; multiplication, division; metric measure]
Category: All,Solar System
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.
Problem 142: Black Holes---Part VIII
[Grade:7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.
Category: All,Universe
Matter that falls into a black hole heats up in an accretion disk, which can emit x-rays and even gamma rays visible from Earth. In this problem, students use a simple algebraic formula to calculate the temperature at various places in an accretion disk.
Problem 141: Exploring a Dusty Young Star
[Grade:4 - 7 | Topics: Algebra I; multiplication, division; scientific notation]
Category: All,Stars
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.
Problem 140: Black Holes---Part VII
[Grade:7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.]
Category: All,Miscellaneous
If you fell into a black hole, how fast would you be traveling? Students use a simple equation to calculate the free-fall speed as they pass through the event horizon.
Problem 139: How Big Is It? - Mars
[Grade:4 - 7 | Topics:image scales; metric measurement; division and multiplication; decimals]
Category: All,Solar System
Students use an image of a crater wall on mars to investigate ancient water gullies discovered in 2008 by the Mars Orbiter.
Problem 138: Black Holes---Part VI
[Grade:7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.]
Category: All,Miscellaneous
Tidal forces are an important gravity phenomenon, but they can be lethal to humansin the vicinity of black holes. This exercise lets students calculate the tidal acceleration between your head and feet while standing on the surface of Earth...and falling into a black hole.
Problem 137: Black Holes---Part V
[Grade:7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.]
Category: All,Miscellaneous
Students explore how Kepler's Third Law can be used to determine the mass of a black hole, or the mass of the North Star: Polaris.
Problem 136: Black Holes---Part IV
[Grade:7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.]
Category: All,Stars
Students explore how much energy is generated by stars and gas falling into black holes. The event horizon radius is calculated from a simple equation, R = 2.95 M, and energy is estimated from E = mc^2.
Problem 135: How Big is It? - Io and Jupiter.
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Solar System
Students work with an image taken by the Cassini spacecraft of Jupiter and its satellite Io. They determine the image scale, and calculate the sizes of various features in the image.
Problem 134: The Last Total Solar Eclipse--Ever!
[Grade:7 - 10 | Topics:Simple linear equations]
Category: All,Helio,Solar System
Students explore the geometry required for a total solar eclipse, and estimate how many years into the future the last total solar eclipse will occur as the moon slowly recedes from Earth by 3 centimeters/year.
Problem 133: How Big is It? - The Mars Rover.
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Solar System
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.
Problem 132: Black Holes - III
[Grade:8 - 12 | Topics:Simple linear equations; scientific notation]
Category: All,Universe
Students learn about how gravity distorts time near a black hole and other massive bodies.
Problem 131: How Big is It? - Las Vegas up close.
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Miscellaneous
Students work with an image taken by the QuickBird imaging satellite of downtown Las Vegas, Nevada. They determine the image scale, and calculate the sizes of streets, cars and buildings from the image.
Problem 130: Black Holes - II
[Grade:8 - 12 | Topics:Simple linear equations; scientific notation]
Category: All,Solar System,Universe
Students learn about how gravity distorts time and causes problems even for the Global Positioning System satellites and their timing signals.
Problem 129: How Big is It? - The Moon up close.
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Solar System
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.
Problem 128: Black Holes - I
[Grade:8 - 12 | Topics:Simple linear equations; scientific notation]
Category: All,Universe
Students learn about the most basic component to a black hole - the event horizon. Using a simple formula, and scientific notation, they examine the sizes of various kinds of black holes.
Problem 127: How Big is It? - The Moon up close.
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Solar System
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.
Problem 126: How Big is It? - A Martian Avalanche!
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Solar System
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!
Problem 125: How Big is It? - Washington DC up close.
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Rockets
Students work with an image taken by ISS astronauts to determine image scale, and search for the smallest things seen in a photograph.
Problem 124: The Moon's Atmosphere!
[Grade:8-10 | Topics:volume of sphere, shell; density-mass-volume; unit conversions]
Category: All,Miscellaneous
Students learn about the moon's very thin atmosphere by calculating its total mass in kilograms using the volume of a spherical shell and the measured density.
Problem 123: A Trillion Here...A Trillion There
[Grade:5-9 | Topics:add, subtract, multiply, divide.]
Category: All,Miscellaneous
Students learn to work with large numbers, which are the heart and soul of astronomical dimensions of size and scale. This activity explores the number 'one trillion' using examples drawn from the economics of the United States and the World. Surprisingly, there are not many astronomical numbers commonly in use that are as big as a trillion.
Problem 122: XZ Tauri's Super CME!
[Grade:8-10 | Topics:Calculate image scale; speed from distance and time; mass:volume:density]
Category: All,Helio,Stars,Rockets,Telescopes
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.
Problem 121: Ice on Mercury?
[Grade:8-10 | Topics:Area of a circle; volume, density, unit conversion]
Category: All,Miscellaneous
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.
Problem 120: Benford's Law
[Grade:8-10 | Topics:Calculating frequency tables; Histogramming; Statistics]
Category: All,Miscellaneous
Students will explore a relationship called Benford's Law, which describes the frequency of the integers 1-9 in various data. This law is used by the IRS to catch fradulent tax returns, but also applies to astronomical data and other surprising situations.
Problem 119: A Star Sheds a Comet Tail!
[Grade:8-10 | Topics:Image scaling; Unit conversion; Calculating speed from distance and time]
Category: All,Solar System,Stars
The GALEX satellite captured a spectacular image of the star Mira shedding a tail of gas and dust nearly 13 light years long. Students use the GALEX image to determine the speed of the star, and to translate the tail structures into a timeline extending to 30,000 years ago.
Problem 118: An Application of the Parallax Effect
[Grade:8-10 | Topics:Pythagorean Theorem; square-root; solving for variables]
Category: All,Helio,Rockets
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.
Problem 117: CME Kinetic Energy and Mass
[Grade:8-10 | Topics:time calculation; Evaluating a simple equation; solving for variables]
Category: All,Helio,Stars
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.
Problem 116: The Comet Encke Tail Disruption Event
[Grade:8-10 | Topics:time calculation; finding image scale; calculating speed from distance and time]
Category: All,Helio,Solar System,Rockets
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.
Problem 115: A Mathematical Model of the Sun
[Grade:8-10 | Topics: scientific notation; volume of a sphere and a spherical shell; density, mass and volume.]
Category: All,Helio
Students will use the formula for a sphere and a shell to calculate the mass of thesun for various choices of its density. The goal is to reproduce the measured mass and radius of the sun by a careful selection of its density in a core region and a shell region. Students will manipulate the values for density and shell size to achieve the correct total mass. This can be done by hand, or by programming an Excel spreadsheet.
Problem 114: The Heliopause...a question of balance
[Grade:8-10 | Topics: Formulas with two variables; scientific notation; spreadsheet programming]
Category: All,Helio
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.
Problem 113: NASA Juggles Four Satellites at Once!
[Grade:8-10 | Topics: Formulas with two variables; scientific notation]
Category: All,Magnetism
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.
Problem 112: Find the Mystery Lines...if you can!
[Grade:5-9 | Topics:scales, ratios, proportions, unit conversion
Category: All,Helio
Students will study the spectrum of the sun and use scaling and clues in the data to identify the lines from a companion table.
Problem 111: Scientific Notation III
[Grade:5-9 | Topics:Scientific notation - multiplication and division]
Category: All,Miscellaneous
In this continuation of the review of Scientific Notation, students will perform simple multiplication and division problems with an astronomy and space science focus.
Problem 110: Scientific Notation II
[Grade:5-9 | Topics:Scientific notation - addition and subtraction]
Category: All,Miscellaneous
In this continuation of the review of Scientific Notation, students will perform simple addition and subtraction problems.
Problem 109: Scientific Notation I
[Grade:5-9 | Topics:Scientific notation - conversion from decimal to SN]
Category: All,Miscellaneous
Scientists use scientific notation to represent very big and very small numbers. In this exercise, students will convert some 'astronomical' numbers into SN form.
Problem 108: A Problem in Satellite Synchrony
[Grade:5-9 | Topics:multiplication; Greatest Common Multiple]
Category: All,Magnetism
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.
Problem 107: Monster Sunspots!
[Grade:5-9 | Topics:multiplication; calculating length from image scale]
Category: All,Solar System
Some sunspots are so big that they can be seen from Earth without a telescope. In this problem, students will use images of three super-spots and calculate their sizes from the image scaling information. They will then order the images from the smallest super-spot to the largest super-spot.
Problem 106: Oscillating Spheres
[Grade:9-11 | Topics:Algebra; calculating with a formula]
Category: All,Stars
Many astronomical bodies have a natural period of oscillation. In this problem, students will use a simple mathematical model to calculate the period of oscillation of a star, a planet, and a neutron star from the estimated densities of these bodies.
Problem 105: The Transit of Mercury
[Grade:9-11 | Topics:image scales; angular measure; degrees, minutes and seconds]
Category: All,Helio,Solar System
As seen from Earth, the planet Mercury occasionally passes across the face of the sun; an event that astronomers call a transit. From images taken by the Hinode satellite, students will create a model of the solar disk to the same scale as the image, and calculate the distance to the sun.
Problem 104: Loopy Sunspots!
[Grade:9-11 | Topics:image scales; cylinder volume calculation; scientific notation; unit conversions]
Category: All,Magnetism
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.
Problem 103: The Mysterious Solar Micro-Flares!
[Grade:6-9 | Topics:image scales; area calculation; unit conversions]
Category: All,Helio
Students will analyze an image taken by the Hinode solar satellite to determine the scale of the image in kilometers per millimeter, then use this to determine the sizes of solar micro-flares. From the number of micro-flares that they count in the image, the area of the image in square kilometers, and the surface area of a spherical sun, they will calculate the total number of micro-flares on the solar surface.
Problem 102: How fast does the sun rotate?
[Grade:6-9 | Topics:image scales; time calculations; speed calculations, unit conversions]
Category: All,Helio
Students will analyze consecutive images taken by the Hinode satellite to determine the sun's speed of rotation, and the approximate length of its 'day'.
Problem 101: Super-Fast Solar Flares!! -
[Grade level: 6-9 | Topics:image scales; time calculations; speed calculations]
Category: All,Helio
Students will analyze consecutive images taken of an erupting solar flare, and use the information provided to calculate the speed of the flare.
Problem 100:The Sunspot Cycle - endings and beginnings -
[Grade level: 6-9 | Topics:graph reading; extrapolation; time calculations]
Category: All,Helio
Students will examine a plot of the sunspot cycle and extract information from the plotted data about the previous sunspot cycle, and make predictions about the next one about to start in 2007.
Problem 99:The Hinode Satellite Views the Sun -
[Grade level: 6-8 | Topics:image interpretation; eye-hand coordination; reading to be informed]
Category: All,Helio,Magnetism
Students will use a full-sun image from the new Hinode satellite to sketch the locations of magnetic fields on the sun's surface using information in the introductory article as a guide.
Problem 98:Solar Flare Reconstruction -
[Grade level: 9-11 | Topics:plotting tabular date; fitting functions; integration]
Category: All,Helio
Students will use data from a solar flare to reconstruct its maximum emission using graphical estimation (pre-algebra), power-law function fitting (Algebra 2), and will determine the area under the profile (Calculus).
Problem 97:Hinode - Closeup of a Sunspot -
[Grade level: 6-8 | Topics:image scales, metric units, unit conversion]
Category: All,Helio
Students will determine the sizes of sunspots and solar granulation cells from a recent image taken by the Hinode solar observatory.
Problem 96:Hinode Satellite Power -
[Grade level: 6-8 | Topics:area of rectangle,area of cylinder, unit conversion]
Category: All,Helio
Students will study the design of the Hinode solar satellite and calculate how much power it can generate from its solar panels.
Problem 95:A Study on Astronaut Radiation Dosages in SPace -
[Grade level: 9-11 | Topics:Graph analysis, interpolation, unit conversion]
Category: All,Rockets
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.
Problem 94:Solar Storms: Odds, Fractions and Percentages -
[Grade level: 6-8 | Topics: Averaging; fractions; percentages; odds; Arithmetic Operations; Venn Diagrams]
Category: All,Helio
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 no one has thought about before? The Venn Diagramming activity is a key element of the activity and is reasonably challenging!
Problem 93:An Introduction to Radiation Shielding -
[Grade level: 9-11 | Topics: Algebra; Volume of a hollow cube; unit conversion]
Category: All,Miscellaneous
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.
Problem 92:A Lunar Transit of the Sun from Space -
[Grade level: 9-11 | Topics: Geometry; parallax; arithmetic]
Category: All,Helio,Solar System,Rockets
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.
Problem 91:Compound Interest -
[Grade level: 8-10 | Topics: Algebra II]
Category: All,Miscellaneous
Students use the 'compound interest' formula to examine rates of growth for space mission costs, and the salaries of astronomers, with allowance for inflation.
Problem 90: A Career in Astronomy -
[Grade level: 6-8 | Topics: graph reading; percentages; interpolation]
Category: All,Miscellaneous
This problem looks at some of the statistics of working in a field like astronomy. Students will read graphs and answer questions about the number of astronomers in this job area, and the rate of increase in the population size and number of advanced degrees.
Problem 89:Atmospheric Shielding from Radiation- III -
[Grade level: 11-12 | Topics: Evaluating an integral, working with exponential functions]
Category: All,Solar System
This is Part III of a 3-part problem on atmospheric shielding. Students use exponential functions to model the density of a planetary atmosphere, then evaluate a definite integral to calculate the total radiation shielding in the zenith (straight overhead) direction for Earth and Mars.
Problem 88:Atmospheric Shielding from Radiation- II -
[Grade level: 9-11 | Topics: Algebra I; evaluating a function for specific values]
Category: All,Miscellaneous
This is the second of a three-part problem dealing with atmospheric shielding. Students use the formula they derived in Part I, to calculate the radiation dosage for radiation arriving from straight overhead, and from the horizon. Students also calculate the 'zenith' shielding from the surface of Mars.
Problem 87: Atmospheric Shielding from Radiation- I -
[Grade level: 9-11 | Topics: Algebra II, trigonometry]
Category: All,Miscellaneous
This is the first part of a three-part problem series that has students calculate how much radiation shielding Earth's atmosphere provides. In this problem, students have to use the relevant geometry in the diagram to determine the algebraic formula for the path length through the atmosphere from a given location and altitude above Earth's surface.
Problem 86:Do Fast CMEs Produce SPEs? -
[Grade level: 5-8 | Topics: Venn Diagrams; counting; calculating percentages and odds]
Category: All,Helio
Recent data on solar proton storms (SPEs) and coronal mass ejections (CMEs) are compa black using Venn Diagrams to see if the speed of a CME makes solar proton storms more likely or not.
Problem 85:The Solar Tsunami! -
[Grade level: 5-8 | Topics: Finding image scale; calculating time differences; calculating speed from distance and time]
Category: All,Helio
Recent data from the Hinode satellite is used to measure the speed of a solar explosion on the surface of the sun using a series of images taken by the satellite at three different times. Students calculate the speed of the blast between the first pair and last pair of images, and determine if the blast wave was accelerating or decellerating in time.
Problem 84:Beyond the Blue Horizon -
[Grade level: 9-11 | Topics: Algebra, Pythagorean Theorem; Experts: DIfferential calculus) ]
Category: All,Solar System
How far is it to the horizon? Students use geometry, and the Pythagorean Theorem, to determine the formula for the distance to the horizon on any planet with a radius, R, from a height, h, above its surface. Additional problems added that involve calculus to determine the rate-of-change of the horizon distance as you change your height.
Problem 83:Luner Meteorite Impact Risks -
[Grade level: 8-10 | Topics: arithmetic; unit conversions; surface area of a sphere) ]
Category: All,Solar System
In 2006, scientists identified 12 flashes of light on the moon that were probably meteorite impacts. They estimated that these meteorites were probably about the size of a grapefruit. How long would lunar colonists have to wait before seeing such a flash within their horizon? Students will use an area and probability calculation to discover the average waiting time.
Problem 82:Some Simple Unit Conversions-
[Grade level: 6-8 | Topics: arithmetic; unit conversions involving 1 to 5 steps) ]
Category: All,Miscellaneous
Students will use a number of obscure English units measures to convert from metric to English units and back, and answer some unusual questions!
Problem 81:The Pressure of a Solar Storm -
[Grade level: 9-11 | Topics: Substituting numbers into equations; filling out missing table entries; data interpretation; mathematical models ]
Category: All,Helio,Magnetism
Students will examine three mathematical models for determining how much pressure a solar storm produces as it affects Earth's magnetic field.
Problem 80:Data Corruption by High Energy Particles -
[Grade level: 6-8 | Topics: Time and speed calculations; interpreting scientific data ]
Category: All,Helio
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.
Problem 79:Correcting Bad Data Using Parity Bits -
[Grade level: 4-6 | Topics: addition, subtraction, comparing the numbers 1 and 0 ]
Category: All,Miscellaneous
Students will see how computer data is protected from damage by radiation 'glitches' using a simple error-detection method involving the parity bit.
Problem 78:Moving Magnetic Filaments Near Sunspots -
[Grade level: 6-8 | Topics: scaling, estimation, speed calculations, time arithmetic ]
Category: All,Helio,Magnetism
Students will use two images from the new, Hinode (Solar-B) solar observatory to calculate the speed of magnetic filaments near a sunspot.
Problem 77:Some Puzzling Thoughts about Radiation! -
[Grade level: 8-10 | Topics: Finding the roots of a quadratic equation; solving for X ]
Category: All,Miscellaneous
Students fill-in the blanks in an essay on radiation risks using a word bank tied to solving quadratic equations to find the right words from a pair of possible 'solutions'.
Problem 76:Radon Gas in the Basement -
[Grade level: 6-8 | Topics: Unit conversion, arithmetic operations]
Category: All,Miscellaneous
This problem introduces students to a common radiation problem in our homes. From a map of the United States provided by the US EPA, students convert radon gas risks into annual dosages.
Problem 75:Parametric Functions and Substitution -
[Grade level: 11-12 | Topics: Algebraic manipulation, integer exponents, scientific notation, significant figures and rounding ]
Category: All,Helio,Solar System,Magnetism
The relationship between the strength of a solar storm and the resulting magnetic disturbance on Earth is given as a series of equations. Students are asked to create new formulae based on these parametric these equations using the method of substitution.
Problem 74:A Hot Time on Mars -
[Grade level: 6-8 | Topics: decimals, unit conversion, graphing and analysis ]
Category: All,Solar System,Rockets
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
Problem 73:Monster Functions in Space Science I. -
[Grade level: 9-11 | Topics: decimals, scientific notation, significant figures ]
Category: All,Magnetism
This problem has students employ a pair of complicated algebraic equations to evaluate the strength of the sun's magnetic field near Earth's orbit.
Problem 72:Systems of Equations in Space Science -
[Grade level: 8-10 | Topics: decimals, solving systems of equations, matrix math, algebraic substitution ]
Category: All,Helio
This problem has students solve two problems involving three equations in three unknowns to learn about solar flares, and communication satellite operating power.
Problem 71:Are the Van Allen Belts Really Deadly? -
[Grade level: 8-10 | Topics: decimals, area of rectangle, graph analysis]
Category: All,Helio
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.
Problem 70:Calculating Total Radiation Dosages at Mars -
[Grade level: 6-8 | Topics: decimals, area of rectangle, graph analysis]
Category: All,Solar System
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.
Problem 69:Single Event Upsets in Aircraft Avionics -
[Grade level: 8-10 | Topics: decimals, unit conversions, graph analysis]
Category: All,Miscellaneous
Radiation is problem for high-altitude commercial and research aircraft. Showers of high-energy neutrons cause glitches in computer electronics and other aircraft systems. This problem investigates the neutron background radiation at 30,000 to 100,000 feet based on actual flight data, and has students calculate how many computer memory glitches will happen over a set amount of flight time.
Problem 68:An Introduction to Space Radiation -
[Grade level: 6-8 | Topics: Reading to be Informed; decimals, fractions, square-roots]
Category: All,Miscellaneous
Students use basic math operations to calculate total dosages from dosage rates, and calculating cancer risks.
Problem 67:Unit Conversion Exercises -
[Grade level: 6-8 | Topics: fractions, decimals, units]
Category: All,Miscellaneous
Radiation dosages and exposure calculations allow students to compare several different ways that scientists use to compare how radiation exposure is delive black and accumulated over time.Like converting 'centimeters per sec' to 'kilometers per year' ,this activity reinforces student Topics in converting from one set of units to another.
Problem 66:Background Radiation and Lifestyles -
[Grade level: 6-8 | Topics: fractions, decimals, unit conversions]
Category: All,Miscellaneous
Living on Earth, you will be subjected to many different radiation environments. This problem follows one person through four different possible futures, and compares the cumulative lifetime dosages.
Problem 65:A Perspective on Radiation Dosages -
[Grade level: 6-8 | Topics: decimals, unit conversions, graphing a timeline, finding areas under curves using rectangles]
Category: All,Solar System
Depending on the kind of career you chose, you will experience different lifetime radiation dosages. This problem compares the cumulative dosages for someone living on Earth, an astronaut career involving travel to the Space Station, and the lifetime dosage of someone traveling to Mars and back.
Problem 64:Solar Activity and Satellite Mathematics -
[Grade level: 4-6 | Topics: Decimals; money; percents]
Category: All,Helio
This activity examines what happens to a single satellite when space weather turns bad
Problem 63 :Solar Activity and Tree Rings - What's the connection? -
[Grade level: 4-6 | Topics: Spreadsheets and technology; decimal math]
Category: All,Helio,Solar System
This activity uses a single tree to compare its growth rings to the sunspot cycle. This is also an interesting suggestion for science fair projects! Here is the accompanying "weekly/tree.xls"Excell Spreadsheet Data File.
Problem 62:Star light...Star bright - A question of magnitude! -
[Grade level: 4-6 | Topics: Positive and negative numbers; decimal math]
Category: All,Stars
Students will calculate the brightness differences between stars using multiplication and division. Working with the number line will be a big help and math review!
Problem 61:Drake's Equation and the Search for Life...sort of! -
[Grade level: 6-8 | Topics: decimal math; evaluating functions for given values of variables]
Category: All,Universe
Students use a formula to estimate how much life there is in the Milky Way.
Problem 60:When is a planet not a planet? -
[Grade level: 6-8 | Topics: Non-mathematical essay; reading to be informed]
Category: All,Solar System
Students will examine this topic by surveying various internet resources that attempt to define the astronomical term 'planet'.
Problem 59:Getting A Round in the Solar System! -
[Grade level: 6-8 | Topics: Data analysis; decimals; ratios; graphing]
Category: All,Helio,Solar System
How big does a body have to be before it becomes round? In this activity, students examine images of asteroids and planetary moons to determine the critical size for an object to become round under the action of its own gravitational field.
Problem 58:How many stars are there? -
[Grade level: 6-8 | Topics: Positive and negative numbers; histogramming; extrapolating data]
Category: All,Stars
In this activity, students will get their first taste of star counting by using a star atlas reproduction and bar-graph the numbers of stars in each magnitude interval. They will then calculate the number of similar stars in the sky by scaling up their counts to the full sky area.
Problem 57:Asteroids and comets and meteors - Oh My! -
[Grade level: 4-6 | Topics: Scale model; Decimal math; Interpreting 2-D graph]
Category: All,Helio,Solar System
Sudents will calculate the scale of the map, and answer questions about the distances between these objects, and the number that cross earth's orbit. A great, hands-on introduction to asteroids in the inner solar system! Links to online data bases for further inquiry are also provided.
Problem 56:The Sombrero Galaxy Close-up -
[Grade level: 9-11 | Topics: Finding the scale of an image; measurement; decimal math]
Category: All,Universe
Students explore the dimensions of this galaxy as well as its finest details, using simple image scaling calculations.
Problem 54:Exploring Distant Galaxies -
[Grade level: 6-8 | Topics: Decimal math; using an online calculator; Histogramming data]
Category: All,Universe
Students will use an actual image of a distant corner of the universe, with the redshifts of galaxies identified to find a galaxy formed only 500 million years after the Big Bang.
Problem 53:Astronomy: A Moving Experience! -
[Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; distance = speed x time; scientific notation]
Category: All,Miscellaneous
In this activity, you will measure the speed of astronomical phenomena using the scaling clues and the time intervals between photographs of three phenomena:
Problem 52:Measuring the size of a Star Cluster -
[Grade level: 4-6 | Topics: Online research; Finding the scale of an image; metric measurement; decimal math]
Category: All,Stars
In this activity, students will determine the photographic scale, and use this to estimate the projected (2-D) distances between the stars in this cluster. They will also use internet and library resources to learn more about this cluster.
Problem 51:Sunspots Close-up and Personal -
[Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; decimal math]
Category: All,Helio
Students will analyze a picture of a sunspot to learn more about its size, and examine the sizes of various other features on the surface of the sun that astronomers study.
Problem 50:Measuring the Speed of a Galaxy. -
[Grade level: 6-8 | Topics: Interpolating data in a graph; decimal math]
Category: All,Universe
In this activity,students will use the formula for the Doppler Shift to analyze the spectrum of the Seyfert galaxy Q2125-431 and determine its speed.
Problem 49:A Spiral Galaxy Up Close. -
[Grade level: 6-8 | Topics: Online research; Finding the scale of an image; metric measurement; decimal math]
Category: All,Universe
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.
Problem 48:Scientific Notation - An Astronomical Perspective. -
[Grade level: 8-10 | Topics: Scientific notation; decimal math]
Category: All,Miscellaneous
This collection of problems will have students reviewing how to perform multiplication and division with large and small numbers, while learning about some interesting astronomical applications.
Problem 47:Discovering the Milky Way by Counting Stars. -
[Grade level: 4-6 | Topics: Tallying data; decimal math]
Category: All,Stars,Universe
Students will use data from a deep-integration image of a region of the sky in Hercules, observed by the 2MASS sky survey project to estimate the number of stars in the sky.
Problem 46:A Matter of Perspective. -
[Grade level: 9-11 | Topics: Geometric proofs]
Category: All,Miscellaneous
This problem will have students examine the geometry of perspective, and how the altitude of an aurora or other object, determines how far away you will be able to see it before it is below the local horizon.
Problem 45:Theories, Facts, Beliefs...Oh My! -
[Grade level: 9-11 | Topics: Non-mathematical essay; reading to be informed]
Category: All,Miscellaneous
This activity presents 36 statements which the student is to evaluate as either a theory, law, fact, hypothesis or belief. Be prepared for some lively discussions!!
Problem 44:Interstellar Distances with the Pythagorean Theorem -
[Grade level: 9-11 | Topics: Decimal math; Pythagorean Theorem; square root]
Category: All,Solar System,Stars
This activity lets students use the Pythagorean distance formula in 3-dimensions to explore stellar distances for a collection of bright stars, first as seen from Earth and then as seen from a planet orbiting the star Polaris.
Problem 43:An Interplanetary Shock Wave
[Grade level: 6-10 | Topics: Time calculations; distance = speed x time ]
Category: All,Helio
Students will use data from a solar storm to track its speed and acceleration as it traveled across the solar system.
Problem 42:Solar Storms in the News -
[Grade level: 6-10 | Topics: Online research; tallying data]
Category: All,Helio
Students will use a newspaper archive to explore how reporters have described the causes of aurora since the 1850's.
Problem 41:Solar Energy in Space
[Grade level: 7-10 | Topics: Area of an irregular polygon; decimal math]
Category: All,Helio
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.
Problem 40:Why do stars rise in the East?
[Grade level 9-10 | Topics: Geometric proof]
Category: All,Solar System,Stars
Students will follow a step-by-step geometric construction procedure to create a figure, and then use basic Euclidean postulates to prove that, because Earth rotates from west to east, stars must rise in the east and set in the west,
Problem 39:Solar Storm Timeline
[Grade level: 7-9 | Topics: time math; decimal math; speed = distance/time]
Category: All,Helio
Students will examine an event timeline for a space weather event and use time addition and subtraction skills to calculate storm durations and speeds.
Problem 38: Solar Eclipses and Satellite Power
[Grade:5 - 8 | Topics: Geometry; decimal math]
Category: All,Helio
Students will create a scaled drawing of the orbits of three satellites around Earth, and calculate how long each satellite will be in the shadow of Earth. They will be asked to figure out how to keep the satellites operating even without sunlight to power their solar panels.
Problem 37: Time Zone Mathematics.
[Grade:5 - 7 | Topics: Time zone math]
Category: All,Miscellaneous
Students will learn about the time zones around the world, and why it is important to keep track of where you are when you see an astronomical phenomenon.
Problem 36: The Space Station Orbit Decay and Space
[Grade:5 - 8 | Topics: Interpreting graphical data; decimal math]
Category: All,Rockets
Students will calculate the orbit decay rates, and investigate why this might be happening.
Problem 35: Exploring the Plasmasphere
[Grade:7 - 9 | Topics: Geometry; ratios; decimal math; time arithmetic]
Category: All,Miscellaneous
Students use an image of the plasmasphere obtained by the IMAGE satellite to calculate how fast it orbits the Earth.
Problem 34: Using the TV Program CSI to Explore Matter
[Grade:7 - 9 | Topics: Geometry; ratios; decimal math]
Category: All,Miscellaneous
Students will read about how a mass spectrometer works - the kind used in the TV Series CSI, and learn how to interpret a simple spectrum to find out which elements are present in a mystery sample.
Problem 33: Magnetic Energy From B to V
[Grade:8 - 10 | Topics: Algebra I; volumes; decimal math; scientific notation]
Category: All,Helio,Magnetism
Students will use formulas for the volume of a sphere and cylinder, and magnetic energy, to calculate the total magnetic energy of two important 'batteries' for space weather phenomena- solar prominences and the Earth's magnetotail.
Problem 32: Solar Proton Events and Satellite Damage
[Grade:7 - 9 | Topics: Interpreting tabular data; histogramming]
Category: All,Helio
Students will examine the statistics for Solar Proton Events since 1996 and estimate their damage to satellite solar power systems.
Problem 31: Airline Travel and Space Weather
[Grade:6 - 8 | Topics: Reading to be informed; decimal math]
Category: All,Miscellaneous
Students will learn about the natural background radiation they are exposed to every day, and compare this to radiation dosages during jet travel.
Problem 29: The Wandering Magnetic North Pole
[Grade:6 - 8 | Topics: Interpreting graphical data; speed = distance/time]
Category: All,Magnetism
This activity will have students read a map and calculate the speed of the 'polar wander' from 300 AD to 2000 AD.
Problem 28: Satellite Power and Cosmic Rays
[Grade:6 - 8 | Topics: Interpreting graphical data; decimal math]
Category: All,Helio
In this activity, students read a graph that shows the electricity produced by a satellite's solar panels, and learn a valuable lesson about how to design satellites for long-term operation in space.
Problem 27: Satellite Failures and the Sunspot Cycle
[Grade:6 - 8 | Topics: Graphing tabular data; decimal math]
Category: All,Helio
In this problem, students compare the sunspot cycle with the record of satellites re-entering the atmosphere and determine if there is a correlation. They also investigate how pervasive satellite technology has become in their daily lives.
Problem 26: Super-sized Sunspots and the Solar Cycle.
[Grade:6 - 8 | Topics: Interpreting tabular data; decimal math]
Category: All,Helio
Students compare the dates of the largest sunspots since 1900 with the year of the peak sunspot cycle. They also compare superspot sizes with the area of earth.
Problem 25: The Distance to Earth's Magnetopause
[Grade:8 - 10 | Topics: Evaluating a function with two variables; completing tabular entries]
Category: All,Helio,Solar System
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.
Problem 24: Reading Between the Lines
[Grade:5 - 7 | Topics: solving for X; distributive law; associative law]
Category: All,Miscellaneous
Students solve simple equations for x, (like 2x + 3 = 5) to discover which words complete an essay on the causes of aurora, and answer questions after reading the completed essay.
Problem 23: Solar Flares and Sunspot Sizes
[Grade:6 - 8 | Topics: Interpreting tabular data; percentages; decimal math ]
Category: All,Helio
Students compare sunspot sizes to the frequency of solar flares and discover that there is no hard and fast rule that relates sunspot size to its ability to produce very large flares.
Problem 22: The Auroral Oval
[Grade:5 - 7 | Topics: Finding the scale of an image; measurement; decimal math]
Category: All,Miscellaneous
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!
Problem 21: Exploring the Plasmasphere
[Grade:7 - 9 | Topics: Finding the scale of an image; decimal math; measurement]
Category: All,Miscellaneous
Students learn that the Pythagorean Theorem is more than a geometric concept. Scientists use a photograph taken by the IMAGE satellite to measure the size of Earth's plasmasphere region using a ruler and protractor.
Problem 20: A Space Science Crossword Puzzle
[Grade:4 - 6 | Topics: Integer arithmetic; associative and distributive laws]
Category: All,Miscellaneous
Students work with positive and negative numbers to solve a crossword puzzle. Good exercise for pre-algebra review of adding and subtracting positive and negative numbers.
Problem 19: An Application of the Pythagorean Theorem
[Grade:8 - 10 | Topics: Squares and square-roots; Pythagorean Theorem in 3-D]
Category: All,Magnetism
This problem is an introduction to magnetism, which is a '3-dimensional vector', and how to calculate magnetic strengths using the Pythagorean Theorem.
Problem 18: Magnetic Forces and Particle Motion
[Grade:9 - 11 | Topics: Algebra I; evaluating a function; scientific notation]
Category: All,Magnetism
Students learn about the spiral-shaped trajectories of charged particles moving in magnetic fields, and calculate some basic properties of this 'cyclotron' motion.
Problem 17: Magnetic Forces and Kinetic Energy
[Grade:6 - 8 | Topics: Square root; time=speed x distance; decimal math; significant figures]
Category: All,Magnetism
Students use the formula for the Kinetic Energy of a charged particle to calculate particle speeds for different voltages, and answer simple questions about lightning, aurora and Earth's radiation belts.
Problem 16: Solar Power and Satellite Design
[Grade:6 - 8 | Topics: Area of irregular polygons]
Category: All,Helio
Students perform simple surface area calculations to determine how much solar power a satellite can generate, compared to the satellite's needs.
Problem 15: Radio Plasma Imaging with IMAGE
[Grade:6 - 8 | Topics: Polar graphs; time = distance x speed; decimal math]
Category: All,Miscellaneous
Students use the Distance=VelocityxTime relationship to determine the distances to plasma clouds seen by the IMAGE satellite.
Problem 14: Kinetic Energy and Particle Motion
[Grade:7 - 9 | Topics: Evaluating a function; square-roots; scientific notation]
Category: All,Miscellaneous
Students learn about kinetic energy and how this concept applies to charged particles. They calculate the speed of a particle for various particle energies.
Problem 13: Plasma Clouds
[Grade:7 - 9 | Topics: Square-root; solving for X; evaluating a function]
Category: All,Miscellaneous
Students use a simple 'square-root' relationship to learn how scientists with the IMAGE satellite measure the density of clouds of plasma in space.
Problem 12: The Ring Current
[Grade:7 - 9 | Topics: Volume of a disk; scientific notation; mass = density x volume]
Category: All,Miscellaneous
Students use the formula for a disk to calculate the mass of the ring current surrounding Earth.
Problem 11: How high is an aurora
[Grade:5 - 8 | Topics: Geometery; angle measure]
Category: All,Miscellaneous
Students use the properties of a triangle to determine how high up aurora are. They also learn about the parallax method for finding distances to remote objects.
Problem 10: The Life Cycle of an Aurora
[Grade:4 - 6 | Topics: Creating a timeline from narrative; ordering events by date and time]
Category: All,Miscellaneous
Students examine two eye-witness descriptions of an aurora and identify the common elements so that they can extract a common pattern of changes.
Problem 9: Aurora Power!
[Grade:5 - 7 | Topics: Interpreting tabular data]
Category: All,Miscellaneous
Students use data to estimate the power of an aurora, and compare it to common things such as the electrical consumption of a house, a city and a country.
Problem 8: Making a Model Planet
[Grade:7 - 9 | Topics: Volume of sphere; mass = density x volume; decimal math; scientific notation]
Category: All,Solar System
Students use the formula for a sphere, and the concept of density, to make a mathematical model of a planet based on its mass, radius and the density of several possible materials (ice, silicate rock, iron, basalt).
Problem 7: Solar Flares, CME's and Aurora
[Grade:5 - 7 | Topics: Venn Diagramming]
Category: All,Helio
Students will use data to construct a simple Venn Diagram, and answer an important question about whether solar flares cause CME's and Aurora.
Problem 5: The November 8, 2004 solar storm
[Grade:6 - 8 | Topics: Time calculations; distance = speed x time]
Category: All,Helio
Students calculate the speed of a CME, and describe their aurora observations through writing and drawing.
Problem 4: Sketching the Northern Lights
[Grade:5 - 7 | Topics: non-mathematical art problem]
Category: All,Miscellaneous
Students read an account of an aurora seen by an observer, and create a drawing or painting based on the description.
Problem 3: Magnetic Storms II
[Grade:6 - 8 | Topics: Interpreting bar graphs; time calculations]
Category: All,Helio,Magnetism
Students learn about the Kp index using a bar graph. They use the graph to answer simple questions about maxima and time.
Problem 2: Satellite Surface Area
its surface. [Grade:7 - 9 | Topics: surface areas; hexagone; decimal math]
Category: All,Helio
Students calculate the surface area of an octagonal cylinder and calculate the power it would yield from solar cells covering
Problem 1: Magnetic Storms I
[Grade:7 - 9 | Topics: Interpreting a graph; time calculations]
Category: All,Helio,Magnetism
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.