## Measurement & Data

## Grade 3-5: Measurement

**Problem 506: A New Belt for the Van Allen Belts**

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

**Problem 464: Big Moons and Small Planets **

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.
[Grade: 3-5 | Topics: scale models; proportions; fractions]
(PDF)

**Problem 423: The Moon as a Black Hole **

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.
[Grade: 3-5 | Topics: Working with a compass; metric ruler]
(PDF)

**Problem 376: The Earth-like Planet Gliese 518g **

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.
[Grade: 3-5 | Topics: scale models; measurement]
(PDF)

**Problem 232: Star Circles-** 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.
[Grade: 8-9 | Topics: Lengths of arcs of circles; angular measure.]

**Problem 161: Earth and Moon to Scale-** Students create a scale model of trhe Earth-Moon system and compare with artistic renditions and actual NASA spacecraft images.
[Grade: 4-6| Topics: Decimals; scaling and similarity]

**Problem 160: The Relative Sizes of the Sun and Stars-** Students work through a series of comparisons of the relative sizes of the sun compablack 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?)
[Grade: 4-6 | Topics: working with fractions; scale models]

**Problem 159: Galaxies to Scale -** Students explore the relative sizes of the Milky Way compablack to other galaxies to create a scale model of galaxies, similar to the methods in Problem 161.
[Grade: 4-6 | Topics: working with fractions; scale models]

**Problem 154: Pan's Highway and Saturn's Rings -** 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.
[Grade: 4-6 | Topics:Finding the scale of an image; measurement; unit conversion]

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

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

**Problem 135 How Big is It? - Io and Jupiter.**
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.
[Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

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

** Problem 131 How Big is It? - Las Vegas up close. **
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.
[Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

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

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

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

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

**Problem 52 Measuring the size of a Star Cluster - **
Astronomers often use a photograph to determine the size of astronomical objects. The
Pleiades is a famous cluster of hundreds of bright 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.
[Grade level: 4-6 | Topics: Online research; Finding the scale of an image; metric measurement; decimal math]

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

## Grade 6-12: Measurement

**Problem 681:A Practical Application of Vector Dot and Cross Products **
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.
[Grade: 10-12 | Topics: vectors; dot and cross product; normal vectors; unit conversions ]
(PDF)

**Problem 673:VAB - An Improved Model for Van Allen Belt Radiation Dose**
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.
[Grade: 9-11 | Topics: Polynomial equations; trigonometric equations; composite finctions f(f(x)); estimating areas under curves]
(PDF)

**Problem 672:VAB - Modeling the Radiation Dose of the Van Allen Probes**
Students create a simple mathematical model of the radiation exposure to the VABP satellites as they travel through the Van Allen belts.
[Grade: 11-12 | Topics: Parametric equations;composite functions f(g(x)); integral calculus ]
(PDF)

**Problem 671:VAB - The Van Allen Probes and Radiation Dose**
Students study radiation dose units and estimate the exposures for a human living on the ground; an astronaut in the ISS, and the Van Allen belt environment.
[Grade: 8-10 | Topics: Unit conversion; rates]
(PDF)

**Problem 669:** VAB - Exploring the Third Belt with the Van Allen Probes
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.
[Grade: 9-12 | Topics: Intersection points of circles and ellipses; graphical and algebraic solutions]
(PDF)

**Problem 668: Meteor Impacts ? How Much Stuff? **
Students integrate a logarithmic function to estimate the number of tons of meteoritic debris that Earth collects every year.
[Grade: 12 | Topics: Integral calculus]
(PDF)

**Problem 667: Exploring Power-laws: Meteor impacts**
Students estimate a function for logarithmic data that describes the number of meteor impacts on Earth every year.
[Grade: 9-12 | Topics: logarithmic graphs; power laws; linear equations]
(PDF)

**Problem 666: SAGE - The Ground Track of the International Space Station**
Students determine how many sunrises and sunset the ISS observes every day.
[Grade: 6-8 | Topics: Working with proportions; time calculations]
(PDF)

**Problem 662: SAGE- Measuring Aerosol Concentration in Parts per Million**

Students learn about parts-per-million units by working with percentage and counting squares in different types of grids.
[Grade: 6-8 | Topics: Unit conversion; integer counting]
(PDF)

**Problem 661: SAGE- Measuring Stratospheric Ozone with SAGE-III**

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.
[Grade: 6-8 | Topics: Unit conversion; reading a data graph ]
(PDF)

**Problem 660: SAGE- Some Basic Properties of the SAGE-III Instrument**

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.
[Grade: 6-8 | Topics: Unit conversion; proportions ]
(PDF)

**Problem 659: VAP- Exploring the Outer Atmosphere ? Gas Density**

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.
[Grade: 6-8 | Topics: scientific notation; scale model; number = density x volume; volume = area x length; length=speed x time. ]
(PDF)

**Problem 658: VAP- Exploring Gas Density in Space**

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.
[Grade: 6-8 | Topics: geometry; density=number/volume; scale models and proportions; scientific notation ]
(PDF)

**Problem 657: VAP- Exploring the Density of Gas in the Atmosphere**

Students examine different ways to represent the density of Earths atmosphere.
[Grade: 6-8 | Topics: Scientific notation; density ]
(PDF)

**Problem 656: VAP- Measuring Earths Magnetic Field in Space**

Students work with satellite data to explore Earths magnetic field through graphing data and comparing it with inverse-square and inverse-cube laws.
[Grade: 9-12 | Topics: minimum and maximum; graphing data; comparing with models of the form 1/r2 and 1/r3 ]
(PDF)

**Problem 655: VAP- Estimating the Total Mass of the Van Allen Belts **

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.
[Grade: 9-12 | Topics:Volume of torus; scientific notation; mass = density x volume ]
(PDF)

**Problem 654: VAP- Exploring the Donut-shaped Van Allen Belts **

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.
[Grade: 9-12 | Topics: Scientific notation; volume of spheres and toriods]
(PDF)

**Problem 653: VAP-How to Use the RBSP Spacecraft to Measure the Mass of Earth! **

Students use a formula to estimate the mass of Earth from data about the orbit of the Van Allen Probes spacecraft.
[Grade: 9-12 | Topics: scientific notation; solving formula with integer exponents ]
(PDF)

**Problem 652: VAP- Telemetry Math**

Students work with data rates for the spacecraft and determine how much data needs to be stored.
[Grade: 6-8 | Topics: megabytes; rates in time]
(PDF)

**Problem 651: VAP- The RBSP Satellite: Working with Octagons **

Students work with the area formula for squares, rectangles and triangles to find the surface area of an octagonal satellite.
[Grade: 9-12 | Topics: areas of simple figures; algebraic manipulation]
(PDF)

**Problem 650: VAP- Working with Areas of Rectangles and Circles **

Students use the formulas for simple rectangle and circle areas to determine the areas of the holes in a satellite panel.
[Grade: 3-5 | Topics: area of a rectangle; area of a circle]
(PDF)

**Problem 649: VAP- Electricity from Sunlight: The RBSP Spacecraft Solar Panels**

Students work with the area of rectangles to calculate the electrical power produced by solar panels.
[Grade: 3-5 | Topics: area of a rectangle; decimal math; unit conversion]
(PDF)

**Problem 648: SAGE- Using Opacity to Find Aerosol Density**

Students examine a mathematical model based on the SAGE geometry and see how it leads to solving a system of linear equations to determine aerosol concentrations at different altitudes.
[Grade: 6-8 | Topics: solving a system of linear equations; scientific notation]
(PDF)

**Problem 647: SAGE- Investigating Opacity and Extinction**

Students work with the properties of filters to prove that the product of exponentials leads to the sum of their exponents.
[Grade: 9-12 | Topics: exponential functions; exponent math]
(PDF)

**Problem 646: SAGE- Air Quality Index and Aerosol Density**

Students see how the Air Quality Index is related to the number of arosols per cubic meter.
[Grade: 6-8 | Topics: density; scientific notation; volume of a sphere; density]
(PDF)

**Problem 645: SAGE- Exploring the Mass and Density of Aerosol Particles**

Students explore the physical sizes of aerosol particles. With unit conversions they convert concentration units of micrograms/m3 to particles/m3.
[Grade: 6-8 | Topics: Unit conversions; scientific notation; volume of a sphere; density]
(PDF)

**Problem 644: SAGE- A Scale Model of Aerosol Sizes**

Students work with proportions and scale to create a scale model of aerosol particles.
[Grade: 6-8 | Topics: unit conversion; metric units nano and micro]
(PDF)

**Problem 643: SAGE- The Sources and Sinks of Carbonyl Sulfide**

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.
[Grade: 6-8 | Topics: Scientific notation; rates]
(PDF)

**Problem 642: SAGE-Three Mathematical Ways to Describe Light Extinction **

Studens explore the three common ways that scientists record extinction using base-10 and base-e functions.
[Grade: 9-12 | Topics: Base-10 and Base-e functions; exponential equations]
(PDF)

**Problem 641: SAGE- A Study of Aerosol Extinction in the Stratosphere**

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.
[Grade: 6-8 | Topics: slope of a line; linear equations; forecasting]
(PDF)

**Problem 640: SAGE- Atmospheric Aerosols by Percentage**

Students examine a table that lists the percentages of different aerosol types according to the location on Earth where they are produced.
[Grade: 3-5 | Topics: percentages; interpreting tabular data]
(PDF)

**Problem 639: SAGE- Aerosol Sources in the Stratosphere**

Students examine the sources for aerosols in the atmosphere and determine their percentage contributions
based upon their individual rates given in megatons/year.
[Grade: 6-8 | Topics: Rates; percentage; pie graphs]
(PDF)

**Problem 638: SAGE- Sunset and Sunrise Geometry **

Students explore the tangent geometry used by the SAGE-III instrument, and work with chords to determine their lengths using the Pyhtagorean formula.
[Grade: 9-12 | Topics: Pythagorean Theorem; chord lengths]
(PDF)

**Problem 637: SAGE-Light Attenuation Using Exponential Functions **

Students work with the extinction formula for light and see how light dimming is an exponetial process.
[Grade: 9-12 | Topics: exponential functions; natural logarithm, e]
(PDF)

**Problem 636: SAGE-Aerosols and Light Dimming **

Students explore how light is dimmed as it passes through a series of filters.
[Grade: 6-8 | Topics: percentage; multiplication ]
(PDF)

**Problem 635: SAGE- Exploring Aerosols**

Students compare aerosol sizes to a human hair, calculate volumes and masses from density.
[Grade: 6-8 | Topics: density; volume; scale ]
(PDF)

**Problem 634: History of Winter - What is a Snowballs Chance on Mars? **

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.
[Grade: 9-12 | Topics: Graph analysis]
(PDF)

**Problem 633: History of Winter - Exploring Temperature and States of Matter **

Students learn how to read a simple phase diagram and how states of matter are related to temperature and pressure.
[Grade: 9-12 | Topics: Rates of Change; Unit conversions; decimal math ]
(PDF)

**Problem 632: History of Winter - Exploring Energy and Temperature **

Students learn about the relationship between temperature and the kinetic energy of particles.
[Grade: 9-12 | Topics: Evaluating equations]
(PDF)

**Problem 631: History of Winter - Snow Density, Mass and Roof Failure **

Students
[Grade: 6-8 | Topics: Density = mass/volume; rates of change; proportions]
(PDF)

**Problem 630: History of Winter - Snow Density and Volume **

Students learn how snow density is measured in the field using cylindrical instruments in a snow pit trench.
[Grade: 6-8 | Topics: Density=mass/volume; metric units; decimal math]
(PDF)

**Problem 629: History of Winter - Snow to Water Ratios **

Students learn how to convert between snow volume and equivalent volumes of liquid water.
[Grade: 6-8 | Topics: Working with tables; decimal math; proportions]
(PDF)

**Problem 628: History of Winter - Snowflake Growth Rates and Surface Area **

Students study change of scale and dilation by investigating showflake growth.
[Grade: 6-8 | Topics: tabular data; rates of change; decimal math]
(PDF)

**Problem 627: History of Winter - The Surface Area of a Snowflake **

Students estimate the area of a single snow flake using the areas of triangles and rectangles.
[Grade: 6-8 | Topics: geometry; areas of triangles and rectangles; decimal math]
(PDF)

**Problem 626: History of Winter - Graphing a Showflake using Symmetry **

Students use a simple plotting exercise and reflection symmetry to create a snowflake.
[Grade: 6-8 | Topics: geometry; symmetry; plotting points on a Cartesian graph]
(PDF)

**Problem 625: SCOOL-Cloud Droplets and Rain Drops **

Students
[Grade: 6-8 | Topics: Volume of a sphere; scientific notation ]
(PDF)

**Problem 624: SCOOL-Cloud Cover, Albedo, Transmission and Opacity **

Students explore the concepts of albedo, transmission and opacity for clouds.
[Grade: 9-12 | Topics: logarithmic functions; percentage]
(PDF)

**Problem 623: SCOOL-Cloud Cover and Solar Radiation **

Students examine the relationship between percentage cloud cover and the amount of sunlight that reaches the ground.
[Grade: 6-8 | Topics: Graph analysis; evaluating functions]
(PDF)

**Problem 622: SCOOL-How Clouds Form - Working with Dew Points and Rates of Change **

Students learn about the dew point and how clouds form from humid, cooling air.
[Grade: 6-8 | Topics: Percentage; rates of change ]
(PDF)

**Problem 621: SCOOL-Working with Rainfall Rates and Water Volume **

Students learn about rain fall rates and how to convert them into the volume of water that falls.
[Grade: 9-12 | Topics: scientific notation; rates of change ]
(PDF)

**Problem 620: SCOOL-Estimating the Mass of a Cloud **

Students use the relationship between volume and density to estimate the mass of a common cumulus cloud.
[Grade: 6-8 | Topics: VOlume of a sphere; scientific notation; mass = density x volume]
(PDF)

**Problem 619: SCOOL-Using Proportions to Estimate the Height of a Cloud **

Students use the method of triangulation to determine the height of a cloud.
[Grade: 6-8 | Topics: geometry of right triangles; proportions]
(PDF)

**Problem 612: Exploring Power-laws: Meteor impacts **

Students work with logarithmic functions, power-laws and explore the mass functiuon of meteors.
[Grade: 9-12 | Topics: logarithmic functions; power-functions; logarithmic graphs]
(PDF)

**Problem 546: The Relative Sizes of Planets and other Objects**

Students use proportional information to determine the relative scales of planets and large moons across the solar system.
[Grade: 3-5 | Topics:scale; proportion]
(PDF)

**Problem 545:Measuring Atmospheric Trace Gases Using Parts Per Million**

Students convert from percentage units to parts per million and compare trace gases in the atmospheres of various planets.
[Grade: 6-8 | Topics: percentages; unit conversions ]
(PDF)

**Problem 544:The Composition of Planetary Atmospheres**

Students study the composition of planetary atmospheres and compare the amounts of certain compounds in them
[Grade: 6-8 | Topics: Pie graphs; percentages; scientific notation]
(PDF)

**Problem 543:Timeline for Planet Formation**

Students calculate time intervals in millions and billions of years from a timeline of events
[Grade: 3-5 | Topics: time calculations; integers]
(PDF)

**Problem 542:The Late Heavy Bombardment Era**

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 during this era.
[Grade: 6-8 | Topics: volume of spheres; proportions]
(PDF)

**Problem 541:How to Build a Planet**

Students study planet growth by using a clay model of planetessimals combining to form a planet by investigating volume addition with spheres.
[Grade: 3-5 | Topics: graphing; counting]
(PDF)

**Problem 558:How Quickly are NEOs Being Discovered?**

Students work with data presented in bar graphs to estimate how many more hazardous Near Earth Objects (NEOS) remein to be found.
[Grade: 6-8 | Topics:bar graphs ]
(PDF)

**Problem 557:The 10000th Near Earth Asteroid 2013 MZ5**

Students graph tabulated data to determine when this asteroid is closest to Earth and its speed at that time.
[Grade: 6-8 | Topics: grapohing tabuklar data; solving a linear equation]
(PDF)

**Problem 552:Cassini Sees Earth From Space - How Bright is it?**

Students explore the logarithmic magnitude scale and estimate how bright Earth appears from Saturn as viewed in a recent Cassini image
[Grade: 9-12 | Topics: logarithms; power laws ]
(PDF)

**Problem 551:Giving Particles a Boost in the van Allen Belts**

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.
[Grade: 6-8 | Topics: equations; scientific notation]
(PDF)

**Problem 512: New NASA Satellite Takes Pictures of Salton Sea **

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

**Problem 506: A New Belt for the Van Allen Belts**

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

**Problem 502:The Frequency of Large Meteor Impacts **

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.
[Grade: 6-8 | Topics: percercentages, areas]
(PDF)

**Problem 499: The Equation of a Magnetic Field Line **

Students use calculus to determine the formula for a magnetic field line.
[Grade: 12 | Topics: differential and integral calculus; slope; parametric equations]
(PDF)

**Problem 498: The Slope of a Magnetic Field Line **

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.
[Grade: 7-8 | Topics: Graphing in the XY plane; midpoint formula; tangent lines to curves]
(PDF)

**Problem 497: Graphing a Magnetic Field Line **

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.
[Grade: 6-8 | Topics: graphing in XY plane; reflection symmetry]
(PDF)

**Problem 486: RBSP Hears Dawn Chorus **

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

**Problem 484: Exploring Water Use in Kansas **

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

**Problem 454: The Closest Approach of Asteroid 2005YU55 - III **

Students work with the equation of a circle and line to find the orbit intersection points, midpoint, and closest distance to earth.
[Grade: 8-10 | Topics: time=distance/speed; scale models; metric math]
(PDF)

**Problem 453: The Closest Approach of Asteroid 2005YU55 - II **

Students work with the properties of circles and angular measure to see where the moon will be at the start of the asteroid encounter.
[Grade: 6-8 | Topics: angular measure; time=distance/speed; scale models; metric math]
(PDF)

**Problem 449: A simple model for the origin of Earth's ocean water **

Students create a simple model of the arrival of water to Earth using three sizes of cometary bodies and their arrival rates.
[Grade: 8-10 | Topics: volume of a sphere; rates of change]
(PDF)

**Problem 448: The Declining Arctic Ice Cap During September **

Students graph the change in Arctic ice surface area, and perform linear and quadratic regressions to model and forecast trends. [Grade: 9-11 | Topics: Statistics; Regression; graphing tabular data]
(PDF)

**Problem 447: The Arctic's Vanishing Ozone Layer **

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? [Grade: 9-11 | Topics: Regression; graphing tabular data]
(PDF)

**Problem 420: Gravity Probe B: Testing Einstein again!**
Students learn about the Lense-Thirring Effect, and calculate its magnitude near Earth's orbit using an algebraic equation with integer and fractional exponents.
[Grade: 9-12 | Topics: algebra; scientific notation, angular measure]
(PDF)

**Problem 414: Radiation Dose and Distance**
Students explore the dosimetry from the Japan 2011 Earthquake and graph the decline of the
radiation dose rates with distance from the nuclear reactors.
[Grade: 9-12 | Topics: unit conversions; amount=rate x time; graphing Log-Log data]
(PDF)

**Problem 413: Exploring Nuclear Decay and Radiation Dose**
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.
[Grade: 9-12 | Topics: unit conversions; amount=rate x time; Solving exponential equations in base-e]
(PDF)

**Problem 412: Radiation Dose and Dose Rate**
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.
[Grade: 6-8 | Topics: unit conversions; amount=rate x time]
(PDF)

**Problem 411: Lifestyles and Radiation Dose**
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.
[Grade: 6-8 | Topics: unit conversions; amount=rate x time]
(PDF)

**Problem 410:Exploring Radiation in your Life**
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.
[Grade: 6-8 | Topics: unit conversions; amount=rate x time]
(PDF)

**Problem 409: The 2011 Japan Earthquake Rocks the Earth**
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.
[Grade: 9-12 | Topics: Algebra; evaluating an equation]
(PDF)

**Problem 408: Estimating the Speed of a Tsunami**
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.
[Grade: 6-8 | Topics: Time arithmetic; time zones; speed = distance/time]
(PDF)

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

**Problem 397: The Changing Pace of Global Warming**
Students work with a table of global temperatures to forecast the temperature change by 2050 using a linear extrapolation.
[Grade: 8-10 | Topics: Graphing tabular data; linear extrapolation; equation of a line y=mx+b]
(PDF)

**Problem 375: Terra Satellite Measures Dangerous Dust**

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

**Problem 317: The Global Warming Debate and the Arctic Ice Cap** 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.
[Grade: 9-11 | Topics: Modeling data with linear equations; forecasting]

**Problem 300: Does Anybody Really Know What Time It Is?** 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.
[Grade: 4-8 | Topics: Graphing; Finding Slopes; forecasting]

**Problem 293: Scientists Track the Rising Tide** 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.
[Grade: 8-10 | Topics: Linear equations and modeling data; forecasting]

**Problem 271: A Simple Model for Atmospheric Carbon Dioxide ** Students work with the known sources of increasing and decreasiong carbon dioxide to create a simple model of the rate of change of atmospheric carbon dioxide.
[Grade: 10-12 | Topics: Algebra I, rates of change, differential calculus]

**Problem 270: Modeling the Keeling Curve with Excel ** Students create a mathematical model of the growth curve of atmospheric carbon dioxide using an Excel Spreadsheet, and create a future forecast for 2050.
[Grade: 11-12 | Topics: Algebra II, properties of functions, Excel Spreadsheet]

**Problem 269: Parts Per Hundred (pph) ** 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.
[Grade: 3-5 | Topics: counting, unit conversion]

**Problem 265: Estimating Maximum Cell Sizes ** Students estimate tyhe maximum size of spherical cells based on the rates with which they
create waste and remove it through their cell walls.
[Grade: 11-12 | Topics: differential calculus, unit conversion]

**Problem 264: Water on Planetary Surfaces ** Students work with watts and Joules to study melting ice.
[Grade: 8-10 | Topics: unit conversion, rates]

**Problem 263: Ice or Water? ** 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 the and quantify the energy required for liquid
water to exist under various conditions.
[Grade: 8-10 | Topics: unit conversion, scientific notation]

**Problem 254: Solar Insolation Changes and the Sunspot Cycle ** 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.
[Grade: 8-10 | Topics: graph analysis, correlations, kilowatt, kilowatt-hours]

**Problem 253: NASA 'Sees' Carbon Dioxide ** A satellite image of atmospheric carbon dioxide is used to estimate the geographic differences and identify human activity.
[Grade: 6-8 | Topics: interpreting a data image, unit conversion, gigatons ]

**Problem 252: Carbon Dioxide Increases ** Students study the Keeling Curve to determine the rates of increase of carbon dioxide in the atmosphere.
[Grade: 6-8 | Topics: graph analysis, slope, rates, unit conversion, parts-per-million, gigatons]

**Problem 251: Energy at Home** Students explore watts and kilowatt-hours as measures of energy and energy consumption.
[Grade: 6-8 | Topics: unit conversions; use of kilo and mega]

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

**Problem 223: Volcanos are a Blast: Working with simple equations-** 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.
[Grade: 9-11 | Topics: Algebra I; significant figures.]

**Problem 222: Kelvin Temperatures and Very Cold Things-** Students convert from Centigrade to Fahrenheit and to Kelvin using three linear equations.
[Grade: 5-8 | Topics: Evaluating simple linear equations for given values.]

**Problem 220: The Many Faces of Energy-** Students convert between several different energy units.
[Grade: 8-10 | Topics: Scientific notation; unit conversions.]

**Problem 212: Finding Mass in the Cosmos-** 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.
[Grade: 9-12| Topics: Scientific Notation; Algebra II; parametric equations]

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

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

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

**Problem 166: The Dollars and Cents of Research -** 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.
[Grade: 4-6 | Topics: percentages, decimal math, simple rates (e.g dollars/hour)]

**Problem 163: Time Intervals -** Students calculate time intervals between a number of astronomical events, from milliseconds to years.
[Grade: 3-5 | Topics: Time calculations; unit conversions; decimal math]

**Problem 161: Earth and Moon to Scale-** Students create a scale model of the Earth-Moon system and compare with artistic renditions and actual NASA spacecraft images.
[Grade: 4-6| Topics: Decimals; scaling and similarity]

Problem 151: Time Zone Math - Students learn about time zones and perform simple clock calculations using common United States and European time zones. [Grade: 3-5 | Topics: time units; addition, subtraction]

**Problem 131 **** How Big is It? - Las Vegas up close.
** 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.
[Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

**Problem 123 ****A Trillion Here...A Trillion There
** 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.
[Grade: 5-9 | Topics:add, subtract, multiply, divide.]

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

**Problem 89 ****Atmospheric Shielding from Radiation- III -
** 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.
[Grade level: 11-12 | Topics: Evaluating an integral, working with exponential functions]

**Problem 88 ****Atmospheric Shielding from Radiation- II -
** 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.
[Grade level: 9-11 | Topics: Algebra I; evaluating a function for specific values]

**Problem 87 **** Atmospheric Shielding from Radiation- I -
** 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.
[Grade level: 9-11 | Topics: Algebra II, trigonometry]

**Problem 84 ****Beyond the Blue Horizon -
** 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.
[Grade level: 9-11 | Topics: Algebra, Pythagorean Theorem; Experts: DIfferential calculus) ]

**Problem 76 ****Radon Gas in the Basement -
** 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.
[Grade level: 6-8 | Topics: Unit conversion, arithmetic operations]

**Problem 46 ****A Matter of Perspective. -
** Why can't we see aurora at lower latitudes on Earth? 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.
[Grade level: 9-11 | Topics: Geometric proofs]

**Problem 37 ****Time Zone Mathematics.** 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. A series of simple time calculations teaches
students about converting from one time zone to another.
[Grade: 5 - 7 | Topics: Time zone math]

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

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

**Problem 31 ****Airline Travel and Space Weather ** Students will read an excerpt from the space weather
book 'The 23rd Cycle' by Dr. Sten Odenwald, and answer questions about
airline travel during solar storms. They will learn about the natural
background radiation they are exposed to every day, and compare this to
radiation dosages during jet travel. [Grade: 6 - 8 | Topics: Reading to be informed; decimal math]

**Problem 30 ****Exploring Earth's Magnetosphere [DOC]** Students will examine a NASA website that discusses
Earth's magnetosphere, and identify the definitions for key phenomena and
parts to this physical system. They will write a short essay that
describes, in their own words, how aurora are produced based on what they
have read at the NASA site. [Grade: 6 - 8 | Topics: non-mathematical; reading to be informed; online research]

**Problem 29 ****The Wandering Magnetic North Pole ** Mapmakers have known for centuries that Earth's
magnetic North Pole does not stay put. This activity will have students
read a map and calculate the speed of the 'polar wander' from 300 AD to
2000 AD. They will use the map scale and a string to measure the distance
traveled by the pole in a set period of time and calculate the wander
speed in km/year. They will answer questions about this changing speed.
[Grade: 6 - 8 | Topics: Interpreting graphical data; speed = distance/time]

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

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

**Problem 19 ****An Application of the Pythagorean
Theorem ** Students learn that the
Pythagorean Theorem is more than a geometric concept. Scientists use it
all the time when calculating lengths, speeds or other quantities. This
problem is an introduction to magnetism, which is a '3-dimensional
vector', and how to calculate magnetic strengths using the Pythagorean
Theorem. [Grade: 8 - 10 | Topics: Squares and square-roots; Pythagorean Theorem in 3-D]

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

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

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

**Problem 11 ****How high is an aurora ** 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.
[Grade: 5 - 8 | Topics: Geometery; angle measure]

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

**Problem 4 ****Sketching the Northern Lights** Students read an account of an aurora seen by an
observer, and create a drawing or painting based on the description.
[Grade: 5 - 7 | Topics: non-mathematical art problem]

**Problem 315: The Mysterious Hexagon on Saturn** A curious hexagon formed by the Saturn polar jet stream, and photographed by the Cassini spacecraft, is
used to determine wind speed and acceleration.
[Grade: 6-9 | Topics: Measuring; Metric Units; speed=distance/time]

**Problem 314: Chandra Studies an Expanding Supernova Shell** Using a millimeter ruler and a sequence of images of a gaseous shell between 2000 and 2007,
students calculate the speed of the material ejected by Supernova 1987A.
[Grade: 6-9 | Topics: Measuring; Metric Units; speed=distance/time]

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

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

**Problem 289: Chandra Spies the Longest Sound Wave in the 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.
[Grade: 6-8 | Topics: metric measurement; scaling; Scientific Notation; exponents]

**Problem 259: Mare Nubium And Las Vegas ** Students compare two satellite images taken at the same resolution to appreciate how large lunar features are compared to more familiar objects.
[Grade: 6-8 | Topics: scale, proportion, ratio]

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

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

**Problem 256: A High-resolution Satellite Photo ** Students examine a satelite photo of the Tennessee Court House from the GEO-1 satellite and determine the sizes of familiar features in the image.
[Grade: 6-8 | Topics: scale, ratios, proportions' angle measure, triangle geometry]

**Problem 255: Temple-1 - Closeup of a Comet ** Students examine an image of the Comet Temple-1 taken by the Dawn spacecraft to determine feature sizes and other details.
[Grade: 6-8 | Topics: scales, proportions ]

**Problem 240: The Eagle Nebula Close-up** Students measure a Hubble image of the famous Eagle Nebula 'Pillars of Creation' to determine the sizes of
arious features compared to our solar system
[Grade: 6-8 | Topics: scale, proportion, angle measure]

**Problem 239: Counting Galaxies with the Hubble Space Telescope ** Students use an image of a small area of the sky to estimate the total number of galaxies in the universe visible from Earth.
[Grade: 6-8 | Topics: area, angular measure]

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

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

**Problem 234: The Hand of Chandra** Students use an image from the Chandra Observatory to measure a pulsar ejecting a cloud of gas.
[Grade: 6-8 | Topics: Scientific Notation; proportions; angle measure]

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

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

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

**Problem 119 **** A Star Sheds a Comet Tail!
** 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.
[Grade: 8-10 | Topics:Image scaling; Unit conversion; Calculating speed from distance and time]

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

**Problem 112 ****How fast does the sun spin?
** Students will use two x-ray images of the sun taken by the Hinode satellite to determine how fast the sun rotates.
[Grade: 5-9 | Topics:calculating map scales; time calculations; unit conversion]

**Problem 107 ****Monster Sunspots!
** 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.
[Grade: 5-9 | Topics:multiplication; calculating length from image scale]

**Problem 105 ****The Transit of Mercury
** 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.
[Grade: 9-11 | Topics:image scales; angular measure; degrees, minutes and seconds]

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

**Problem 99 ****The Hinode Satellite Views the Sun -
** 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.
[Grade level: 6-8 | Topics:image interpretation; eye-hand coordination; reading to be informed]

**Problem 97 ****Hinode - Closeup of a Sunspot -
** Students will determine the sizes of sunspots and solar granulation cells from a recent image
taken by the Hinode solar observatory.
[Grade level: 6-8 | Topics:image scales, metric units, unit conversion]

**Problem 85 ****The Solar Tsunami! -
** 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.
[Grade level: 5-8 | Topics: Finding image scale; calculating time differences; calculating speed from distance and time]

**Problem 78 ****Moving Magnetic Filaments Near Sunspots -
** Students will use two images from the new, Hinode (Solar-B) solar observatory to calculate the speed of
magnetic filaments near a sunspot. The images show the locations of magnetic features at two different times. Students
calculate the image scales in kilometers/mm and determine the time difference to estimate the speeds of the selected
features.
[Grade level: 6-8 | Topics: scaling, estimation, speed calculations, time arithmetic ]

**Problem 63 ****
Solar Activity and Tree Rings - What's the connection? -
** Trees require sunlight to grow, and we know that solar
activity varies with the sunspot cycle. Can an average tree sense solar activity cycles and
change the way it grows from year to year? 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 Excell Spreadsheet Data File.
[Grade level: 4-6 | Topics: Spreadsheets and technology; decimal math]

**Problem 52 ****Measuring the size of a Star Cluster -
** Astronomers often use a photograph to determine the size of astronomical objects. The
Pleiades is a famous cluster of hundreds of bright 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.
[Grade level: 4-6 | Topics: Online research; Finding the scale of an image; metric measurement; decimal math]

**Problem 51 ****Sunspots Close-up and Personal -
** 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.
[Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; decimal math]

**Problem 50 ****Measuring the Speed of a Galaxy. -
** Astronomers can measure the speed of a galaxy by using the Doppler Shift. By studying
the spectrum of the light from a
distant galaxy, the shift in the wavelength of certain spectral lines from elements such as hydrogen, can be decoded to
give the speed of the galaxy either towards the Milky Way or away from it. 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.
[Grade level: 6-8 | Topics: Interpolating data in a graph; decimal math]

**Problem 47 ****Discovering the Milky Way by Counting Stars. -
** It is common to say that there are about 8,000 stars visible to the naked eye in
both hemispheres of the sky, although from a typical urban setting, fewer
than 500 stars are actually visible. 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. This number is a lower-limit to the roughly 250 to 500 billion stars that
may actually exist in the Milky Way.
[Grade level: 4-6 | Topics: Tallying data; decimal math]

**Problem 46 ****A Matter of Perspective. -
** Why can't we see aurora at lower latitudes on Earth? 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.
[Grade level: 9-11 | Topics: Geometric proofs]

**Problem 29 ****The Wandering Magnetic North Pole ** Mapmakers have known for centuries that Earth's
magnetic North Pole does not stay put. This activity will have students
read a map and calculate the speed of the 'polar wander' from 300 AD to
2000 AD. They will use the map scale and a string to measure the distance
traveled by the pole in a set period of time and calculate the wander
speed in km/year. They will answer questions about this changing speed.
[Grade: 6 - 8 | Topics: Interpreting graphical data; speed = distance/time]

**Problem 26 ****Super-sized Sunspots and the Solar
Cycle.** Students compare the dates of
the largest sunspots since 1900 with the year of the peak sunspot cycle.
They check to see if superspots are more common after sunspot maximum or
before. They also compare superspot sizes with the area of earth.
[Grade: 6 - 8 | Topics: Interpreting tabular data; decimal math]

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

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

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

**Problem 150: Cosmic Bar Graphs -** Students interpret simple bar graphs taken from astronomical data.
[Grade: 3-5 | Topics: finding maxima and minima; fractions; extrapolating data]

**Problem 100 The Sunspot Cycle - endings and beginnings - **
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.
[Grade level: 6-9 | Topics:graph reading; extrapolation; time calculations]

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

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

**Problem 587: Comet Encounters after Discovery **

Students examine how often newly discovered comets approach Earth and become a hazard, and how soon after discovery these close passes can occur.
[Grade: 3-5 | Topics: Averaging, percentages]
(PDF)

**Problem 586: Searching for Comets **

Students use tabular data on the detection of new comets since 1999 to explore detection rates over time.
[Grade: 3-5 | Topics: Percentages]
(PDF)

**Problem 582: How do Telescopes Magnify? **

Students use a simple ratio formula to calculatethe magnification of a telescope.
[Grade: 3-5 | Topics: division of two decimal numbers; evaluating simple ratios. ]
(PDF)

**Problem 581: How Telescopes Work **

Students compare how much light a telescope can gather compared to the human eye.
[Grade: 3-5 | Topics: Area of a circle ]
(PDF)

**Problem 570: Curiosity Heads for Mt Sharp **

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.
[Grade: 3-5 | Topics: averaging numbers in a table; time = distance/speed]
(PDF)

**Problem 563:Comet ISON and its Close Encounter with Mars**

Students use tabular data to determine the date and time of closest approach to Mars
[Grade: 3-5 | Topics: graphing tabular data]
(PDF)

**Problem 560:The Orbit of Comet ISON**

Students explore how close Comet ISON will get to Mercury, Venus, Earth and Mars during its 2013 passage.
[Grade: 3-5 | Topics: Interpreting tabular data; graphing ]
(PDF)

**Problem 541:How to Build a Planet**

Students study planet growth by using a clay model of planetessimals combining to form a planet by investigating volume addition with spheres.
[Grade: 3-5 | Topics: graphing; counting]
(PDF)

**Problem 198: Solar Storm Timeline-** Students read a narrative about the events involved in a solar storm, creates a chronology for the sequence of events, and answer some simple time-related questions.
[Grade: 6-8| Topics: Time calculations.]

**Problem 100 The Sunspot Cycle - endings and beginnings - **
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.
[Grade level: 6-9 | Topics:graph reading; extrapolation; time calculations]

## Properties of Numbers, Fractions, Percentage, Scientific Notation, Unit Conversions

**Problem 556:IRIS Explores the Solar Transition Region**

Students use an image from IRIS to examine the sizes and equivalent energy of bright regions in the solar transition region.
[Grade: 6-8 | Topics: percentage; proportion; scale; scientific notation; volume of a cylinder]
(PDF)

**Problem 555:Exploring Your Weight Across the Solar System**

Students estimate their weight on different planets, moons and asteroids.
[Grade: 6-8 | Topics: proportions]
(PDF)

**Problem 545:Measuring Atmospheric Trace Gases Using Parts Per Million**

Students convert from percentage units to parts per million and compare trace gases in the atmospheres of various planets.
[Grade: 6-8 | Topics: percentages; unit conversions ]
(PDF)

**Problem 544:The Composition of Planetary Atmospheres**

Students study the composition of planetary atmospheres and compare the amounts of certain compounds in them
[Grade: 6-8 | Topics: Pie graphs; percentages; scientific notation]
(PDF)

**Problem 539:Visiting the Planets at the Speed of Light**

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.
[Grade: 6-8 | Topics: Proportions; unit conversions; time = distance/speed; metric units]
(PDF)

**Problem 538:How Big is Our Solar System?**

Students work with proportions to convert solar system distances into Astronomical Units for the 8 planets.
[Grade:6-8 | Topics: Proportions; unit conversions]
(PDF)

**Problem 493: Fun with Gears and Fractions **

Students learn about how simple fractions are used to describe gears and gear trains that reduce or increase speed.
[Grade: 4-7 | Topics: multiplying simple fractions]
(PDF)

**Problem 446: Arctic Ozone Hole Continues to Grow in 2011 **

Students estimate the area of the Arctic ozone hole, and work with the concept of parts-per-million to estimate total ozone volume lost. [Grade: 6-8 | Topics: Area of rectangle; volume; percentage]
(PDF)

**Problem 444: Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine - II **

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

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

**Problem 400: The Most Distant Objects in the 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.
[Grade: 6-8 | Topics: Working with millions and billions; elapsed time]
(PDF)

**Problem 399: A Galactic City in the Far Reaches of the Universe**
Students work with an image of a distant cluster of galaxies to determine its scale compared to nearby galaxies.
[Grade: 6-8 | Topics: Scale; proportion; metric measurement; unit conversion]
(PDF)

**Problem 398: The Crab Nebula - Exploring a pulsar up close!**
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.
[Grade: 6-8 | Topics: Scale drawings; unit conversion; distance = speed x time]
(PDF)

**Problem 356: Calculating Molecular Mass**

Students count hydrogen, carbon and oxygen atoms in a molecule of adefovir dipivoxil and calculate its mass and formula.[Grade: 6-8 | Topics: Counting; Scientific Notation]
(PDF)

**Problem 345: How many stars are there?**

A starfield image taken by the 2MASS survey is analyzed to estimate how many stars are in the sky. [Grade: 6-8 | Topics: Scaling; unit conversion; angular measure]
(PDF)

**Problem 344: Hubble Spies an Asteroid - Yes it does move!**

The track of an asteroid in a Hubble image of a cluster of galaxies is analyzed to determine speed of the asteroid.[Grade: 6-8 | Topics: Scaling; unit conversion; speed=distance/time]
(PDF)

**Problem 342: The Rate of Oil Leakage in the Gulf Oil Spill of 2010** 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.
[Grade: 6-8 | Topics: unit conversions; rates; image scale]

**Problem 341: Recent Events: A Perspective on Carbon Dioxide** 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.
[Grade: 6-8 | Topics: unit conversions; rates ]

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

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

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

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

**Problem 301: Planetary Alignments** Students combine a geometric model with number series to calculate when planets will 'line up' in a simple solar system.
[Grade: 4-8 | Topics: Number series; geometry; Least Common Multiple]

**Problem 294: Star Cluster Math** A simple counting exercise involving star classes lets students work with percentages and ratios.
[Grade: 4-6 | Topics: Counting; percentage; scaling]

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

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

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

**Problem 260: Some Famous Unit Conversion Errors ** Students examine three famous unit conversion errors that led to catastrophic failures and near-death experiences.
[Grade: 6-8 | Topics: unit conversion, metric measure]

**Problem 301: Planetary Alignments** Students combine a geometric model with number series to calculate when planets will 'line up' in a simple solar system.
[Grade: 4-8 | Topics: Number series; geometry; Least Common Multiple]

**Problem 300: Does Anybody Really Know What Time It Is?** 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.
[Grade: 4-8 | Topics: Graphing; Finding Slopes; forecasting]

**Problem 297: Atoms - How Sweet They Are!** A simple counting activity is based on atoms in a sugar molecule. Students calculate ratios and percantages
of various atomic types in the molecule.
[Grade: 4-8 | Topics: Counting; Ratios; percentage]

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

**Problem 267: Identifying Materials by their Reflectitity** 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.
[Grade: 6-8 | Topics: percentage, interpreting tabular data, area ]

**Problem 260: Some Famous Unit Conversion Errors** Students examine three famous unit conversion errors that led to catastrophic failures and near-death experiences.
[Grade: 6-8 | Topics: unit conversion, metric measure]

**Problem 251: Energy at Home** Students explore watts and kilowatt-hours as measures of energy and energy consumption.
[Grade: 6-8 | Topics: unit conversions; use of kilo and mega]

**Problem 253: NASA 'Sees' Carbon Dioxide ** A satellite image of atmospheric carbon dioxide is used to estimate the geographic differences and identify human activity.
[Grade: 6-8 | Topics: interpreting a data image, unit conversion, gigatons ]

**Problem 252: Carbon Dioxide Increases ** Students study the Keeling Curve to determine the rates of increase of carbon dioxide in the atmosphere.
[Grade: 6-8 | Topics: graph analysis, slope, rates, unit conversion, parts-per-million, gigatons]

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

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

**Problem 231: Star Magnitudes and Decimals-** Students work with the stellar magnitude scale to determine the brightness differences between stars.
[Grade: 5-8 | Topics: Multiplying decimals.]

**Problem 195: Unit Conversions III-** Students work with more unit conversions and use them to solve a series of practical problems in science and solar energy.
[Grade: 6-10| Topics: unit conversions.]

**Problem 171: Are U Really Nuts?-** Students work with four unit conversion problems that are a bit tricky!
[Grade: 6-8 | Topics: unit conversions]

**Problem 123 ****A Trillion Here...A Trillion There **
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.
[Grade: 5-9 | Topics:add, subtract, multiply, divide.]

**Problem 111 ****Scientific Notation III **
In this continuation of the review of Scientific Notation,
students will perform simple multiplication and division problems with an astronomy and space science
focus.
[Grade: 5-9 | Topics:Scientific notation - multiplication and division]

**Problem 110 ****Scientific Notation II **
In this continuation of the review of Scientific Notation,
students will perform simple addition and subtraction problems.
[Grade: 5-9 | Topics:Scientific notation - addition and subtraction]

**Problem 109 ****Scientific Notation I **
Scientists use scientific notation to
represent very big and very small numbers. In this
exercise, students will convert some 'astronomical' numbers into SN form.
[Grade: 5-9 | Topics:Scientific notation - conversion from decimal to SN]

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

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

**Problem 82 ****Are U nuts? - **
Students will use a number of obscure English units measures to convert from metric to English units and back, and answer some
unusual questions!
[Grade level: 6-8 | Topics: arithmetic; unit conversions involving 1 to 5 steps) ]

**Problem 67 ****Unit Conversion Exercises -**
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.
[Grade level: 6-8 | Topics: fractions, decimals, units]

**Problem 64 ****Solar Activity and Satellite Mathematics - **
When solar storms cause satellite problems, they can also cause satellites to lose money.
The biggest source of revenue from communications satellites comes from transponders that relay television programs, ATM
transactions and many other vital forms of information. They are rented to many different customers and can cost nearly
$2 million a year for each transponder. This activity examines what happens to a single satellite when space weather
turns bad! [Grade level: 4-6 | Topics: Decimals; money; percents]

**Problem 58 ****How many stars are there? - **
For thousands of years, astronomers have counted the stars to
determine just how vast the heavens are. Since the 19th century, 'star gauging' has been
an important
tool for astronomers to assess how the various populations of stars are distributed within
the Milky Way. In fact, this was such an important aspect of astronomy between 1800-1920 that
many cartoons often show a frazzled astronomer looking through a telescope, with a long
ledger at his knee - literally counting the stars through the eyepiece! 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.
[Grade level: 6-8 | Topics: Positive and negative numbers; histogramming; extrapolating data]

**Problem 48 ****Scientific Notation - An Astronomical Perspective. - **
Astronomers use scientific notation because the numbers they work with are usually..astronomical in size. 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. They will learn about the planet Osiris, how long it takes to
download all of
NASA's data archive, the time lag for radio signals to Pluto, and many more real-world applications.
[Grade level: 8-10 | Topics: Scientific notation; decimal math]

**Problem 39 ****Solar Storm Timeline ** How long does a solar storm last? How fast does it travel? Students will examine
an event timeline for a space weather event and use time addition and subtraction skills to
calculate storm durations and speeds. [Grade level: 7-9 | Topics: time math; decimal math; speed = distance/time]

## Graphs, Graphical Analysis and Rates

**Problem 577: Designing a Telescope System **

Students design two telescopes given information about the desired properties for conducting research.
[Grade: 6-8 | Topics: graphing inequalities; evaluating simple equations ]
(PDF)

**Problem 566:Exploring Light Brightness and the Inverse Square Law**

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.
[Grade: 6-8 | Topics: graphing tabular data; surface area of a sphere; ]
(PDF)

**Problem 562:Exploring the Orbit of Comet ISON**

Students use tabulated data to estimate when this comet will make its closest approach to the sun in 2013.
[Grade: 6-8 | Topics: graphing tabular data; scale; measurement; distance between points]
(PDF)

**Problem 558:How Quickly are NEOs Being Discovered?**

Students work with data presented in bar graphs to estimate how many more hazardous Near Earth Objects (NEOS) remein to be found.
[Grade: 6-8 | Topics:bar graphs ]
(PDF)

**Problem 557:The 10000th Near Earth Asteroid 2013 MZ5**

Students graph tabulated data to determine when this asteroid is closest to Earth and its speed at that time.
[Grade: 6-8 | Topics: graphing tabular data; solving a linear equation]
(PDF)

**Problem 486: RBSP Hears Dawn Chorus - I**

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

**Problem 471: Investigating the Launch of the Juno Spacecraft **

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

**Problem 470: The Launch of the Juno Spacecraft - Ascent to orbit **

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

**Problem 459: A piece of history - space shuttle thermal tiles **

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

**Problem 453: The Closest Approach of Asteroid 2005YU55 - II **

Students work with the properties of circles and angular measure to see where the moon will be at the start of the asteroid encounter.
[Grade: 6-8 | Topics: angular measure; time=distance/speed; scale models; metric math]
(PDF)

**Problem 408: Estimating the Speed of a Tsunami**
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.
[Grade: 6-8 | Topics: Time arithmetic; time zones; speed = distance/time]
(PDF)

**Problem 405: Discovering Earth-like Worlds by their Color **
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
[Grade: 6-8 | Topics: graphing tabular data; interpreting graphical data]
(PDF)

**Problem 395: Death 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
[Grade: 6-9 | Topics: Scientific Notation; percentages; rates of change]
(PDF)

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

**Problem 386: Whacky Spacecraft Orbits - They only seem crazy!**

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.
[Grade: 6-8 | Topics: distance=speedxtime; scientific notation; unit conversion]
(PDF)

**Problem 384: Detecting the Most Distant SUpernova in the Universe**

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.
[Grade: 6-8 | Topics: Analyzing a graph; interpreting mathematical models]
(PDF)

**Problem 358: A Flyby of Asteroid Lutetia**

The Rosette mission flew by an asteroid. An application of the Pythagorean Theorem and angular size.[Grade: 6-8 | Topics: image scale; Pythagorean Theorem; rates]
(PDF)

**Problem 355: Astronaut Bone Loss**

From a graph, students predict how much bone loss an astronaut experiences during a long-duration stay in space.[Grade: 6-8 | Topics: Rates; linear equations]
(PDF)

**Problem 354: Earth's Polar Wander - The Chandler Wobble**

Students plot the circular shape of the track of the North Pole during a 2-year period and estimate the speed of movement. [Grade: 6-8 | Topics: Graphing ordered pairs]
(PDF)

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

**Problem 300: Earth's Rotation Changes and the Length of the Day?** 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.
[Grade: 4-8 | Topics: Graphing; Finding Slopes; forecasting]

**Problem 90 **** A Career in Astronomy - **
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.
[Grade level: 6-8 | Topics: graph reading; percentages; interpolation]

**Problem 227: Working With Rates-** Students examine mixed rates for a variety of situations and their connections to ratios.
[Grade: 6-8 | Topics: Ratios; scientific notation; unit conversion.]

**Problem 226: Rates and Slopes: An astronomical perspective-** Students determine the slopes for two linear graphs and make the connection to rates with mixed units.
[Grade: 7-9 | Topics: Finding the slope of a linear graph.]

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

**Problem 502:The Frequency of Large Meteor Impacts **

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.
[Grade: 6-8 | Topics: percercentages, areas]
(PDF)

**Problem 487: The Hubble eXtreme Deep Field **

Students use the Hubble XDF to estimate the number of galaxies in the visible universe.
[Grade: 6-8 | Topics: Counting, areas, proportions ]
(PDF)

**Problem 468: How Common are X-Class Solar Flares? **

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
[Grade: 5-7 | Topics: mean, median, percentage]
(PDF)

**Problem 460: Fermi Explores the High-Energy Universe**

Students work with percentages to explore the identities of the 1873 gamma-ray sources detected by NASAs Fermi Observatory
[Grade: 6-8 | Topics: percentages; pie graphs]
(PDF)

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

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

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

**Problem 372: LRO Determines Lunar Cratering History **

Students count large craters on an LRO coded image of the lunar surface to estimate whether the impacting asteroids
that produced the largest
craters were from the same population of asteroids during the two different epocs of impacts.
[Grade: 6-8 | Topics: Scaled images; probability; percentages]
(PDF)

**Problem 253: NASA 'Sees' Carbon Dioxide ** A satellite image of atmospheric carbon dioxide is used to estimate the geographic differences and identify human activity.
[Grade: 6-8 | Topics: interpreting a data image, unit conversion, gigatons ]

**Problem 252: Carbon Dioxide Increases ** Students study the Keeling Curve to determine the rates of increase of carbon dioxide in the atmosphere.
[Grade: 6-8 | Topics: graph analysis, slope, rates, unit conversion, parts-per-million, gigatons]

**Problem 211: Where Did All the Stars Go?-** Students learn why NASA photos often don't show stars because of the way that cameras take pictures of bright and faint objects.
[Grade: 6-8| Topics: multiplication; division; decimal numbers.]

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

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

**Problem 152: The Hubble Law -** 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.
[Grade: 6-8 | Topics: Plotting data; determining the slope of the data;]

**Problem 120 ****Benford's Law
** 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.
[Grade: 8-10 | Topics:Calculating frequency tables; Histogramming; Statistics]

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

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

**Problem 90 **** A Career in Astronomy -
** 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.
[Grade level: 6-8 | Topics: graph reading; percentages; interpolation]

**Problem 86 ****Do Fast CMEs Produce SPEs? -
** 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.
[Grade level: 5-8 | Topics: Venn Diagrams; counting; calculating percentages and odds]

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

**Problem 53 ****Astronomy: A Moving Experience! -
** Objects in space move. To figure out how fast they move,
astronomers use many different techniques depending on what they are investigating.
In this activity, you will measure the speed of astronomical phenomena using the scaling
clues and the time intervals between photographs of three phenomena: A supernova
explosion, a coronal mass ejection, and a solar flare shock wave.
[Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; distance = speed x time; scientific notation]

**Problem 32 ****Solar Proton Events and Satellite
Damage** Students will examine the
statistics for Solar Proton Events since 1996 and estimate their damage to
satellite solar power systems. [Grade: 7 - 9 | Topics: Interpreting tabular data; histogramming]

**Problem 28 ****Satellite Power and Cosmic Rays ** Most satellites operate by using solar cells to
generate electricity. But after years in orbit, these solar cells produce
less electricity because of the steady impact of cosmic rays. 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. Basic math ideas: Area
calculation, unit conversions, extrapolation and interpolation of graph
trends. [Grade: 6 - 8 | Topics: Interpreting graphical data; decimal math]

**Problem 27 ****Satellite Failures and the Sunspot
Cycle ** There are over 1500 working
satellites orbiting Earth, representing an investment of 160 billion
dollars. Every year, between 10 and 30 of these re-enter the atmosphere.
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. [Grade: 6 - 8 | Topics: Graphing tabular data; decimal math]

**Problem 9 ****Aurora Power!**
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. [Grade: 5 - 7 | Topics: Interpreting tabular data]

**Problem 8 ****Making a Model Planet** 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). [Grade: 7 - 9 | Topics: Volume of sphere; mass = density x volume; decimal math; scientific notation]

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

**Problem 564:Exploring the Stars in Orion - Light Year Madness**

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?
[Grade: 6-8 | Topics: time lines; time intervalcalculations; time = distance/speed ]
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**Problem 507: Exploring the Launch of the Falcon 9**

Students use data from the launch of the Falcon 9 booster to determine its speed and acceleration.
[Grade: 6-8 | Topics: speed=distance/time; Time calculations]
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**Problem 505: SDO Sees Coronal Rain - Estimating Plasma Speeds**

Students estimate the speed of plasma streamers near the solar surface using images from a Solar Dynamics Observatory.
[Grade: 6-8 | Topics: scale models; speed=distance/time; proportions]
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**Problem 488: RBSP and the Location of Dawn Chorus - II **

Students use hypothetical information from the twin RBSP spacecraft to triangulate the location of the Chorus signal near Earth using angle measurements, graphing and protractors to identify the intersection point of the CHorus signals.
[Grade: 6-8 | Topics: Angles; graphing; protractors ]
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**Problem 452: The Closest Approach of Asteroid 2005YU55 - I **

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.
[Grade: 6-8 | Topics: time=distance/speed; scale models; metric math]
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**Problem 451: The Spectacular Cat's Eye Planetary Nebula **

Students measure the diameter of the nebula and use speed information to estimate the age of the nebula
[Grade: 6-8 | Topics: time=distance/speed; scale models; metric math]
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**Problem 445: LRO - The relative ages of lunar surfaces **

Students examine two Apollo landing areas using images from the LRO spacecraft to estimate the relative ages of the two regions using
crater counting. [Grade: 6-8 | Topics: scale; histogramming]
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**Problem 438: The Last Flight of the Space Shuttle Endeavor **

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

Students use tabular data to determine the launch speed of the Saturn V rocket from the launch pad.
[Grade: 6-8 | Topics: tabular data, graphing, metric measurement, speed=distance/time]
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**Problem 436: Space Shuttle Challenger Deploys the INSAT-1B Satellite **

Students use a sequence of images to determine the launch speed of the satellite from the Space Shuttle cargo bay.
[Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time]
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**Problem 435: Apollo-17 Launch from Lunar Surface **

Students use a sequence of images to determine the speed of ascent of the Apollo-17 capsule from the lunar surface.
[Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time]
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**Problem 434: Dawn Spacecraft Sees Asteroid Vesta Up-Close! **

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.
[Grade: 6-8 | Topics: scale, metric measurement]
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**Problem 433: Space Shuttle Atlantis - Plume Speed **

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

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

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

Students use a sequence of images from a video of the launch to determine speed from the time
interval between the images, and the scale of each image.
[Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time]
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**Problem 429: Tracking a Sea Turtle from Space **

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.
[Grade: 4-6| Topics: scale, metric measurement, speed=distance/time]
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**Problem 404: STEREO Spacecraft give 360-degree Solar View**
Students use STEREO satellite images to determine which features can be seen from Earth and which cannot. They learn
about the locations and changing positions of the satellites with respect to Earth's orbit.
[Grade: 6-8 | Topics: angular measure, extrapolation; distance = speed x time]
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**Problem 267: Identifying Materials by their Reflectivity ** 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.
[Grade: 6-8 | Topics: percentage, interpreting tabular data, area ]

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

**Problem 247: Space Mobile Puzzle ** 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.
[Grade: 6-8 | Topics: metric measure, algebra 1, geometry]

**Problem 245: Solid Rocket Boosters** Students learn how SRBs actually create thrust, and study the Ares-V booster to estimate its thrust.
[Grade: 6-8 | Topics: volume, area, unit conversions]

**Problem 238: Satellite Drag and the Hubble Space Telescope ** Satellite experience drag with the atmosphere, which eventually causes them to burn up in the atmosphere. Students study
various forecasts of the althtiude of the Hubble Space Telescope to estimate its re-entry year.
[Grade: 6-8 | Topics: interpreting graphical data; predicting trends]

**Problem 209: How to make faint things stand out in a bright world!-** Students learn that adding images together often enhances faint things not seen in only one image; the power of averaging data.
[Grade: 6-8| Topics: multiplication; division; decimal numbers.]

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

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

**Problem 134 ****The Last Total Solar Eclipse--Ever!
** 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.
[Grade: 7 - 10 | Topics:Simple linear equations]

**Problem 124 ****The Moon's Atmosphere!
** 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.
[Grade: 8-10 | Topics:volume of sphere, shell; density-mass-volume; unit conversions]

**Problem 115 ****A Mathematical Model of the Sun
** Students will use the formula for a sphere and a shell to calculate the mass of the
sun 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.
[Grade: 8-10 | Topics: scientific notation; volume of a sphere and a spherical shell; density, mass and volume.]

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

**Problem 83 ****Luner Meteorite Impact Risks -
** 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.
[Grade level: 8-10 | Topics: arithmetic; unit conversions; surface area of a sphere) ]

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

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

**Problem 68 ****An Introduction to Space Radiation -
** Read about your natural background radiation dosages, learn about
Rems and Rads, and the difference between low-level dosages and high-level dosages. Students use
basic math operations to calculate total dosages from dosage rates, and calculating cancer risks.
[Grade level: 6-8 | Topics: Reading to be Informed; decimals, fractions, square-roots]

**Problem 66 ****Background Radiation and Lifestyles -
** 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.
[Grade level: 6-8 | Topics: fractions, decimals, unit conversions]

**Problem 54 ****Exploring Distant Galaxies -
** Astronomers determine the redshifts of distant
galaxies by using spectra and measuring the wavelength shifts for familiar
atomic lines. The larger the redshift, denoted by the letter Z, the more distant the galaxy.
In this activity, students will use an actual image of a distant corner of the universe, with the redshifts
of galaxies identified. After histogramming the redshift distribution, they will use an
on-line cosmology calculator to determine the 'look-back' times for the galaxies and
find the one that is the most ancient galaxy in the field. Can students find a galaxy formed only
500 million years after the Big Bang?
[Grade level: 6-8 | Topics: Decimal math; using an online calculator; Histogramming data]

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

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

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

**Problem 31 ****Airline Travel and Space Weather ** Students will read an excerpt from the space weather
book 'The 23rd Cycle' by Dr. Sten Odenwald, and answer questions about
airline travel during solar storms. They will learn about the natural
background radiation they are exposed to every day, and compare this to
radiation dosages during jet travel. [Grade: 6 - 8 | Topics: Reading to be informed; decimal math]

**Problem 10 ****The Life Cycle of an Aurora** Students examine two eye-witness descriptions of an
aurora and identify the common elements so that they can extract a common
pattern of changes. [Grade: 4 - 6 | Topics: Creating a timeline from narrative; ordering events by date and time]

**Problem 64 ****Solar Activity and Satellite Mathematics -
** When solar storms cause satellite problems, they can also cause satellites to lose money.
The biggest source of revenue from communications satellites comes from transponders that relay television programs, ATM
transactions and many other vital forms of information. They are rented to many different customers and can cost nearly
$2 million a year for each transponder. This activity examines what happens to a single satellite when space weather
turns bad! [Grade level: 4-6 | Topics: Decimals; money; percents]

**Problem 671:VAB - The Van Allen Probes and Radiation Dose**
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.
[Grade: 8-10 | Topics: Unit conversion; rates]
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**Problem 227: Working With Rates-** Students examine mixed rates for a variety of situations and their connections to ratios.
[Grade: 6-8 | Topics: Ratios; scientific notation; unit conversion.]

**Problem 226: Rates and Slopes: An astronomical perspective-** Students determine the slopes for two linear graphs and make the connection to rates with mixed units.
[Grade: 7-9 | Topics: Finding the slope of a linear graph.]

**Problem 65 ****A Perspective on Radiation Dosages -
** 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.
[Grade level: 6-8 | Topics: decimals, unit conversions, graphing a timeline, finding areas under curves using rectangles]

**Problem 134 ****The Last Total Solar Eclipse--Ever!
** 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.
[Grade: 7 - 10 | Topics:Simple linear equations]

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

**Problem 54 ****Exploring Distant Galaxies -
** Astronomers determine the redshifts of distant
galaxies by using spectra and measuring the wavelength shifts for familiar
atomic lines. The larger the redshift, denoted by the letter Z, the more distant the galaxy.
In this activity, students will use an actual image of a distant corner of the universe, with the redshifts
of galaxies identified. After histogramming the redshift distribution, they will use an
on-line cosmology calculator to determine the 'look-back' times for the galaxies and
find the one that is the most ancient galaxy in the field. Can students find a galaxy formed only
500 million years after the Big Bang?
[Grade level: 9-11 | Topics: Decimal math; using an online calculator; Histogramming data]

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

**Problem 57 ****Asteroids and comets and meteors - Oh My! -
** Astronomers have determined the orbits for over 30,000 minor planets
in the solar system, with hundreds of new ones discovered every year. Working from a map of the locations
of these bodies within the orbit of Mars, students 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.
[Grade level: 4-6 | Topics: Scale model; Decimal math; Interpreting 2-D graph]

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

**Problem 102 ****How fast does the sun rotate?
** 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'.
[Grade: 6-9 | Topics:image scales; time calculations; speed calculations, unit conversions]

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

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

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

**Problem 53 ****Astronomy: A Moving Experience! -
** Objects in space move. To figure out how fast they move,
astronomers use many different techniques depending on what they are investigating.
In this activity, you will measure the speed of astronomical phenomena using the scaling
clues and the time intervals between photographs of three phenomena: A supernova
explosion, a coronal mass ejection, and a solar flare shock wave.
[Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; distance = speed x time; scientific notation]

**Problem 377: Deep Impact: Approaching Comet Hartley-2 **

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.
[Grade: 8-10 | Topics: linear modeling from data; inverse-square law]
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