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Mathematics Weekly Page
This page contains sets sorted by science topic area. The Nationl Academy of Science website includes a complete statement of the national mathematics standards for each grade. These may be found at Unifying Concepts and Processes. Click on the topics below to bring up the NAS page describing the relevant Standards.

Properties of Objects and Materials

Problem 233: The Milky Way: A mere cloud in the cosmos- Students compare the average density of the Milky Way with the density of the universe. [Grade: 8-10 | Topics: Volume of disk, density, scientific notation]

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 200: The Moon's Density - What's Inside?- Students develop a simple mathematical model of the moon's interior using two nested spheres with different densities. [Grade: 9-12| Topics: Volume of a sphere; mass = density x volume.]

Problem 190: Modeling a Planetary Nebula - Students use calculus to create a mathematical model of a planetary nebula [Grade: 10-12| Topics: Algebra, Integral calculus]

Problem 178: The Mass of the Moon - Students use the period and altitude of a NASA lunar spacecraft to determine the mass of the moon. [Grade: 8-11| Topics: Algebra]

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

Problem 60 When is a planet not a planet? - In 2003, Dr. Michael Brown and his colleagues at CalTech discovered an object nearly 30% larger than Pluto, which is designated as 2003UB313. It is also known unofficially as Xenia, after the famous Tv Warrior Princess! Is 2003UB313 really a planet? In this activity, students will examine this topic by surveying various internet resources that attempt to define the astronomical term 'planet'. How do astronomers actually assign names to astronomical objects? Does 2003UB313 deserve to be called a planet, or should it be classified as something else? What would the new classification mean for asteroids such as Ceres, or objects such as Sedna, Quaoar and Varuna? [Grade level: 9-11 | Topics: Non-mathematical essay; reading to be informed]

Problem 59 Getting A Round in the Solar System! - How big does a body have to be before it becomes round? In this activity, students examine images of asteroids and planetary moons to determine the critical size for an object to become round under the action of its own gravitational field. Thanks to many Internet image archives this activity can be expanded to include dozens of small bodies in the solar system to enlarge the research data for this problem. Only a few example images are provided, but these are enough for the student to get a rough answer! [Grade level: 9-11 | Topics: Data analysis; decimals; ratios; graphing]

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: 9-11 | Topics: Positive and negative numbers; histogramming; extrapolating data]

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: 9-11 | Topics: Scale model; Decimal math; Interpreting 2-D graph]

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

Position and Motion of Objects

Problem 168: Fitting Periodic Functions - Distant Planets- Students work with data from a newly-discoveblack extra-solar planet to determine its orbit period and other parameters of a mathematical model. [Grade: 9-12 | Topics: trigonometry; functions; algebra]

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

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: 9-11 | Topics: Finding image scale; calculating time differences; calculating speed from distance and 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: 9-11 | Topics: Finding the scale of an image; metric measurement; distance = speed x time; scientific notation]

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 ]

Properties of Matter

Problem 233: The Milky Way: A mere cloud in the cosmos- Students compare the average density of the Milky Way with the density of the universe. [Grade: 8-10 | Topics: Volume of disk, density, scientific notation]

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 200: The Moon's Density - What's Inside?- Students develop a simple mathematical model of the moon's interior using two nested spheres with different densities. [Grade: 9-12| Topics: Volume of a sphere; mass = density x volume.]

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

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 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.]

Motions and Forces

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 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 210: The Mathematics of Ion Rocket Engines- Students learn about the basic physics of ion engines, calculating speeds. [Grade: 9-12| Topics: Scientific Notation; Algebra II; evaluating formulae.]

Problem 202: The Dawn Mission - Ion Rockets and Spiral Orbits- Students determine the shape of the trajectory taken by a spacecraft using a constant-thrust ion motor using differential and integral calculus for arc lengths. [Grade: 9-12| Topics: Calculus - Arc lengths.]

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 192: The Big Bang - Cosmic Expansion - Students explore the expansion of the universe pblackicted by Big Bang cosmology [Grade: 10-12| Topics: Algebra, Integral Calculus]

Problem 188: Cross Sections and Collision Times - Students explore the relationship between density, speed and size in determining how quickly particles collide in a gas. [Grade: 9-11| Topics: Algebra; Area]

Problem 186: Collapsing Gas Clouds and Stability- Students use the derivative to find an extremum of an equation governing the pressure balance of an interstellar cloud. [Grade: 11-12| Topics: differentiation; finding extrema; partial derivitives]

Problem 184: The Ant and the Turntable: Frames of reference - Students pblackict the motion of an ant crawling from the center of a spinning CDrom to the edge. They also use calculus to estimate the length of the spiral path seen by a stationary observer. [Grade: 11-12| Topics: integration; parametric equations; polar coordinates]

Problem 183: Calculating Arclengths of Simple Functions- Students determine the basic equation for arclength and its integral, and evaluate it for simple polar functions. [Grade: 11-12| Topics: calculus; integration; parametric equations]

Problem 181: Extracting Oxygen from Moon Rocks- Students use a chemical equation to estimate how much oxygen can be liberated from a sample of lunar soil. [Grade: 9-11| Topics: ratios; scientific notation; unit conversions]

Problem 179: Is There a Lunar Meteorite Impact Hazard? - Students work with areas, probability and impact rates to estimate whether lunar colonists are in danger of meteorite hazards. [Grade: 5-7| Topics: Area; unit conversions; rates]

Problem 178: The Mass of the Moon - Students use the period and altitude of a NASA lunar spacecraft to determine the mass of the moon. [Grade: 8-11| Topics: Algebra]

Problem 157: Space Shuttle Launch Trajectory - I - Students use the parametric equation for the altitude and range for an actual Shuttle launch to determine the speed and acceleration of the Shuttle during launch and orbit insertionh [Grade: 11-12 | Topics: Algebra; Calculus; Parametric Equations; Differentiation

Problem 155: Tidal Forces: Let 'er rip! - Students explore tidal forces and how satelites are destroyed by coming too close to their planet. [Grade: 7-10| Topics: Algebra; number substitution]

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

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

Problem 106 Oscillating Spheres Many astronomical bodies have a natural period of oscillation. In this problem, students will use a simple mathematical model to calculate the period of oscillation of a star, a planet, and a neutron star from the estimated densities of these bodies. [Grade: 9-11 | Topics:Algebra; calculating with a formula]

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 81 The Pressure of a Solar Storm - Students will examine three mathematical models for determining how much pressure a solar storm produces as it affects Earth's magnetic field. They will learn that magnetism produces pressure, and that this accounts for many of the details seen in solar storms. [Grade level: 9-11 | Topics: Substituting numbers into equations; filling out missing table entries; data interpretation; mathematical models ]

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 14 Kinetic Energy and Particle Motion Students learn about kinetic energy and how this concept applies to charged particles. They calculate the speed of a particle for various particle energies. [Grade: 7 - 9 | Topics: Evaluating a function; square-roots; scientific notation]

Structure of Atoms

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

Problem 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: 9-11 | 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]

Structure of Matter

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 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 77 Some Puzzling Thoughts about Radiation! - Students fill-in the blanks in an essay on radiation risks using a word bank tied to solving quadratic equations to find the right words from a pair of possible 'solutions'. [Grade level: 9-11 | Topics: Finding the roots of a quadratic equation; solving for X ]

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: 9-11 | Topics: Unit conversion, arithmetic operations]

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: 9-11 | 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: 9-11 | Topics: decimals, area of rectangle, graph analysis]

Problem 70 Calculating Total Radiation Dosages at Mars - This problem uses data from the Mars Radiation Environment Experiment (MARIE) which is orbiting Mars, and measures the daily radiation dosage that an astronaut would experience in orbit around Mars. Students will use actual plotted data to calculate the total dosage by adding up the areas under the data curve. This requires knowledge of the area of a rectangle, and an appreciation of the fact that the product of a rate (rems per day) times the time duration (days) gives a total dose (Rems), much like the product of speed times time gives distance. Both represent the areas under their appropriate curves. Students will calculate the dosages for cosmic radiation and solar proton flares, and decide which component produces the most severe radiation problem. [Grade level: 9-11 | 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: 9-11 | 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: 9-11 | Topics: fractions, decimals, unit conversions]

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: 9-11 | Topics: decimals, unit conversions, graphing a timeline, finding areas under curves using rectangles]

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]

Chemical Reactions

Problem 181: Extracting Oxygen from Moon Rocks- Students use a chemical equation to estimate how much oxygen can be liberated from a sample of lunar soil. [Grade: 9-11| Topics: ratios; scientific notation; unit conversions]

Transfer of Energy

Problem 210: The Mathematics of Ion Rocket Engines- Students learn about the basic physics of ion engines, calculating speeds. [Grade: 9-12| Topics: Scientific Notation; Algebra II; evaluating formulae.]

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

Problem 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]

Light

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

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

Problem 203: Light Travel Times- Students determine the time it takes light to reach various objects in space. [Grade: 6-8| Topics: Scientific Notation; Multiplication; time = distance/speed.]

Problem 203: Light Travel Times- Students determine the time it takes light to reach various objects in space. [Grade: 6-8| Topics: Scientific Notation; Multiplication; time = distance/speed.]

Problem 191: Why are hot things black? - Students explore the Planck Function using graphing skills, and calculus for experts, to determine the relationship between temperature and peak wavelength. [Grade: 10-12| Topics: Algebra, graphing, differential calculus]

Heat

Problem 188: Cross Sections and Collision Times - Students explore the relationship between density, speed and size in determining how quickly particles collide in a gas. [Grade: 9-11| Topics: Algebra; Area]

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]

Electricity

Problem 208: Optimization- Students determine the optimal dimensions of an hexagonal satellite to maximize its surface area given its desiblack volume. [Grade: 9-12| Topics: Calculus; differentiation.]

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]

Magnetism

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: 9-11 | Topics: scaling, estimation, speed calculations, time arithmetic ]

Problem 73 Monster Functions in Space Science I. - This problem has students employ a pair of complicated algebraic equations to evaluate the strength of the sun's magnetic field near Earth's orbit. The equations are a model of the sun's magnetic field in space based on actual research by a solar physicist. This introduces students to a real-world application of mathematical modeling, and extracting p blackictions from theoretical models that can be tested. Students are provided the values for the relevant variables, and through substitution, calculate the numerical values for two 'vector' components of the sun's magnetic field near Earth's orbit. [Grade level: 9-11 | Topics: decimals, scientific notation, significant figures ]

Problem 33 Magnetic Energy From B to V Students will use formulas for the volume of a sphere and cylinder, and magnetic energy, to calculate the total magnetic energy of two important 'batteries' for space weather phenomena- solar prominences and the Earth's magnetotail. This requires scientific notation, a calculator, and experience with algebraic equations with integer powers of 2 and 3. [Grade: 8 - 10 | Topics: Algebra I; volumes; decimal math; scientific notation]

Problem 18 Magnetic Forces and Particle Motion Students learn about the spiral-shaped trajectories of charged particles moving in magnetic fields, and calculate some basic properties of this 'cyclotron' motion. [Grade: 9 - 11 | Topics: Algebra I; evaluating a function; scientific notation]

Problem 17 Magnetic Forces and Kinetic Energy Students use the formula for the Kinetic Energy of a charged particle to calculate particle speeds for different voltages, and answer simple questions about lightning, aurora and Earth's radiation belts. [Grade: 6 - 8 | Topics: Square root; time=speed x distance; decimal math; significant figures]

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]

Objects in the Sky

Problem 233: The Milky Way: A mere cloud in the cosmos- Students compare the average density of the Milky Way with the density of the universe. [Grade: 8-10 | Topics: Volume of disk, density, scientific notation]

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

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 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 44 Interstellar Distances with the Pythagorean Theorem - If you select any two stars in the sky and calculate how far apart they are, you may discover that even stars that appear to be far apart are actually close neighbors in space. This activity lets students use the Pythagorean distance formula in 3-dimensions to explore stellar distances for a collection of bright stars, first as seen from Earth and then as seen from a planet orbiting the star Polaris. Requires a calculator and some familiarity with algebra and square-roots. [Grade level: 9-11 | Topics: Decimal math; Pythagorean Theorem; square root]

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 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]

Changes in the Earth and Sky

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: 9-11 | Topics: Interpolating data in a graph; 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 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 23 Solar Flares and Sunspot Sizes Students compare sunspot sizes to the frequency of solar flares and discover that there is no hard and fast rule that relates sunspot size to its ability to produce very large flares. [Grade: 6 - 8 | Topics: Interpreting tabular data; percentages; 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]

Earth in the Solar System

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]

Energy in the Earth System

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]

Natural Hazards

Problem 179: Is There a Lunar Meteorite Impact Hazard? - Students work with areas, probability and impact rates to estimate whether lunar colonists are in danger of meteorite hazards. [Grade: 5-7| Topics: Area; unit conversions; rates]

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

Problem 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: 9-11 | 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 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: 9-11 | Topics: arithmetic; unit conversions; surface area of a sphere) ]

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: 9-11 | Topics: Time and speed calculations; interpreting scientific data ]

Problem 79 Correcting Bad Data Using Partity Bits - Students will see how computer data is protected from damage by radiation 'glitches' using a simple error-detection method involving the parity bit. They will reconstruct an uncorrupted sequence of data by checking the '8th bit' to see if the transmitted data word has been corrupted. By comparing copies of the data sent at different times, they will reconstruct the uncorrupted data. [Grade level: 9-11 | Topics: addition, subtraction, comparing the numbers 1 and 0 ]

Problem 77 Some Puzzling Thoughts about Radiation! - Students fill-in the blanks in an essay on radiation risks using a word bank tied to solving quadratic equations to find the right words from a pair of possible 'solutions'. [Grade level: 9-11 | Topics: Finding the roots of a quadratic equation; solving for X ]

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: 9-11 | Topics: Unit conversion, arithmetic operations]

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: 9-11 | 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: 9-11 | Topics: decimals, area of rectangle, graph analysis]

Problem 70 Calculating Total Radiation Dosages at Mars - This problem uses data from the Mars Radiation Environment Experiment (MARIE) which is orbiting Mars, and measures the daily radiation dosage that an astronaut would experience in orbit around Mars. Students will use actual plotted data to calculate the total dosage by adding up the areas under the data curve. This requires knowledge of the area of a rectangle, and an appreciation of the fact that the product of a rate (rems per day) times the time duration (days) gives a total dose (Rems), much like the product of speed times time gives distance. Both represent the areas under their appropriate curves. Students will calculate the dosages for cosmic radiation and solar proton flares, and decide which component produces the most severe radiation problem. [Grade level: 9-11 | Topics: decimals, area of rectangle, graph analysis]

Problem 69 Single Event Upsets in Aircraft Avionics - Radiation is problem for high-altitude commercial and research aircraft. Showers of high-energy neutrons cause glitches in computer electronics and other aircraft systems. This problem investigates the neutron background radiation at 30,000 to 100,000 feet based on actual flight data, and has students calculate how many computer memory glitches will happen over a set amount of flight time. [Grade level: 9-11 | Topics: decimals, unit conversions, 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: 9-11 | 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: 9-11 | Topics: fractions, decimals, unit conversions]

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: 9-11 | Topics: decimals, unit conversions, graphing a timeline, finding areas under curves using rectangles]

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 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 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 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 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 23 Solar Flares and Sunspot Sizes Students compare sunspot sizes to the frequency of solar flares and discover that there is no hard and fast rule that relates sunspot size to its ability to produce very large flares. [Grade: 6 - 8 | Topics: Interpreting tabular data; percentages; 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 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]

Science and Technology in Society

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 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: 9-11 | Topics: Time and speed calculations; interpreting scientific data ]

Problem 79 Correcting Bad Data Using Partity Bits - Students will see how computer data is protected from damage by radiation 'glitches' using a simple error-detection method involving the parity bit. They will reconstruct an uncorrupted sequence of data by checking the '8th bit' to see if the transmitted data word has been corrupted. By comparing copies of the data sent at different times, they will reconstruct the uncorrupted data. [Grade level: 9-11 | Topics: addition, subtraction, comparing the numbers 1 and 0 ]

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: 9-11 | Topics: Decimals; money; percents]

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