Space Math VII - PDF
This collection of activities is based on a weekly series of space science problems distributed to thousands of teachers during the 2010-2011 school year. The problems were intended for students looking for additional challenges in the mathematics and physical science curriculum. The problems deal with modern science and engineering issues, often involving actual research data.
-COLLECTION  03-12 
16 days ago
Astrobiology Math - PDF
This book introduces many topics in the emerging subject of astrobiology: The search for life beyond Earth. It covers concepts in evolution, the detection of extra-solar planets, habitability, Drake's Equation, and the properties of planets such as temperature and distance from their star.
-COLLECTION  06-12 
february 2012
Remote Sensing Math - PDF
This book covers many topics in remote sensing, satellite imaging, image analysis and interpretation. Examples are culled from earth science and astronomy missions. Students learn about instrument resolution and sensitivity as well as how to calibrate a common digital camera, and how to design a satellite imaging system.
-COLLECTION  03-12 
february 2012
Algebra 2 Math - PDF
This book follows the topic order of a standard high school Algebra 2 textbook (McDougal-Littell 2005), but provides supplementary problems related to space science and astronomy. Topics include scientific notation, polynomial equations, matrices, trigonometric functions, exponential and power functions, probability, statistics, and complex numbers.
-COLLECTION  09-12 
february 2012
Transit Math - PDF
Although planets, stars and other celestial bodies move through space in complicated ways, space is so vast that rarely do such bodies collide. However, when someone watches these movements from a distant vantage point, it sometimes looks as though collisions occur because of the perspective. The introduction of Transit Math clearly explains the apparent "collisions," eclipses, transits and occultations to middle school students. The variety of concepts in this 44-problem collection includes synodic periods, planetary conjunctions, geometry, fractions, linear equations and probability. The problems are authentic glimpses of modern science and engineering issues, often involving actual research data. Each word problem includes background information. The one-page assignments are accompanied by one-page teachers answer keys.
-COLLECTION  03-12 
february 2012
Space Weather Math - PDF
Students explore the way in which the sun interacts with Earth to produce space weather and the ways in which astronomers study solar storms to predict when adverse conditions may pose a hazard for satellites and human operation in space. Space Weather Math supplements the Space Weather Action Center site as students track a solar storm from the sun until it impacts our Earth's magnetosphere. The variety of concepts in this 96-problem collection includes concepts such as sunspot cycles, solar flares, coronal mass ejections, graph analysis, unit conversions, linear equations and probability. Each word problem includes background information. The one-page assignments are accompanied by one-page teachers answer keys.
-COLLECTION  03-12 
february 2012
Electromagnetic Math - PDF
Electromagnetic Math is designed to supplement teaching about electromagnetism. Students explore the simple mathematics behind light and other forms of electromagnetic energy including the properties of waves, wavelength, frequency, the Doppler shift, and the various ways that astronomers image the universe across the electromagnetic spectrum to learn more about the properties of matter and its movement. This collection of 84 problems provides a variety of practical application in mathematics and science concepts including proportions, analyzing graphs, evaluating functions, the inverse-square law, parts of a wave, types of radiation, and energy. Each one-page assignment includes background information. One-page answer keys accompany the assignments.
-COLLECTION  06-12 
february 2012
464: Big Moons and Small Planets - PDF
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.
03-05  scale-models  proportions  fractions 
february 2012
463: A Simple Fuel Gauge in a Cylindrical Tank - PDF
Rockets use fuel tanks that can be approximated as cylinders. In this simple geometric exercise, students work the formula for the volume of a cylinder to add a fuel gauge at the right level to indicate how much fuel remains.
07-09  volume-of-cylinders  proportions 
february 2012
462: Using a Gravity Lens to Weigh a Cluster of Galaxies - PDF
Students explore how the geometry of a gravity lens can be used to measure the mass of the object producing the gravity.
09-12  algebra  scientific-notation 
february 2012
461: Cassini Delivers Holiday Treats from Saturn - PDF
Students explore proportions and angular size using images of Saturn's moons Titan and Dione
07-09  scale-models  proportions 
february 2012
460: Fermi Explores the High-Energy Universe - PDF
Students work with percentages to explore the identities of the 1873 gamma-ray sources detected by NASAs Fermi Observatory
06-08  percentages  pie-graphs 
february 2012
459: A piece of history - space shuttle thermal tiles - PDF
Students explore volume density and mass using the Space Shuttle thermal tiles. Get your own free tile from NASA too!
06-08  mass=densityxvolume  metric-conversions 
february 2012
458: Playing Baseball on the Earth-like Planet Kepler-22b! - PDF
The recently-confirmed Earth-like planet Kepler-22b by the Kepler Observatory is a massive planet orbiting its star in the temperature zone suitable for liquid water. This problem explores the gravity and mass of this planet, and some implications for playing baseball on its surface!
08-10  scale-models  proportions  scientific-notation  metric-math  evaluating-equations 
february 2012
457: The Interplanetary Voyage of MSL - PDF
Students use the properties of ellipses to determine the formula for the Hohmann Transfer Orbit taking the Mars Science Laboratory to Mars in 2012.
10-11  geometry  properties-of-ellipses 
february 2012
456: The Launch of the Mars Science Laboratory (MSL) in 2011 - PDF
Students use a sequence of launch images to determine the Atlas V's launch speed and acceleration. By determining the scale of each image, they estimate average speeds during the first 4 seconds after lift-off.
08-10  time=distance/speed  scale-models  metric-math 
february 2012
455: The Night Launch of STEREO in 2006 - PDF
An example of old news seen in a different way! Students use a spectacular time-lapse photo of the launch of the STEREO mission obtained by photographer Dominic Agostini in 2006 to study parabolic curves.
08-10  time=distance/speed  scale-models  metric-math  equation-of-a-parabola  curve-fitting 
february 2012
454: The Closest Approach of Asteroid 2005YU55 03 - PDF
Students work with the equation of a circle and line to find the orbit intersection points, midpoint, and closest distance to earth.
08-10  time=distance/speed  scale-models  metric-math 
february 2012
453: The Closest Approach of Asteroid 2005YU55 02 - PDF
Students work with the properties of circles and angular measure to see where the moon will be at the start of the asteroid encounter.
06-08  angular-measure  time=distance/speed  scale-models  metric-math 
february 2012
452: The Closest Approach of Asteroid 2005YU55 01 - PDF
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.
06-08  time=distance/speed  scale-models  metric-math 
february 2012
451: The Spectacular Cat's Eye Planetary Nebula - PDF
Students measure the diameter of the nebula and use speed information to estimate the age of the nebula
06-08  time=distance/speed  scale-models  metric-math 
february 2012
450: Mapping Dark Matter in a Distant Cluster - PDF
Students explore the changing density of dark matter within a distant cluster of galaxies to see if the density of dark matter is uniform inside the cluster.
08-10  volume-of-a-sphere  shell  density 
february 2012
449: A simple model for the origin of Earth's ocean water - PDF
Students create a simple model of the arrival of water to Earth using three sizes of cometary bodies and their arrival rates.
08-10  volume-of-a-sphere  rates-of-change 
february 2012
448: The Declining Arctic Ice Cap During September - PDF
Students graph the change in Arctic ice surface area, and perform linear and quadratic regressions to model and forecast trends.
09-11  statistics  regression  graphing-tabular-data 
february 2012
447: The Arctic's Vanishing Ozone Layer - PDF
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?
09-11  regression  graphing-tabular-data 
february 2012
446: Arctic Ozone Hole Continues to Grow in 2011 - PDF
Students estimate the area of the Arctic ozone hole, and work with the concept of parts-per-million to estimate total ozone volume lost.
06-08  area-of-rectangle  volume  percentages 
february 2012
445: LRO - The relative ages of lunar surfaces - PDF
Students examine two Apollo landing areas using images from the LRO spacecraft to estimate the relative ages of the two regions using crater counting.
06-08  scale  histogramming 
february 2012
444: Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine 02 - PDF
Students determine how often the two stars Kepler 16 A and B will line up with Tatooine on the same day of the year.
06-08  comparing-two-sequences-of-numbers  patterns  least-common-multiple 
february 2012
443: Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine 01 - PDF
Students explore the orbit speeds of Tatooine and Kepler-16B and predict how often the two stars line up with the planet to create an 'eclipse'.
06-09  angle-measure  angular-speed 
february 2012
442: Modeling the Atmospheric Re-entry of UARS - PDF
Students graph the altitude of the UARS satellite in the weeks before re-enrty to explore the accelerating effects of atmospheric drag. They create a mathematical model that fits the data, and use this to make their own prediction of the re-entry date.
08-11  graphing-data  linear-equations  exponential-and-power-functions 
february 2012
441: Exploring the new planet Kepler 16b called 'Tatooine'
Using the tangent function, students estimate the angular diameter and separation of the two stars in the Kepler 16 binary system as viewed from the planet's surface...if it had one!!
08-10  angle-measure  tangent 
february 2012
440: LRO explores the Apollo 12 landing area on the moon - PDF
Students use a recent image obtained by the LRO spacecraft to estimate how far astronauts walked to get to various points in the landing area. They also estimate how many craters are in this area and the average impact time between crater events.
06-08  image-scales  metric-measurement 
february 2012
439: Chandra Sees a Distant Planet Evaporating - PDF
The planet CoRot2b is losing mass at a rate of 5 million tons per second. Students estimate how long it will take for the planet to lose its atmosphere
06-08  scientific-notation  rate=amount/time 
february 2012
438: The Last Flight of the Space Shuttle Endeavor - PDF
Students use tabular data and graphing to determine the launch speed and acceleration of the Space Shuttle from the launch pad.
06-08  tabular-data  graphing  metric-measurement  speed=distance/time 
february 2012
437: Saturn V Rocket Launch Speed and Height - PDF
Students tabular data to determine the launch speed of the Saturn V rocket from the launch pad.
06-08  graphing  metric-measurement  speed=distance/time 
february 2012
436: Space Shuttle Challenger Deploys the INSAT-1B Satellite - PDF
Students use a sequence of images to determine the launch speed of the satellite from the Space Shuttle cargo bay.
06-08  scale  metric-measurement  speed=distance/time 
february 2012
435: Apollo-17 Launch from Lunar Surface - PDF
Students use a sequence of images to determine the speed of ascent of the Apollo-17 capsule from the lunar surface.
06-08  scale  metric-measurement  speed=distance/time 
february 2012
434: Dawn Spacecraft Sees Asteroid Vesta Up-Close! - PDF
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.
06-08  scale  metric-measurement 
february 2012
433: Space Shuttle Atlantis: Plume Speed - PDF
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.
06-08  scale  metric-measurement  speed=distance/time 
february 2012
432: Space Shuttle Atlantis: Exhaust Speed - PDF
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.
06-08  scale  metric-measurement  speed=distance/time 
february 2012
431: Space Shuttle Atlantis: Launch Speed - PDF
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.
06-08  scale  metric-measurement  speed=distance/time 
february 2012
430: Space Shuttle Atlantis: Ascent to Orbit - PDF
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.
06-08  scale  metric-measurement  speed=distance/time 
february 2012
429: Tracking a Sea Turtle from Space - PDF
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.
04-06  scale  metric-measurement  speed=distance/time 
february 2012
427: Black Hole: Up Close! - PDF
Students explore how the color of a light bulb changes as it gets close to a black hole, demonstrating the principle of the gravitational 'red shift'.
09-12  evaluating-an-equation-with-one-variale  square-root  metric-units  nanometers 
june 2011
426: Black Holes: Hot Stuff! - PDF
Students explore the temperature of matter falling into a black hole using a simple equation to calculate the gas temperature at different distances.
09-12  evaluating-an-equation-with-one-variable  fractional-exponents 
june 2011
425: Exploring a Full-Sized Black Hole - PDF
Students explore how the speed of an orbiting satellite changes if it were near a black hole with five times the mass of our Earth. 
06-08  evaluating-an-equation-with-one-variable  square-root  speed=distance/time  circumference-of-a-circle 
june 2011
424: Exploring Black Holes - PDF
Students compare the sizes of the planets in our solar system if they were actually black holes. They use a compass and metric ruler to create circles that are the actual sizes of the 'black hole' planets.
03-05  working-with-a-compass  metric-ruler 
june 2011
423: Moon as a Black Hole! - PDF
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. 
03-05  working-with-a-compass  metric-ruler 
june 2011
422: Supercomputers: Getting the Job Done FAST! - PDF
Students use a simple counting problem to explore how much faster a supercomputer is compared to as hand-calculation. 
06-08  algebra 
june 2011
421: Lense-Thirring Effect Near the Sun and a Neutron Star - PDF
Students work with a formula for the Lense-Thirring Effect and estimate how large it will be in orbit around our sun, and in the intense gravitational field of a dense neutron star. 
09-12  algebra  scientific-notation  angular-measure 
june 2011
420: Gravity Probe-B : Testing Einstein Again! - PDF
Students learn about the Lense-Thirring Effect, and calculate its magnitude near Earth's orbit using an algebraic equation with integer and fractional exponents.
09-12  algebra  scientific-notation  angular-measure 
june 2011
419: Space Shuttle: Fly Me to the Moon? - PDF
Students discuss the popular misconception that the Space Shuttle can travel to the moon by examining the required orbit speed change and the capacity of the Shuttle engines to provide the necessary speed changes.
06-08  amount=ratextime 
june 2011
418: Supercomputers: Modeling Colliding Neutron Stars! - PDF
Students use a series of time-lapse images calculated using a supercomputer to determine the speed of collision of two neutron stars, and whether they will form a black hole afterwards. 
08-10  distance=speedxtime  scale-models  triangle-and-circle-geometry  circumference-of-a-circle 
june 2011
417: Estimating the Size and Mass of a Black Hole - PDF
Students use a simple formula to estimate the size of a black hole located 3.8 billion light years from Earth, recently studied by NASA's Chandra and Swift satellites.
08-10  distance=speedxtime 
june 2011
416: Kepler Probes the Interior of Red Giant Stars - PDF
Students use the properties of circular arcs to explore sound waves inside stars. 
08-10  geometry-of-circles-and-arcs  distance=speedxtime 
june 2011
415: Mercury and the Moon: Similar but Different! - PDF
Students explore the mass and volume of mercury compared to the moon by using the formula for a sphere and scale changes.
08-10  scale  volume-of-sphere  mass=densityxvolume 
june 2011
414: Radiation Dose and Distance - PDF
Students explore the dosimetry from the Japan 2011 Earthquake and graph the decline of the radiation dose rates with distance from the nuclear reactors. 
09-12  unit-conversions  amount=ratextime  graphing-log-log-data 
june 2011
413: Exploring Nuclear Decay and Radiation Dose - PDF
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.
09-12  unit-conversions  amount=ratextime  solving-exponential  solving-exponential-equations-in-base-e 
june 2011
412: Radiation Dose and Dose Rate - PDF
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. 
06-08  unit-conversions  amount=ratextime 
june 2011
411: Lifestyles and Radiation Dose - PDF
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.
06-08  unit-conversions  amount=ratextime 
june 2011
410: Exploring Radiation in your Life - PDF
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. 
06-08  unit-conversions  amount=ratextime 
june 2011
409: 2011 Japan Earthquake Rocks the Earth - PDF
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.
09-12  algebra  evaluating-an-equation 
june 2011
408: Estimating the Speed of a Tsunami - PDF
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.
06-08  time-arithmetic  time-zones  speed=distance/time 
june 2011
407: Cryo-testing the Webb Space Telescope ISIM - PDF
Students explore scaling by creating an enlarged geometric model of the ISIM to better appreciate the small changes due to expansion and contraction 
06-08  scale-models  proportions  unit-conversions 
june 2011
406: Growing Grapes in the Middle of the Desert - PDF
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 
06-08  areas-of-irregular-regions  unit-conversions 
june 2011
405: Discovering Earth-like Worlds by Their Color - PDF
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 
06-08  graphing-tabular-data  interpreting-graphical-data 
june 2011
001 Magnetic Storms I - PDF
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.
07-09  interpreting-a-graph  time-calculations 
march 2011
002 Satellite Surface Area - PDF
Students calculate the surface area of an octagonal cylinder and calculate the power it would yield from solar cells covering its surface.
07-09  surface-area  hexagons  decimal-math 
march 2011
003 Magnetic Storms II - PDF
Students learn about the Kp index using a bar graph. They use the graph to answer simple questions about maxima and time. 
06-08  interpreting-bar-graphs  time-calculations 
march 2011
004 Sketching the Northern Lights - PDF
Students read an account of an aurora seen by an observer, and create a drawing or painting based on the description. 
05-07  non-mathematical-art-problem 
march 2011
005 The November 8, 2004 solar storm - PDF
Students calculate the speed of a CME, and describe their aurora observations through writing and drawing.
06-08  time-calculations  distance=speedxtime 
march 2011
006 Observing the Sun's rotation - PDF
Students use a Sunspotter to track sunspots during the week of November 7, 2004, and calculate the rotation period of the sun.
06-08  lab-exercise-using-a-sunspotter-to-measure-sun's-rotation 
march 2011
007 Solar Flares, CME's, and Aurora - PDF
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. 
05-07  Venn-diagramming 
march 2011
008 Making a Model Planet - PDF
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).
07-09  volume-of-sphere  mass=densityxvolume  decimal-math  scientific-notation 
march 2011
009 Aurora Power! - PDF
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.
05-07  interpreting-tabular-data 
march 2011
010 The Life Cycle of an Aurora - PDF
Students examine two eye-witness descriptions of an aurora and identify the common elements so that they can extract a common pattern of changes. 
04-06  creating-a-timeline-from-narrative  ordering-events-by-date-and-time 
march 2011
011 How high is an aurora? - PDF
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.
05-08  geometry  angle-measure 
march 2011
012 The Ring Current - PDF
Students use the formula for a disk to calculate the mass of the ring current surrounding Earth.
07-09  volume-of-a-disk  scientific-notation  mass=densityxvolume 
march 2011
013 Plasma Clouds - PDF
Students use a simple 'square-root' relationship to learn how scientists with the IMAGE satellite measure the density of clouds of plasma in space.
07-09  square-root  solving-for-x  evaluating-functions 
march 2011
014 Kinetic Energy and Particle Motion - PDF
Students learn about kinetic energy and how this concept applies to charged particles. They calculate the speed of a particle for various particle energies. 
07-09  evaluating-functions  square-root  scientific-notation 
march 2011
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