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Mathematics Weekly Page
This page contains sets sorted by mathematics topic area. The National Council of Teachers of Mathematics website includes a complete statement of the national mathematics standards for each grade. These may be found at Principles and Standards for School mathematics. Click on the topics below to bring up the NCTM page describing the relevant Standards.

Numbers and Operations

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

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 158: The Solar Neighborhod within 17 Light Years - Students create a scale model of the local solar neighborhood and determine the shortest travel distances to several stars. [Grade: 6-8 | Topics: Plotting polar coordinates using a ruler and compass; decimal math]

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 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 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 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 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 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 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: 4-6 | Topics: addition, subtraction, comparing the numbers 1 and 0 ]

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 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 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 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]

Algebra

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 221: Pulsars and Simple Equations- Students work with linear equations describing the rotation period of a pulsar, and evaluate the equations for various conditions. Students use the equations to pblackict intersection points in time. [Grade: 6-8 | Topics: Evaluating simple one-variable equations]

Problem 219: Variables and Expressions from Around the Cosmos- Students evaluate linear equations describing a variety of astronomical situations. [Grade: 6-8 | Topics: Evaluating simple one-variable equations.]

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 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 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 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 164: Equations with One Variable- Students work with equations like '4.3 = 3.26D' to solve for D in a number of simple astronomical problems involving distances, speed and temperature conversion. [Grade: 6-8 | Topics: equations in one variable; multiplication; division; decimals]

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]

P>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 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 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 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 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 61 Drake's Equation and the Search for Life...sort of! - Way back in the 1960's Astronomer Frank Drake invented an equation that helps us estimate how much life, especially the intelligent kind, might exist in our Milky Way. It has been a lively topic of discussion in thousands of college astronomy courses for the last 30 years. In this simplified version, your students will get to review what we now know about the planetary universe, and come up with their own estimates. The real fun is in doing the research to track down plausible values (or their ranges) for the factors that enter into the equation, and then write a defense for the values that they choose. Lots of opportunity to summarize basic astronomical knowledge towards the end of an astronomy course, or chapter. [Grade level: 6-8 | Topics: decimal math; evaluating functions for given values of variables]

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 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 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 ]

Geometry, Areas, Volumes

Problem 333: Hubble: Seeing a Dwarf Planet Clearly Based on a recent press release, students use the published photos to determine the sizes of the smallest discernible features and compare them to the sizes of the 48-states in the USA. They also estimate the density of Pluto and compare this to densities of familiar substances to create a 'model' of Pluto's composition. A supplementary Inquiry Problem asks students to model the interior in terms of two components and estimate what fraction of Pluto is composed of rock or ice. [Grade: 8-12 | Topics: scales and ratios; volume of sphere; density=mass/volume]

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

Problem 275: Water on the Moon! Students estimate the amount of water on the moon using data from Deep Impact/EPOXI and NASA's Moon Minerology Mapper experiment on the Chandrayaan-1 spacecraft. [Grade: 8-10 | Topics: Geometry, Spherical volumes and surface areas, Scientific notation]

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

Problem 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 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 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 189: Stellar Temperature, Size and Power- Students work with a basic equation to explore the relationship between temperature, surface area and power for a selection of stars. [Grade: 8-10| Topics: Algebra]

Problem 177: Lunar Cratering: Probability and Odds- Students work with crater counting to estimate the area coveblack by craters and how to convert this into impact probabilities. [Grade: 4-7| Topics: Area; probability]

Problem 174: A Matter of Timing - Students study satellites of Saturn to work out graphically how often they will line up. [Grade: 3-6| Topics: scale model; time calculation; fractions; working with rulers and compasses]

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

Problem 103 The Mysterious Solar Micro-Flares! Students will analyze an image taken by the Hinode solar satellite to determine the scale of the image in kilometers per millimeter, then use this to determine the sizes of solar micro-flares. From the number of micro-flares that they count in the image, the area of the image in square kilometers, and the surface area of a spherical sun, they will calculate the total number of micro-flares on the solar surface. [Grade: 6-9 | Topics:image scales; area calculation; unit conversions]

Problem 96 Hinode Satellite Power - Students will study the design of the Hinode solar satellite and calculate how much power it can generate from its solar panels. [Grade level: 6-8 | Topics:area of rectangle,area of cylinder, 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 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: 8-10 | Topics: Geometry; parallax; arithmetic]

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: 6-8 | 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: 6-8 | Topics: Data analysis; decimals; ratios; graphing]

Problem 38 Solar Eclipses and Satellite Power From the ground we see total solar eclipses where the New Moon passes directly between Earth and Sun. Satellites use solar cells to generate electricity, but this is only possible when the Earth is not 'eclipsing' the sun. Students will create a scaled drawing of the orbits of three satellites around Earth, and calculate how long each satellite will be in the shadow of Earth. They will be asked to figure out how to keep the satellites operating even without sunlight to power their solar panels. [Grade: 5 - 8 | Topics: Geometry; 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 16 Solar Power and Satellite Design Students perform simple surface area calculations to determine how much solar power a satellite can generate, compared to the satellite's needs. [Grade: 6 - 8 | Topics: Area of irregular polygons]

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 6 Observing the Sun's rotation Students use a Sunspotter to track sunspots during the week of November 7, 2004, and calculate the rotation period of the sun. [Grade: 6 - 8 | Topics: Lab exercise using a 'Sunspotter' to measure sun's rotation]

Problem 2 Satellite Surface Area Students calculate the surface area of an octagonal cylinder and calculate the power it would yield from solar cells covering its surface. [Grade: 7 - 9 | Topics: surface areas; hexagone; decimal math]

Measurement

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 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 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]

Data Analysis and Probability

Problem 262: LRO Explore 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 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 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 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 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 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 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 Solving

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 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 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]

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