# National Aeronautics and Space Administration

## Math problems about our Sun

Problem 537:A Solar Storm Number Puzzle
Students solve 10 problems using positive and negative numbers, addition, subtraction and multiplication to find the missing words in a short essay about solar storms. [Grade:3-5 | Topics: integer arithmetic; positive and negative numbers] [Click here]

Problem 556:IRIS Explores the Solar Transition Region
Students use an image from IRIS to examine the sizes and equivalent energy of bright regions in the solar transition region. [Grade: 6-8 | Topics: percentage; proportion; scale; scientific notation; volume of a cylinder] [Click here]

Problem 516: Hinode Observes a Solar Eclipse from Space
Students work with simple proportions to estimate the diameter of the sun using the Moon and the Moon's distance. [Grade: 3-5 | Topics: Proportions; time intervals; calendar arithmetic] [Click here]

Problem 514: Solar Flares and the Stormy Sun
Students work with simple averaging and explore the latest sunspot cycle to find their averages for 2012 and 2013. [Grade: 3-5 | Topics: Averaging integers; rounding] [Click here]

Problem 505: SDO Sees Coronal Rain - Estimating Plasma Speeds
Students estimate the speed of plasma streamers near the solar surface using images from a Solar Dynamics Observatory. [Grade: 6-8 | Topics: scale models; speed=distance/time; proportions] [Click here]

Problem 468: How Common are X-Class Solar Flares?
Students use simple statistics to determine the solar flare frequency during a sunspot cycle to estimate the time between X-class flares during the current sunspot cycle [Grade: 5-7 | Topics: mean, median, percentage] [Click here]

Problem 467: Estimating Magnetic Field Speeds on the Sun
Students use two images from the Solar Dynamics Observatory to estimate the speed of the X-class solar flare on March 6, 2012. [Grade: 6-8 | Topics: speed=distance/time; scale model; metric measurement] [Click here]

Problem 466: Exploring the Solar Wind and Coronal Mass Ejections
Students use two images of the solar storm during March 2012 to estimate the speed of the solar wind and a coronal mass ejection. They also estimate arrival times for the CME at Earth and Neptune. [Grade: 3-5 | Topics: scale models; proportions; fractions] [Click here]

Problem 455: The Night Launch of STEREO in 2006
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. [Grade: 8-10 | Topics: time=distance/speed; scale models; metric math; equation of a parabola; curve fitting] [Click here]

Problem 404: STEREO Spacecraft give 360-degree Solar View Students use STEREO satellite images to determine which features can be seen from Earth and which cannot. They learn about the locations and changing positions of the satellites with respect to Earth's orbit. [Grade: 6-8 | Topics: angular measure, extrapolation; distance = speed x time] [Click here]

Problem 395: Death Stars Some stars create super-flares that are capable of eliminating life on planets that orbit close to the star. Students learn about these flares on common red-dwarf stars and compare them to flares on our own sun [Grade: 6-9 | Topics: Scientific Notation; percentages; rates of change] [Click here]

Problem 373: Parker Solar Probe - Having a hot time near the sun!
Students use a simple equation to estimate the temperature reached by the Solar Probe spacecraft as it gets close to the sun. [Grade: 8-10 | Topics: Evaluating a function; square roots and forth roots] [Click here]

Problem 366: Parker Solar Probe - Working with angular diameter
Students use the tangent formula to determine the angular diameter of the sun as seen by the Solar Probe spacecraft as it approaches the sun. [Grade: 8-10 | Topics: angular measure; tangent formula; angular size] [Click here]

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

Problem 336: SDO: Measuring the Speed of an Eruptive Prominence Students use recent First Light images of the Sun from SDO to calculate the speed of a prominence using a sequence of scaled images and computing position shift over the time interval of the images. [Grade: 6-8 | Topics: image scales; speed=distane/time ] [Click here]

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] [Click here]

Problem 318: The Internal Density and Mass of the Sun Students use a simple, spherically symmetric, density profile to determine the mass of the sun using integral calculus. [Grade: 11-12 | Topics: Algebra II; Polynomials; integral calculus] [Click here]

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

Problem 298: Seeing Solar Storms in STEREO - II Students explore the geometry of stereo viewing by studying a solar storm viewed from two satellites. [Grade: 10-12 | Topics: Geometry; Trigonometry] [Click here]

Problem 296: Getting an Angle on the Sun and Moon Students explore angular size and scale by comparing two images of the sun and moon which have identical angular size, but vastly different scales. [Grade: 8-10 | Topics: Geometry; angle measure; scale; proportion] [Click here]

Problem 286: STEREO Watches the Sun Kick Up a Storm Students use images from the STEREO observation of a 'solar tsunami' to estimate its speed and kinetic energy. [Grade: 9-12 | Topics: metric measurement; scaling; Scientific Notation; unit conversion; evaluating a simple 2-variable formula for kinetic energy ] [Click here]

Problem 274: IBEX Uses Fast-moving Particles to Map the Sky! Students learn about Kinetic Energy and how particle energies and speeds are related to each other in a simple formula, which they use to derive the speed of the particles detected by the IBEX satellite. [Grade: 8-10 | Topics: Algebra I, Scientific notation] [Click here]

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] [Click here]

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

Problem 263: Ice or Water? Whether a planetary surface contains ice or liquid water depends on how much heat is available. Students explore the concepts of Specific heat and Latent Heat of Fusion to better understand the and quantify the energy required for liquid water to exist under various conditions. [Grade: 8-10 | Topics: unit conversion, scientific notation] [Click here]

Problem 254: Solar Insolation Changes and the Sunspot Cycle Students compare changes in the amount of solar energy reaching earth with the 11-year sunspot cycle to predict the impact on designing a photovoltaic system for a home. [Grade: 8-10 | Topics: graph analysis, correlations, kilowatt, kilowatt-hours] [Click here]

Problem 248: Seeing Solar Storms in STEREO - I Students work out the details of stereoscopic vision using elementary properties of triangles and the Law of Cosines to determine the distance from earth of a solar storm cloud. [Grade: 8-10 | Topics: geometry, Law of Cosines, V = D/T] [Click here]

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

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] [Click here]

Problem 199: Solar Storm Energy and Pie Graphs- Students study two Pie graphs describing solar flares and draw conclusions about percentages and their various forms of energy. [Grade: 6-8| Topics: Interpreting Pie Graphs.] [Click here]

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

Problem 176: Solar Storms: Sequences and Probabilities I - Students continue their study of a stormy week on the sun by working out the probabilities for joint events. [Grade: 4-7| Topics: probability; numerating possible outcomes] [Click here]

Problem 175: Solar Storms: Sequences and Probabilities II - Students work out the probabilities for various combinations of solar storms during a given week. [Grade: 4-7| Topics: probability; numerating possible outcomes] [Click here]

Problem 160: The Relative Sizes of the Sun and Stars- Students work through a series of comparisons of the relative sizes of the sun compared to other stars, to create a scale model of stellar sizes using simple fractional relationships. ( e.g if Star A is 6 times larger than Star B, and Star C is 1/2 the size of Star B, how big is Star C in terms of Star A?) [Grade: 4-6 | Topics: working with fractions; scale models] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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.] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

Problem 98 Solar Flare Reconstruction - Students will use data from a solar flare to reconstruct its maximum emission using graphical estimation (pre-algebra), power-law function fitting (Algebra 2), and will determine the area under the profile (Calculus). [Grade level: 9-11 | Topics:plotting tabular date; fitting functions; integration] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

Problem 86 Do Fast CMEs Produce SPEs? - Recent data on solar proton storms (SPEs) and coronal mass ejections (CMEs) are compared 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] [Click here]

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] [Click here]

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 ] [Click here]

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 ] [Click here]

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 predictions 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 ] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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 ] [Click here]

Problem 42 Solar Storms in the News - Students will use a newspaper archive to explore how reporters have described the causes of aurora since the 1850's. They will see how some explanations were popular for a time, then faded into oblivion, as better scientific explanations were created. [Grade level: 6-10 | Topics: Online research; tallying data] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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] [Click here]

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 ] [Click here]

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] [Click here]

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