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An Archive of Math and Science Problems
This page contains a collection of math and reading activities, which features topics from solar and space science. You may also find problems that use data from various observatories, inluding Hinode, Hubble, and Spitzer.
For the complete collection of activities in solar science and astronomy, visit our Previous Problems, Sorted by Category page or the Image Education Center's
Space Science Problem of the Week.
Current
Problems:
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.]
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-discovered planet orbiting this young star.
[Grade: 6-10| Skills: 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| Skills: Geometry; Angle measurement]
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| Skills: unit conversions.]
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| Skills: Time calculations]
Problem 193: Fluid Level in a Spherical Tank - Students explore the relationship between volume, and the height of fluid in a spherical tank as fluid is being drained at a constant rate.
[Grade: 10-12| Skills: Algebra, differential calculus, related rates]
Problem 192: The Big Bang - Cosmic Expansion - Students explore the expansion of the universe predicted by Big Bang cosmology
[Grade: 10-12| Skills: Algebra, Integral Calculus]
Problem 191: Why are hot things red? - Students explore the Planck Function using graphing skills, and calculus for experts, to determine the relationship between temperature and peak wavelength.
[Grade: 10-12| Skills: Algebra, graphing, differential calculus]
Problem 190: Modeling a Planetary Nebula - Students use calculus to creatse a mathematical model of a planetary nebula
[Grade: 10-12| Skills: Algebra, Integral calculus]
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| Skills: Algebra]
Problem 188: Cross Sections and Collision Times - Students explore the relationship between density, speed and size in determining how quickly particles collide in a gas.
[Grade: 9-11| Skills: Algebra; Area]
Problem 187: Differentiation- Students explore partial derivatives by calculating rates of change in simple equations taken from astrophysics.
[Grade: 11-12| Skills: differentiation; algebra]
Problem 186: Collapsing Gas Clouds and Stability- Students use the derivative to find an extremum of an equation governing the pressure balance of an interstellar cloud.
[Grade: 11-12| Skills: differentiation; finding extrema; partial derivitives]
Problem 185: The International Space Station: Follow that graph!- Students use a plot of the orbit altitude of the ISS to predict its re-entry year after the peak of the next solar activity cycle.
[Grade: 6-8| Skills: extrapolating a simple graph; estimation; forecasting]
Problem 184: The Ant and the Turntable: Frames of reference - Students predict the motion of an ant crawling from the center of a spinning CDrom to the edge. They also use calculus to estimate the length of the spiral path seen by a stationary observer.
[Grade: 11-12| Skills: integration; parametric equations; polar coordinates]
Problem 183: Calculating Arc Lengths of Simple Functions- Students determine the basic equation for arclength and its integral, and evaluate it for simple polar functions.
[Grade: 11-12| Skills: calculus; integration; parametric equations]
Problem 182: Our Neighborhood in the Milky Way- Students create a scale model of the local Milky Way and estimate distances and travel times for a series of voyages.
[Grade: 6-8| Skills: scale models; speed-distance-time]
Problem 181: Extracting Oxygen from Moon Rocks- Students use a chemical equation to estimate how much oxygen can be liberated rom a sample of lunar soil.
[Grade: 9-11| Skills: ratios; scientific notation; unit conversions]
Problem 180: Planets, Fractions and Scales- Students work with relative planet comparisons to determine the actual sizes of the planets given the diameter of Earth.
[Grade: 4-6| Skills: scale models; decimals; fractions]
Problem 179: Is There a Lunar Meteorite Impact Hazard? - Students work with areas, probability and impact rates to estimate whether lunar colonists are in danger of meteorite hazards.
[Grade: 5-7| Skills: Area; unit conversions; rates]
Problem 178: The Mass of the Moon - Students use the period and altitude of a NASA lunar spacecraft to determine the mass of the moon.
[Grade: 8-11| Skills: Algebra]
Problem 177: Lunar Cratering: Probability and Odds- Students work with crater counting to estimate the area covered by craters and how to convert this into impact probabilities.
[Grade: 4-7| Skills: Area; probability]
Problem 176: Solar Storms: Sequences and Probabilities II - Students continue their study of a stormy week on the sun by working out the probabilities for joint events.
[Grade: 4-7| Skills: probability; numerating possible outcomes]
Problem 175: Solar Storms: Sequences and Probabilities I - Students work out the probabilities for various combinations of solar storms during a given week.
[Grade: 4-7| Skills: probability; numerating possible outcomes]
Problem 174: A Matter of Timing - Students study satellites of Saturn to work out graphically how often they will line up.
[Grade: 3-6| Skills: scale model; time calculation; fractions; working with rulers and compasses]
Problem 173: Groups, Clusters and Individuals- Students determine the number of individual objects given the number of groups and the number of individuals in an average group for clusters of stars and galaxies.
[Grade: 3-5 | Skills: multiplication]
Problem 172: The Stellar Magnitude Scale- Students learn about positive and negative numbers using a popular brightness scale used by astronomers.
[Grade: 3-6| Skills: number relationships; decimals; negative and positive numbers]
Previous Problems:
Problem 171: Are U Really Nuts? [DOC]- Grade level: 6-8
Students work with four unit conversion problems that are a bit tricky!
[Skills: unit conversions]
Problem 170: Measuring Star Temperatures [PDF] - Grade level: 6-8
Students use a simple formula to determine the temperatures of stars, and to use a template curve to analyze data for a specific star to estimate its temperature.
[Skills: algebra, graph analysis]
Problem 169: The Limiting Behavior of Functions [PDF] - Grade level: 9-12
Students work with two complex formulae to determine their limiting behavior as the independent variables approach infinity and zero.
[Skills: algebra II, pre-calculus]
Problem 168: Fitting Periodic Functions - Distant Planets [PDF] - Grade level: 9-12
Students work with data from a newly-discovered extra-solar planet to
determine its orbit period and other parameters of a mathematical model.
[Topics: trigonometry; functions; algebra]
Problem 167: Areas and Probabilities [PDF] - Grade level: 4-6
Students work with various means of estimating probabilities using a comparison of areas.
[Skills: percentages, calculating areas, probability]
Problem 166: The Dollars and Cents of Research - Students work with dollar amounts, hourly salary rates, percentages to explore various models of the cost of scientific research as seen by the individual scientist.
[Grade: 4-6 | Skills: percentages, decimal math, simple rates (e.g dollars/hour)]
Problem 165: Fractions in Space - Students explore the many ways that simple fractions come up in the study of planetary motion.
[Grade: 3-5 | Skills: working with fractions; time calculations]
Problem 164: Equations with One Variable- Students work with equations like '4.3 = 3.26D' to solve for D in a numer of simple astronomical problems involving distances, speed and temperature conversion.
[Grade: 6-8 | Skills: equations in one variable; multiplication; division; decimals]
Problem 161: Earth and Moon to Scale- Students create a scale model of trhe Earth-Moon system and compare with artistic renditions and actual NASA spacecraft images.
[Grade: 4-6| Skills: Decimals; scaling and similarity]
Problem 160: The Relative Sizes of the Sun and Stars- Students work through a series of comparisons of the relative sizes of the sun 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 | Skills: working with fractions; scale models]
Problem 159: Galaxies to Scale - Students explore the relative sizes of the Milky Way compared to other galaxies to create a scale model of galaxies, similar to the methods in Problem 161.
[Grade: 4-6 | Skills: working with fractions; scale models]
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 | Skills: Plotting polar coordinates using a ruler and compass; decimal math]
Problem 157: Space Shuttle Launch Trajectory - I - Students use the parametric equation for the altitude and range for an actual Shuttle
launch to determine the speed and acceleration of the Shuttle during launch and orbit insertionh
[Grade: 11-12 | Skills: Algebra; Calculus; Parametric Equations; Differentiation
Problem 156: Spectral Classification of Stars- Students use actual star spectra to classify them into specific spectral types according to a standard rubric.
[Grade: 9-12 | Skills: Working with patterns in data, simple sorting logic]
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