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National Aeronautics and Space Administration Thaolar M S M Thaolar I National Aeronautics and Space Administration S M olar a th i This collection of activities is based on a weekly series of space science problems distributed to thousands of teachers during the 2005- 2012 school years. They were intended for students looking for additional challenges in the math and physical science curriculum in grades 5 through 12. The problems were created to be authentic glimpses of modern science and engineering issues, often involving actual research data. The problems were designed to be ‘one-pagers’ with a Teacher’s Guide and Answer Key as a second page. This compact form was deemed very popular by participating teachers. This book is an expanded edition of the previous Hinode math solar problem book, with many new problems added to the original collection that were created by SpaceMath@NASA since 2009 For more weekly classroom activities about astronomy and space visit the NASA website, http://spacemath.gsfc.nasa.gov Add your email address to our mailing list by contacting Dr. Sten Odenwald at [email protected] Front and back cover credits: Front) Main image: SDO Solar Image of Transit of Venus, June 6, 2012; Small images, top left to right - SOHO/EIT Helium 304A image; Optical image KPNO; 20cm Radio Image, NRAO/VLA Back) Hinode soft x-ray imagery (Hinode/JAXA/NRL) This booklet was created through an education grant NNH06ZDA001N- EPO from NASA's Science Mission Directorate. Space Math http://spacemath.gsfc.nasa.gov Table of Contents ii Grade Page Acknowledgments i Table of Contents ii Mathematics Topic Matrix v How to use this Book ix Alignment with Standards x Teacher Comments xi The Relative Sizes of the Sun and Stars 3-5 1 Monster Sunspots 3-5 2 Solar Surface Details with the Swedish Vacuum Telescope 3-5 3 Close-up of a Sunspot by Hinode 3-5 4 An Extreme Ultraviolet Image of the Sun 3-5 5 Radio Image of the Sun 3-5 6 A Gamma-Ray Image of the Sun 3-5 7 X-Ray Image of the Sun 3-5 8 Hinode Sees Mysterious Solar Micro-flares 3-5 9 X-Ray Image of the Sun 3-5 10 Solar Storm Timeline - Narrative 3-5 11 Solar Storm Timeline - Tabular 3-5 12 Solar flares 3-5 13 Sunspots and Solar Flares 3-5 14 Solar Flares and the Sunspot Cycle 3-5 15 How Common are X-Class Solar Flares? 3-5 16 SPEs and the Sunspot Cycle 3-5 17 Solar Dynamics Observatory: Giga,Tera, Peta and Exabytes 3-5 18 Hinode Satellite Power 3-5 19 Sunspot Size and the Sunspot Cycle 3-5 20 Sunspot Cycles Since 1900 3-5 21 Are you ready for Sunspot Cycle 24? 3-5 22 Solar Storms: Odds, Fractions and Percentages 3-5 23 Studying Solar Storms with Venn Diagrams 3-5 24 Space Weather Indicators 3-5 25 Sunspot cycles 3-5 26 Solar Irradiance Changes and the Sunspot Cycle 3-5 27 Sunspots and Satellite Re-entry 3-5 28 Satellite Failures and Outages During Cycle 23 3-5 29 Changing Perspectives on the Sun's Diameter 3-5 30 The Sun in Visible Light 3-5 31 SDO Reveals Details on the Surface of the Sun 3-5 32 Getting an Angle on the Sun and Moon 6-8 33 The Last Total Solar Eclipse…Ever! 6-8 34 STEREO Spacecraft give 360o Solar View 6-8 35 Space Math http://spacemath.gsfc.nasa.gov Table of Contents (contd) iii Grade Page General Angles and Radian Measure 6-8 36 The Magnetic Classification of Sunspots 6-8 37 Solar Irradiance Changes and the Sunspot Cycle 6-8 38 How fast does the sun spin? 6-8 39 The Speed of a Coronal Mass Ejection 6-8 40 Measuring the Speed of a Prominence with SDO 6-8 41 Estimating Magnetic Field Speeds on the Sun 6-8 42 Exploring the Solar Wind and Coronal Mass Ejections 6-8 43 STEREO Watches the Sun Kick Up a Storm! 6-8 44 Measuring the Speed of a Solar Tsunami! 6-8 45 Estimating Halo CME Speeds 6-8 46 An Interplanetary Shock Wave 6-8 47 Estimating Halo CME Arrival Times 6-8 48 Histogram of Halo CME Speeds: 1996-2008 6-8 49 Predicting the Direction of Motion of a CME 6-8 50 Fastest Halo CME Speeds by Year and Month 6-8 51 Solar Storms: Sequences and Probabilities I 6-8 52 Are you ready for Sunspot Cycle 24? 6-8 53 Solar Storm Energy and Pie Graphs 6-8 54 Probability of Compound Events 6-8 55 How often do solar storms occur? 6-8 56 Cosmic Rays and the Sunspot Cycle 6-8 57 Active Region Evolution and Energy Release 6-8 58 M-flares as Predictors of X-flares 6-8 59 Find the mystery lines...if you can! 6-8 60 Death Stars 9-12 61 Exploring the Nighttime Launch of STEREO 9-12 62 Do fast CMEs produce intense SPEs? 9-12 63 Seeing Solar Storms in STEREO - II 9-12 64 Seeing Solar Storms in STEREO 9-12 65 Right Triangle Trigonometry 9-12 66 Hinode Studies Loopy Sunspots! 9-12 67 The Most Important Equation in Astronomy! 9-12 68 The Sun in Hydrogen Light 9-12 69 Radio Image of the Sun - I 9-12 70 Radio Image of the Sun - II 9-12 71 Radio Image of the Sun - III 9-12 72 The Solar Spectrum from Gamma to Radio 9-12 73 The Energy of Light - I 9-12 74 The Energy of Light - II 9-12 75 Space Math http://spacemath.gsfc.nasa.gov Table of Contents (contd) iv Grade Page The Flow of Light Energy: Power 9-12 76 CME Kinetic Energy and Mass 9-12 77 Combinations and the Binomial Theorem 9-12 78 Combinations and the Binomial Theorem 9-12 79 Finding Binomial Probabilities using Combinations 9-12 80 Finding Trinomial Probabilities 9-12 81 Normal Distributions 9-12 82 Solar Probe Plus: Working with angular diameter 9-12 83 Solar Probe Plus- Having a hot time near the sun! 9-12 84 Finding Mass in the Cosmos 9-12 85 A Mathematical Model of the Sun 9-12 86 The Law of Sines 9-12 87 The Law of Cosines 9-12 88 Law of Cosines 9-12 89 Functions and their Graphs: Sunspot numbers 9-12 90 Matrix operations 9-12 91 Algebraic Expressions and Models 9-12 92 Polynomial Modeling with Technology 9-12 93 Graphing Simple Rational Functions 9-12 94 Hot Gas and Cold Gas 9-12 95 Using the Doppler Shift to Study Gas 9-12 96 Spectroscopy and Gas Density - Elementary 9-12 97 Density Structure of an Active Region 9-12 98 Plasma Speeds in Active Regions 9-12 99 Useful Links 100 Space Math http://spacemath.gsfc.nasa.gov Mathematics Topic Matrix v Topic Problem Numbers 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 Inquiry X X Technology, X X X X X X X X X X X rulers Numbers, patterns, X X X X X X X X X X X X percentages Averages X X X X X X X X Time, distance, speed Areas and X X X volumes Scale drawings X X X X X X X X X X X X Geometry X Scientific Notation Unit X Conversions Fractions X Graph or Table X X X X X X X X X X X X X X X X Analysis Solving for X Evaluating Fns Modeling Probability X X Rates/Slopes Logarithmic Fns Polynomials Power Fns Conics Piecewise Fns Trigonometry Integration Differentiation Limits Space Math http://spacemath.gsfc.nasa.gov Mathematics Topic Matrix (cont'd) vi Topic Problem Numbers 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 Inquiry X Technology, X X X X X X X X X X rulers Numbers, patterns, X X X X X X X X X X X percentages Averages X X X X X Time, distance, X X X X X X X X X X X X X speed Areas and X volumes Scale drawings X X X X X X X X X X Geometry X X X Scientific X X Notation Unit Conversions Fractions Graph or Table X X X X X X X X X X X X X X Analysis Solving for X Evaluating Fns X X X Modeling Probability X X Rates/Slopes X X X Logarithmic Fns Polynomials X Power Fns Conics Piecewise Fns Trigonometry Integration Differentiation Limits Space Math http://spacemath.gsfc.nasa.gov Mathematics Topic Matrix (cont'd) vii Topic Problem Numbers 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 Inquiry X X Technology, rulers Numbers, patterns, X percentages Averages Time, distance X ,speed Areas and volumes X X X X Scale drawings X X X X Geometry X X X X X X X X X Scientific X X X X X X X X X Notation Unit Conversions X Fractions Graph or Table X X X X X X X X X X X Analysis Solving for X Evaluating Fns X X X X X X X X X Modeling X X Probability X X X X Rates/Slopes X Logarithmic Fns X Polynomials X Power Fns Exponential Fns Conics Piecewise Fns Trigonometry X X X X Matrices X Integration Differentiation Limits Space Math http://spacemath.gsfc.nasa.gov Mathematics Topic Matrix (cont'd) viii Topic Problem Numbers 9 9 9 9 9 9 4 5 6 7 8 9 Inquiry X Technology, X X rulers Numbers, patterns, percentages Averages Time, distance X X X ,speed Areas and volumes Scale drawings X X Geometry Scientific X X Notation Unit Conversions Fractions Graph or Table X X X Analysis Solving for X Evaluating Fns X X Modeling Probability Rates/Slopes Logarithmic Fns Polynomials Power Fns Exponential Fns Conics Piecewise Fns Trigonometry Integration Differentiation Limits Space Math http://spacemath.gsfc.nasa.gov How to use this book ix Teachers continue to look for ways to make math meaningful by providing students with problems and examples demonstrating its applications in everyday life.
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