## Year 10: Problems 537 to Present

**Problem 682:NASA’s Kepler Mission Detects 715 New Planets **
Students work with the statistics of the detected candidate planets to estimate the number of planetary systems in the Milky Way and the number of earth-sized planets.
[Grade: 6-8 | Topics: percentage; histograms; population sampling; scaling and proportion ]
(PDF)

**Problem 681:A Practical Application of Vector Dot and Cross Products **
Students work with coordinate vectors describing the corners of the roof of a house, calculate the area of the roof using dot products; calculate the normal vector to the roof using cross products; and the amount of sunlight striking the roof using dot products to determine how much solar power could be generated by solar panels on the roof.
[Grade: 10-12 | Topics: vectors; dot and cross product; normal vectors; unit conversions ]
(PDF)

**Problem 680:A Pulsar Shot Out from a Supernova Explosion! **
Students study the speed of a pulsar ejected from a supernova explosion, and describe what would happen if the dense star collided with a star like the sun.
[Grade: 6-8 | Topics: Scientific notation; speed=distance/time; unit conversions; density ]
(PDF)

**Problem 679:Shipping Cargo to the International Space Station**
Students work with kilograms and watts to determine the cargo capacity for re-supply missions to the International Space Station.
[Grade: 4-6 | Topics: addition, division, multiplication of 3 and 4-digit numbers. ]
(PDF)

**Problem 678:VAB-Navigating a Magnetic Field with Vector Dot Products!**
Students work with vectors to determine a spacecrafts orientation relative to Earths magnetic field. They compute the expected strength of the magnetic field parallel and perpendicular to the spacecraft motion vector.
[Grade: 10-12 | Topics: vectors; dot products; vector projections ]
(PDF)

**Problem 677:VAB-Navigating in a Magnetic Field Using Linear Equations**
Students model spacecraft motion and the local magnetic field direction using two linear equations, then determine the line perpendicular to the spacecraft motion and the angle of motion relative to the magnetic field.
[Grade: 8-10 | Topics: graphing linear equations; equation of line perpendicular to another line; geometry ]
(PDF)

**Problem 676:VAB-Navigating in a Magnetic World!**
Students explore how some satellites navigate in space using Earth's magnetic field and its orientation to the spacecraft.
[Grade: 7-10 | Topics: coordinate plotting; geometry; graphing data ]
(PDF)

**Problem 675:VAB-Earth’s Magnetic Field and the Van Allen Probes**
Students explore Earth's magnetic field as seen by spacecraft in their orbit to determine the local 'compass direction' of the magnetic field.
[Grade: 7-10 | Topics: coordinate plotting; properties of right triangles; Pythagorean theorem]
(PDF)

**Problem 674:VAB - Exploring the Orbit of the Van Allen Probes**
Students explore the speed of the spacecraft in their orbit around Earth using coordinate graphing, time differences, pythagorean theorem and unit conversions.
[Grade: 7-10 | Topics: coordinate plotting; unit conversion; rates ]
(PDF)

**Problem 673:VAB - An Improved Model for Van Allen Belt Radiation Dose**
Students use a detailed model of the path of a satellite and the radiation dose rate along the path to calculate the total radiation dose to the spacecraft.
[Grade: 9-11 | Topics: Polynomial equations; trigonometric equations; composite functions f(f(x)); estimating areas under curves]
(PDF)

**Problem 672:VAB - Modeling the Radiation Dose of the Van Allen Probes**
Students create a simple mathematical model of the radiation exposure to the VABP satellites as they travel through the Van Allen belts.
[Grade: 11-12 | Topics: Parametric equations;composite functions f(g(x)); integral calculus ]
(PDF)

**Problem 671:VAB - The Van Allen Probes and Radiation Dose**
Students study radiation dose units and estimate the exposures for a human living on the gropund; an astronaut in the ISS, and the Van Allen belt environment.
[Grade: 8-10 | Topics: Unit conversion; rates]
(PDF)

**Problem 670:VAB - Exploring the Third Belt with the Van Allen Probes**
Students use the elliptical equation for the orbit of NASAs Van Allen Probes spaccecraft, and a circle representing the location of the new Van Allen belt, to find where they intersect along the orbit of the spacecraft.
[Grade: 9-12 | Topics: Intersection points of circles and ellipses; graphical and algebraic solutions]
(PDF)

**Problem 669: HST - Exploring Two Nearby Stars to the Sun.**
Students explore two nearby stars Ross 128 and Gliese 445 and determine when they will be the nearest stars to our sun by working with quaddratic equations that model their distances.
[Grade: 9-12 | Topics: Working with quadratic equations; intersection points of quadratic functions]
(PDF)

**Problem 668: Meteor Impacts – How Much Stuff? **
Students integrate a powerlaw function to estimate the number of tons of meteoritic debris that Earth collects every year.
[Grade: 12 | Topics: Integral calculus]
(PDF)

**Problem 667: Exploring Power-laws: Meteor impacts**
Students estimate a function for logarithmic data that describes the number of meteor impacts on Earth every year.
[Grade: 9-12 | Topics: logarithmic graphs; power laws; linear equations]
(PDF)

**Problem 666: SAGE - The Ground Track of the International Space Station**
Students determine how many sunrises and sunset the ISS observes every day.
[Grade: 6-8 | Topics: Working with proportions; time calculations]
(PDF)

**Problem 665: Kepler - Kepler’s Latest Count on Goldilocks Planets**
Students examine the statistics of the latest candidate planets beyond our solar system, work with poercentages and a bar graph, and estimate the number of earth-like planets in our Milky Wy.
[Grade: 6-8 | Topics: percentages, bar graphs, estimation]
(PDF)

**Problem 664: HST - The Sun’s Nearest Companions…At least for now!**
Students study a graph that models the distances from the sun of seven nearby stars over a 100,000 year time span. They determine the minimum distances and a timeline of which star will be the suns new closest neighbor in space in the next 80,000 years.
[Grade: 6-8 | Topics: Graphical data; finding minimum from a plotted curve]
(PDF)

**Problem 663: HST - The Hubble Search for the Farthest Galaxy in the Universe**
Students learn about the recent discovery of z8_GND_5296 what may be the farthest known galaxy in our visible universe whose light left the galaxy
when the universe was only 700 million years old. They use a simple linear equation to estimate the galaxys
look-back time, and learn about the cosmological redshift.
[Grade: 6-8 | Topics: working with simple equations; solving for X]
(PDF)

**Problem 662: SAGE- Measuring Aerosol Concentration in Parts per Million**

Students learn about parts-per-million units by working with percentage and counting squares in different types of grids.
[Grade: 6-8 | Topics: Unit conversion; integer counting]
(PDF)

**Problem 661: SAGE- Measuring Stratospheric Ozone with SAGE-III**

Students use a data graph to identify the ozone layer from its concentration of ozone, and use parts-per-million to compare ozone concentration to the atmosphere density.
[Grade: 6-8 | Topics: Unit conversion; reading a data graph ]
(PDF)

**Problem 660: SAGE- Some Basic Properties of the SAGE-III Instrument**

Students examine the mass, data, pointing accuracy and power of the SAGE-III instrument and use unit conversions to translate the units into pounds, watts and degrees.
[Grade: 6-8 | Topics: Unit conversion; proportions ]
(PDF)

**Problem 659: VAP- Exploring the Outer Atmosphere – Gas Density**

Students estimate examine the density of gas in the Van Allen belts and use it to estimate how many atoms the Van Allen Probes will encounter.
[Grade: 6-8 | Topics: scientific notation; scale model; number = density x volume; volume = area x length; length=speed x time. ]
(PDF)

**Problem 658: VAP- Exploring Gas Density in Space**

Students explore how gas density is related to the average distances between molecules in the air using a simple geometric mode of a cube with 64 cells.
[Grade: 6-8 | Topics: geometry; density=number/volume; scale models and proportions; scientific notation ]
(PDF)

**Problem 657: VAP- Exploring the Density of Gas in the Atmosphere**

Students examine different ways to represent the density of Earths atmosphere.
[Grade: 6-8 | Topics: Scientific notation; density ]
(PDF)

**Problem 656: VAP- Measuring Earths Magnetic Field in Space**

Students work with satellite data to explore Earths magnetic field through graphing data and comparing it with inverse-square and inverse-cube laws.
[Grade: 9-12 | Topics: minimum and maximum; graphing data; comparing with models of the form 1/r2 and 1/r3 ]
(PDF)

**Problem 655: VAP- Estimating the Total Mass of the Van Allen Belts **

Students estimate the total mass of the Van Allen belts and compare it to the mass of a donut using the formula for a torus.
[Grade: 9-12 | Topics:Volume of torus; scientific notation; mass = density x volume ]
(PDF)

**Problem 654: VAP- Exploring the Donut-shaped Van Allen Belts **

Students estimate the volume of the Van Allen belts in terms of the volume of Earth using a formula for the volume of a torus.
[Grade: 9-12 | Topics: Scientific notation; volume of spheres and toriods]
(PDF)

**Problem 653: VAP-How to Use the Van Allen Probes Spacecraft to Measure the Mass of Earth! **

Students use a formula to estimate the mass of Earth from data about the orbit of the Van Allen Probes spacecraft.
[Grade: 9-12 | Topics: scientific notation; solving formula with integer exponents ]
(PDF)

**Problem 652: VAP- Telemetry Math**

Students work with data rates for the spacecraft and determine how much data needs to be stored.
[Grade: 6-8 | Topics: megabytes; rates in time]
(PDF)

**Problem 651: VAP- The Van Allen Probes Satellite: Working with Octagons **

Students work with the area formula for squares, rectangles and triangles to find the surface area of an octagonal satellite.
[Grade: 9-12 | Topics: areas of simple figures; algebraic manipulation]
(PDF)

**Problem 650: VAP- Working with Areas of Rectangles and Circles **

Students use the formulas for simple rectangle and circle areas to determine the areas of the holes in a satellite panel.
[Grade: 3-5 | Topics: area of a rectangle; area of a circle]
(PDF)

**Problem 649: VAP- Electricity from Sunlight: The Van Allen Probes Spacecraft Solar Panels**

Students work with the area of rectangles to calculate the electrical power produced by solar panels.
[Grade: 3-5 | Topics: area of a rectangle; decimal math; unit conversion]
(PDF)

**Problem 648: SAGE- Using Opacity to Find Aerosol Density**

Students examine a mathematical model based on the SAGE-III geometry and see how it leads to solving a system of linear equations to determine aerosol concentrations at different altitudes.
[Grade: 6-8 | Topics: solving a system of linear equations; scientific notation]
(PDF)

**Problem 647: SAGE- Investigating Opacity and Extinction**

Students work with the properties of filters to prove that the product of exponentials leads to the sum of their exponents.
[Grade: 9-12 | Topics: exponential functions; exponent math]
(PDF)

**Problem 646: SAGE- Air Quality Index and Aerosol Density**

Students see how the Air Quality Index is related to the number of aerosols per cubic meter.
[Grade: 6-8 | Topics: density; scientific notation; volume of a sphere; density]
(PDF)

**Problem 645: SAGE- Exploring the Mass and Density of Aerosol Particles**

Students explore the physical sizes of aerosol particles. With unit conversions they convert concentration units of micrograms/m3 to particles/m3.
[Grade: 6-8 | Topics: Unit conversions; scientific notation; volume of a sphere; density]
(PDF)

**Problem 644: SAGE- A Scale Model of Aerosol Sizes**

Students work with proportions and scale to create a scale model of aerosol particles.
[Grade: 6-8 | Topics: unit conversion; metric units nano and micro]
(PDF)

**Problem 643: SAGE- The Sources and Sinks of Carbonyl Sulfide**

Students explore a molecule important in forming stratospheric aerosols. They calculate total rates of change from
a table of sources and sinks, and estimate the change in the number of molecules per year.
[Grade: 6-8 | Topics: Scientific notation; rates]
(PDF)

**Problem 642: SAGE-Three Mathematical Ways to Describe Light Extinction **

Studens explore the three common ways that scientists record extinction using base-10 and base-e functions.
[Grade: 9-12 | Topics: Base-10 and Base-e functions; exponential equations]
(PDF)

**Problem 641: SAGE- A Study of Aerosol Extinction in the Stratosphere**

Students work with a table of atmospheric extinction at different altitudes and latitudes to graph selected data and draw a straight line thrlough the graphed data to estimate the slope. They create a linear equation from the graph and use it to predict the extinction at a different altitude.
[Grade: 6-8 | Topics: slope of a line; linear equations; forecasting]
(PDF)

**Problem 640: SAGE- Atmospheric Aerosols by Percentage**

Students examine a table that lists the percentages of different aerosol types according to the location on Earth where they are produced.
[Grade: 3-5 | Topics: percentages; interpreting tabular data]
(PDF)

**Problem 639: SAGE- Aerosol Sources in the Stratosphere**

Students examine the sources for aerosols in the atmosphere and determine their percentage contributions
based upon their individual rates given in megatons/year.
[Grade: 6-8 | Topics: Rates; percentage; pie graphs]
(PDF)

**Problem 638: SAGE- Sunset and Sunrise Geometry **

Students explore the tangent geometry used by the SAGE-III instrument, and work with chords to determine their lengths using the Pyhtagorean formula.
[Grade: 9-12 | Topics: Pythagorean Theorem; chord lengths]
(PDF)

**Problem 637: SAGE-Light Attenuation Using Exponential Functions **

Students work with the extinction formula for light and see how light dimming is an exponetial process.
[Grade: 9-12 | Topics: exponential functions; natural logarithm, e]
(PDF)

**Problem 636: SAGE-Aerosols and Light Dimming **

Students explore how light is dimmed as it passes through a series of filters.
[Grade: 6-8 | Topics: percentage; multiplication ]
(PDF)

**Problem 635: SAGE- Exploring Aerosols**

Students compare aerosol sizes to a human hair, calculate volumes and masses from density.
[Grade: 6-8 | Topics: density; volume; scale ]
(PDF)

**Problem 634: History of Winter - What is a Snowballs Chance on Mars? **

Students explore the phase diagrams for water and carbon dioxide and discover whether astronauts would be able to create snowballs on mars made from carbon dioxide ice.
[Grade: 9-12 | Topics: Graph analysis]
(PDF)

**Problem 633: History of Winter - Exploring Temperature and States of Matter **

Students learn how to read a simple phase diagram and how states of matter are related to temperature and pressure.
[Grade: 9-12 | Topics: Rates of Change; Unit conversions; decimal math ]
(PDF)

**Problem 632: History of Winter - Exploring Energy and Temperature **

Students learn about the relationship between temperature and the kinetic energy of particles.
[Grade: 9-12 | Topics: Evaluating equations]
(PDF)

**Problem 631: History of Winter - Snow Density, Mass and Roof Failure **

Students
[Grade: 6-8 | Topics: Density = mass/volume; rates of change; proportions]
(PDF)

**Problem 630: History of Winter - Snow Density and Volume **

Students learn how snow density is measured in the field using cylindrical instruments in a snow pit trench.
[Grade: 6-8 | Topics: Density=mass/volume; metric units; decimal math]
(PDF)

**Problem 629: History of Winter - Snow to Water Ratios **

Students learn how to convert between snow volume and equivalent volumes of liquid water.
[Grade: 6-8 | Topics: Working with tables; decimal math; proportions]
(PDF)

**Problem 628: History of Winter - Snowflake Growth Rates and Surface Area **

Students study change of scale and dilation by investigating showflake growth.
[Grade: 6-8 | Topics: tabular data; rates of change; decimal math]
(PDF)

**Problem 627: History of Winter - The Surface Area of a Snowflake **

Students estimate the area of a single snow flake using the areas of triangles and rectangles.
[Grade: 6-8 | Topics: geometry; areas of triangles and rectangles; decimal math]
(PDF)

**Problem 626: History of Winter - Graphing a Showflake using Symmetry **

Students use a simple plotting exercise and reflection symmetry to create a snowflake.
[Grade: 6-8 | Topics: geometry; symmetry; plotting points on a Cartesian graph]
(PDF)

**Problem 625: SCOOL-Cloud Droplets and Rain Drops **

Students
[Grade: 6-8 | Topics: Volume of a sphere; scientific notation ]
(PDF)

**Problem 624: SCOOL-Cloud Cover, Albedo, Transmission and Opacity **

Students explore the concepts of albedo, transmission and opacity for clouds.
[Grade: 9-12 | Topics: logarithmic functions; percentage]
(PDF)

**Problem 623: SCOOL-Cloud Cover and Solar Radiation **

Students examine the relationship between percentage cloud cover and the amount of sunlight that reaches the ground.
[Grade: 6-8 | Topics: Graph analysis; evaluating functions]
(PDF)

**Problem 622: SCOOL-How Clouds Form - Working with Dew Points and Rates of Change **

Students learn about the dew point and how clouds form from humid, cooling air.
[Grade: 6-8 | Topics: Percentage; rates of change ]
(PDF)

**Problem 621: SCOOL-Working with Rainfall Rates and Water Volume **

Students learn about rain fall rates and how to convert them into the volume of water that falls.
[Grade: 9-12 | Topics: scientific notation; rates of change ]
(PDF)

**Problem 620: SCOOL-Estimating the Mass of a Cloud **

Students use the relationship between volume and density to estimate the mass of a common cumulus cloud.
[Grade: 6-8 | Topics: Volume of a sphere; scientific notation; mass = density x volume]
(PDF)

**Problem 619: SCOOL-Using Proportions to Estimate the Height of a Cloud **

Students use the method of triangulation to determine the height of a cloud.
[Grade: 6-8 | Topics: geometry of right triangles; proportions]
(PDF)

**Problem 618: Voyager 1 Begins its Interstellar Journey **

Students calculate speeds, light travel times and density for the Voyager 1 encounter with the interstellar medium beyond the orbit of Pluto.
[Grade: 6-8 | Topics: speed=distance/time; time = distance/speed; number = density x volume]
(PDF)

**Problem 617: The Basic Mathematics of Rocket Engines - I **

Students learn about and calculate specific impulse and thrust.
[Grade: 9-12 | Topics: proportions; unit conversions; rates of change]
(PDF)

**Problem 616: Adding a Level Gauge to a Conical Tank **

Students work with the formula for the volume of a cone
[Grade: 6-8 | Topics:geometry; volume of a cone ]
(PDF)

**Problem 615: Radiation Levels on the Surface of Mars **

Students explore radiation dosages on mars and in interplanetary space
[Grade: 6-8 | Topics: unit conversions; graph analysis; rates ]
(PDF)

**Problem 614: A Simple Gauge in a Tank - II **

Students work with the formula for the volume of a conical solid to design a gas tank gauge.
[Grade: 6-8 | Topics: geometry; volume of a cone; tangents ]
(PDF)

**Problem 613: Measuring the Speed of Gas Near a Black Hole **

Students use a graph of intensity and time to estimate thhe orbit period of matter around a black hole.
[Grade: 6-8 | Topics: time; graph analysis]
(PDF)

**Problem 612: Exploring Power-laws: Meteor impacts **

Students work with logarithmic functions, power-laws and explore the mass functiuon of meteors.
[Grade: 9-12 | Topics: logarithmic functions; power-functions; logarithmic graphs]
(PDF)

**Problem 611:Angular Size : The Moon and Stars **

Students explore angular size using a simple proportional equation
[Grade: 6-8 | Topics:scale; proportion; angle measure ]
(PDF)

**Problem 610: Calculating the Volume of the J-2x Rocket Engine Bell **

Students explore conical volumes by examining the diemnsions of a large rocket engine.
[Grade: 6-8 | Topics:volume of a conical solid; solving a quadratic equation for a selected value of X]
(PDF)

**Problem 609: Volumes of Solids - Packing for a trip to the Moon **

Students calculate volumes of rectangular solids and pack a volume-limited travel kit used by astronauts.
[Grade: 3-5 | Topics: volume of rectangular solids; integers]
(PDF)

**Problem 608: Constellations in 3D **

Students create a 3-d model of the constellation Orion and explore how stars are located in space and how this perspective changes from different vantage points.
[Grade: 6-8 | Topics: geometry; scale]
(PDF)

**Problem 607: The Launch of LADEE to the Moon **

Students plot the altitude, range and speed of the LADEE rocket launch and investigate rates of change including acceleration by graphing the tabular data and determining the slope of the graph using the definition of the slope of a line between two points.
[Grade: 6-8 | Topics: Graphing tabular data; determining the slope of a line; rates of change]
(PDF)

**Problem 606: Global Warming and the Sun’s Evolving Luminosity **

Students work with two functions that relate the brightness of the sun to its age L(t), and the temperature of earth to the suns brightness, T(L) to create a new function that gives the temperature of earth over time T(t).
[Grade: 9-12 | Topics: working with equations; eliminating common variables; functions]
(PDF)

**Problem 605: The Solar System Beyond the Orbit of Neptune **

Students compute the volume and density of the Kuiper Belt located beyond the orbit of Neptune, and estimate how far apart the objects are located compared to the earth-sun distance.
[Grade: 9-12 | Topics: volume of a disk; density = number/volume ]
(PDF)

**Problem 603: The Temperature of Earth without Carbon Dioxide **

Students study a computer model to determine the temperature of Earth if there were no carbon dioxide in the atmosphere. They also determine the albedo of earth given different amounts of ice cap coverage determined by the computer model.
[Grade: 9-12 | Topics: evaluating functions; trigonometry; surface area of a sphere ]
(PDF)

**Problem 602: Transit of Phobos Across the Sun Viewed from Mars **

Students investigate the geometry of a martian moon passing across the face of the sun using angular measure and proportions.
[Grade: 6-8 | Topics: proportions; angle measure; similar triangles]
(PDF)

**Problem 601: Gravity and Escape Speed **

Students calculate the escape speed for various planets using a simple 'square root' equation.
[Grade: 6-8 | Topics: evaluating functions; square-roots ]
(PDF)

**Problem 600: Reading a Speed vs Time Graph - acceleration **

Students read a graph to determine how speed is related to acceleration as the area under a curve.
[Grade: 9-12 | Topics:areas of rectangles and triangles; interpreting graphical data ]
(PDF)

**Problem 599: Exploring Artificial Gravity **

Students work with centrifugal forces to calculate the acceleration of County Fair rides; rotating spacecraft and the acceleration of rockets to see if artificial gravity can be created.
[Grade: 9-12 | Topics: evaluating functions]
(PDF)

**Problem 598: Gravity and Energy **

Students the energy equation E = mgh to expore the energy of falling water near Earths surface to calculate the energy of a water fall.
[Grade: 6-8 | Topics: evaluating functions; unit conversions]
(PDF)

**Problem 597: The Physics of Rock Throwing **

Students study the motion of a thrown rock to explore the parabolic shape of the rocks motion.
[Grade: 9-12 | Topics: quadratic equations; parametric equations; parabolas ]
(PDF)

**Problem 596: Distance Traveled Under Free Fall by Gravity **

Students explore accelerated motion and distance traveled using an equation that related distance to time-squared, and solve the equation under various conditions.
[Grade: 6-8 | Topics: solving for X; quadratic monomials; square roots]
(PDF)

**Problem 595: Gravity and Falling Bodies **

Students work with simple linear equations to study the speed of falling bodies under gravity.
[Grade: 6-8 | Topics:linear equations; solving for x ]
(PDF)

**Problem 594: A Number Puzzle about the Origin of Our Universe **

Students learn about the Big Bang by solving a number puzzle for missing words using solutions to a variety of problems taken from Algebra 1 topics.
[Grade: 6-8 | Topics: distance between two points; slopes; linear equations; dilations; scientific notation]
(PDF)

**Problem 593:A Number Puzzle about Planets Beyond our Solar System **

Students solve a puzzle by finding the missing words keyed to solutions for the roots of quadratic equations
[Grade: 6-8 | Topics: quadratic equations; factoring ]
(PDF)

**Problem 592: Apparent Sizes of Objects from Jupiter’s Moon Europa **

Students explore how the angular sizes of the moons of Jupiter depend on the actual sizes and distances from the observer, and can sometimes allow eclipses of the sun as viewed from Europa.
[Grade: 6-8 | Topics: angle measure; proportions; geometry ]
(PDF)

**Problem 591: The Occulting Moons of Mars **

Students explore the moons of mars and their eclipses during an event seen by the CUriosity rover on August 1, 2013.
[Grade: 6-8 | Topics: working with poroportions; angular measure; geometry]
(PDF)

**Problem 590: Magnetic Storms, Aurora and the Kp Index **

Students use simple math, percentage and probability to estimate how common intense magnetic storms are by using the magnetic Kp index and its statistics.
[Grade: 3-5 | Topics: averaging; percentage; working with tables ]
(PDF)

**Problem 589: Coronal Mass Ejections and Radiation Storms **

Students explore the frequencies of coronal mass ejections and radiation storms to determine how common both are during sunspot maximum in 2013.
[Grade: 3-5 | Topics: percentage; averaging; probability; working with tables ]
(PDF)

**Problem 588: Solar Flares **

Students explore the frequencies of intense solar flares to determine their average numbers each day during sunspot maximum in 2013.
[Grade: 3-5 | Topics: averaging; odds; percentage]
(PDF)

**Problem 587: Comet Encounters after Discovery **

Students examine how often newly discovered comets approach Earth and become a hazard, and how soon after discovery these close passes can occur.
[Grade: 3-5 | Topics: Averaging, percentages]
(PDF)

**Problem 586: Searching for Comets **

Students use tabular data on the detection of new comets since 1999 to explore detection rates over time.
[Grade: 3-5 | Topics: Percentages]
(PDF)

**Problem 585: Exploring Comet Orbits **

Students explore the elliptical orbit of Halleys Comet and determine its period and the speed of the comet.
[Grade: 6-8 | Topics: speed=distance/time]
(PDF)

**Problem 584: Comparing Comets Up Close with NASA Spacecraft **

Students compare five comets and determine size ranges and percentages.
[Grade: 3-5 | Topics: percentages; volume of a cube]
(PDF)

**Problem 583: Buying a Telescope **

Students compare several telescopes and select the one with the best performance and lowest cost.
[Grade: 6-8 | Topics: simple ratio formula; decimal math]
(PDF)

**Problem 582: How do Telescopes Magnify? **

Students use a simple ratio formula to calculate the magnification of a telescope.
[Grade: 3-5 | Topics: division of two decimal numbers; evaluating simple ratios. ]
(PDF)

**Problem 581: How Telescopes Work **

Students compare how much light a telescope can gather compared to the human eye.
[Grade: 3-5 | Topics: Area of a circle ]
(PDF)

**Problem 580: Measuring Gravity with a Pendulum **

Students design pendulum clocks for mars and the moon, and how pendulums can be used for mining on Earth.
[Grade: 6-8 | Topics: evaluating square-root equations; scientific notation ]
(PDF)

**Problem 579: The Scale of an Image with a Telescope **

Students desigh digital cameras for telescopes given information about the image scale of the telescope and the pixel dimensions.
[Grade: 6-8 | Topics: area; evaluating simple equations; unit conversions]
(PDF)

**Problem 578: Digital Camera Math **

Students learn about digital cameras and how to interpret formats, megapixels and angular resolution.
[Grade: 6-8 | Topics: integer math; area of a square]
(PDF)

**Problem 577: Designing a Telescope System **

Students design two telescopes given information about the desired properties for conducting research.
[Grade: 6-8 | Topics: graphing inequalities; evaluating simple equations ]
(PDF)

**Problem 576: Telescope Resolution - How much detail can you see? **

Students determine the resolving power of a telescope and the limit to the finest details that can be see for a telescope of a specific diameter.
[Grade: 6-8 | Topics: Angular measure; arcseconds; simple equations ]
(PDF)

**Problem 575: Telescope Field of View - How much can you see? **

Students calculate the angular field of view for various telescopes using a simple formula of the form: F = A/B
[Grade: 6-8 | Topics: Angular measure; degrees]
(PDF)

**Problem 574: Telescope Light Gathering Ability - Seeing Faint Stars **

Students calculate the light gathering ability of various telescopes compared to the human eye.
[Grade: 6-8 | Topics: Area of a circle ]
(PDF)

**Problem 573: Calculating the Magnification of a Telescope **

Students fill in missing numbers in a table using proportions and evaluating a simple equation for magnification.
[Grade: 6-8 | Topics: proportions]
(PDF)

**Problem 572: How Saturns Moon Mimas Created the Cassini Division **

Students calculate the acceleration of gravity in Cassinis Division and estimate the number of years to eject these particles.
[Grade: 9-12 | Topics: scientific notation; evaluating a formula for gravity; unit conversions]
(PDF)

**Problem 571: Focal Lengths, Apertures and F/numbers **

Students learn about the basic terms that define the performance of a digital camera or a telescope.
[Grade: 6-8 | Topics: fractions; integer division; evaluating simple equations ]
(PDF)

**Problem 570: Curiosity Heads for Mt Sharp **

Tabular data is used to estimate how long it will take the Curiosity rover to reach the base of Mt Sharp using data from its porevious week travels.
[Grade: 3-5 | Topics: averaging numbers in a table; time = distance/speed]
(PDF)

**Problem 569: Orbit Speeds and Times for Saturns Rings **

Students learn about the orbit speeds of ring particles and how orbit periods in the Cassini Division relate to the orbit of the moon Mimas.
[Grade: 6-8 | Topics: square root formulae; circumference of circle; speed = distance/time ]
(PDF)

**Problem 568: Ios Volcanoes and Resurfacing **

Students examine how volcanic activity on Jupiters satellite Io can lead to fresurfacing the entire moon in less than a million years covering all new craters.
[Grade: 6-8 | Topics: Surface aea of a sphere; rates; scientific notation]
(PDF)

**Problem 567:Exploring Parabolas - The shape of a satellite dish**

Students use the equation for a parabola to determine the focus location for a solar cooker and a sound amplifier dish given their diameters and depths.
[Grade: 9-12 | Topics: geometry; properties of parabolas]
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**Problem 566:Exploring Light Brightness and the Inverse Square Law**

Students collect data and explore the inverse square law using a light meter. They deduce the formula for the brightness of a lamp given its distance and wattage.
[Grade: 6-8 | Topics: graphing tabular data; surface area of a sphere; ]
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**Problem 565:Mapping Earth from Space - Swaths and Coverage**

Students explore how satellite observing swaths add up to give full coverage of earths surface.
[Grade: 6-8 | Topics: geometry;scale model; working with square roots ]
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**Problem 564:Exploring the Stars in Orion - Light Year Madness**

Students explore the light year and its relationship to light travel time for observing events in different parts of space.When would colonists at different locations observe the star Betelgeuse become a supernova?
[Grade: 6-8 | Topics: time lines; time interval calculations; time = distance/speed ]
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**Problem 563:Comet ISON and its Close Encounter with Mars**

Students use tabular data to determine the date and time of closest approach to Mars
[Grade: 3-5 | Topics: graphing tabular data]
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**Problem 562:Exploring the Orbit of Comet ISON**

Students use tabulated data to estimate when this comet will make its closest approach to the sun in 2013.
[Grade: 6-8 | Topics: graphing tabular data; scale; measurement; distance between points]
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**Problem 561:Exploring the Evaporating Exoplanet HD189733b**

Students estimate how quickly this planet will lose its atmosphere and evaporate at its present loss rate of 6 million tons/second
[Grade: 6-8 | Topics:mass=densityx volume; rates; volume of a sphere ]
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**Problem 560:The Orbit of Comet ISON**

Students explore how close Comet ISON will get to Mercury, Venus, Earth and Mars during its 2013 passage.
[Grade: 3-5 | Topics: Interpreting tabular data; graphing ]
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**Problem 559:Comet ISON Losing Mass as it Approaches the Sun.**

Students estimage how much mass the comet will loose at its present rate.
[Grade: 6-8 | Topics: volume of a sphere; rates; mass=density x volume]
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**Problem 558:How Quickly are NEOs Being Discovered?**

Students work with data presented in bar graphs to estimate how many more hazardous Near Earth Objects (NEOS) remein to be found.
[Grade: 6-8 | Topics:bar graphs ]
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**Problem 557:The 10000th Near Earth Asteroid 2013 MZ5**

Students graph tabulated data to determine when this asteroid is closest to Earth and its speed at that time.
[Grade: 6-8 | Topics: graphing tabular data; solving a linear equation]
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**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]
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**Problem 555:Exploring Your Weight Across the Solar System**

Students estimate their weight on different planets, moons and asteroids.
[Grade: 6-8 | Topics: proportions]
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**Problem 554:Exploring Volcanoes and Geysers Across the Solar System**

Students determine the ejection speed and heights of gasses vented by geysers and volcanoes.
[Grade: 6-8 | Topics: solving square root equations; ]
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**Problem 553:Colliding Galaxies - The future of our Milky Way**

Students explore the collision of two galaxies and estimate from their present speed, separation and acceleration how long it will be before they have collided.
[Grade: 9-12 | Topics: unit conversions; scientific notation; ballistic equation; solvimg quadratic equations]
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**Problem 552:Cassini Sees Earth From Space - How Bright is it?**

Students explore the logarithmic magnitude scale and estimate how bright Earth appears from Saturn as viewed in a recent Cassini image
[Grade: 9-12 | Topics: logarithms; power laws ]
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**Problem 551:Giving Particles a Boost in the van Allen Belts**

Students examine a ball bouncing down a flight of stairs and compare this to how van Allen particles gain their energy from numerous small boosts.
[Grade: 6-8 | Topics: equations; scientific notation]
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**Problem 550:Comparing the Rings of the Outer Planets**

Students compare the dimensions of the rings of Jupiter, Saturn, Uranus and Neptune to the radius of each planet, and the location of the break up Tidal Limit to test an idea of how the rings may have formed.
[Grade: 6-8 | Topics: scale model; proportions; number line ]
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**Problem 549:Saturns Rings- Shadows from Moons and Ringlets**

Students use an image of a ring of Saturn to investigate its thickness using shadows cast by ringlet material kicked up by a passing moon.
[Grade: 6-8| Topics: scales; proportions; triangle geometry; angle measurement]
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**Problem 548:Saturns Rings - A close-up study**

Students use a Cassini image of Saturns rings to calculate the sizes of the smallest rings, and how their thicknesses change with distance from Saturn.
[Grade: 3-5 | Topics: measurement; scales; proportions; metric measure; bar graphs]
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**Problem 547:The Rings of Saturn**

Students explore the volume and mass of the rings of saturn to estimate the number of ring particles and their separations, and the radius of the equivalent spherical body.
[Grade: 9-12 | Topics: volume of a ring and a sphere; scientific notation]
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**Problem 546: The Relative Sizes of Planets and other Objects**

Students use proportional information to determine the relative scales of planets and large moons across the solar system.
[Grade: 3-5 | Topics:scale; proportion]
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**Problem 545:Measuring Atmospheric Trace Gases Using Parts Per Million**

Students convert from percentage units to parts per million and compare trace gases in the atmospheres of various planets.
[Grade: 6-8 | Topics: percentages; unit conversions ]
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**Problem 544:The Composition of Planetary Atmospheres**

Students study the composition of planetary atmospheres and compare the amounts of certain compounds in them
[Grade: 6-8 | Topics: Pie graphs; percentages; scientific notation]
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**Problem 543:Timeline for Planet Formation**

Students calculate time intervals in millions and billions of years from a timeline of events
[Grade: 3-5 | Topics: time calculations; integers]
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**Problem 542:The Late Heavy Bombardment Era**

Students estimate the average arrival time of large asteroids that impacted the moon. They work with the formula for the volume of a sphere to estimate how much additional mass was added to the moon and Earth durung this era.
[Grade: 6-8 | Topics: volume of spheres; proportions]
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**Problem 541:How to Build a Planet**

Students study planet growth by using a clay model of planetessimals combining to form a planet by investigating volume addition with spheres.
[Grade: 3-5 | Topics: graphing; counting]
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**Problem 540:Travel Times by Spacecraft Around the Solar System**

Students explore how long it takes our fastest rockets to reach each of the planets.
[Grade: 6-8 | Topics: time=distance/speed; metric conversion]
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**Problem 539:Visiting the Planets at the Speed of Light**

Students learn about the light travel times to the 8 planets by converting the distances in Astronomical Units to travel times at the speed of light.
[Grade: 6-8 | Topics: Proportions; unit conversions; time = distance/speed; metric units]
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**Problem 538:How Big is Our Solar System?**

Students work with proportions to convert solar system distances into Astronomical Units for the 8 planets.
[Grade:6-8 | Topics: Proportions; unit conversions]
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**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]
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