## Statistics & Probability

**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 Diagramming]

**Problem 150: Cosmic Bar Graphs -** Students interpret simple bar graphs taken from astronomical data.
[Grade: 3-5 | Topics: finding maxima and minima; fractions; extrapolating data]

**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 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 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 502:The Frequency of Large Meteor Impacts **

Students examine how often a large meteor should be visible like the one that exploded over Russia on February 14, 2013. This asteroid had a mass of 10,000 tons and injured over 1000 people.
[Grade: 6-8 | Topics: percercentages, areas]
(PDF)

**Problem 487: The Hubble eXtreme Deep Field **

Students use the Hubble XDF to estimate the number of galaxies in the visible universe.
[Grade: 6-8 | Topics: Counting, areas, proportions ]
(PDF)

**Problem 468: How Common are X-Class Solar Flares? **

Students use simple statistics to determine the solar flare frequency during the last 11-year
sunspot cycle to estimate the time between X-class flares during the current sunspot cycle
[Grade: 5-7 | Topics: mean, median, percentage]
(PDF)

**Problem 460: Fermi Explores the High-Energy Universe**

Students work with percentages to explore the identities of the 1873 gamma-ray sources detected by NASAs Fermi Observatory
[Grade: 6-8 | Topics: percentages; pie graphs]
(PDF)

**Problem 403: The Goldilocks Planets - Not too hot or cold**
Students use a table of the planets discovered by the Kepler satellite, and estimate the number of planets in our
Milky Way galaxy that are about the same size as Earth and located in their Habitable Zones.
They estimate the average temperature of the planets, and study their tabulated properties using histograms.
[Grade: 6-8 | Topics: Averaging; histogramming]
(PDF)

**Problem 402: Kepler- Earth-like planets by the score! II**
Students use recent Kepler satellite data summarized in tabular form to estimate the number of planets in the Milky Way galaxy
that are about the same size as our Earth, and located in their Habitable Zones were liquid water may exist.
[Grade: 6-8 | Topics: Percentage; re-scaling sample sizes]
(PDF)

**Problem 401: Kepler - Earth-like planets by the score! I**
Students use recent Kepler satellite data to estimate the number of Earth-like planets in the Milky Way galaxy.
[Grade: 6-8 | Topics: Percentage; histograms; Re-scaling sample sizes]
(PDF)

**Problem 372: LRO Determines Lunar Cratering History **

Students count large craters on an LRO coded image of the lunar surface to estimate whether the impacting asteroids
that produced the largest
craters were from the same population of asteroids during the two different epocs of impacts.
[Grade: 6-8 | Topics: Scaled images; probability; percentages]
(PDF)

**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 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 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 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 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]