## The Number System

## Integers

**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]
(PDF)

**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]
(PDF)

**Problem 301: Planetary Alignments** Students combine a geometric model with number series to calculate when planets will 'line up' in a simple solar system.
[Grade: 4-8 | Topics: Number series; geometry; Least Common Multiple]

**Problem 269: Parts Per Hundred (pph) ** Students work with a common unit to describe the number of objects in a population. Other related quantities are the part-per-thousand, part-per-million and part-per-billion.
[Grade: 3-5 | Topics: counting, unit conversion]

**Problem 268: Planetary Conjunctions ** Students study a simple solar system with three planets and work out how often planets will 'line up'.
[Grade: 3-5 | Topics: geometry, time, patterns]

**Problem 243: ISS - Orbit Altitude Changes ** Students read an essay describing the increases and decreases in the International Space Station orbit, and
calculate the final orbit altitude after all the changes are applied.
[Grade: 3-5 | Topics: combining positive and negative mixed numbers; fractions]

**Problem 228: Nuclear Arithmetic ** Students use the equation N = A - Z to solve for A, Z or N given values for the other two variables.
[Grade: 4-6 | Topics: Evaluating a simple equation.]

**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 | Topics: multiplication]

**Problem 20: A Space Science Crossword Puzzle** Students work with positive and negative numbers to
solve a crossword puzzle. The theme is 'Scientists use math to explore
Nature'. Good exercise for pre-algebra review of adding and subtracting
positive and negative numbers.
[Grade: 4 - 6 | Topics: Integer arithmetic; associative and distributive laws]

## Positive and Negative Numbers

**Problem 231: Star Magnitudes and Decimals-** Students work with the stellar magnitude scale to determine the brightness differences between stars.
[Grade: 5-8 | Topics: Multiplying decimals.]

**Problem 172: The Stellar Magnitude Scale-** Students learn about positive and negative numbers using a popular brightness scale used by astronomers.
[Grade: 3-6| Topics: number relationships; decimals; negative and positive numbers]

**Problem 62: Star light...Star bright - A question of magnitude! -**
Since the time of the ancient Greek astronomer Hipparchus, astronomers have measured and cataloged the brightness of stars
according to the 'apparent magnitude scale'. This activity lets students experience this peculiar numbering system
where bright stars have small numbers (even negative: our sun is a -26 magnitude!) and faint stars have large numbers
(faintest stars are +29 magnitudes). Students will calculate the
brightness differences between stars using multiplication and division. Working with the number line will be a big
help and math review!
[Grade level: 4-6 | Topics: Positive and negative numbers; decimal math]

## Properties of Numbers, Fractions, Percentage, Scientific Notation, Unit Conversions

**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 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]
(PDF)

**Problem 555:Exploring Your Weight Across the Solar System**

Students estimate their weight on different planets, moons and asteroids.
[Grade: 6-8 | Topics: proportions]
(PDF)

**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 ]
(PDF)

**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]
(PDF)

**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]
(PDF)

**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]
(PDF)

**Problem 493: Fun with Gears and Fractions **

Students learn about how simple fractions are used to describe gears and gear trains that reduce or increase speed.
[Grade: 4-7 | Topics: multiplying simple fractions]
(PDF)

**Problem 446: Arctic Ozone Hole Continues to Grow in 2011 **

Students estimate the area of the Arctic ozone hole, and work with the concept of parts-per-million to estimate total ozone volume lost. [Grade: 6-8 | Topics: Area of rectangle; volume; percentage]
(PDF)

**Problem 444: Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine - II **

Students determine how often the two stars Kepler 16 A and B will line up with Tatooine on
the same day of the year. [Grade: 6-8 | Topics: comparing two sequences of numbers; patterns, Least Common Multiple]
(PDF)

**Problem 407: Cryo-testing the Webb Space Telecope ISIM**
Students explore scaling by creating an enlarged geometric model of the ISIM to better
appreciate the small changes due to expansion and contraction
[Grade: 6-8 | Topics: scale models; proportions; unit conversion]
(PDF)

**Problem 400: The Most Distant Objects in the Universe**
Students use a table of the most distant known events and objects in the universe to create a timeline of the universe
soon after the Big Bang.
[Grade: 6-8 | Topics: Working with millions and billions; elapsed time]
(PDF)

**Problem 399: A Galactic City in the Far Reaches of the Universe**
Students work with an image of a distant cluster of galaxies to determine its scale compared to nearby galaxies.
[Grade: 6-8 | Topics: Scale; proportion; metric measurement; unit conversion]
(PDF)

**Problem 398: The Crab Nebula - Exploring a pulsar up close!**
Students work with a photograph to determine its scale and the time taken by light and matter to reach a specified distance from the pulsar.
[Grade: 6-8 | Topics: Scale drawings; unit conversion; distance = speed x time]
(PDF)

**Problem 356: Calculating Molecular Mass**

Students count hydrogen, carbon and oxygen atoms in a molecule of adefovir dipivoxil and calculate its mass and formula.[Grade: 6-8 | Topics: Counting; Scientific Notation]
(PDF)

**Problem 345: How many stars are there?**

A starfield image taken by the 2MASS survey is analyzed to estimate how many stars are in the sky. [Grade: 6-8 | Topics: Scaling; unit conversion; angular measure]
(PDF)

**Problem 344: Hubble Spies an Asteroid - Yes it does move!**

The track of an asteroid in a Hubble image of a cluster of galaxies is analyzed to determine speed of the asteroid.[Grade: 6-8 | Topics: Scaling; unit conversion; speed=distance/time]
(PDF)

**Problem 342: The Rate of Oil Leakage in the Gulf Oil Spill of 2010** Students use still images from a video of the oil emitted by the leaking British Petrolium oil well in the Gulf of Mexico to
estimate the rate of oil leakage in gallons per day.
[Grade: 6-8 | Topics: unit conversions; rates; image scale]

**Problem 341: Recent Events: A Perspective on Carbon Dioxide** Students compare the carbon dioxide generated by the 2010 Icelandic volcano and the Gulf Oil Spill to see the relative contributions to the atmosphere of a natural and man-made catastrophe.
[Grade: 6-8 | Topics: unit conversions; rates ]

**Problem 339: Terra Satellite Spies the Great Gulf Oil Catastrophe of 2010** Students use a Terra satellite image of the oil slick in the Gulf of Mexico to calculate its area, mass and thickness.
[Grade: 6-8 | Topics: image scales; area of a circle; metric conversions ]

**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]

**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]

**Problem 316: Counting Craters on the Hubble Space Telescope** Students count craters on a piece of the Wide Field Planetary
Camera recovered from the Hubble Space Telescope in 2009. They determine the cratering rate and use this to predict
how many impacts the solar panels on the International Space Station experiences each day.
[Grade: 6-9 | Topics: Counting; Area; density]

**Problem 315: The Mysterious Hexagon on Saturn** A curious hexagon formed by the Saturn polar jet stream, and photographed by the Cassini spacecraft, is
used to determine wind speed and acceleration.
[Grade: 6-9 | Topics: Measuring; Metric Units; speed=distance/time]

**Problem 314: Chandra Studies an Expanding Supernova Shell** Using a millimeter ruler and a sequence of images of a gaseous shell between 2000 and 2005,
students calculate the speed of the material ejected by Supernova 1987A.
[Grade: 6-9 | Topics: Measuring; Metric Units; speed=distance/time]

**Problem 301: Planetary Alignments** Students combine a geometric model with number series to calculate when planets will 'line up' in a simple solar system.
[Grade: 4-8 | Topics: Number series; geometry; Least Common Multiple]

**Problem 294: Star Cluster Math** A simple counting exercise involving star classes lets students work with percentages and ratios.
[Grade: 4-6 | Topics: Counting; percentage; scaling]

**Problem 289: Chandra Spies the Longest Sound Wave in the Universe** Students use an image of sound waves produced by a massive black hole to determine wavelength, and comparisons with
musical scale to find how many octaves this sound wave is below the wavelength of middle-C.
[Grade: 6-8 | Topics: metric measurement; scaling; Scientific Notation; exponents]

**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]

**Problem 262: LRO Explores 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 260: Some Famous Unit Conversion Errors ** Students examine three famous unit conversion errors that led to catastrophic failures and near-death experiences.
[Grade: 6-8 | Topics: unit conversion, metric measure]

**Problem 301: Planetary Alignments** Students combine a geometric model with number series to calculate when planets will 'line up' in a simple solar system.
[Grade: 4-8 | Topics: Number series; geometry; Least Common Multiple]

**Problem 300: Does Anybody Really Know What Time It Is?** Students use tabulated data for the number of days in a year from 900 million years ago to the present, to estimate
the rate at which an Earth day has changed using a linear model.
[Grade: 4-8 | Topics: Graphing; Finding Slopes; forecasting]

**Problem 297: Atoms - How Sweet They Are!** A simple counting activity is based on atoms in a sugar molecule. Students calculate ratios and percantages
of various atomic types in the molecule.
[Grade: 4-8 | Topics: Counting; Ratios; percentage]

**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]

**Problem 267: Identifying Materials by their Reflectitity** The reflectivity of a material can be used to identify it. This is important when surveying the lunar surface for
minerals, and also in creating 'green' living environments on Earth.
[Grade: 6-8 | Topics: percentage, interpreting tabular data, area ]

**Problem 260: Some Famous Unit Conversion Errors** Students examine three famous unit conversion errors that led to catastrophic failures and near-death experiences.
[Grade: 6-8 | Topics: unit conversion, metric measure]

**Problem 251: Energy at Home** Students explore watts and kilowatt-hours as measures of energy and energy consumption.
[Grade: 6-8 | Topics: unit conversions; use of kilo and mega]

**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 251: Energy at Home** Students explore watts and kilowatt-hours as measures of energy and energy consumption.
[Grade: 6-8 | Topics: unit conversions; use of kilo and mega]

**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 235: Scientific Data: The gift that keeps on giving! ** Students learn about gigabytes and terabytes of data and the rates of data generation by NASA missions and how to store it.
[Grade: 6-8 | Topics: metric units; rates; money]

**Problem 234: The Hand of Chandra** Students use an image from the Chandra Observatory to measure a pulsar ejecting a cloud of gas.
[Grade: 6-8 | Topics: Scientific Notation; proportions; angle measure]

**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| Topics: unit conversions.]

**Problem 171: Are U Really Nuts?-** Students work with four unit conversion problems that are a bit tricky!
[Grade: 6-8 | Topics: unit conversions]

**Problem 123 ****A Trillion Here...A Trillion There **
Students learn to work with large numbers, which are the heart and soul of
astronomical dimensions of size and scale. This activity explores the number 'one trillion' using examples drawn from
the economics of the United States and the World. Surprisingly, there are not many astronomical numbers commonly in use that are as big as a trillion.
[Grade: 5-9 | Topics:add, subtract, multiply, divide.]

**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]

**Problem 110 ****Scientific Notation II **
In this continuation of the review of Scientific Notation,
students will perform simple addition and subtraction problems.
[Grade: 5-9 | Topics:Scientific notation - addition and subtraction]

**Problem 109 ****Scientific Notation I **
Scientists use scientific notation to
represent very big and very small numbers. In this
exercise, students will convert some 'astronomical' numbers into SN form.
[Grade: 5-9 | Topics:Scientific notation - conversion from decimal to SN]

**Problem 108 ****A Problem in Satellite Synchrony **
The THEMIS program uses five satellites in five different
orbits to study Earth's magnetic field
and its changes during a storm. This problem asks students to use the periods of the
five satellites to figure out
when all 5 satellites will be lined-up
as seen from Earth. They will do this by finding the Greatest Common Multiple of the
five orbit periods, first for the case of 2 or 3 satellites, which can be easily
diagrammed with concentric circles,
then the case for all five satellites together.
[Grade: 5-9 | Topics:multiplication; Greatest Common Multiple]

**Problem 105 ****The Transit of Mercury **
As seen from Earth, the planet Mercury occasionally passes
across the face of the sun; an event that astronomers call a transit. From images taken by the
Hinode satellite, students will create a model of the solar disk to the same scale as the
image, and calculate the distance to the sun.
[Grade: 9-11 | Topics:image scales; angular measure; degrees, minutes and seconds]

**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 82 ****Are U nuts? - **
Students will use a number of obscure English units measures to convert from metric to English units and back, and answer some
unusual questions!
[Grade level: 6-8 | Topics: arithmetic; unit conversions involving 1 to 5 steps) ]

**Problem 67 ****Unit Conversion Exercises -**
Radiation dosages and exposure calculations allow students to
compare several different ways that scientists use to compare how radiation exposure is delive black
and accumulated over time.Like converting 'centimeters per sec' to 'kilometers per year' ,this
activity reinforces student Topics in converting from one set of units to another.
[Grade level: 6-8 | Topics: fractions, decimals, units]

**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]

**Problem 58 ****How many stars are there? - **
For thousands of years, astronomers have counted the stars to
determine just how vast the heavens are. Since the 19th century, 'star gauging' has been
an important
tool for astronomers to assess how the various populations of stars are distributed within
the Milky Way. In fact, this was such an important aspect of astronomy between 1800-1920 that
many cartoons often show a frazzled astronomer looking through a telescope, with a long
ledger at his knee - literally counting the stars through the eyepiece! In this activity, students will get their first taste of star counting by
using a star atlas reproduction and bar-graph the numbers of stars in each magnitude interval.
They will then calculate the number of similar stars in the sky by scaling up their counts to the full
sky area.
[Grade level: 6-8 | Topics: Positive and negative numbers; histogramming; extrapolating data]

**Problem 48 ****Scientific Notation - An Astronomical Perspective. - **
Astronomers use scientific notation because the numbers they work with are usually..astronomical in size. This
collection of problems will have students reviewing how to perform multiplication and division with large and small numbers, while
learning about some interesting astronomical applications. They will learn about the planet Osiris, how long it takes to
download all of
NASA's data archive, the time lag for radio signals to Pluto, and many more real-world applications.
[Grade level: 8-10 | Topics: Scientific notation; decimal math]

**Problem 47 ****Discovering the Milky Way by Counting Stars. - **
It is common to say that there are about 8,000 stars visible to the naked eye in
both hemispheres of the sky, although from a typical urban setting, fewer
than 500 stars are actually visible. Students will use data from a deep-integration image of a
region of the sky in Hercules, observed by the 2MASS sky survey project to estimate the number
of stars in the sky. This number is a lower-limit to the roughly 250 to 500 billion stars that
may actually exist in the Milky Way.
[Grade level: 4-6 | Topics: Tallying data; decimal math]

**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]