## Structure and Properties of Matter

**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 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 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 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 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 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 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 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 267: Identifying Materials by their Reflectivity ** 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 264: Water on Planetary Surfaces ** Students work with watts and Joules to study melting ice.
[Grade: 8-10 | Topics: unit conversion, rates]

**Problem 222: Kelvin Temperatures and Very Cold Things-** Students convert from Celsius to Fahrenheit and to Kelvin using three linear equations.
[Grade: 5-8 | Topics: Evaluating simple linear equations for given values.]

**Problem 313: Exploring the Big Bang with the LHC** Two simple equations allow students to compute the temperature and energy of matter soon after the
Big Bang, and compare these with energies available at the LHC.
[Grade: 9-12| Topics: ALgebra; Scientific Notation; Unit conversions]

**Problem 312: Exploring the Large Hadron Collider** The Large Hadron Collider collides protons at very high energy to create new forms of matter. Students explore
unit conversions related to energy and mass.
[Grade: 9-12 | Topics: Scientific Notation]

**Problem 307: The Elementary Particle Masses** Students compare the masses and mass differences between elementary particles using units common to physics
such as the electron Volt.
[Grade: 9-12 | Topics: Scientific Notation; unit conversion]

## Chemical Reactions

**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 181: Extracting Oxygen from Moon Rocks** Students use a chemical equation to estimate how much oxygen can be liberated from a sample of lunar soil.
[Grade: 9-11| Topics: ratios; scientific notation; unit conversions]

## Nuclear Processes

**Problem 483: The Radioactive Dating of a Star in the Milky Way! **

Students explore Cayrel's Star, whose age has been dated to 12 billion years using a radioisotope dating technique involving the decay of uranium-238.
[Grade: 9-12 | Topics: half-life; exponential functions; scientific notation]
(PDF)

**Problem 414: Radiation Dose and Distance**
Students explore the dosimetry from the Japan 2011 Earthquake and graph the decline of the
radiation dose rates with distance from the nuclear reactors.
[Grade: 9-12 | Topics: unit conversions; amount=rate x time; graphing Log-Log data]
(PDF)

**Problem 413: Exploring Nuclear Decay and Radiation Dose**
Students compare the dose rates measured from the same location in Japan on two different days, then determine the
half-life of the radioisotope causing the radiation exposure by comparing the derived half-life with those of Cesium-137 and Iodine-131.
[Grade: 9-12 | Topics: unit conversions; amount=rate x time; Solving exponential equations in base-e]
(PDF)

**Problem 412: Radiation Dose and Dose Rate**
Students use radiation measurements across Japan to calculate the total absorbed doses from the 2011 nuclear reactor failures. They also
calculate the total dose for passenger trips on jets and the Concorde.
[Grade: 6-8 | Topics: unit conversions; amount=rate x time]
(PDF)

**Problem 411: Lifestyles and Radiation Dose**
Students see how the kind of lifestyle you lead determines most of your annual absorbed radiation dose.
Some factors are under your control, and some are not.
[Grade: 6-8 | Topics: unit conversions; amount=rate x time]
(PDF)

**Problem 410:Exploring Radiation in your Life**
Students use a pie grap to calculate the total dose and dose rate for various factors that determine your annual radiation exposure while living on Earth.
[Grade: 6-8 | Topics: unit conversions; amount=rate x time]
(PDF)

**Problem 66 ****Background Radiation and Lifestyles -
** Living on Earth, you will be subjected to many different radiation
environments. This problem follows one person through four different possible futures, and compares the
cumulative lifetime dosages.
[Grade level: 6-8 | Topics: fractions, decimals, unit conversions]

**Problem 65 ****A Perspective on Radiation Dosages -
** Depending on the kind of career you chose, you will experience different
lifetime radiation dosages. This problem compares the cumulative dosages for someone living on Earth, an astronaut
career involving travel to the Space Station, and the lifetime dosage of someone traveling to Mars and back.
[Grade level: 6-8 | Topics: decimals, unit conversions, graphing a timeline, finding areas under curves using rectangles]

**Problem 310: Energy and Mass - Same things but different!** Students use unit conversions to explore the relationship between mass and energy.
[Grade: 8-10 | Topics: Unit COnversions; Scientific Notation]

**Problem 309: The Energy of Empty Space** Students explore the energy of 'empty space' and its relationship to the mass of the Higgs Boson
using a simple quartic polynomial.
[Grade: 10-12 | Topics: Properties of functions; polynomials; Critical points]

**Problem 308: The Higgs Boson and the Mystery of Mass** The search for the Higgs Boson is underway at the Large Hadron Collider (LHC). In this problem, students
explore how the mass of this particle is believed to depend on the energies used to form it by studying a simple quartic polynomial.
[Grade: 10-12 | Topics: Properties of functions; polynomials; Critical points]

**Problem 307: The Elementary Particle Masses** Students compare the masses and mass differences between elementary particles using units common to physics
such as the electron Volt.
[Grade: 9-12 | Topics: Scientific Notation; unit conversion]

## Forces and Interactions

**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 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 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 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 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 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 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; ]
(PDF)

**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]
(PDF)

**Problem 499: The Equation of a Magnetic Field Line **

Students use calculus to determine the formula for a magnetic field line.
[Grade: 12 | Topics: differential and integral calculus; slope; parametric equations]
(PDF)

**Problem 498: The Slope of a Magnetic Field Line **

Students graph a magnetic field line in the First Quadrant, then calculate the
segment midpoints using the Midpoint Formula, and then draw tangent lines at each midpoint to determine compass direction.
[Grade: 7-8 | Topics: Graphing in the XY plane; midpoint formula; tangent lines to curves]
(PDF)

**Problem 497: Graphing a Magnetic Field Line **

Students plot points along a magnetic field line in the First Quadrant,
then use reflection symmetry to complete the field line shape in all four quadrants.
[Grade: 6-8 | Topics: graphing in XY plane; reflection symmetry]
(PDF)

**Problem 420: Gravity Probe B: Testing Einstein again!**
Students learn about the Lense-Thirring Effect, and calculate its magnitude near Earth's orbit using an algebraic equation with integer and fractional exponents.
[Grade: 9-12 | Topics: algebra; scientific notation, angular measure]
(PDF)

## Energy

**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 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 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]
(PDF)

**Problem 307: The Elementary Particle Masses** Students compare the masses and mass differences between elementary particles using units common to physics
such as the electron Volt.
[Grade: 9-12 | Topics: Scientific Notation; unit conversion]

**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 264: Water on Planetary Surfaces ** Students work with watts and Joules to study melting ice.
[Grade: 8-10 | Topics: unit conversion, rates]

**Problem 220: The Many Faces of Energy-** Students convert between several different energy units.
[Grade: 8-10 | Topics: Scientific notation; unit conversions.]

**Problem 313: Exploring the Big Bang with the LHC** Two simple equations allow students to compute the temperature and energy of matter soon after the
Big Bang, and compare these with energies available at the LHC.
[Grade: 9-12| Topics: ALgebra; Scientific Notation; Unit conversions]

**Problem 312: Exploring the Large Hadron Collider** The Large Hadron Collider collides protons at very high energy to create new forms of matter. Students explore
unit conversions related to energy and mass.
[Grade: 9-12 | Topics: Scientific Notation]

**Problem 310: Energy and Mass - Same things but different!** Students use unit conversions to explore the relationship between mass and energy.
[Grade: 8-10 | Topics: Unit COnversions; Scientific Notation]

**Problem 309: The Energy of Empty Space** Students explore the energy of 'empty space' and its relationship to the mass of the Higgs Boson
using a simple quartic polynomial.
[Grade: 10-12 | Topics: Properties of functions; polynomials; Critical points]

**Problem 308: The Higgs Boson and the Mystery of Mass** The search for the Higgs Boson is underway at the Large Hadron Collider (LHC). In this problem, students
explore how the mass of this particle is believed to depend on the energies used to form it by studying a simple quartic polynomial.
[Grade: 10-12 | Topics: Properties of functions; polynomials; Critical points]

**Problem 307: The Elementary Particle Masses** Students compare the masses and mass differences between elementary particles using units common to physics
such as the electron Volt.
[Grade: 9-12 | Topics: Scientific Notation; unit conversion]

## Waves and Electromagnetic Radiation

**Problem 320: Star Light...Star Bright** A simple polynomial function is used to determine the temperature of a star from its
brightness at two different visible wavelengths.
[Grade: 10-12 | Topics: Algebra II; Polynomials; maxima and minima]

**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| Topics: Algebra, graphing, differential calculus]

**Problem 156: Spectral Classification of Stars-** Students use actual star spectra to classify them into specific spectral types according to a standard ruberic.
[Grade: 5-8 | Topics: Working with patterns in data; simple sorting logic