## Ratios & Proportional Relationships

**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]
(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 465: Comparing Planets Orbiting other Stars **

Students use simple fraction arithmetic to determine the relative sizes of several new planets recently discovered by the Kepler mission,
and compare these sizes to that of Jupiter and Earth.
[Grade: 3-5 | Topics: scale models; proportions; fractions]
(PDF)

**Problem 464: Big Moons and Small Planets **

Students work with a scaled drawing of 26 large moons in the solar system, and together with an exercise in using simple
fractions, explore the relative sizes of the moons compared to Earth.
[Grade: 3-5 | Topics: scale models; proportions; fractions]
(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 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 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 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 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 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 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 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 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 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 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]

## Rates and Slopes

**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 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 227: Working With Rates-** Students examine mixed rates for a variety of situations and their connections to ratios.
[Grade: 6-8 | Topics: Ratios; scientific notation; unit conversion.]

**Problem 226: Rates and Slopes: An astronomical perspective-** Students determine the slopes for two linear graphs and make the connection to rates with mixed units.
[Grade: 7-9 | Topics: Finding the slope of a linear graph.]

**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 134 ****The Last Total Solar Eclipse--Ever!
** Students explore the geometry required for a
total solar eclipse, and estimate how many years into the future the last total solar
eclipse will occur as the moon slowly recedes from Earth by 3 centimeters/year.
[Grade: 7 - 10 | Topics:Simple linear equations]