Intermediate Space Math Activities (Grades 6-8)

Exploring Space Math

This section introduces learners to the wonders of the universe through intermediate level mathematics. Designed for middle school educators and students, from grades 6-8, these activities apply critical math skills, including algebra, data analysis, geometry, proportional reasoning, and scientific notation, to real-world NASA missions and astrophysical phenomena.

Table of Contents (Anchor Menu)

To help you easily navigate this extensive library, resources have been subcategorized by Core Math Skills. Use the Table of Contents below to jump directly to the materials that best fit your classroom's needs.

Arithmetic↓	Algebra, Equations & Functions ↓	Data Analysis & Graphing ↓	Geometry, Measurement & Formulas↓
Ratios, Proportions & Percentages↓	Scale Models & Conversions↓	Rates & Speed↓	Scientific Notation↓

____________________________________________________________________________________________

Arithmetic

Back to Top ↑

Resource Title & Link	Description
Estimating the Speed of a Tsunami (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page71.pdf) ↗	In these three math problems students use the tsunami arrival times and earthquake start time for the devastating 2011 Japan Earthquake to estimate the speed of a tsunami as it crosses the Pacific Ocean.
Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine - II (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page18.pdf) ↗	In these four math problems students determine how often the two stars Kepler 16 A and B will line up with Tatooine on the same day of the year.
Time Zone Mathematics. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/WeekAL.pdf) ↗	In this math activity students will learn about the time zones around the world, and why it is important to keep track of where you are when you see an astronomical phenomenon.
Planetary Alignments (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page41.pdf) ↗	In these two math problems students combine a geometric model with number series to calculate when planets will 'line up' in a simple solar system.
Telling Time on Mars - Earth Days and Mars Sols (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight7.pdf) ↗	In these four math problems students work with two clocks on Earth and Mars and learn about earth and mars time given that a day on Mars is 40 minutes longer than an Earth day.
Exploring the Stars in Orion - Light Year Madness (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/IRAD-1.pdf) ↗	In these five math problems students explore the light year and its relationship to light travel time for observing events in different parts of space.
How many stars are there? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/2page19.pdf) ↗	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.
Where Did All the Stars Go? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page66.pdf) ↗	In these four math problems, students learn why NASA photos often don't show stars because of the way that cameras take pictures of bright and faint objects.
Star Magnitudes and Decimals (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page69.pdf) ↗	In these five math problems tudents work with the stellar magnitude scale to determine the brightness differences between stars.
Measuring the Speed of Gas Near a Black Hole (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page72.pdf) ↗	In these two math problems students use a graph of intensity and time to estimate thhe orbit period of matter around a black hole.
A Trillion Here...A Trillion There (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page24.pdf) ↗	In these 11 math problems students learn to work with large numbers, which are the heart and soul of astronomical dimensions of size and scale.
Scheduling Events in Time for Launch (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight3.pdf) ↗	In this math problem students learn about scheduling many events along a timeline by planning a family trip.
The STEREO Mission: getting the message across- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page59.pdf) ↗	In these five math problems students learn about how the transmission of data is affected by how far away a satellite is for the two satellites in the STEREO constellation.
A Problem in Satellite Synchrony (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page11.pdf) ↗	In these four math problems students use the periods of the five THEMIS satellites to figure out when all 5 satellites will be lined-up as seen from Earth.
IBEX Creates an Unusual Image of the Sky! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page68.pdf) ↗	In these two math problems 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.
How to make faint things stand out in a bright world!- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page63.pdf) ↗	In these five math problems students learn that adding images together often enhances faint things not seen in only one image, the power of averaging data.
Discovering the Milky Way by Counting Stars. - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/2page7.pdf) ↗	In this math activity students estimate the number of stars in the sky using data from a deep-integration image of a region of the sky in Hercules, observed by the 2MASS sky survey.

______________________________________________________________________________________________

Algebra, Equations & Functions

Back to Top ↑

Resource Title & Link	Description
SAGE- Using Opacity to Find Aerosol Density (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page107.pdf) ↗	In these three problems students examine a mathematical model based on the SAGE-III geometry to determine aerosol concentrations at different altitudes.
SAGE- A Study of Aerosol Extinction in the Stratosphere (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page100.pdf) ↗	In these four problems 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.
Reading Between the Lines (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/WeekY.pdf) ↗	In this activity students solve simple equations to discover which words complete an essay on the causes of aurora, and answer questions after reading the completed essay.
Exploring the Evaporating Exoplanet HD189733b (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page24.pdf) ↗	In these five math problems students estimate how quickly this planet will lose its atmosphere and evaporate at its present loss rate of 6 million tons/second
Drake's Equation and the Search for Life...sort of! - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/2page18.pdf) ↗	In these seven math problems students use a formula to estimate how much life there is in the Milky Way.
Distance Traveled Under Free Fall by Gravity (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page56.pdf) ↗	In these five math problems students explore accelerated motion and distance traveled using an equation that related distance to time-squared, and solve the equation under various conditions.
Measuring Gravity with a Pendulum (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page39.pdf) ↗	In these three math problems students design pendulum clocks for mars and the moon, and how pendulums can be used for mining on Earth.
Gravity and Falling Bodies (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page55.pdf) ↗	In these three math problems students work with simple linear equations to study the speed of falling bodies under gravity.
Gravity and Escape Speed (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page61.pdf) ↗	In these four math problems students calculate the escape speed for various planets using a simple 'square root' equation.
Variables and Expressions from Around the Cosmos- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page81.pdf) ↗	In these seven math problems students evaluate linear equations describing a variety of astronomical situations.
Kelvin Temperatures and Very Cold Things- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page78.pdf) ↗	In these six math problems students convert from Centigrade to Fahrenheit and to Kelvin using three linear equations.
Gravity and Energy (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page58.pdf) ↗	In these three math problems students the energy equation E = mgh to expore the energy of falling water near Earths surface to calculate the energy of a water fall.
The Closest Approach of Asteroid 2005YU55 - I (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page25.pdf) ↗	In these five math problems students work with a scaled drawing of the orbit of the moon and the asteroid trajectory to predict where the asteroid will be relative to earth and the orbit of the moon.
Orbit Speeds and Times for Saturns Rings (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page28.pdf) ↗	In these five math problems 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.
LL Pegasi - A Perfect Spiral in Space (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page15.pdf) ↗	In these five math problems students explore the timing of the pattern of the star LL Pegasi and estimate the size and age of this gas.
The Spectacular Cat's Eye Planetary Nebula (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page24.pdf) ↗	In these three math problems students measure the diameter of the nebula and use speed information to estimate the age of the nebula
Pulsars and Simple Equations (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page79.pdf) ↗	In these six math problems students work with linear equations describing the rotation period of a pulsar, and evaluate the equations for various conditions.
Exploringa Full-sized Black Hole (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page30.pdf) ↗	In these three math problems students explore how the speed of an orbiting satellite changes if it were near a black hole with five times the mass of our Earth.
Estimating the diameter of the SN1979c black hole (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page53.pdf) ↗	In this math problems students use simple equations to learn about the various definitions for the sizes of black holes in terms and apply this to the black hole in the galaxy M-100
Supercomputers; Getting the job done FAST! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page46.pdf) ↗	In these four math problems students use a simple counting problem to explore how much faster a supercomputer is compared to as hand-calculation.
Whacky Spacecraft Orbits - They only seem crazy! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page36.pdf) ↗	In these three math problems students investigate the loopy orbit of the THEMIS/Artemis spacecraft as they are being inserted into lunar orbit.
A piece of history - space shuttle thermal tiles (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page34.pdf) ↗	In these three math problems students explore volume density and mass using the Space Shuttle thermal tiles. Get your own free tile from NASA too!
A Number Puzzle about the Origin of Our Universe (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page54.pdf) ↗	In this math activity tudents 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.
HST - The Hubble Search for the Farthest Galaxy in the Universe (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page114.pdf) ↗	In these three math problems students learn about the recent discovery of z8_GND_5296 what may be the farthest known galaxy in our visible universe.

______________________________________________________________________________________________

Data Analysis & Graphing

Back to Top ↑

Resource Title & Link	Description
History of Winter - Graphing a Showflake using Symmetry (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/85Mod11Prob1.pdf) ↗	In these three math problems students use a simple plotting exercise and reflection symmetry to create a snowflake.
History of Winter - Snowflake Growth Rates and Surface Area (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/87Mod11Prob3.pdf) ↗	In these three math problems students study change of scale and dilation by investigating showflake growth.
History of Winter - Snow to Water Ratios (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/88Mod11Prob1.pdf) ↗	In these two math problems students learn how to convert between snow volume and equivalent volumes of liquid water.
The Composition of Planetary Atmospheres (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page7.pdf) ↗	In these five math problems students study the composition of planetary atmospheres and compare the amounts of certain compounds in them
Carbon Dioxide Increases (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Energy16.pdf) ↗	In these math problems students study the Keeling Curve to determine the rates of increase of carbon dioxide in the atmosphere.
NASA 'Sees' Carbon Dioxide (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/NASA1.pdf) ↗	In these four math problems students use a satellite image of atmospheric carbon dioxide to estimate the geographic differences and identify human activity.
The Fastest Sea Level Rise in the United States (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page5.pdf) ↗	In these two math problems students look at which part of the United States is sinking the fastest.
Investigating the atmosphere of Super-Earth GJ-1214b (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page55.pdf) ↗	In these two math problems students investigate the interior of an exoplanet to estimate the thickness of its atmosphere given the mass size and density of the planet.
The Goldilocks Planets - Not too hot or cold (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page66.pdf) ↗	In these five math problems students use a table of the planets discovered by the Kepler satellite to estimate the average temperature of the planets, and study their tabulated properties using histograms.
The Launch of LADEE to the Moon (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page66.pdf) ↗	In these three math problems students plot the altitude, range and speed of the LADEE rocket launch and investigate rates of change including acceleration by graphing the tabular data.
Earth's Rotation Changes and the Length of the Day? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page58.pdf) ↗	In these three math problems 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.
Earth's Polar Wander - The Chandler Wobble (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page17.pdf) ↗	In these six math problems students plot the circular shape of the track of the North Pole during a 2-year period and estimate the speed of movement.
The 10000th Near Earth Asteroid 2013 MZ5 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page20.pdf) ↗	In these three math problems students graph tabulated data to determine when this asteroid is closest to Earth and its speed at that time.
How Quickly are NEOs Being Discovered? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page21.pdf) ↗	In these five math problems students work with data presented in bar graphs to estimate how many more hazardous Near Earth Objects (NEOS) remein to be found.
Getting A Round in the Solar System! - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/2page20.pdf) ↗	in this math activity students examine images of asteroids and planetary moons to determine the critical size for an object to become round under the action of its own gravity.
Exploring the Orbit of Comet ISON (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page25.pdf) ↗	In these three math problems students use tabulated data to estimate when this comet will make its closest approach to the sun in 2013.
The Curiosity Rover on the Move. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page16.pdf) ↗	In these four math problems students plot the position of the Curiosity Rover on a cartesian grid covering the satellite image of the landing area.
Spectral Classification of Stars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page43.pdf) ↗	In these three math problems students use actual star spectra to classify them into specific spectral types according to a standard ruberic.
Measuring Star Temperatures (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page55.pdf) ↗	In these two math problems students use a simple formula to determine the temperatures of stars, and to use a template curve to analyze data for a specific star to estimate its temperature.
HST - The Sun’s Nearest Companions…At least for now! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page115.pdf) ↗	In these five math problems students study a graph that models the distances from the sun of seven nearby stars over a 100,000 year time span.
Exploring Light Brightness and the Inverse Square Law (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/IRAD-3.pdf) ↗	In these four math problems 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.
Designing a Telescope System (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page36.pdf) ↗	In this math activity, students design two telescopes given information about the desired properties for conducting research.
Saturn V Rocket Launch Speed and Height (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page2.pdf) ↗	In these four math problems students use tabular data to determine the launch speed of the Saturn V rocket from the launch pad.
The Last Flight of the Space Shuttle Endeavor (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page3.pdf) ↗	In these four math problems students use tabular data and graphing to determine the launch speed and acceleration of the Space Shuttle from the launch pad.
The Hubble Law - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page1.pdf) ↗	In these six math problems 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 Hubble's Constant.
Detecting the Most Distant SUpernova in the Universe (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7page37.pdf) ↗	In these two math problems students use a graph to compare the brightness of supernova produced by three different masses of stars, and predict whether the Webb Space Telescope can see them.

______________________________________________________________________________________________

Geometry, Measurement & Formulas

Back to Top ↑

Resource Title & Link	Description
Arctic Ozone Hole Continues to Grow in 2011 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page20.pdf) ↗	In these math probltudents estimate the area of the Arctic ozone hole, and work with the concept of parts-per-million to estimate total ozone volume lost.
SCOOL-Estimating the Mass of a Cloud (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/79Clouds3.pdf) ↗	In these math problems, students use the relationship between volume and density to estimate the mass of a common cumulus cloud.
SCOOL-Cloud Droplets and Rain Drops (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/84Clouds8.pdf) ↗	In these math problems, students explore some of the properties of water droplets in clouds, assuming that the droplets are perfect spheres.
SCOOL-Using Proportions to Estimate the Height of a Cloud (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/78Clouds1.pdf) ↗	In these four math problems, students use the method of triangulation to determine the height of a cloud.
History of Winter - The Surface Area of a Snowflake (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/86Mod11Prob2.pdf) ↗	In these two math problems students estimate the area of a single snow flake using the areas of triangles and rectangles.
Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine - I (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page15.pdf) ↗	In these five mah problems students explore the orbit speeds of Tatooine and Kepler-16B and predict how often the two stars line up with the planet to create an 'eclipse'.
Areas Under Curves: An astronomical perspective- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page75.pdf) ↗	In these five math problems students work with a bar graph of the number of planet discoveries since 1995 to evaluate the total discoveries, as areas under the graph, for various combinations of time periods.
Kepler: The hunt for Earth-like planets- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page87.pdf) ↗	In these six problems students compare the area of a star with the area of a planet to determine how the star's light is dimmed when the planet passes across the star as viewed from Earth.
Lunar Cratering: Probability and Odds- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page18.pdf) ↗	In these eight math problems students work with crater counting to estimate the area covered by craters and how to convert this into impact probabilities.
Is There a Lunar Meteorite Impact Hazard? - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page22.pdf) ↗	In these three math problems students work with areas, probability and impact rates to estimate whether lunar colonists are in danger of meteorite hazards.
Chandra Studies an Expanding Supernova Shell (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page94.pdf) ↗	In this math activity students use a millimeter ruler and images of a gaseous shell (2000-05), to calculate the speed of ejected material by Supernova 1987A.
The Late Heavy Bombardment Era (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page5.pdf) ↗	In this math activity students estimate the average arrival time of large asteroids that impacted the moon.
The Closest Approach of Asteroid 2005YU55 - II (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page26.pdf) ↗	In this math problem students work with the properties of circles and angular measure to see where the moon will be at the start of the asteroid encounter.
Counting Craters on the Hubble Space Telescope (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page99.pdf) ↗	In these six math problems students count craters on a piece of the Wide Field Planetary Camera recovered from the Hubble Space Telescope in 2009.
Apparent Sizes of Objects from Jupiter’s Moon Europa (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page51.pdf) ↗	In these four math problems sudents 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.
The Mysterious Hexagon on Saturn (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page97.pdf) ↗	A curious hexagon formed by the Saturn polar jet stream, and photographed by the Cassini spacecraft, is used to determine wind speed and acceleration.
Comet ISON Losing Mass as it Approaches the Sun. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page22.pdf) ↗	In these two math problems students estimage how much mass the comet will loose at its present rate.
Ios Volcanoes and Resurfacing (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page27.pdf) ↗	In these five math problems students examine how volcanic activity on Jupiter's satellite Io can lead to resurfacing the entire moon in less than a million years covering all new craters.
The Work Area In Front of the Lander (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight4.pdf) ↗	In these four math problems students estimate the area in front of the InSight lander where experiments will be conducted and instruments moved with a single robotic arm.
Seeing the Martian Surface with IDC (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight8.pdf) ↗	In these four math problems students learn about the IDC camera and calculate resolution and how many images are needed to map the InSight landing area.
Exploring a Possible InSight Landing Area on Mars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight20.pdf) ↗	In these eleven math problems students work with latitude and longitude and scaled images of mars to locate the InSight proposed landing area, and describe the terrain of the landing area.
Methane Lakes on Titan (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page148.pdf) ↗	In these four math problems students use an image of the surface of Titan to estimate how much methane is present in the lakes that fill the image compared to Lake Tahoe.
Exploring Water Use in Kansas (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page10.pdf) ↗	In these three math problems students use Landsat imagery (1972, 2011) to determine how much water is being used for irrigation in a small region of Kansas.
Growing Grapes in the Middle of the Desert (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page69.pdf) ↗	In these three math problems students use a dramatic Earth Observatory-1 satellite image of agriculture in Namibia to estimate the total cultivated area and water needs of grape growing under desert conditions
New NASA Satellite Takes Pictures of Salton Sea (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page38.pdf) ↗	In these three math problems students work with image of agricultural area to estimate the percentage of area cultivated and the total rainfall in gallons per year.
Digital Camera Math (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page37.pdf) ↗	In these three math problems students learn about digital cameras and how to interpret formats, megapixels and angular resolution.
A Simple Fuel Gauge in a Cylindrical Tank (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page37.pdf) ↗	In these three math problems students work the formula for the volume of a cylinder to add a fuel gauge at the right level to indicate how much fuel remains.
Calculating the Volume of the J-2x Rocket Engine Bell (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page69.pdf) ↗	In these three math problems students explore conical volumes by examining the dimensions of a large rocket engine.
A Simple Gauge in a Tank - II (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page73.pdf) ↗	In these three math problems students work with the formula for the volume of a conical solid to design a gas tank gauge.
Adding a Level Gauge to a Conical Tank (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page75.pdf) ↗	In these three math problems students work with the formula for the volume of a cone
Exploring the InSight Lander Telemetry Data Flow (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight9.pdf) ↗	In these four math problems students explore how long it takes to transmit digital data using examples from downloading songs from their computer to their ipod.
Telescope Light Gathering Ability - Seeing Faint Stars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page33.pdf) ↗	In these two math problems students calculate the light gathering ability of various telescopes compared to the human eye.
The Scale of an Image with a Telescope (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page38.pdf) ↗	In these three math problems students design digital cameras for telescopes given information about the image scale of the telescope and the pixel dimensions.
Telescope Field of View - How much can you see? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page34.pdf) ↗	In these two math problems students calculate the angular field of view for various telescopes using a simple formula of the form F = A/B
Telescope Resolution - How much detail can you see? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page35.pdf) ↗	In these three math problems 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.
The Hubble eXtreme Deep Field (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page7.pdf) ↗	In these seven math problems students use the Hubble XDF to estimate the number of galaxies in the visible universe.
Chandra Spies the Longest Sound Wave in the Universe (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page93.pdf) ↗	In these three math problems students use an image of sound waves produced by a massive black hole to determine wavelength.

______________________________________________________________________________________________

Ratios, Proportions & Percentages

Back to Top ↑

Resource Title & Link	Description
VAP- Exploring Gas Density in Space (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/RBSP10.pdf) ↗	In these math problems, students explore how gas density is related to the average distances between molecules in the air using a simple geometric model of a cube with 64 cells.
SCOOL-How Clouds Form - Working with Dew Points and Rates of Change (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/81Clouds5.pdf) ↗	In these math problems, students learn about the dew point and how clouds form from humid, cooling air.
Measuring Atmospheric Trace Gases Using Parts Per Million (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page8.pdf) ↗	In these three problems students convert from percentage units to parts per million and compare trace gases in the atmospheres of various planets.
History of Winter - Snow Density and Volume (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/89Mod11Prob2.pdf) ↗	In these three math problems students learn how snow density is measured in the field using cylindrical instruments in a snow pit trench.
History of Winter - Snow Density; Mass and Roof Failure (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/90Mod11Prob3.pdf) ↗	In these two math problems, students invesrtigate how snow causes buildings to collapse.
SAGE- Aerosols and Light Dimming (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page95.pdf) ↗	In these three problems students explore how light is dimmed as it passes through a series of filters.
SAGE- Exploring Aerosols (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page94.pdf) ↗	In these three problems students compare aerosol sizes to a human hair, calculate volumes and masses from density.
SAGE- Air Quality Index and Aerosol Density (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page105.pdf) ↗	In these two problems students see how the Air Quality Index is related to the number of aerosols per cubic meter.
Kepler - Earth-like planets by the score! I (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page64.pdf) ↗	In these three problems students use recent Kepler satellite data to estimate the number of Earth-like planets in the Milky Way galaxy.
Kepler- Earth-like planets by the score! II (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page65.pdf) ↗	in these three problems students use recent Kepler satellite data to estimate the number of planets in the Milky Way galaxy about the same size as our Earth, and in their Habitable Zones.
Kepler - Kepler’s Latest Count on Goldilocks Planets (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page117.pdf) ↗	In these two problems students examine the statistics of the latest candidate planets beyond our solar system, work with percentages and a bar graph, and estimate the number of earth-like planets in our Milky Way.
NASA’s Kepler Mission Detects 715 New Planets (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page130.pdf) ↗	In these four math problems 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.
Kepler's First Look at 700 Transiting Planets (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page7.pdf) ↗	In these three math problems, students do a statistical study of the 700 transits seen during the first 43 days of the mission.
Atoms - How Sweet They Are! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page35.pdf) ↗	In this math activity tudents calculate ratios and percentages of various atomic types in the molecule.
Identifying Materials by their Reflectivity (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/MMM1.pdf) ↗	In these four math problems students learn how the reflectivity of a material can be used to identify it - important when surveying the lunar surface for minerals, and also in creating 'green' living environments on Earth.
Unit Conversion Exercises - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/3Page1.pdf) ↗	Radiation dosages and exposure calculations allow students to compare several different ways that scientists use to compare how radiation exposure is delivered and accumulated over time.
The Frequency of Large Meteor Impacts (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page26.pdf) ↗	In these three math problems students examine how often a large meteor should be visible like the one that exploded over Russia on February 14, 2013.
Transit of Phobos Across the Sun Viewed from Mars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page62.pdf) ↗	In these three math problems students investigate the geometry of a martian moon passing across the face of the sun using angular measure and proportions.
The Occulting Moons of Mars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page50.pdf) ↗	In these four math problems students explore the moons of mars and their eclipses during an event seen by the Curiosity rover on August 1, 2013.
Visiting the Planets at the Speed of Light (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page2.pdf) ↗	In these four math problems students learn about the light travel times to the eight planets by converting the distances in Astronomical Units to travel times at the speed of light.
A Distant Supernova Remnant Discovered (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page43.pdf) ↗	In these two math problems students work with proportions and scaling to discover the size of the supernova remnant compared to the distance from the Sun to the nearest star Alpha Centauri.
Focal Lengths; Apertures and F/numbers (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page30.pdf) ↗	In these two math problems students learn about the basic terms that define the performance of a digital camera or a telescope.
Working With Rates- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page73.pdf) ↗	In these twenty math problems students examine mixed rates for a variety of situations and their connections to ratios.
Fun with Gears and Fractions (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page14.pdf) ↗	In these four math problems students learn about how simple fractions are used to describe gears and gear trains that reduce or increase speed.
SAGE - The Ground Track of the International Space Station (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page111.pdf) ↗	In these four math problems students determine how many sunrises and sunset the ISS observes every day.
Calculating the Magnification of a Telescope (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page32.pdf) ↗	In these two math problems students fill in missing numbers in a table using proportions and evaluating a simple equation for magnification.
Buying a Telescope (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page42.pdf) ↗	In these three math problems students compare several telescopes and select the one with the best performance and lowest cost.
Fermi Explores the High-Energy Universe (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page33.pdf) ↗	In these three math problems students work with percentages to explore the identities of the 1873 gamma-ray sources detected by NASAs Fermi Observatory

______________________________________________________________________________________________

Scale Models & Conversions

Back to Top ↑

Resource Title & Link	Description
SAGE- A Scale Model of Aerosol Sizes (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page103.pdf) ↗	In these five math problems students work with proportions and scale to create a scale model of aerosol particles.
SAGE- Exploring the Mass and Density of Aerosol Particles (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page104.pdf) ↗	In these two math problems students explore the physical sizes of aerosol particles. With unit conversions they convert concentration units of micrograms/m3 to particles/m3.
SAGE- Some Basic Properties of the SAGE-III Instrument (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page108.pdf) ↗	In these four math problems 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.
SAGE- Measuring Stratospheric Ozone with SAGE-III (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page109.pdf) ↗	In these three math problems students use a data graph to identify the ozone layer and use parts-per-million to compare ozone concentration to the atmosphere density.
SAGE- Measuring Aerosol Concentration in Parts per Million (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page110.pdf) ↗	In these three problems students learn about parts-per-million units by working with percentage and counting squares in different types of grids.
Recent Events; A Perspective on Carbon Dioxide (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page157.pdf) ↗	In these four problems students compare the carbon dioxide generated by the 2010 Icelandic volcano and the Gulf Oil Spill.
The Rate of Oil Leakage in the Gulf Oil Spill of 2010 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page158.pdf) ↗	In these four math problems students use images of a leaking oil well in the Gulf of Mexico to estimate the rate of oil leakage in gallons per day.
Terra Satellite Spies the Great Gulf Oil Catastrophe of 2010 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page155.pdf) ↗	In these five math problems students use a Terra satellite image of the oil slick in the Gulf of Mexico to calculate its area, mass and thickness.
Hubble Sees a Distant Planet- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page62.pdf) ↗	In these four math problems students study an image of the dust disk around the star Fomalhaut and determine the orbit period and distance of a newly-discovered planet orbiting this young star.
How Big is It? - The Moon up close. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page44.pdf) ↗	In this math activity students work with an image from Lunar Orbiter IV spacecraft to determine image scale, and search for the smallest things seen in a photograph.
How Big is It? - The Moon up close. (orbiter 3) (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page45.pdf) ↗	In this math activity students work with an image from Lunar Orbiter III spacecraft to determine image scale, and search for the smallest things seen in a photograph.
Angular Size: The Moon and Stars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page70.pdf) ↗	In these four math problems students explore angular size using a simple proportional equation
LRO Sees Apollo-11 on the Moon! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page1.pdf) ↗	In these three math problems students use the latest image from the Lunar Reconnaissance Orbiter of the Apollo-11 landing site to explore lunar features at 1-meter resolution.
LRO and the Apollo-11 Landing Site (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Lunar17.pdf) ↗	In these three math problems students examine a map of the Apollo-11 landing area and determine how well various features will be visible to the Lunar Reconnaissance Orbiter.
LRO's First Image of Mare Nubium (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Lunar18.pdf) ↗	In these three math problems students examine the first image of this lunar region using the high-resolution camera image provided by the Lunar Reconnaissance Orbiter.
LRO - Searching for Lunar Boulders (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Lunar21.pdf) ↗	In these two math problems students use a recent image of the Apollo-11 landing area to search for large lunar boulders.
LRO Explores Lunar Surface Cratering (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Lunar22.pdf) ↗	In these three math problems students count the number of craters in various size ranges from a high-resolution image of the lunar surface.
LRO Determines Lunar Cratering History (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page33.pdf) ↗	In these four math problems tudents count large craters on an LRO coded image of the lunar surface to study the impacting asteroids that produced the largest craters.
LRO explores the Apollo 12 landing area on the moon (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page12.pdf) ↗	In these three math problems students use a recent image obtained by the LRO spacecraft to estimate how far astronauts walked to get to various points in the landing area.
LRO - The relative ages of lunar surfaces (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page16.pdf) ↗	In these four math problems students examine two Apollo landing areas using images from the LRO spacecraft to estimate the relative ages of the two regions using crater counting.
Grail Spacecraft Creates a New Crater on the Moon (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page35.pdf) ↗	In these five math problems tudents work with images of the Grail impact sites to estimate the diameter of the crater created after the spacecraft impacted the moon.
How big is it? - Asteroid Eros surface (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page50.pdf) ↗	In this math activity students calculate the scale of an image of the surface of the asteroid Eros from the NEAR mission, and determine how big rocks and boulders are on its surface.
How Big is It? - Io and Jupiter. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page49.pdf) ↗	In this math activity students work with an image of Jupiter and its satellite Io. They determine the image scale, and calculate the sizes of various features in the image.
A Hot Time on Mars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/3Page4.pdf) ↗	In this math activity students examine the total radiation dosage that explorers would receive on a series of 1000 km journeys across the martian surface.
How Big is It? - A Martian Avalanche! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page51.pdf) ↗	In this math activity students work with a Mars Reconnissance Orbiter image to determine image scale, and search for the smallest things seen in the photograph.
Mars, How Big Is It? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page47.pdf) ↗	In this math activity students use an image of a crater wall on Mars to investigate ancient water gullies discovered in 2008 by the Mars Orbiter.
The Martian Dust Devils (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page2.pdf) ↗	In these six math problems students determine the speed and acceleration of a Martian dust devil from time laps images and information about the scale of the image.
Taking a stroll around a martian crater! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page50.pdf) ↗	In these four math problems students use a recent photograph of a crater on Mars to estimate its circumference and the time it will take NASA's Opportunity Rover to travel once around its edge.
Comparing the Rings of the Outer Planets (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page13.pdf) ↗	In these two math problems 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.
Saturns Rings- Shadows from Moons and Ringlets (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page12.pdf) ↗	In these four math problems 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.
Hubble Spies an Asteroid - Yes it does move! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page20.pdf) ↗	In these two math problems students analyze the track of an asteroid in a Hubble image of a cluster of galaxies to determine speed of the asteroid.
A Flyby of Asteroid Lutetia (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page2.pdf) ↗	In these three math problems, students apply the Pythagorean Theorem to angular size.
Dawn Spacecraft Sees Asteroid Vesta Up-Close! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page13.pdf) ↗	In these four math problems students use an image of the asteroid to determine the diameters of craters and mountains using a millimeter ruler and the scale of the image in meters per millimeter.
Tempel-1 - Close-up of a Comet (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Deep1.pdf) ↗	In these four math problems students examine an image of the Comet Tempel-1 taken by the Deep Impact spacecraft to determine feature sizes and other details.
How Big is It? - The Mars Rover. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page48.pdf) ↗	In these five math problems students work with an image taken by the Mars Orbiter satellite of the Spirit landing site and calculate the sizes of various surface features from the image.
Comparing the InSight Landing Area to a City Block! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight19.pdf) ↗	In these four math problems students use scaled images to compare the sizes of familiar urban neighborhood with the unfamiliar martian landscape.
Measuring the size of a Star Cluster - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/2page12.pdf) ↗	In this activity, students will determine the photographic scale, and use this to estimate the projected (2-D) distances between the stars in a star cluster.
How many stars are there? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page21.pdf) ↗	In these four math problems students analyze a starfield image taken by the 2MASS survey to estimate how many stars are in the sky.
Constellations in 3D (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page67.pdf) ↗	In this math activity 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.
Details from an Exploding Star (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page24.pdf) ↗	In these three math problems students work with an image from the Hubble Space Telescope of the Crab Nebula to calculate scales and sizes of various features.
The Crab Nebula - Exploring a pulsar up close! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page60.pdf) ↗	In these three math problems 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.
Energy at Home (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Energy3.pdf) ↗	In these two math problems students explore watts and kilowatt-hours as measures of energy and energy consumption.
Exploring Temperature Change in Earth’s Outer Crust (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight10.pdf) ↗	In these four math problems students explore the rate of temperature change in the crust of Earth and Mars and learn about units expressed as degrees C/km.
Astronomy; A Moving Experience! - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/2page8.pdf) ↗	In this math activity, students measure the speed of astronomical phenomena using the scaling clues and the time intervals between photographs of three phenomena.
How Big is It? - Washington DC up close. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page43.pdf) ↗	In this math activiy students work with an image taken by ISS astronauts to determine image scale, and search for the smallest things seen in a photograph.
How Big is It? - Las Vegas up close. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page46.pdf) ↗	In these five math problems students work with an image taken by the QuickBird imaging satellite of downtown Las Vegas, Nevada.
Mapping Earth from Space - Swaths and Coverage (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/IRAD-2.pdf) ↗	In these six math problems students explore how satellite observing swaths add up to give full coverage of earths surface.
Some Simple Unit Conversions- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/3Page17.pdf) ↗	In this math activity students will use a number of obscure English units measures to convert from metric to English units and back, and answer some unusual questions!
More Unit Conversions- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page50.pdf) ↗	In these three math problems students work with four unit conversion problems that are a bit tricky!
Some Famous Unit Conversion Errors (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page53.pdf) ↗	In this math problem students examine three famous unit conversion errors that led to catastrophic failures and near-death experiences.
A High-resolution Satellite Photo (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Lunar16.pdf) ↗	In these four math problems students examine a satellite photo of the Tennessee Court House from the GEO-1 satellite and determine the sizes of familiar features in the image.
Cryo-testing the Webb Space Telecope ISIM (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page70.pdf) ↗	In these two math problems students explore scaling by creating an enlarged geometric model of the ISIM to better appreciate the small changes due to expansion and contraction
Apollo-17 Launch from Lunar Surface (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page5.pdf) ↗	In these two math problems students use a sequence of images to determine the speed of ascent of the Apollo-17 capsule from the lunar surface.
Space Shuttle Atlantis - Ascent to Orbit (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page7.pdf) ↗	In these four math problems students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image.
Space Shuttle Atlantis - Launch Speed (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page8.pdf) ↗	In these four math problems students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image.
Space Shuttle Atlantis - Exhaust Speed (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page9.pdf) ↗	In these three math problems students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image.
Space Shuttle Atlantis - Plume Speed (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page10.pdf) ↗	In these four math problems students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image.
The Launch of the Juno Spacecraft - Ascent to orbit (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/JUNO8.pdf) ↗	In these four math problems students use tabulated altitude and range data following the launch of the Juno mission, to determine the speed of the rocket as it travels to arth orbit.
Investigating the Launch of the Juno Spacecraft (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/JUNO7.pdf) ↗	In these three math problems students use a series of images from a launch video to determine the scale of each image and determine the speed of the rocket as it leaves the gantry.
Space Shuttle Challenger Deploys the INSAT-1B Satellite (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page6.pdf) ↗	In these four math problems students use a sequence of images to determine the launch speed of the satellite from the Space Shuttle cargo bay.
Our Neighborhood in the Milky Way- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page30.pdf) ↗	In these two math problems students create a scale model of the local Milky Way and estimate distances and travel times for a series of voyages.
Exploring the Cosmos with Supercomputers (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7page43.pdf) ↗	In these three math problems students use two images created by a supercomputer calculation to explore the size and accuracy of computer models of the distanct universe.
A Spiral Galaxy Up Close. - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/2page10.pdf) ↗	In these three math problems students will compute the image scale (light years per millimeter) in a photograph of a nearby spiral galaxy, and explore the sizes of the features found in the image.
A Galactic City in the Far Reaches of the Universe (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page62.pdf) ↗	In these three math problems students work with an image of a distant cluster of galaxies to determine its scale compared to nearby galaxies.
Planck Mission Sees the Ancient Universe Clearly (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page36.pdf) ↗	In these four math problems students work with an image of the universe when it was 370,000 years old and determine the sizes of the features seen in the image compared to the Milky Way.

______________________________________________________________________________________________

Rates & Speed

Back to Top ↑

Resource Title & Link	Description
SAGE- Aerosol Sources in the Stratosphere (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page98.pdf) ↗	In these three math problems students examine the sources of aerosols in the atmosphere and determine their percentage contributions based upon their individual rates given in megatons/year.
Astronaut Bone Loss (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page18.pdf) ↗	From a graph, students predict how much bone loss an astronaut experiences during a long-duration stay in space.
Exploring Comet Orbits (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page44.pdf) ↗	In these four math problems students explore the elliptical orbit of Halleys Comet and determine its period and the speed of the comet.
The InSight Seismographic Station - Wave arrival times (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page34.pdf) ↗	In these three math problems students use the circumference of Mars and the speed of shock waves in the martian crust to estimate the arrival times of the waves at the InSight Lander.
VAP- Telemetry Math (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/RBSP4.pdf) ↗	In these three math problems students work with data rates for the spacecraft and determine how much data needs to be stored.
The Space Shuttle; Fly me to the moon? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page85.pdf) ↗	In these four math problems students discuss the misconception that the Space Shuttle can travel to the moon.
Fly Me To the Moon!- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page26.pdf) ↗	In these two math problems students learn some basic principles and terminology about how spacecraft change their orbits to get to the moon.
Exploring the Launch of the Falcon 9 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page33.pdf) ↗	In these five math problems students use data from the launch of the Falcon 9 booster to determine its speed and acceleration.

______________________________________________________________________________________________

Scientific Notation

Back to Top ↑

Resource Title & Link	Description
VAP- Exploring the Density of Gas in the Atmosphere (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/RBSP9.pdf) ↗	In these math problems, students examine different ways to represent the density of Earth;s atmosphere.
SAGE- The Sources and Sinks of Carbonyl Sulfide (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page102.pdf) ↗	In these three problems students explore a molecule important in forming stratospheric aerosols. They calculate total rates of change from a table of sources and sinks.
Chandra Sees a Distant Planet Evaporating (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page11.pdf) ↗	In these two problems, students estimate how long it will take for the planet CoRot2b to lose its atmosphere.
Calculating Molecular Mass (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page10.pdf) ↗	Students count hydrogen, carbon and oxygen atoms in a molecule of adefovir dipivoxil and calculate its mass and formula.
Light Travel Times- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page41.pdf) ↗	In these three math problems students determine the time it takes light to reach various objects in space.
The Hand of Chandra (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page88.pdf) ↗	In these three math problems students use an image from the Chandra Observatory to measure a pulsar ejecting a cloud of gas.
Death Stars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page59.pdf) ↗	In these four math problems students learn about flares on common red-dwarf stars and compare them to flares on our own sun
Exploring a Dusty Young Star (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page40.pdf) ↗	In these five math problems students use Spitzer satellite data to learn about how dust emits infrared light and calculate the mass of dust grains from a young star in the nebula NGC-7129.
The Expanding Gas Shell of U Camelopardalis (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page2.pdf) ↗	In these two math problems students explore the expanding U Camelopardalis gas shell imaged by the Hubble Space Telescope, to determine its age and the density of its gas.
A Pulsar Shot Out from a Supernova Explosion! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page128.pdf) ↗	In these four math problems 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.
Scientific Notation I (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page12.pdf) ↗	Scientists use scientific notation to represent very big and very small numbers. In this math activity, students will convert some 'astronomical' numbers into scientific notation form.
Scientific Notation II (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page13.pdf) ↗	In this math activity students will perform simple addition and subtraction problems with scientific notation.
Scientific Notation III (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page14.pdf) ↗	In this math activity students will perform simple multiplication and division problems in scientific notation with an astronomy and space science focus.

______________________________________________________________________________________________

Table of Contents (Anchor Menu)

To help you easily navigate this extensive library, resources have been subcategorized by Core Math Skills. Use the Table of Contents below to jump directly to the materials that best fit your classroom's needs.

Arithmetic↓	Algebra, Equations & Functions ↓	Data Analysis & Graphing ↓	Geometry, Measurement & Formulas↓
Ratios, Proportions & Percentages↓	Scale Models & Conversions↓	Rates & Speed↓	Scientific Notation↓

______________________________________________________________________________________________

Back to Top ↑