


Mathematics Skill or Topic Area: Solving Simple Equations 

Next Gen Science Standards PS1: Matter and Its Interactions; ETS1: Engineering Design; ETS2: Links Among Engineering, Technology, Science, and Society Common Core ELA for Science: RST.68.2. Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions. RST.68.8. Distinguish among facts, reasoned judgment based on research findings, and speculation in a text. RST.68.9. Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic. Common Core Math Standard: CC.7.EE.4 Use variables to represent quantities in a realworld or mathematical problem. 

Video Engagement: Cryogenics  The Cold Hard Facts Discover the everyday applications of cryogenics from magnetic scans to the hightech space telescopes like the James Webb Space Telescope. Learn about absolute zero and the Kelvin temperature scale (7 minutes). View Program 


Explore math connections with SpaceMath@NASA 

Problem I  Kelvin Temperatures and Very Cold Things  Students convert from Celsius and Fahrenheit and to Kelvin using three linear equations. Topics include evaluating simple linear equations for given values. [Open PDF] Problem II  The Goldilocks Planets  Not too hot or cold.  Students use a table of the planets discovered by the Kepler satellite, and estimate the number of planets in our Milky Way galaxy that are about the same size as Earth and located in their Habitable Zones. They estimate the average temperature of the planets, and study their tabulated properties using histograms. Topics include working with Kelvin temperatures; averaging; histogramming. [Open PDF] Explain your thinking: Write your own problem  Using information found in the Math Connection problems, the press release or the video program, create your own math problem that involves converting from one temperature scale to another and solve it. Explain why you set the problem up this way, and how you might find its answer. Evaluate your understanding: Challenge Problem  The Moon is at a distance of 1 AU from the sun and has a nighttime temperature of 120 K. Pluto is located at 35 AU from the sun and has a temperature of 55K. Quaoar is located 45 AU from the sun and has a temperature of 50 K. Eris is at a distance of 70 AU from the sun and has a temperature of 40 K. A new dwarf planet 2010EK139 is located 100 AU from the sun. What is its temperature in Kelvins, Celsius and Fahrenheit? Explain how you arrived at this answer. Answer: First plot a graph of temperature (range from 1 to 130 K) versus distance (range from 0 to 120 AU) for the known bodies. Use the trend in the data to create a mathematical curve that smoothly passes through all the points and extends to 120 AU. Identify the temperature corresponding to x = 100 AU to get about T = 35 K. Convert this to Celsius using C = Kelvin  273 =  238 and Fahrenheit = 9/5(238)+32 = 460.


NASA / JPL 3D Solar System 

Extend your new knowledge  As objects move closer and farther from the sun in their orbits, their temperatures will change as the amount of sunlight reaching their surfaces varies. Students will use Eyes on the Solar System to calculate the temperatures of distant objects beyond the orbit of Pluto. [ Open PDF ] 
