


Mathematics Skill or Topic Area: Ratios, Propotions and Similarity 

Next Gen Science Standards ESS1: Earth’s Place in the Universe; 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.8.G.4: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. CC.8.G.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems.


Video Engagement: Mercury’s MESSENGER Reveals Mysteries How long is a day on Mercury? Why does the planet have a 600 degree range in temperature? MESSENGER, NASA’s first mission to Mercury in 30 years, will capture stunning imagery, determine the composition of the surface and measure Mercury’s unusual magnetic field (6 minutes). View Program 


Explore math connections with SpaceMath@NASA 

Problem I  Comparing Planets Orbiting Other Stars  Students use simple fraction arithmetic and proportions 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 [ Open PDF ] Problem II  Angular Size and Similar Triangles  A critical concept in astronomy is angular size, measured in degrees, minutes or arcseconds. This is a review of the basic properties of similar triangles for a fixed angle and the proportional relationships among the sides of similar triangles. [ Open PDF ] Problem III  Planet Fractions and Scales  Students work with relative planet comparisons to determine the actual sizes of the planets given the diameter of Earth. [ 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. Explain why you set the problem up this way, and how you might find its answer. Evaluate your understanding: Challenge Problem: Mercury and the Moon: Similar but Different.  Mercury is 1.4 times the diameter of the Moon and its density is 1.6 times greater that the Moon. Given that mass = density times volume, and that the volume of a sphere is proportional to the cube of its diameter, by what factor is Mercury more massive than our Moon? [Answer: Mass = 1.6 x (1.4)(1.4)(1.4) = 1.6 x 2.7 = 4.3, so the mass of Mercury is 4.3 times greater than the mass of our Moon, even though Mercury is only 1.4 times larger in diameter.] 

NASA / JPL 3D Solar System 

Extend your new knowledge  Visit Mercury using the EOSS simulator and explore the changing size of the Sun as viewed from the MESSENGER spacecraft. [ Open PDF ] 
