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6th grade Math and Science Integrated Lesson Science Standards in Unit 9 SPI 0607.6.1 Use data to draw conclusions about the major components of the universe. SPI 0607.6.2 Explain how the relative distance of objects from the earth affects how they appear. Math Standards in Unit 9: 6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 6.RP.A.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Guiding Questions: What are the major components of the universe? What does the data tell us about the components of the universe? How does the relative distance between the objects in the universe affect the way these appear from Earth? When classifying bodies in the solar system, what characteristics are considered? Explain the importance of these characteristics. What characteristics define a planet? Clear Targets: I can determine equivalent ratios. I can compare equivalent ratios to find missing values in a table. I can make tables of equivalent ratios relating quantities with whole-number measurements. In Science class: 1. Infer: How are planets classified? 2. What are the characteristics of each planet? Distance from sun Period Rotation Period of revolution Diameter Temperature Gravity Composition 3. Analyzing Data and Planet Classification: • Group planets by their characteristics. • Determine which planets share similar characteristics. • Create a classification system for the planets and justify your grouping system. • How could you extend your classification system to other members of our solar system such as moons, comets, asteroids, and meteoroids? In Math Class: Set: How far away are the planets from the sun? What is the size of planets in our solar system? View http://youtu.be/HEheh1BH34Q I. Comparing the Sizes of the Sun, Earth, Moon and Jupiter-2D Size Comparison The diameter of the Sun is 1,392,000 km, while the equatorial diameter of the Earth is 12,756 km. Compared to the Earth the Sun is HUGE. 1. The sun’s diameter is 1,392,000 km. If the sun’s diameter of 1,392,000 km is represented by a 55 cm or 22 inches poster board, determine the following calculations (or find the equivalent ratio): Moon is 3,475 km= _______________ Earth is 12,756 km= ______________ Jupiter is 142,984 km= ________________ Key: Sun 1,392,000 is to 55 cm ______________________________ Moon 3,475 is to _______ cm Moon is 3,475 km= 0.14 cm of poster board Earth is 12,756 km= 0.50 cm of poster board Jupiter is 142,984 km= 5.65 cm of poster board 2. Create a model Use one full poster board as your sun’s diameter. Draw a line and label inside of this poster board each of the diameters calculated above. Explain: How many times bigger is the sun in comparison to? Earth? ____________ Moon? ____________ Jupiter? ____________ II. Comparing Earth size to other Universe Components When examining universe components and their sizes, scientists use the Earth size as a frame of reference instead of the sun due to its enormous size. Scientists question how many times bigger or smaller is a given object in space when compared to Earth size. Using planet Earth size in diameter, calculate the ratio from Earth to a given object in space. Once you calculate the ratio, write a statement explaining the relationship between Earth size and the object in space. (Teacher Note: This will review expressions. Ex sun is 110 times bigger than the Earth or 110x.) Earth size is 12, 756 km in diameter. Charon is 1,184 in diameter. Calculate the equivalent ratio of Charon to Earth. EX. 1,184: 12,756: or 1,184 to 12, 756 or 1,184/12,756 Complete the following table by finding the missing data: Name Diameter (km) Equivalent Ratio to Earth Earth 12,756 12,756/12,756= 1 Charon 1,184 1,184/12,756= 0.09 Mercury 4,879 Venus 12,104 Mars 0.53 Ceres 0.07 Jupiter 142,984 Saturn 9.45 Uranus 4.01 Neptune 49,528 Pluto 2,390 Combined data from Science Textbook and http://www.pbs.org/newshour/extra Key Name Earth Charon Mercury Venus Mars Ceres Jupiter Saturn Uranus Neptune Pluto Diameter (km) 12,756 1,184 4,879 12,104 6,794 950 142,984 120,536 51,118 49,528 2,390 Equivalent Ratio to Earth 12,756/12,756= 1 1,184/12,756= 0.09 0.38 0.95 0.53 0.07 11.21 9.45 4.01 3.88 0.19 Rank the universe components from smallest to largest using their equivalent ratio to Earth. Universal Component Ranking based on Equivalent Ratio to Earth Ceres 0.07 Charon 0.09 Pluto 0.19 Mercury 0.38 Mars 0.53 Venus 0.95 Earth 1.00 Neptune 3.88 Uranus 4.01 Saturn 9.45 Jupiter 11.21 Which components are smaller than Earth? Ceres and Charon (both are moons) and Pluto (dwarf planet), Mercury, Mars and Venus. Which components are larger than Earth? Neptune, Uranus, Saturn and Jupiter III. Meter Stick Distance Scale of the Solar System Another important relationship for scientists is how far planets are from the sun. If the Solar system were reduced about six trillion times, Pluto on an average will be about one meter from the sun. On this scale, the sun itself will be about 0.2 millimeters in diameter. This is about the size of a pin. The distance between the sun and Earth is approximately 150,000,000 kilometers (150 million km) or one Astronomical Unit (AU). Calculate the distance from the sun in Astronomical Units for each component: Planet Distance from Sun in Distance from the Kilometers Sun in Astronomical Units Mercury 57,910,000 Venus 108,200,000 Earth 149,600,000 1.00 AU Mars 227,940,000 Jupiter 778,330,000 Saturn 1,424,600,000 Uranus 2,873,550,000 Neptune 4,501,000,000 *Pluto 5,945,900,000 Key Planet Distance from Sun in Kilometers Distance from the Sun in Astronomical Units Mercury 57,910,000 0.39 AU Venus 108,200,000 0.72 AU Earth 149,600,000 1.00 AU Mars 227,940,000 1.52 AU Jupiter 778,330,000 5.20 AU Saturn 1,424,600,000 9.52 AU Uranus 2,873,550,000 19.21 AU Neptune 4,501,000,000 30.09 AU *Pluto 5,945,900,000 39.75 AU Data from http://idahoptv.org/ntti/nttilessons/lessons2000/lau1.html Steps for Meter Stick Scale: 1. Use the meter stick scale from 0 to 100 centimeters to place the 8 planets and Pluto. 2. Place the sun at the 0 centimeters or beginning mark of the meter stick. 3. Pluto is 39.75 AU from the sun. If we round this distance to the nearest whole number, Pluto is 40 AU from the sun. Place Pluto at the 100 centimeters mark or end of the meter stick. 4. Create a distance scale for the reminder planets and place on the appropriate place. Show your calculations. Explain how mathematical principles and equivalent ratios help us understand the size of the planets, their location in the Solar System and their distance from the sun. Explain using 1-2 examples. Resources: A Universal Idea by Jeffery Patterson and Brandy J. Merwin, published in The Science Teacher on May 2002, pp 22 -26 What is Pluto? http://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-pluto58.html The Controversy Over Pluto: Planet or Astronomic Oddball? http://static.nsta.org/files/ss1501_18.pdf Planetary Fact Sheet - Ratio to Earth Values http://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_ratio.html Ceres and Pluto- Dwarf Planets as a New Way of Thinking about an Old Solar System: Teacher Guide https://www.nasa.gov/pdf/301000main_Dwarf_Planets_Guide.pdf Student Activity https://www.nasa.gov/pdf/301001main_Dwarf_Planets_Activity.pdf Comparing the Size of the Sun to Earth http://www.suntrek.org/sun-as-a-star/sun-and-earth/comparing-size-sun-andearth.shtml Planetary Distance Data http://idahoptv.org/ntti/nttilessons/lessons2000/lau1.html