SOLAR SYSTEM As part of a solar system unit, this math lesson plan uses the diameters of the planets to teach place value, rounding and ordering numbers skills. Background for Solar System Math Lesson Plan This lesson can be used as part of an earth science unit on the solar system. Before being taught this lesson, students should have already had an introductory lesson on the solar system, and should know general information about the eight planets and the dwarf planet Pluto, including their names, relative sizes, and order from the sun. In this lesson, students will put the planets in order of size by their diameters in miles. This lesson addresses content standards on place value and comparing and ordering numbers. Students should already be familiar with place value, and be able to name the place value of numbers to the ten thousands place, and should also be familiar with rounding. Solar System Math Lesson Plan Diameter of the Planets Mercury 3,032 miles Venus 7,521 miles Earth 7,926 miles Mars 4,221 miles Jupiter 88,846 miles Saturn 74,897 miles Uranus 31,763 miles Neptune 30,775 miles Pluto 1,485 miles 1. Review place value by pointing to various numerals and asking students what the place value is for that numeral. For example, what is the place value of the 2 in Mercury's diameter, (ones place), what is the value of the 9 in Earth's diameter (hundreds place). Go over all of the places from ones to ten thousands, and check for understanding.
2. Ask how many planets have diameters with numbers in the ten thousands place, and what are the planets (there are four, Jupiter, Saturn, Uranus and Neptune.) 3. Ask students to round these values to the nearest 10,000. Remind students of the rules for rounding: look at the number to the right, and if it is 5 or above, round up; if it is less than 5, leave it as it is. Verbally go over how to round each planet's diameter. Round Jupiter, Saturn, Uranus and Neptune to the nearest 10,000, and the others to the nearest 1,000. 4. Ask students which planet has the greatest diameter (Jupiter), which planet has the smallest diameter (Pluto, the dwarf planet, and Mercury, the smallest "regular" planet), and which planet has a diameter that is most similar to that of Earth (Venus). Ask students what other two planets are very similar in size (Neptune and Uranus.) Practice and Assessment for Solar System Math Lesson Plan As an assessment to check for understanding, pass out a worksheet that has the names and diameters of each planet so that students will not have to copy the information down from the board. Have students first round the values to the nearest 10,000 or 1,000 as they did in the verbal part of the lesson, and write the rounded-off numbers next to the original numbers. Have students then make a list of the planets in order of size from largest to smallest. (Jupiter, Saturn, Uranus, Neptune, Earth, Venus, Mars, Mercury, Pluto.) Circulate and give students help as needed. When they are finished, collect the papers and review the order of the planets with the class as a whole. This completes the solar system third grade math lesson plan. Resources NASA Planetary Fact Sheet: http://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_british.html Read more: http://www.brighthub.com/education/k- 12/articles/64946.aspx#ixzz0rIRG2C00
PROBLEMS (about all planets): 1.- The composition of Pluto is not yet known. Sean estimates that Pluto is a mixture of twenty-nine percent rock and the rest of the planet is made of water. What percent of Pluto does Sean estimate to be water? 2.- It takes Mars six hundred eighty-six and two tenths Earth days to orbit the sun. How much quicker is Earth's revolution? 3.- It takes Mercury fifty-eight and six tenths Earth days for a complete rotation and eighty-eight Earth days for a complete revolution. How does Mercury's time for a complete rotation compare to that of Earth's? 4.- Uranus is two thousand, eight hundred seventy-five million kilometers from the sun, and Venus is one hundred eight million kilometers from the sun. How much further from the sun is Venus? 5.- Destiny is an astronomer. She estimated that during Mercury's day, the planet reached a high temperature of seven hundred eighty-one degrees Fahrenheit. Destiny estimated that during the night, the temperature dropped one thousand, sixty-seven degrees Fahrenheit from the high temperature. What was Destiny's estimate for the low temperature? 6.- Pluto's radius is about 715 miles. Neptune's diameter is about 15,270 miles. The diameter of Pluto is how much smaller than Neptune's diameter? 7.- Uranus made a complete rotation from 4:53 a.m. to 10:09 p.m. To the nearest hour, how long is Uranus' rotation? 8.- It takes Neptune sixty-seven hundredths Earth days for a complete rotation and zero hundred sixty thousand, one hundred forty-eight Earth days for a complete revolution. How many days, rounded to the nearest ten days, does it take Neptune to make a complete orbit around the sun? 9.- Saturn's average distance from the sun is one thousand, four hundred twentynine million kilometers. What is Saturn's average distance from the sun rounded to the nearest ten million kilometers? 10.- The diameter of Saturn is seventy-four thousand, nine hundred seventy-seven miles. What is the diameter of Saturn rounded to the nearest ten thousand miles? 11.- The diameter of Venus is seven thousand, five hundred nineteen miles. What is the diameter of Venus rounded to the nearest thousand miles?
12.- The diameter of Mercury is three thousand, thirty-one miles. What is the diameter of Mercury rounded to the nearest hundred miles? 13.- It takes Jupiter forty-one hundredths Earth days for a complete rotation and four thousand, three hundred twenty-nine Earth days for a complete revolution. Rebecca is sixty-four Earth years old. If Rebecca had lived on Jupiter, how many years old would she be (to the nearest tenth)? 14.- The mass of Venus is 4.87 x 10 24 kg. The mass of Saturn is 5.68 x 10 26 kg. How much larger is the mass of Saturn in scientific notation? 15.- Jordan estimated the radius of Venus to be 3308 miles. The real diameter of Venus is 7519 miles. How close was Jordan's estimate, as a percent of Venus' real diameter? 16.- The ratio of the diameter of an asteroid to the diameter of Pluto is 34 to 143. The diameter of Pluto is 1.43 x 10 3 miles. What is the diameter of the asteroid? 17.- James weighs forty-three kilograms on Earth and thirty-nine kilograms on Venus. Steven weighs seventy-two kilograms on Earth. How much would Steven weigh on Venus? 18.- On average, Neptune is 4,504,000,000 kilometers from the sun. Venus is on average only 108,000,000 kilometers from the sun. On average and in scientific notation, how much further is Neptune from the sun? 19.- The masses of two asteroids weigh 4.82 x 10 2 kilograms. The larger asteroid weighs sixty-six kilograms more than three times the weight of the smaller asteroid. What is the weight of the smaller asteroid? 20.- It takes Jupiter forty-one hundredths Earth days for a complete rotation and four thousand, three hundred twenty-nine Earth days for a complete revolution. Noah's age on Jupiter would be seventy and five tenths years less than his Earth age. How old is Noah in Earth years? 21.- Two comets are 7.8 x 10 4 kilometers apart. The first comet is traveling at 7.8 x 10 4 kilometers per hour. The other comet is heading in the opposite direction at 1.26 x 10 5 kilometers per hour. If the current time is 11:45 a.m., when will the comets be 1,200,000 kilometers apart? 22.- Three times Morgan's Earth weight is one hundred sixty-six and three tenths kilograms more than her weight on Pluto. How much does Morgan weigh?
MERCURY PROBLEMS: 1. One year on Mercury is 88 Earth days long. You have been on Mercury for 25 years. How many Earth days have passed? 2. One year on Mercury = about 4 Earth Years. How old would you be if you lived on Mercury? 3. Three Mercurys are about the same size as one Earth. If you lived on a planet which was 65 times as large as Earth, how many Mercurys could fit inside of it? 4. The Earth has to spin around 176 times before Mercury spins around once. How many spins would Earth have made when Mercury completed 25 spins? 5. One year on Mercury is 88 Earth days long. If you were 43 Mercury years old, how many Earth Days old would you be? URANO PROBLEMS: Icy Logic! Logic Problem: Uranus has 21 moons. Several of these are called "icy moons." 5 of the icy moons are named Miranda, Ariel, Umbriel, Titania, and Oberon. They were discovered by three different astronomers in 3 different years. Kuiper discovered one moon, Lassel discovered 2 (both in the same year), and Herschel discovered two moons in one year, also. They all have different diameters: 470 km, 1160 km, 1170 km, 1520 km, and 1580 km. 2 have many craters on their surfaces and 3 do not. Figure out which moon is which by using the clues below. Use the chart to help organize your information! 5 of Uranus's Icy Moons Moon Miranda Ariel Umbriel Oberon Titania Diameter (in Km.) Discoverer Year Discovered Many Craters?
Clues: 1. Ariel's diameter is 10 kilometers less than Umbriel's. 2. Miranda has the smallest diameter, many craters, and was discovered in 1948, but not by Lassell. 3. Ariel has many craters, but Umbriel doesn't. They were discovered together in 1787. 4. Titania and Oberon were discovered by Herschel. 5. Titania does not have the largest diameter. To calculate relative weight: Multiply your weight by the relative gravity of each planet. For example if I weighed 200 lbs on Earth, I would multiply.38 X 200 to discover what my weight on Mercury would be. 200 X.38 = 76.00, so I would weigh 76 pounds on Mercury. Use the back of the sheet or your own paper to calculate the range, mean, median and mode of the data set. Write the answers on the lines provided. Solar System Weight Chart Planet Name Relative gravity of Planet My Weight X relative gravity Mercury 0.38 Venus 0.91 Earth 1 Mars 0.38 Jupiter 2.34 Saturn 1.06 Uranus 0.92 Neptune 1.19 Pluto 0.06 The Range of this data set is The Median of this data set is The Mode of this data set is The Mean of this data set is
A scale model of our solar system The goal of this activity is to build a scale model of our solar system. Often we see pictures of planet whose sizes and orbits are in proportion, but they are not on the same scale. To overcome that issue, this activity includes two parts: 1) building scale models for the planets, and 2) spacing the planets the appropriate distances from the sun. 1. Use the diameter of the earth as the basis on which to build your model. First, determine the sizes of the other planets compared to Earth. Divide the radius of the other planets by the earth s radius to calculate how much bigger or smaller than Earth these planets are. For example, Uranus radius divided by Earth s radius is equal to 4.01. This means that in your model, the planet Uranus should be about four times the radius or diameter of Earth. Enter these numbers in your table. 2. Now find a size that works for building your model. Pick a round object, or make a ball of clay, that you think would be a good size for Earth. Measure its diameter. In your model, that length will be equal to 7928 miles. Given that size for the earth, how big will the biggest model planet have to be? How big will the smallest model planet have to be? 3. Once you have found a size for Earth that is reasonable, record your scale factor and fill in the lengths of the scaled diameters for the planets. Find or create objects that are fairly close to the size that the planets should be. Record those objects on the chart. 4. The diameter of the Sun is 863,886 miles. It is the largest object in our solar system. How many times bigger is the Sun s diameter than the earth s? Using your scale factor, if you built a model of the Sun, what would its diameter be? Do you have any object around you that would be close to the size of the Sun? You now have a scale models of the planets. You still need to figure the distance from the Sun for each of the model planets. And you need to use the same scale so you get a better understanding of the size of our solar system. 5. In calculating the sizes of the planets, you used the diameter of the earth as the unit of measure. Use the diameter of the earth, 7,928 miles, as the unit of measure here too. For each of the planets, divide their distance from the Sun by the diameter of the earth to find out how far each planet is from the Sun in terms of the earth s diameter. Record your data in the table for each planet. 6. Now use the numbers you just calculated, the Distance from Sun in terms of the diameter of the Earth, and multiply them by your scale factor to determine how far each planet should be from the Sun in your model. 7. Convert your data to other units to get a better grasp of the size of your scale model. 8. Will your model fit on football field? Within your city? Within your state? 9. Pick a place to be the Sun and find out where you would have to go to create your scale models of the planets Mercury, Venus, and Earth.
Diameter (in miles) Diameter in Terms of Earth s Diameter Length of Scaled Diameter Object Used Sun Mercury 3,032 Venus 7,522 Earth 7,928 Mars 4,222 Jupiter 88,864 Saturn 74,914 Uranus 31,770 Neptune 30,782 Pluto 1,442 Scale factor: In our model 7928 miles = (include the units) Distance from Sun (in miles) Sun - Mercury 35,991,000 Venus 67,246,000 Earth 92,976,000 Mars 141,665,000 Jupiter 483,732,000 Saturn 886,843,000 Uranus 1,784,320,000 Neptune 2,794,929,000 Pluto 3,675,253,000 Distance from Sun in Terms of Diameter of Earth Distance from Sun in Terms of Scaled Units
Apéndice 1b: Datos del Sistema Solar 2 Datos físicos Radio Masa Rotación Dimensiones Nombre (km) (kg) Dens Abo Vo (dias) (km) --------- ------- ------- ---- --- ----- ------ ---------- Sol 695000 1.99e30 1.41? -26. 24.6 Mercurio 2440 3.30e23 5.43.11-1.9 58.6 Venus 6052 4.87e24 5.24.65-4.4-243 Tierra 6378 5.97e24 5.52.37-0.99 Marte 3397 6.42e23 3.93.15-2.0 1.03 Jupiter 71492 1.90e27 1.33.52-2.7 0.41 Saturno 60268 5.68e26 0.69.47 0.7 0.45 Urano 25559 8.68e25 1.32.51 5.5-0.72 Neptuno 24766 1.02e26 1.64.41 7.8 0.67 Plutón 1137 1.27e22 2.06.55 13.6-6.39 (z) Luna 1738 7.35e22 3.34.12-12.7 S Phobos 11 1.08e16 1.9.06 11.3 S 13.5 x 10.8 x 9.4 Deimos 6 1.80e15 1.8.07 12.3 S 7.5 x 6.1 x 5.5 Metis 20 9.56e16 2.8.05 17.5? Adrastea 10 1.91e16 4.5.05 18.7? 12.5 x 10 x 7.5 Amalthea 94 7.17e18 1.8.05 14.1 S 135 x 83 x 75 Thebe 50 7.77e17 1.5.05 16.0 S 55 x 45 Io 1821 8.93e22 3.53.61 5.0 S Europa 1565 4.80e22 2.99.64 5.3 S Ganymede 2634 1.48e23 1.94.42 4.6 S Callisto 2403 1.08e23 1.85.20 5.6 S Leda 8 5.68e15 2.7? 20.2? Himalia 93 9.56e18 2.8? 15.0 0.4 Lysithea 18 7.77e16 3.1? 18.2? Elara 38 7.77e17 3.3? 16.6 0.5 Ananke 15 3.82e16 2.7? 18.9? Carme 20 9.56e16 2.8? 17.9? Pasiphae 25 1.91e17 2.9? 16.9? Sinope 18 7.77e16 3.1? 18.0? Pan 10??.5?? Atlas 15??.9 18.0? 20 x 10 Prometheus 46 2.70e17 0.7.6 15.8? 72 x 43 x 32 Pandora 42 2.20e17 0.7.9 16.5? 57 x 42 x 31 Epimetheus 57 5.59e17 0.6.8 15.7 S 69 x 55 x 55 Janus 89 1.98e18 0.65.8 14.5 S 99 x 96 x 76 Mimas 199 3.75e19 1.14.5 12.9 S Enceladus 249 7.30e19 1.12.99 11.7 S Tethys 530 6.22e20 1.00.9 10.2 S Telesto 15??.5 18.7? 17 x 14 x 13 Calypso 13??.6 19.0? 17 x 11 x 11 Dione 560 1.05e21 1.44.7 10.4 S Helene 16??.7 18.4? 18 x 16 x 15 Rhea 764 2.31e21 1.24.7 9.7 S Titan 2575 1.35e23 1.88.21 8.3 S
Hyperion 143 1.77e19 1.4.3 14.2 chaotic 185 x 140 x 113 Iapetus 718 1.59e21 1.02.2 11.1 S (y) Phoebe 110 4.00e18 0.7.06 16.5 0.4 115 x 110 x 105 Cordelia 13??.07 24.0? Ophelia 16??.07 24.0? Bianca 22??.07 23.0? Cressida 33??.07 22.0? Desdemona 29??.07 22.0? Juliet 42??.07 22.0? Portia 55??.07 21.0? Rosalind 27??.07 22.0? Belinda 34??.07 22.0? Puck 77??.07 20.0? Miranda 236 6.59e19 1.20.27 16.5 S 240 x 234 x 233 Ariel 581 1.35e21 1.67.34 14.4 S 581 x 578 x 578 Umbriel 585 1.17e21 1.40.18 15.3 S Titania 789 3.53e21 1.71.27 14.0 S Oberon 761 3.01e21 1.63.24 14.2 S Caliban 30 22 Sycorax 60 20 Naiad 29??.06 25.0? Thalassa 40??.06 24.0? Despina 74??.06 23.0? Galatea 79??.06 23.0? Larissa 96??.06 21.0? 104 x 89 Proteus 209??.06 20.0? 218 x 208 x 201 Triton 1353 2.15e22 2.05.7 13.6 S Nereid 170??.2 18.7? Charon 586 1.90e21 2.24.32 15.5 S (z) Leyenda: Radio Radio ecuatorial en km. Masa en kilogramos incluyendo atmósferas pero no satélites. Dens Densidad en g/cm3. Abo albedo geométrico del objeto Vo magnitude en luz visible en la oposición. Rotación Periodo Sidéreo de rotación ecutorial en días (negativa=retrógrada; S=sincrona). Dimensiones Radio para los objetos no esféricos. Notas: (y) La magnitud de Iapetus varia de 10.2 a 11.9 (z) la masa, el radio y densidad de Plutón y Charon son aun algo inciertas ( ) Algunos datos están dados con más decimales de los que deberían.