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Copyright © Wright Group/McGraw-Hill Project Masters Project Masters PROJECT7 Testing Paper Airplane Designs, Part 1 Copyright © Wright Group/McGraw-Hill 388 Name Date Time Student-Designed Airplanes1.Complete the following after you conduct test flights of student-designed paper airplanes. a.Number of models tested b.Minimum distance feet c.Median distance feet d.Maximum distance feet Schultz-Designed Airplanes 2.Complete the following after you conduct test flights of Schultz-designed airplanes. a.Number of models tested b.Minimum distance feet c.Median distance feet d.Maximum distance feet 3.Select the 3 student-designed and 3 Schultz-designed airplanes that flew the farthest. Test these 6 planes again. Record the results in the table below. Name of Designer Distance Rank (1st to 6th) Student feetStudent feetStudent feetLouis Schultz feetLouis Schultz feet Louis Schultz feet PROJECT2 Name Date Time Modeling Distances in the Solar System cont. Copyright © Wright Group/McGraw-Hill 361 You probably need a different scale for distances of the planets from the Sun than for diameters of the planets. Discuss with your class what scale to use. Two important points to consider: How much space do you have to display the model? How much space will be taken up by the Sun? Deciding on a Scale 8.In the scale we are using for distance, represents . 9.In the model, my Planet Team’s planet should be placed (how far?) from the Sun. Building the Model First, the class should decide which part of the Sun to measure from. Then, working in teams, use a tape measure to place your planet the correct distance from the Sun. Finally, fill in as much information as you can on your team’s Planet Information Label (Math Masters,p. 363). You will fill in the missing information later. You can add details to the model by including some of the features of the solar system described on Math Masters,page 362. Record these details on the lines below. Details/features of the solar system our team will add to the model:

PROJECT 1 The Solar System Copyright © Wright Group/McGraw-Hill 350 Name Date Time Our solar system consists of the Sun, 9 planets and their moons, and a large number of asteroids, comets, and meteors. The Sun is at the center of the solar system. Astronomers estimate that the solar system formed between 4 and 5 billion years ago. A huge, slowly rotating cloud of particles pulled together to form the Sun. Planets, moons, and other objects formed from particles in the outer portion of the cloud. From time to time, you can see Mercury, Venus, Mars, Jupiter, and Saturn in the night sky. For most of history, people thought these were the only planets other than Earth. Then, using increasingly powerful telescopes, astronomers spotted Uranus in 1781, Neptune in 1846, and Pluto in 1930. Astronomers might never have found Neptune and Pluto if they had not been guided by mathematical predictions that told them where to aim their telescopes. The 4 planets closest to the Sun—Mercury, Venus, Earth, and Mars—are called the rocky dwarfs because they are small and made mostly of rock. Jupiter, Saturn, Uranus, and Neptune are huge balls of frozen gas and liquid with small solid cores. These planets are called the gas giants or Jovian planets. They have multiple moons and rings. Knowledge of the solar system is growing rapidly. On July 29, 2005, Dr. Mike Brown and his colleagues announced the discovery of a tenth planet beyond Pluto. At that time, the planet’s temporary name was 2003 UB313. The planet’s permanent name, as well as information about its size and surface temperature, became available after this edition of Everyday Mathematicshad already gone to press. Pluto NeptuneUranusSaturn JupiterMars Jupiter Earth Venus Mercury Mars Sun

PROJECT 1 Name Date Time Movement of the Planets Copyright © Wright Group/McGraw-Hill 351 Today most people know that Earth revolves around the Sun. Long ago, almost everyone believed that the entire universe revolved around Earth. That idea certainly corresponds to what we can see with our own eyes: Every day the Sun rises in the east and sets in the west. At night, the Moon, planets, and stars move steadily through the sky. In the second century A.D., an Egyptian mathematician and astronomer named Claudius Ptolemaeus (Ptolemy) published a book called the Almagest.In it, he gave a mathematical description of the universe asgeocentric,or Earth-centered. Ptolemy’s theory of how the Sun, planets, and stars move through space was widely accepted for the next 1,400 years. In 1543, the Polish astronomer Nicolaus Copernicus (1473–1543) described a different view of the universe in his book On the Revolutions of the Celestial Spheres.After 30 years of research, he concluded that the planets—including Earth—have a heliocentricmovement: They actually revolve around the Sun. The apparent motion of heavenly bodies through the sky is due primarily to Earth’s rotation. This idea had been proposed by Greek scholars as early as the third century B.C. but had been ignored. Copernicus’s theory did not perfectly explain the movement of all the planets that were known at the time, but it led scientists in a new direction. Astronomer Tycho Brahe (1546–1601) gathered large quantities of data in a search for the true laws of planetary motion. Although Brahe died before he could complete his theory, his assistant, Johannes Kepler (1571–1630) developed mathematical models that correctly explained the observed motions of the planets. Kepler showed that planetary orbits are elliptical (oval) rather than circular. He also demonstrated that the Moon is a satellite of Earth. In Everyday Mathematics,you have developed mathematical models to describe situations, represent relationships, and solve problems. These models include number sentences and graphs. You are solving problems that are simpler than Kepler’s, but you are following the same approach that he used. You can read more about problem solving on pages 258 and 259 in the Student Reference Book.

PROJECT 1 Planet Data Copyright © Wright Group/McGraw-Hill 352 Name Date Time The tables on this page and the next provide estimates of diameters and distances from the Sun, rounded to 2 significant digits.The data are presented in U.S. customary units and metric units. In your explorations, you can choose which units to work with. The diameterof a sphereis the length of a line segment that passes through the center of the sphere and has endpointson the sphere. Planets are not quite spheres, so an average diameter is used in the data tables. Planets move around the Sun in orbits that are ellipses(ovals), somewhat affected by the gravitational pulls of other planets. Estimates of average distances from the Sun are accurate enough for anything done in the Sixth Grade Everyday Mathematicssolar system projects. Sun Pluto Elliptical orbit diameter sphere Solar System Data Table 1 Average Average Distance from the Sun Surface Temperature Planet Diameter (Miles) (Degrees Fahrenheit) (Miles) Mercury 3,000 36,000,000 or 3.6 º 10 7 290 to 800 Venus 7,500 67,000,000 or 6.7 º 10 7 850 to 910 Earth 7,900 93,000,000 or 9.3 º 10 7 130 to 140 Mars 4,200 140,000,000 or 1.4 º 10 8 190 to 80 Jupiter 89,000 480,000,000 or 4.8 º 10 8 240 to 150 Saturn 75,000 890,000,000 or 8.9 º 10 8 290 to 150 Uranus 32,000 1,800,000,000 or 1.8 º 10 9 350 Neptune 31,000 2,800,000,000 or 2.8 º 10 9 350 Pluto 1,400 3,700,000,000 or 3.7 º 10 9 350 Sun 860,000 5,400 to 36,000,000

PROJECT 1 Name Date Time Planet Data continued Copyright © Wright Group/McGraw-Hill 353 Solar System Data Table 2 Average Average Distance from the Sun Surface Temperature Planet Diameter (Kilometers) (Degrees Celsius) (Kilometers) Mercury 4,900 58,000,000 or 5.8 ∗10 7 180 to 430 Venus 12,000 110,000,000 or 1.1 ∗10 8 450 to 490 Earth 13,000 150,000,000 or 1.5 ∗10 8 90 to 60 Mars 6,800 230,000,000 or 2.3 ∗10 8 90 to 10 Jupiter 140,000 780,000,000 or 7.8 ∗10 8 150 to 100 Saturn 120,000 1,400,000,000 or 1.4 ∗10 9 180 to 160 Uranus 51,000 2,900,000,000 or 2.9 ∗10 9 200 Neptune 49,000 4,500,000,000 or 4.5 ∗10 9 190 Pluto 2,300 5,900,000,000 or 5.9 ∗10 9 230 to 220 Sun 1,400,000 3,000 to 20,000,000 Using Estimates and Comparing Big Numbers Here is one strategy for comparing big numbers. ProblemCompare the distance of Earth from the Sun with the distances of Mars and Neptune from the Sun. ThinkEarth to Sun 150,000,000 km, or 150 million km Mars to Sun 230,000,000 km, or 230 million km Neptune to Sun 4,500,000,000 km, or 4,500 million km AskAbout how many 150 millions are in 230 million? In 4,500 million? Another strategy is to compare distances in scientific notation. It is important to compare like powers of 10. Write equivalent names to make the division easier. ThinkEarth to Sun 1.5 º 10 8km, or 15 º 10 7km Mars to Sun 2.3 º 10 8km, or 23 º 10 7km Neptune to Sun 4.5 º 10 9km, or 45 º 10 8km, or 450 º 10 7km AskAbout how many 15s are in 23? In 450?

PROJECT 1 Life on Other Planets Copyright © Wright Group/McGraw-Hill 354 Name Date Time The unmanned Mariner 4 spacecraft flew past Mars on July 14, 1965, collecting the first close-up photographs of an inner solar-system planet. Since those first flyby images were taken, we have asked whether life ever arose on Mars. Life, as we understand it, requires water. Scientists believe that if life ever evolved on Mars, it did so in the presence of a long-standing supply of water. Over 30 years ago, NASA launched two identical spacecraft (Vikings 1 and 2), each consisting of an orbiter and a lander. Each orbiter-lander pair flew together and entered Mars’ orbit. After taking pictures, the orbiters separated and descended to the planet’s surface for the purpose of data collection. The landers conducted three experiments designed to look for possible signs of life. While the experiments revealed unexpected chemical activity in the Martian soil, they provided no clear evidence for the presence of living microorganisms near the landing sites. Exploration missions of the past decade have landed robotic rovers with far greater mobility than that of the Vikinglanders. The rovers carry a sophisticated set of instruments that collect and analyze surface samples. By studying rock and soil samples, scientists hope to determine whether water was involved in soil and rock formation and thereby identify areas on the planet that may have been favorable for life in the past. In 1976, the Viking Iorbiter took the first photographs of the Cydonia region of Mars, showing an unusual mountain that seemed to resemble a face. Some people suggested that the face was a monument built by an extraterrestrial civilization. But scientists believed this resemblance was accidental, partly due to the angle of light at the time the photo was taken and partly due to the complicated image enhancement used to process the data that was available at the time. On May 28, 2001 the Mars Global Surveyor took a new photo of this feature. Although the landform has the same general shape as in earlier photographs, details provided by the higher-resolution photograph reveal the “face” to be a naturally formed hill.

PROJECT 1 Name Date Time What Can You Learn from the Data Tables? Copyright © Wright Group/McGraw-Hill 355 1. Look at the data on planet diameters on Math Masters,pages 352 and 353. Describe any patterns you see. List some ideas or questions that the data suggest to you. 2. Look at the data on average distance from the Sun. Are the planets evenly spaced? Describe any patterns you see in the average-distance data. 3. Look at the data on surface temperature. Is it likely that there is life on other planets today? Why or why not? For more information about life on other planets, read Math Masters,page 354.

PROJECT 1 Data Analysis Copyright © Wright Group/McGraw-Hill 356 Name Date Time One way to explore and understand a data table is to make another table that compares the same information to a common measure. Use Solar System Data Table 1 or 2 (pages 352 and 353) to fill in the table as described below. 1. Compare the diameters of other planets with the diameter of Earth. Use estimates. For example, the diameter of Mars (4,200 miles, or 6,800 kilometers) is about 1 2the diameter of Earth (7,900 miles or 13,000 kilometers). 2. The average distance from Earth to the Sun is called one astronomical unit. This unit is important for measuring distances in the solar system. Compare each planet’s distance from the Sun to Earth’s distance from the Sun. Use estimates. For example, the distance of Jupiter from the Sun (480 million miles, or 780 million kilometers) is about 5 times the distance of Earth from the Sun (93 million miles, or 150 million kilometers). diameter circlesphere diameter How Do Other Planets Compare to Earth? Diameter Compared to Distance from Sun Compared Planet Earth’s Diameter to Earth’s Distance from Sun Mercury About 3 8 or 1 2 About 1 3 Venus Mars Jupiter Saturn Uranus Neptune Pluto

PROJECT 2 Name Date Time Starting the Model Copyright © Wright Group/McGraw-Hill 357 1. Choose a Measurement System In order to build a scale model of the solar system, the class needs to make some decisions. Will we measure in U.S. customary units(in. and mi) or in metric units(cm and km)? Astronomers and astronauts use metric units. On the other hand, U.S. customary units may make the model easier to relate to personal references. For example, if the diameter of Earth is 1 inch (about the length of a toe), then the Sun’s diameter is about 9 feet, almost twice the height of most sixth-grade students. Discuss the advantages and disadvantages of each measurement system. Then make a class decision. We will use units. 2. Choose a Scale Now the class needs to make another decision. Which scale will we use to model the relative sizes of the Sun and the planets? The scaletells how many units in the real solar system are represented by 1 unit in the scale model of the solar system. Suggestions: U.S. Customary UnitsYou might let 1 inch represent 8,000 miles (1 inch to 8,000 miles, or 1 in.:8,000 mi). 8,000 miles is approximately the diameter of Earth. If the diameter of Earth is represented by 1 inch, about how many inches would represent the diameter of Jupiter? Metric UnitsYou might let 1 centimeter represent 5,000 kilometers (1 centimeter to 5,000 kilometers, or 1 cm:5,000 km). These are easy numbers to work with and to remember. We will use this scale for size: 3. Divide into Planet Teams The class should divide into 8 Planet Teams, a team for each planet except Earth. My Planet Team will model this planet:

PROJECT 2 Modeling the Sizes of Planets and the Sun Copyright © Wright Group/McGraw-Hill 358 Name Date Time 1. My Planet Team’s planet is . 2. Its average diameter is . (Remember to give the diameter in the same system of units — metric or U.S. customary — that you will use to build the model.) 3. In our scale model of planet size, represents . 4. How can you use the scale to figure out how large your planet should be in the model? Discuss with your teammates and write your answer below. 5. What will be the diameter of your planet in the model? 6. a. What will be the diameter of the Sun in the model? b. How many feet or meters is this?

PROJECT 2 Name Date Time Making a Scale Model of Your Planet Copyright © Wright Group/McGraw-Hill 359 To make a 2-dimensional scale model of your planet, your Planet Team needs a pencil, ruler, scissors, tape, compass, and colored construction paper. If possible, use the chart at the right to select the color(s) of paper for your planet. 1. Use a ruler to draw a line segment equal in length to the diameter your planet should have in the model. If you are modeling Jupiter or Saturn, you may need to tape 2 sheets of paper together. 2. Find the midpoint(middle) of this line segment and mark a dot there. 3. Use a compass to draw a circle. The center of the circle should be at the midpoint you marked. Put the point of the compass on the dot. Put the pencil on one endpoint of the line segment and draw the circle. If your compass is too small, tie a string around a pencil near the point. Hold the point of the pencil on one endpoint of the line segment. Pull the string tightly and hold it down at the dot (midpoint) on the line segment. Keeping the string tight, swing the pencil around to draw a circle. 4. Cut out and label the circle. 5. Share your work with other Planet Teams. Planet Color Mercury Orange Venus Yellow Earth Blue, brown, green Mars Red Jupiter Yellow, red, brown, white Saturn Yellow Uranus Green Neptune Blue Pluto Yellow

PROJECT 2 Modeling Distances in the Solar System Copyright © Wright Group/McGraw-Hill 360 Name Date Time 1. My Planet Team’s planet is . 2. Its average distance from the Sun is . 3. Now that you have modeled the size of your planet, you need to figure out how far to place it from the Sun. How could you do this? To model the distances between planets and the Sun, your class needs to make several decisions. Finding a Scale 4. Can you use the same scalefor distance that you used for size? This would provide an excellent picture of planetary sizes and distances but may not be possible. Why not? Discuss with your classmates. 5. If 1 inch represents 8,000 miles, how many inches from the Sun should Earth be placed? 6. How many feet is this? 7. Would a model of the entire solar system using this scale be possible anywhere in your school building?

PROJECT 2 Name Date Time Modeling Distances in the Solar System cont. Copyright © Wright Group/McGraw-Hill 361 You probably need a different scale for distances of the planets from the Sun than for diameters of the planets. Discuss with your class what scale to use. Two important points to consider: How much space do you have to display the model? How much space will be taken up by the Sun? Deciding on a Scale 8. In the scale we are using for distance, represents . 9. In the model, my Planet Team’s planet should be placed (how far?) from the Sun. Building the Model First, the class should decide which part of the Sun to measure from. Then, working in teams, use a tape measure to place your planet the correct distance from the Sun. Finally, fill in as much information as you can on your team’s Planet Information Label (Math Masters,p. 363). You will fill in the missing information later. You can add details to the model by including some of the features of the solar system described on Math Masters,page 362. Record these details on the lines below. Details/features of the solar system our team will add to the model:

PROJECT 2 Some Solar System Features Copyright © Wright Group/McGraw-Hill 362 Name Date Time You can add more detail to the model by including some or all of the following celestial bodies. AsteroidsThese are large pieces of rock that are too small to be considered planets. They range in size from big boulders to small mountains. Ceres, one of the largest asteroids, has a diameter of 580 miles, or 940 kilometers. Most asteroids are in what is known as the Asteroid Belt. The Asteroid Belt lies between Mars and Jupiter, about 180 to 270 million miles (290 to 430 million kilometers) from the Sun. To date, more than 18,000 asteroids have been identified in this region of the solar system. They can be represented in the model by small pen dots on pieces of paper or stick-on notes. MoonsMars, Jupiter, Saturn, Uranus, and Neptune each have 2 or more moons. Mercury and Venus have no moons. The largest moons of Jupiter and Saturn are larger than Mercury and Pluto. Jupiter has at least 17 moons. Its 4 largest moons and their diameters are shown in the table. Saturn has at least 18 moons. The largest is Titan. Its diameter is 3,100 miles (5,200 kilometers). Earth’s moon has a diameter of 2,200 miles (3,750 kilometers). It is slightly less than 1 3the size of Earth. RingsScientists have known for a long time that Saturn is surrounded by large, beautiful rings. When the Voyagerspacecraft visited Jupiter, Neptune, and Uranus in the 1980s, scientists discovered that these planets also have rings, although they are considerably smaller than Saturn’s. Saturn’s rings are made up of frozen water particles ranging in size from tiny grains to blocks of ice that are 30 yards in diameter. The rings are only a few miles thick, but they extend from the planet for 50,000 miles (80,000 kilometers). Moon Diameter Ganymede 3,200 mi, or 5,300 km Callisto 2,900 mi, or 4,800 km Io 2,200 mi, or 3,600 km Europa 1,900 mi, or 3,100 km

PROJECT 2 Name Date Time Planet Information Label Copyright © Wright Group/McGraw-Hill 363 Planet name: Average diameter: The planet’s average diameter is about the diameter of Earth. Average distance from the Sun: How long would it take to fly from the planet to the Sun, assuming your rate of travel is 500 mph? Time sunlight takes to reach the planet: How long does it take the planet to orbit the Sun? Since 1776, this planet has orbited the Sun about times. What is the length of time it would take to reach the planet from Earth if you were to travel at a rate of 20,000 miles per hour? In our lifetime, humans might be able to travel 50,000 miles per hour in space. At this rate, how long would it take to reach the planet? ? ?

PROJECT 2 Conclusions Copyright © Wright Group/McGraw-Hill 364 Name Date Time 1. Suppose you had used the scale for planet diameters to also represent distances of planets from the Sun. Keep the same position for the Sun that you used in your model. a. How far away from your model Sun would Earth be? b. Where in your school or town might Earth be located? c. How far away from your model Sun would Neptune be? d. Where in your school or town might Neptune be located? 2. Suppose you had used the scale for distances of planets from the Sun to also represent the diameter of Earth. a. What would be the diameter of the model Earth? b. If the model Earth were made with exactly that diameter, could you see it without a magnifying glass? (Hint:Pencil leads in some mechanical pencils are 0.5 mm, or about 1,02 00 of an inch, thick.) 3. Suppose you were explaining to someone how big the largest planet in the solar system is, compared to Earth. a. What would be an easy multiple to use? b. What other comparison might you use to make the difference easier to understand (for example, the costs or sizes of two common objects)? 4. Similarly, suppose you were explaining how big the Sun is, compared to even the largest planet in the solar system. a. What would be an easy multiple to use? b. What other comparison might you use to make the difference easier to understand? 5. Choose a fact you have learned about the solar system. Make up a question for a trivia game based on that fact.

PROJECT 3 Name Date Time Travel Times between Earth and the Sun Copyright © Wright Group/McGraw-Hill 365 New York San Francisco Distances in the solar system are very large. For example, the average distance from Earth to the Sun is about 93,000,000 miles, or about 150,000,000 kilometers. To understand distances in the solar system, it helps to compare them to distances you can understand more easily. To travel a distance equal to the distance from Earth to the Sun, about how many times would you need to cross the United States between New York and San Francisco? About times If a plane flew at 500 miles per hour (800 kilometers per hour) without stopping, about how long would it take to travel the distance from Earth to the Sun? About hours, or days, or years It takes sunlight about minutes to travel from the Sun to Earth. Distance fromabout 3,000 miles (mi), or New York to San Franciscoabout 4,800 kilometers (km) Time to fly by jet fromabout 6 hours at 500 mi per hr, or New York to San Franciscoabout 6 hours at 800 km per hr Speed of lightabout 186,000 mi per sec, or about 298,000 km per sec

PROJECT 3 Estimate Travel Times Copyright © Wright Group/McGraw-Hill 366 Name Date Time Use what you have learned about travel times between Earth and the Sun to make similar comparisons for your model planet. The planet I helped model is . Its average distance from the Sun is . This distance is equal to crossing the United States times. It would take about to fly this distance at 500 miles per hour. It takes sunlight about to reach this planet. Add this information to your team’s Planet Information Label. Share your work with your classmates. Use their numbers to help you complete the following table. PlanetNumber of Time to Fly the Time Sunlight Average Trips across Distance from Takes to Reach Distance from U.S. to Equal Planet to Sun Planet Sun (Miles) Distance from (Years) (Minutes) Planet to Sun Mercury 36,000,000 Venus 67,000,000 Earth 93,000,000 Mars 140,000,000 Jupiter 480,000,000 Saturn 890,000,000 Uranus 1,800,000,000 Neptune 2,800,000,000 Pluto 3,700,000,000

PROJECT 3 Name Date Time Describe a Distance Copyright © Wright Group/McGraw-Hill 367 1. The distance between Pluto and the Sun is very large. How could you describe this distance to help a friend understand it? 2. The speed of lightis about 300,000,000 meters per second. At that rate, light can travel around the world about 7 times in 1 second. a. Express the speed of light in scientific notation. b. Express the speed of light in centimeters per second. The speed of light is about cm per second. c. A light-year is the distance that light travels in 1 year. Explain how you would estimate the number of centimeters in a light-year.

PROJECT 4 Spaceship Earth Copyright © Wright Group/McGraw-Hill 368 Name Date Time To be a successful space traveler, you must be able to find your way back to Earth. This may not be easy. You do not feel it, but at this moment you are traveling through space at incredible speeds. Earth spins around like a top. In 24 hours, it makes 1 complete rotation.At the equator, the distance around Earth is about 25,000 miles. In the middle of the United States, the distance is about 21,000 miles. This means that if you live in the middle of the United States, you travel about 21,000 miles every day. At the same time Earth is rotating, it is moving in its orbit around the Sun. In 1 year, Earth makes 1 complete revolution,or trip, around the Sun. This trip is approximately 600,000,000 (or 6 10 8) miles long. 21,000 miles 25,000 miles Sun Earth600,000,000 miles Movement of the Planets around the Sun All the planets are in motion, rotating like tops and revolving around the Sun. Compared to Earth, some planets move fast, but others are quite slow. Understanding planetary motion is key for space travel. You must know where to aim the spaceship. Solar System Data Table 3 Average Speed in Time to Revolve Time to Rotate Planet Orbit: Miles per Once around the Sun: Once: Earth Days Earth Day Earth Days or Years or Hours Mercury 2,600,000 88 days 59 days Venus 1,900,000 223 days 243 days Earth 1,600,000 365 days 24 hours Mars 1,300,000 686 days 25 hours Jupiter 700,000 12 years 10 hours Saturn 520,000 29 years 11 hours Uranus 360,000 84 years 16 hours Neptune 290,000 165 years 18 hours Pluto 250,000 249 years 6 days Source:Richard Lewis. The IIlustrated Encyclopedia of the Universe, Harmony Books, 1983.

PROJECT 4 Name Date Time Rotating and Revolving with Earth Copyright © Wright Group/McGraw-Hill 369 During 1 rotation of Earth, a person at the equator travels about 25,000 miles. The farther north of the equator a person is, the smaller the distance of rotation becomes. 1. Estimate how many miles a person travels during 1 hour of rotation. a. At the equator About miles b. In Los Angeles About miles c. In Seattle About miles d. In Anchorage About miles 2. a. Estimate the distance of 1 rotation for your location. For example, if you live in Chicago—which is farther from the equator than Philadelphia but closer than Seattle—you might say 18,000 miles. About miles b. How far have you rotated in the past hour? About miles c. How far have you rotated in the past minute? About miles 3. Earth travels about 600,000,000 miles (in scientific notation: 6 º 10 8) around the Sun in 1 year. Estimate how far Earth (with you on it) travels in its orbit around the Sun during various time periods. Complete the following statements. a. In 1 month, Earth travels about miles. b. In 1 day, Earthtravels about miles. c. In the past hour, Earth traveled about miles. d. In the past minute, Earthtraveled about miles. City Distance of One Rotation Honolulu, HI 24,000 mi Los Angeles, CA 21,000 mi Philadelphia, PA 19,000 mi Seattle, WA 17,000 mi Anchorage, AK 13,000 mi

PROJECT 4 Movement of Planets around the Sun Copyright © Wright Group/McGraw-Hill 370 Name Date Time Read the paragraph under Movement of the Planets around the Sun on Math Masters,page 368, and look at the information in Solar System Data Table 3. Then work with your Planet Team to complete the following. 1. Record some observations about the information in the table. For example, which planets rotate faster than Earth? About the same as Earth? Slower than Earth? 2. Since the Declaration of Independence was signed in 1776, about how many times has Earth revolved around the Sun? 3. a. About how many times has your team’s planet traveled around the Sun since 1776? b. Share results with your classmates to complete the list below. 4. Use what you have learned to add information to your team’s Planet Information Label. Approximate Number of Revolutions around the Sun Since 1776 MercuryMars Uranus Venus Jupiter Neptune Earth Saturn Pluto

PROJECT 4 Name Date Time Minimum Distances Copyright © Wright Group/McGraw-Hill 371 The constant movement of planets complicates space travel. Planets move at different speeds, so exact calculations are needed to figure out the directions spaceships should travel. Another challenge is that the distances between Earth and other planets are always changing. Scientists use complex mathematical computer models to calculate the relationship of Earth to the other planets and to plot the data needed to send space probes to other planets. There are also some facts that we can use to make rough estimates of some things we might want to know for space travel. All the planets except Pluto travel in nearly circular orbits, with the Sun at the center. For all planets except Pluto, orbits are almost in the same plane. This means that when the planets pass each other on the same radius from the Sun, the minimum distance can be calculated from the information in the Solar System Data Tables on Math Masters,pages 352 and 353. This can be seen in the diagram below. Earth revolves quickly around the Sun compared with all the planets except Mercury and Venus. This means that at least once every year, Earth and each of the outer planets line up on the same radius from the Sun, at the minimum distance. The times are predictable, too. It is harder to predict when Earth will line up with Mercury and Venus. (For Pluto the situation is even more difficult. You might want to take on the problem as a challenge, but it can’t be done using only the information on these pages.) Earth Mars Minimum distance Sun Earth Maximum distance Sun Mars

PROJECT 4 Minimum/Maximum Distances of Planets Copyright © Wright Group/McGraw-Hill 372 Name Date Time Read Minimum Distances on Math Masters,page 371. Then work with your Planet Team, unless you are on the Pluto team. Your teacher will tell the Pluto team what to do. Use the information on Math Masters,page 352 or 353 to estimate the distance between Earth and your planet when they are closest to each other. Round your estimate to 2 significant digits and write it in scientific notation. Share estimates with the other teams to fill in the estimated minimum distances in the table below. Then complete the Estimated Maximum Distance column. (Hint:Add Earth’s distance from the Sun to each planet’s distance from the Sun.) Summary 1. How would you describe to a friend the motion of Earth on its axis and around the Sun? 2. When you return from a space trip, will Earth be in the same place as when you left? Explain. 3. About how many times have you rotated and revolved since you were born? Rotated: Revolved: PlanetEstimated Minimum Distance Estimated Maximum Distance from Earth (mi or km) from Earth (mi or km) Mercury Venus Mars Jupiter Saturn Uranus Neptune

PROJECT 5 Name Date Time Travel to Other Planets in Your Lifetime? Copyright © Wright Group/McGraw-Hill 373 You have explored the solar system. You have learned about the size, distance, and motion of each planet. You are ready to offer an informed opinion on travel to other planets. Fill in the basic facts about the planet you plan to visit. Then estimate the answers to the questions on the rest of this page and the next page. Work on your own, but consult with your teacher or classmates if you are unsure about what to do. My planet Here are some facts I know about this planet. (This information is on Math Masters,pp. 352, 353, and 368.) Surface temperature Average diameter Average distance from the Sun Earth days or years to orbit the Sun How Far Will You Need to Travel? Estimated minimum distance from Earth (See Math Masters,p. 372.) How Long Will It Take to Travel to Your Planet? Suppose a spaceship with people on it can travel at about 25,000 miles per hour. At this speed, how long will it take to reach your planet? If you could travel at 25,000 miles per hour, would it be possible to visit your planet and return to Earth in your lifetime? If not, how much faster would you need to travel? times faster At the faster speed, how long would it take to go to your planet and return?

PROJECT 5 Travel to Other Planets in Your Lifetime? cont. Copyright © Wright Group/McGraw-Hill How long would your trip take if you could travel at 50,000 miles per hour? 100,000 miles per hour? Write the results for your planet in the table below. Share your results with your classmates, and get information from them to complete as much of the table as possible. Try to complete the Planet Information Labels posted in the solar system model. 374 Name Date Time Planet 25,000 miles/hour 50,000 miles/hour 100,000 miles/hour Mercury Venus Mars Jupiter Saturn Uranus Neptune Pluto Estimated Travel Time in Hours to the Planets

PROJECT 5 Name Date Time Travel to Other Planets in Your Lifetime? cont. Copyright © Wright Group/McGraw-Hill 375 Conclusions 1. Do you think it might be possible to travel to your planet and return in your lifetime? Why or why not? 2. Which planets are most likely to be explored by humans? Why do you think so? 3. Some scientists believe that it makes sense to send people to explore other planets. Some scientists believe that other planets should be explored only with computers, cameras, and scientific instruments aboard space probes. Choose one of these positions, or one in between, and defend your choice. 4. If you were one of the first people to go on a trip to another planet, what items would you take to represent your beliefs and interests?

PROJECT 5 Your Age on Another Planet Copyright © Wright Group/McGraw-Hill 376 Name Date Time We use the time it takes Earth to make one trip around the Sun to keep track of our ages. When you tell someone how old you are, you are telling how many times Earth has traveled around the Sun since you were born. 1. a. Today my age is years, months, and days. b. I have been on Earth a total of about days. If you lived on a different planet, you would have a different age counted in the year of that planet. For example, on Venus, 1 year (the time it takes for Venus to travel around the Sun) equals 223 Earth days. 2. a. How many Earth days are there in a year on Mars? b. How many Earth days are there in a year on Jupiter? 3. Estimate how old you would be today on the following planets by finding the number of times they have revolved around the Sun since you were born. Venus Mars Jupiter PlanetTime to Orbit the Sun (Earth Days) Mercury 88 Venus 223 Earth 365 Mars 686 Jupiter 4,380 Saturn 10,585 Uranus 30,660 Neptune 60,225 Pluto 90,885 Source: Universal Almanac

PROJECT 6 Name Date Time Predicting Body Sizes Copyright © Wright Group/McGraw-Hill 377 Anthropometryis the study of human body sizes and proportions. An anthropometristgathers data on the size of the body and its components. Body-size data are useful to engineers, architects, industrial designers, interior designers, clothing manufacturers, and artists. Automotive engineers use body-size data to design vehicles and to set standards for infant and child safety seats. Architects take body-size data into account when designing stairs, planning safe kitchens and bathrooms, and providing access space for people who use wheelchairs. Clothing manufacturers use body-size data to create sewing patterns. Not even identical twins are exactly alike. Body sizes and proportions differ depending on age, sex, and ethnic or racial attributes. There are no perfect rules that can be used to exactly predict one body measurement given another body measurement. For example, no rule can exactly predict a person’s weight given the person’s height, or height given arm length. There are imperfect rules and rules of thumb that can be useful in relating one body measurement to another. This project investigates two such imperfect rules. The first rule is sometimes used to predict the height of an adult when the length of the adult’s tibia is known. The tibiais the shinbone. When the measurements are in inches, the rule is Height (2.6 º Length of Tibia) 25.5 The second rule relates the circumference of a person’s neck to the circumference of the person’s wrist. Circumference of Neck 2 º Circumference of Wrist As part of this project, you will collect some body-size data for an adult male, an adult female, and yourself. Combine your data with data collected by your classmates. Then you will evaluate how helpful the rules are to predict body sizes for adults and sixth graders. thigh bone (femur) kneecap (patella) calf bone (fibula) shinbone (tibia) ankle bone (talus) Measure distance between top of foot and middle ofpatella. Measure around the neck. Measure around skinny part of wrist. Avoid the knob.

PROJECT 6 Anthropometry Project Copyright © Wright Group/McGraw-Hill Tibia and Height Data 1. The tibia is the shinbone. It is easiest to measure the tibia with a yardstick. Place the yardstick on the ankle so that one end is firmly against the top of the foot. The person being measured bends and straightens his or her knee while you feel the patella (the kneecap) and locate its top and bottom. The person being measured straightens the knee while you read the yardstick at the middle of the patella. Measure to the nearest 1 4inch. You can also use a tape measure to measure the tibia. The person being measured should hold one end of the tape so you have a free hand to feel for the top and bottom of the patella. Measure the tibia of two adults; then have one of them measure your tibia. Tibia (to the nearest 1 4inch): Adult male: inches Adult female: inches You: inches 2. Measure the height of the same two adults and your own height. Be sure that everyone removes her or his shoes before being measured. Height (to the nearest 1 2inch): Adult male: inches Adult female: inches You: inches 378 Name Date Time thigh bone (femur) kneecap (patella) calf bone (fibula) shinbone (tibia) ankle bone (talus) Measure distance between top of foot and middle of kneecap.

PROJECT 6 Name Date Time Anthropometry Project continued Copyright © Wright Group/McGraw-Hill 379 Neck and Wrist Data Use a tape measure to measure both the neck and the wrist. If you don’t have a flexible tape measure, use a piece of string and then measure the string length with a ruler. 3. Measure the neck as shown at the right. Be gentle! Circumference of neck (to the nearest 1 4inch): Adult male: inches Adult female: inches You: inches 4. Measure the wrist around the thinnest part as shown at right. Circumference of wrist (to the nearest 1 8inch): Adult male: inches Adult female: inches You: inches Graph Your Data Plot your data on 2 classroom graphs. These are the symbols to use: Open blue circles for adult male data Solid red circles for adult female data Solid black squares for data about you Measure around skinny part of wrist.Avoid the knob.

PROJECT 6 Anthropometry Project: Tibia and Height Copyright © Wright Group/McGraw-Hill 1. The following rule is sometimes used to predict the height of an adult when the length of the adult’s tibia is known. Measurements are in inches. (Reminder:Your tibia is your shinbone.) Height (2.6 º Length of Tibia) 25.5 Do you think that this rule can exactly predict a person’s height when the length of the person’s tibia is known? Explain. 2. Use the rule in Problem 1 to complete the table. Find the predicted height for each tibia length. You may use your calculator. 380 Name Date Time 3. Your teacher will draw a prediction lineon the grid where you plotted your research data. It passes through points that exactly follow the rule for predicting height given the tibia length. Use the prediction line to answer the following questions. a. The predicted height for a person with a 15 1 4 -inch tibia is about inches. b. The predicted height for a person with a -inch tibia is about 5 ft 0 in. 4. a. How closely does the prediction line approximate the actual data points for adult males? Explain. Tibia Length Height Predicted 11 in. in. 14 in.in. 19 in.in. 17 1 2 in.in.

PROJECT 6 Name Date Time Anthropometry Project: Tibia and Height cont. Copyright © Wright Group/McGraw-Hill 381 b. How closely does the prediction line approximate the actual data points for adult females? Explain. c. How closely does the prediction line approximate the actual data points for students in your class? Explain. 5. Scientists can use a single bone from a human skeleton to estimate the height of an adult who lived many centuries ago. If they have a tibia, they can use the rule: Height (2.6 º Length of Tibia) 25.5 a. The skeleton of a Neanderthal man who lived about 40,000 years ago contained a tibia about 14 3 4inches long. Estimate the man’s height. in. b. The tibia of a partial skeleton of a 20,000-year-old adult was reconstructed and found to be about 12 1 2inches long. Estimate the person’s height. in. 6. Paul measured his baby sister’s tibia (4 inches long) and then used the rule to estimate her height. “That’s crazy!” said Paul when he saw the result. a. What was Paul’s estimate of his baby sister’s height? in. b. Why did he say that the estimate was “crazy”?

PROJECT 6 Anthropometry Project: Neck and Wrist Copyright © Wright Group/McGraw-Hill 382 Name Date Time Use the neck and wrist data that you and your classmates collected on the graph posted in the classroom to answer the following questions about the wrist-to-neck rule. Circumference of Neck  2 Circumference of Wrist 1. How closely does the prediction line approximate the actual data points for adult males? for adult females? for sixth graders? The following passage is from Gulliver’s Travels by Jonathan Swift. The setting is Lilliput, a country where the people are only 6 inches high. “Two hundred seamstresses were employed to make me shirts … . The seamstresses took my measure as I lay on the ground, one standing at my neck, and another at my mid leg, with a strong cord extended, that each held by the end, while the third measured the length of the cord with a rule of an inch long. Then they measured my right thumb and desired no more; for by a mathematical computation, that twice round the thumb is once round the wrist, and so on to the neck and the waist,and by the help of my old shirt, which I displayed on the ground before them for a pattern, they fitted me exactly.” This passage provides three rules: Circumference of Wrist 2 º Circumference of Thumb Circumference of Neck 2 º Circumference of Wrist Circumference of Waist 2 º Circumference of Neck 2. Based on the data you and your classmates collected, how well do you think Gulliver’s new clothes fit? Explain.

PROJECT 6 Name Date Time Height-and-Tibia or Neck-and-Wrist Grid Copyright © Wright Group/McGraw-Hill 383 " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " "

PROJECT 7 How Far Can You Throw a Sheet of Paper? Copyright © Wright Group/McGraw-Hill 384 Name Date Time 1. Paper Folding Work in a group of 3 or 4 students. You will need 6 sheets of paper, transparent tape, and a tape measure or yardstick. Leave one paper unfolded. Fold one paper in half. Fold one paper in half 2 times. Fold one paper in half 3 times. Fold one paper in half 4 times. Fold one paper in half 5 times. For each of the folded papers, use tape to secure the edges and keep the paper from unfolding. Use no more than 3 inches of tape for each folded paper. Write the number of folds on each folded paper. 2. Distance Testing Agree on a baseline from which to throw each paper. Throw each paper (including the unfolded one) 3 times. Don’t worry if the paper hits the floor, ceiling, or walls before it lands. You may throw the paper in any way you want. Try to throw each paper as far as possible. a. Measure all distances to the nearest foot. Record the best distance for each kind of paper in the table below. unfolded 1 fold 2 folds 3 folds 4 5 b. If your teacher has put a table of Class Distances on the board, record the distances collected by your group in the table. Distance (to the nearest foot)Unfolded 1 Fold 2 Folds 3 Folds 4 Folds 5 Folds Group Distances

PROJECT 7 Name Date Time How Far Can You Throw a Sheet of Paper? cont. Copyright © Wright Group/McGraw-Hill 385 3. Use the data in the completed table of Group Distances to complete the table below. 4. Which paper(s) consistently traveled the longest distance? The shortest distance? How do you think the surface area of the paper, its shape, the method of throwing, and other factors affected how far the paper traveled? 5. Generations of students, much to the dismay of generations of teachers, have perfected a way of using the air to throw a sheet of paper a great distance. Can you describe how they do it? Landmark Unfolded 1 Fold 2 Folds 3 Folds 4 Folds 5 Folds Maximum Median Minimum Landmarks for Class Distances

PROJECT 7 How Far Can You Throw a Sheet of Paper? cont. Copyright © Wright Group/McGraw-Hill 386 Name Date Time 6. Graphing the Test Data Use the results in the Landmarks for Class Distances table on Math Masters, page 385 to make a bar graph. The graph should have 6 bars. Draw a bar for unfolded paper, a bar for 1 fold, a bar for 2 folds, and so on. The height of each bar should be the maximum distance thrown. Mark the median and minimum distances on each bar as shown at the right. 12345 Distance (ft) 0 10 20 30 40 50 60 Landmarks for Class Distances 0 Number of Folds 1 (fold) Distance (ft) 0 10 15 Example 5 maximum median minimum

PROJECT 7 Name Date Time Build a Paper Airplane Copyright © Wright Group/McGraw-Hill 387 Design ObjectiveTo produce a paper airplane that will fly the greatest possible distance. Rules 1. Your paper airplane design must be original. 2. Use 8 1 2"-by-11" paper or smaller. The paper must be of normal thickness. Do not use construction paper or card stock. You may construct your paper airplane out of this page, if you wish. 3. Assemble the plane only by folding, cutting, and taping. Do not use more than 3 inches of tape. You may cut the 3 inches of tape into any number of smaller pieces. Do not use glue or other adhesives, string, paper clips, or other objects. You may need to try several different designs before you find a design that you believe will fly the greatest possible distance. Good luck!

PROJECT 7 Testing Paper Airplane Designs, Part 1 Copyright © Wright Group/McGraw-Hill 388 Name Date Time Student-Designed Airplanes 1. Complete the following after you conduct test flights of student-designed paper airplanes. a. Number of models tested b. Minimum distance feet c. Median distance feet d. Maximum distance feet Schultz-Designed Airplanes 2. Complete the following after you conduct test flights of Schultz-designed airplanes. a. Number of models tested b. Minimum distance feet c. Median distance feet d. Maximum distance feet 3. Select the 3 student-designed and 3 Schultz-designed airplanes that flew the farthest. Test these 6 planes again. Record the results in the table below. Name of Designer Distance Rank (1st to 6th) Student feet Student feet Student feet Louis Schultz feet Louis Schultz feet Louis Schultz feet

PROJECT 7 Name Date Time First International Paper Airplane Competition Copyright © Wright Group/McGraw-Hill 389 The First International Paper Airplane Competition was held during the winter of 1966–67 and was sponsored by Scientific Americanmagazine. The 11,851 entries (about 5,000 from children), from 28 different countries, were original designs for paper airplanes. They were entered into one of the following categories: Duration aloft (The winning designs flew for 9.9 and 10.2 seconds.) Distance flown (The winning designs flew 58 feet, 2 inches and 91 feet, 6 inches.) Aerobatics (stunts performed in flight) Origami (the traditional Japanese art or technique of folding paper into a variety of decorative or representational forms) Contestants were permitted to use paper of any weight and size. The smallest entry received, entered in the distance category, measured 0.08 inch by 0.00003 inch. However, this entry was found to be made of foil, not paper. The largest entry received, also entered in the distance category, was 11 feet long. It flew 2 times its length when tested. Scientific Americanawarded a winner’s trophy to two designers, a nonprofessional and a professional, in each category. Nonprofessionals were people not professionally involved in air travel. Professionals were “people employed in the air travel business, people who build non-paper airplanes, and people who subscribe to Scientific Americanbecause they fly so much.” The winners received a trophy called The Leonardo,named after Leonardo da Vinci (1452–1519), whom Scientific Americanrefers to as the Patron Saint of Paper Airplanes. Da Vinci, known for many accomplishments in the fields of painting and sculpture, was also an architect, engineer, and inventive builder. Studying the flight of birds, da Vinci believed that it would be possible to build a flying apparatus that would enable humans to soar through the air. He designed several wing-flapping machines, suggested the use of rotating wings similar to those of the modern helicopter, and invented the air screw, which is similar to the modern propeller. More information about the First International Paper Airplane Competition, as well as templates and directions for making each of the winning designs, can be found in The Great International Paper Airplane Book,by Jerry Mander, George Dippel, and Howard Gossage (Simon and Schuster, 1971). Self-portrait of Leonardo da Vinci done in red chalkThe Leonardo

PROJECT 7 A Winning Paper Airplane Design Copyright © Wright Group/McGraw-Hill 390 Name Date Time midpoint " right of midpoint " left of midpoint midpoint 45° 82°45° 82° 1 4 1 4 The design plan shown below was submitted by Louis Schultz, an engineer. Schultz’s paper airplane flew 58 feet, 2 inches and was a winner in the distance category for nonprofessionals. The professional winner in the distance category was Robert Meuser. His paper airplane flew 91 feet, 6 inches. 1. Follow the directions below to make an accurate copy of the design plan on an 8 1 2"-by-11" sheet of paper. a. Use a ruler to find the midpoints at the top and bottom of the paper. Mark these points. Draw a center line connecting the midpoints to match the subsequent labels. b. Mark 2 points that are 1 4inch away from the midpoint at the top of the paper. c. Use a protractor to make two 45° angles as shown. Mark them with dashed lines. d. Use a protractor to make two 82° angles as shown. Mark them with dashed lines. Louis Schultz’s Paper Airplane Design Plan

PROJECT 7 Name Date Time A Winning Paper Airplane Design cont. Copyright © Wright Group/McGraw-Hill 391 front back back front back front center line 2. Assemble the paper airplane as shown below. Be very careful to make precise folds. Make the folds on a table. When making a fold, first press down on the paper with your finger. Then go over this fold with a pen or a ruler on its side. It is important that you do notuse your fingernails to make folds. (Using your fingernail causes more than one fold to be made in a small area. This fold will move as you attempt to make the rest of the plane.) a. Fold the paper back and forth along the center line to get a sharp crease. Then unfold. b. Fold corners along the dashed lines as shown. Use a small piece of tape to secure each corner, as shown in the sketch. c. With the back side of the paper facing you, fold the right side of the paper toward the center so that the edges highlighted in the sketch meet. Use a small piece of tape to secure the flap in the position shown in the sketch. Do the same to the other side.

PROJECT 7 A Winning Paper Airplane Design cont. Copyright © Wright Group/McGraw-Hill 392 Name Date Time top view bottom view tape front d. Flip the paper to the front side. Fold in half along the center line so that the front side is now inside. Your paper airplane should look like this. e. Take the top flap of the paper and fold it outward along the dashed lines. (Look for these dashed lines on the inside of the plane.) Do the same to the other flap. Your paper airplane should now look like this. f. Tape the wings together on top of the airplane. Then tape the bottom as shown, making sure to secure all loose flaps.

PROJECT 7 Name Date Time Testing Paper Airplane Designs, Part 2 Copyright © Wright Group/McGraw-Hill 393 1st 2nd 3rd 4th 5th 6th Distance (ft) 0 10 20 30 40 50 Name 1. Draw a bar graph below to show the distance traveled by each of the 6 planes as recorded in the table on Math Masters,page 388. 2. Describe the test-flight results. Did student-designed airplanes perform better or worse than airplanes built using Schultz’s design? 3. Which do you think works best for distance: a. a paper airplane that uses air to assist the motion of the paper? b. a piece of paper, folded very tightly (like the 5-fold paper), which cuts through the air? Explain.

PROJECT 7 Experiments with Air Copyright © Wright Group/McGraw-Hill 394 Name Date Time Air is a real substance, just as water, earth, and maple syrup are real substances. Because air is a substance, it offers resistance,or opposition, to the movement of objects through it. Imagine dropping a penny into a bottle of maple syrup. The penny will eventually fall to the bottom of the bottle, but the maple syrup will slow its progress. In other words, the maple syrup will offer resistance to the movement of the penny. Air works in much the same way—objects can move through it, but the air offers resistance to the movement of those objects. Did you know that this resistance can serve a helpful purpose? Try the following experiments to see how resistance can help an object such as an airplane move through the air more efficiently. The Kite Effect 1. Hold one end of an 8 1 2"-by-11" sheet of paper as shown—forefinger on top, supported by the thumb and second finger on the bottom. Notice that the paper in the illustration is tilted slightly, so the opposite end of the paper is a bit higher than the end being held. 2. Push the paper directly forward as shown. You will notice that the end of the paper that is opposite the end you are holding tilts up. When the tilted surface of the paper pushes against the air, the air pushes back. This partially slows the paper down and partially lifts it up. The sheet of paper has some of the characteristics of an airplane wing. The wings of an airplane are set at an angle so the front edge is higher than the back edge. In this way, the lower surface of the airplane wing uses the air resistance to achieve a small amount of lift.

PROJECT 7 Name Date Time Experiments with Air continued Copyright © Wright Group/McGraw-Hill 395 The Vacuum Effect 1. Hold the small end of a 2"-by-6" strip of paper between your thumb and forefinger as shown—thumb on top. The paper should fall in a curve. 2. Blow across the top of the paper as shown. As you blow across the top of the paper, notice that the end of the paper that is opposite the end you are holding tilts up. Air rushing over the upper surface of the paper causes the air pressure on the upper surface to decrease. When the air pressure on the upper surface becomes less than the air pressure on the lower surface, the higher pressure underneath lifts the paper. This sheet of paper has some of the characteristics of an airplane wing. Only the lower surface of an airplane wing is flat; the upper surface is curved, or arched. In this way, the upper surface of an airplane wing also uses air resistance to achieve lift. The kite effect and the vacuum effect contribute to the total lift of an airplane. However, the vacuum effect is responsible for about 80% of it. Additional Sources of Information about Paper Airplanes Here are three books about paper airplanes: The Best Paper Airplanes You'll Ever Fly by the editors of Klutz (Klutz, 1998). The Great International Paper Airplane Bookby Jerry Mander, George Dippel, and Howard Gossage (Simon and Schuster, 1971, and Galahad Books, 1998). The World Record Paper Airplane Bookby Ken Blackburn and Jeff Lamers (Workman, 1994). You may also want to search the Internet for “paper airplanes.” 12

PROJECT 8 Cross Sections of a Clay Cube Copyright © Wright Group/McGraw-Hill 396 Name Date Time Form a clay cube. Draw your prediction of the shape of the cross sectionthat will be formed by the first cut shown below. After making the cut, draw the actual shape and describe (name) the shape. Re-form the cube and repeat these steps for the other cuts. Clay CubePredicted Shape Actual Shape Description of Cross Section of Cross Section of Shape

PROJECT 8 Name Date Time Cross Sections of a Clay Cylinder Copyright © Wright Group/McGraw-Hill 397 Form a clay cylinder. Draw your prediction of the shape of the cross section that will be formed by the first cut shown below. After making the cut, draw the actual shape and describe (name) the shape. Re-form the cylinder and repeat these steps for the other cuts. Clay CylinderPredicted Shape Actual Shape Description of Cross Section of Cross Section of Shape

PROJECT 8 Cross Sections of a Clay Cone Copyright © Wright Group/McGraw-Hill 398 Name Date Time Form a clay cone. Draw your prediction of the shape of the cross section that will be formed by the first cut shown below. After making the cut, draw the actual shape and describe (name) the shape. Re-form the cone and repeat these steps for the other cuts. Clay ConePredicted Shape Actual Shape Description of Cross Section of Cross Section of Shape

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