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This activity has been updated since it first appeared in the March 1992 issue of the AIMS Newsletter. This is the updated version.

Topic Coordinate graphing Key Question How do you build a coordinate graph? Learning Goal Students will make an outline drawing of the space shuttle on graph paper by locating and connecting coordinate points. Math Ordered pairs Coordinate graph Integrated Processes Observing Recording data Materials Student pages Rulers Pencils Background Information Graphs are ways to arrange data for comparison or other purposes. Graphs can help people see patterns or relationships in data that may not be obvious by looking only at numbers, which are more abstract. In order to make a coordinate graph, you must have a set of ordered pairs that are plotted as points on the coordinate plane. The first number in the ordered pair gives the horizontal or x coordinate of the point, and the second gives the vertical or y coordinate. It is important to note that the order of the two numbers in an ordered pair makes a difference. The ordered pair (5,1) produces a different point than the ordered pair (1,5). To graph an ordered pair, find the first coordinate on the horizontal or x axis, and the second coordinate on the vertical or y axis. The point where lines going through these two coordinates intersect graphs the ordered pair. Thus, each ordered pair can be graphed as a point on the coordinate plane. Normally, coordinate graphs are used to graph functions. This activity is intended to give students practice in finding points on the coordinate plane represented by ordered pairs. Management 1. This activity is meant as an application of coordinate graphing skills rather than as an introduction to these skills. 2. An overhead of the graph can be made and the first few points and lines done together as a class. 3. Level 1 deals only with the positive quadrant of the coordinate plane. Level 2 includes all four quadrants. 4. Students may find it easier to keep their place if they make a check after each ordered pair as it is plotted. 5. It is important that students connect the points in order for each part. When all the points are plotted for Part 1, they will lift their pencils and plot points for Part 2, connecting them as they go. They will continue this until all points and all parts are completed. Procedure Level 1 1. Ask the Key Question and state the Learning Goal. 2. Define and discuss graphs at a level appropriate for you class. 3. Have the students use the ordered pairs listed in Level 1 to plot the first two coordinate points. Tell them to draw a line segment connecting the two points using a ruler. Guide them to plot the third coordinate point and draw a line segment from the second point to the third point. 4. Direct students to continue this procedure until all the points in Level 1 have been plotted and connected. 5. Have students follow the same procedure for each part until all parts are completed. Level 2 1. Follow the same procedure as in Level 1, adding the explanation for negative values on both horizontal and vertical axes. 2. Have students complete the graph. 1 2005 AIMS Education Foundation

Connecting Learning 1. In an ordered pair, how do you where to plot the points? 2. Where would you plot (12, 17)? 3. Did you have any difficulties? Explain. 4. If you made any errors, how did you discover them? 5. What other things could you draw using ordered pairs plotted on a coordinate grid? Extensions 1. Have students draw other pictures on the coordinate plane and make a list of the ordered pairs used for their coordinate points. Students can exchange lists and graph each others pictures. 2. Have students draw the space shuttle using a different scale. 2 2005 AIMS Education Foundation

Key Question How do you build a coordinate graph? Learning Goal make an outline drawing of the space shuttle on graph paper by locating and connecting coordinate points. 3 2005 AIMS Education Foundation

Astronaut Level 1 Make a drawing of a space shuttle using points. 1. Carefully plot the first point in Part 1 below. Find the first number of the ordered pair on the horizontal axis and the second on the vertical axis. Make a dot where the two lines intersect. Locate the second point in Part 1 in the same way. Using a ruler, draw a line segment connecting the first and second points. Find the third point and make a dot. Draw a line segment connecting the second and third points. 2. Plot and connect the rest of the points in Part 1, drawing one line segment at a time. 3. Plot and connect the coordinate points in Part 2. 4. Continue plotting points and connecting them. Some points are repeated. * * * * * * * * * * Part 1 Part 2 Part 5 Part 7 Part 10 (15,1) (12,12) (17,25) (18,10) (14,4) (15,4) (12,32) (16,24) (16,10) (14,1) (8,5) (13,34) (16,25) (16,9) (15,0) (9,8) (14,32) (17,26) (18,9) (11,0) (15,16) (18,25) (18,8) (12,1) (15,25) Part 3 (18,24) (16,8) (12,4) (16,28) (14,15) (17,25) (17,29) (14,34) Part 8 Part 11 (18,28) (17,39) Part 6 (19,9) (20,4) (19,25) (20,34) (13,10) (21,9) (20,1) (19,16) (20,15) (13,8) (19,0) (25,8) (15,8) Part 9 (23,0) (26,5) Part 4 (15,10) (19,8) (22,1) (19,4) (20,32) (19,9) (22,4) (19,1) (21,34) (20,10) (15,1) (22,32) (21,9) (22,12) (21,8) 4 2005 AIMS Education Foundation

Astronaut 40 Y Level 1 35 30 25 20 15 10 5 0 0 5 10 15 20 25 30 5 2005 AIMS Education Foundation X

Astronaut Level 2 Draw a space shuttle using points with coordinates in all four quadrants. 1. Carefully plot the first point in Part 1 below. Find the first number in the first ordered pair on the horizontal axis and then the second number on the vertical axis. Make a dot where the two lines intersect. Locate the second point in Part 1 in the same way. Use a ruler to draw a line segment connecting the two points. Find the third point and draw a line segment connecting the second and third points. 2. Continue this procedure until all the points in Part 1 are connected. 3. Plot the points listed for Part 2. Draw line segments connecting the points, as before. 4. Continue plotting points and drawing line segments, finishing each part before you go on to the next. Some points are repeated. * * * * * * * * * * Part 1 Part 2 Part 5 Part 7 Part 10 (-2, -18) (-3,-3) (-3,-15) (-4,-9) (2,-10) (-2,-15) (-3,15) (-3,-18) (-4,-11) (4,-10) (-9,-14) (0,20) (-2,-19) (-2,-11) (-8,-11) (3,15) (-6,-19) (-2,-9) Part 11 (-3,-3) (3,-3) (-5,-18) (0,-18) (-2,6) (-5,-15) Part 8 (0,-14) (-1,9) Part 3 (1,-9) (0,10) (-5,-6) Part 6 (-1,-9) Part 12 (1,9) (-5,13) (3,-15) (-1,-10) (-1,5) (2,6) (-4,15) (3,-18) (1,-10) (-1,6) (3,-3) (-3,13) (2,-19) (1,-11) (0,7) (8,-11) (6,-19) (-1,-11) (1,6) (9,-14) Part 4 (5,-18) (1,5) (2,-15) (3,13) (5,-15) Part 9 (0,6) (2,-18) (4,15) (2,-11) (-1,5) (-2,-18) (5,13) (2,-10) (5,-6) (3,-9) (4,-10) (4,-11) 6 2005 AIMS Education Foundation

Astronaut Level 2 20 Y 15 10 5-15 -10-5 0 5 10 15 X -5-10 -15-20 7 2005 AIMS Education Foundation

Specifications (rounded to the nearest unit) Length System: 56 meters Orbiter: 37 meters Height System: 23 meters Orbiter: 17 meters Wingspan of Orbiter: 24 meters Weight Gross lift-off: 1,995,840 kilograms Orbiter landing: 84,778 kilograms Thrust Solid-rocket boosters (2): 12,899,200 newtons of thrust at sea level Orbiter main engines (3): 1,668,000 newtons of thrust at sea level Cargo bay diameter: 18 meters Equivalents: 1 meter = 3.1 feet 1 kilogram = 2.2 pounds 1 newton = 3.6 ounces of force 8 2005 AIMS Education Foundation

Space Shuttles A space shuttle is one of several reusable spacecraft that is launched into orbit by rockets and then returns to the Earth s surface as a glider that lands on a runway. Before space shuttles were developed, the National Aeronautics and Space Administration (NASA) had used single-use rockets to launch people and payloads into orbit; for each fl ight a brand-new rocket was needed. The Space Transportation System In the early 1970s NASA established the Space Transportation System (STS) to improve the space program; it was hoped that eventually private business would use and help pay the cost of the space program. STS research included the development of a reusable space shuttle, along with the improvement of launch facilities, mission control, supporting centers, tracking, and data-relay systems. After many delays, the space shuttle program began in earnest in the early 1980s. Despite a number of problems, it demonstrated its usefulness in a series of missions. The STS enjoyed much success until January, 1986, when the Challenger exploded shortly after lift-off. This disaster forced a long delay in the program while NASA tried to fi nd out what had gone wrong. The space shuttle program was resumed in late 1988. The STS is currently in operation, although it is limited to launching government satellites and doing scientifi c research. Space Shuttle Components The space shuttle has three main sections: the orbiter, the external fuel tank, and the solid-fuel booster rockets. The shuttle has a mass of 2 million kilograms (2250 tons) at launch and stands 56 meters (184 feet) tall. It can carry a cargo of almost 30,000 kilograms (over 30 tons) into Earth s orbit. The orbiter is the part of the shuttle that looks like a jet plane. It is 24 meters (78 feet) from wing tip to wing tip and 37 meters (122 feet) long. During launch, its three main rockets help propel it into orbit using the fuel from the external tank. In orbit it becomes a maneuverable spaceship that can launch satellites and provide a place to conduct scientifi c experiments. During reentry and landing, it becomes a glider. The crew stays in the two-deck front compartment. The mid-section contains the cargo hold, or payload bay, which is 5 meters (15 feet) wide and 18 meters (60 feet) long. The tail contains the three main engines and maneuvering engine pods. Each of the main engines, which burn hydrogen and oxygen, produces up to 213,000 kilograms (235 tons) of thrust. The external fuel tank, which contains liquid hydrogen and liquid oxygen, acts as the backbone of the shuttle; the orbiter and booster rockets are attached to it. It is 47 meters (154 feet) 9 2005 AIMS Education Foundation

tall and just over 8 meters (27 feet) wide. It holds over 700,000 kilograms (almost 800 tons) of fuel for the three main engines on the orbiter. Two solid-fuel booster rockets provide the extra thrust needed for take-off. They burn for just over two minutes and help lift the shuttle to the upper atmosphere where its three main engines work more effi ciently. Each booster rocket is 45 meters (149 feet) tall and 4 meters (12 feet) wide and produces an average thrust of 1,200,000 kilograms (1325 tons). A Typical Space Shuttle Mission A few seconds before lift-off, the shuttle s three main engines are started. The two solidfuel booster rockets are ignited and the hold-down bolts are released. The shuttle begins its ascent straight up, away from the launch pad. After it clears the gantry (the structure around it on the launch pad), the shuttle rotates so that the orbiter is beneath the fuel tank and continues to ascend at an angle. Just over two minutes into the trip, the solid-fuel booster rockets burn out. They are jettisoned and descend by parachute into the ocean where they can be recovered. The shuttle continues to accelerate under the power of the three main engines. After about eight and a half minutes, the three main engines are shut down and the external fuel tank is jettisoned. The tank falls back into the atmosphere, where friction causes it to burn up. The orbiter uses its orbit-adjust engines to push it into fi nal Earth orbit. While in orbit, the shuttle goes around the Earth every 90 minutes. Besides routine maintenance and safety procedures, the shuttle s crew members conduct science experiments, collect data on the effects of weightlessness, and launch satellites. When the shuttle is ready to return to Earth, the shuttle orbital maneuvering engines are fi red as retrorockets. This slows the shuttle and it falls from its orbit and enters the upper atmosphere. Here it heats up tremendously because of friction. Protected by the special tiles on its underside, the shuttle continues its descent back to Earth. The friction of the atmosphere causes the shuttle to slow down more and more. As it enters the lower atmosphere, it becomes more maneuverable; the astronauts are able to glide in for a landing. 10 2005 AIMS Education Foundation

Connecting Learning 1. In an ordered pair, how do you where to plot the points? 2. Where would you plot (12, 17)? 3. Did you have any difficulties? Explain. 4. If you made any errors, how did you discover them? 5. What other things could you draw using ordered pairs plotted on a coordinate grid? 11 2005 AIMS Education Foundation