1 00:00:00,000 --> 00:00:06,780 Hi everybody, and welcome back to Jamestown Settlement. 2 00:00:06,780 --> 00:00:12,080 Now so far, we've seen some of the science involved in investigating these ancient mysteries, 3 00:00:12,080 --> 00:00:17,520 but now let's take a look at the math concepts used, and I bet you'll know a few of them. 4 00:00:17,520 --> 00:00:23,960 Now you know that a number line is a series of numbers that begin at the origin, zero, 5 00:00:23,960 --> 00:00:29,640 and move away from that origin in both a positive direction and a negative direction toward 6 00:00:29,680 --> 00:00:36,680 infinity. Each division of a number line always represents the same increment. We use number 7 00:00:37,280 --> 00:00:43,760 lines to compare data. Sometimes when scientists compare data, they use number lines. Now on 8 00:00:43,760 --> 00:00:50,600 a number line, the number to the left is always less in value than the number to the right. 9 00:00:50,600 --> 00:00:56,700 You can graph integers on a number line by drawing a dot. For example, let's graph five 10 00:00:56,700 --> 00:01:03,500 on the number line. Now start at the origin and move five spaces to the right. Okay, now 11 00:01:03,500 --> 00:01:09,340 let's graph negative three on the number line. Start again at the origin and move three spaces 12 00:01:09,340 --> 00:01:16,340 to the left. Let's take a couple of minutes and try the following example. Draw a number 13 00:01:16,380 --> 00:01:23,380 line from negative ten to ten. Graph the integers nine and negative seven. Graph the number 14 00:01:26,940 --> 00:01:32,180 you think might be their opposite integers. Teachers, this might be a good time to pause 15 00:01:32,180 --> 00:01:38,380 the tape so that students can give this a try. Welcome back, guys. Well, let's see how 16 00:01:38,380 --> 00:01:43,780 you did. The number line you made should have looked like this, with the origin or zero 17 00:01:43,780 --> 00:01:49,040 in the middle. Each integer on the number line has an opposite integer that is equally 18 00:01:49,040 --> 00:01:55,180 distanced from the origin. For example, let's look at the number nine. It is nine spaces 19 00:01:55,220 --> 00:02:02,220 from the origin to the right. Its opposite integer is negative nine. Both numbers are 20 00:02:02,420 --> 00:02:08,540 an equal distance on the number line from the origin. You should have also plotted negative 21 00:02:08,540 --> 00:02:13,940 seven and seven using the same method. Now don't worry if you didn't get it right the 22 00:02:13,940 --> 00:02:19,420 first time. You can try again later, now that you know how. Now that you understand number 23 00:02:19,420 --> 00:02:25,020 lines, let's continue. Depending on the data that scientists are analyzing, they may need 24 00:02:25,020 --> 00:02:30,700 to use what we call the rectangular coordinate system. Now this system consists of not one, 25 00:02:30,700 --> 00:02:36,300 but two number lines. These number lines cross at their origins and are perpendicular to 26 00:02:36,300 --> 00:02:43,300 each other. The area they create is called a plane. A plane is a two-dimensional object. 27 00:02:43,580 --> 00:02:49,100 The central point where the two lines cross is called the origin. Each number line now 28 00:02:49,220 --> 00:02:55,580 has a special name. The horizontal number line is called the x-axis. The vertical number 29 00:02:55,580 --> 00:03:02,580 line is called the y-axis. Now the x and y axes divide the plane into four sections called 30 00:03:03,180 --> 00:03:10,180 quadrants. These quadrants are labeled counterclockwise as the first, second, third, and fourth. Now 31 00:03:11,180 --> 00:03:17,180 remember, where the two axes cross is called the origin. Points to the right and above 32 00:03:17,180 --> 00:03:24,180 the origin are labeled with positive numbers. One, two, three, et cetera. Points to the 33 00:03:24,180 --> 00:03:30,180 left and below the origin are labeled with negative numbers. Negative one, negative two, 34 00:03:30,180 --> 00:03:35,180 negative three, and so forth. When plotting numbers in the rectangular coordinate system, 35 00:03:36,180 --> 00:03:42,180 we use coordinates. Now these coordinates are the addresses of those points and are 36 00:03:42,180 --> 00:03:47,180 called ordered pairs. The first coordinate, then, is called the x-coordinate. The second 37 00:03:47,180 --> 00:03:53,180 is called the y-coordinate. Now we always write these coordinates as pairs, with the 38 00:03:53,180 --> 00:03:59,180 first number representing the x-axis position and the second number representing the y-axis 39 00:03:59,180 --> 00:04:04,180 position. So what do you think the ordered pair is? For example, the x-coordinate is 40 00:04:04,180 --> 00:04:10,180 the ordered pair is for the origin. Well, if you guessed zero, zero, you are absolutely 41 00:04:10,180 --> 00:04:15,180 right. Let's take a closer look. We use ordered pairs of numbers to describe positions of 42 00:04:15,180 --> 00:04:22,180 points on the rectangular plane. The ordered pair 2, 3 means over positive 2 and up positive 43 00:04:22,180 --> 00:04:32,180 3. However, the ordered pair 3, 2 means over positive 3 and up positive 2. Where do you 44 00:04:32,180 --> 00:04:38,180 suppose the point negative 3, negative 2 is located? Well, in this case, the x-coordinate 45 00:04:38,180 --> 00:04:44,180 is a negative number. You would move three places to the left of the origin. And since 46 00:04:44,180 --> 00:04:51,180 the y-coordinate is a negative number, you would move two spaces down. Working in groups, 47 00:04:51,180 --> 00:05:00,180 let's see if you can graph the following coordinate pairs. E equals 4, negative 2. C 48 00:05:00,180 --> 00:05:15,180 equals 2, 0. A equals 0, 1. P equals negative 2, negative 1. And S equals negative 4, 1. 49 00:05:16,180 --> 00:05:21,180 Teachers, this would be a good time to pause while students give this a try. Okay guys, 50 00:05:21,180 --> 00:05:29,180 let's see how you did. Here is what your coordinate points should look like. Don't be discouraged 51 00:05:29,180 --> 00:05:34,180 if yours doesn't come out perfect the first time. Later on, you can go back and try it 52 00:05:34,180 --> 00:05:39,180 again. You know, many times scientists have to go back and recheck their work to correct 53 00:05:40,180 --> 00:05:45,180 their mistakes. Now that you know how to plot points using the rectangular coordinate system, 54 00:05:45,180 --> 00:05:50,180 can you think of when you might have already used this system? Norbert and Zot are using 55 00:05:50,180 --> 00:05:57,180 it right now. We use the rectangular coordinate system all the time. In fact, knowing how 56 00:05:57,180 --> 00:06:02,180 to locate points on a coordinate grid can actually help you locate points on a map. 57 00:06:02,180 --> 00:06:08,180 Let's take a look at Norbert and Zot. Can you describe their position? Can you describe 58 00:06:08,180 --> 00:06:14,180 their position now? By using a coordinate system, it is much easier to describe the 59 00:06:14,180 --> 00:06:21,180 position of objects in the real world. A coordinate is a point on a line. Two lines perpendicular 60 00:06:21,180 --> 00:06:27,180 to each other create a plane. Positions in this plane are labeled using two coordinates 61 00:06:27,180 --> 00:06:32,180 called an ordered pair. Now in the science world, maps are an example of how we use the 62 00:06:32,180 --> 00:06:37,180 rectangular coordinate system to describe the location of items on the Earth's surface. 63 00:06:37,180 --> 00:06:43,180 This special type of map is called a topographical map. Sometimes scientists need to plot data 64 00:06:43,180 --> 00:06:50,180 that is three-dimensional. To describe three-dimensional images, we can just simply add another axis 65 00:06:50,180 --> 00:06:55,180 to our rectangular coordinate system and plot points in three dimensions. Let's visit with 66 00:06:55,180 --> 00:07:00,180 the students in Pasadena, Texas, who used the rectangular coordinate system to complete 67 00:07:00,180 --> 00:07:05,180 a math and science activity. Hello, and welcome to Sophomore Intermediate School. We want 68 00:07:05,180 --> 00:07:09,180 to show you a cool activity that you can try in your own classroom. You can view and 69 00:07:09,180 --> 00:07:13,180 download this detailed description of how to do this lesson in your classroom from the 70 00:07:13,180 --> 00:07:18,180 NASA Connect website. Working in groups, we built imaginary environments instead of shoe 71 00:07:18,180 --> 00:07:24,180 boxes. We had to keep it top secret from all the other groups. Some of us included cool 72 00:07:24,180 --> 00:07:29,180 features like ponds, mountains, and trees. Next, we covered our environments with foil 73 00:07:29,180 --> 00:07:34,180 that had a grid marked on it. Then came the fun part. We created our shoe box environments 74 00:07:34,180 --> 00:07:39,180 with another group. We got to act like investigators trying to figure out what the environment 75 00:07:39,180 --> 00:07:44,180 in the box was without actually seeing it. We took turns using a screw to probe what 76 00:07:44,180 --> 00:07:49,180 might be in the box. Each person measured the depth of their probe. On our data sheets, 77 00:07:49,180 --> 00:07:53,180 we were careful to match our measurements for each probe to the correct coordinates 78 00:07:53,180 --> 00:07:58,180 of the foil grid. We were only allowed to choose 50 different probes. This made me really 79 00:07:59,180 --> 00:08:04,180 realize just how accurate scientists would have to be when they map an area of land. 80 00:08:04,180 --> 00:08:08,180 Some groups used their data to create topographical maps of what they thought was in the shoe 81 00:08:08,180 --> 00:08:13,180 boxes. Other groups used a graphing program to create their topographical maps. The best 82 00:08:13,180 --> 00:08:18,180 part was when we got to look inside the shoe boxes and compare our drawings to what was 83 00:08:18,180 --> 00:08:23,180 really there. I'll bet that's how explorers will feel when they finally visit some place 84 00:08:23,180 --> 00:08:30,180 like Mars. We hope you try this activity with your class. That looks like so much 85 00:08:30,180 --> 00:08:35,180 fun. I wish I could have been there with you. Now let's take a look at how NASA's only 86 00:08:35,180 --> 00:08:41,180 archaeologist, Tom Seaver, and other researchers are using the Rectangular Coordinate System, 87 00:08:41,180 --> 00:08:46,180 Remote Sensing, and GIS to answer questions about an ancient culture.