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Third segment of NASA Connect Hidden Treasures explaining the number lines and the rectangular coordinate system. This segement provides an interactive activity where students draw a number line and graph points on the number line. After graphing points on the number line the students are asked to draw a rectangular coordinate system and graph coordinate pairs in the four quadrants. Next the segment describes how rectangular coordinate systems are used in maps. The segment ends with a student exercise where students use covered shoe boxes to identify the topography of an environment their classmates created.
Hi everybody, and welcome back to Jamestown Settlement.
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Now so far, we've seen some of the science involved in investigating these ancient mysteries,
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but now let's take a look at the math concepts used, and I bet you'll know a few of them.
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Now you know that a number line is a series of numbers that begin at the origin, zero,
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and move away from that origin in both a positive direction and a negative direction toward
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infinity. Each division of a number line always represents the same increment. We use number
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lines to compare data. Sometimes when scientists compare data, they use number lines. Now on
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a number line, the number to the left is always less in value than the number to the right.
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You can graph integers on a number line by drawing a dot. For example, let's graph five
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on the number line. Now start at the origin and move five spaces to the right. Okay, now
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let's graph negative three on the number line. Start again at the origin and move three spaces
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to the left. Let's take a couple of minutes and try the following example. Draw a number
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line from negative ten to ten. Graph the integers nine and negative seven. Graph the number
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you think might be their opposite integers. Teachers, this might be a good time to pause
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the tape so that students can give this a try. Welcome back, guys. Well, let's see how
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you did. The number line you made should have looked like this, with the origin or zero
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in the middle. Each integer on the number line has an opposite integer that is equally
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distanced from the origin. For example, let's look at the number nine. It is nine spaces
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from the origin to the right. Its opposite integer is negative nine. Both numbers are
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an equal distance on the number line from the origin. You should have also plotted negative
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seven and seven using the same method. Now don't worry if you didn't get it right the
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first time. You can try again later, now that you know how. Now that you understand number
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lines, let's continue. Depending on the data that scientists are analyzing, they may need
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to use what we call the rectangular coordinate system. Now this system consists of not one,
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but two number lines. These number lines cross at their origins and are perpendicular to
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each other. The area they create is called a plane. A plane is a two-dimensional object.
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The central point where the two lines cross is called the origin. Each number line now
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has a special name. The horizontal number line is called the x-axis. The vertical number
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line is called the y-axis. Now the x and y axes divide the plane into four sections called
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quadrants. These quadrants are labeled counterclockwise as the first, second, third, and fourth. Now
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remember, where the two axes cross is called the origin. Points to the right and above
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the origin are labeled with positive numbers. One, two, three, et cetera. Points to the
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left and below the origin are labeled with negative numbers. Negative one, negative two,
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negative three, and so forth. When plotting numbers in the rectangular coordinate system,
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we use coordinates. Now these coordinates are the addresses of those points and are
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called ordered pairs. The first coordinate, then, is called the x-coordinate. The second
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is called the y-coordinate. Now we always write these coordinates as pairs, with the
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first number representing the x-axis position and the second number representing the y-axis
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position. So what do you think the ordered pair is? For example, the x-coordinate is
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the ordered pair is for the origin. Well, if you guessed zero, zero, you are absolutely
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right. Let's take a closer look. We use ordered pairs of numbers to describe positions of
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points on the rectangular plane. The ordered pair 2, 3 means over positive 2 and up positive
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3. However, the ordered pair 3, 2 means over positive 3 and up positive 2. Where do you
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suppose the point negative 3, negative 2 is located? Well, in this case, the x-coordinate
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is a negative number. You would move three places to the left of the origin. And since
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the y-coordinate is a negative number, you would move two spaces down. Working in groups,
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let's see if you can graph the following coordinate pairs. E equals 4, negative 2. C
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equals 2, 0. A equals 0, 1. P equals negative 2, negative 1. And S equals negative 4, 1.
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Teachers, this would be a good time to pause while students give this a try. Okay guys,
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let's see how you did. Here is what your coordinate points should look like. Don't be discouraged
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if yours doesn't come out perfect the first time. Later on, you can go back and try it
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again. You know, many times scientists have to go back and recheck their work to correct
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their mistakes. Now that you know how to plot points using the rectangular coordinate system,
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can you think of when you might have already used this system? Norbert and Zot are using
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it right now. We use the rectangular coordinate system all the time. In fact, knowing how
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to locate points on a coordinate grid can actually help you locate points on a map.
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Let's take a look at Norbert and Zot. Can you describe their position? Can you describe
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their position now? By using a coordinate system, it is much easier to describe the
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position of objects in the real world. A coordinate is a point on a line. Two lines perpendicular
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to each other create a plane. Positions in this plane are labeled using two coordinates
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called an ordered pair. Now in the science world, maps are an example of how we use the
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rectangular coordinate system to describe the location of items on the Earth's surface.
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This special type of map is called a topographical map. Sometimes scientists need to plot data
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that is three-dimensional. To describe three-dimensional images, we can just simply add another axis
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to our rectangular coordinate system and plot points in three dimensions. Let's visit with
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the students in Pasadena, Texas, who used the rectangular coordinate system to complete
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a math and science activity. Hello, and welcome to Sophomore Intermediate School. We want
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to show you a cool activity that you can try in your own classroom. You can view and
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download this detailed description of how to do this lesson in your classroom from the
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NASA Connect website. Working in groups, we built imaginary environments instead of shoe
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boxes. We had to keep it top secret from all the other groups. Some of us included cool
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features like ponds, mountains, and trees. Next, we covered our environments with foil
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that had a grid marked on it. Then came the fun part. We created our shoe box environments
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with another group. We got to act like investigators trying to figure out what the environment
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in the box was without actually seeing it. We took turns using a screw to probe what
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might be in the box. Each person measured the depth of their probe. On our data sheets,
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we were careful to match our measurements for each probe to the correct coordinates
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of the foil grid. We were only allowed to choose 50 different probes. This made me really
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realize just how accurate scientists would have to be when they map an area of land.
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Some groups used their data to create topographical maps of what they thought was in the shoe
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boxes. Other groups used a graphing program to create their topographical maps. The best
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part was when we got to look inside the shoe boxes and compare our drawings to what was
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really there. I'll bet that's how explorers will feel when they finally visit some place
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like Mars. We hope you try this activity with your class. That looks like so much
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fun. I wish I could have been there with you. Now let's take a look at how NASA's only
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archaeologist, Tom Seaver, and other researchers are using the Rectangular Coordinate System,
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Remote Sensing, and GIS to answer questions about an ancient culture.
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- Idioma/s:
- Materias:
- Matemáticas
- Niveles educativos:
- ▼ Mostrar / ocultar niveles
- Nivel Intermedio
- Autor/es:
- NASA LaRC Office of Education
- Subido por:
- EducaMadrid
- Licencia:
- Reconocimiento - No comercial - Sin obra derivada
- Visualizaciones:
- 828
- Fecha:
- 28 de mayo de 2007 - 16:54
- Visibilidad:
- Público
- Enlace Relacionado:
- NASAs center for distance learning
- Duración:
- 08′ 47″
- Relación de aspecto:
- 4:3 Hasta 2009 fue el estándar utilizado en la televisión PAL; muchas pantallas de ordenador y televisores usan este estándar, erróneamente llamado cuadrado, cuando en la realidad es rectangular o wide.
- Resolución:
- 480x360 píxeles
- Tamaño:
- 52.77 MBytes