Geogebra Introductory Activity

Transcription

1 1. Logon to your computer. Geogebra Introductory Activity 2. Go to and in the middle of the page click on the picture (NOT THE DOWNLOAD BUTTON). This is a web applet that will load. Give it a bit as sometimes it takes up to a minute to start. 3. Once Geogebra has loaded, use the diagram below to familiarize yourself with the layout of the program. Key items are: 1) Drawing Pad 2) Toolbar 3) Algebra Window 4) Input Field 5) Input Options 6) Undo/Redo Buttons Page 1

2 Now let s use the tools to create objects. Let s start with a point. A. Creating a point 7) Take your cursor and click on the point tool. 8) Then click within the drawing to draw a point. You should see something like: 9) Repeat this and draw a second point in the drawing area. B. Drawing a Ray 1) Use your cursor to move and select the line tool. Click directly on the lower right arrow to access the menu for the button (red on the highlighted button). 2) Choose the menu item labeled ray through two points. Page 2

3 3) Select the endpoint for the ray (point A) 4) Select the point for the ray to extend through indefinitely (point B) Congratulations you should have a ray that looks like the following: C. Drawing A Line 1) Place two points in the drawing pad area 2) Choose the line menu (see above) and choose Line Through Two Points. 3) Select the first point for the line, and then the second point for the line Congratulations you should have a figure that looks like the following: D. Clearing the Screen If you want a new screen, the best thing to do is to create a new drawing. 1) Go to the file button 2) On the pull-down menu, click on new (don t save the previous drawing) Another option is to do the following: Choose the Edit menu at the top of the page. Page 3

4 Click Select All at the bottom of the edit menu. When everything is highlight, press your delete key to clear everything from your drawing pad. E. Drawing a line Segment 1) Use your cursor to move and select the Line Tool menu and click directly on the lower right arrow to access the menu for the button. 2) Click on the tool Segment between Two Points. 3) Now click anywhere in the drawing pad area. Page 4

5 4) Then, click a second point on the drawing pad. You should now have a line segment. F. Drawing a polygon There is a polygon tool to help create triangles, quadrilaterals etc. 1) Go to the polygon tool. 2) Click on the tool and then move your cursor to the drawing pad. 3) Click in the area to create points, if it is a triangle use three points. 4) **To finish the polygon you must click on the first point that you drew.** Congratulations! You should have a picture that looks like the following: G. Measuring an Angle The program will measure the angles of the triangle accurately. To do this, complete the following steps: 1) Choose the Angle Tool 2) Now select the three points of the angle you want to measure moving in a clockwise fashion. (in other words select the three vertices of your triangle) 3) The angle measure will be in green. Page 5

6 Congratulations! You can now measure angles. Try this for the other two angles in your triangle. Your picture should look like the following: H. Object Properties: You can modify and change the properties of your objects. Let s assume you don t want your points to be labeled A, B, and C in the previous triangle. You can change these values. 1) Right click on the point A. 2) On the menu select the Basic tab and change the name to D. Page 6

7 3) Repeat this process for the other two points using E and F. **You can change multiple points from this menu by highlighting them in the menu screen on the left as shown and then completing a process like Show label. Algebra The program also allows you to create algebraic functions. The input bar at the bottom of the page will take functions entered into the space. Create a new page to start this section. You should have two sets of axis (X & Y) on the screen. These can be turned on and off. Go to the view tab at the top and the first selection is Axis. One click turns them on and one click turns them off. There is also a Grid button to turn on the grid for the screen. Do this so that we can more accurately view our graphs. I. Graphing a Line: Graphing a line is fairly simple. We use the Input Bar at the bottom of the screen. If you need help finding it, turn back to the diagram on the first page. Page 7

8 1) Type y=3x+2 in the input bar 2) Hit Enter 3) You should have a graph of the function on your screen. J. Algebra Screen You are probably wondering about the algebra screen on the right side of the page. Your screen looks like the following: The program has created a line named a with the values you specified. The speed of the graphing is great. Add another line to the graph. (y = -x + 3) K. Intersections: You can find intersections using the above process and then finding the point of intersection. Here is how to do it: 1) Graph a line. 2) Graph a second line. 3) Go to the toolbar and select the drop-down menu for the point tool. 4) Select Intersect Two Objects. 5) Go to the Algebra screen on the left and click the first line, then click the second line. Page 8

9 6) The intersection point will be drawn on the graph and the coordinates are displayed in the Algebra window. ***The lines may be selected from the graph as well by hovering the mouse over the line. ****Each tool selected has simple instructions displayed on the toolbar if you are unsure of how to use it. For example, the intersection button directions are shown below on the far right of the toolbar. Notice you can click directly on the intersection point as well. L. Inequalities: (Version 4.0 and above) Just as you did with linear equations, the program will graph inequalities. 1. Use the input bar and enter y <= 2x Then try y < -2x Notice the line is solid and the shading is completed for you, or in the case of the strict inequality you have a dotted line. M. Zoom & Exponentials: One of the new Algebra standards (F.LE.3) states Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Geogebra can help you visualize this with a graph and the use of the zoom tool. 1) Create a new picture and graph y = 9x +2 2) Add to the graph the function y = 2 x +1 Page 9

10 3) The initial screen should look something like this: Most students would view this and think the linear equation continues in excess of the exponential based on the limited view. 4) Use the drop-down menu from the Move tool (last button on the right) and select Zoom out 5) Place your cursor at the origin and click once. Continue this until you can see the exponential cross over and exceed the linear equation. 6) This same zooming process can be achieved by rolling the scroll ball on your mouse. Challenges: See if you can do the following tasks: 1) Draw a quadrilateral and measure all four angles 2) Change the color of your quadrilateral to something other than mauve. 3) Move an object once you have drawn it 4) Move a point that is part of your drawing without moving the entire drawing 5) Move the label for a point, or make it disappear entirely 6) Draw a circle Page 10

11 7) Rotate an object about a point 8) Draw two parallel lines 9) Measure the length of a segment 10) Draw a set of perpendicular lines 11) Write your name on the drawing pad 12) Graph a line, but turn off the points 13) Draw a line of best fit for a given set of points Page 11