Getting Started with GeoGebra Using Technology to Uncover Mathematics Day 3 Dave Brown dabrown@ithaca.edu

Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

Getting Started with GeoGebra 10/18/2012 Getting Started with GeoGebra Techniques & Tools in this Workshop GeoGebra Website Webstart vs. Applet Start Basic GeoGebra Window New Point tool Move tool Free and Dependent Objects Ithaca College Mathematics

Getting Started with GeoGebra 10/18/2012 Getting Started with GeoGebra Techniques & Tools in this Workshop Commands Save File New vs. New Window Grid and Axes – Turning on/off Regular Polygon tool Show Object / Show Label Ithaca College Mathematics

Getting Started with GeoGebra Techniques & Tools in this Workshop Object Properties - Changing Label Options – Right Pane: Basic Tab Category – Left Pane: Selecting Multiple Objects Undo and Redo Polygon tool Animation

Getting Started with GeoGebra 10/18/2012 Getting Started with GeoGebra Techniques & Tools in this Workshop Slider tool Circle with Center and Radius tool Play and Pause buttons Zoom and Pan (Move Drawing Pad) Object Properties Fill – Right Pane: Style Tab Color – Right Pane: Color Tab Ithaca College Mathematics

Getting Started with GeoGebra Techniques & Tools in this Workshop Line through 2 Points tool Perpendicular line tool Parallel line tool Intersect 2 Objects tool Insert Text tool Dynamic Text

Getting Started with GeoGebra Techniques & Tools in this Workshop Geometry Explorations and Tools menu Lines vs. Linear Functions Spreadsheet View Cell Addresses Inputting formulas with numbers/functions Copying Create List of Points

Getting Started with GeoGebra Where is GeoGebra? Open browser (Safari, FireFox, …) Type in: geogebra.org See Download link

First Time GeoGebra Tabs Download here

Getting started with GeoGebra Can you install a program on your computer? Yes Choose appropriate platform Program will download and you install it once. You get icon on desktop and you start from there. No Use JAVA Applet Some school LANs do NOT allow you to install. So you will use Applet Start each time within your browser.

Getting Started with GeoGebra Using Web App Type in: geogebra.org See “Start creating” link

GeoGebra Window Command Line GeoGebra Tools

GeoGebra Window More GeoGebra Tools

GeoGebra Window Free Objects Dependent Objects Algebra View

GeoGebra Window DRAWING PAD Graphics View

10/18/2012 GeoGebra Window Spreadsheet View Ithaca College Mathematics

GeoGebra Window Command List Input Bar

Understanding Objects Objects - Algebraic Free objects (dark blue) you can click and drag them anywhere Dependent objects Semi-dependent (light blue) you can click and drag them within their parent object (i.e. the object on which they depend) Dependent (black) you cannot drag them (they will move with their parent object)

Understanding Objects Activate (click on) the New point tool Click once inside the first quadrant. You will get a free point A. Click again somewhere along the x-axis. You will get a semi-dependent point B. Click again on (0,0). You will get a (completely) dependent point C.

Object Values Current Values

Object Definitions Definitions

Moving Objects Activate (click on) the Move tool Click and drag point A. It will go anywhere. Click and drag point B. It will only go along the x-axis. Click and drag C. It won’t move. Important: GeoGebra is case-sensitive! A is NOT a.

Understanding Objects anywhere along x-axis cannot move

Save File – What’s next? Save your file Standard command with filename: file_one File type is ggb New Goal: Create a Dynamic Square New File – 2 ways File -> New Window (Ctrl+N) opens new file without closing current file File -> New closes current file and opens new blank file

New: Closes current file. Opens new (blank) file. New Window vs. New New Window: Opens another “instance” of GeoGebra. Now you have 2 files open. New: Closes current file. Opens new (blank) file.

Dynamic Square Command: File -> New Turn on Grid Right-click in blank space in Drawing Pad. Select Grid

Dynamic Square Definitions of a square? Regular polygon with 4 sides GeoGebra: Regular polygon tool

Dynamic Square Regular polygon with 4 sides Select and click once to get Point A. Click again to get Point B. Dialog box will open … 4 is there… click on OK.

Dynamic Square Regular polygon with 4 sides Notice: The values of a, b, c and d are their lengths. The value of poly1 is its area. Points A and B are FREE objects. Segments a,b,c,d and poly1 are “together”.

Square Dynamics What can you move? Before moving, you need to select Move tool. You can click and drag point A or point B. Since these are free points, you can change the dimensions of the square – but notice that it is always a square!

Square Dynamics You can click and drag point A or point B. You can click and drag the square itself. This will only move the square - the dimensions of the square depend on A and B!

Labels, Names and Values We want to “label” the square with its area.

Labels, Names and Values Step 1: Turn on the label. Right-click inside of square. Click on Show Label. By default, the label is the Name of the object. Here the name is poly1

Labels, Names and Values Step 2: Change the label from Name to Value. Right-click inside of square. Select Object Properties (bottom of list).

Labels, Names and Values Object Properties: Basic Tab Click on Close.

Object Properties Let’s do that again. Right-click on ANY object; select Object Properties. or Edit -> Properties or Ctrl+E In the Object Properties windows … Choose an object or category in the left pane. Move this window off to the right so you see changes as you make them. Try the options on other tabs! Click on Close when you are done.

Object Properties Category:Segment 10/18/2012 Ithaca College Mathematics

Undo and Redo Forget to change to the Move tool? Oops, I created objects I don’t want. Don’t like your changes? Undo Redo Here:

Save File – What’s next? Save your file Filename: file_two (or whatever). New Goal: When is a square not a square? Use Polygon tool to create a “square”. Use Move tool to move any of the vertices and change the shape of this quadrilateral.

Square – not a Square? Command: File -> New Polygon tool Click at (-1,-1), (4,-1) (4,4), (-1,4) (or any 4 square points) Click again on A. (Make it say Point A!) You see a square. But all 4 vertices are blue = free. You have a quadrilateral (4-sided polygon).

Square – not a Square? You have a quadrilateral (4-sided polygon). Now – not to be boring … too late . Please notice that we NEVER clicked on the axes! because we don’t want our points “tied” to the axes.

Save File – What’s next? Save your file New Goal: Create an Animation Filename: file_three (or whatever). New Goal: Create an Animation Use Slider tool to define radius Use Circle with center and radius tool … to make circles with various radii. Animate the circles

Animation – Slider first Command: File -> New Turn off Grid (right-click in DP, click on Grid). Turn off Axes (right-click in DP, click on Axes). We create a slider – why? Sliders can be animated - either manually (click & drag) or automatically (play & pause) Slider is a number whose value can be changed.

Animation - Slider first Make a slider a from [0,2] increment 0.01 . Select Slider tool . Click in the Drawing pad (upper right). Type 0 (min), 2 (max) and 0.01 (increment) Click on Apply.

Circles from the slider Want circles whose radii depend on the slider. Select Circle with center and radius tool. Click in the Drawing pad (to get center point A). Type a in the dialog box and click on OK. The radius of the circle is the value of the slider!

Automated Animation Turn on animation Right-click on slider. Click on Animation on. Slider will start to move. Radius of circle will increase and then decrease. Pause/ Play button is in bottom left of Drawing Pad.

Manual Animation Press the Pause button Activate the Move tool. Click and drag the slider point to change the value of a manually. Sliders can be set to increase, decrease, oscillate or random. Both manual and automated animation work “better” if the width of the slider is a multiple of interval of the slider.

More circles from the slider Again, select Circle with center and radius tool. Click in the Drawing pad (to get center point B). Type a/2 in the dialog box and click on OK. Repeat 1-3 with radius a/3 Repeat 1-3 with radius 2*a Repeat 1-3 with radius 3*a Press Play button to animate again. Use Move tool to click and drag circles.

Zooming and Panning Zoom Pan Use your mouse scroll button to zoom in and out. Place mouse pointer in Drawing pad and scroll. Use Zoom out tool and Zoom in tool. Zooming is not “undoable”. Pan Use shift + mouse click & drag to pan Place mouse pointer in Drawing pad, press and hold Shift key and then click & drag mouse. Use Move drawing pad tool. Panning can be “undone”. Use

Fill in the circles with color Fill the circles Right-click on any circle and choose Object properties. Click and drag the Properties window to one side so you can see the Drawing pad. Click on category Point. Click on the Basic tab and deselect Show Label Click on category Conic. Click on the Basic tab and deselect Show Label. Click on the Color tab and Click & drag Opacity to 50. Click on each circle at left and then pick a color at right. You can also use drop down tools in the Graphics menu

Fill in the circles with color Drag Properties Window to side! Then you can see your changes!

Position Circles and Turn off Points Position your circles before you turn off the points! Right-click on any object and choose Object properties. Click on the category Points and on the Basic tab and deselect Show object. If you want to re-position the circles, you must first turn-on the points again. To do this, right-click on any object and select Object properties. (Ctrl+E) Now you have access to the Points again! Turn them on and then re-position.

Our result …

Save File – What’s next? Save your file New Goal: Create a Rectangle Filename: file_four(or whatever). New Goal: Create a Rectangle We want A and C to be the free vertices. Use Line tool to create base line. Use tools perpendicular (and parallel ) Use tool Intersect 2 objects Dynamic Text with tool

Dynamic Rectangle Command: File -> New Make a base line Select the Line tool . Click left Point A, then right Point B and we get line a. Point A is bottom left vertex of rectangle. Point B is just a point! Make Point C top right vertex of rectangle. Select New point tool and Click once in top right to get Point C.

Dynamic Rectangle Need a perpendicular at Point C to line a. Select Perpendicular line tool. Click once on Point C (make it glow). Click once on line segment a (make it glow). You get a line b perpendicular to the base line a through C. Need intersection point of line a and line b. Select Intersect two objects tool. (Under New Point) Click on the intersection point of the two lines.

Dynamic Rectangle Rename this point B. Right-click on point D. Select Rename from list. Type in B and click on OK. Notice “old” B is renamed B1

Dynamic Rectangle Need vertex D. You know the tools: and . Try to do it yourself …

Dynamic Rectangle Need vertex D. Select Perpendicular line tool Click on Point C and then on line b. Click on Point A and then on line a. Select Intersection of two objects tool Click on intersection point of the new lines. Make the rectangle using the polygon tool Select Polygon tool and click on A, B, C, D and A.

Dynamic Rectangle

Dynamic Rectangle Hide (don’t delete!) what you don’t want to see. Color and decide on label displays. With everything Cleaned up

Hiding – not Deleting For fun, try deleting point B1 What happens? Why? Only free points A and C remain. The definition of line a depends on the point B1. And everything else depends on line a. So without point B1 …. Rule: When in doubt, hide it! Undo deleting B1

Dynamic Text Want text that tells the Area of the rectangle Select Insert text tool Click in Drawing pad somewhere away from rectangle. Type Area = Choose Objects Then poly1 and click on OK.

Dynamic Rectangle Test that the text changes with the rectangle. Activate the Move tool and change your rectangle.

Save File – What’s next? Save your geometry exploration files Filenames: whatever you like New Goal: Create a Function & Spreadsheet Use Input bar to create a function Use function to create a spreadsheet.

Line vs. Linear Function Command: File -> New Click in the Input Bar (bottom left) Type y=-x+4 and hit Enter. This is a line Type f(x)=-x+4 and hit Enter. This is the same line, but now it is a function. We have done many things with lines. We can do different things with functions.

Linear Function Want a table of values for this function We will make a table for 6 x-values x = 0,1,2,3,4,5 Open the Spreadsheet Command: View -> Spreadsheet VERY IMPORTANT: Spreadsheet cells are ALWAYS a capital letter (case-sensitive)!

Linear Function Click in A1 and type 0 and hit Enter. Click in B1 and type =f(A1) and hit Enter. Click in A2 and type =A1+1 and hit Enter. READY TO COPY B1 to B2 (just like Excel) 1. Click in B1 to highlight it. 2. Click and drag little blue square (bottom right B1) down 1 cell to B2.

Linear Function READY TO COPY A2 and B2 down Click in A2 and drag to B2 to highlight both cells. Click and drag little blue corner of B2 down to B6.

Linear Function Make a list of the points. Click in A1 and drag to B6 to highlight A1:B6. Right-click on one of marked cells. Select: Create -> List of Points

Linear Function Save your file Filename: whatever you like.

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