GeoGebra's User Interface

Below you can see the [img][/img] [i]Graphics View [/i]and [img][/img] [i]Algebra View[/i] of GeoGebra, which form one of GeoGebra's pre-defined [url=][i]Math Apps[/i][/url], the [img][/img] [i]Graphing Calculator[/i]. Check out the user interface and familiarize yourself with its most important features.[br][br][table][tr][td][i]Toolbar[/i][/td][td][img][/img] [/td][/tr][tr][td][i]Style Bar[/i] button[/td][td][img][/img][/td][/tr][tr][td][i]Menu [/i]button[/td][td][icon][/icon][/td][/tr][tr][td][i]Undo[/i] / [i]Redo [/i]buttons[/td][td][icon][/icon][icon][/icon][/td][/tr][/table][br][u]Note[/u]: You may want to open the [img][/img] [i]Math Apps[/i] menu using the [img][/img] [i]Menu [/i]button, in order to select a different [i]Math App [/i](e.g. [img][/img] [i]Geometry[/i], [img][/img] [i]Spreadsheet[/i], [img][/img] [i]CAS[/i], [img][/img] [i]3D Grapher[/i], [img][/img] [i]Probability[/i]).
Graphing Calculator
How does GeoGebra Work?
In GeoGebra, geometry and algebra work side by side:[br][br]Using the provided geometry tools in the Toolbar you can create geometric constructions on the [img][/img][i]Graphics View[/i] with your mouse. At the same time the corresponding coordinates and equations are displayed in the [img][/img][i] Algebra View[/i]. [br][br]On the other hand, you can directly enter algebraic input, commands, and functions into the [i]Input Field[/i] by using the keyboard. While the graphical representation of all objects is displayed in the [img][/img][i] Graphics View[/i], their algebraic numeric representation is shown in the [img][/img][i]Algebra View.[/i] 
Flexible user interface
The user interface of GeoGebra is flexible and can be adapted to your needs.[br][br][b]Examples[/b][br]If you want to use GeoGebra in early middle school, you might want to work with a blank sheet in the [img][/img] [i]Graphics View[/i] and use geometry tools. Later on, you might want to introduce the [img][/img] [i]coordinate system[/i] using a [img][/img] [i]grid[/i] (accessible from the [img][/img] [i]Style Bar[/i]) to facilitate working with integer coordinates. [br][br]In high school, you might want to use algebraic input in order to guide your students through algebra on into calculus, or use the CAS for symbolic computations.
Different views of mathematics
GeoGebra offers the following [i][url=]Views[/url][/i]:[br][br][table][tr][td][img][/img][/td][td][i]Graphics View[/i][/td][td][/td][td][img][/img][/td][td][i]3D Graphics View[/i][/td][/tr][tr][td][img][/img][/td][td][i]Algebra View[/i][/td][td][/td][td][img][/img][/td][td][i]Computer Algebra System (CAS) View[/i][/td][/tr][tr][td][img][/img][/td][td][i]Spreadsheet View[/i][/td][td][/td][td][img][/img][/td][td][i]Probability Calculator View[/i][/td][/tr][/table][br]These different [i]Views[/i] can be shown or hidden using the [img][/img] [i]View[/i] menu. For quick access to several predefined user interface configurations, you may want to try the [img][/img] [i]Math Apps [/i]menu.
Other components of the user interface
You may also customize GeoGebra’s user interface to meet your personal needs by changing the default [i][url=]Math Apps[/url][/i] and adding other components. [br][list][*][img][/img] [url=][i]Menu[/i][/url][/*][*][i][url=]Algebra Input Bar[/url][/i][/*][*][img][/img] [url=][i]Style Bar[/i][/url][/*][*][i][url=]Navigation Bar[/url][/i][/*][*][i][url=]Virtual Keyboard[/url][/i][/*][/list]GeoGebra’s user interface also provides a variety of [url=]dialogs[/url]. Different [url=]accessibility features[/url] as well as [url=]keyboard shortcuts[/url] allow you to access many features of GeoGebra more conveniently.

Using Tools to Construct Tangents to a Circle

Back to school...
[list=1][*][size=100]Use the [i]Navigation Bar[/i] in the figure below to review the construction process of tangents to a circle.[br][/size][/*][*][size=100]Try to re-create this construction yourself.[/size][/*][*][size=100]Write down a construction protocol and explain every one of your construction steps.[/size][/*][/list]
Tangents to a circle construction
Try it yourself...
Construction protocol
Write down your construction protocol and explain your construction steps.
Try to answer the following questions about the construction process
Which [i]Tools[/i] did you use in order to recreate the construction?
Were there any new [i]Tools [/i]involved in the suggested construction steps? If yes, how did you find out how to operate the new [i]Tool[/i]?
Did you notice anything about the [i]Toolbar[/i] you used to re-create the construction?
Do you think your students could work with such a Dynamic Worksheet and find out about construction steps on their own?

Exploring Parameters of a Quadratic Polynomial

Back to school...
[size=100]In this activity you will explore the impact of parameters on a quadratic polynomial. You will experience how GeoGebra could be integrated into a ‘traditional’ teaching environment and used for active and student-centered learning.[/size]
Follow the instructions of this activity and write down your results and observations while working with GeoGebra. Your notes will help you during the following discussion of this activity.
[table] [tr] [td][size=100]1.[/size][/td] [td][icon][/icon][/td][td][size=100]Type [code]f(x) = x^2[/code] into the [i]Algebra Input[/i] and hit the [i]Enter[/i] key.[br][u]Task[/u]: Which shape does the function graph have?[/size][/td][/tr] [tr] [td][size=100]2.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_move.png[/icon][/size][/td] [td][size=100]Use the [i]Move[/i] tool in order to drag the graph of the polynomial in the [img][/img] [i]Graphics View[/i] and watch how the equation in the [img][/img] [i]Algebra View[/i] adapts to your changes.[/size][/td][/tr] [tr] [td][size=100]3.[/size][/td] [td][size=100][center][icon][/icon][/center][/size][/td] [td]Change the function graph so that the corresponding equation matches [br][list][*][i]f(x) = (x + 2)²[/i][/*][*][i]f(x) = x² - 3[/i], and [/*][*][i]f(x) = (x - 4)² + 2[/i].[br][/*][/list][/td][/tr] [tr] [td][size=100]4.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_move.png[/icon][/size][/td] [td][size=100]Double-click the equation of the polynomial. Use the keyboard to change the equation to [code]f(x) = 3 x^2[/code]. How does the function graph change?[br][/size][/td][/tr][tr] [td][size=100]5.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_move.png[/icon][/size][/td] [td][size=100]Repeat changing the equation by typing in different values for the parameter (e.g. 0.5, -2, -0.8, 3).[/size][/td][/tr][/table]
Think about and answer the following questions
How can a setting like this be integrated into a ‘traditional’ teaching environment?
In which way could the dynamic exploration of parameters of a polynomial possibly affect your students’ learning?
Please write down your ideas for other mathematical topics that could be taught in a similar learning environment?

Tools used in this Chapter

In this chapter, you are going to work with the following tools. Please make sure you know how to use them and try them out below prior to working on the following tasks.[br]You may [b]activate a [/b][i][b]Tool[/b] [/i]by clicking on the button showing the corresponding icon.[br]GeoGebra's [i]Tools[/i] are organized in [i]Toolboxes[/i], containing similar [i]Tools, [/i]or [i]Tools [/i]that generate the same type of new object. You can [b]open a [/b][i][b]Toolbox[/b] [/i]by clicking on a [i]Tool [/i]button and selecting a [i]Tool [/i]from the appearing list.[br][br][table][tr][td][icon][/icon][/td][td][b]Slider[/b][br]Click on any free place in the [img][/img] [i]Graphics View[/i] to create a slider for a number or an angle. The appearing dialog window allows you to specify the [i]Name[/i], [i]Interval [min, max][/i], and [i]Increment[/i] of the number or angle, as well as the [i]Alignment[/i] and [i]Width[/i] of the slider (in pixels), and its [i]Speed[/i] and [i]Animation [/i]modality.[/td][/tr][tr][td][icon][/icon][/td][td][b]Intersect[/b][br]Click on the intersection point of two objects to get this one intersection point. Successively click on both objects to get all intersection points.[br][/td][/tr][tr][td][icon][/icon][/td][td][b]Point[/b][br]Click in the [i][img][/img] Graphics View[/i] in order to create a new point.[/td][/tr][tr][td][icon][/icon][/td][td][b]Segment[/b][br]Click twice in the [img][/img] [i]Graphics View[/i] or select two already existing points in order to create a segment between them.[br][/td][/tr][tr][td][icon]/images/ggb/toolbar/mode_slope.png[/icon][/td][td][b]Slope[/b][br]By selecting a line, this tool returns you the slope of a line and shows a slope triangle in the [img][/img] [i]Graphics View[/i].[/td][/tr][tr][td][icon][/icon][/td][td][b]Show / Hide Object[/b][br]Highlight all objects that should be hidden, then switch to another tool in order to apply the visibility changes![/td][/tr][tr][td][icon][/icon][/td][td][b]Point on Object[/b][br]Click on an already existing object in order to create a point on this object.[/td][/tr][tr][td][icon]/images/ggb/toolbar/mode_tangent.png[/icon][/td][td][b]Tangents[/b][br]Select a point and a function in order to create the tangent line to the function.[/td][/tr][/table][br]When you select a [i]Tool[/i], a [b][i]Tooltip [/i]appears[/b] explaining how to use this [i]Tool[/i].[br][u]Hint[/u]: Don’t forget to read the Tooltip if you are not sure about how to use a tool.[br][u]Hint[/u]: If you want to know more about this [i]Tool[/i], click on the [i]Tooltip[/i]. This opens a web page providing more detailed information for the selected [i]Tool[/i].
Try it yourself...

Take another GeoGebra Tour...

Introduction to GeoGebra
[size=100]The following Introductory Materials of the sequence "Introduction to GeoGebra" are available on the GeoGebra Materials Platform:[/size][list=1][*][size=100][url=]Basic Geometric Constructions[/url][br][/size][/*][*][size=100][url=]Algebraic Input, Commands, and Functions[/url][/size][/*][*][size=100][url=]Visualizing Mathematical Concepts[/url][/size][/*][/list]
The official GeoGebra Manual
[size=100]For further information please also see the [url=]Official GeoGebra Manual[/url].[/size]