Tutorial:Hojas de Cálculo y Vista Gráfica
GeoGebra ofrece perspectivas o Vistas diferentes de cada objeto matemático: una Vista Gráfica (disponible en dos ventanas diferentes); una, numérica, Vista Algebraica y además, una Vista de Hoja de Cálculo.
- Esta multiplicidad permite apreciar los objetos matemáticos en tres registros diferentes: gráfico en la Vista Gráfica (como en el caso de puntos, gráficos de funciones), algebraico en la Vista Algebraica (como coordenadas de puntos, ecuaciones) y en celdas de una Vista de Hoja de Cálculo.
Cada registro del mismo objeto se vincula dinámicamente a las demás en una adaptación automática y recíproca que asimila los cambios producidos en cualquiera de ellas, más allá de cuál fuera la que lo creara originalmente.
- Además, a partir de cierta versión en adelante, está disponible una Vista Algebraica CAS que respalda el desarrollo de ciertos cálculos, numéricos y simbólicos y las principales operaciones algebraicas así como el acceso a derivadas, integrales, resolución de ecuaciones y/o ecuaciones diferenciales y variedad de otras.
Entradas a las Celdas de la Hoja de Cálculo
Toda celda de la de GeoGebra tiene una denominación específica que permite dirigirse a cada una. Por ejemplo, la celda en la fila 1 de la columna A se llama A1.
En las celdas de una hoja de cálculo, pueden ingresarse tanto números como cualquier otro tipo de objeto tratado por GeoGebra (sean coordenadas de puntos, funciones, comandos, textos) en general y, desde ya, matemáticos - específicamente geométrico - en particular. Cuando corresponde, también aparece de inmediato, en la Vista Gráfica, la representación del objeto ingresado en la celda, cuyo nombre coincide con el de la celda de la hoja de cálculo a partir de la cual fue creado (por ejemplo: A5, C1, D3, etc.).
Registro en la Hoja de Cálculo
Preparativos
- Abrir a una nueva ventana de GeoGebra.
- Seleccionar, en el menú correspondiente, dentro de las Menú Apariencias – Hoja de Cálculo y Gráficos.
Pasos de Construcción
| 1 |  |
Create a slider a with default interval and increment 1.  Aviso: Select tool Slider and click in the Graphics View to set the position for the slider. In the appearing dialog window change the increment to 1 and click the Apply button. |
| 2 | Create point A by entering A = (a, 2a) into the Input Bar. Aviso: The value of slider a determines the x-coordinate of point A while the y-coordinate is a multiple of this value. | |
| 3 |  |
Show the label of point A in the Graphics View. |
| 4 |  |
Change the value of slider a to examine different positions of point A. |
| 5 |    |
Use tools Move Graphics View, as well as Zoom In and Zoom Out to adjust the visible part of the Graphics View and make point A visible in all positions. |
| 6 |  |
Record the coordinates for different positions of point A to the spreadsheet:
|
Copia Relativa y Ecuaciones Lineales
Preparativos
- Open a new GeoGebra window.
- Go to Perspectives – Spreadsheet & Graphics.
Pasos de Construcción
| 1 | |
Activate tool Move Graphics View and drag the origin of the coordinate system close to the lower left corner of the Graphics View. |
| 2 | In the Spreadsheet View, click on cell A1 enter the point coordinates (0, 0). | |
| 3 | In the Spreadsheet View, click on cell A2 enter the point coordinates (1, 1). | |
| 4 | |
Show the labels of both points in the Graphics View. |
| 5 | |
Relative copy the inserted point coordinates to other cells in column A:
|
| 6 | |
Use tools Move Graphics View, as well as Zoom In and Zoom Out to adjust the visible part of the Graphics View and make point A visible in all positions. |
Desafío Nro. 1: Examine the coordinates of the point sequence
What sequence of numbers is created if you apply the "relative copy" feature of the GeoGebra spreadsheet the way it is described above?
Aviso: Examine the x-coordinates of all created points and come up with a conjecture about how they are related. Then, check your conjecture using the ycoordinates of the points.
Desafío Nro. 2: Find the matching equation
Make a prediction about an equation that would create a graph going through all points of this sequence. Enter this equation into the Input bar in order to check your prediction.
Mejor Ajuste Lineal
Preparativos
- Open a new GeoGebra window.
- Go to Perspectives – Spreadsheet & Graphics.
- In the Options Menu set the Labeling to New Points Only.
Pasos de Construcción
| 1 | Enter the following numbers into the spreadsheet cells of column A:
A1: 1 A2: 5 A3: 2 A4: 8 A5: -2 | |
| 2 | Enter the following numbers into the spreadsheet cells of column B:
B1: -1 B2: 2 B3: 3 B4: 4 B5: 1 | |
| 3 |  |
Use tool Two Variable regression Analysis in order to create the function that best fits your data points. Highlight the cells and then click the tool. |
| 4 | Try to find the function that best fits your points by selecting different Regression Models. |
Desafío Nro. 1: Examine the regression models
Why do some models not work with the points you entered? Enter different points and try the Two Variable regression Analysis again.
Desafío Nro. 2: Polynomial Regression
Select the Polynomial Regression Model and observe what happens to the function when you change the order of the polynomial function.
Importing Data from other Spreadsheets
- Select and copy the data you want to import (e.g. use the keyboard shortcut Ctrl + C in order to copy the data to your computer’s clipboard).
- Open a GeoGebra window and show the Spreadsheet View.
- Click on the spreadsheet cell that should contain the first data value.
- Paste the data from your computer’s clipboard into GeoGebra’s Spreadsheet View. In order to do so, you can either use the keyboard shortcut Ctrl + V or right click (MacOS: Ctrl - click) on the highlighted cell and select Paste from the appearing context menu.
Exploring Basic Statistics
Yesterday, you gave a mathematics quiz to the 25 students of your 1st period math class. After the quiz, you asked your students to rate the difficulty of the quiz on a scale from 1 ("very easy") to 5 ("very difficult").
- 4 of your students rated the quiz "very easy" (1)
- 6 students rated the quiz "easy" (2)
- 6 other students rated the quiz "difficult" (4)
- 1 student rated the quiz "very difficult" (5)
- The rest of the students thought the difficulty of the quiz was "ok" (3).
Desafío Nro. 1: Create a histogram
Enter the data into GeoGebra’s spreadsheet and create a histogram that visualizes this data.
- Use the One Variable Analysis Tool in order to create a histogram.
- Change the slider Classes in the appearing window to control the number of bars that are shown in your histogram.
- Enhance the histogram by setting the classes manually and changing the start and width parameter.
Desafío Nro. 2: Determine mean and median
- Make a prediction for mean and median of the data you collected.
- Compare your solution by checking the left table of the One Variable Statistics window.
