# Tutorial:Combining Spreadsheet View & Graphics View

GeoGebra provides different views of mathematical objects: a Graphics View, a numeric Algebra View and a Spreadsheet View. Thereby, all representations of the same object are linked dynamically and adapt automatically to changes made to any of the representations, no matter how they were initially created.

In GeoGebra’s Spreadsheet View every cell has a specific name that allows you to directly address each cell. For example, the cell in column A and row 1 is named A1.
Note: These cell names can be used in expressions and commands in order to address the content of the corresponding cell.

You can not only use numbers in spreadsheet cells, but all types of mathematical objects that are supported by GeoGebra (e.g., coordinates of points, functions, lines). If possible, GeoGebra inmediately displays the graphical representation of the object you enter into a spreadsheet cell in the Graphics View as well. Thereby, the name of the object matches the name of the spreadsheet cell used to initially create it (e.g., A5, C1). {{note|By default, spreadsheet objects are classified as auxiliary objects in the Algebra View. You can show or hide these auxiliary objects by selecting Auxiliary Objects from the styling bar at the top of the Algebra View.

### Preparations

• Open a new GeoGebra window.
• Go to Perspectives – Spreadsheet & Graphics.

### Construction Steps

 1 Create a slider a with default interval and increment 1. Hint: 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. Hint: 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: Select tool Record to Spreadsheet. Then, click on point A in order to highlight it. Note: The coordinates for the actual position of point A are immediately entered into cells A1 (x-coordinate) and B1 (y-coordinate) of the spreadsheet. Now, change the value of slider a in order to record the coordinates of all other possible positions of point A to the spreadsheet as well. Note: Do not switch to another tool before moving the slider.

## Relative Copy and Linear Equations

### Preparations

• Open a new GeoGebra window.
• Go to Perspectives – Spreadsheet & Graphics.

### Construction Steps

 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: Highlight both cells A1 and A2 by using the mouse. Click on the little square at the lower right corner of the highlighted cell range. Hold the mouse button down and drag the pointer down to cell A11. 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.

### Task 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?

Hint: 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.

### Task 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.

## Best Fit Line

### Preparations

• Open a new GeoGebra window.
• Go to Perspectives – Spreadsheet & Graphics.
• In the Options Menu set the Labeling to New Points Only.

### Construction Steps

 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.

### Task 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.

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

Note: GeoGebra allows you to copy and paste data from other spreadsheet software into the GeoGebra spreadsheet
• 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).

### Task 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.

### Task 2: Determine mean and median

1. Make a prediction for mean and median of the data you collected.
2. Compare your solution by checking the left table of the One Variable Statistics window.
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