Tutorial:Spreadsheet View and Basic Statistics Concepts
Introduction to GeoGebra’s Spreadsheet View
Spreadsheet Cells Input
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.
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 immediately 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).
Customize the User Interface and Toolbar
The user interface of GeoGebra can be customized by using the View menu. For example, you can show different parts of the interface (e.g. the Spreadsheet view) by checking the corresponding menu item in the View menu (e.g. Spreadsheet).
Record to Spreadsheet Feature
Preparations
 Open a new GeoGebra window.
 Go to Perspectives – Spreadsheet & Graphics.
 Show the Input Bar (View Menu).
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 xcoordinate of point A while the ycoordinate 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:

Tasks
Task 1:Examine the pattern of yvalues in column B
You could give this construction to your students and let them explore the pattern in column B, which is created by the ycoordinates of different positions of point A. Encourage your students to make a prediction about a function graph that runs through all different positions of point A. Have your students enter the corresponding function into the Input bar in order to check if their prediction was correct (e.g. students enter f(x) = 2x to create a line through all points).
Task 2: Create a new problem
Change the ycoordinate of point A in order to create a new problem:
 Right click (MacOS: Ctrlclick) on point A and select Object Properties… from the appearing context menu.
 In tab Basic you can change the ycoordinate of point A in the text field Definition to, for example, a^2.
 Use the other tabs of the Properties dialog in order to change the color (tab Color) or size (tab Style) of point A.
 Close the Properties dialog when you have made all desired changes.
 Repeat steps 7 to 9 of the instructions above in order to record the coordinates of the new positions of point A to the spreadsheet. Note: If you didn’t delete the old values in columns A and B, GeoGebra automatically uses the next two empty columns (e.g. columns C and D) in order to record the new values for xcoordinates and ycoordinates.
Relative Copy and Linear Equations
Preparations
 Open a new GeoGebra window.
 Go to Perspectives – Spreadsheet & Graphics.
 Show the Input Bar.
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:
 
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?
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.
Task 3: Create a new problem
Change the coordinates of the initial points in order to create a sequence of points that can be examined by your students.
Version 1: Change the initial points in the Spreadsheet View Double click in cell A2 and change the coordinates of the corresponding point to (1, 2). After hitting the Enterkey, all points that depend on point A2 automatically adapt to this change, both in the Spreadsheet view as well as in the Graphics view.
Version 2: Change the initial points in the Graphics View Activate tool Move and drag point A2 to a different position in the coordinate system. Immediately, all dependent points dynamically adapt to these changes both in the Graphics View as well as in the Spreadsheet View.
Investigating Number Patterns
Let’s investigate how the surface of a cube changes depending on the length of its edges.
Preparations with Paper and Pencil
Calculate the surface of a cube for the given length e of its edges. Pick at least two edge lengths from each table but do not pick the same numbers as your neighbor.
Preparations in GeoGebra
 Open a new GeoGebra window.
 Switch to Perspectives – Spreadsheet & Graphics.
 Show the Input Bar (View Menu).
 In the Options Menu set the Labeling to New Points Only.
Construction Steps
Create a Scatter Plot from your Data
1  Enter the following numbers into the spreadsheet cells of column A: A1: 1 A2: 2  
2  Highlight cells A1 and A2. Relative copy the values to cell A10 in order to create a sequence of different edge lengths. Hint: This creates the integers from 1 to 10.
 
3  In column B, enter the surface values you calculated earlier next to the corresponding edge length of the cube. Hint: You may collaborate with your neighbors to complete the table.
 
4  Select cell B1 and relative copy the formula down to cell B10.  
5  Create a Scatter Plot:
Note: The values in column A determine the xcoordinates and the values in column B specify the ycoordinates of the plotted points.
Hint: The points created from the data are displayed in the Algebra View as a list of points. By default, GeoGebra calls this list L1.
 
6  Use tool Move Graphics view in order to change the scale of the yaxis so that all points are visible in the Graphics view. Hint: Select tool Move Graphics view. Click on the yaxis and drag it down until you can see the 600 tick mark.

Investigate the Number Pattern in Column B
7  In cell C2, enter the formula = B2B1 to compute the difference of the two successive surface values. Hint: After entering the equal sign, you can click on cell B2 in order to enter its name into the active cell C2.
 
8  Select cell C2 and relative copy the formula down to cell C10.  
9  In cell D3, enter the formula = C3C2 to compute the difference of the two successive differences.  
10  Select cell D3 and relative copy the formula down to cell D10. 
Task 1
Examine the number sequences in columns C and D. Make a conjecture about the polynomial function that runs through all points plotted in the Graphics view and allows you to compute the surface of a cube for any given edge length e.
 Is it possible to determine the degree of this polynomial by investigating the sequences of differences you generated in columns C and D?
 Explain to your neighbor why we were repeatedly calculating differences of successive values and what they actually mean.
 Is it possible to determine the coefficient of the polynomial by investigating the sequences of differences you generated in columns C and D?
 Would this also work if the values in column A are not successive integers (e.g. 1, 3, 5,…)? Give a reason for your answer.
Check your Conjecture about the Polynomial
Enhance your Construction
Task 2
 Try if this concept of investigating sequences of differences of two successive function values works for all polynomials f(x) = a x^n.
 What modifications in the Spreadsheet view and Graphics view are necessary to be able to easily determine the constant of polynomials f(x) = a x^n + b?
Scatter Plot and Best Fit Line
Preparations
 Open a new GeoGebra window.
 Switch to Perspectives – Spreadsheet & Graphics.
 Show the Input Bar (View Menu).
 In the Options Menu set the Labeling to New Points Only.
Construction Steps
Importing Data from other Spreadsheets
 Select and copy the data you want to import (e.g. use the keyboard shortcut CtrlC 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 (e.g. use the shortcut CtrlV (MacOS: CmdV) or right click (MacOS: Ctrlclick) on the highlighted cell and select Paste).
Challenge of the Day: Explore Basic Statistics Commands
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.
 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
 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.