Tutorial:Creating and Enhancing Dynamic Worksheets with GeoGebra

Lower and Upper Sum

You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between a function and the x-axis, which can be used to introduce the concept of integral to students.

Preparations

• Open a new GeoGebra window.
• Switch to Perspectives – Algebra & Graphics.

Construction Steps

1		Enter the cubic polynomial f(x) = -0.5x3 + 2x2 – x + 1.
2		Create two points A and B on the x-axis. Hint: These points will determine the interval which restricts the area between the function and the x-axis.
3		Create slider for the number n with Interval 1 to 50 and Increment 1.
4		Enter uppersum = UpperSum[f, x(A), x(B), n]. Hint: x(A) gives you the x-coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower and upper sum.
5		Enter lowersum = LowerSum[f, x(A), x(B), n].
6		Insert dynamic text Upper Sum = and select uppersum from Objects.
7		Insert dynamic text Lower Sum = and select lowersum from Objects.
8		Calculate the difference diff = uppersum – lowersum.
9		Insert dynamic text Difference = and select diff from Objects.
10		Enter integral = Integral[f, x(A), x(B)].
11		Insert dynamic text Integral = and select integral from Objects.
12		Fix slider and text using the Properties Dialog.

Task

Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum. 1. Compare the values of the upper sum / lower sum to the value of the integral for different values of slider n. What do you notice? 2. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?

Reducing the Size of the GeoGebra Window

GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.

• If you don’t want to include the Algebra View you need to hide it prior to the export.
• Move your figure (or the relevant section) to the upper left corner of the Graphics View using the Move Graphics View Tool.
  Hint: You might want to use tools Zoom in and Zoom out in order to prepare your figure for the export process.

• Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below).
  Hint: The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.

Note: Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.

Upload to GeoGebra

After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the File Menu.

• File – Share…

• The GeoGebra website opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.

• Fill in the information for your students. If you want, you can also select to show the Toolbar, the Input Bar or the Menubar. Click Continue.
• Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.
• Finish your Upload with the Save button.

Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.

Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)

Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.

• Export – Dynamic Worksheet as Webpage
  Hint: You could also use the key combination Ctrl + Shift + W.

• Fill in the text fields in the appearing window in the Export as Webpage Tab (title of the worksheet, name of the author, and date).
• Type a short explanation of the dynamic figure into the text field Text above the construction.
• Enter tasks and directions for students into the text field Text below the construction.
• Click Export and save your dynamic worksheet.
  Hint: GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the GeoGebra_Introduction folder prior to saving your dynamic worksheet.

Tips and Tricks for Creating Dynamic Worksheets

• After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes.
  Hint: You can change the text of the dynamic worksheet in the same way.

• GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.
• Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.
• Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.

Enhancing Dynamic Worksheets

The export dialog window for Export as Webpage consists of two tabs: General and Advanced. In the last activity you used tab General in order to add explanations, tasks and directions to the dynamic figure prior to the export. You will now learn how to enhance your dynamic worksheet by including different features in the interactive figure using the tab Advanced.