GeoGebra and Webbased Learning Objects
GeoGebra; being coded in both Java and HTML5 forms, can be run on multiple computer and tablet platforms and integrates well with the web. Thus it is an ideal tool for teachers who wish to use online spaces to share resources with their classes. Many such resources have been created by GeoGebra users and are shared via GeoGebraTube. You might find the learning objects you need there, but if not, GeoGebra provides tools that should make it possible for you to construct any resource you require for your courses. This workshop will lead you through the steps in creating and sharing a learning object. We will construct one particular resource, but the process should provide a template for you to use to build other learning objects for your class.
The HTML5 version of GeoGebra can run within a browser window and thus is accessible on computers on which either Java or the Java code for GeoGebra have not been installed. Thus the HTML5 version has somewhat wider applicability and for this workshop we will use GeoGebra in this form. Clicking here will open a new tab holding the GeoGebra software.
In GeoGebra the File > Share function allows you to upload a GeoGebra applet to GeoGebraTube. The uploaded applet is a fully functioning copy of GeoGebra with the constructions you added prior to the Share. During the uploading process you have the opportunity to also add explanatory text and/or student instructions or guiding questions to appear above and/or below the applet. You may then send your students to GeoGebraTube to work with the learning object you have created or if you wish download the worksheet and run it locally or mount it on your course website. Alternatively, GeoGebraTube will provide you with a link to your applet and you could place this on a course website or you could use the code provided by GeoGebraTube to embed your applet in a webpage you create or in a page in a course wiki or LMS.
Click here to see the example webpage, Score a Basket, designed to introduce students to the significance of the parameters a, h, and k in the general quadratic function
y = a(xh)^{2} + k
A Problem: Wolfe Island Cable Cost
We will construct a learning object related to a problem with a real context. Using a tool such as GeoGebra makes it easier for instructors and students to work with real data since computational complexities are handled by the software.

In 2009 Canadian Renewable Energy Corporation (CREC) connected its Wolfe Island Wind Farm to the Ontario electric power grid and now delivers about 594 gigawatthours (GW·h) of renewable energy annually. One of the issues in the development of this project was the route of the cable to take power from CREC's collector substation on the island across to the mainland at Kingston. This involved the laying of both land cable on Wolfe Island and a water cable across the channel between the island and Kingston.
The point at which the cable would come ashore at Kingston was dictated by the location of an existing Hydro One transformer station, but CREC had some choice concerning the point on Wolfe Island where the cable could enter the water. Since laying cable is costly on land or in water, but more so in water, CREC wished to determine the least expensive route. The costs per km of laying the cable were $20.5M on land and $31.4M in the water. How could CREC determine the best route and what would this minimum cost be?


It is possible to embed images in GeoGebra windows and overlay these with mathematical objects, thus making more explicit the link between the real world and mathematical models. We will use this embedding of pictures when developing the sample applet and generate a tool that appears as in the mage below. The applet is more than simply an image. It is a dynamic tool that students can manipulate to explore the relationship between the point at which the cable enters the water (distance along the shore from point E) and the cost. Click on the image below to open the applet in a browser window and then drag the purple point.
Learning Object Construction Steps
The construction of our learning object involves a number of separate tasks. Links to wiki pages giving instructions for each task are provided below. None of the tasks is very difficult, but in some cases there are quite a few details. At the end of each task page there is an image of GeoGebra in a form close to what you should have. If you are stuck at any point you could pick up on the process by clicking on the image and opening the GeoGebra applet in your web browser.
 Inserting the Wolfe Island image on the Graphics 2 View of GeoGebra
 Adding key points and information related to the power cable route
 Introducing the cost variables
 Plotting the cost curve
 Adding a Spreadsheet recording of the data
 Uploading the applet to GeoGebraTube
 Providing student access to your learning object
The development of an effective online learning object is really essentially a pedagogical task rather than technical. With time and resources technical details can be addressed. The pedagogical questions are more difficult. In this particular workshop you have been preparing a GeoGebra construction according to a plan developed by someone else. In a nonworkshop situation you would want to begin by asking general questions such as:
 What do I want the students to learn? What are the expected outcomes of using this learning object?
 What tasks will the students perform?
 What resources will I provide in the learning object?
 What should be the division of labour? How much of the problem solving should I carry out in the development of the GeoGebra applet and how much should be left to the students?
 What questions should be asked to guide the students' use of the learning object?
Some of the above questions have already been addressed by the instructions you followed in constructing the GeoGebra applet, but some remain to be answered before the learning object webpage is created. When uploading the applet to GeoGebraTube you will be able to delete certain of the GeoGebra tools if you do not wish them to be available to the students. In the applet linked above (Wolfe Island Cable Cost) access to GeoGebra tools has been removed and the only action available to students is dragging the point at which the cable will enter the water. Students could use this tool to explore the relationship between the location of entry into the water and the cost of the cable. With the relationship illustrated in the spreadsheet data and associated plotted points, students could visually identify the solution to the problem. If a more precise answer was desired students could use pencil and paper or GeoGebra to construct an algebraic solution and manipulate that to determine exact values.
During uploading to GeoGebraTube you will also have the option of creating a worksheet that holds instructions and questions to appear above and/or below the GeoGebra applet. For the steps below, illustrating how students might employ GeoGebra to solve the problem, I have built such a GeoGebraTube worksheet; holding the applet as a fully functioning copy of GeoGebra with all tools available. Students could then use these tools to address the questions and tasks presented on the worksheet below the applet. In a real teaching situation one would not likely include all the questions and tasks given on the worksheet. The particular tasks would depend upon the grade level of the course and mathematical experience of the students. Also some of the steps to complete these tasks are quite involved and a teacher would need to ensure that students had considerable knowledge of GeoGebra before presenting this assignment. The pages linked below are included here to illustrate the power of GeoGebra in providing alternate routes to a solution to the problem posed above.
Examples of How Students Could Use GeoGebra Tools to Investigate and Solve the Cable Cost Problem
 Determining a solution by inspection of the curve and spreadsheet
 Using the Algebra View to construct a function model
 Using the Spreadsheet View, Two Variable Regression Analysis tool to generate a function model
 Using the CAS View tools to manipulate the function model to obtain a precise solution
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