Compass+Straightedge with GeoGebra


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A presentation on how to make strict compass and straightedge constructions with GeoGebra.

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Compass+Straightedge with GeoGebra

  1. 1. The 7th International Conference for Informatics and Information Technology - CIIT 2010<br />Feb 24-27, 2011, Bitola, FYR Macedonia<br />Compass & Straightedge with GeoGebra<br />Linda Fahlberg-Stojanovska<br />VitomirStojanovski<br />University St. Clement of Ohrid - Bitola<br />
  2. 2. Effective technology<br />The most effective educational technologies are the ones that require little or no behavioral change on the part of the teacher or the learner. <br />They should not increase cognitive load, nor should they require extensive training or technical support.<br />Dr. Andrew Van Schaack, Vanderbilt U.<br />
  3. 3. Goal: Mathematics Education<br />One of our main goals in mathematics education is teaching logical thinking skills. <br />That is, the ability to look at a problem and see what is given, what is required and the steps neededto get from the given to the required. And how to check the result.<br />
  4. 4. Why Compass & Straightedge?<br />We have very, very small set of tools. <br />The problems state specifically what is given and what is required. <br />Every construction is based on previous constructions – previous learning. <br />The construction is visible and measurable. We can see it; we can check it physically to see whether it is correct.<br />
  5. 5. Why Compass & Straightedge?<br />Creativity and Thinking<br />Construct a 30° angle. How many ways?<br /> Draw an equilateral triangle and bisect one of the angles?<br /> Draw a right-triangle with hypotenuse double the length of a side?<br /> …<br />
  6. 6. Why Compass & Straightedge?<br />Teaches logical thinking skills<br />Fun and creative<br />Usually is required learning<br />
  7. 7. What tools in C&S?<br />A pencil <br />A compass and <br />A straightedge.<br />
  8. 8. What can we do with these tools?<br />With a pencil<br />draw points and<br />GeoGebra New Point Tool<br />mark intersectionpoints.<br />GeoGebra Intersection Tool<br />
  9. 9. What can we do with these tools?<br />With a straightedge<br />draw line through 2 points GeoGebra Line Tool<br />draw segment between 2 points<br /> GeoGebra Segment Tool<br />draw ray from 1 point through 2nd point<br />GeoGebra Ray Tool<br />
  10. 10. What can we do with these tools?<br />With a compass<br />measure a length between 2 points for a radius and then draw a circle with centered at a 3rd point with that radius.<br />GeoGebra Compass Tool<br />
  11. 11. Our toolbar in GeoGebra for C&S<br />
  12. 12. Construction worksheet<br />The BasicConstruct.ggb<br />Ready-to-use worksheet with the GeoGebra toolbar for C&S<br />Available online (post it freely) at: <br /><br />Download and open it with GeoGebra <br /><br />
  13. 13. First construction<br /># 1 Copy a line segment<br /><br />YouTube Screencast - Show and Tell<br />Online interActivity with GeoGebra<br />Printable and online materials<br />Online DIY worksheet for making construction<br />Metadata<br />
  14. 14. First construction<br /># 1 Copy a line segment<br />Given a line segment AB and a line with a point P on it.<br />Copy the line segment AB onto the line so that P corresponds to A.<br />We can start with blank and have kiddies draw the line segment and line or<br />We can put AB and line on BasicConstruct.ggb<br />
  15. 15. Second construction<br /># 2 Copy a triangle<br />Given a triangle ABC and a line with a point P on it.<br />Copy the triangle so that P corresponds to A and the base of the triangle is on the line.<br />We can start with blank and have kiddies draw the triangle and line or<br />We can ΔABC and line on BasicConstruct.ggb<br />
  16. 16. Getting Started with C&S<br /><br />Printable materials <br />Online interActivity with GeoGebra and/or Download<br />Links to pages on the 7 basic constructions<br />Шестар-и-линијар<br />На македонски<br />
  17. 17. FOSS (Free and open source software)<br />Can be used on school LANs<br />Can be used offline<br />Many, many applications<br />Ready to use applets are available<br />Is easy to use, powerful and dynamic<br />Teachers and students can work anywhere<br />Students can build animations, simulators, …<br />Why GeoGebra?<br />
  18. 18. References<br />, pencasts, GeoGebra,…)<br /> (compass and straightedge)<br />GeoGebra YouTube Channel<br /><br /><br /><br />Linda Fahlberg-Stojanovska:<br />