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USING GEOMETER’S SKETCHPAD TO INCREASE STUDENT COMPREHENSION

USING GEOMETER’S SKETCHPAD TO INCREASE STUDENT COMPREHENSION. Fernando Mota Rodriguez Buena Park High School frodriguez@fjuhsd.k12.ca.us Maria Saldivar Fernandez Buena Park High School mfernandez@fjuhsd.k12.ca.us Isaura DeLeon Buena Park High School ideleon @fjuhsd.k12.ca.us

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USING GEOMETER’S SKETCHPAD TO INCREASE STUDENT COMPREHENSION

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  1. USING GEOMETER’S SKETCHPAD TO INCREASE STUDENT COMPREHENSION Fernando Mota Rodriguez Buena Park High School frodriguez@fjuhsd.k12.ca.us Maria Saldivar Fernandez Buena Park High School mfernandez@fjuhsd.k12.ca.us Isaura DeLeon Buena Park High School ideleon@fjuhsd.k12.ca.us Presented OCMC March 9, 2007 http://taselm.fullerton.edu

  2. Outline of the Presentation • Some comments about GSP • Getting Started: Some menus and commands • Transform Menu and Scripts • Some Investigations • Some Examples from Class • Questions and Conclusions

  3. Some Comments about GSP: • GSP is extremely friendly, powerful and self-contained, but not perfect. • The power of GSP lies on the ability to preserve the properties of Euclidean constructions when figures are dragged. • Strong tool for pedagogical purposes. • Constructions can be copied and pasted in other program documents (like a word processor) but they become static. • Photos can be pasted in GSP docs. • Mathematical investigations are enticed. • Also good for analytic geometry.

  4. The tool palette

  5. The menus The Construct Menu

  6. The Transform Menu

  7. Dragging is not a Drag • Construct • Transform • Drag • The math is underneath CONSTRUCT a human-like figure using circles and segments. CONSTRUCT and SELECT (i.e., “MARK”) a line of reflection, and USE the transform menu to reflect your figure. Then DRAG some (or all) parts. INVESTIGATE!

  8. Using an iterative tool: A Script for an Equilateral Triangle • CONSTRUCT segment AB • CONSTRUCT a circle with center at A and radius AB. • CONSTRUCT a circle with center at B and radius AB. • CONSTRUCT the intersection of two circles. Label it C. • CONSTRUCT segments AC and BC. • HIDE auxiliary circles

  9. The Custom Tool • TO CREATE A SCRIPT FOR THE TRIANGLE: • SELECT the vertices and sides of the triangle • OPEN the custom tool and select NEW • NAME the script

  10. TO CREATE A MIDSEGMENT OF EQUILATERAL TRIANGLE: • SELECT one side of the triangle • Go to CONSTRUCT menu and select MIDPOINT • Repeat the same process for another side of the triangle

  11. INVESTIGATIONS: • Lets measure the midsegment and the side of the triangle. • What is the relationship of the base of the triangle and the midsegment? • Does it hold for all sides of the triangle and their corresponding midsegment.

  12. INVESTIGATIONS: • Draw the other two midsegments of the triangle. • How many triangles do you see? • Are there any relationships among the inscribed triangles? Areas? Perimeters?

  13. INVESTIGATIONS: • Area of an equilateral triangle. • Formula - Derivation

  14. INVESTIGATIONS: • Construct a hexagon using the equilateral triangle script. • Are there any relationships among the area of one equilateral triangle and the area of the hexagon? YES!!

  15. Conclusions and Questions

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