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@fjuhsd.k12.ca.us Presented OCMC March 9, 2007http://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!

9. 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

10. The Custom Tool TO CREATE A SCRIPT FOR THE TRIANGLE: 1)SELECT the vertices and sides of the triangle 2)OPEN the custom tool and select NEW 3)NAME the script

11. TO CREATE A MIDSEGMENT OF EQUILATERAL TRIANGLE: 1)SELECT one side of the triangle 2)Go to CONSTRUCT menu and select MIDPOINT 3)Repeat the same process for another side of the triangle

12. INVESTIGATIONS: 1)Lets measure the midsegment and the side of the triangle. 2)What is the relationship of the base of the triangle and the midsegment? 3)Does it hold for all sides of the triangle and their corresponding midsegment.

13. INVESTIGATIONS: 1)Draw the other two midsegments of the triangle. 2)How many triangles do you see? 3)Are there any relationships among the inscribed triangles? Areas? Perimeters?

14. INVESTIGATIONS: 1)Area of an equilateral triangle. 2)Formula - Derivation

15. INVESTIGATIONS: 1)Construct a hexagon using the equilateral triangle script. 2)Are there any relationships among the area of one equilateral triangle and the area of the hexagon? YES!!

16. Conclusions and Questions