USING GEOMETER’S USING GEOMETER’S SKETCHPAD TO INCREASE SKETCHPAD TO INCREASE

STUDENT COMPREHENSIONSTUDENT COMPREHENSIONFernando Mota Rodriguez

Buena Park High Schoolfrodriguez@fjuhsd.k12.ca.us

Maria Saldivar FernandezBuena Park High School

mfernandez@fjuhsd.k12.ca.us

Isaura DeLeonBuena Park High School

ideleon@fjuhsd.k12.ca.us

Presented OCMCMarch 9, 2007

http://taselm.fullerton.eduhttp://taselm.fullerton.edu

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

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.

The tool palette

The menus

The Construct Menu

The Transform Menu

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!

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

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

TO CREATE A MIDSEGMENT OF EQUILATERAL TRIANGLE:

1) SELECT one side of the triangle2) Go to CONSTRUCT menu and select

MIDPOINT3) Repeat the same process for another

side of the triangle

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.

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?

B

A C

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

B

A C

I

H

G F

E

D

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!!YES!!

I

H

G F

ED

J

Conclusions and Questions