Using the Geometer's Sketchpad in your Classroom
I. Introduction

The Geometer's Sketchpad has the potential to change the teaching and learning of geometry from the memorization of definitions and proofs to a subject that is meaningful and dynamic. The sketchpad allows teachers and students to transform, manipulate, and measure figures after they have been created. Figures can be created using the Euclidean tools e.g., compass and straight edge. Sketchpad 4 can be used to teach Euclidean, coordinate, transformational, analytic, and fractal Geometry.  With the Geometer's Sketchpad, a variety of figures can be constructed:

1. Simple textbook figures.
2. Working models of the Pythagorean Theorem.
3. Perspective drawings.
4. Escher-like tessellations.
5. Fractals.
6. Animated sine waves

Also,  Sketchpad's has the capability to define, combine, evaluate, graph, and differentiate functions. This makes Sketchpad the perfect tool for algebra and calculus as well as for geometry.

The Geometer's Sketchpad allows the user to construct an unlimited array of figures. These figures can then be transformed, while preserving the geometric relationships of the constructions. It also provides continuous updates of all related parts and measured quantities as figures are transformed with the mouse. Users are motivated through a wide variety of fun and challenging investigations, explorations, demonstrations, problems and puzzles.

The Geometer's Sketchpad is a geometry exploration tool that enables students to explore relationships dynamically so that they can see change in geometric figures as they manipulate them. The Geometer's Sketchpad broadens the scope of what is possible to do in geometry.

In particular Sketchpad 4's  animation features are more powerful, flexible, and easier-to-use.  Multi-page Sketchbooks make it easy to assemble related activities and package them with activity-specific tools, archive work, create electronic portfolios and presentations, develop curriculum, and design activities. Split/Merge and editing of calculations and functions allow easy modification of sketches.   Styled text enhances professional appearance; mathematical text increases authenticity and enhanced graphics allow full color capability for objects and text, background color for striking visual effect, and highlighting for easier, more accurate constructions.  Use of parametric color adds an "extra dimension" in any visualization, ranging from simple mathematical finger-painting activities at the early grades to surface plots at the higher grades.  The interface in Sketchpad 4 allows beginners to get up to speed quickly.  For instance, selecting multiple objects is easier than ever.  The experienced Sketchpad user will find their skills are upwardly transferable to GSP 4.

One of Sketchpad 4's most useful enhancements is the ability to integrate web-based resources into Sketchpad activities and publish "live" Dynamic Geometry® activities on the Web.  Another useful enhancement is the custom tool box.  Easy-to-create custom tools extend and customize Sketchpad's mathematics.  GSP 4 fully supports Windows® and Macintosh® platforms on the same CD-ROM.


II. The sum of the angles of a triangle is 180 degrees
 A. Method 1
  1. Draw a triangle by choosing the vertex tool and placing three  vertices on a blank sketch.
  2. Choose the pointer tool and mark all three vertices.
  3. Click on the construct menu and choose line segments.
  4. Label each vertex by choosing the hand and clicking on each  vertex in turn.
  5. Choose the pointer tool and click on vertex A. then hold the shift key down and click on B, then C.
  6. Move your mouse to the Measure menu and click on angle. The measure of <ABC should appear on your screen.
  7. Repeat this proceedure with angles C and A.
  8. Move your mouse to the Measure menu and click on calculator.   A calculator should appear on your screen.
  9. Move your mouse to the measure of <ABC on your screen and  click on it.  It should appear on your calculator screen. Press +.     Repeat this for a second angle.  Select the third angle but press  ok after the third angle instead of +.
  10. <ABC+<ACB+<CAB = 180o should appear on your screen.

B. Method 2
  1. Draw any triangle as in method 1.
  2. Choose in order vertex A then B, i.e. choose the pointer tool and click on vertex A, then hold down your shift key and click on B.
  3. Move the mouse to the transform menu and choose mark vector AB.
  4. Move the mouse to the edit menu and choose Select all.
  5. Move the mouse to the transform menu and choose translate, then choose by marked vector and click on ok.
  6. Mark C and C', then move the mouse to the construct menu and choose line segment.


 

III. The area of a triangle is dependent on the base and height
 A. Construct a line segment near the bottom of the window and parallel to the bottom of the window.
 B. Construct a point near the upper left hand corner of your screen.
 C. Mark this point and the line segment.  Move your mouse to the construct menu and choose parallel line.
 D. Choose this new line and construct a point on the line
 E. Construct line segments from this new point to the end vertices of the line segment forming a triangle
 F. Construct the polygon interior of this triangle.
 G. Measure the area of this triangle



In the two figures above the base and height are the same.  However, in the figure below the base has changed.

The script for creating this figure is given below.  Note that you must begin with three given points. Given:
Point B
Point A
Point C
---------------
Steps:
1. Let [j] = Segment between Point A and Point B.
2. Let [k] = Parallel to Segment [j] through Point C.
3. Let [D] = Random point on Line [k].
4. Let [m] = Segment between Point [D] and Point A.
5. Let [n] = Segment between Point [D] and Point B.
6. Let [1] = Polygon interior with vertices B, A and [D].
7. Let Measurement [1] = Area(Polygon [1]).


IV. Centroid of Triangle

The Centroid of a triangle is created with the following steps.
1.    Construct a triangle,
2.    then the midpoints of each side, and
3.    then connecting each midpoint with the opposite vertex.
the point where these segments intersect is called the centroid.
What happens when you move one of the vertices of the triangle?
Can you say anything about the area of the smaller triangles?
What about the length of the line segments?


V. Constructing an equilateral triangle
In this section we will construct an equilateral triangle.  The sketchpad can accomplish anything a student can do with a ruler, compass, and protractor.  The first step is to construct any line segment and then two circles.  Each circle has the line segment as its radius.

The next step is to connect the ends of the line segment with the intersection of the two circles.

The last step is to hide the circles.

A script for creating this eqilateral triangle is given below.
Given:
Point B
Point A
---------------
Steps:
1. Let [j] = Segment between Point A and Point B.
2. Let [1] = Circle with center at Point A passing through Point B.
3. Let [2] = Circle with center at Point B passing through Point A.
4. Let [C] = Intersection of Circle [1] and Circle [2].
5. Let [k] = Segment between Point [C] and Point A.
6. Let [m] = Segment between Point [C] and Point B.


VI. Sum of the Exterior Angles of a Pentagon


VII. Project:Tesselate the plane with a triangle.


VIII. Project: Build a ferris wheel that turns.

Notes:

(1) The Geometer's Sketchpad implements the teaching and learning of mathematics as recommended by the National Council of Teachers of Mathematics (NCTM).

(2) The Geometer's Sketchpad was developed by Key Curriculum Press and is available for both the IBM and Macintosh platforms. Furthermore, scripts and drawings are interchangeable between the platforms.

(3) Additional resources are available at Swarthmore College 's web site - http://mathforum.org/ and http://www.keypress.com/