Type of Class:
         High School Geometry Class

Related VA SOL’s: G.9 and G.2

Time Frame:
          90 minute block class

Objectives:

• Students will understand how to use transformations to tessellate a polygon.

• Students will be able to use Geometer’s Sketchpad^â to make tessellations and transform objects.

Materials:

• Computer per student (or per pair) with Geometer’s Sketchpad^â

• Scissors and paper for each pair of students

• Tutorial/Hint sheet

• How to Make a Script worksheet

 Procedures:

1. Give each pair of students a pair of scissors and a piece of paper.  Have them draw any type of quadrilateral and cut out six or seven congruent copies of that shape.  With their shapes, have them physically construct a tessellation by fitting the pieces together.  Instruct students to discuss how to use transformations (i.e. reflections, rotations, translations, dilations) to tessellate their object. [Note:  It is assumed that students have already studied transformations.]  Have pairs get into groups and share the different ways they transformed their shapes to tessellate the plane.

2. Put each student (or pair if necessary) at a computer with Geometer’s Sketchpad^â.  Give them a brief tutorial on how to translate, rotate and reflect objects in Sketchpad^â. 

3. Have students create a quadrilateral in Sketchpad^â.  Construct a quadrilateral and construct the midpoints of each side. Next construct a point in the interior of your quadrilateral, near the center.  Construct line segments from each midpoint to the point in the interior.  Select the vertices of one of the interior quadrilaterals.  Go to the Construct menu and choose Quadrilateral Interior.  Now you can right click inside your colored quadrilateral and choose Color, then change the color to anything you desire.  Color each of the four interior quadrilaterals a different color.

4. Have students create their own quadrilateral tessellation on Sketchpad^â using transformations.  You may want to give students a hint if they seem to be having difficulty figuring out how to use the transformation(s) to tessellate their object.  [See the Tutorial page for a hint.]  Students need to have the following criteria in their tessellation:

• Name and date at the top of their page;

• The shape is a quadrilateral;

• There are four different colors used in the quadrilateral;

• The object is tessellated at least 20 times and there needs to be at least 4 rows and 4 columns of the object; and

• A mathematical explanation of the process they used to create the tessellation, including describing the transformations used.

5. After students finish creating their tessellation, have them save their file to a class disk.

6.  Students should now know how to tessellate their object rather quickly.  Have students create a script in Geometer’s Sketchpad^â that tessellates an object five or six times.  Give them a sheet that explains how to make a script.

 Assessment:
          Students should be assessed on their tessellation by whether they have completed the assignment and met all of the criteria and on whether they used transformations to tessellate their object.  The scripts should be used to assess how students decided to tessellate their quadrilateral.  In the following class period, if different students found different ways to tessellate their objects, you might also have them share their scripts with the class and explain what they did.