MOVING MOTIONS: Examining Translations, Rotations, and Reflections with Geometer's Sketchpad (GSP)
Presented By: Charmaine Cureton
CTSE 5040/6040, Write Up #3
December 5, 2007
Problem: We will be looking at the different transformations that can be done using GSP and using a triangle and a quadrilateral. From this we will then see how changes to the placement of the orignial shape or changing constraints can affect the image constructed from a translation, rotation, or reflection.
DISCUSSION:
In my investigation, I explored how translations, rotations, and reflections
can be done using GSP.
You will discover that there are multiple ways in which one can rotate, translate or reflect an image using GSP.
Getting Started:
First we must open up Geometer's Sketchpad. After opening, go to the EDIT menu
and then select PREFERENCES. Click the tab that says TEXT and then check the
box that says show labels FOR ALL NEW POINTS and check the box that says NEW
SKETCHES. Make sure that THIS SKETCH is also selected. Now you are ready to
begin.
To make this easier to the eye, we will use the same triangle in each exploration. The triangle used is below. But feel free to draw your own triangle. You do this by selecting the segment tool (should have points on both ends) and draw a segment. Take the end of the segment and draw another segment. Your two segments should be connected. Now construct another segment from the last point of the 2nd segment to the 1st point of the 1st segment. You should now have a triangle.
Starting Triangle |
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Implications for Instruction
I really enjoyed this investigation and I feel that students will also. I hope that they learn a great deal about the various ways to translate, rotate, and reflect images. I feel that these activities would be a great lesson to teach before or after WRITE UP #2. Write Up #2 dealt with transformations using an equation. This could enforce the content knowledge on transformations. The use of triangles and quadrilaterals will show students how basic shapes can create different shapes such as trapezoids. Students will also enjoy these activities because they will get to manipulate the pictures. These activities are perfect for those who need visual representations to learn. Students will also come to conclusions of their own once they measure some of the angles or lengths of the figures that are created. Students might have difficulty at first when they are asked to select the triangle. Selecting the triangle means that you need to select the interior and exterior of the triangle. If they only select the sides, only the sides will be translated, rotated, or reflected. Students might also have trouble if they make a mistake. If a student puts a point in the wrong place and then deletes the point, the next point that they make will jump to the next letter. This could confuse students, but they could always change the point to whatever they wish the name of the point to be. The great thing about this write up is that students are not limited to one type of figure. They are allowed to construct the triangle and quadrilateral of their choice. Students can change the colors to fit their personality and this will get them engaged in the activity. I personally enjoyed the colors of GSP. Not being limited in my ability engages me into learning. I do not like being like everyone else. Students in the high school grades will feel the same. The technology involved in GSP can increase the learning of students who have access to the program. The constuction of shapes does not take long at all. Students can also get more accurate measurements using GSP instead of using other instruments that could result in human error. GSP will allow students to focus more on the mathematical content rather than written work or work from a textbook. This activity could extend into learning about proofs or learning the properties of angles. The images that were constructed after drawing segments to the corresponding vertices, brings out several mathematics terms. These could lead into alternate interior angles, similar triangles, point of symmetry, etc. I believe that students and teachers would enjoy this lesson. |
Reference:
Dynamic Geometry Software for Exploring Mathematics. (2001). The Geometer's
Sketchpad. Version 4.06. KCP Technologies. Inc.