Creating Carnival Tickets with the Geometer’s Sketchpad
Using Translations, Tessellations, and Quadrilaterals
1. First construct a line segment, we’ll call it AB. Make sure to label the points, A and B.
2. Create a point somewhere above AB and label it C.
3. Mark AB as a vector, by selecting it, clicking on the transform tool, and selecting mark as vector, then select point C.
4. With point C selected, use the transform option to translate AB with point C.
5. With the translation in place, close off the rest of the polygon for a parallelogram like figure.
6. Use the line segment tool to create multiple little segments from point A to C, much like a torn section of paper.
7. Making sure that AB is still the marked vector, select all the little line segments from the previous step and translate them.
8. Select all the vertices of the shape and use the construct tool to fill in the interior. Use any color you’d like.
9. Keep AB as your vector and then select the interior of the shape.
10. Translate the shape. And repeat this, by selecting the newly created shape each time, until they disappear off of the page.
11. Then make BA your new vector and repeat the translating with the colored interior.
12. Make sure that each alternating shape is a different color.
13. Using the Polygon Edge tool, create another parallelogram within the first one. This does not have to be perfect. Do this for each of the shapes your created while tessellating.
14. Make sure that the new shapes are not the same color as the first ones and then use your text tool to make up any kind of ticket information you’d like. (Optional, hide any unwanted lines and vertices from the original shape)
And voila, there is your finished line of carnival tickets.
A. How has the program allowed you to explore geometry in the classroom this semester?
With the use of Geometer’s Sketchpad, I have been able to understand the concepts that we have covered in class on a more in depth level. I have been able to not only review ideas that we have gone over in class, but also gotten hands on experience with working with these various concepts thanks to the assignments we have been given for the program. Aside from what was covered in class, simply being able to work on my own and look at all the different tools in the program has introduced me to more geometric concepts. I have been able to look more at what makes a polygon and how they can vary in shape and size, not just be regular. And working with polygons more is just one of the things I have had the chance to explore with GSP. I hope to continue using it to learn and understand more about geometry as a whole.
B. What are the uses of the program in your future classroom?
The uses of this program in my own future classroom will be many and varied. I can use it as a way to introduce basic shapes, teach about angles and measurements, how to work with rigid motions, and a number of different things. Most of which will probably be in class demonstrations followed by students replicating their own versions of the assignments. I hope that it will be a hands on tool that will not only help to teach students further about geometry, in all different grade levels, but also help to keep them interested in the subject as a whole.
C. What are the strengths and/or weaknesses of the program?
The strengths of this program definitely lie within how it offers more hands on experience for students to be able to work with concepts that, at times, can be very confusing. They are able to try an assignment and work with a geometric concept at their own pace with their own thought processes and hands. Its weaknesses, however, are that it can be rather confusing, especially to start with. Students need to have very clear instructions to be able to properly use the tools that the program offers and work with the concepts, at least until they have become more accustomed to it. A different format for the program with more clearly labelled tools would definitely not hurt it, particularly for younger students who may be using it. But with both its goods and bads, I would definitely suggest it for anyone learning or teaching geometry to use GSP.