Introduction
We use Geometry everyday in our lives. Geometric shapes and figures are visible in the manipulations that you have in video gaming. We are going to investigate transformations in Geometry and how it is used in construction. You will create a presentation that illustrates the information that you found in your internet search.
Task
You will investigate one of the transformations in Geometry (translation, reflection, rotation, dilation, and other combinations. Through the Internet, you will be able to explore several websites, like Mathsnet.net, that have interactive manipulatives dealing with transformation.
They will also give an assignment to assess learning and give feedback based on what the students learned or did not learn.
The presentation should have five parts:
1. definitions with vocabulary
2. examples (visual) of your transformation
3. explain your transformation using the Cartesian plane
4. proper notation used to express your transformation
5. uses of your transformation in the real world list several with visual examples
Process
1) Select a transformation from the math gift box.
2) Go through the internet activity on Mathsnet.net. Search the Internet for visual examples, definitions, and simple matrix algorithms to express the transformation.
3) Save the visual models that you would need in your presentation.
4) Create a PowerPoint presentation.
The presentation should include the picture, definitions, coordinate grid model with notation, and real world examples.
Each slide should be unique, do not use a definition more than once.
Remember to go to this site first and do the activities pertaining to your topic.
http://www.mathsnet.net/transform/index.html
Need a reminder regarding definitions and terms?
Here is a list of sites to get you started.
http://www.mathsnet.net/transformations/index.html
http://192.107.108.56/portfolios/d/desimone_g/discover2/2transfor.htm
http://www.glencoe.com/sec/math/geometry/geo/geo_04/extra_examples
http://www.glencoe.com/sec/math/geometry/geo/geo_04/vocabulary_review/index.php
http://mathworld.wolfram.com/topics/Transformations.html
http://argyll.epsb.ca/jreed/math9/strand3/transformations.htm
http://www.e-zgeometry.com/geoglossary/ezglossary.htm
Resources - General
Geometry textbook
25+ computers in a computer lab
proxima data projector with the teacher computer
microsoft powerpoint
access to the internet
Resources - Links
transformation
Evaluation Rubric
| Exemplary | Accomplished | Developing | Beginnings | Score | |
| Transformation Content | All content about transformation throughout the presentation is accurate. There are no factual errors. | Most of the content about transformation is accurate but there is one piece of information that might be inaccurate. | The content about transformation is generally accurate, but one piece of information is clearly flawed or inaccurate | Content about transformation is typically confusing or contains more than one factual error | |
| Use of Graphics and Displays | All graphics are attractive (size and colors) and support the theme/content of the presentation. | A few graphics are not attractive but all support the theme/content of the presentation. | All graphics are attractive but a few do not seem to support the theme/content of the presentation. | Several graphics are unattractive AND detract from the content of the presentation. | |
| Organization of Information | Information is organized in a clear, logical way. It is easy to anticipate the type of material that might be on the next card. | Most information is organized in a clear, logical way. One card or item of information seems out of place. | Some information is logically sequenced. An occasional card or item of information seems out of place. | There is no clear plan for the organization of information. | |
| Effectiveness of Material | Project includes all material needed to gain a comfortable understanding of the topic. It is a highly effective study guide. | Project includes most material needed to gain a comfortable understanding of the material but is lacking one or two key elements. It is an adequate study guide. | Project is missing more than two key elements. It would make an incomplete study guide. | Project is lacking several key elements and has inaccuracies that make it a poor study guide. | |
| Math Terminology and Notation | Correct terminology and notation are always used, making it easy to understand what was done. | Correct terminology and notation are usually used, making it fairly easy to understand what was done. | Correct terminology and notation are used, but it is sometimes not easy to understand what was done. | There is little use, or a lot of inappropriate use, of terminology and notation. |
Conclusion
Conclusion
Congratulations! You have learned about four basic forms of transformations (rotation, reflection, Dilation, and translation)in Geometry. By completing this task, you have taken responsibility of your learning. Through your investigation and preparing a powerpoint lesson you have achieved a level of mastery achieved by few.
Standards
Grade 10 Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects, andtransformations to analyze mathematical situations and solve problems.
Benchmark A. Formally define geometric figures.
6. Identify the reflection and rotation symmetries of two- and
three-dimensional figures.
Benchmark D. Use coordinate geometry to represent and examine the properties of geometric figures.
Benchmark E. Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology.
7. Perform reflections and rotations using compass and
straightedge constructions and dynamic geometry software.
Benchmark F. Represent and model transformations in a coordinate plane and describe the results.
8. Derive coordinate rules for translations, reflections and
rotations of geometric figures in the coordinate plane.
9. Show and describe the results of combinations of translations,
reflections and rotations (compositions); e.g., perform
compositions and specify the result of a composition as the
outcome of a single motion, when applicable.
Grade 10 Math Processes
E. Use a variety of mathematical representations flexibly and
appropriately to organize, record and communicate mathematical
ideas.
F. Use precise mathematical language and notations to represent
problem situations and mathematical ideas.
G. Write clearly and coherently about mathematical thinking and
ideas.
H. Locate and interpret mathematical information accurately, and
communicate ideas, processes and solutions in a complete and
easily understood manner
Credits
hspace picture
www.maths.warwick.ac.uk/.../hspace.html
escher14 picture
www.hongik.ac.kr/~ymkim/art/escher/escher.htm