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Exploring Transformations and Tessellations: A Journey in Geometry

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Discover the fascinating world of transformations and tessellations in this engaging mathematical activity. Learn to identify and create transformed images using translations, reflections, and rotations. Follow step-by-step instructions to manipulate and repeat designs, culminating in your very own tessellation project. Access online resources for interactive practice and exploration of tessellations. Enhance your understanding of geometric concepts while having fun creating stunning visual patterns!

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Exploring Transformations and Tessellations: A Journey in Geometry

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  1. Tessellate! Math Standard 4.17c

  2. Introductory Questions • Take a look at this picture. • Can you identify the original drawing? • How do you think this was created?

  3. Transformations • The design was created by transforming a polygon into a new design. • There are three types of transformations: • Translation (slide) • Reflection (flip) • Rotation (turn) • Let’s look at each one!

  4. Translation • A translation (slide) is a transformation in which an image is formed by moving every point on a figure the same distance in the same direction. starting figure

  5. Reflection • A reflection (flip) is a transformation in which a figure is flipped over a line called the line of reflection. All corresponding points in the image and original image are equally distant from the line of reflection. Line of reflection

  6. Rotation • A rotation (turn) is a transformation in which an image is formed by turning the original image about a point.

  7. Practice • How has this image been transformed? • Translation (slide) • Reflection (flip) • Rotation (turn) • Answer: Rotation (turn)

  8. Practice • How has this image been transformed? • Translation (slide) • Reflection (flip) • Rotation (turn) • Answer: Reflection (flip) • Where is the line of reflection?

  9. Practice • How has this image been transformed? • Translation (slide) • Reflection (flip) • Rotation (turn) • Answer: Translation (slide)

  10. Putting It Together • Now we are going to practice manipulating an image and repeating it over and over to create our own tessellation. • http://www.shodor.org/interactivate/activities/tessellate/

  11. Computer Time • Now that you know about transforming figures and tessellations, you can visit “Tessellation Town” to practice what you have learned. • Logon to Mrs. Ashley’s portaportal (aashley) and go to fourth grade-Tessellation Town.

  12. Resources • Mrs. Stone’s Fifth Grade Math Class tessellation projects • Tessellate! http://www.shodor.org/interactivate/activities/tessellate/ • Tessellation Town http://www.mathcats.com/explore/tessellationtown.html

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