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Fractals using Virtual Manipulatives

Fractals using Virtual Manipulatives. Mary Corkery. Definition. Fractal: Patterns can be found in many objects in nature, including broccolli. This pattern of repeated shapes at different scales is part of fractal geometry. Math Objectives. Understand Iteration Self-Similarity Fractal.

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Fractals using Virtual Manipulatives

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  1. Fractals usingVirtual Manipulatives Mary Corkery

  2. Definition • Fractal: • Patterns can be found in many objects in nature, including broccolli. This pattern of repeated shapes at different scales is part of fractal geometry. Select Math ,Gizmos and Fractals

  3. Math Objectives • Understand • Iteration • Self-Similarity • Fractal Select Math ,Gizmos and Fractals

  4. Mass Curriculum Frameworks • G.G.5 • G.M.3 • 10.P.1 Select Math ,Gizmos and Fractals

  5. Language Goals ELPBO Objectives • Essential vocabulary R.1.14.a • Fractals, Iteration, Self-Similarities, means • Use Essential vocab in Speaking W.1.8.b • Use Essential vocab in Writing W.1.8.b • Show understanding of Essential vocab by Listening to teacher and group members S.1.2 Select Math ,Gizmos and Fractals

  6. WWW.SelectMath.com Select Math ,Gizmos and Fractals

  7. WWW.SELECTMATH.COM Select Math ,Gizmos and Fractals

  8. Essential questions • What is a Iteration? • What is Self-Similarity? • What is a Fractal? Select Math ,Gizmos and Fractals

  9. What is a Iteration? • Process of repeating the same procedure over and over again Select Math ,Gizmos and Fractals

  10. What is Self-Similarity? • When we look at the smaller and smaller details of a figure, and we find the same geometric characteristics as the original form. • Self-Similarity is an important characteristic of Fractals Select Math ,Gizmos and Fractals

  11. What is a Fractal? • Fractal is a geometric figure created by iterations. The pattern’s structure appears to go on infinitely. Select Math ,Gizmos and Fractals

  12. FractalsSierpinski Triangle Iteration 0 Select Math ,Gizmos and Fractals

  13. FractalsSierpinski – Iteration -1 Select Math ,Gizmos and Fractals

  14. FractalSierpinksi – Iteration 2 Select Math ,Gizmos and Fractals

  15. FractalSierpinski – Iteration 3 Select Math ,Gizmos and Fractals

  16. FractalsThe Koch SnowflakeThe Algorithm • Step One. • Start with a large equilateral triangle. • Step Two. • Make a Star. • Divide one side of the triangle into three equal parts and remove the middle section. • Replace it with two lines the same length as the section you removed. • Do this to all three sides of the triangle. • Do it again and again. • Do it infinitely many times and you have a fractal. Select Math ,Gizmos and Fractals

  17. Fractals –Koch Snowflake Steps 1-4 Select Math ,Gizmos and Fractals

  18. Dynamic Fractals Select Math ,Gizmos and Fractals

  19. Dynamic Fractals Select Math ,Gizmos and Fractals

  20. Dynamic Fractals Select Math ,Gizmos and Fractals

  21. Dynamic Fractals Select Math ,Gizmos and Fractals

  22. Dynamic Fractals Select Math ,Gizmos and Fractals

  23. Dynamic Fractals Select Math ,Gizmos and Fractals

  24. Dynamic Fractals Select Math ,Gizmos and Fractals

  25. Lesson Objectives Content Objectives. • Understand iteration • Understand self-similarity • Understand Fractals • Language Objectives • Discuss iteration in small groups • Discuss self-similarity in small groups • Describe how to create a Fractal Select Math ,Gizmos and Fractals

  26. Materials • Suggested materials for a class of 15 students • Overhead projector • White board • Ruler • Geometry book( Glencoe) • Markers • Graph paper Select Math ,Gizmos and Fractals

  27. Launch • Vocabulary • Think, Pair, Share,Worksheet • Connect to prior knowledge • Iteration • Similar triangles,polygons,… Select Math ,Gizmos and Fractals

  28. Explore • Practice/Application • Students will work in their groups and use white boards to draw successive fractal iterations. Select Math ,Gizmos and Fractals

  29. Accommodations • Teacher will circulate among student groups to answer questions and make sure that the groups are on the right track Select Math ,Gizmos and Fractals

  30. Summary /Review • Students will summarize the goals of the lessons by orally presenting their solutions on the white board to the entire class Select Math ,Gizmos and Fractals

  31. Bibliography • Geometry Glencoe mathematics • Massachusetts mathematics curriculum • English language Proficiency Benchmarks and Outcomes for ELLs (ELPBO ) Select Math ,Gizmos and Fractals

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