Fractals using Virtual Manipulatives

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Fractals usingVirtual Manipulatives

• Mary Corkery

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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.

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Math Objectives

• Understand
• Iteration
• Self-Similarity
• Fractal

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Mass Curriculum Frameworks

• G.G.5
• G.M.3
• 10.P.1

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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

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WWW.SelectMath.com
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WWW.SELECTMATH.COM
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Essential questions

• What is a Iteration?
• What is Self-Similarity?
• What is a Fractal?

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What is a Iteration?

• Process of repeating the same procedure over and
  over again

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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

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What is a Fractal?

• Fractal is a geometric figure created by
  iterations. The patterns structure appears to
  go on infinitely.

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FractalsSierpinski Triangle Iteration 0
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FractalsSierpinski Iteration -1
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FractalSierpinksi Iteration 2
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FractalSierpinski Iteration 3
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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.

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Fractals Koch Snowflake Steps 1-4
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Dynamic Fractals
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Dynamic Fractals
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Dynamic Fractals
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Dynamic Fractals
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Dynamic Fractals
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Dynamic Fractals
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Dynamic Fractals
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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

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Materials

• Suggested materials for a class of 15 students
• Overhead projector
• White board
• Ruler
• Geometry book( Glencoe)
• Markers
• Graph paper

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Launch

• Vocabulary
• Think, Pair, Share,Worksheet
• Connect to prior knowledge
• Iteration
• Similar triangles,polygons,

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Explore

• Practice/Application
• Students will work in their groups and use white
  boards to draw successive fractal iterations.

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Accommodations

• Teacher will circulate among student groups to
  answer questions and make sure that the groups
  are on the right track

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Summary /Review

• Students will summarize the goals of the lessons
  by orally presenting their solutions on the white
  board to the entire class

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Bibliography

• Geometry Glencoe mathematics
• Massachusetts mathematics curriculum
• English language Proficiency Benchmarks and
  Outcomes for ELLs (ELPBO )