Interactive
CK-12 Foundation

Exponential Growth: Exponential, Fractal Snowflakes

For Students 10th - 12th Standards
Examine an exponential growth model. Using a fractal, learners calculate the perimeters of each stage. When comparing the consecutive perimeters, a pattern emerges. They use the pattern to build an equation and make conclusions.
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Alice in Fractalland

For Teachers 4th - 8th Standards
Take your class on a field trip to Fractalland where they'll learn all about number and shape patterns. Based on Disney's movie Alice in Wonderland, this resource takes young mathematicians on an adventure as they explore patterns in...
Lesson Plan
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Geometric Fractals and the Chaos Game

For Teachers 8th - 10th
Students define fractals and patterns. They explore how a seemingly random process can result in a pattern. Students practice probability and fractions skills by playing the chaos game online.
Lesson Plan
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Fractals

For Teachers 10th - Higher Ed
Students explore the concept of fractals. In this fractal lesson plan, students use applets to explore Koch's Snowflake, Sierpinski's Triangle, and other fractals. Students develop these concepts through exploration and teacher guided...
Lesson Plan
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Using Cabri Geometry to Create Fractals

For Teachers 9th - 12th Standards
Learners construct the Sierpinski Triangle using Cabri Jr. They use a step-by-step guide to construct the Sierpinski Triangle on their graphing calculator and then discuss the formula for constructing a nth stage Sierpinski Triangle.
Lesson Plan
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Fun With Fractals

For Teachers 7th - 11th
Students use fractals to analyze nature. In this geometry lesson, students work in groups using technology and math to communicate. They identify where in the real world fractal can be seen.
Lesson Plan
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Finding Patterns in Fractals

For Teachers 7th - 8th
Students discover patterns and sequences. They use a website to explore patterns and fractals. Students share their discovery of fractals and their patterns with the class. They develop a list of patterns used in everyday life.
Lesson Plan
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Fractal and the Dragon Curve

For Teachers 11th - 12th
Students explore Fractal designs. In this geometry lesson, students observe the different polygons created in nature and relate it to math. They define polygons on planes and rotate polygons about a point.
Lesson Plan
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Fractals Rock

For Teachers 9th - 11th
Students identify the repeated sequences of a pattern. In this geometry lesson, students identify fractals in patterns and nature. They construct a fractal tree and make conjectures.
Lesson Plan
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Fractals Rock: Investing the Fractal Tree

For Teachers 9th - 10th
Students investigate the relationship between fractals and sequences. In this geometry lesson, students build a fractal tree. They investigate different career fields where fractals are used in the real world.
Lesson Plan
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Creating Fractals

For Teachers 8th - 10th
Students solve problems using fractals. For this geometry lesson, students identify properties of fractals. They find patterns in their surroundings and relate it to the real world and math.
Lesson Plan
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The Dragon Curve Fractal

For Teachers 8th - 11th
Pupils identify the properties of a dragon curve. In this geometry instructional activity, students identify sequences and patterns as they solve fractals. They investigate patterns found in nature.
Lesson Plan
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Fractals: Koch Snowflake

For Teachers 9th - 11th
Students investigate the properties of Koch's snowflake. In this geometry lesson plan, students investigate fractals and patterns. They create Koch's snowflake using Cabri software.
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The Fractal Geometry of Nature

For Teachers 8th - 10th
Students identify patterns found in nature. In this algebra lesson, students model situation in nature using fractals. They investigate biological geometric structures and draw conclusion based on geometric concepts.
Lesson Plan
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The Fractal Coast

For Teachers 9th - 11th
Students investigate measuring as it relates to the real world. In this geometry lesson, students measure distances as they discuss fractals and how it relates to measuring. They measure both linear and non-linear distances.
Lesson Plan
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Fractal Fern

For Teachers 8th - 10th
Students identify the location of coordinate pairs of an image. For this geometry lesson, students perform transformation and identify the image and pre-image point of location. They apply the concept of fractals to...
Lesson Plan
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Pyramid in The Desert

For Teachers 9th - 11th
Students investigate the Sierpinski triangle and calculate the ratio and area of the triangle. In this fractals instructional activity, students calculate parts of a Sierpincki triangle. They use Google Earth to help them construct the...
Lesson Plan
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Why Study Fractals?

For Teachers 9th - 12th
High schoolers explore the concept of fractals. In this fractals activity, students use the website to research where fractals occur in nature. High schoolers research what fractals are and how fractals are used to solve real world...
Lesson Plan
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Patterns in Fractals

For Teachers 8th - 10th
Students explore the concept of fractal patterns. In this fractal pattern instructional activity, students use an applet about the Hilbert Curve to answer questions about rectangles and other polygons. Students derive the fractal pattern...
Lesson Plan
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The Sierpinski Triangle

For Teachers 9th - 10th
Students investigate the Sierpinski triangle. In this geometry lesson, students define fractal curves and its relationship to triangles. They identify repeating sequences and relate it to fractals.
Lesson Plan
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The Mandelbrot Set

For Teachers 10th - 12th
Students explore the concept of Mandelbrot sets and Julia sets. In this Mandelbrot and Julia set lesson, students use a function integrator applet to investigate two-variable function iterations. Students use Julia set and Mandelbrot set...
Lesson Plan
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Pascal's Triangle

For Teachers 7th - 11th
Students explore the concept of Pascal's Triangle. In this Pascal's Triangle lesson, students use an applet called 'Coloring Multiples' to explore Pascal's Triangle. Students develop patterns starting with various numbers in Pascal's...
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The Chaos Game

For Teachers 6th - 12th
Students measure and predict the behavior of a fractal.  In this investigative lesson plan students divide into groups, and participate in an activity that includes drawing triangles and coloring vertices. 
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Koch Snowflake

For Teachers 9th - 10th
Young scholars investigate Koch's Snowflake. In this geometry lesson, students identify the properties of creating Koch's snowflake. They solve problems dealing with fractals and patterns.

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