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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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PPT
Curated OER

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...
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Lesson Plan
Curated OER

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.
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Lesson Plan
Curated OER

Fractals

For Teachers 10th - Higher Ed
Students explore the concept of fractals. In this fractal instructional activity, students use applets to explore Koch's Snowflake, Sierpinski's Triangle, and other fractals. Students develop these concepts through exploration and...
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Lesson Plan
Curated OER

Fractals, An Inquiry

For Teachers 6th - 8th
Learners observe and discuss several different fractal drawings and relate them to patterns they see in nature. They use an online fractal tool to create and modify a fractal image and then create their own fractal image with paint.
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Lesson Plan
Curated OER

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.
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Lesson Plan
Curated OER

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.
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Lesson Plan
Curated OER

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.
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Lesson Plan
Curated OER

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.
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Lesson Plan
Curated OER

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.
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Lesson Plan
Curated OER

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.
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Lesson Plan
Curated OER

The Dragon Curve Fractal

For Teachers 8th - 11th
Young scholars identify the properties of a dragon curve. In this geometry lesson, students identify sequences and patterns as they solve fractals. They investigate patterns found in nature.
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Lesson Plan
Curated OER

Creating Fractals

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

The Fractal Geometry of Nature

For Teachers 8th - 10th
Young scholars 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.
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Lesson Plan
Curated OER

Fractal Fern

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

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 lesson, students calculate parts of a Sierpincki triangle. They use Google Earth to help them construct the different parts...
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Lesson Plan
Curated OER

Why Study Fractals?

For Teachers 9th - 12th
Students explore the concept of fractals. In this fractals lesson, students use the website to research where fractals occur in nature. Students research what fractals are and how fractals are used to solve real world problems.
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Lesson Plan
Curated OER

Fractal Fraction Fun

For Teachers K - 8th
Students discover the interesting patterns and shapes referred to as "fractals."  In this geometry lesson, students utilize pieces of colored construction paper to create the branches of a fractal tree.  Students discuss the rules and...
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Lesson Plan
Curated OER

Fractals, An Inquiry: Day 4

For Teachers 6th - 8th
Students put their growing understanding of the scientific inquiry process to work. They use paint to implement their plans to experiment with how changing one aspect of the fractal making process influences their appearance.
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Lesson Plan
Curated OER

Patterns in Fractals

For Teachers 8th - 10th
Pupils explore the concept of fractal patterns. In this fractal pattern lesson, students use an applet about the Hilbert Curve to answer questions about rectangles and other polygons. Pupils derive the fractal pattern when dividing...
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Lesson Plan
Curated OER

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.
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Lesson Plan
Curated OER

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...
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Lesson Plan
Curated OER

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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Lesson Plan
Curated OER

Fractals: Koch Snowflake

For Teachers 9th - 11th
Pupils investigate the properties of Koch's snowflake. For this geometry lesson, students investigate fractals and patterns. They create Koch's snowflake using Cabri software.

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