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Organization: North Carolina Standard Course of Study
Grade Band: Pre-Calculus
Standard Goal: The learner will use relations and functions to solve problems.
| An Introduction to Arithmetic and Geometric Sequences |
Lesson: Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.
| | An Introduction to Arithmetic and Geometric Sequences |
Lesson: Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.
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Two Variable Function Pump |
Activity: Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form. This is an introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.
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Sequencer |
Activity: Learn about number patterns in sequences and recursions by specifying a starting number, multiplier, and add-on. The numbers in the sequence are displayed on a graph, and they are also listed below the graph.
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| Introduction to Fractals: Infinity, Self-Similarity and Recursion |
Lesson: Introduces students to the ideas involved in understanding fractals.
| | Introduction to Fractals: Infinity, Self-Similarity and Recursion |
Lesson: Introduces students to the ideas involved in understanding fractals.
| | Patterns in Fractals |
Lesson: Introduces students to the idea of finding number patterns in the generation of several different types of fractals.
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Tortoise and Hare Race |
Activity: Step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence and limits to an infinite sequence.
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Another Hilbert Curve Generator |
Activity: Students work step-by-step through the generation of a different Hilbert-like Curve (a fractal made from deforming a line by bending it), allowing them to explore number patterns in sequences and geometric properties of fractals.
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Cantor's Comb |
Activity: Learn about fractions between 0 and 1 by repeatedly deleting portions of a line segment, and also learn about properties of fractals. Parameter: fraction of the segment to be deleted each time.
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Hilbert Curve Generator |
Activity: Step through the generation of a Hilbert Curve -- a fractal made from deforming a line by bending it, and explore number patterns in sequences and geometric properties of fractals.
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Koch's Snowflake |
Activity: Step through the generation of the Koch Snowflake -- a fractal made from deforming the sides of a triangle, and explore number patterns in sequences and geometric properties of fractals.
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Tortoise and Hare Race |
Activity: Step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence and limits to an infinite sequence.
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| Introduction to Fractals: Geometric Fractals |
Lesson: Outlines the approach to building fractals by cutting out portions of plane figures.
| | Introduction to Fractals: Infinity, Self-Similarity and Recursion |
Lesson: Introduces students to the ideas involved in understanding fractals.
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Cantor's Comb |
Activity: Learn about fractions between 0 and 1 by repeatedly deleting portions of a line segment, and also learn about properties of fractals. Parameter: fraction of the segment to be deleted each time.
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Directable Fire!! |
Activity: Run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos. Parameters: Probability that a tree will set fire to each of its eight neighbors.
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Flake Maker |
Activity: Create your own fractals by drawing a "line deformation rule" and stepping through the generation of a geometric fractal. Parameters: Grid type, number of bending points on the line.
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Fractured Pictures |
Activity: Generate complicated geometric fractals by specifying starting polygon and scale factor.
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Koch's Snowflake |
Activity: Step through the generation of the Koch Snowflake -- a fractal made from deforming the sides of a triangle, and explore number patterns in sequences and geometric properties of fractals.
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Sequencer |
Activity: Learn about number patterns in sequences and recursions by specifying a starting number, multiplier, and add-on. The numbers in the sequence are displayed on a graph, and they are also listed below the graph.
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Sierpinski's Carpet |
Activity: Step through the generation of Sierpinski's Carpet -- a fractal made from subdividing a square into nine smaller squares and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.
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Sierpinski's Triangle |
Activity: Step through the generation of Sierpinski's Triangle -- a fractal made from subdividing a triangle into four smaller triangles and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.
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Tortoise and Hare Race |
Activity: Step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence and limits to an infinite sequence.
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