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North Carolina Standard Course of Study Advanced Functions and Modeling Algebra:Competency Goal 2: The learner will use functions to solve problems.
Lesson (...)
Lesson: Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.
Activity (...)
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.
Activity: Enter a set of data points, then derive a function to fit those points. Manipulate the function on a coordinate plane using slider bars. Learn how each constant and coefficient affects the resulting graph.
Activity: Generate complicated geometric fractals by specifying starting polygon and scale factor.
Activity: A more advanced version of Slope Slider, this activity allows the manipulation of the constants and coefficients in any function thereby encouraging the user to explore the effects on the graph of the function by changing those numbers.
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.
Activity: Enter a complex value for "c" in the form of an ordered pair of real numbers. The applet draws the fractal Julia set for that seed value.
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.
Activity: Enter a set of data points and a function or multiple functions, then manipulate those functions to fit those points. Manipulate the function on a coordinate plane using slider bars. Learn how each constant and coefficient affects the resulting graph.
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.
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.
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.
Activity: Explore fractals by investigating the relationships between the Mandelbrot set and Julia sets.
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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