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North Carolina Standard Course of Study Integrated Mathematics III Geometry and Measurement:Competency Goal 2: The learner will use properties of geometric figures to solve problems.
Lesson (...)
Lesson: Outlines the approach to playing the chaos game and how it relates to geometric fractals.
Lesson: Outlines the approach to building fractals by cutting out portions of plane figures.
Lesson: Introduces students to the ideas involved in understanding fractals.
Lesson: Looks at how irregular fractals can be generated and how they fit into computer graphics.
Lesson: Introduces students to lines, rays, line segments, and planes.
Lesson: Introduces students to the idea of finding number patterns in the generation of several different types of fractals.
Lesson: Students learn about how probability can be represented using geometry.
Lesson: A capstone lesson to allow students to build a working definition of fractal.
Lesson: Introduces all of the 2 variable function and prisoner/escapee notions necessary to understand the Mandelbrot set.
Activity (...)
Activity: Practice your knowledge of acute, obtuse, and alternate angles. Also, practice relationships
between angles - vertical, adjacent, alternate, same-side, and corresponding. Angles is one of
the Interactivate assessment explorers.
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: Learn the relationship between perimeter and area. A shape will be automatically generated with the perimeter that you choose. Calculate the area of this shape. Area Explorer is one of the Interactivate assessment explorers.
Activity: Build a "floor tile" by dragging the corners of a quadrilateral. Learn about tessellation of quadrilateral figures when the shape you built is tiled over an area.
Activity: Generate complicated geometric fractals by specifying starting polygon and scale factor.
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: Learn the relationship between perimeter and area. A shape will be automatically generated with the area that you choose. Calculate the perimeter of this shape. Perimeter Explorer is one of the Interactivate assessment explorers.
Activity: This activity operates in one of two modes: auto draw and create shape mode, allowing you to explore relationships between area and perimeter. Shape Builder is one of the Interactivate assessment explorers.
Activity: Learn the relationship between perimeter and area. A random shape will be automatically generated. Calculate the area and perimeter of this shape. Shape Explorer is one of the Interactivate assessment explorers.
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: Learn about how the Pythagorean Theorem works through investigating the standard geometric proof. Parameters: Sizes of the legs of the triangle.
Activity: Manipulate dimensions of polyhedra, and watch how the surface area and volume change. Parameters: Type of polyhedron, length, width and height. Surface Area and Volume one of the Interactivate assessment explorers.
Activity: Create a tessellation by deforming a triangle, rectangle or hexagon to form a polygon that tiles the plane. Corners of the polygons may be dragged, and corresponding edges of the polygons may be dragged. Parameters: Colors, starting polygon.
Activity: Explore fractals by investigating the relationships between the Mandelbrot set and Julia sets.
Activity: Calculate the area of a triangle drawn on a grid. Learn about areas of triangles and about the Cartesian coordinate system. Triangle Explorer is one of the Interactivate assessment explorers.
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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