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North Carolina Standard Course of Study Technical Mathematics I Geometry and Measurement:Competency Goal 2: The learner will measure and apply geometric concepts to solve problems.
Lesson (...)
Lesson: Introduces students to quadrilaterals with an emphasis on defining characteristics of parallelograms, rectangles, and trapezoids.
Lesson: Introduces students to acute, obtuse, and right angles as well as relationships between angles formed by parallel lines crossed by a transversal.
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 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.
Lesson: Introduces students to concepts of transformations.
Lesson: Explore the mathematical nature of art and tilings and looks at the role of math in nature and our culture.
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: Calculate the length of one side of an automatically generated right triangle by using the Pythagorean Theorem, and then check your answers. Pythagorean 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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