Aligned Resources
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NCTM Grades 9-12 Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems
Lesson (...)
Lesson: This lesson utilizes the concepts of cross-sections of three-dimensional figures to demonstrate the derivation of two-dimensional shapes.
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: 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: Explore cross sections of different geometric solids: cone, double cone, cylinder, pyramid, and prism. Manipulate the cross section with slider bars, and see how the graphical representation changes.
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.
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: InteGreat! allows the user to visually explore the idea of integration through approximating the integral value with partitions. The user controls the number of partitions, the upper and lower limits, and the method used to estimate the integral.
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: Plot ordered pairs on the graph, and they will be connected in the order that they are input. This enables you to decide how the pairs should be connected, rather than having the computer connect them from left to right.
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: 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.
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