Aligned Resources
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Alaska Performance Standards Grade 9 Geometry:The student demonstrates a conceptual understanding of geometric drawings or constructions.
Lesson (...)
Lesson: Introduces students to acute, obtuse, and right angles as well as relationships between angles formed by parallel lines crossed by a transversal.
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: 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: Build your own polygon and transform it in the Cartesian coordinate system. Experiment with reflections across any line, revolving around any line (which yields a 3-D image), rotations about any point, and translations in any direction.
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: 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: Determine the fractal dimensions of several line-deformation fractals. Input the scale factor and number of similar copies, and the dimension will be calculated. Fractal Dimensions is one of the Interactivate assessment explorers.
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: Measure angles, distances, and areas in several different images (choices include maps, aerial photos, and others). A scale feature allows the user to set the scale used for measuring distances and areas.
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: 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: Play the Chaos Game by experimenting with probabilities. Learn about an apparently random process with a not-so-random, geometric fractal result.
Activity: Explore fractals by investigating the relationships between the Mandelbrot set and Julia sets.
Activity: Explore the world of translations, reflections, and rotations in the Cartesian coordinate system by transforming squares, triangles and parallelograms. Parameters: Shape, x or y translation, x or y reflection, angle of rotation.
Activity: Build your own polygon and transform it in the Cartesian coordinate system. Experiment with reflections across any line, rotations about any point, and translations in any direction. Parameters: Shape, x or y translation, x or y reflection, angle of rotation
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