Alaska Performance Standards
Grade 6
Geometry
The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.
Lessons (9)
Introduces students to acute, obtuse, and right angles as well as relationships between angles formed by parallel lines crossed by a transversal.
Students learn about classifying angles by their measure and in relation to angles formed by two lines crossed by a transversal.
Outlines the approach to building fractals by cutting out portions of plane figures.
Explores lines, planes, angles, and polygons in tessellations.
Introduces students to the idea of finding number patterns in the generation of several different types of fractals.
Examines plane symmetry.
Introduces all of the 2 variable function and prisoner/escapee notions necessary to understand the Mandelbrot set.
Introduces students to concepts of transformations.
Explore the mathematical nature of art and tilings and looks at the role of math in nature and our culture.
Activities (16)
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.
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.
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.
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.
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.
Generate complicated geometric fractals by specifying starting polygon and scale factor.
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.
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.
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.
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.
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.
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.
Play the Chaos Game by experimenting with probabilities. Learn about an apparently random process with a not-so-random, geometric fractal result.
Explore fractals by investigating the relationships between the Mandelbrot set and Julia sets.
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.
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