Chapter 11: Lessons and Activities

Activity Name Activity Description
TransmoGrapher Students 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.
Floor Tiles Students learn about tessellation on quadrilateral figures by dynamically changing the shape of the quadrilateral through dragging corners.
Tessellate! Students deform 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.
Flake Maker Students create their own fractals by specifying a "line deformation rule" and stepping through the generation of a geometric fractal. Parameters: Grid type, number of bending points on the line.
Coloring Multiples in Pascal's Triangle Students color numbers in Pascal's Triangle by rolling a number and then clicking on all entries that are multiples of the number rolled, thereby practicing multiplication tables investigating number patterns, and investigating fractal patterns.
Coloring Remainders in Pascal's Triangle Students color numbers in Pascal's Triangle by rolling a number and then clicking on all entries that have the same remainder when divided by the number rolled, thereby practicing multiplication tables, investigating number patterns, and investigating fractal patterns.
Surface Area & Volume Students manipulate dimensions of polyhedra, and watch how the surface area and volume change. Parameters: Type of polyhedron, length, width and height.

Lesson Name General Lesson Description
Surface Area and Volume Introduces students to the concepts of surface area and volume.
Geometry in Tessellations Explores lines, planes, angles and polygons in tessellations.
Symmetry in Tessellations Examines plane symmetry.
Visual Patterns in Tessellations Explores the mathematical nature of art and tilings and looks at the role of math in nature and our culture.
Translations, Reflections, and Rotations Introduces students to the concepts of transformations.
Introduction to Fractals: Infinity, Self-Similarity and Recursion Introduces the ideas and motivates the activities.
Geometric Fractals Outlines the approach to building fractals by cutting out portions of plane figures.