Patterns

Every day of our lives, we observe, use and create a variety of patterns. In the morning, we walk across the tile pattern on the bathroom floor. In school, children use patterns to trace pictures or make shapes. At work, we analyze data to see if there is a pattern. Patterns can be visual, numerical, verbal, natural, man-made or many other forms. In this module students create and extend patterns. Lesson 1 Introducing Patterns Students are asked to analyze pictures and identify the pattern. They also develop a definition of pattern. Lesson 2 Introduction to Tessellations Students create their own tessellations with regular polygons. Lesson 3 Angling for Patterns Students explore the angles of regular polygons and the vertex of a tessellation. Lesson 4 Translating the Language of Tessellations Students investigate transformations and symmetries. They also make their own tiles to tessellate. Lesson 5 Introduction to Polyhedra Students move the concept of tessellation to three dimensions to explore the five platonic solids. Lesson 6 Building Polyhedra Students use tools to draw patterns for regular polyhedra. The patterns are then used to construct models of the five platonic solids. Lesson 7 Feeling A Bit Edgy Students use their models to discover the relationship among the vertices, edges and faces of regular polyhedra. Lesson 8 Fractal Patterns Students are introduced to the language of fractals. They practice iteration by creating the Koch curve. Lesson 9 Recursive Relations Building on the idea of iteration from the previous lesson, students are introduced symbolic iteration. Lesson 10 Square and Triangular Numbers Students explore pictorial and algebraic representations of square and triangular numbers. Lesson 11 Polygonal Number Patterns Students represent pentagonal and hexagonal numbers pictorially. They also utilize difference tables to predict a future polygonal number. Lesson 12 The Fibonacci Sequence The Fibonacci numbers are introduced using the story of successive rabbit generations. Lesson 13 The Golden Ratio and Fibonacci Numbers Students investigate the Golden Ratio and its relationship to the Fibonacci numbers. Lesson 14 Pascal's Triangle and Algebraic Patterns Students create Pascal's triangle and utilize it to expand expressions of the form (x+1)^n. Lesson 15 Pattern Collections Students apply their knowledge of various types of patterns to present and evaluate pattern collections of classmates. Compare this module to traditional course topics in the Matrix of Course Competencies. If one of the lessons has a link, you can preview that lesson. Other modules: Beat Ratios Functions Exp. Growth Data & Graphs Representing Data Finance Geometry Sampling Non-linear Behavior Linear Behavior Sets and Logic Patterns Probability Systems Right Tri. Trig.