Quilters have been practicing geometric principles for centuries. Since straight seams are easier to sew than curved ones, the grid naturally evolved as the basis for their designs. This book is a resource for experimenting with traditional patchwork quilt patterns. It provides students a hands-on understanding of geometric concepts. It contains…

Pattern manifests itself in many ways through properties such as symmetry, repetition, translation, and illusion. This guide, appropriate for use with grades 6-12, presents patterns that are formed entirely by straight lines, yet appear to contain or be formed by curves. Exploring these geometrical shapes offers an opportunity to discover various…

The Golden Section, also known as the "Golden Mean" and the "Divine Proportion," is a ratio found in art and nature that has mathematical properties. This book explores these geometric and algebraic properties in a variety of activities. Construction problems, designs using the pentagon and pentagram, and opportunities to work…

Mathematics can be used to analyze musical rhythms, to study the sound waves that produce musical notes, to explain why instruments are tuned, and to compose music. This book explores the relationship between mathematics and music through proportions, patterns, Fibonacci numbers or the Golden Ratio, geometric transformations, trigonometric…

This book explores a class of geometric patterns called tessellations, a pattern made up of one or more shapes which completely cover a surface without any gaps or overlaps. Focus in on one of the more elementary types of tessellations and investigation of them through concepts basic to art, geometry, and design. The seven chapters look at which…

This document presents activities and information related to Fibonacci numbers, which are based upon the Golden Ratio, in areas of the arts, sciences, and mathematics. The work is organized into eight chapters: (1) "Origins and Definitions"; (2) "Fibonacci Numbers in Nature"; (3) "Fibonacci Numbers in Art and…

The activities presented in this guide are designed for elementary age students, and intended to provide hands-on, integrated learning experiences. A learning station format is indicated for open ended activities which include a "Preliminary Activity: Free Exploration First!", an "Introductory Activity: Architect/Builder", and…

Investigated whether 3- to 6-year-olds in a Montessori school created more symmetrical than asymmetrical designs when working with building materials. Found that symmetry occurred in designs of children as young as age 3, with the tendency increasing with age. Examined the need for increased use of building materials for teaching symmetry in the…

Describes some developmental changes in children's free creations with pattern blocks and demonstrates how to build on this natural interest to teach Logo programing. (PK)

This updated reprint of a classic work presents design analysis of geometric patterns and information helpful to constructing mathematical drawings of industrial and achitectural features. Both simple and complex designs are given. Problems combine both algebra and geometry. The work is divided into six chapters which are further divided into…

This module, designed to help students find and identify various geometric shapes and solids, contains 26 worksheets. Topics covered by these worksheets include: identification and grouping of objects with particular patterns, work with pentagons, hexagons, spirals, and symmetry. Teaching suggestions are included. (MK)