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This guide contains hands-on mathematics activities to connect middle-school students to the traditional knowledge of their grandparents and elders. Because girls often lose interest in math at the middle-school level, and because women in some communities (especially in rural areas) are seldom involved in work with an obvious math basis, the activities explore common practices associated with women for generations. The guide has two sections. "Pieces of Mine: The Mathematics of Quilting" leads students into the worlds of plane geometry, symmetry, and tessellations. Through quilting, students take a hands-on approach to mathematics, spatial sense, culture, and history. Activities include a symmetry hunt, 2-D geometry with pattern blocks, and designing quilt patterns. "Crafty Mathematician: Making Art through Mathematics" provides mathematical skill-building activities while helping learners understand the math embodied in many craft activities. Students explore Cartesian coordinates, 2-D and 3-D geometry, measurement, symmetry, and volume. Activities include making ornaments, pictures, boxes, and a kaleidoscope. Each section includes an introduction, cautions, community connections, benefits to learners and communities, ideas for additional projects, readings, leader background information, activity descriptions, and handouts. (SV)

This document describes a game that provides students with practice in recognizing the point symmetry of designs. It contains information on the objective of the game, game preparation, and rules for playing. Play cards are included (four to a page). (ASK)

Presents an educational mathematical activity from Africa. Shows how one child explored the game of Julirde, a game of the mosque emphasizing problem solving and symmetry. Offers several suggestions for exploring the game from the central African country of Cameroon in the elementary school mathematics classroom. (ASK)

Explains from fundamentals how the periodic table became the way it is and in doing so, touches on quantum theory and the important concept of symmetry. (SAH)

Describes how students connect culture and mathematics by using tessellating and symmetrical patterns in the designs of architecture, pottery, blankets, and baskets as models to create geometric designs for a quilt. (Author/YDS)

Helps students identify the animal that corresponds to the year of their birth according to the Chinese zodiac. Defines the structure of the Chinese zodiac so that the subsets of compatibles and opposites form closed substructures with interesting mathematical properties. (ASK)

Symmetry is an important mathematical concept that plays an extremely important role as a problem solving technique. Presents examples of problems from several branches of mathematics that can be solved using different types of symmetry. Discusses teachers' attitudes and beliefs regarding the use of symmetry in the solutions of these problems. (Contains 21 references.) (Author/ASK)

Presents two activities on addition, one for classifying and one for symmetry. (ASK)

Discusses the geometric features of a building called the Alhambra in a city in the southernmost region of Australia called Granada. Describes plane patterns and analyzes those patterns while focusing on the plane symmetry. (ASK)

Examines activities and children's thinking in four main areas of the Geometry Standard in the National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics": (1) properties of shapes; (2) locations and spatial relationships; (3) transformations and symmetry; and (4) visualization. (Author)

Describes a unit of study focusing on tessellations to show students another view of mathematics. (Author)

Presents an investigation that guides students in detecting vertical and horizontal lines of symmetry as well as rotational symmetry in the decorative designs of wrought-iron doors. (ASK)

Features activities designed to enhance students' spatial reasoning ability combining geometry, language arts, and visual arts. (ASK)

Discussion material and exercises related to pre-algebra groups are provided in this five chapter manual. Chapter 1 (mappings) focuses on restricted domains, order of operations (parentheses and exponents), rules of assignment, and computer extensions. Chapter 2 considers finite number systems, including binary operations, clock arithmetic, properties of operational systems, multiplicative systems, and subtraction/division. Other operational groups are considered in chapter 3. Additional topics include the cancellation law, non-commutative groups, and designs from finite systems. Chapter 4 focuses on integers, discussing set of integers, (Z,+) as a commutative group, subtraction, multiplication/division, order of operations, exponents, and absolute value. Transformational geometry is the major focus of chapter 5. Topics discussed in this chapter include: symmetry, plotting points, translations, translations and groups, line reflections, rotations, isometries, and dilation. Each chapter concludes with a set of review questions. In addition, a set of cumulative review questions for chapters 1-3 is included. (JN)

Learning objectives and suggested activities, monitoring procedures and resources for the Washington K-3 Small Schools Science Curriculum are based on the rationale that "young children need the opportunity to observe, classify, predict, test ideas again and again in a variety of contexts, ask questions, explain, discuss ideas, fail, and succeed. Along the way they will manipulate ideas and materials and, to a great extent, exercise control over their own effort. They can be questioned in such a way as to suggest relationships not previously recognized or have their attention directed to unnoticed events." The curriculum is divided into seven scope areas: change, cycles, energy, environment, organisms, property of matter, and symmetry. Activities presented enable the student to: identify changes in plants and animals due to maturation; notice daily weather changes; understand seasonal changes; describe different forms of energy used in daily experience; classify things as living or non-living, plant or animal; and group objects according to color, shape, weight, size and texture. Observing, discussing, poetry and story writing, chart keeping, scrapbook making and arranging teacher-supplied pictures in sequential order are suggested as monitoring techniques. Discussions of format, goals for the Washington Common Schools, and science program goals are included. (NEC)

This document is the seventh of seven units developed by the Math Network Curriculum Project. Each unit, designed to be a 2-week module, is a teacher's guide which includes detailed directions along with the courseware and software needed. Teacher intervention in the non-computer activities that begin each unit is required, and the consistent use of small-group instruction makes the units usable in a standard classroom if two microcomputers are present. The Turtle Symmetry Unit helps students to learn to identify and draw designs by employing the principles of mirror symmetry and rotational symmetry. They also study and create "families" of designs--sets of designs which have common characteristics yet differ in patterned ways. This unit requires class use of the Turtleworks computer program (developed by Bill Finzer) and included with the teacher's guide to Turtle Geometry. It was developed for use on a Commodore PET Computer with at least 16K of RAM using 4.0 BASIC. (MNS)

Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for students to explore a topic in depth and to make connections among representations. (ASK)

Presents activities that demonstrate how technology can help students discover the mathematics in nature. Claims that these experiences can clarify students' vision of the symmetry of beauty that fills the world beyond the computer. Concludes that the use of flexible software tools helps students explore how a shape is affected when they change such variables as the number of axes of rotations. (ASK)

The Minnesota School Mathematics and Science Teaching (MINNEMAST) Project is characterized by its emphasis on the coordination of mathematics and science in the elementary school curriculum. Units are planned to provide children with activities in which they learn various concepts from both subject areas. Each subject is used to support and reinforce the other where appropriate, with common techniques and concepts being sought and exploited. Content is presented in story fashion. The stories serve to introduce concepts and lead to activities. Imbedded in the pictures that accompany the stories are examples of the concepts presented. This unit provides students with a graphic method of addition which is useful both as a checking device and as an advance in what the student did in Unit 16. Three different techniques of using graphs and linear functions for addition are presented. This approach integrates ideas of geometric symmetry and with number relationships under addition and subtraction. Worksheets and commentaries to the teacher are provided and additional activities are suggested. (JP)

The Minnesota School Mathematics and Science Teaching (MINNEMAST) Project is characterized by its emphasis on the coordination of mathematics and science in the elementary school curriculum. Units are planned to provide children with activities in which they learn various concepts from both subject areas. Each subject is used to support and reinforce the other where appropriate, with common techniques and concepts being sought and exploited. Content is presented in story fashion. The stories serve to introduce concepts and lead to activities. Imbedded in the pictures that accompany the stories are examples of the concepts presented. This unit extends the work on symmetry presented in an earlier unit. As well as mirror reflections and translatory motion, symmetry about a point is developed. Activities focus on finding and creating patterns. In the process children are led to discover a number of geometric relationships. Worksheets and commentaries to the teacher are provided and additional activities are suggested. (JP)

The Minnesota School Mathematics and Science Teaching (MINNEMAST) Project is characterized by its emphasis on the coordination of mathematics and science in the elementary school curriculum. Units are planned to provide children with activities in which they learn various concepts from both subject areas. Each subject is used to support and reinforce the other where appropriate, with common techniques and concepts being sought and exploited. Content is presented in story fashion. The stories serve to introduce concepts and lead to activities. Imbedded in the pictures that accompany the stories are examples of the concepts presented. This unit presents a fundamental geometric concept of rigid motion. Two types of simple motion are presented to help children to find what patterns are unchanged by these motions; the two forms are simple translatory symmetry or repeating patterns, and bilateral symmetry or mirror reflection. In the process, children discover a number of geometrical relationships. This unit will provide the initial formative concepts necessary for various operations with symmetry. Worksheets and commentaries to the teacher are provided and additional activities are suggested. (JP)

This volume is the fourteenth in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by first-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of five groups of lessons and activities. The purposes and procedures for each activity are discussed. Examples of questions and discussion topics are given, and in several cases ditto masters, stories for reading aloud, and other instructional materials are included in the book. This unit continues the study of symmetry begun in Unit 7 of this series. The five sections are devoted to: (1) rotational symmetry, (2) repeating patterns and translational symmetry, (3) bilateral symmetry, (4) symmetry in sound and movement, and (5) other interesting patterns. (SD)

This volume is the seventh in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by kindergarten teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of four groups of activities. The purposes and procedures for each activity are discussed. Examples of questions and discussion topics are given, and in several cases ditto masters, stories for reading aloud, and other instructional materials are included in the book. The sections of this unit concern: (1) rotational symmetry, (2) repeating patterns, (3) bilateral symmetry; and (4) symmetry in sound and movement. A bibliography of books related to symmetry is provided for the teacher. (SD)

Presents the classroom activity of finding a Hamiltonian circuit that helps students understand the properties of geometric shapes and symmetry. (ASK)