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This paper describes a classroom, instructor-led activity designed to show how graphic calculators can be used to explore coordinate geometry. The activity involves digitizing an image of a hand and transforming the image through geometrical transformations. Teaching notes and calculator instructions are included as are blackline masters. Also included are Internet links to related resources. A vocabulary list student worksheet, table of coordinate points student worksheet, and a teacher's assessment rubric are appended. (MM)

Investigates the idea of the center of mass of a polygon and illustrates centroids of polygons. Connects physics, mathematics, and technology to produces results that serve to generalize the notion of centroid to polygons other than triangles. (KHR)

This nineteenth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 17. First, a time allotment for each of the chapters in Units 17 and 18 is given. Then, for each of the chapters in Unit 17, the goals for that chapter are discussed, the mathematics is explained, some teaching suggestions are given, answers to exercises are provided, and sample test questions are included. (DT)

This set of 11 teacher-prepared Learning Activity Packages (LAPs) in intermediate algebra covers number systems; exponents and radicals; polynomials and factoring; rational expressions; coordinate geometry; relations, functions, and inequalities; quadratic equations and inequalities; Quadratic functions; systems of equations and inequalities; complex numbers; and probability. Each unit contains a rationale for the material being covered; a list of behavioral objectives; a list of resources including texts (with reading assignments and problem sets specified), tape recordings, commercial games, filmstrips, and transparencies; a problem set for student self-evaluation; suggestions for advanced study; and references. (DT)

A set of 11 teacher-prepared Learning Activity Packages (LAPs) in beginning algebra, these units cover sets, properties of operations, operations over real numbers, open expressions, solution sets of equations and inequalities, equations and inequalities with two variables, solution sets of equations with two variables, exponents, factoring and polynomials, functions, and equations and their applications. Each unit contains a rationale for the material; a list of behavioral objectives; a list of resources including texts (with reading assignments and problem sets specified), tape recordings, commercial games, filmstrips, and transparencies; a problem set for student self-evaluation; suggestions for advanced study; and references. (DT)

This is one in a series of manuals for teachers using SMSG high school supplementary materials. The pamphlet includes commentaries on the sections of the student's booklet, answers to the exercises, and sample test questions. Topics covered include the coordinate system, distance formula, planes and first degree equations in three variables, the graph of a first degree equation in three variables, intersecting planes, and parametric equations. (MP)

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include a three dimensional coordinate system, distance formula, the equation of a plane, first degree equations in three variables, systems of first degree equations in three variables, and the line of intersection of two intersecting planes. (MP)

This is one in a series of manuals for teachers using SMSG high school supplementary materials. The pamphlet includes commentaries on the sections of the student's booklet, answers to the exercises, and sample test questions. Topics covered include definitions, parallel and perpendicular lines, distance formula, midpoint formula, linear equations, and circles. (MP)

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include graphs, slope, distance, mid-point, proof, equations, and circles. (MP)

This is unit twelve of a fifteen-unit SMSG secondary school text for high school students. The text is devoted almost entirely to mathematical concepts which all citizens should know in order to function satisfactorily in our society. Chapter topics include rigid motions and coordinates, squares and rectangles, and square roots and real numbers. (MP)

This is unit eleven of a fifteen-unit SMSG secondary school text for high school students. The text is devoted almost entirely to mathematical concepts which all citizens should know in order to function satisfactorily in our society. Chapter topics include coordinate geometry and problem analysis. (MP)

This is unit fifteen of a fifteen-unit SMSG secondary school text for high school students. The text is devoted almost entirely to mathematical concepts which all citizens should know in order to function satisfactorily in our society. Chapter topics include analyzing geometric figures and measurement. (MP)

This is part one of a two-part manual for teachers using SMSG high school text materials. The commentary is organized into four parts. The first part contains an introduction and a short section on estimates of class time needed to cover each chapter. The second or main part consists of a chapter-by-chapter commentary on the text. The third part is a collection of essays on topics that cannot conveniently be dealt with in the main part of the commentary in connection with a particular passage. The fourth part contains answers to Illustrative Text Items and the solutions to the problems. Chapter topcis include: introduction to formal geometry; sets, points, lines, and planes; distance and coordinate systems, angles; congruence; parallelism; and similarity. (MN)

This is part two of a two-part manual for teachers using SMSG high school text materials. The commentary is organized into four parts. The first part contains an introduction and a short section on estimates of class time needed to cover each chapter. The second or main part consists of a chapter-by-chapter commentary on the text. The third part is a collection of essays on topics that cannot conveniently be dealt with in the main part of the commentary in connection with a particular passage. The fourth part contains answers to Illustrative Test Items and the solutions to the problems. Chapter topics include: coordinates in a plane; perpendicularity, parallelism, and coordinates in space; directed segments and vectors; polygons and polyhedrons; and circles and spheres. (MN)

This is the teacher's guide to the SMSG text ANALYTIC GEOMETRY. The text is designed to be used as a one-semester course for 12th grade students. Included in this guide are: (1) suggested length of study for each chapter; (2) discussion of each chapter that is in the student text; (3) comments keyed to the pages of the student's text to provide explanation and background for the teacher; (4) answers to exercises; and (5) discussion of supplementary materials in the text. (RH)

This text provides a one-semester study of analytic geometry for secondary school students. It is designed for use at the 12th grade level. A deliberate effort was made to tie this text to previous SMSG texts; the usual language of sets, ordered pairs, number properties, etc. are included. This flavor is what distinguishes this book from others in the field. Ten chapters included in the book are: (1) Analytic Geometry; (2) Coordinates and the Line; (3) Vectors and their Applications; (4) Proofs by Analytic Methods; (5) Graphs and their Equations; (6) Curve Sketching and Locus Problems; (7) Conic Sections; (8) The Line and the Plane in 3-Space; (9) Quadric Surfaces; and (10) Geometric Transformations. Also included are an index and a section of supplements to the various chapters. (RH)

Describes the habits of mind that would be most desirable for students to develop. In high school for example, content-specific habits would include geometric habits of mind that support the mathematical approaches, and algebraic ways of thinking that complement the geometric approaches. (AIM)

Presents an activity in which students draw a picture, analyze each line and curve, and write the symbolic equations represented by the graph. Includes reproducible student worksheets. (MKR)

Presents activities which use graphing calculators to explore parametric equations of spirals, circles, and polygons. (MKR)

Discusses activities to teach Cartesian graphing to young children in a conceptual way. Activities are organized around the concepts of finding one's way around in a plane and using the plane to represent variables in two dimensions by graphing equations in the usual way. (25 references) (MKR)

Presents a lesson plan detailing an interdisciplinary mathematics/science activity in which students find the balance and center of gravity of a map of the United States. Contains reproducible student worksheets. (MKR)

Uses conic sections, trigonometric functions, and polar coordinates to solve the problem of determining the shape of a baseball outfield fence, given the distances along the foul lines and to straightaway center field. Graphing programs and calculators are utilized to plot different solutions. (MDH)

Entering a value into a calculator and repeatedly performing a function f(x) on the calculator can lead to the solution of the equation f(x)=x. Explores the outcomes of performing this iterative process on the calculator. Discusses how patterns of the resulting sequences converge, diverge, become cyclic, or display chaotic behavior. (MDH)

Describes the Geometer's Sketchpad, a geometric construction kit composed of three manipulatable, dynamic, linked, multiple representation environments: the coordinate system, formulas, and graphs. Examines the use of the environments for studying parameter effects of linear and quadratic functions and for solving linear equations. (MDH)

Develops the Pythagorean Theorem in the context of the Van Hiele levels by presenting activities appropriate for each level. Activities point to preparatory development (level 0), give 3 different versions of Euclid's proof (levels 1, 2, and 3), give some generalizations of the theorem (level 3), and explore the Pythagorean relationship in other geometry systems (level 4). (MDH)

Presents a cooperative-learning lesson in which high school students visit stations equipped with different tools to establish the midpoint of a Pixy Stix, a brand of candy-filled straw. Provides solutions for two potential stations, suggestions to extend the activity, and two activity worksheets. (MDH)

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics" provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. When completed, the Addenda Series is expected to consist of 22 supporting books designed to interpret and illustrate how the vision could be translated into new classroom practices. Targeted at mathematics instruction in grades K-6, 5-8, and 9-12, the themes of problem solving, reasoning, communication, and connections are woven throughout the materials, as is the view of assessment as a means of guiding instruction. The goal of the "Connecting Mathematics" book in the 9-12 series is to link the content proposed in "Curriculum and Evaluation Standards" to that of current programs. "Connecting Mathematics" reflects the new methodologies and supplies classroom-ready activities suited for cooperative group work that require students to experiment, collect data, search for patterns, make conjectures, and verify discoveries with the solutions given in the appendix. A special "Try This" feature provides extra exercises, problems, and explorations for use with students. The captioned margin notes, "Teaching Matters" and "Assessment Matters", provide helpful instructional ideas for introducing topics, using calculators and computers, and assessing student achievement. The chapters are: (1) Connecting with Functions; (2) Connecting with Matrices; (3) Data Analysis: A Context for Connections; (4) Building and Using Connections in Reasoning; and (5) Building and Using Connections in Problem Solving. (MDH)

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics" provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. When completed, it is expected that the Addenda Series will consist of 22 supporting books designed to interpret and illustrate how the vision could be translated into new classroom practices. Targeted at mathematics instruction in grades K-6, 5-8, and 9-12, the themes of problem solving, reasoning, communication, and connections are woven throughout the materials, as is the view of assessment as a means of guiding instruction. The goal of the "Geometry from Multiple Perspectives" book in the 9-12 series is to link the content proposed in the "Curriculum and Evaluation Standards" document to that of current programs. Ways for blending coordinate and transformation geometry with conventional geometry are described and supported by specific examples. The examples are presented in the booklet's 10 chapters in the form of comprehensive activities for which the solutions and hints for implementation are given in the appendix; in addition, each chapter has several "Try This" features that provide exercises, problems, and explorations for use with students. The chapters are: (1) Why Should Geometry be Considered from Multiple Perspectives? (2) Elements of Contemporary Geometry; (3) Triangles from Multiple Perspectives; (4) Quadrilaterals from Multiple Perspectives; (5) Polygons from Multiple Perspectives; (6) Solids: Expanded Perspectives; (7) Reasoning about Shapes Using Coordinates and Transformations; (8) Congruence from Multiple Perspectives; (9) Similarity from Multiple Perspectives; and (10) Reasoning, Justification, and Proof. (MDH)