Teaching the Common Core Math Standards with Hands-On Activities, Grades 3-5

Judith A. Muschla, Gary Robert Muschla e Erin Muschla-Berry

Jossey-Bass | 2014 | 301 páginas | rar - pdf |4,5 Mb

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With the common core math curriculum being adopted by forty-three states, it is imperative that students learn to master those key math standards. Teaching the Common Core Math Standards with Hands-On Activities, Grades 3-5 is the only book currently available that provides activities directly correlated to the new core curriculum for math. This text assists teachers with instructing the material and allows students to practice the concepts through use of the grade-appropriate activities included.

Students learn in different ways, and Teaching the Common Core Math Standards with Hands-On Activities, Grades 3-5 acknowledges that fact through the inclusion of suggestions for variations and extensions of each concept to be used for students with different abilities and learning styles. The activities and lessons are as diverse as the students in your classroom. Inside Teaching with Common Core Math Standards With Hands-On Activities Grades 3-5, you will find:

• Clear instructions to help you cover the skills and concepts for the new math core curriculum

• Engaging activities that enforce each core math standard for your students

• Various suggestions for ways to instruct the concepts to reach the diverse learning styles of your students

• Complete coverage of mathematical calculations, mathematical reasoning, and problem-solving strategies appropriate for grades 3-5

Teaching the Common Core Math Standards with Hands-On Activities, Grades 3-5 prepares students to achieve success in the important area of mathematics. As your students gain an understanding of the common core standards, they will build confidence in their ability to grasp and manipulate mathematical concepts as they move forward to the next level.

Outro livro da mesma série:

Teaching the common core math standards with hands-on activities, grades 6-8 por Judith A Muschla; Gary Robert Muschla; Erin Muschla-Berry Idioma: Inglês   Editora: San Francisco : Jossey-Bass, 2012.

The king of infinite space : Euclid and his Elements

David Berlinski 

Basic Books |  2013 | 187 páginas | pdf | 1,3  Mb

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Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclid’s Elements, arguably the most influential book in the history of mathematics In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, scientists and thinkers from Copernicus to Newton to Einstein have relied on Euclid’s axiomatic system, a method of proof still taught in classrooms around the world. Euclid’s use of elemental logic—and the mathematical statements he and others built from it—have dramatically expanded the frontiers of human knowledge.
The King of Infinite Space presents a rich, accessible treatment of Euclid and his beautifully simple geometric system, which continues to shape the way we see the world.

Contents
Preface xi
I Signs of Men 1
II An Abstraction from the Gabble 11
III Common Beliefs 19
IV Darker by Definition 33
V The Axioms 45
VI The Greater Euclid 57
VII Visible and Invisible Proof 77
VIII The Devil’s Offer 91
IX The Euclidean Joint Stock Company 117
X Euclid the Great 147
Teacher’s Note 155
A Note on Sources 157
Appendix: Euclid’s Definitions 159
Index 163


Outros livros do mesmos autor:

One, two, three : absolutely elementary mathematics por David Berlinski Idioma: Inglês   Editora: New York : Pantheon Books, ©2011.

Infinite ascent : a short history of mathematics por David Berlinski Idioma: Inglês   Editora: New York : Modern Library, 2005.

Geometric Puzzle Design

Stewart Coffin

A K Peters/CRC Press | 2007 - 2ª edição | pdf | 5,4 Mb

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This book discusses how to design "good" geometric puzzles: two-dimensional dissection puzzles, polyhedral dissections, and burrs. It outlines major categories of geometric puzzles and provides examples, sometimes going into the history and philosophy of those examples. The author presents challenges and thoughtful questions, as well as practical design and woodworking tips to encourage the reader to build his own puzzles and experiment with his own designs. Aesthetics, phychology, and mathematical considerations all factor into the definition of the quality of a puzzle.

Contents
Preface vii
Introduction ix
1 Two-Dimensional Dissections 1
2 Two-Dimensional Combinatorial Puzzles 17
3 Misdirection-Type Puzzles 37
4 Variations on Sliding Block Puzzles 41
5 Cubic Block Puzzles 45
6 Interlocking Block Puzzles 55
7 The Six-Piece Burr 59
8 Larger (and Smaller) Burrs 69
9 The Diagonal Burr 81
10 The Rhombic Dodecahedron and Its Stellations 87
11 Polyhedral Puzzles with Dissimilar Pieces 99
12 Intersecting Prisms 107
13 Puzzles that Make Different Shapes 113
14 Coordinate-Motion Puzzles 117
15 Puzzles Using Hexagonal or Rhombic Sticks 121
16 Split Triangular Sticks 129
17 Dissected Rhombic Dodecahedra 133
18 Miscellaneous Confusing Puzzles 139
19 Triacontahedral Designs 143
20 Puzzles Made of Polyhedral Blocks 153
21 Intermezzo 161
22 Theme and Variations 167
23 Blocks and Pins 175
24 Woodworking Techniques 187
Finale 197
Bibliography 199

Index 201

The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth

Paul Hoffman

Hyperion | 1999 | 335 páginas | pdf | 13 Mb

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Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.

Geometry of Complex Numbers

Hans Schwerdtfeger

Dover Publications | 1979 | 200 Páginas | rar - epub | 11,7 Mb

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Since its initial publication in 1962, Professor Schwerdtfeger's illuminating book has been widely praised for generating a deeper understanding of the geometrical theory of analytic functions as well as of the connections between different branches of geometry. Its focus lies in the intersection of geometry, analysis, and algebra, with the exposition generally taking place on a moderately advanced level. Much emphasis, however, has been given to the careful exposition of details and to the development of an adequate algebraic technique.
In three broad chapters, the author clearly and elegantly approaches his subject. The first chapter, Analytic Geometry of Circles, treats such topics as representation of circles by Hermitian matrices, inversion, stereographic projection, and the cross ratio. The second chapter considers in depth the Moebius transformation: its elementary properties, real one-dimensional projectivities, similarity and classification of various kinds, anti-homographies, iteration, and geometrical characterization. The final chapter, Two-Dimensional Non-Euclidean Geometries, discusses subgroups of Moebius transformations, the geometry of a transformation group, hyperbolic geometry, and spherical and elliptic geometry. For this Dover edition, Professor Schwerdtfeger has added four new appendices and a supplementary bibliography.Advanced undergraduates who possess a working knowledge of the algebra of complex numbers and of the elements of analytical geometry and linear algebra will greatly profit from reading this book. It will also prove a stimulating and thought-provoking book to mathematics professors and teachers.

Elementary Mathematics from an Advanced Standpoint: Geometry

Felix Klein

Dover Publications | 2004 | 224 páginas | rar - epub | 6,2 Mb

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This text begins with the simplest geometric manifolds, the Grassmann determinant principle for the plane and the Grassmann principle for space; and more. Also explores affine and projective transformations; higher point transformations; transformations with change of space element; and the theory of the imaginary. Concludes with a systematic discussion of geometry and its foundations

CONTENTS
Introduction
Part One: The Simplest Geometric Manifolds
I. Line-Segment, Area, Volume, as Relative Magnitudes
Definition by means of determinants; interpretation of the sign
Simplest applications, especially the cross ratio
Area of rectilinear polygons
Curvilinear areas
Theory of Amsler’s polar planimeter
Volume of polyhedrons, the law of edges
One-sided polyhedrons
II. The Grassmann Determinant Principle for the Plane
Line-segment (vectors)
Application in statics of rigid systems
Classification of geometric magnitudes according to their behavior under transformation of rectangular coordinates
Application of the principle of classification to elementary magnitudes
III. The Grassmann Principle for Space
Line-segment and plane-segment
Application to statics of rigid bodies
Relation to Mobius’ null-system
Geometric interpretation of the null-system
Connection with the theory of screws
IV. Classification of the Elementary Configurations of Space according to their Behavior under Transformation of Rectangular Coordinates
Generalities concerning transformations of rectangular space coordinates
Transformation formulas for some elementary magnitudes
Couple and free plane magnitude as equivalent manifolds
Free line-segment and free plane magnitude (“polar” and “axial” vector)
Scalars of first and second kind
Outlines of a rational vector algebra
Lack of a uniform nomenclature in vector calculus
V. Derivative Manifolds
Derivatives from points (curves, surfaces, point sets)
Difference between analytic and synthetic geometry
Projective geometry and the principle of duality
Plücker’s analytic method and the extension of the principle of duality (line coordinates)
Grassmann’s Ausdehnungslehre; n-dimensional geometry
Scalar and vector fields; rational vector analysis
Part Two: Geometric Transformations
Transformations and their analytic representation
I. Affine Transformations
Analytic definition and fundamental properties
Application to theory of ellipsoid
Parallel projection from one plane upon another
Axonometric mapping of space (affine transformation with vanishing determinant)
Fundamental theorem of Pohlke
II. Projective Transformations
Analytic definition; introduction of homogeneous coordinates
Geometric definition: Every collineation is a projective transformation
Behavior of fundamental manifolds under projective transformation
Central projection of space upon a plane (projective transformation with vanishing determinant)
Relief perspective
Application of projection in deriving properties of conics
III. Higher Point Transformations
1. The Transformation by Reciprocal Radii
Peaucellier’s method of drawing a line
Stereographic projection of the sphere
2. Some More General Map Projections
Mercator’s projection
Tissot theorems
3. The Most General Reversibly Unique Continuous Point Transformations
Genus and connectivity of surfaces
Euler’s theorem on polyhedra
IV. Transformations with Change of Space Element
1. Dualistic Transformations
2. Contact Transformations
3. Some Examples
Forms of algebraic order and class curves
Application of contact transformations to theory of cog wheels
V. Theory of the Imaginary
Imaginary circle-points and imaginary sphere-circle
Imaginary transformation
Von Staudt’s interpretation of self-conjugate imaginary manifolds by means of real polar systems
Von Staudt’s complete interpretation of single imaginary elements
Space relations of imaginary points and lines
Part Three: Systematic Discussion of Geometry and Its Foundations
I. The Systematic Discussion
1. Survey of the Structure of Geometry
Theory of groups as a geometric principle of classification
Cayley’s fundamental principle: Projective geometry is all geometry
2. Digression on the Invariant Theory of Linear Substitutions
Systematic discussion of invariant theory
Simple examples
3. Application of Invariant Theory to Geometry
Interpretation of invariant theory of n variables in affine geometry of Rn with fixed origin
Interpretation in projective geometry of Rn−1
4. The Systematization of Affine and Metric Geometry Based on Cayley’s Principle
Fitting the fundamental notions of affine geometry into the projective system
Fitting the Grassmann determinant principle into the invariant-theoretic conception of geometry. Concerning tensors
Fitting the fundamental notions of metric geometry into the projective system
Projective treatment of the geometry of the triangle
II. Foundations of Geometry
General statement of the question: Attitude to analytic geometry
Development of pure projective geometry with subsequent addition of metric geometry
1. Development of Plane Geometry with Emphasis upon Motions
Development of affine geometry from translation
Addition of rotation to obtain metric geometry
Final deduction of expressions for distance and angle
Classification of the general notions surface-area and curve-length
2. Another Development of Metric Geometry—the Role of the Parallel Axiom
Distance, angle, congruence, as fundamental notions
Parallel axiom and theory of parallels (non-euclidean geometry
Significance of non-euclidean geometry from standpoint of philosophy
Fitting non-euclidean geometry into the projective system
Modern geometric theory of axioms
3. Euclid’s Elements
Historical place and scientific worth of the Elements
Contents of thirteen books of Euclid
Foundations
Beginning of the first book
Lack of axiom of betweenness in Euclid; possibility of the sophisms
Axiom of Archimedes in Euclid; horn-shaped angles as example of a system of magnitudes excluded by this axiom

Solve this math activities for students and clubs

(Classroom Resource Materials)
James S. Tanton

The Mathematical Association of America | 2001 | 240 páginas | rar - pdf  | 3,1 Mb 

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Sophisticated mathematics is accessible to all. This book proves it! This is a collection of intriguing mathematical problems and activities linked by common themes that all involve working with objects from our everyday experience. Learn about the mathematics of a bagel, a checkerboard and a pile of laundry for example. Discover for yourself that wheels need not be round, that braids need not have free ends, that it's always best to turn around twice - and more! Mathematics is all around us, we all do mathematics every day. The activities contained in this book are immediate, catchy and fun, but upon investigation, begin to unfold into surprising layers of depth and new perspectives. The necessary mathematics, in increasing levels of difficulty, is explained fully along the way. Mathematics educators will find this an invaluable resource of fresh and innovative approaches to topics in mathematics.

Contents
Activities and problem statements. Distribution dilemmas
Weird shapes
Counting on the odds ... and evens
Dicing slicing and avoiding bad bits
'Impossible' paper tricks
Tiling challenges
Things that won't fall down
Mobius madness : tortuous twists on a classic theme
Infamous bicycle problem
Making surfaces in 3 and 4 dimensional space
Paradoxes in probability theory
Don't turn around just once!
It's all in a square
Bagel math
Capturing chaos
Who has the advantage?
Laundry math
Get knotted
Tiling and walking
Automata antics
Bubble trouble
Halves and doubles
Playing with playing cards
Map mechanics
Weird lotteries
Flipped out
Parts that do not add up to their whole
Making the sacrifice
Problems in parity
Chessboard maneuvers
Hints, some solutions and further thoughts. 
Solutions and discussions.