Mathematics for Secondary School Teachers

Elizabeth G. Bremigan, Ralph J. Bremigan e John D. Lorch

Mathematical Association of America | 2011 | páginas | rar - pdf | 3,9 Mb

link (password : matav)

Mathematics for Secondary School Teachers, which is intended for prospective educators in middle and high school, balances discovery learning with direct instruction.
Written to develop a deeper understanding of the mathematics that will be taught, the book presents topics of central importance in the secondary school mathematics curriculum, notably, functions, polynomials, trigonometry, exponential and logarithmic functions, numbers and operations, and measurements.
Beyond the goals of conceptual understanding and computational fluency, readers of the book can devise their own mathematical explanations and arguments; create examples and visual representations; remediate typical student errors and misconceptions; and analyze students’ work.
A broad collection of exercises of varying degrees of difficulty is integrated with the text. Instructors are able to emphasize the following:
Basics: The exploration of key precollege topics from intuitive and rigorous points of view;
Connections: The exploration of relationships among topics, using tools from college-level mathematics;
Extensions: The exploration of college-level mathematical topics that have a compelling relationship to precollege mathematics.
By taking into account the diverse mathematical backgrounds of preservice teachers and the varied goals of teacher preparation programs, the authors have written a textbook whose subject matter addresses a wide range of learning objectives appropriate for future teachers.
Mathematics for Secondary School Teachers can also be used in licensing programs; as a supplement to mathematics methods courses; as a text for graduate courses for in-service teachers; and as a resource for faculty development.

Table of ContentsPreface
To the Student
To the Instructor
1. Functions
2. Lines in the Plane
3. Quadratic Polynomials
4. Trigonometry
5. Hyperbolic Trigonometry
6. Numbers
7. Operations in Number Theory
8. Topics in Number Theory
9. Exponentiation
10. Exponential and Logarithmic Functions: History, Computation, and Application
11. Transcendental Functions and Complex Numbers
12. Beyond Quadratics: Higher Degree Polynomials
13. Measurement
Appendix A: Log Tables
Index

Understanding Mathematics for Young Children A guide for teachers of children 3–8

Derek Haylock e Anne Cockburn

SAGE Publications Ltd | 2013 - 4ª edição | 344 páginas | rar - epub | 2,4 Mb

link (password: matav)


'This book was a delight to read. The mathematical content is excellent and the approach to explaining complex concepts is exceptionally good!' -Dr Jennifer Way, University of Sydney

'I'm a really big fan of this book: it is the single most influential text in my experience of working with primary maths teachers in the last 12 years' - Andy Tynemouth, Every Child Counts National Adviser, Edge Hill University

'Every teacher of maths should read this book! It helped me realize why some children are struggling with doing simple word problems' -Amazon reader review

If you are a teacher or student teacher in a nursery or primary school, you need a secure understanding of the mathematical ideas behind the material you will use in the classroom. To help young children develop their understanding of mathematics, you need to develop your own understanding of how mathematics is learnt.

In this indispensible book, the authors help you to understand mathematical concepts and how children come to understand them, and also help develop your own confidence with mathematical activities.

Each chapter of this book includes:

-Real-life examples and illustrations from children and teachers in the classroom

-The research behind some of the concepts and teaching approaches discussed

-Pauses to reflect and discuss your own mathematical knowledge and experience

-Age-appropriate classroom activities to try with your class or group.

Contents
Understanding Mathematics 
Understanding Number and Counting 
Understanding Addition and Subtraction 
Understanding Multiplication and Division 
Understanding the Principles of Arithmetic 
Understanding Calculations through Patterns and Pictures 
Understanding Place Value 
Understanding Measurement 
Understanding Shape and Space 
Understanding Data Handling 
Understanding Problem Solving and Reasoning in Mathematics

The Math Teachers Know: Profound Understanding of Emergent Mathematics

Brent Davis e Moshe Renert 

Routledge | 2013 | 150 páginas | rar - pdf | Mb

link (password: matav)

What sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledge–that is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers’ mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the complexity of this knowledge and offers strategies to uncover it, analyze it, and re-synthesize it in ways that will make it more available for teaching. Emerging from 10 years of collaborative inquiry with practicing teachers, it is simultaneously informed by the most recent research and anchored to the realities of teachers’ lives in classrooms.

CONTENTSAcknowledgments | vii
1. teachers’ mathematics: framing the question | 1
1 Mathematics-for-Teaching: A Working Definition
5 What’s the Question? Three Framings of Mathematics-for-Teaching
12 The Bigger Picture: Making Sense of M4T by Grappling with Why Math Matters
15 Where Are We Going with This?
2. knowing and learning (mathematics): some game-changing insights | 17
17 “Thou Shalt Not” – A Teacher Dares to Divide by Zero
20 Complexity Science
23 Knowing
27 Learning
33 Where Are We Going with This?
3. substructing emergent mathematics: cultivating an open disposition | 35
35 Is 1 Prime?
39 Concept Study
42 Substructing
44 Emergent Mathematics
47 Open Dispositions
48 Where Are We Going with This?
4. concept study: teachers co-constructing mathematics | 49
49 Pulling Together, Not Just Pulling Apart
53 Collective Cognition
56 Structures of Concept Study
58 Emphasis 1: Realizations
61 Emphasis 2: Landcapes
66 Emphasis 3: Entailments
70 Emphasis 4: Blends
75 Where Are We Going with This?
5. pedagogical problem solving: the emergence of a community of experts | 77
77 Pedagogical Problem Solving
80 A Community of Experts
83 Mathematics Teaching and Listening
87 A Depth and Breadth of Mathematical Knowledge
90 Knowledge of How Mathematics is Produced
93 Where Are We Going with This?
6. concept study in the classroom: enacting an open way of being | 95
95 A Concept Study of Circles
96 Four Quadrants of M4T
99 What’s Interesting about Circles? Emergent Problem Solving
102 Do Circles Exist? Student Agency in Mathematical Knowledge Production
104 Rope around the Equator: Cultural Mathematics
106 Are Circles Efficient? An Open Way of Being
110 Where Are We Going with This?
7. the mathematics teachers (need to) know: profound understanding of emergent mathematics | 111
111 Zero and Function
117 Profound Understanding of Emergent Mathematics
120 All That and More ...
125 Where Are We Going with This?
References | 129
Index | 137

100 Commonly Asked Questions in Math Class: Answers That Promote Mathematical Understanding, Grades 6-12

Alfred S. (Steven) Posamentier, William L. Farber, Terri L. (Lynn) Germain-Williams e Elaine S. Paris

Corwin | 2013 | 232 páginas | rar - epub | 2,23 Mb

link (password: matav)

100 ways to get students hooked on math!

That one question got you stumped? Or maybe you have the answer, but it’s not all that compelling. Al Posamentier and his coauthors to the rescue with this handy reference containing fun answers to students’100 most frequently asked math questions. Even if you already have the answers, Al’s explanations are certain to keep kids hooked.

• Teach to the Common Core’s math content standards

• Promote inquiry and process in mathematical thinking

• Build procedural skills and conceptual understanding

• Encourage flexibility in problem solving

• Emphasize efficient test-taking strategies

Contents
Introduction
Chapter One   General Questions
1. Why do I have to learn mathematics?
2. Is there a language connection between mathematical terms and common English words?
3. How many leaves are on a tree?
4. Why do we have to learn about the history of mathematics?
5. Who introduced the Hindu-Arabic numbers to the Western world, and when?
6. What are the three famous problems of antiquity?
7. What are the Fibonacci numbers?
8. What is the golden ratio?
9. Is there a smallest number, and is there a largest number?
10. Why is infinity not a number?
11. How large is infinity?
12. Is there anything larger than infinity?
13. Can the union of two sets ever be equal to the intersection of the two sets?
14. How can we determine how many subsets a given set has?
15. How can we avoid making an error in a “proof” that leads to a generalization?
16. How does a calculator function?
17. Which is correct—my calculating, the calculator, or the computer?
18. What are conic sections?
19. What is a mathematical group?
20. What is a mathematical ring?
21. What is a mathematical field?
22. What are the three famous laws that Johannes Kepler discovered about planetary motion involving the ellipse?
Notes
Chapter Two   Arithmetic Questions
23. What is the difference between a number and a digit?
24. What are the differences between cardinal, ordinal, and nominal numbers?
25. What are the natural numbers, and does the number zero belong to the natural numbers?
26. How can we remember the order of operations using PEMDAS?
27. What is a fraction?
28. What is a rational number?
29. How can one convert a decimal number to a fraction?
30. What is so special about the Pascal triangle?
31. How can the product of two numbers be smaller than both of its factors?
32. If the temperature rises from 80°F to a temperature of 88°F, why is it wrong to say it became 10% warmer?
33. How do the values of the following differ: abc, (ab)c, (ab)c, abc?
34. Why is division by zero not permissible?
35. Why is x· 0 = 0?
36. What is 0!?
37. What is the largest number that can be represented in the decimal system with three digits (and without using any other symbols)?
38. What is a prime number?
39. Does the number 1 belong to the prime numbers?
40. How many prime numbers are there?
41. What is a palindrome?
42. What are successive percentages?
Notes
Chapter Three   Algebra Questions
43. Why is the product of two negative numbers positive?
44. Why must a and b be positive in order for the following to hold true?
45. Why is it advantageous to rationalize the denominator?
46. What is meant by the “absolute value” of a variable?
47. What is a variable? A term? An expression? An equation?
48. How can we have students realize that the average of rates is not simply the arithmetic mean?
49. Why does 0.99999 . . .= 1?
50. Is a road with a slope of 20% twice as steep as a road with a 10% slope?
51. Is there a number that differs from its reciprocal by 1?
52. What is a determinant, and how can it be used to solve a system of linear equations?
53. How do the arithmetic, geometric, and harmonic means compare in magnitude?
54. What is a function?
55. What is meant by the inverse of a function?
56. Can a function be equal to its inverse?
57. What is a 1–1 onto function?
58. Where does the quadratic formula come from?
59. What is a parabola?
60. How can you find the turning point of a parabola?
61. What is an ellipse?
62. What is a hyperbola?
63. When does one use the Law of Sines?
64. When does one use the Law of Cosines?
65. What is the difference between y= arccos x and y= cos–1 x?
66. What is a vector?
67. Why can a vector not be divided by a vector?
68. What is i?
69. What is e?
Notes
Chapter Four   Geometry Questions
70. Why is the diagonal of a square longer than its side?
71. How can you demonstrate that the circumference of a circle is 2πr?
72. How can you demonstrate that the area of a circle is equal to πr2?
73. Can a triangle contain two right angles?
74. Why must the sum of any two sides of a triangle be greater than the third side?
75. How do the terms “acute angle” and “obtuse angle” relate to the English language?
76. Can trigonometry be used to prove the Pythagorean theorem?
77. How is the distance formula derived?
78. How can the Pythagorean theorem be used to determine if an angle of a triangle is acute or obtuse?
79. What is a Platonic solid?
80. What is a golden rectangle?
81. What is a golden triangle?
82. From which point in a triangle is the sum of the distances to the three vertices smallest?
83. What is the sum of the distances from a point in a triangle to its three sides?
84. What is President James A. Garfield’s proof of the Pythagorean theorem?
85. What is the nine-point circle?
86. How can the Pythagorean theorem be proved by paper folding?
87. How can we prove that the sum of the measures of the angles of any triangle is 180° using paper folding?
88. What figure is created by joining the midpoints of any quadrilateral?
89. How can the concurrency of the medians of a triangle be proved in one step?
Notes
Chapter Five   Probability Questions
90. What is the fundamental principle of counting?
91. What does it mean when the probability of an event is 1? Is 0?
92. What are mutually exclusive events?
93. What is the probability of either or both of two events happening?
94. What is the difference between combinations and permutations?
95. What is the difference between correlation and causation?
96. What is the Pascal triangle?
97. What is binomial probability?
98. What is the birthday problem?
99. How can algebra help us to understand a probability question?
100. What kind of averages are batting averages?

The big benefits? You’ll discover high-interest ways to

Resources for Preparing Middle School Mathematics Teachers

Cheryl Beaver, Laurie Burton, Maria Fung, e Klay Kruczek, Editors

The Mathematical Association of America | 2013 | páginas | rar - pdf |2,97 Mb

link (password : matav)

Middle school mathematics teachers occupy a unique place in the mathematical development of students. These teachers need to be proficient in all elementary mathematics topics, together with some secondary mathematics topics. They demand a special kind of preparation that differs from both that of their elementary and secondary colleagues. The Mathematics Education of Teachers (MET) document published by the Conference Board of the Mathematical Sciences set forth criteria for the preparation of mathematics middle school teachers which made it critical that special programs and courses for this group emerge.
This collection of articles is in response to the MET document and the result of several gatherings of mathematics educators and mathematicians training middle school teachers. We, the editors of this volume, under the sponsorship of the Committee on the Mathematical Education of Teachers, organized two contributed paper sessions at the Joint Mathematics Meetings entitled “Content Courses for the Mathematical Education of Middle School Teachers” in 2007 and “Curriculum Materials for Pre-service Middle School Mathematics Teachers” in 2008. We invited participants from these two sessions as well as colleagues heavily involved in the mathematics education of middle school teachers to write articles on both programs and courses.
We have chosen the articles that appear in this volume for several purposes: to disseminate various middle school programs structures, to detail methods of teaching specific middle school teachers content courses, and to share materials and resources. While each article describes the unique program or course of its respective institution, each also includes a common core of information to provide some consistency to the volume. In particular, all articles describing middle school programs contain information about the host institution, a history of the program, degree and testing requirements for the program and for state licensure, learning goals and objectives for the program and courses, and any available assessment data. When applicable information is included about particular courses, for example, some articles provide sample activities or syllabi and some have a description of courses in the appendix. Most articles have links to websites containing further information about the program, courses, state requirements, or resources that can be downloaded and used directly.
We expect that the reader of this volume will be either a faculty member who is new to the teaching of courses for middle school mathematics teachers or a seasoned teacher of pre-service teachers who is interested in trying some new approaches and perhaps starting a middle school program at his or her institution.

Contents
Preface vii
I Programs for Middle School Teachers
A. Pre-service Training Programs 1
1 Preparing Middle Grades Mathematics Teachers at Georgia College & State University
Angel R. Abney, Nancy B. Mizelle, and Janet Shiver 3
2 The Mathematics forMiddle School Teachers Program atWestern Oregon University
Cheryl Beaver, Rachel Harrington, and Klay Kruczek 15
3 Connecting Middle SchoolMathematics with CollegeMathematics: A Core ofMathematics Courses for
Middle Grade Mathematics Teachers
Ira J. Papick 23
4 The Middle School Program at the University ofWisconsin Oshkosh
Jennifer Szydlik, John Beam, Eric Kuennen, and Carol Seaman 29
5 The Master of Arts in Middle School Mathematics Program at Salem (MA) State University
Julie A. Belock 39
6 The Math in the Middle Institute: Strengthening Middle Level Teachers’ Mathematical and Pedagogical
Capacities
Ruth M. Heaton, W. James Lewis, and Wendy M. Smith 47
7 A Professional Development Program forMiddle School Math Teachers in Maryland
M. Elizabeth Mayfield and Christy Danko Graybeal 59
8 Discrete Mathematics: A Course in Problem Solving for 21st Century Middle School Teachers
Tanya Cofer, Valerie A. DeBellis, Cathy Liebars, Joseph G. Rosenstein, Bonnie Saunders, and Margaret Wirth 71
9 Guided Discovery in a Discrete Mathematics Course forMiddle School Teachers
Mary Flahive and Reva Kasman 85
10 Geometry forMiddle Grades Teachers at Northern Kentucky University
Bethany Noblitt 99
11 A Number and Algebra Course for Middle School Math Teachers
Michael Mays and David Miller 119
12 Vertically Connecting Precalculus and Calculus with Middle School Mathematics
Theresa Jorgensen 135
13 Visual College Algebra for Teachers
Laurie J. Burton and Klay T. Kruczek 143
14 Probability and Statistics for Prospective Middle Grades Teachers
Jennifer Szydlik, John Beam, Eric Kuennen, and Carol Seaman 157
15 Vermont Middle Level Mathematics Initiative: Courses and Materials for Mathematics Educators
George Ashline and Marny Frantz 169
16 Challenging Yet Accessible Mathematics Courses for Middle Level Teachers
Ruth M. Heaton, W. James Lewis, Michelle R. Homp, Steven R. Dunbar, and Wendy M. Smith 181

Explorations for Bassarear's Mathematics for Elementary School Teachers

Tom Bassarear

Cengage Learning | 2011 - 5ª edição | 317 páginas | rar - pdf | 3,9 Mb

link (password: matav)

This manual contains open-ended activities for the student to practice and apply the knowledge they learn from the main text. When students begin teaching, they can use the activities as models in their own classrooms.

CONTENTS
Preface xi
1 Foundations for Learning Mathematics 1
EXPLORATION 1.1 Patterns, Problem Solving, and Representations 2
EXPLORATION 1.2 Patterns in Multiplication 5
EXPLORATION 1.3 Real-life Problems 8
EXPLORATION 1.4 Patterns and Proof 9
EXPLORATION 1.5 Magic Squares 12
EXPLORATION 1.6 Magic Triangle Puzzles 17
2 Fundamental Concepts 21
SECTION 2.1 Exploring Sets 21
EXPLORATION 2.1 Understanding Venn Diagrams 22
EXPLORATION 2.2 Gathering and Interpreting Data 23
SECTION 2.2 Exploring Algebraic Thinking 24
EXPLORATION 2.3 Exploring Equivalence 24
EXPLORATION 2.4 Relationships Between Variables 27
EXPLORATION 2.5 Connecting Graphs and Words 29
EXPLORATION 2.6 Growth Patterns 32
SECTION 2.3 Exploring Numeration 37
EXPLORATION 2.7 Alphabitia 37
EXPLORATION 2.8 Different Bases 43
EXPLORATION 2.9 A Place Value Game 46
EXPLORATION 2.10 How Big Is Big? 47
3 The Four Fundamental Operations of Arithmetic 49
EXPLORATION 3.1 Computation in Alphabitia 49
SECTION 3.1 Exploring Addition 51
EXPLORATION 3.2 Mental Addition 51
EXPLORATION 3.3 Addition: Children’s Algorithms and Alternative Algorithms 52
EXPLORATION 3.4 Addition and Number Sense 54
SECTION 3.2 Exploring Subtraction 55
EXPLORATION 3.5 Mental Subtraction 55
EXPLORATION 3.6 Subtraction: Children’s Algorithms and Alternative Algorithms 56
EXPLORATION 3.7 Subtraction and Number Sense 58
SECTION 3.3 Exploring Multiplication 59
EXPLORATION 3.8 Patterns in the Multiplication Table 59
EXPLORATION 3.9 Mental Multiplication 63
EXPLORATION 3.10 Differences Between Multiplication and Addition 64
EXPLORATION 3.11 Cluster or String Problems 65
EXPLORATION 3.12 Understanding the Standard Multiplication Algorithm 66
EXPLORATION 3.13 Alternative Algorithms for Multiplication 67
EXPLORATION 3.14 Multiplication and Number Sense 69
SECTION 3.4 Exploring Division 70
EXPLORATION 3.15 Different Models of Division 70
EXPLORATION 3.16 Understanding Division Computation 71
EXPLORATION 3.17 Mental Division 72
EXPLORATION 3.18 Dealing with Remainders 73
EXPLORATION 3.19 The Scaffolding Algorithm 74
EXPLORATION 3.20 Understanding the Standard Algorithm 75
EXPLORATION 3.21 Division and Number Sense 76
EXPLORATION 3.22 Developing Operation Sense 77
EXPLORATION 3.23 Operation Sense in Games 78
EXPLORATION 3.24 How Many Stars? 79
4 Number Theory 81
SECTION 4.1 Exploring Divisibility and Related Concepts 81
EXPLORATION 4.1 Taxman 82
SECTION 4.2 Exploring Prime and Composite Numbers 85
EXPLORATION 4.2 Factors 85
EXPLORATION 4.3 Finding All Factors of a Number 91
SECTION 4.3 Exploring Greatest Common Factor and Least Common Multiple 92
EXPLORATION 4.4 African Sand Drawings 92
EXPLORATION 4.5 Cycles 94
5 Extending the Number System 97
SECTION 5.1 Exploring Integers 97
EXPLORATION 5.1 Understanding Integer Addition 98
EXPLORATION 5.2 Understanding Integer Subtraction 99
EXPLORATION 5.3 Understanding Integer Multiplication 100
EXPLORATION 5.4 Understanding Integer Division 101
SECTION 5.2 Exploring Fractions and Rational Numbers 102
EXPLORATION 5.5 Making Manipulatives 102
EXPLORATION 5.6 Sharing Brownies 103
EXPLORATION 5.7 Partitioning 104
EXPLORATION 5.8 Equivalent Fractions 109
EXPLORATION 5.9 Developing Fraction Sense 110
SECTION 5.3 Exploring Operations with Fractions 111
EXPLORATION 5.10 Ordering Fractions 111
EXPLORATION 5.11 Adding Fractions 115
EXPLORATION 5.12 Making Sense of Wholes and Units 116
EXPLORATION 5.13 Multiplying Fractions 118
EXPLORATION 5.14 An Alternative Algorithm for Dividing Fractions 119
EXPLORATION 5.15 Remainders 120
EXPLORATION 5.16 Meanings of Operations with Fractions 121
EXPLORATION 5.17 Developing Operation Sense 122
SECTION 5.4 Exploring Beyond Integers and Fractions: Decimals, Exponents,
and Real Numbers 124
EXPLORATION 5.18 Decimals and Base Ten Blocks 124
EXPLORATION 5.19 Exploring Decimal Algorithms 125
EXPLORATION 5.20 Patterns in Repeating Decimals 126
EXPLORATION 5.21 Developing Decimal Sense 128
EXPLORATION 5.22 The Right Bucket: A Decimal Game 130
EXPLORATION 5.23 Target: A Decimal Game 133
EXPLORATION 5.24 A Real-life Problem in College 137
6 Proportional Reasoning 139
SECTION 6.1 Exploring Ratio and Proportion 139
EXPLORATION 6.1 Which Ramp Is Steeper? 140
EXPLORATION 6.2 Using Qualitative Reasoning to Develop Proportional Reasoning 141
EXPLORATION 6.3 Using Proportional Reasoning to Interpret Data 142
EXPLORATION 6.4 Unit Pricing and Buying Generic 145
EXPLORATION 6.5 Proportional Reasoning and Functions 146
SECTION 6.2 Exploring Percents 147
EXPLORATION 6.6 Percents 147
EXPLORATION 6.7 Do You Get What You Pay For? 149
EXPLORATION 6.8 Reducing, Enlarging, and Percents 150
EXPLORATION 6.9 Mice on Two Islands 152
7 Uncertainty: Data and Chance 153
SECTION 7.1 The Process of Collecting and Analyzing Data 153
EXPLORATION 7.1 Population Growth and Density 154
EXPLORATION 7.2 Collecting Data to Understand a Population: Typical Person 155
EXPLORATION 7.3 Exploring the Concept of Average 156
EXPLORATION 7.4 Explorations for Gathering and Analyzing Data 159
SECTION 7.2 Going Beyond the Basics 161
EXPLORATION 7.5 How Many Drops of Water Will a Penny Hold? 161
EXPLORATION 7.6 How Accurate Can You Get the Whirlybird to Be? 162
EXPLORATION 7.7 Exploring Relationships Among Body Ratios 163
EXPLORATION 7.8 Collecting Data to Make a Decision:
What Container Best Keeps Coffee Hot? 165
EXPLORATION 7.9 Explorations for Comparing Two Sets of Data 166
EXPLORATION 7.10 Collecting Data of Your Choice 169
EXPLORATION 7.11 Designing and Conducting a Survey 170
SECTION 7.3 Exploring Concepts Related to Chance 171
EXPLORATION 7.12 Heads and Tails and Probability 171
EXPLORATION 7.13 What Is the Probability of Having the Same Number of Boys and Girls? 172
EXPLORATION 7.14 What Is the Probability of Rolling Three Doubles in a Row? 173
EXPLORATION 7.15 What’s in the Bag? 174
EXPLORATION 7.16 How Many Boxes Will You Probably Have to Buy? 176
EXPLORATION 7.17 More Simulations 177
EXPLORATION 7.18 Using Sampling to Estimate a Whole Population 178
EXPLORATION 7.19 Fair Games 179
SECTION 7.4 Exploring Counting and Chance 181
EXPLORATION 7.20 License Plates 181
EXPLORATION 7.21 Native American Games 182
8 Geometry as Shape 185
EXPLORATION 8.1 Geoboard Explorations 185
EXPLORATION 8.2 Tangram Explorations 191
EXPLORATION 8.3 Polyomino Explorations 197
SECTION 8.1 Exploring Basic Concepts of Geometry 203
EXPLORATION 8.4 Manhole Covers 203
EXPLORATION 8.5 Proof 207
EXPLORATION 8.6 Using Geometric Knowledge to Make Angles 208
SECTION 8.2 Exploring Two-Dimensional Figures 209
EXPLORATION 8.7 “What Do You See?” and “Make It from Memory” 209
EXPLORATION 8.8 Making Shapes from Folding a Square 213
EXPLORATION 8.9 Definitions and Language 214
EXPLORATION 8.10 The Sum of the Angles in a Polygon 216
EXPLORATION 8.11 Congruence 217
EXPLORATION 8.12 Polygons with Various Attributes 219
EXPLORATION 8.13 Polygons and Relationships 221
SECTION 8.3 Exploring Three-Dimensional Figures 225
EXPLORATION 8.14 Exploring Polyhedra 225
EXPLORATION 8.15 Relationships Among Polyhedra 227
EXPLORATION 8.16 Regular Polyhedra 228
EXPLORATION 8.17 Block Buildings 229
EXPLORATION 8.18 Cross Sections 233
EXPLORATION 8.19 Nets 234
9 Geometry as Transforming Shapes 241
EXPLORATION 9.1 Geoboard Explorations 241
EXPLORATION 9.2 Tangram Explorations 251
EXPLORATION 9.3 Polyomino Explorations 252
SECTION 9.1 Exploring Translations, Reflections, and Rotations 256
EXPLORATION 9.4 Reflections (Flips) 256
EXPLORATION 9.5 Paper Folding 263
EXPLORATION 9.6 Developing Rotation Sense 271
SECTION 9.2 Symmetry and Tessellations 275
EXPLORATION 9.7 Symmetries of Common Polygons 275
EXPLORATION 9.8 Symmetry Groups 276
EXPLORATION 9.9 Tessellations 281
EXPLORATION 9.10 Quilts 287
SECTION 9.3 Exploring Similarity 299
EXPLORATION 9.11 Similarity with Pattern Blocks 299
EXPLORATION 9.12 Similar Figures 301
10 Geometry as Measurement
SECTION 10.1 Exploring Systems of Measurement 303
EXPLORATION 10.1 How Far Is It? 303
EXPLORATION 10.2 How Tall? 305
EXPLORATION 10.3 How Thick? 306
EXPLORATION 10.4 How Much Is a Million? 307
SECTION 10.2 Exploring Perimeter and Area 308
EXPLORATION 10.5 What Does Mean? 308
EXPLORATION 10.6 Exploring the Meaning of Area 309
EXPLORATION 10.7 Exploring Area on Geoboards 310
EXPLORATION 10.8 Exploring the Area of a Circle 315
EXPLORATION 10.9 Can You Make the Quilt Pattern? 316
EXPLORATION 10.10 How Much Will the Carpet Cost? 317
EXPLORATION 10.11 Irregular Areas 318
EXPLORATION 10.12 Exploring Relationships Between Perimeter and Area 319
EXPLORATION 10.13 Functions, Geometric Figures, and Geoboards 321
SECTION 10.3 Exploring Surface Area and Volume 327
EXPLORATION 10.14 Understanding Surface Area 327
EXPLORATION 10.15 Understanding Volume 328
EXPLORATION 10.16 Determining Volumes of Irregularly Shaped Objects 330
EXPLORATION 10.17 Paper Towels 331
EXPLORATION 10.18 Measurement, Ambiguity, and Precision 332
EXPLORATION 10.19 Applying Volume Concepts 333
Endnotes E-1
Index I-1
Cutouts
BASE TEN GRAPH PAPER
OTHER BASE GRAPH PAPER
OTHER BASE GRAPH PAPER
OTHER BASE GRAPH PAPER
OTHER BASE GRAPH PAPER
GEOBOARD DOT PAPER
ISOMETRIC DOT PAPER
POLYOMINO GRID PAPER
POLYOMINO GRID PAPER
POLYOMINO GRID PAPER
POLYOMINO GRID PAPER
TANGRAM TEMPLATE
REGULAR POLYGONS
EXPLORING THE AREA OF A CIRCLE

Livro relacionado

Mathematics for elementary school teachers por Tom Bassarear Editora:  Cengage Learning, ©2011.

A problem solving approach to mathematics for elementary school teachers

Rick Billstein, Shlomo Libeskind e Johnny W. Lott

 Pearson | 2012 - 11ª edição | 1042 páginas | rar - pdf | 30,4 Mb

link (password: matav)

More than 350,000 students have prepared for teaching mathematics with A Problem Solving Approach to Mathematics for Elementary School Teachers since its first edition, and it remains the gold standard today. This text not only helps students learn the material by promoting active learning and developing skills and concepts—it also provides an invaluable reference to future teachers by including professional development features and discussions of today’s standards.

The Eleventh Edition is streamlined to keep students focused on what is most important. The Common Core State Standards (CCSS) have been integrated into the book to keep current with educational developments. The Annotated Instructor’s Edition offers new Integrating Mathematics and Pedagogy (IMAP) video annotations, in addition to activity manual and e-manipulative CD annotations, to make it easier to incorporate active learning into your course. MyMathLab® is available to offer auto-graded exercises, course management, and classroom resources for future teachers.

Table of Contents
1. An Introduction to Problem Solving
1-1 Mathematics and Problem Solving
1-2 Explorations with Patterns
1-3 Reasoning and Logic: An Introduction
2. Numeration Systems and Sets
2-1 Numeration Systems
2-2 Describing Sets
2-3 Other Set Operations and Their Properties
3. Whole Numbers and Their Operations
3-1 Addition and Subtraction of Whole Numbers
3-2 Algorithms for Whole-Number Addition and Subtraction
3-3 Multiplication and Division of Whole Numbers
3-4 Algorithms for Whole-Number Multiplication and Division
3-5 Mental Mathematics and Estimation for Whole-Number Operations
4. Number Theory
4-1 Divisibility
4-2 Prime and Composite Numbers
4-3 Greatest Common Divisor and Least Common Multiple
Online Module: Clock & Modular Arithmetic
5. Integers
5-1 Integers and the Operations of Addition and Subtraction
5-2 Multiplication and Division of Integers
6. Rational Numbers and Proportional Reasoning
6-1 The Set of Rational Numbers
6-2 Addition, Subtraction, and Estimation with Rational Numbers
6-3 Multiplication and Division of Rational Numbers
6-4 Ratios, Proportions, and Proportional Reasoning
7. Decimals: Rational Numbers and Percent
7-1 Introduction to Decimals
7-2 Operations on Decimals
7-3 Nonterminating Decimals
7-4 Percents and Interest
8. Real Numbers and Algebraic Thinking
8-1 Real Numbers
8-2 Variables
8-3 Equations
8-4 Functions
8-5 Equations in a Cartesian Coordinate System
Online Module: Using Real Numbers in Equations
9. Probability
9-1 How Probabilities Are Determined
9-2 Multistage Experiments with Tree Diagrams and Geometric Probabilities
9-3 Using Simulations in Probability
9-4 Odds, Conditional Probability, and Expected Value
9-5 Using Permutations and Combinations in Probability
10. Data Analysis/Statistics: An Introduction
10-1 Designing Experiments/Collecting Data
10-2 Displaying Data: Part I
10-3 Displaying Data: Part II
10-4 Measures of Central Tendency and Variation
10-5 Abuses of Statistics
11. Introductory Geometry
11-1 Basic Notions
11-2 Linear Measure
11-3 Curves, Polygons, and Symmetry
11-4 More About Angles
Online Module: Networks
12. Congruence and Similarity with Constructions
12-1 Congruence through Constructions
12-2 Other Congruence Properties
12-3 Other Constructions
12-4 Similar Triangles and Similar Figures
Online Module: Trigonometry Ratios via Similarity
13. Congruence and Similarity with Transformations
13-1 Translations and Rotations
13-2 Reflections and Glide Reflections
13-3 Dilations
13-4 Tessellations of the Plane
14. Area, Pythagorean Theorem, and Volume
14-1 Areas of Polygons and Circles
14-2 The Pythagorean Theorem, Distance Formula, and Equation of a Circle
14-3 Geometry in Three Dimensions
14-4 Surface Areas
14-5 Volume, Mass, and Temperature
Online Appendices
Spreadsheets
Graphing calculators
Geometer’s Sketchpad
GeoGebra

A request from Ramadan Badawi

Mathematical reasoning for elementary teachers

 Calvin T. Long, Duane W. DeTemple e Richard S. Millman

Pearson | 2011 -6ª edição |  949 páginas | rar - pdf | 21,5 Mb

link (password : matav)

Mathematical Reasoning for Elementary Teachers presents the mathematical knowledge needed for teaching, with an emphasis on whyfuture teachers are learning the content as well as when and how they will use it in the classroom. The Sixth Edition has been streamlined to make it easier to focus on the most important concepts. The authors continue to make the course relevant for future teachers, including the new features like Examining School Book Pages, as well as the hallmark features like Into the Classroom discussions and Responding to Students questions. Activities, classroom videos, and resources for professional development for future teachers are also available at www.pearsonhighered.com/teachingmath

Table of Contents
1. Thinking Critically
1.1 An Introduction to Problem Solving
1.2 Pólya's Problem-Solving Principles
1.3 More Problem-Solving Strategies
1.4 Algebra as a Problem-Solving Strategy
1.5 Additional Problem-Solving Strategies
1.6 Reasoning Mathematically
2. Sets and Whole Numbers
2.1 Sets and Operations on Sets
2.2 Sets, Counting, and the Whole Numbers
2.3 Addition and Subtraction of Whole Numbers
2.4 Multiplication and Division of Whole Numbers
3. Numeration and Computation
3.1 Numeration Systems Past and Present
3.2 Nondecimal Positional Systems
3.3 Algorithms for Adding and Subtracting Whole Numbers
3.4 Algorithms for Multiplication and Division of Whole Numbers
3.5 Mental Arithmetic and Estimation
4. Number Theory
4.1 Divisibility of Natural Numbers
4.2 Tests for Divisibility
4.3 Greatest Common Divisors and Least Common Multiples
5. Integers
5.1 Representations of Integers
5.2 Addition and Subtraction of Integers
5.3 Multiplication and Division of Integers
6. Fractions and Rational Numbers
6.1 The Basic Concepts of Fractions and Rational Numbers
6.2 Addition and Subtraction of Fractions
6.3 Multiplication and Division of Fractions
6.4 The Rational Number System
7. Decimals, Real Numbers, and Proportional Reasoning
7.1 Decimals and Real Numbers
7.2 Computations with Decimals
7.3 Proportional Reasoning
7.4 Percent
8. Algebraic Reasoning and Connections with Geometry
8.1 Algebraic Expressions, Functions, and Equations
8.2 Graphing Points, Lines, and Elementary Functions
8.3 Connections Between Algebra and Geometry
9. Geometric Figures
9.1 Figures in the Plane
9.2 Curves and Polygons in the Plane
9.3 Figures in Space
9.4 Networks
10. Measurement: Length, Area, and Volume
10.1 The Measurement Process
10.2 Area and Perimeter
10.3 The Pythagorean Theorem
10.4 Surface Area and Volume
11. Transformations, Symmetries, and Tilings
11.1 Rigid Motions and Similarity Transformations
11.2 Patterns and Symmetries
11.3 Tilings and Escher-like Designs
12. Congruence, Constructions, and Similarity
12.1 Congruent Triangles
12.2 Constructing Geometric Figures
12.3 Similar Triangles
13. Statistics: The Interpretation of Data
13.1 Organizing and Representing Data
13.2 Measuring the Center and Variation of Data
13.3 Statistical Inference
14. Probability
14.1 Experimental Probability
14.2 Principles of Counting
14.3 Permutations and Combinations
14.4 Theoretical Probability
Appendices
A. Manipulatives in the Mathematics Classroom
B. Getting the Most out of Your Calculator
C. A Brief Guide to the Geometer's Sketchpad
D. Resources

Mathematics: for Elementary School Teacher

Tom Bassarear 

Cengage Learning | 2011 - 5ª edição | 745 páginas | rar - pdf | 23,4 Mb

link (password: matav)

Intended for the one- or two-semester course required of Education majors, MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS, 5E, offers future teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect content to the hands-on activities in the corresponding Explorations Manual. Bassarear presents real-world problems, problems that require active learning in a method similar to how archaeologists explore an archaeological find: they carefully uncover the site, slowly revealing more and more of the structure. The author demonstrates that there are many paths to solving a problem, and that sometimes, problems have more than one solution. With this exposure, future teachers will be better able to assess student needs using diverse approaches

Contents
1 Foundations for Learning Mathematics 1
SECTION 1.1 Getting Started and Problem Solving 2
INVESTIGATIONS
1.1A Pigs and Chickens 7
1.1B Coin Problem? 12
SECTION 1.2 Patterns and Communication 14
INVESTIGATIONS
1.2A Sequences and Patterns 15
1.2B Patterns in Multiplying by 11 19
1.2C Pascal’s Triangle 21
1.2D Communicating Patterns in a Magic Square 22
SECTION 1.3 Reasoning and Proof 26
INVESTIGATIONS
1.3A Does Your Answer Make Sense? 26
1.3B Inductive Thinking with Fractions 27
1.3C Deductive Reasoning and Venn Diagrams 32
Data Highlights: Group Projects 123
Linking Concepts: Writing Projects 125
USING TECHNOLOGY 126
1.3D Why Is the Sum of Two Even Numbers an
Even Number? 33
1.3E Darts, Proof, and Communication 34
1.3F The Nine Dots Problem 35
1.3G How Many Games in the Tournament? 36
SECTION 1.4 Representation and Connections 39
INVESTIGATIONS
1.4A How Long Will It Take the Frog to Get out
of the Well? 40
1.4B How Many Pieces of Wire? 44
LOOKING BACK ON CHAPTER1 49
CHAPTER 1 SUMMARY 50
CHAPTER 1 REVIEW EXERCISES 51
2 Fundamental Concepts 53
SECTION 2.1 Sets 54
INVESTIGATIONS
2.1A Classifying Quadrilaterals 54
2.1B Describing Sets 56
2.1C How Many Subsets? 58
2.1D Translating Among Representations 63
2.1E Finding Information from Venn Diagrams 63
SECTION 2.2 Algebraic Thinking 68
INVESTIGATIONS
2.2A A Variable by Any Other Name Is Still a Variable 69
2.2B Baby-sitting 73
2.2C Choosing Between Functions 74
2.2D Matching Graphs to Situations 76
2.2F Looking for Generalizations 79
2.2G How Many Dots? 80
SECTION 2.3 Numeration 87
INVESTIGATIONS
2.3A Relative Magnitude of Numbers 98
2.3B What If Our System Was Based on One Hand? 99
2.3C How Well Do You Understand Base Five? 100
2.3D Base Sixteen 101
LOOKING BACK ON CHAPTER 2 106
CHAPTER 2 SUMMARY 107
CHAPTER 2 REVIEW EXERCISES 108
3 The Four Fundamental Operations of Arithmetic 111
SECTION 3.1 Understanding Addition 112
INVESTIGATIONS
3.1A A Pattern in the Addition Table 116
3.1B Mental Addition 117
3.1C Children’s Strategies for Adding Large Numbers 120
3.1D An Alternative Algorithm 123
3.1E Addition in Base Five 123
3.1F Children’s Mistakes 125
3.1G What Was the Total Attendance? 127
3.1H Estimating by Making Compatible Numbers 128
3.1I Number Sense with Addition 130
SECTION 3.2 Understanding Subtraction 133
INVESTIGATIONS
3.2A Mental Subtraction 137
3.2B Children’s Strategies for Subtraction with Large Numbers 139
3.2C An Alternative Algorithm 141
3.2D Children’s Mistakes in Subtraction 142
3.2E Rough and Best Estimates with Subtraction 143
3.2F Number Sense with Subtraction 143
SECTION 3.3 Understanding Multiplication 148
INVESTIGATIONS
3.3A A Pattern in the Multiplication Table 153
3.3B Mental Multiplication 154
3.3C An Alternative Algorithm 159
3.3D Why Does the Trick for Multiplying by 11 Work? 159
3.3E Multiplication in Base Five 160
3.3F Children’s Mistakes in Multiplication 162
3.3G Developing Estimation Strategies for Multiplication 162
3.3H Using Various Strategies in a Real-life Multiplication Situation 163
3.3I Number Sense with Multiplication 164
SECTION 3.4 Understanding Division 170
INVESTIGATIONS
3.4A Mental Division 174
3.4B Understanding Division Algorithms 175
3.4C The Scaffolding Algorithm 177
3.4D Children’s Mistakes in Division 178
3.4E Estimates with Division 180
3.4F Number Sense with Division 181
3.4G Applying Models to a Real-life Situation 182
3.4H Operation Sense 183
LOOKING BACK ON CHAPTER 3 189
CHAPTER 3 SUMMARY 190
CHAPTER 3 REVIEW EXERCISES 191
4 Number Theory 195
SECTION 4.1 Divisibility and Related Concepts 196
INVESTIGATIONS
4.1A Interesting Dates 196
4.1B Patterns in Odd and Even Numbers 198
4.1C Understanding Divisibility Relationships 200
4.1D Determining the Truth of an Inverse Statement 201
4.1E Understanding Why the Divisibility Rule for 3 Works 202
4.1F Divisibility by 4 and 8 204
4.1G Creating a Divisibility Rule for 12 207
SECTION 4.2 Prime and Composite Numbers 211
INVESTIGATIONS
4.2A The Sieve of Eratosthenes 212
4.2B Numbers with Personalities: Perfect and Other Numbers 217
SECTION 4.3 Greatest Common Factor and Least Common Multiple 220
INVESTIGATIONS
4.3A Cutting Squares Using Number Theory Concepts 220
4.3B Methods for Finding the GCF 222
4.3C Relationships Between the GCF and the LCM 227
4.3D Going Deeper into the GCF and the LCM 228
LOOKING BACK ON CHAPTER 4 232
CHAPTER 4 SUMMARY 232
CHAPTER 4 REVIEW EXERCISES 233
5 Extending the Number System 235
SECTION 5.1 Integers 236
INVESTIGATIONS
5.1A Subtraction with Integers 242
5.1B The Product of a Positive and a Negative Number 243
SECTION 5.2 Fractions and Rational Numbers 247
INVESTIGATIONS
5.2A Rational Number Contexts: What Does Mean? 248
5.2B Wholes and Units: Sharing Brownies 250
5.2C Unitizing 251
5.2D Fundraising and Thermometers 253
5.2E Partitioning with Number Line Models 254
5.2F Partitioning with Area Models 255
5.2G Partitioning with Set Models 256
5.2H Determining an Appropriate Representation 257
5.2I Sharing Cookies 260
5.2J Ordering Rational Numbers 262
5.2K Estimating with Fractions 262
SECTION 5.3 Understanding Operations with Fractions 268
INVESTIGATIONS
5.3A Using Fraction Models to Understand Addition of Fractions 268
5.3B Connecting Improper Fractions and Mixed Numbers 270
5.3C Mental Addition and Subtraction with Fractions 271
5.3D Estimating Sums and Differences with Fractions 273
5.3E Understanding Multiplication of Rational Numbers 274
5.3F Division of Rational Numbers 278
5.3G Estimating Products and Quotients 280
5.3H When Did He Run Out of Gas? 282
5.3I They’ve Lost Their Faculty! 283
SECTION 5.4 Beyond Integers and Fractions: Decimals, Exponents, and Real Numbers 288
INVESTIGATIONS
5.4A Base Ten Blocks and Decimals 290
5.4B When Two Decimals Are Equal 291
5.4C When Is the Zero Necessary and When Is It Optional? 292
5.4D Connecting Decimals and Fractions 293
5.4E Ordering Decimals 294
5.4F Rounding with Decimals 296
5.4G Decimals and Language 297
5.4H Decimal Sense: Grocery Store Estimates 300
5.4I Decimal Sense: How Much Will the Project Cost? 301
5.4J How Long Will She Run? 302
5.4K Exponents and Bacteria 302
5.4L Scientific Notation: How Far Is a Light-Year? 304
5.4M Square Roots 306
LOOKING BACK ON CHAPTER 5 312
CHAPTER 5 SUMMARY 313
CHAPTER 5 REVIEW EXERCISES 314
6 Proportional Reasoning 315
SECTION 6.1 Ratio and Proportion 316
INVESTIGATIONS
6.1A Unit Pricing—Is Bigger Always Cheaper? 319
6.1B How Many Trees Will Be Saved? 320
6.1C How Much Money Will the Trip Cost? 321
6.1D Reinterpreting Old Problems 322
6.1E Using Estimation with Ratios 322
6.1F Comparing Rates 324
6.1G Is the School on Target? 327
6.1H Finding Information from Maps 328
6.1I From Raw Numbers to Rates 329
6.1J How Much Does That Extra Light Cost? 330
SECTION 6.2 Percents 335
INVESTIGATIONS
6.2A Who’s the Better Free-Throw Shooter? 336
6.2B Understanding a Newspaper Article 337
6.2C Buying a House 340
6.2D Sale? 342
6.2E What Is a Fair Raise? 343
6.2F How Much Did the Bookstore Pay for the Textbook? 344
6.2G The Copying Machine 345
6.2H 132% Increase? 346
6.2I Saving for College 348
6.2J How Much Does That Credit Card Cost You? 350
LOOKING BACK ON CHAPTER 6 354
CHAPTER 6 SUMMARY 355
CHAPTER 6 REVIEW EXERCISES 355
7 Uncertainty: Data and Chance 357
SECTION 7.1 The Process of Collecting and Analyzing Data 359
INVESTIGATIONS
7.1A What Is Your Favorite Sport? 360
7.1B How Many Siblings Do You Have? 363
7.1C Going Beyond a Computational Sense of Average 368
7.1D How Many Peanuts Can You Hold in One Hand? 369
7.1E How Long Does It Take Students to Finish the Final Exam? 373
7.1F Videocassette Recorders 379
7.1G Fatal Crashes 382
7.1H Hitting the Books 385
SECTION 7.2 Going Beyond the Basics 396
INVESTIGATIONS
7.2A How Many More Peanuts Can Adults Hold
Than Children? 396
7.2B Scores on a Test 399
7.2C Which Battery Do You Buy? 400
7.2D Understanding Standard Deviation 403
7.2E Analyzing Standardized Test Scores 406
7.2F How Long Should the Tire Be Guaranteed? 407
7.2G Comparing Students in Three Countries 412
7.2H Grade Point Average 415
7.2I What Does Amy Need to Bring Her GPA Up to 2.5? 416
SECTION 7.3 Concepts Related to Chance 424
INVESTIGATIONS
7.3A Probability of Having 2 Boys and 2 Girls 427
7.3B Probability of Having 3 Boys and 2 Girls 430
7.3C Probability of Having at Least 1 Girl 431
7.3D 50-50 Chance of Passing 432
7.3E What Is the Probability of Rolling a 7? 433
7.3F What Is the Probability of Rolling a 13 with 3 Dice? 435
7.3G “The Lady or the Tiger” 436
7.3H Gumballs 438
7.3I Is This a Fair Game? 440
7.3J What About This Game? 440
7.3K Insurance Rates 442
SECTION 7.4 Counting and Chance 447
INVESTIGATIONS
7.4A How Many Ways to Take the Picture? 447
7.4B How Many Different Election Outcomes? 449
7.4C How Many Outcomes This Time? 451
7.4D Pick a Card, Any Card! 453
7.4E So You Think You’re Going to Win the Lottery? 454
LOOKING BACK ON CHAPTER 7 456
CHAPTER 7 SUMMARY 457
CHAPTER 7 REVIEW EXERCISES 458
8 Geometry as Shape 463
SECTION 8.1 Basic Ideas and Building Blocks 463
INVESTIGATIONS
8.1A Playing Tetris 465
8.1B Different Objects and Their Function 466
8.1C Point, Line, and Plane 472
8.1D Measuring Angles 478
SECTION 8.2 Two-Dimensional Figures 484
INVESTIGATIONS
8.2A Recreating Shapes from Memory 485
8.2B All the Attributes 487
8.2C Classifying Figures 487
8.2D Why Triangles Are So Important 491
8.2E Classifying Triangles 492
8.2F Triangles and Venn Diagrams 494
8.2G Congruence with Triangles 498
8.2H Quadrilaterals and Attributes 500
8.2I Challenges 501
8.2J Relationships Among Quadrilaterals 502
8.2K Sum of the Interior Angles of a Polygon 506
8.2L What Are My Coordinates? 509
8.2M Understanding the Distance Formula 510
8.2N The Opposite Sides of a Parallelogram Are Congruent 510
8.2O Midpoints of Any Quadrilateral 512
SECTION 8.3 Three-Dimensional Figures 518
INVESTIGATIONS
8.3A What Do You See? 520
8.3B Connecting Polygons to Polyhedra 521
8.3C Features of Three-Dimensional Objects 523
8.3D Prisms and Pyramids 526
8.3E Different Views of a Building 528
8.3F Isometric Drawings 529
8.3G Cross Sections 530
8.3H Nets 531
LOOKING BACK ON CHAPTER 8 537
CHAPTER 8 SUMMARY 538
CHAPTER 8 REVIEW EXERCISES 539
9 Geometry as Transforming Shapes 543
SECTION 9.1 Congruence Transformations 546
INVESTIGATIONS
9.1A Understanding Translations 547
9.1B Understanding Reflections 549
9.1C Understanding Rotations 550
9.1D Understanding Translations, Reflections, and Rotations 552
9.1E Connecting Transformations 555
9.1F Transformations and Art 557
SECTION 9.2 Symmetry and Tessellations 563
INVESTIGATIONS
9.2A Reflection and Rotation Symmetry in Triangles 566
9.2B Reflection and Rotation Symmetry in Quadrilaterals 567
9.2C Reflection and Rotation Symmetry in Other Figures 568
9.2D Letters of the Alphabet and Symmetry 568
9.2E Patterns 569
9.2F Symmetries of Strip Patterns 572
9.2G Analyzing Brick Patterns 575
9.2H Which Triangles Tessellate? 580
9.2I Which Regular Polygons Tessellate? 581
9.2J Tessellating Trapezoids 583
9.2K More Tessellating Polygons 585
9.2L Generating Pictures Through Transformations 587
SECTION 9.3 Similarity 595
INVESTIGATIONS
9.3A Understanding Similarity 596
9.3B Similarity Using an Artistic Perspective 598
9.3C Using Coordinate Geometry to Understand
Similarity 599
LOOKING BACK ON CHAPTER 9 601
CHAPTER 9 SUMMARY 602
CHAPTER 9 REVIEW EXERCISES 602
10 Geometry as Measurement 605
SECTION 10.1 Systems of Measurement 606
INVESTIGATIONS
10.1A Developing Metric Sense 611
10.1B Converting Among Units in the Metric System 614
SECTION 10.2 Perimeter and Area 619
INVESTIGATIONS
10.2A What Is the Length of the Arc? 620
10.2B Converting Units of Area 625
10.2C Using the Pythagorean Theorem 626
10.2D Understanding the Area Formula for Circles 627
10.2E A 16-Inch Pizza Versus an 8-Inch Pizza 628
10.2F How Big Is the Footprint? 628
10.2G Making a Fence with Maximum Area 630
SECTION 10.3 Surface Area and Volume 637
INVESTIGATIONS
10.3A Are Their Pictures Misleading? 646
10.3B Finding the Volume of a Hollow Box 647
10.3C Surface Area and Volume 648
LOOKING BACK ON CHAPTER 10 654
CHAPTER 10 SUMMARY 655
CHAPTER 10 REVIEW EXERCISES 655

Primary Mathematics: Audit and Test: Assesing Your Knowledge And Understanding

Claire Mooney, Mike Fletcher
Learning Matters; Third Edition  | 2007 | 51 páginas | pdf | 447 kb

link


This book supports trainees on primary initial teacher training courses where a secure knowledge and understanding of mathematics is required for the award of Qualified Teacher Status (QTS). A rigorous test enables trainees to identify their strengths and weaknesses in mathematics and this can be revisited in order to monitor and evaluate progress towards QTS. Trainees are able to direct their studies more usefully and quickly develop confidence in topics they find difficult. This edition is fully up to date with the 2007 QTS Standards.

Contents
Introduction 1
Part 1 Mathematics background 5
Part 2 Interest in mathematics 6
Part 3 Perceived competence and confidence in mathematics 7
Competence 7
Making sense of your perceived competence 9
Confidence 10
Making sense of your perceived confidence 11
Part 4 Mathematics test 12
Number 12
Algebra – patterns and relationships 15
Shape and space 17
Statistics 23
Probability 23
Measures 24
Equations and graphs 25
Reasoning and proof 27
Making sense of your test results 27
Part 5 Answers to test questions 29
Part 6 Targets for further development 42
Part 7 Revision and further reading 43

Primary Mathematics

Heather Cooke

 (Developing Subject Knowledge series)

Paul Chapman Educational Publishing | 2001 | 208 páginas | PDF | 993 kb

link
depositfiles.com (PDF | 1,4 MB)

Primary Mathematics is a purpose-written distance-learning text originally produced as Passport to Mathematics by The Open University's Centre for Mathematics Education. In its new form it contains additional audit material to support trainee teachers.

The task-driven text emphasizes strategies and processes and is very different from the usual style of mathematics textbooks. Each of the sections is designed to stand-alone so that they can be studied in any order. Trainees have reported that the material not only helped them to raise their knowledge and understanding to the required standard but also greatly improved their mathematical confidence.

Primary Mathematics is designed for self-study, but the material can also been used as a resource for face-to-face and electronic and conferencing tuition. Important mathematical ideas are indexed and cross-referenced to emphasize connections within mathematics.

Contents:

Learning and Doing 
Number and Measure 
Statistics and Measuring 
Number and Algebra 
Geometry and Algebra 
Chance and Reasoning 
Proof and Reasoning 
Practice Exercises

The Mathematics that Every Secondary School Math Teacher Needs to Know

Alan Sultan

Routledge | 2010 | 740 páginas | PDF | 4,4 Mb

link direto
link

What knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the deep mathematical insight they need to engage their students in learning mathematics in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining.

Features include Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great "MATH-N-SIGHT":

M Multiple Approaches/Representations
A Applications to Real Life
T Technology
H History
N Nature of Mathematics: Reasoning and Proof
S Solving Problems
I Interlinking Concepts: Connections
G Grade Levels
H Honing of Mathematical Skills
T Typical Errors

This text is aligned with the recently released Common Core State Standards, and is ideally suited for a capstone mathematics course in a secondary mathematics certification program. It is also appropriate for any methods or mathematics course for pre- or in-service secondary mathematics teachers, and is a valuable resource for classroom teachers.