sexta-feira, 4 de abril de 2014

Using Children’s Literature to Teach Problem Solving in Math: Addressing the Common Core in K–2

Jeanne White


Routledge | 2013 | 111 páginas | rar - pdf | 516 kb

link (password: matav)

Learn how to use children’s literature to engage students in mathematical problem solving. Teaching with children’s literature helps build a positive math environment, encourages students to think abstractly, shows students the real-world purposes of math, builds content-area literacy, and appeals to students with different learning styles and preferences. This practical book provides specific children’s book ideas and standards-based lessons that you can use to bring math alive in your own classroom.
Special Features:
  • Step-by-step ideas for using children’s literature to teach lessons based on the Common Core Standards for Mathematical Content in kindergarten, first, and second grade
  • Scripting, modeling, and discussion prompts for each lesson
  • Information on alignment to the Standards for Mathematical Practice and how to put them into student-friendly language
  • Reference to a wide variety of specific children’s literature that can provide a context for young children learning to engage in the standards
  • Differentiated activities for students who are early, developing, and advanced problem solvers
Contents
About the Author ix
Acknowledgments xi
Introduction: Using Children’s Literature to Teach
Problem Solving in Math 1
Types of Problem Solvers 2
Creating a Problem-Solving Community 3
1 Make Sense and Persevere 5
Early Problem Solvers 6
Seven Blind Mice—Decomposing Numbers 6
Developing Problem Solvers 10
MATH-Terpieces: The Art of Problem Solving—Using 2 and 3 Addends to Find a Sum 10
Advanced Problem Solvers 12
Splash!—Representing Addition and Subtraction Problems 12
2 Reason Abstractly 15
Early Problem Solvers 16
Ten Flashing Fireflies—Exploring the Commutative Property of Addition 16
Rooster’s Off to See the World—Exploring the Associative Property of Addition 17
Developing Problem Solvers 19
Each Orange Had 8 Slices—Demonstrating Fluency for Addition 19
Advanced Problem Solvers 21
How Many Mice?—Representing and Solving Problems With Addition and Subtraction 21
3 Construct Arguments 23
Early Problem Solvers 24
How Many Seeds in a Pumpkin?—Skip-Counting and Comparing Three-Digit Numbers 24
Developing Problem Solvers 27
Mall Mania—Adding Two-Digit Numbers Using Various Strategies 27
Advanced Problem Solvers 29
Spaghetti and Meatballs for All!—Creating Composite Shapes 29
4 Create a Model 33
Early Problem Solvers 33
The Doorbell Rang—Representing Addition in Various Ways 33
Developing Problem Solvers 38
Bigger, Better, Best!—Using Addition With Rectangular Arrays 38
Advanced Problem Solvers 42
Alexander, Who Used to be Rich Last Sunday—Solving Word Problems With Money 42
5 Use Mathematical Tools 47
Early Problem Solvers 48
Earth Day-Hooray!—Using Place Value to Add and Subtract 48
Developing Problem Solvers 52
Mummy Math—Recognizing Attributes of 3D Objects 52
Advanced Problem Solvers 54
Measuring Penny—Measuring in Standard and Nonstandard Units 54
6 Attend to Precision 59
Early Problem Solvers 59
If You Were a Quadrilateral—Identifying Quadrilaterals 59
Developing Problem Solvers 62
Lemonade for Sale—Representing and Interpreting Data 62
Advanced Problem Solvers 65
Measuring Penny—Relating Addition and Subtraction to Length 65
7 Look for Structure 69
Early Problem Solvers 69
The Button Box—Identifying Attributes for Sorting 69
Developing Problem Solvers 73
Patterns in Peru—Describing Relative Positions 73
Advanced Problem Solvers 76
The Greedy Triangle—Exploring Attributes of Shapes 76
8 Apply Repeated Reasoning 81
Early Problem Solvers 82
Bunches of Buttons: Counting by Tens—Counting to 100 by Tens 82
Developing Problem Solvers 85
How Big is a Foot?—Iterating Length Units 85
Advanced Problem Solvers 87
The King’s Commissioners—Representing Tens and Ones 87
Next Steps 91
Appendix: Common Addition and Subtraction Situations 93
References 95

Elementary Statistics: Picturing the World

Ron Larson e Betsy Farber

Pearson | 2014 - 6ª edição |705 páginas | rar - pdf |12,4 Mb

link (password : matav)

5.ª edição - 2012

Statistics opens a window to the modern world, and this market-leading text makes it easy to understand! Larson and Farber’s Elementary Statistics: Picturing the World, Sixth Edition, provides stepped out instruction, real-life examples and exercises, and the use of technology to offer the most accessible approach. The authors carefully develop theory through strong pedagogy, and examples show how statistics is used to picture and describe the world. In keeping with the premise that students learn best by doing, it includes more than 210 examples and more than 2300 exercises, to make the concepts of statistics a part of students’ everyday lives.



Contents
PART ONE. DESCRIPTIVE STATISTICS
1. Introduction to Statistics
1.1. An Overview of Statistics
1.2. Data Classification
            Case Study: Rating Television Shows in the
            United States
1.3. Data Collection and Experimental Design
            Activity: Random Numbers
            Uses and Abuses
Chapter Summary
Review Exercises
Chapter Quiz
Chapter Test
            Real Statistics-Real Decisions-Putting It All Together
            History of Statistics-Timeline
            Technology: Using Technology in Statistics
2. Descriptive Statistics
2.1. Frequency Distributions and Their Graphs
2.2. More Graphs and Displays
2.3. Measures of Central Tendency
            Activity: Mean Versus Median
2.4. Measures of Variation
            Activity: Standard Deviation
            Case Study: Business Size
2.5. Measures of Position
            Uses and Abuses
Chapter Summary
Review Exercises
Chapter Quiz
Chapter Test
            Real Statistics-Real Decisions-Putting It All Together
            Technology: Parking Tickets
            Using Technology to Determine Descriptive
            Statistics
Cumulative Review: Chapters 1 and 2
PART TWO. PROBABILITY & PROBABILITY DISTRIBUTIONS
3. Probability
3.1. Basic Concepts of Probability and Counting
            Activity: Simulating the Stock Market
3.2. Conditional Probability and the Multiplication Rule
3.3. The Addition Rule
            Activity: Simulating the Probability of Rolling a 3 or 4
            Case Study: United States Congress
3.4. Additional Topics in Probability and Counting
            Uses and Abuses
Chapter Summary
Review Exercises
Chapter Quiz
Chapter Test
            Real Statistics-Real Decisions-Putting It All Together
            Technology: Simulation: Composing Mozart
            Variations with Dice
4. Discrete Probability Distributions
4.1. Probability Distributions
4.2. Binomial Distributions
            Activity: Binomial Distribution
            Case Study: Distribution of Number of Hits in
            Baseball Games
4.3. More Discrete Probability Distributions
            Uses and Abuses
Chapter Summary
Review Exercises
Chapter Quiz
Chapter Test
            Real Statistics-Real Decisions-Putting It All Together
            Technology: Simulation: Using Poisson
            Distributions as Queuing Models
5. Normal Probability Distributions
5.1. Introduction to Normal Distributions and the Standard Normal Distribution
5.2. Normal Distributions: Finding Probabilities
5.3. Normal Distributions: Finding Values
            Case Study: Birth Rates in America
5.4. Sampling Distributions and the Central Limit Theorem
            Activity: Sampling Distributions
5.5. Normal Approximations to Binomial Distributions
            Uses and Abuses
Chapter Summary
Review Exercises
Chapter Quiz
Chapter Test
            Real Statistics-Real Decisions-Putting It All Together
            Technology: Simulation: Age Distribution in the
            United States
Cumulative Review: Chapters 3 to 5
PART THREE. STATISTICAL INFERENCE
6. Confidence Intervals
6.1. Confidence Intervals for the Mean (¡ Known)
6.2. Confidence Intervals for the Mean (¡ Unknown)
            Activity: Confidence Intervals for a Mean
            Case Study: Marathon Training
6.3. Confidence Intervals for Population Proportions
            Activity: Confidence Intervals for a Proportion
6.4. Confidence Intervals for Variance and Standard Deviation
            Uses and Abuses
Chapter Summary
Review Exercises
Chapter Quiz
Chapter Test
            Real Statistics-Real Decisions-Putting It All Together
            Technology: Simulation: Most Admired Polls
            Using Technology to Construct Confidence
            Intervals
7. Hypothesis Testing with One Sample
7.1. Introduction to Hypothesis Testing
7.2. Hypothesis Testing for the Mean (¡ Known)
7.3. Hypothesis Testing for the Mean (¡ Unknown)
            Activity: Hypothesis Test for a Mean
            Case Study: Human Body Temperature: What's
            Normal?
7.4. Hypothesis Testing for Proportions
            Activity: Hypothesis Test for a Proportion
7.5. Hypothesis Testing for Variance and Standard Deviation
A Summary of Hypothesis Testing
            Uses and Abuses
Chapter Summary
Review Exercises
Chapter Quiz
Chapter Test
            Real Statistics-Real Decisions-Putting It All Together
            Technology: The Case of the Vanishing Women
            Using Technology to Perform Hypothesis Tests
8. Hypothesis Testing with Two Samples
8.1. Testing the Difference Between Means (Independent Samples, ¡1 and ¡2 Known)
8.2. Testing the Difference Between Means (Independent Samples, ¡1 and ¡2 Unknown)
8.3. Testing the Difference Between Means (Dependent Samples)
8.4. Testing the Difference Between Proportions
A Summary of Hypothesis Testing
            Uses and Abuses
Chapter Summary
Review Exercises
Chapter Quiz
Chapter Test
            Real Statistics-Real Decisions-Putting It All Together
            Technology: Tails over Heads
            Using Technology to Perform Two-Sample
            Hypothesis Tests
Cumulative Review: Chapters 6 to 8
PART FOUR. MORE STATISTICAL INFERENCE
9. Correlation and Regression
9.1 Correlation
            Activity: Correlation by Eye
9.2. Linear Regression
            Activity: Regression by Eye
            Case Study: Correlation by Body Measurements
9.3. Measures of Regression and Prediction Intervals
9.4. Multiple Regression
A Summary of Hypothesis Testing
            Uses and Abuses
Chapter Summary
Review Exercises
Chapter Quiz
Chapter Test
            Real Statistics-Real Decisions-Putting It All Together
            Technology: Nutrients in Breakfast Cereals
10. Chi-Square Tests and the F-Distribution
10.1. Goodness-of-Fit Test
10.2. Independence
            Case Study: Food Safety Survey
10.3. Comparing Two Variances
10.4. Analysis of Variance
            Uses and Abuses
Chapter Summary
Review Exercises
Chapter Quiz
Chapter Test
            Real Statistics-Real Decisions-Putting It All Together
            Technology: Teacher Salaries
Cumulative Review: Chapters 9 and 10

quinta-feira, 3 de abril de 2014

Math Stuff

Theoni Pappas 

 Wide World Publishing, Tetra | 2002 | 225 páginas | rar - pdf | 6,7 Mb

link (password: matav)

Whether one is adjusting the settings of a camera, doing financial planning, or just talking about the weather, everyone is involved in mathematics every day. Theoni Pappas explores some of the many areas in which one least expects to find "math stuff." Readers learn how computers get stressed out, how epaper works, and how codes and numbers affect the body.

TABLE OF CONTENTS
Introduction ix
The pea counts 2
mathematics behind your genes
The mathematics of peace 12
The millennium clock 16
Chaos theory 21
Cricket math 26
Mathematical private eyes 27
ratios hold the clues
Holyhedrons 30
Fractals, fractals everywhere 32
Smart dust, MEMS 40
What’s it all about?
Starcage 44
the works of Akio Hizume
In search of AI 50
mathematics & artificial intelligence
Art in nature/nature in art 60
Andy Goldsworthy
Do bees count? 64
e-paper & mathematics 65
Mathematics mints a coin 70
The sound of mathematics 72
music & mathematics
Mathematics engineers your finances 82
Numbers, numbers everywhere 85
You’ve come a long way ! 89
Icosa shelters 95
mathematically designed shelters
Computers get stressed out too! 98
lock-up, crash, freeze
mathematics & the pomegranate 101
rhombic dodecahedron & sphere packing

Differential Equations of My Young Years



Vladimir Maz'ya e Arkady Alexeev

Birkhäuser | 2014 | 204 páginas | rar - pdf | 7,7 Mb

link (password: matav)

Vladimir Maz'ya (born 1937) is an outstanding mathematician who systematically made fundamental contributions to a wide array of areas in mathematical analysis and in the theory of partial differential equations. In this fascinating book he describes the first thirty years of his life. He starts with the story of his family, speaks about his childhood, high school and university years, describe his formative years as a mathematician. Behind the author's personal recollections, with his own joys, sorrows and hopes, one sees a vivid picture of the time. He speaks warmly about his friends, both outside and inside mathematics. The author describes the awakening of his passion for mathematics and his early achievements. He mentions a number of mathematicians who influenced his professional life. The book is written in a readable and inviting way sometimes with a touch of humor. It can be of interest for a very broad readership.

Contents
1. Family and Early Childhood .. 1
1.1 The Beginning . . 1
1.2 The Time of Peace Is Over . . 5
1.3 My Mother’s Story . . 6
1.4 My Father’s Story .. 10
1.5 In Sverdlovsk . .. 15
1.6 Back to Leningrad .  20
1.7 Postage Stamps .. 21
1.8 Crime Without Punishment . 23
1.9 From the Kiosk to House No. 19/18  . 23
1.10 Life in the “Small Room” on Marat Street . . 26
1.11 Aunt Rita and Lusya .. 30
1.12 Lusya, Ella and the Sinclairs  . 31
1.13 Uncle Aron, Bathhouse and Chess  . 32
1.14 Mother and My First Library . 33
1.15 Durian  . 35
1.16 Our Room . . 35
1.17 The Kitchen and the Toilet . . 39
1.18 Life Has Become Better . . 40
1.19 Even the Sun Has Spots .. 42
2 Boyhood . . 45
2.1 It Is So Difficult to Become an “A” Student . . 45
2.2 The Importance of Being an “A” Student . . 50
2.3 Slingshots  . 52
2.4 Illnesses . . 53
2.5 “Physcult” and Sports . 56
2.6 To Me the Most Important Art Was the Movies  . 59
2.7 A Sharp Kid . . 59
2.8 Foreign Languages  . 63
2.9 My Interests . 64
2.10 Poetry . . 66
2.11 Fimka. 67
2.12 The First Place in the District!  . 69
3 High School Life . . . . 73
3.1 In the Sixth Grade . . 73
3.2 In the Seventh Grade  . 75
3.3 The Indecent Topic  . 75
3.4 My Circle of Reading . 77
3.5 I Chose Mathematics .  . 78
3.6 A Circle at the Palace of Pioneers .  . 79
3.7 Two Lectures for School Children .  . 82
3.8 Murderers in Doctors’ Smocks . . 83
3.9 The English Teacher .  . 84
3.10 Arkady Alexeev .. 87
3.11 Alexeev’s Story . . . 88
4 Mathematics and Other Activities . . 91
4.1 Vanity of Vanities, All Is Vanity .  91
4.2 You Cannot Live Without Women. No! . . 95
4.3 Phase Transition . 97
4.4 My First Mathmech Year .  97
4.5 Student Contests . . 99
4.6 We Lead Our Life in Major Key . . 101
4.7 A Mysterious ID  . 103
4.8 Musical Moments (Leonid Druz)  . 105
4.9 Valery Maisky . .  . 117
4.10 The Authorities Did Not Like Me .  . 120
4.11 How I Did Not Become a Dissident .  122
4.12 Misha Danilov . . 123
5 Mathmech Life .. 129
5.1 The Mathmech Cafeteria .. 129
5.2 Fractional Derivatives . . 130
5.3 Something New at Last! . .. . 130
5.4 Student Scientific Society (SSS) and Tseitin .. 132
5.5 “Quasi-publication” and S. M. Lozinsky . 133
5.6 The Mathmech Choir . 139
5.7 My Doubts and S. G. Mikhlin’s Advice  . 139
5.8 A Few Words About Mikhlin .  . 142
5.9 In the Fourth Year . . 144
5.10 The Virgin Soil . . 147
5.11 In My Fifth Year .  . 148
5.12 Bakelman’s Special Course . . 149
5.13 Job Placement . . 152
5.14 Siegfried . . 154
6. Dissertations and the Years After .. 157
6.1 Steel Sheets and YMS . . . 157
6.2 Possibility and Reality .  . 158
6.3 Defense at the Moscow State University . . 159
6.4 Defense at the Leningrad University . 163
6.5 About V. I. Smirnov . . . 166
6.6 An Order: Scatter the Composed Type .  . 167
6.7 About the “Big Seminar” .. 168
6.8 After the Defense of the Doctor’s Degree Dissertation .  170
6.9 One Hour Late, Lose the Whole Year . .. 175
6.10 A Similar Topic . 176
6.11 Non-Travels to Foreign Countries . . 176
6.12 Counterexamples to a Hilbert Problem  . 178
6.13 Talent .. 181
6.14 Farewell, My Young Years! . . 182
6.15 How Many Medium Range Rockets Were There? . 185
6.16 Under Close Surveillance? . . 186
Index .  . 189

Dr. Crypton and His Problems: Mind Benders from Science Digest

 Dr. Crypton
 St Martins Pr | 1982 | 191 páginas | djvu | 1,7 Mb
link

link1

" The mysterious Dr. Crypton (presumably a friend  of Superman except that he has a superbrain instead  of a superbody) has assembled a super collection of puzzles and curiosities involving mathematics, words, and anything at all that lends itself to logical  and creative thinking. A delightful book to read and ponder. " 
-Martin Gardner

Contents 
Acknowledgments vii
Questions by Isaac Asimov ix
1. An Enigmatic Evening with Microwave Cornbread 1
2. The Intragalactic Cabaret 14
3. The Case of the Fatal Forfex 23
4. Palindromes: No Lemons! No Melon! 31
5. Sleight of Mind in Katmandu 42
6. Shockley: Sperm Hustler Offers Compatible  Kinky Ladies Einsteinish Young 50
7. Zeno of Elea: The First Paradoxologist 57
8. The Well-Hung Natives and Twenty-three  Other Conundrums 67
9. The Logistics of Armchair Ornithology 115
10. Lora Does a Mobius Strip 121
11. The BANG and Other Phrenetic Phrases 143
12. How's Your Resistance? (There's No Place like Ohm) 148
14. Triskaidekaphobia 151
15. Freud and the Number 23 158
16. The Puzzles of Nympholepts: Lewis Carroll and
Vladimir Nabokov 165
17. The Talk of the Town 178 



Mathematical Connections: A Companion for Teachers

(Classroom Resource Material) 

Al Cuoco

The Mathematical Association of America | 2005 | 261 páginas | pdf | 6,3 Mb

link
link1

This book is about some of the topics that form the foundations for high school mathematics. It focuses on a closely-knit collection of ideas that are at the intersection of algebra, arithmetic, combinatorics, geometry, and calculus. Most of the ideas are classical: methods for fitting polynomial functions to data, for summing powers of integers, for visualizing the iterates of a function defined on the complex plane, or for obtaining identities among entries in Pascal's triangle. Some of these ideas, previously considered quite advanced, have become tractable because of advances in computational technology. Others are just beautiful classical mathematics, topics that have fallen out of fashion and that deserve to be resurrected While the book will appeal to many audiences, one of the primary audiences is high school teachers, both practicing and prospective. It can be used as a text for undergraduate or professional courses, and the design lends itself to self-study. Of course, good mathematics for teaching is also good for many other uses, so readers of all persuasions can enjoy exploring some of the beautiful ideas presented in the pages of this book.

Contents
1. Difference tables and polynomial fits. Doing it with sums
Doing it with differences
Finding a formula: combinatorial polynomials
Making it formal: the [delta] operator
Going the other way: polynomials to tables
Conversions
From Newton to Lagrange
Agreeing to disagree
2. Form and function: the algebra of polynomials. Polynomials
The basic theorems
Coefficients and values
Up a level
Transformations
Coefficients and zeros.
3. Complex numbers, complex maps, and trigonometry. Complex numbers
The complex plane
The geometry behind multiplying
Trigonometric identities
Complex maps
Julia sets and the Mandelbrot set.
4. Combinations and locks. Combinatorial proofs and identities
The simplex lock
Some approaches to the simplex lock problem
Connections to the Mahler basis.
5. Sums of powers. Summatory polynomials
Bernoulli's method.

Mathematical Mysteries: the beauty and magic of numbers

 Calvin C. Clawson

Plenum Press | 1996 | 322 páginas | rar - pdf | 7,7 Mb

link (password: matav)

Why seemingly unrelated mathematical truths are connected in simple and beautiful equations continues to stump even mathematicians. This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician’s treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements,Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

CONTENTS

Introduction 1
CHAPTER 1 Discovery of the Number Sequence 8
CHAPTER 2 Numbers and the Occult 39
CHAPTER 3 Sequences and Series 53
CHAPTER 4 The Family of Numbers 77
CHAPTERS Story for a Rich Man 95
CHAPTER 6 Exotic Connections 116
CHAPTER 7 Closing in on the Primes 145
CHAPTER 8 Primes in Depth 164
CHAPTER 9 Primes and Secret Codes 184
CHAPTER 10 The Remarkable Ramanujan
CHAPTER 11 Ramanujan's Equations
CHAPTER 12 Goldbach's Conjecture
CHAPTER 13 Deepest Mysteries
CHAPTER 14 Into the Stratosphere
EndNotes
Suggested Reading
Index


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