Fostering Children's Number Sense in Grades K-2: Turning Math Inside Out

(New 2013 Curriculum & Instruction Titles)

Gregory Nelson

Pearson | 2013 | 173 páginas | rar - pdf | 2,5 Mb

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Fostering Children's Number Sense in Grades K-2 is a powerful, hands-on resource that helps in-service teachers, curriculum coaches, and math intervention specialists ensure children’s deep understanding of addition and subtraction in ways that enable long-term growth. Packed with child-centered instructional strategies, powerful and engaging learning materials, and revealing assessment tools, the book is clearly laid out and cross-referenced to the Common Core State Standards.

Contents

SECTION 1:  GETTING STARTED

Chapter 1:  Rethinking Number Sense

What math is not

Children’s readiness to be mathematicians

How we should teach math

What the experts and the research tell us

Math inside out

Chapter 2:  How to Teach Math This Way

Logistics

Space

Preparing the teaching materials

“Math time”

Work, not play

Learner-centered instruction

How we tend to teach…and why

Creating the learning community you want

Teacher-led lessons

The perils of group work

The role of the teacher as the children work

Keeping everyone safe

Authentic assessment

Teaching tips

Helping children talk about what they know

Three levels of vocabulary acquisition

Concrete before abstract

The same thing many ways

Errors are information

Competition

Answer keys, or no answer keys?

Study group discussion starters: Turning math inside out

SECTION 2:  EMERGENCE OF SECURE PLACE-VALUE AWARENESS

Chapter 3:  Place-Value Awareness Launch Points

What this is, and why it is important

What comes before, and how to get there

Logical quantification (K.NCC.4b)

Accurate counting to ten (K.NCC.1, K.NCC.4, K.NCC.5)

Connecting numerals to quantities (K.NCC.3)

Concepts and skills being reinforced at this developmental stage

The teen counting numbers have 10 as a base (K.NBT.1)

The use of zero as a place holder (1.NBT.2c)

The part-whole concept extended to the place value system (K.NBT.1, 1.NBT.2)

Place value versus face value (1.NBT.2)

The 10:1 relationship between units and tens (1.NBT.2a)

Directionality in reading multi-digit numerals (1.NBT.1)

Counting on using place value categories (K.CC.1, K.CC.2, 1.NBT.1)

Counting backwards through the decades

Estimating larger quantities

Greater than/less than in the place value system (1.NBT.3)

The relationship between hundreds and tens (2.NBT.1)

Launch points

Teen boards

Tens boards

Hands Up #1

“How Old Are We?” books

Hundreds board

Estimation activities (Unifix cubes; Cuisenaire rods; ten frames)

Race to a 100

Chapter 4:  Place-Value Awareness Check Points

Assessment probes

Cuisenaire teens

Hundred chain

Page walk

Hundreds board magic windows

Arrow math

Decade transition boards

How Many Now? — Variation #1

How Many Now? — Variation #2

How Many Now? — Variation #3

How Many Now? — Variation #4

Study group discussion starters: Secure place-value awareness

SECTION 3:  SECURE PART-WHOLE AWARENESS AND THE EMERGENCE OF ADDITION-SUBTRACTION FLUENCY

Chapter 5:  Addition-Subtraction Fluency Launch Points

What this is, and why it is important

What comes before, and how to get there

Basic part-whole awareness (K.OA.3)

Concepts and skills being reinforced in this chapter

Part-whole patterns for numbers up to 20 (K.OA.3, K.OA.4)

Decomposition and composition of numbers (K.OA.3, K.NBT.1, 1.OA.1, 1.OA.6)

The commutative property of addition (1.OA.3, 2.NBT.5, 2.NBT.6)

Addition and subtraction as inverse operations (1.OA.1, 1.OA.4, 1.OA.6, 1.NBT.4, 2.NBT.9)

Launch points

Hands Up #2 — Addition/subtraction

Ten-bar-in-a-cave game

Addition/subtraction using equal-arm balance scale

Addition/subtraction using ten-frames

Double-nines dominoes sorting

Domino trains or squares

Directional rods with addition/subtraction rack

Addition/subtraction using segmented Cuisenaire rods and 1-100 rack

Addition/subtraction using double-fives abacus

Chapter 6:  Addition-Subtraction Fluency Check Points

Assessment probes

Pursuit game

Ten-frame flash cards

Fact family triominoes

Parts Of calculator drill

Counting On calculator drill

Addition/subtraction war with playing cards

Addition/subtraction using torque balance scale

More teaching tips

Addition trumps subtraction

The perils of “Mad Minute” drills

Bridging from the concrete to paper-and-pencil

The real scoop on those dreaded word problems

The order in which number-sense based memorization develops

Study group discussion starters: Secure part-whole awareness and the emergence of addition-subtraction fluency

SECTION 4:  EXTENDING PLACE-VALUE AWARENESS
AND ADDITION-SUBTRACTION BEYOND THE HUNDREDS

Chapter 7:  Place-Value Fluency and Multi-Digit Addition-Subtraction Launch Points

Concepts and skills being reinforced in this chapter

A place value is determined by how many positions it is to the left of the units column (2.NBT.1, 2.NBT.4)

Zero as a place holder (2.NBT.1b, 2.NBT.3)

The maximum face value is 9 in any place-value column

10:1 exchange rates (2.NBT.1a, 2.NBT.7)

Exponential growth in a place-value system

The counting sequence in a place-value system

When combining or removing quantities, only digits in the same place-value location can be combined or decreased (2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.8, 2.NBT.9)

Composing and decomposing bundles of ten to move them from one place-value category to another can be done at any level of the place-value system as a tool of problem-solving (2.NBT.8, 2.NBT.11)

Standard algorithms can be used to efficiently solve multi-digit addition and subtraction problems, but alternative algorithms and strategies are sometimes preferable (2.NBT.10, 2.NBT.12, 2.NBT.13)

Launch points

200 board

Make-your-own place-value materials

Bank game with place-value blocks and place-value cards

Place-value materials sorter tray

Hundred and thousand extensions of ten-frames and Hand Game cards

Expanded notation strip

Modeling multi-digit addition-subtraction with exchanging

Mental math problem sets

Decimeter rods, meter rods, centimeter rods, metric measuring tape, and metric trundle wheel

Reading and writing really big numerals

Chapter 8:  Place-Value Fluency and Multi-Digit Addition-Subtraction Check Points

Assessment probes

Hundred-square in a cave game

Wacky numbers

I have, who has? game

Parts-of calculator drill

Skip-counting calculator drill

Target game

What’s wrong with this picture? sets

Final teaching tips

Words matter

Keeping children fluid

Teaching as improv

Collaboration and transformation

Keeping your eye on the prize

Study group discussion starters: Extended place-value awareness and addition-subtraction beyond the hundreds

Appendices

Appendix A:  Research-based teaching-learning paths

Appendix B:  Assessment templates — Use for individual child, tracking progress over time

Appendix C:  Assessment templates — Use for whole class, tracking outcomes of a particular lesson or activity

Mathematical cranks

Underwood Dudley 

The Mathematical Association of America | 1992 | páginas | djvu |4,6  Mb

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A delightful collection of articles about people who claim they have achieved the mathematically impossible (squaring the circle, duplicating the cube); people who think they have done something they have not (proving Fermat's Last Theorem); people who pray in matrices; people who find the American Revolution ruled by the number 57; people who have in common eccentric mathematical views, some mild (thinking we should count by 12s instead of 10s), some bizarre (thinking that second-order differential equations will solve all problems of economics, politics and philosophy). This is a truly unique book. It is written with wit and style and is a part of folk mathematics.

Contents
Introduction v 
Alphabet, Application of Pyramid Height to the 1 
American Revolution, The Role of 57 in the 4 
Applied Mathematics 9 
Base for the Number System, The Best - 20 
Bitterness, Cranks' 32 
Calculus, Celestial 38 
Cantor's Diagonal Process 40 
Congressional Record, Mathematics in the 46 
Constant Society, The 50 
Consultation, Lack of, of Cranks with Experts 53 
Crank, Case Study of a 55. 
Crank, The Making of a 67 
Deduction, The Joy of 78 
Duplication of the Cube 86 
Ellipse, Circumference of an 93 
Encouraging Cranks, The Folly of 97 
Equations, Solving 102 
Fermat's Last Theorem 105 
Fermat's Little Theorem 135 
Fifth Postulate, Euclid's 137 
Four-Color Theorem, The ." 159 
Godel's Theorem 167 
Goldbach Conjecture, The 171 
Greed 179 
Incomprehensibility of Crank's Works 182 
Infinity, Difficulties with 184 
Insanity 189 
Legislating Pi 192 
Linear Programming, Conspiracy Involving 198 
Magic Squares 200 
Mail, Crank 205 
Megalomania 208 
Money to be Made in Mathematics, Lack of 222 
Nines, Casting Out 226 
Nonagons, Regular 231 
Notation, Nonstandard 235 
Number Theory, The Lure of 239 
Perfect Numbers 242 
Phi 245 
Prayer, Matrix 251 
Primes, The Secret of the 254 
Primes, Twin, Existence of Infinitely Many 256 
Prolificity, Crank's 260 
Puzzle, A 269 
Pythagoreans, Neo- 271 
Pythagoreans, The Mystery of the 274 
Quadrature of the Circle 279 
Set Theory 322 
Signs, The Rule of 324 
Solution to a Puzzle 330 
Sphere, Philosophy of the 331 
Statistics, Parameter Estimation in 334 
Taxonomy, Mathematical 337 
Time, Wasted ....! 339 
Topology, Applied 341 
Trisection of the Angle 342 
Van der Pol's Equation 349 
Notes 353 

Index 363

Number words and number symbols a cultural history of numbers

Karl Menninger

Dover Publications Inc. | 1992 | 512 páginas | epub | 15 Mb

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Classic study discusses number sequence and language and explores written numerals and computations in many cultures. "The historian of mathematics will find much to interest him here both in the contents and viewpoint, while the casual reader is likely to be intrigued by the author's superior narrative ability.

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

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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

More Mathematical Puzzles of Sam Loyd

Sam Loyd e Martin Gardner

Dover Publications | 1960 | 201 páginas | djvu | 3,9 Mb

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Gardner's second collection of amusing, thought-provoking problems and puzzles from Loyd's Cyclopedia — perhaps the most exciting collection of puzzles ever assembled in one volume. Arithmetic, algebra, speed and distance problems, game theory, counter and sliding block problems, similar topics. 166 problems.

Contents
Plane Geometry Problems
Geometrical Dissection Problems
Route, Tracing, and Topological Problems
Counter and Sliding Block Problems
Solid Geometry Problems 
Arithmetic and Algebraic Problems 
Speed and Distance Problems 

Game Theory Problems 

Operations Research Problems
Physics and Calculus Problems 

To mock a mockingbird

Raymond M. Smullyan 

Knopf | 1985 | 257 páginas | rar - epub | 2,11 Mb

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In this entertaining and challenging new collection of logic puzzles, Raymond Smullyan—author of What Is the Name of This Book? And The Lady or the Tiger?—continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time.
In the first part of the book, he transports us once again to that wonderful realm where knights, knaves, twin sisters, quadruplet brothers, gods, demons, and mortals either always tell the truth or always lie, and where truth-seekers are set a variety of fascinating problems. The section culminates in an enchanting and profound metapuzzle (a puzzle about a puzzle), in which Inspector Craig of Scotland Yard gets involved in a search of the Fountain of Youth on the Island of Knights and Knaves.
In the second and larger section, we accompany the Inspector on a summer-long adventure into the field of combinatory logic (a branch of logic that plays an important role in computer science and artificial intelligence). His adventure, which includes enchanted forests, talking birds, bird sociologists, and a classic quest, provides for us along the way the pleasure of solving puzzles of increasing complexity until we reach the Master Forest and—thanks to Gödel’s famous theorem—the final revelation.
To Mock a Mockingbird will delight all puzzle lovers—the curious neophytes as well as the serious students of logic, mathematics, or computer science.

Contents
Other Books by This Author
Title Page
Copyright
Dedication
Acknowledgments
Preface
PART I · LOGIC PUZZLES
1 The Prize—and Other Puzzles
2 The Absentminded Logician
3 The Barber of Seville
4 The Mystery of the Photograph
PART II · KNIGHTS, KNAVES, AND THE FOUNTAIN OF YOUTH
5 Some Unusual Knights and Knaves
6 Day-Knights and Night-Knights
7 Gods, Demons, and Mortals
8 In Search of the Fountain of Youth
PART III · TO MOCK A MOCKINGBIRD
9 To Mock a Mockingbird
10 Is There a Sage Bird?
11 Birds Galore
12 Mockingbirds, Warblers, and Starlings
13 A Gallery of Sage Birds
PART IV · SINGING BIRDS
14 Curry’s Lively Bird Forest
15 Russell’s Forest
16 The Forest Without a Name
17 Gödel’s Forest
PART V · THE MASTER FOREST
18 The Master Forest
19 Aristocratic Birds
20 Craig’s Discovery
PART VI · THE GRAND QUESTION!
21 The Fixed Point Principle
22 A Glimpse into Infinity
23 Logical Birds
24 Birds That Can Do Arithmetic
25 Is There an Ideal Bird?
Epilogue
Who’s Who Among the Birds