Algebraic and arithmetic structures: a concrete approach for elementary school teachers
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Free Press
1976
|
| Edition: | 1. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXXV, 683 S. Ill., graph. Darst. |
| ISBN: | 0029022703 |
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MARC
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| 007 | t | ||
| 008 | 931207s1976 ad|| |||| 00||| eng d | ||
| 020 | |a 0029022703 |9 0-02-902270-3 | ||
| 035 | |a (OCoLC)1974987 | ||
| 035 | |a (DE-599)BVBBV008764699 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-824 | ||
| 050 | 0 | |a QA135.5 | |
| 082 | 0 | |a 372.7/3/0973 |2 18 | |
| 084 | |a SM 610 |0 (DE-625)143295: |2 rvk | ||
| 100 | 1 | |a Bell, Max S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algebraic and arithmetic structures |b a concrete approach for elementary school teachers |c developed cooperatively by Max S. Bell ; Karen C. Fuson ; Richard A. Lesh |
| 250 | |a 1. print. | ||
| 264 | 1 | |a New York |b Free Press |c 1976 | |
| 300 | |a XXXV, 683 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathématiques - Étude et enseignement (Primaire) | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |x Study and teaching (Elementary) | |
| 700 | 1 | |a Fuson, Karen C. |e Verfasser |4 aut | |
| 700 | 1 | |a Lesh, Richard |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005790302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005790302 | ||
Record in the Search Index
| _version_ | 1804123111281393664 |
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| adam_text | preface xxv
introduction xxvii
part a number systems: sets, relations, operations, uses 1
uniti: 1.1 Introduction 3
preliminary 1.2 Problem Set: Uses of
whole number Whole Numbers 4 1.2.1 Collecting uses of whole
ideas numbers 4
1 1.2.2 Whole numbers used in
gathering and recording data 5
1.2.3 The natural order of whole
numbers 8
1.2.4 Whole number lines 10
1.2.5 Whole numbers for identi¬
fication or coding 12
1.2.6 Summary 14
1.3 Activity: Basic Set Ideas 14
1.4 Activity: Relations for
Whole Numbers: Is
Equal To, Is Less
Than, Is Greater Than 16 1.4.1 Learning to count 18
1.4.2 Comparing sets without
counting 19
1.4.3 Comparing measures 21
1.4.4 Properties of relations 24
1.5 Summary and Pedagogical
Remarks 27
unit 2: 2.1 Introduction 32
addition 2.2 Activity: The Meaning of
Of Whole Addition of Whole
numbers Numbers 33 2.2.1 Addition of whole number
32 counts 33
2.2.2 Addition of whole number
measures using rods 35
2.2.3 Addition of whole number
measures using number lines 36
vii
2.2.4 Counts or hops on the
number line 37
2.2.5 Addition with slide rule
made from number lines 37
2.3 Activity: Properties of
Addition of Whole
Numbers 39 2.3.1 Closure 39
2.3.2 Uniqueness of sums;
equivalence classes of sums 39
2.3.3 Zero as the identity for
addition of whole numbers 41
2.3.4 Whole numbers have no
additive inverses 43
2.3.5 The commutative property of
addition of whole numbers 43
2.3.6 The associative property of
addition of whole numbers 44
2.3.7 A do as you please
property for addition of
whole numbers 45
2.4 Summary and Pedagogical
Remarks 46
unit 3: 3.1 Introduction 49
multiplication 3.2 Activity: The Meaning of
Of whole Multiplication of Whole
numbers Numbers 50 3.2.1 Multiplication of counts using
49 repeated addition 50
3.2.2 Multiplication with measures
using repeated addition 50
3.2.3 Multiplication using arrays 52
3.2.4 Cartesian products;
combinations 55
3.2.5 Connections among arrays,
tree diagrams, Cartesian
products 59
3.3 Activity: Properties of
Multiplication of Whole
Numbers 61 3.3.1 Closure, uniqueness,
equivalence classes of
products 62
3.3.2 The identity element for
multiplication 63
3.3.3 Whole numbers have no
multiplicative inverse 63
3.3.4 Multiplication property of
zero 64
3.3.5 Commutative property of
multiplication of whole
numbers 65
3.3.6 Associative property of mul¬
tiplication of whole numbers 65
3.3.7 The do as you please
property of multiplication 66
3.3.8 The distributive property of
multiplication over addition 67
3.4 Summary and Pedagogical
Remarks 69
unit 4: 4.1 Introduction 73
subtraction 4.2 Classroom Notes: The
Of Whole Meaning of Subtraction
numbers of Whole Numbers 74 4.2.1 Take away situations with
73 counts or with measures 74
4.2.2 Comparison situations
with counts and measures 76
4.2.3 Number lines in subtraction 78
4.2.4 Addition-Subtraction Links 79
4.3 Classroom Notes:
Properties of Whole
Number Subtraction 80 4.3.1 Subtraction of whole
numbers is not closed 80
4.3.2 Uniqueness; equivalence
classes of differences 80
4.3.3 Zero is a right identity, but
not a left identity, for
subtraction 81
4.3.4 For subtraction, every whole
number is its own inverse 81
4.3.5 Subtraction of whole numbers
is not commutative 81
4.3.6 Subtraction of whole numbers
is not associative 81
4.3.7 There is not a do as you
please property for
subtraction of whole
numbers 81
4.4 Work sheets on Subtrac¬
tion of Whole Numbers 82 4.4.1 Take-away situations with
counts 82
4.4.2 Take-away situations with
measures 83
4.4.3 Comparison (how much
more) with counts 83
4.4.4 Comparison (how much
more) with measures 84
4.4.5 Number lines and rods used
for subtraction 85
4.4.6 Addition-subtraction links 85
4.5 Summary and Pedagogical
Remarks 87
unit 5: 5.1 Introduction 89
division 5.2 Activity: The Meaning and
Of whole Sources of Division of
numbers Whole Numbers 89 5.2.1 Exploration of division 90
89 5.2.2 Sources of division 90
5.2.3 Sources of division 91
5.2.4 Sources of division with
measures 92
5.2.5 Sources of division with
measures 93
5.2.6 Remainders in division 93
5.3 Problem Set: Links
between Division and
Multiplication of Whole
Numbers 95 5.3.1 Checking division by
multiplying 95
5.3.2 Checking when there are
remainders p = (n x q) + r 96
5.3.3 Multiplication-division links:
arrays, repeated addition,
and repeated subtraction 97
5.3.4 Using a multiplication table
to do division 98
5.3.5 Division by a whole number
versus multiplication by a
fraction 99
5.4 Problem Set: Properties of
Division of Whole
Numbers 100 5.4.1 Closure property 100
5.4.2 A substitute for closure of
division of whole numbers 101
5.4.3 Uniqueness; equivalence
classes of quotients 101
5.4.4 The number 1 as a right
identity 102
5.4.5 Inverses 102
5.4.6 Commutativity 103
5.4.7 Associativity 103
5.4.8 Division 0/zero by a
nonzero whole number 104
5.4.9 Division fry zero: Impossible! 104
5.5 Summary and Pedagogical
Remarks 105
unit 6: 6.1 Introduction 108
extension 6.2 Activity: Blue and White
Of the Numbers 109 6.2.1 The basic rule for equivalence 109
whole numbers 6.2.2 Addition of BW numbers 111
to the 6.2.3 Subtraction of BW numbers 113
integers 6.2.4 Multiplication of BW
108 numbers 114
6.2.5 Division of RW numbers 116
6.3 Activity: A Measure
Embodiment of Integers
With Directed Rods 117 6.3.1 Making the embodiment 117
6.3.2 Addition 117
6.3.3 Subtraction 119
6.3.4 Multiplication 120
6.3.5 Division 121
6.4 Problem Set: Extending
the Set of Whole Numbers
to the Integers 122 6.4.1 Uses of integers in common
life 122
6.4.2 Uses of integers in
mathematics 124
6.4.3 Extension of the whole num¬
bers to integers on the num¬
ber line 125
6.5 Problem Set: Relations
and Operations with the
Integers 127 6.5.1 The is less than relation 128
6.5.2 The opposite of operation 128
6.5.3 The absolute value of
operation 129
6.5.4 Addition of integers 131
6.5.5 Subtraction of integers 131
6.5.6 The multiplication operation 132
6.5.7 The division operation 136
6.6 Problem Set: The
Properties of Integers 137 6.6.1 Introductory remarks 137
6.6.2 Some useful theorems
about the system of integers 139
6.7 Pedagogical Remarks 141
unit 7: 7.1 Introduction 144
extension 7.2 Problem Set: Why Bother
of the with Fractions? Sources
integers and Uses 148 7.2.1 Various motivations for
to the fractions 148
rational 7.2.2 Fractions as used in the
numbers common world 151
1 44 7.3 Activity: Paper Strips as
Embodiments of (Rational)
Fractions 155 7.3.1 The set of rational fractions
embodied by paper folding 155
7.3.2 Relations: is equal to,
is less than, is greater
than 156
7.3.3 Multiplication of fractions
using paper strips 157
7.3.4 Multiplicative inverse:
reciprocals 158
7.3.5 Division of fractions using
paper strips 159
7.4 Activity: Fractions with
Number Line and Rod
Embodiments 159 7.4.1 Making and using the
number line 160
7.4.2 Equivalence classes of
fractions 161
7.4.3 Using the number line to
explore the is less than,
is greater than, and is
equal to relations 164
7.4.4 Addition of fractions with
rods on the number line 165
7.4.5 Subtraction of fractions with
rods on the number line 169
7.4.6 Division of fractions with
rods on the number line 171
7.5 Problem Set: A Fraction
Potpourri 173 7.5.1 Fractions as operators on
sets of objects or on
measures 173
7.5.2 Other uses of rods to
embody fraction work 174
7.5.3 Addition-only methods
for getting equivalent
fractions 175
7.5.4 Equivalent fractions and
multiplication of fractions
by marking rectangular units 176
7.5.5 Justifying the multiply by
the reciprocal of the divisor
rule for division of fractions 177
7.5.6 More on why zero denomi¬
nators or divisions by zero
are never allowed 178
7.6 Summary of Properties of
the System of Rational
Fractions 179 7.6.1 General remarks 179
7.6.2 The set of rational fractions 180
7.6.3 Equivalence 181
7.6.4 Is greater than or is less
than 181
7.6.5 Addition 181
7.6.6 Multiplication 182
7.6.7 Subtraction 182
7.6.8 Division 182
7.6.9 Properties of operations
with rational numbers that
parallel properties of opera¬
tions with integers 182
7.6.10 New properties 183
7.6.11 Other useful properties 183
7.7 Pedagogical Remarks 184
part b algorithms and numeration 1 87
uniti: 1.1 Introduction 189 1.1.1 Algorithms 189
the algorithm 1.1.2 Brief historical background
for addition of algorithms 191
Of whole 1.1.3 Uses of addition 193
numbers 1.1.4 This text s approach to
o;3 algorithms for whole number
operations 195
1.2 Activity: The Addition
Algorithm for Base-Four
Whole Numbers 197 1.2.1 Base-four words 197
1.2.2 The trade rules for base-four
blocks 199
1.2.3 Addition with base-four
blocks 201
1.2.4 Trade rules for the base-four
chip computer 203
1.2.5 Addition with the base-four
chip computer 204
1.2.6 Trading and adding with the
base-four rod computer 205
1.3 Activity: The Addition
Algorithm for Base-Ten
Whole Numbers 209 1.3.1 Addition with base-ten
blocks 209
1.3.2 Addition with the base-ten
chip computer 210
1.3.3 Addition with the base-ten
rod computer 211
1.4 Problem Set: Analysis of
the Addition Alogrithm 213 1.4.1 An intermediate form of the
addition algorithm 213
1.5 Pedagogical Remarks 223
unit 2: 2.1 Introduction 229 2.1.1 Uses of subtraction 229
the algorithm 2.2 Activity: The Subtraction
for Algorithm for Base-Four
subtraction Numbers 231 2.2.1 Subtraction with base-four
of whole blocks 231
numbers 2.2.2 Subtraction with the base-four
229 chip computer 233
2.2.3 Subtraction with the base-four
rod computer 233
2.3 Activity: The Subtraction
Algorithm for Base-Ten
Whole Numbers 235 2.3.1 Subtraction with base-ten
blocks 235
2.3.2 Subtraction with the base-ten
chip computer 235
2.3.3 Subtraction with the base-ten
rod computer 236
2.3.4 Take-away and comparison
methods of using embodi¬
ments for the subtraction
algorithm 236
2.4 Problem Set: Analysis of
the Subtraction Algorithm 238
2.5 Pedagogical Remarks 248
unit 3: 3.1 Introduction 251 3.1.1 Uses of multiplication 252
the algorithm 3.2 Activity: Development of
for the Shift Rules with
multiplication Base-Eight Multiplication
Of Whole Pieces 253 3.2.1 How the multiplication
numbers pieces work 253
251 3.2.2 Shift rules: total approach
with the multiplication pieces 256
3.2.3 Shift rules: piece-by-piece
approach with the multipli¬
cation pieces 258
3.3 Activity: Development of
Shift Rules with the Base-
Eight Chip Computer 259 3.3.1 How the base-eight chip
computer works 259
3.3.2 Shift rules: total approach
on the base-eight chip
computer 261
3.3.3 Shift rules: place-by-place
approach on the base-eight
chip computer 263
3.4 Activity: The Copy Multi¬
plication Algorithm for
Base Eight 264 3.4.1 The copy multiplication
algorithm with base-eight
multiplication pieces 264
3.4.2 The copy multiplication
algorithm on the base-eight
chip computer 266
3.4.3 The copy multiplication
algorithm symbolically 269
3.5 Activity: The Place-Value
Multiplication Algorithm
for Base Eight 270 3.5.1 The intermediate place-value
algorithm on the base-eight
chip computer 271
3.5.2 The intermediate place-value
algorithm using base-eight
tables 273
3.5.3 The compact place-value
algorithm 274
3.6 Problem Set: Analysis of
the Multiplication
Algorithm for Whole
Numbers 275
3.7 Pedagogical Remarks 289
unit 4: 4.1 Introduction 292 4.1.1 Uses of division 292
algorithms 4.2 Activity: Division
for the Algorithms for Base-Eight
division Whole Numbers 294 4.2.1 The copy division algorithm
Of whole with base-eight multiplication
numbers pieces 294
292 4.2.2 The copy algorithm on the
base-eight chip computer 296
4.2.3 The division place-value
algorithm on the base-eight
chip computer 297
4.3 Activity: Division
Algorithms for Base-Ten
Whole Numbers 299 4.3.1 The copy division algorithm
with base-ten multiplication
pieces 299
4.3.2 The copy division algorithm
on the base-ten chip computer 300
4.3.3 The place-value division
algorithm on the base ten
chip computer 301
4.4 Problem Set: Analysis of
the Division Algorithms
for Whole Numbers 302
4.5 Pedagogical Remarks 312
unit 5: 5.1 Introduction 316 5.1.1 Historical background of
decimals: decimals 317
basic operations, 5.1.2 Uses of decimal fractions 319
algorithms, 5.2 Activity and Problem Set:
and the The Metric System 323 5.2.1 Language for the metric
metric system system 324
316 5.2.2 The metric measures 325
5.2.3 Summary of the metric
system 332
5.2.4 English Metric-conversions 334
5.2.5 Developing continuing aware¬
ness of the metric system 337
5.3 Activity: The Meaning of
Addition, Subtraction,
Multiplication, and
Division of Decimals 337 5.3.1 How the embodiments for
decimals work 338
5.3.2 Relations for decimals 340
5.3.3 Addition of decimals 340
5.3.4 Subtraction of decimals 341
5.3.5 Multiplication of decimals 343
5.3.6 Division of decimals 348
5.4 Activity: Algorithms for
Addition, Subtraction,
Multiplication, and
Division of Decimals 353 5.4.1 The chip computer for
decimals 353
5.4.2 Addition and subtraction
algorithms for decimals 355
5.4.3 The multiplication algorithm
for decimals 356
5.4.4 A division algorithm for
decimals 359
5.5 Problem Set: Analysis of
Decimals 361 5.5.2 Exponential notation 365
5.5.3 Scientific notation 367
5.5.4 Approximations using
powers of ten 368
5.5.5 Orders of magnitude 370
5.5.6 A brief look at logarithms 371
5.6 Pedagogical Remarks 373
unit 6: 6.1 Introduction—Some
the extension Reminders and Some
Of the Questions 377 6.1.1 The basic definition of
national numbers rational numbers 378
to the 6.1.2 The number line 378
real numbers 6.1.3 Terminating and repeating
377 decimals 378
6.1.4 Closure of operations 379
6.1.5 Applications of mathematics
to the common world 379
6.1.6 Summary 379
6.2 Changing Rational
Fraction to Decimals
and Vice Versa 379 6.2.1 Changing a rational fraction
to a repeating decimal 379
6.2.2 Why must the decimal form
of a rational fraction be a
repeating decimal? 381
6.2.3 Changing repeating decimals
to fractions 382
6.2.4 Two equivalent ways to
define rational number 383
6.3 Problem Set: Do Non-
Rational Numbers Exist? 384 6.3.1 The square root operation 384
6.3.2 VI as the length of a segment 386
6.3.3 V2 on the number line 387
6.3.4 At least one nonrational
number exists 387
6.3.5 Some other nonrational
numbers 390
6.4 Properties of the Real
Numbers 393
6.5 Ratios and Proportions
Again 394 6.5.1 Examples of ratios, propor¬
tions, and percents from
common life situations 395
6.5.2 Some examples typical of
those found on school mathe¬
matics achievement tests 396
6.6 Pedagogical Remarks 397
unit 7: 7.1 Introduction 399
analysis of 7.2 Reading and Activity: A
different Brief History of Number
systems Of Words and Number
numeration Symbols, of Means of
399 Recordkeeping and of Cal¬
culation with Numbers 400 7.2.1 The needs for numbers 400
7.2.2 Number words 403
7.2.3 Number symbols 408
7.2.4 Recordkeeping 411
7.2.5 Calculation 413
7.3 Activity: Some Systems of
Numeration 415 7.3.1 Babylonian numeration
systems 416
7.3.2 Greek numeration systems 419
7.3.3 Chinese numeration systems 423
7.4 Problem Set: Analysis of
Characteristics of Numer¬
ation Systems 426 7.4.1 Six characteristics of
numeration systems 427
7.4.2 Characteristics of various
numeration systems 427
7.4.3 Disparities between our
number words and our
number symbols 429
7.5 Problem Set: Advantages
of Various Numeration
Systems 431 7.5.1 A comparison of the s stems
from Section 7.3 431
7.5.2 Advantages and disadvan¬
tages of the decimal system
of numeration 433
7.6 Non-ten Number Bases 436 7.6.1 Base four 437
7.6.2 Base eight 438
7.6.3 Base five 439
7.6.4 Base twelve 440
7.6.5 Base* 440
7.6.6 Advantages of different bases 441
7.7 Pedagogical Remarks 442
part c underlying mathematical concepts and structures 449
uniti: 1.1 Introduction 45 j
Sets 1.2 Number Concepts and
and Basic Ideas About Sets 45 j 1.2.1 Piaget s number conservation
logic tasks 452
451 1.2,2 One-to-one correspondence 452
1.2.3 An area problem 456
1.2.4 A number-area problem 457
1.2.5 A problem about subsets 458
1.2.6 Nonanalytic thinking 459
1.2.7 Centering 459
1.3 Attribute Games 460 1.3.1 One-difference sequence 460
1.3.2 Two-difference sequences 461
1.3.3 One-difference matrices 462
1.3.4 Two-difference matrices 462
1.3.5 Graeco-Latin squares 463
1.3.6 Guess the block 464
1.4 The Words Same and
Different 464 1.4.1 Some issues to consider 465
1.5 SETS: A Discussion
Session 468
1.6 Problems 472
1.7 Operations on Sets and
Relations Between Sets 473 1.7.1 Operations on sets 475
1.7.2 Intersections 476
1.7.3 Unions 477
1.7.4 Complements 477
1.7.5 Relations between sets 478
1.7.6 Some laws about sets 479
1.8 Logic and Electrical
Circuits 480 1.8.1 Parallel and series circuits 480
1.8.2 More complicated circuits 482
1.9 Logic 485 1.9.1 A brain teaser 485
1.9.2 Compound sentences and
truth tables 485
1.9.3 Conditional sentences 486
1.9.4 Logical precision 488
1.9.5 The quantifiers all, some,
and none 490
1.9.6 Validity versus truth 491
1.9.7 Logic problem for fun 492
1.10 Pedagogical Remarks 494
unit 2: 2.1 Introduction 496
relations 2.2 Family Relationships 497
496 2.3 Ordered Pairs 499
2.4 Structural Properties of
Relations 502
2.5 Inverses 505
2.6 Reviewing Some
Properties 506 2.6.1 Is a divisor of 506
2.6.2 Is a subset of 507
2.6.3 Is relatively prime to 507
2.7 Equivalence Relations 508 2.7.1 Equivalence classes 509
2.7.2 Activity 511
2.8 Functions 511 2.8.1 One-to-one, one-to-many.
many-to-one, and many-to-
many relations 512
2.8.2 Functions 514
2.8.3 Function machines 515
2.8.4 A function machine game 516
2.8.5 Problems 518
2.9 From Relations to
Coordinate Graphs 518
2.10 Pedagogical Remarks 524
unit 3: 3.1 Introduction 525
displaying 3.2 Organizing and Simplifying
information Information 530 3.2.1 Interpreting achievement
with graphs test scores 530
525 3.3 Some Common Graphs
and Their Properties 533
3.4 Selecting and Drawing
Appropriate Graphs 540 3.4.1 Selecting an appropriate
graph 540
3.4.2 Choosing appropriate scales 542
3.4.3 Making comparisons between
sets of data 544
3.4.4 Making estimations and
predictions 545
3.4.5 Supporting a position 550
3.5 Picturing Locations 551
3.6 Coordinates 553 3.6.1 A geoboard tournament 553
3.6.2 Using numbers to describe
positions 554
3.6.3 Rectangular coordinates 556
3.7 Some Introductory Ideas
in Analytic Geometry 557
3.8 Slide Rules 565 3.8.1 The multiplicative slide rule 565
3.8.2 The additive slide rule 567
3.9 Pedagogical Remarks 568
unit 4: 4.1 Introduction 569 4.1.1 Refreshing your memory
operations about some basic facts 570
569 4.1.2 Finger multiplication and
The basic facts 571
4.2 Binary Operations 571 4.2.1 Operating on colored rods 572
4.2.2 Adding rows of numbers 573
4.2.3 Multiplying rows of
numbers 573
4.2.4 Turning a square 574
4.2.5 Mod four addition 576
4.3 The Closure Property 577 4.3.1 Adding colored rods 578
4.3.2 Addition mod orange 578
4.3.3 The mod ten number line 579
4.3.4 The different-from
operation 580
4.4 The Associative Property 580
4.5 The Commutative
Property 581 4.5.1 Invariance moves on a
triangle 583
4.5.2 Permutations on poker chips 586
4.5.3 Checking for properties 589
4.6 Identity Elements 590 4.6.1 The turned-to operation 591
4.7 Inverse Elements 591 4.7.1 Mod ten addition 592
4.7.2 Mod ten multiplication 593
4.8 Groups 593
4.9 Isomorphisms 595 4.9.1 Multiplication mod yellow 596
4.9.2 Permutations on poker
chips 597
4.9.3 Turning a square 599
4.9.4 Comparing several systems 599
4.9.5 A mystery number system 601
4.9.6 Optional projects 602
4.10 The Distributive Property 604 4.10.1 Counting numbers 604
4.10.2 Colored rods 605
4.10.3 The mod ten number line 605
4.11 Exponentiation 606 4.11.1 Some properties of
exponentiation 606
4.11.2 Summarizing the properties
of exponentiation 609
4.12 Summary of Properties
of Operations 610
4.13 Pedagogical Remarks 612
unit 5: 5.1 Introduction 613
problem 5.2 Figurate Numbers 615 5.2.1 Pyramid numbers 615
solving in 5.2.2 Triangle numbers 616
number theory 5.2.3 Finding patterns 617
613 5.2.4 Investigating differences 618
5.2.5 Optional problems 620
5.2.6 Problems posed by students 620
5.3 Prime and Composite
Numbers 621 5.3.1 Line and rectangle numbers 622
5.3.2 The sieve of Eratosthenes 622
5.3.3 Factorization 624
5.3.4 Least common multiple 625
5.3.5 Greatest common factor 626
5.3.6 Divisibility rules 627
5.3.7 Problems 628
5.4 Finding Number Patterns 629 5.4.1 Tow tables of numbers 631
5.5 Pascal s Triangle 632 5.5.1 Situations related to
Pascal s triangle 633
5.5.2 Patterns in Pascal s triangle 636
5.6 The Fibonacci Sequence 638 5.6.1 The divine proportion 639
5.6.2 Human anatomy 640
5.6.3 Fibonacci numbers in biology 641
5.6.4 Fibonacci numbers in music 641
5.6.5 Patterns in the Fibonacci
sequence 642
5.7 Problems 643
5.8 Pedagogical Remarks 646
appendix I: how to get the laboratory materials for this book 649
appendix II: bibliography and references 662
index 669
|
| any_adam_object | 1 |
| author | Bell, Max S. Fuson, Karen C. Lesh, Richard |
| author_facet | Bell, Max S. Fuson, Karen C. Lesh, Richard |
| author_role | aut aut aut |
| author_sort | Bell, Max S. |
| author_variant | m s b ms msb k c f kc kcf r l rl |
| building | Verbundindex |
| bvnumber | BV008764699 |
| callnumber-first | Q - Science |
| callnumber-label | QA135 |
| callnumber-raw | QA135.5 |
| callnumber-search | QA135.5 |
| callnumber-sort | QA 3135.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SM 610 |
| ctrlnum | (OCoLC)1974987 (DE-599)BVBBV008764699 |
| dewey-full | 372.7/3/0973 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 372 - Primary education (Elementary education) |
| dewey-raw | 372.7/3/0973 |
| dewey-search | 372.7/3/0973 |
| dewey-sort | 3372.7 13 3973 |
| dewey-tens | 370 - Education |
| discipline | Pädagogik Mathematik |
| edition | 1. print. |
| format | Book |
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| id | DE-604.BV008764699 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:24:34Z |
| institution | BVB |
| isbn | 0029022703 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005790302 |
| oclc_num | 1974987 |
| open_access_boolean | |
| owner | DE-824 |
| owner_facet | DE-824 |
| physical | XXXV, 683 S. Ill., graph. Darst. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Free Press |
| record_format | marc |
| spelling | Bell, Max S. Verfasser aut Algebraic and arithmetic structures a concrete approach for elementary school teachers developed cooperatively by Max S. Bell ; Karen C. Fuson ; Richard A. Lesh 1. print. New York Free Press 1976 XXXV, 683 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques - Étude et enseignement (Primaire) Mathematik Mathematics Study and teaching (Elementary) Fuson, Karen C. Verfasser aut Lesh, Richard Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005790302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bell, Max S. Fuson, Karen C. Lesh, Richard Algebraic and arithmetic structures a concrete approach for elementary school teachers Mathématiques - Étude et enseignement (Primaire) Mathematik Mathematics Study and teaching (Elementary) |
| title | Algebraic and arithmetic structures a concrete approach for elementary school teachers |
| title_auth | Algebraic and arithmetic structures a concrete approach for elementary school teachers |
| title_exact_search | Algebraic and arithmetic structures a concrete approach for elementary school teachers |
| title_full | Algebraic and arithmetic structures a concrete approach for elementary school teachers developed cooperatively by Max S. Bell ; Karen C. Fuson ; Richard A. Lesh |
| title_fullStr | Algebraic and arithmetic structures a concrete approach for elementary school teachers developed cooperatively by Max S. Bell ; Karen C. Fuson ; Richard A. Lesh |
| title_full_unstemmed | Algebraic and arithmetic structures a concrete approach for elementary school teachers developed cooperatively by Max S. Bell ; Karen C. Fuson ; Richard A. Lesh |
| title_short | Algebraic and arithmetic structures |
| title_sort | algebraic and arithmetic structures a concrete approach for elementary school teachers |
| title_sub | a concrete approach for elementary school teachers |
| topic | Mathématiques - Étude et enseignement (Primaire) Mathematik Mathematics Study and teaching (Elementary) |
| topic_facet | Mathématiques - Étude et enseignement (Primaire) Mathematik Mathematics Study and teaching (Elementary) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005790302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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