Mathematical circle diaries, year 1: complete curriculum for grades 5 to 7
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berkeley, Calif. [u.a.]
MSRI Mathematical Sciences Research Inst. [u.a.]
2013
|
| Schriftenreihe: | MSRI mathematical circles library
11 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 335 S. Ill. |
| ISBN: | 9780821887455 |
Internformat
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Datensatz im Suchindex
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| adam_text | Titel: Mathematical circle diaries, year 1
Autor: Burago, Anna
Jahr: 2013
Contents
Acknowledgments xi
Preliminaries 1
What is a Mathematical Circle? 1
About This Book 2
About the Author 3
Why I Wrote This Book 4
Target Age Groups 5
Part 1. Session Plans 7
Introduction 9
A Few Words about Problem Sets 10
Session 1: How to Solve a Problem 11
Before the Session 11
The Session Plan 12
Introductions and Math Warm-up 12
What is a Mathematical Circle? 13
Discussion of the Day: What Does it Mean to Solve a
Problem? 13
A Few Words about Problem Sets and Homework 19
Session 1 Problem Set 19
Session 2: Knights and Liars 23
Math Warm-up 23
Problem Set From the Previous Class 24
Discussion of the Day, Part 1: Cause and Effect Problems 24
Discussion of the Day, Part 2: Knights-and-Liars Problems 25
Session 2 Problem Set 28
Session 3: How to Turn Lies into Truth 31
Math Warm-up 32
Discussion of the Day: Negation of Logical Statements 33
Session 3 Problem Set 34
vi Contents
Session 4: Mathematical Auction 37
Math Warm-up 37
The Game of Mathematical Auction 37
Mathematical Auction Problems 40
Session 4 Problem Set 41
Session 5: Word Problems and Common Sense 43
Math Warm-up 43
Discussion of the Day: Draw a Picture — Solve the Problem! 43
Discussion of the Day, Part 2: Working Together 46
Session 5 Problem Set 47
Session 6: More Word Problems 51
Math Warm-up 51
Discussion of the Day: Of Pigs and Hens 52
Session 6 Problem Set 53
Session 7: Odd and Even Numbers I. Magic Paper Cups 57
Math Warm-up 57
Discussion of the Day: Odd and Even Numbers. Parity 58
Session 7 Problem Set 60
Session 8: Odd and Even Numbers II. Definitions and Properties 63
Math Warm-up 63
Discussion of the Day: How to Define Odd and Even Numbers 63
Parity of Sums and Differences 65
Parity of a Product 69
Session 8 Problem Set 69
Session 9: Halloween Math Hockey I 71
Math Warm-up 71
Math Hockey 71
Math Hockey I Problems 72
Session 9 Problem Set 74
Session 10: Odd and Even Numbers III. Alternations 77
Math Warm-up 77
Discussion of the Day: Alternations 77
Session 10 Problem Set 81
Session 11: Weighings and Counterfeit Coins 85
Math Warm-up 85
Discussion of the Day: Balance Scales and Counterfeit Coins 86
Session 11 Problem Set 89
Session 12: Mathematical Olympiad I 91
Math Warm-up 91
Event of the Day: Math Olympiad 92
Contents vii
Math Olympiad I. First Page of Problems 93
Math Olympiad I. Second Page of Problems 93
Math Olympiad I. Additional Problems 94
Session 13: Meet the Cube. First Lesson in 3D Geometry 97
Math Warm-up 98
Discussion of the Day: Cubes 98
Cube Nets 100
Meet the Cube Exercises 101
Session 13 Problem Set 102
Session 14: Cross Sections. Second Lesson in 3D Geometry 105
Math Warm-up 105
Discussion of the Day: Cross Sections 106
Session 14 Problem Set 110
Session 15: Mathematical Auction 113
Math Warm-up 113
Event of the Day: The Game of Mathematical Auction 113
Mathematical Auction Problems 114
Session 15 Problem Set 115
Session 16: Combinatorics I 117
Math Warm-up 117
Discussion of the Day: Introduction to Combinatorics 117
Session 16 Problem Set 124
Session 17: Combinatorics II 127
Math Warm-up 127
Discussion of the Day: The Slot Rule and Permutations without
Repetitions 127
Session 17 Problem Set 134
Session 18: Mathematical Hockey II 137
Math Warm-up 137
Event of the Day: Math Hockey Game 137
Math Hockey II Problems 138
Session 18 Problem Set 139
Session 19: Numerical Puzzles I. Runaway Digits 141
Math Warm-up 141
Discussion of the Day: Runaway Digits 142
Session 19 Problem Set 144
Session 20: Numerical Puzzles II. Encrypted Problems 147
Math Warm-up 147
Discussion of the Day: Encrypted Problems 147
Session 20 Problem Set 150
viii Contents
Session 21: Mathematical Olympiad II 153
Event of the Day: Math Olympiad 153
Math Olympiad II. First Page of Problems 154
Math Olympiad II. Second Page of Problems 155
Math Olympiad II. Additional Problems 156
Session 22: Divisibility I. Definition and Properties 157
Math Warm-up 157
Discussion of the Day: Divisibility 158
How Many Factors? 159
Divisibility: More Definitions 159
Notation for Divisibility 160
Divisibility Properties 161
Session 22 Problem Set 163
Session 23: Divisibility II. Prime Numbers and Prime Factorization 165
Math Warm-up 165
Discussion of the Day: Prime Numbers and Divisibility 165
Prime Factor Decomposition 166
Prime Factorization Tree 168
Prime Factorization and Divisibility 168
The Prime Factorization of a Product 170
Session 23 Problem Set 171
Session 24: Mathematical Auction 173
Math Warm-up 173
The Game of Mathematical Auction 173
Mathematical Auction Problems 174
Session 24 Problem Set 174
Session 25: Divisibility III. Divisibility Rules 177
Math Warm-up 177
Discussion of the Day: Divisibility Rules 177
Divisibility and Cryptography 181
Session 25 Problem Set 182
Session 26: Divisibility IV. Relatively Prime Numbers 185
Math Warm-up 185
Discussion of the Day: Relatively Prime Numbers 185
Session 26 Problem Set 188
Session 27: Mathematical Games of Strategy I 191
Math Warm-up 191
Discussion of the Day: Games and Winning Strategies 191
Session 27 Problem Set 195
Session 28: Mathematical Games of Strategy II 197
Contents jx
Math Warm-up 197
Discussion of the Day: Complements 197
Pseudogames 199
Session 28 Problem Set 200
Session 29: Mathematical Olympiad III 203
Math Warm-up 203
Event of the Day: Math Olympiad 204
Math Olympiad III. First Page of Problems 204
Math Olympiad II. Second Page of Problems 205
Math Olympiad II. Additional Problems 206
Part 2. Mathematical Contests and Competitions 209
Mathematical Contests 211
Mathematical Auction 213
Rules of Mathematical Auction 213
A Sample Round of Mathematical Auction Game 215
Team Work 216
Advice for the Teacher 216
Example Math Auction Problems 217
Mathematical Hockey 219
Mathematical Hockey Rules 219
Advice for the Teacher 220
Mathematical Olympiads 223
Types of Olympiads 223
Olympiad Problems 224
Planning for an Oral Olympiad 225
Olympiad Rules 225
Olympiads in This Book 226
Awards and Prizes 226
Short Entertaining Math Games 229
Jotto and Math Jotto 229
Nim 229
Black Box 230
Part 3. More Teaching Advice 233
How to be a Great Math Circle Teacher 235
Math Circle Day-to-Day 239
A Typical Session in Our Circle 239
A Math Entertainment Session in Our Circle 241
How to Organize a Session in Your Circle 242
x Contents
A Few More Ideas on the Layout of a Session 243
How to Keep a Circle Journal 243
How to Organize Problem-Solving Time 244
More Questions? 247
Part 4. Solutions 249
Session 1: How to Solve a Problem 251
Session 2: How to Solve a Problem and Explain a Solution 254
Session 3: How to Turn Lies into Truth 257
Session 4: Mathematical Auction 259
Session 5: Word Problems and Common Sense 260
Session 6: More Word Problems 262
Session 7: Odds and Evens - Magic Paper Cups 266
Session 8: Odds and Evens - Definitions and Properties 269
Session 9: Math Hockey I 271
Session 9: Problem Set Solutions 272
Session 10: Odds and Evens - Alternation 274
Session 11: Weighing and Fake Coins 276
Session 12: Math Olympiad I 279
Session 13: Meet The Cube 283
Session 14: Cross Sections 285
Session 15: Problem Set Solutions 288
Session 16: Combinatorics I 291
Session 17: Combinatorics II 295
Session 18: Math Hockey II 298
Session 18: Problem Set Solutions 299
Session 19: Runaway Digits 301
Session 20: Encrypted Problems 303
Session 21: Math Olympiad II 305
Session 22: Divisibility I 310
Session 23: Divisibility II 313
Session 24: Problem Set Solutions 316
Session 25: Divisibility III 318
Session 26: Divisibility IV 321
Session 27: Mathematical Games of Strategy I 323
Session 28: Mathematical Games of Strategy II 326
Session 29: Math Olympiad 328
Bibliography 335
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| spelling | Burago, Anna 1967- Verfasser (DE-588)1036800784 aut Mathematical circle diaries, year 1 complete curriculum for grades 5 to 7 Anna Burago Berkeley, Calif. [u.a.] MSRI Mathematical Sciences Research Inst. [u.a.] 2013 XII, 335 S. Ill. txt rdacontent n rdamedia nc rdacarrier MSRI mathematical circles library 11 Curriculum (DE-588)4010781-4 gnd rswk-swf Sekundarstufe 1 (DE-588)4054365-1 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf (DE-588)4167168-5 Lehrerhandbuch gnd-content Mathematikunterricht (DE-588)4037949-8 s Sekundarstufe 1 (DE-588)4054365-1 s Curriculum (DE-588)4010781-4 s DE-604 MSRI mathematical circles library 11 (DE-604)BV024626790 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027456127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burago, Anna 1967- Mathematical circle diaries, year 1 complete curriculum for grades 5 to 7 MSRI mathematical circles library Curriculum (DE-588)4010781-4 gnd Sekundarstufe 1 (DE-588)4054365-1 gnd Mathematikunterricht (DE-588)4037949-8 gnd |
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| title | Mathematical circle diaries, year 1 complete curriculum for grades 5 to 7 |
| title_auth | Mathematical circle diaries, year 1 complete curriculum for grades 5 to 7 |
| title_exact_search | Mathematical circle diaries, year 1 complete curriculum for grades 5 to 7 |
| title_full | Mathematical circle diaries, year 1 complete curriculum for grades 5 to 7 Anna Burago |
| title_fullStr | Mathematical circle diaries, year 1 complete curriculum for grades 5 to 7 Anna Burago |
| title_full_unstemmed | Mathematical circle diaries, year 1 complete curriculum for grades 5 to 7 Anna Burago |
| title_short | Mathematical circle diaries, year 1 |
| title_sort | mathematical circle diaries year 1 complete curriculum for grades 5 to 7 |
| title_sub | complete curriculum for grades 5 to 7 |
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| topic_facet | Curriculum Sekundarstufe 1 Mathematikunterricht Lehrerhandbuch |
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