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Mathematical Circle Diaries, Year 1: Complete Curriculum for Grades 5 to 7 [Pehme köide]

  • Formaat: Paperback / softback, 335 pages, kaal: 620 g
  • Sari: MSRI Mathematical Circles Library
  • Ilmumisaeg: 30-Jan-2013
  • Kirjastus: American Mathematical Society
  • ISBN-10: 0821887459
  • ISBN-13: 9780821887455
Teised raamatud teemal:
  • Formaat: Paperback / softback, 335 pages, kaal: 620 g
  • Sari: MSRI Mathematical Circles Library
  • Ilmumisaeg: 30-Jan-2013
  • Kirjastus: American Mathematical Society
  • ISBN-10: 0821887459
  • ISBN-13: 9780821887455
Teised raamatud teemal:
Early middle school is a great time for children to start their mathematical circle education. This time is a period of curiosity and openness to learning. The thinking habits and study skills acquired by children at this age stay with them for a lifetime. Mathematical circles, with their question-driven approach and emphasis on creative problem-solving, have been rapidly gaining popularity in the United States. The circles expose children to the type of mathematics that stimulates development of logical thinking, creativity, analytical abilities and mathematical reasoning. These skills, while scarcely touched upon at school, are in high demand in the modern world. This book contains everything that is needed to run a successful mathematical circle for a full year. The materials, distributed among 29 weekly lessons, include detailed lectures and discussions, sets of problems with solutions, and contests and games. In addition, the book shares some of the know-how of running a mathematical circle. The curriculum, which is based on the rich and long-standing Russian math circle tradition, has been modified and adapted for teaching in the United States. For the past decade, the author has been actively involved in teaching a number of mathematical circles in the Seattle area. This book is based on her experience and on the compilation of materials from these circles. The material is intended for students in grades 5 to 7. It can be used by teachers and parents with various levels of expertise who are interested in teaching mathematics with the emphasis on critical thinking. Also, this book will be of interest to mathematically motivated children. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Acknowledgments xi
Preliminaries 1(6)
What is a Mathematical Circle?
1(1)
About This Book
2(1)
About the Author
3(1)
Why I Wrote This Book
4(1)
Target Age Groups
5(2)
Part 1 Session Plans
7(202)
Introduction
9(1)
A Few Words about Problem Sets
10(1)
Session 1 How to Solve a Problem
11(12)
Before the Session
11(1)
The Session Plan
12(1)
Introductions and Math Warm-up
12(1)
What is a Mathematical Circle?
13(1)
Discussion of the Day: "What Does it Mean to Solve a Problem?"
13(6)
A Few Words about Problem Sets and Homework
19(4)
Session 1 Problem Set
19(4)
Session 2 Knights and Liars
23(8)
Math Warm-up
23(1)
Problem Set From the Previous Class
24(7)
Discussion of the Day, Part 1 Cause and Effect Problems
24(1)
Discussion of the Day, Part 2 Knights-and-Liars Problems
25(3)
Session 2 Problem-Set
28(3)
Session 3 How to Turn Lies into Truth
31(6)
Math Warm-up
32(1)
Discussion of the Day: Negation of Logical Statements
33(4)
Session 3 Problem Set
34(3)
Session 4 Mathematical Auction
37(6)
Math Warm-up
37(1)
The Game of Mathematical Auction
37(3)
Mathematical Auction Problems
40(3)
Session 4 Problem Set
41(2)
Session 5 Word Problems and Common Sense
43(8)
Math Warm-up
43(1)
Discussion of the Day: "Draw a Picture---Solve the Problem!"
43(8)
Discussion of the Day, Part 2 Working Together
46(1)
Session 5 Problem Set
47(4)
Session 6 More Word Problems
51(6)
Math Warm-up
51(1)
Discussion of the Day: Of Pigs and Hens
52(5)
Session 6 Problem Set
53(4)
Session 7 Odd and Even Numbers I. Magic Paper Cups
57(6)
Math Warm-up
57(1)
Discussion of the Day: Odd and Even Numbers. Parity
58(5)
Session 7 Problem Set
60(3)
Session 8 Odd and Even Numbers II. Definitions and Properties
63(8)
Math Warm-up
63(1)
Discussion of the Day: How to Define Odd and Even Numbers
63(2)
Parity of Sums and Differences
65(4)
Parity of a Product
69(2)
Session 8 Problem Set
69(2)
Session 9 Halloween Math Hockey I
71(6)
Math Warm-up
71(1)
Math Hockey
71(1)
Math Hockey I Problems
72(5)
Session 9 Problem Set
74(3)
Session 10 Odd and Even Numbers III. Alternations
77(8)
Math Warm-up
77(1)
Discussion of the Day: Alternations
77(8)
Session 10 Problem Set
81(4)
Session 11 Weighings and Counterfeit Coins
85(6)
Math Warm-up
85(1)
Discussion of the Day: Balance Scales and Counterfeit Coins
86(5)
Session 11 Problem Set
89(2)
Session 12 Mathematical Olympiad I Math Warm-up
91(6)
Event of the Day: Math Olympiad
92(1)
Math Olympiad I. First Page of Problems
93(1)
Math Olympiad I. Second Page of Problems
93(1)
Math Olympiad I. Additional Problems
94(3)
Session 13 Meet the Cube. First Lesson in 3D Geometry
97(8)
Math Warm-up
98(1)
Discussion of the Day: Cubes
98(2)
Cube Nets
100(1)
"Meet the Cube" Exercises
101(4)
Session 13 Problem Set
102(3)
Session 14 Cross Sections. Second Lesson in 3D Geometry
105(8)
Math Warm-up
105(1)
Discussion of the Day: Cross Sections
106(7)
Session 14 Problem Set
110(3)
Session 15 Mathematical Auction
113(4)
Math Warm-up
113(1)
Event of the Day: The Game of Mathematical Auction
113(1)
Mathematical Auction Problems
114(3)
Session 15 Problem Set
115(2)
Session 16 Combinatorics I
117(10)
Math Warm-up
117(1)
Discussion of the Day: Introduction to Combinatorics
117(10)
Session 16 Problem Set
124(3)
Session 17 Combinatorics II
127(10)
Math Warm-up
127(1)
Discussion of the Day: The Slot Rule and Permutations without Repetitions
127(10)
Session 17 Problem Set
134(3)
Session 18 Mathematical Hockey II
137(4)
Math Warm-up
137(1)
Event of the Day: Math Hockey Game
137(1)
Math Hockey II Problems
138(3)
Session 18 Problem Set
139(2)
Session 19 Numerical Puzzles I. Runaway Digits
141(6)
Math Warm-up
141(1)
Discussion of the Day: Runaway Digits
142(5)
Session 19 Problem Set
144(3)
Session 20 Numerical Puzzles II. Encrypted Problems
147(6)
Math Warm-up
147(1)
Discussion of the Day: Encrypted Problems
147(6)
Session 20 Problem Set
150(3)
Session 21 Mathematical Olympiad II
153(4)
Event of the Day: Math Olympiad
153(1)
Math Olympiad II. First Page of Problems
154(1)
Math Olympiad II. Second Page of Problems
155(1)
Math Olympiad II. Additional Problems
156(1)
Session 22 Divisibility I. Definition and Properties
157(8)
Math Warm-up
157(1)
Discussion of the Day: Divisibility
158(1)
How Many Factors?
159(1)
Divisibility: More Definitions
159(1)
Notation for Divisibility
160(1)
Divisibility Properties
161(4)
Session 22 Problem Set
163(2)
Session 23 Divisibility II. Prime Numbers and Prime Factorization
165(8)
Math Warm-up
165(1)
Discussion of the Day: Prime Numbers and Divisibility
165(1)
Prime Factor Decomposition
166(2)
Prime Factorization Tree
168(1)
Prime Factorization and Divisibility
168(2)
The Prime Factorization of a Product
170(3)
Session 23 Problem Set
171(2)
Session 24 Mathematical Auction
173(4)
Math Warm-up
173(1)
The Game of Mathematical Auction
173(1)
Mathematical Auction Problems
174(3)
Session 24 Problem Set
174(3)
Session 25 Divisibility III. Divisibility Rules
177(8)
Math Warm-up
177(1)
Discussion of the Day: Divisibility Rules
177(4)
Divisibility and Cryptography
181(4)
Session 25 Problem Set
182(3)
Session 26 Divisibility IV. Relatively Prime Numbers
185(6)
Math Warm-up
185(1)
Discussion of the Day: Relatively Prime Numbers
185(6)
Session 26 Problem Set
188(3)
Session 27 Mathematical Games of Strategy I
191(6)
Math Warm-up
191(1)
Discussion of the Day: Games and Winning Strategies
191(6)
Session 27 Problem Set
195(2)
Session 28 Mathematical Games of Strategy II
197(6)
Math Warm-up
197(1)
Discussion of the Day: Complements
197(2)
Pseudogames
199(4)
Session 28 Problem Set
200(3)
Session 29 Mathematical Olympiad III
203(6)
Math Warm-up
203(1)
Event of the Day: Math Olympiad
204(1)
Math Olympiad III. First Page of Problems
204(1)
Math Olympiad II. Second Page of Problems
205(1)
Math Olympiad II. Additional Problems
206(3)
Part 2 Mathematical Contests and Competitions
209(24)
Mathematical Contests
211(2)
Mathematical Auction
213(1)
Rules of Mathematical Auction
213(2)
A Sample Round of Mathematical Auction Game
215(1)
Team Work
216(1)
Advice for the Teacher
216(1)
Example Math Auction Problems
217(2)
Mathematical Hockey
219(1)
Mathematical Hockey Rules
219(1)
Advice for the Teacher
220(3)
Mathematical Olympiads
223(1)
Types of Olympiads
223(1)
Olympiad Problems
224(1)
Planning for an Oral Olympiad
225(1)
Olympiad Rules
225(1)
Olympiads in This Book
226(1)
Awards and Prizes
226(3)
Short Entertaining Math Games
229(1)
Jotto and Math Jotto
229(1)
Nim
229(1)
Black Box
230(3)
Part 3 More Teaching Advice
233(16)
How to be a Great Math Circle Teacher
235(4)
Math Circle Day-to-Day
239(1)
A Typical Session in Our Circle
239(2)
A Math Entertainment Session in Our Circle
241(1)
How to Organize a Session in Your Circle
242(1)
A Few More Ideas on the Layout of a Session
243(1)
How to Keep a Circle Journal
243(1)
How to Organize Problem-Solving Time
244(3)
More Questions?
247(2)
Part 4 Solutions
249(86)
Session 1 How to Solve a Problem
251(3)
Session 2 How to Solve a Problem and Explain a Solution
254(3)
Session 3 How to Turn Lies into Truth
257(2)
Session 4 Mathematical Auction
259(1)
Session 5 Word Problems and Common Sense
260(2)
Session 6 More Word Problems
262(4)
Session 7 Odds and Evens - Magic Paper Cups
266(3)
Session 8 Odds and Evens - Definitions and Properties
269(2)
Session 9 Math Hockey I
271(1)
Session 9 Problem Set Solutions
272(2)
Session 10 Odds and Evens - Alternation
274(2)
Session 11 Weighing and Fake Coins
276(3)
Session 12 Math Olympiad I
279(4)
Session 13 Meet The Cube
283(2)
Session 14 Cross Sections
285(3)
Session 15 Problem Set Solutions
288(3)
Session 16 Combinatorics I
291(4)
Session 17 Combinatorics II
295(3)
Session 18 Math Hockey II
298(1)
Session 18 Problem Set Solutions
299(2)
Session 19 Runaway Digits
301(2)
Session 20 Encrypted Problems
303(2)
Session 21 Math Olympiad II
305(5)
Session 22 Divisibility I
310(3)
Session 23 Divisibility II
313(3)
Session 24 Problem Set Solutions
316(2)
Session 25 Divisibility III
318(3)
Session 26 Divisibility IV
321(2)
Session 27 Mathematical Games of Strategy I
323(3)
Session 28 Mathematical Games of Strategy II
326(2)
Session 29 Math Olympiad
328(7)
Bibliography 335
Anna Burago, Prime Factor Math Circle, Seattle, WA, USA