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Math Circles for Elementary School Students: Berkeley 2009 and Manhattan 2011 [Pehme köide]

  • Formaat: Paperback / softback, 166 pages, kõrgus x laius: 229x152 mm, kaal: 340 g, Illustrations
  • Sari: MSRI Mathematical Circles Library
  • Ilmumisaeg: 30-Oct-2014
  • Kirjastus: American Mathematical Society
  • ISBN-10: 1470416956
  • ISBN-13: 9781470416959
  • Formaat: Paperback / softback, 166 pages, kõrgus x laius: 229x152 mm, kaal: 340 g, Illustrations
  • Sari: MSRI Mathematical Circles Library
  • Ilmumisaeg: 30-Oct-2014
  • Kirjastus: American Mathematical Society
  • ISBN-10: 1470416956
  • ISBN-13: 9781470416959
The main part of this book describes the first semester of the existence of a successful and now highly popular program for elementary school students at the Berkeley Math Circle. The topics discussed in the book introduce the participants to the basics of many important areas of modern mathematics, including logic, symmetry, probability theory, knot theory, cryptography, fractals, and number theory. Each chapter in the first part of this book consists of two parts. It starts with generously illustrated sets of problems and hands-on activities. This part is addressed to young readers who can try to solve problems on their own or to discuss them with adults. The second part of each chapter is addressed to teachers and parents. It includes comments on the topics of the lesson, relates those topics to discussions in other chapters, and describes the actual reaction of math circle participants to the proposed activities.

The supplementary problems that were discussed at workshops of Math Circle at Kansas State University are given in the second part of the book.

The book is richly illustrated, which makes it attractive to its young audience.

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.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

Arvustused

The book is richly illustrated, which makes it attractive to its young audience." - Zentralblatt MATH

"Why are there so few math circles, particularly for younger children? One of the reasons is the belief that very young kids are simply not ready for complex math. Another reason is that finding deep and engaging math activities, adapted for this younger audience, is itself a challenge. Natasha Rozhkovskaya's new book, Math Circles for Elementary School Students, helps deal with both these difficulties. Click here to view online video review." - Moebuis Noodles

Foreword xi
Acknowledgments xv
Part I. Berkeley Math Circle 1(124)
Introduction: Berkeley 2009
3(2)
Lesson 1
5(6)
Drawing links and knots
5(5)
At the lesson
10(1)
Lesson 2
11(6)
Mysterious pictures
11(1)
Secret code
12(3)
At the lesson
15(1)
Answers
16(1)
Lesson 3
17(12)
Two logic problems
17(1)
About fractals and the powers of numbers
18(4)
Sierpinski triangle
22(2)
Fractal snowflake
24(1)
At the lesson
25(1)
Answers
26(3)
Lesson 4
29(8)
Squares and squares of numbers
29(1)
Cubes and cubes of numbers
30(1)
Homonyms and definitions in mathematics
30(2)
Random Maze
32(2)
At the lesson
34(1)
Answers
35(2)
Lesson 5
37(8)
Pascal's triangle
37(1)
Divisibility criterion by 3
38(2)
Problems with matchsticks
40(1)
Difficult situation
41(1)
At the lesson
42(1)
Answers
43(2)
Lesson 6
45(8)
Weekend
45(1)
About sausages
45(1)
Flower pots
46(1)
Magic triangle
46(1)
An experiment with a triangle (The sum of angles in a triangle is 180°)
46(1)
An experiment with a quadrilateral (The sum of angles in a convex quadrilateral is equal to 360°)
47(2)
At the lesson
49(2)
Answers
51(2)
Lesson 7
53(6)
The game "Points on a circle"
53(1)
Three puzzles
54(2)
At the lesson
56(1)
Answers
57(2)
Lesson 8
59(8)
Two short problems
59(1)
Mysterious pictures
60(1)
Arithmetic operations
61(1)
Tropical arithmetic
62(1)
At the lesson
63(1)
Answers
64(3)
Lesson 9
67(6)
Beehive and clock
67(1)
Pizza
67(2)
No-glue paper chain
69(1)
Logic game "A not A"
69(1)
At the lesson
70(1)
Answers
71(2)
Lesson 10
73(10)
Negations
73(3)
Yes and No
76(2)
About the game 20Q
78(1)
At the lesson
79(2)
Answers
81(2)
Lesson 11
83(6)
Problems about guests
83(1)
The Treasure Island
84(1)
River Crossing problems
85(1)
At the lesson
86(1)
Answers
87(2)
Lesson 12
89(12)
Knights and a dragon
89(1)
One mirror
89(1)
Two mirrors
90(3)
Old lady in the mirrors
93(1)
Kaleidoscope
93(3)
Symmetry
96(2)
At the lesson
98(2)
Answers
100(1)
Lesson 13
101(10)
Pets
101(1)
Gnomes
101(2)
Silent cooperation
103(1)
Random choice with equally likely outcomes
104(1)
How to choose something absolutely randomly
104(2)
At the lesson
106(2)
Answers
108(3)
Lesson 14
111(8)
Christmas problems
111(6)
At the lesson
117(1)
Answers
118(1)
Lesson 15
119(6)
Boys and girls
119(3)
Race
122(1)
At the lesson
123(1)
Answers
124(1)
Part II. Manhattan Math Circle Seminar 125
Introduction: Manhattan 2011
127(2)
M.1 Counting rhymes
129(4)
M.2 Arithmetic
133(4)
M.3 More coded pictures
137(4)
M.4 Make your own problem
141(2)
M.5 Cut the square
143(4)
M.6 Siege of the fortress
147(2)
M.7 More logic problems
149(2)
M.8 Estimates
151(2)
M.9 Problems with unknowns
153(2)
M.10 Knots, links, and paths
155(4)
M.11 How old are you?
159(2)
M.12 No solutions
161(4)
M.13 The Pigeon Hole Principle
165
Natasha Rozhkovskaya, Kansas State University, Manhattan, KS USA.