Givental, Laura
Math circle by the bay : Topics for the grades 1-5 - USA: AMS, [c2018] - 171 p
Chapter 1. Numbers as Geometric Shapes
Examples of Figurate Numbers
Square Numbers
Rectangular Arrangements
Triangular Numbers
Quick Summations
Cubic Numbers
Pyramids
Chapter 2. Combinatorics
Coloring Beads
Mumbo Language
Ice Cream Cones
Nowhere York City
The Handshake Problem
Sides and Diagonals
Same Problems with 10 Objects
Apples, Oranges, and More
Problems about Numbers
Harder Problems
Chapter 3. Fibonacci Numbers
Building Strips with Squares and Dominoes
Parking Problems
Counting Routes
Fibonacci Sequence in Nature
Extension to the Left
Even/Odd Pattern
Divisibility by 3
Sum of the First n Consecutive Fibonacci Numbers
Fibonacci Rectangles and Fibonacci Spiral
Honeybees’ Ancestral Tree
Chapter 4. Pascal’s Triangle
Paths in Mouseville
Hockey Stick Pattern
Diagonals in Pascal’s Triangle
Rows in Pascal’s Triangle
Extending Pascal’s Triangle
Fibonacci Numbers in Pascal’s Triangle
Sierpinski Triangle
Counting Odd and Even Numbers in Pascal’s Triangle
Pascal’s Triangle Modulo 3
Chapter 5. Area
Playing with Squares
Areas of Similar Shapes
SAME SHAPE SAME SIZE
Rotation by a Right Angle
Area of a Tilted Square
Pythagorean Theorem
Area of a Parallelogram and Area of a Triangle
Pick’s Formula
Chapter 6. Selected Warmup and Challenging Problems
This book is based on selected topics that the authors taught in math circles for elementary school students at the University of California, Berkeley; Stanford University; Dominican University (Marin County, CA); and the University of Oregon (Eugene). It is intended for people who are already running a math circle or who are thinking about organizing one. It can be used by parents to help their motivated, math-loving kids or by elementary school teachers. We also hope that bright fourth or fifth graders will be able to read this book on their own.
The main features of this book are the logical sequence of the problems, the description of class reactions, and the hints given to kids when they get stuck. This book tries to keep the balance between two goals: inspire readers to invent their own original approaches while being detailed enough to work as a fallback in case the teacher needs to prepare a lesson on short notice. It introduces kids to combinatorics, Fibonacci numbers, Pascal's triangle, and the notion of area, among other things. The authors chose topics with deep mathematical context. These topics are just as engaging and entertaining to children as typical “recreational math” problems, but they can be developed deeper and to more advanced levels.
9781470447854
QA13.5
Math circle by the bay : Topics for the grades 1-5 - USA: AMS, [c2018] - 171 p
Chapter 1. Numbers as Geometric Shapes
Examples of Figurate Numbers
Square Numbers
Rectangular Arrangements
Triangular Numbers
Quick Summations
Cubic Numbers
Pyramids
Chapter 2. Combinatorics
Coloring Beads
Mumbo Language
Ice Cream Cones
Nowhere York City
The Handshake Problem
Sides and Diagonals
Same Problems with 10 Objects
Apples, Oranges, and More
Problems about Numbers
Harder Problems
Chapter 3. Fibonacci Numbers
Building Strips with Squares and Dominoes
Parking Problems
Counting Routes
Fibonacci Sequence in Nature
Extension to the Left
Even/Odd Pattern
Divisibility by 3
Sum of the First n Consecutive Fibonacci Numbers
Fibonacci Rectangles and Fibonacci Spiral
Honeybees’ Ancestral Tree
Chapter 4. Pascal’s Triangle
Paths in Mouseville
Hockey Stick Pattern
Diagonals in Pascal’s Triangle
Rows in Pascal’s Triangle
Extending Pascal’s Triangle
Fibonacci Numbers in Pascal’s Triangle
Sierpinski Triangle
Counting Odd and Even Numbers in Pascal’s Triangle
Pascal’s Triangle Modulo 3
Chapter 5. Area
Playing with Squares
Areas of Similar Shapes
SAME SHAPE SAME SIZE
Rotation by a Right Angle
Area of a Tilted Square
Pythagorean Theorem
Area of a Parallelogram and Area of a Triangle
Pick’s Formula
Chapter 6. Selected Warmup and Challenging Problems
This book is based on selected topics that the authors taught in math circles for elementary school students at the University of California, Berkeley; Stanford University; Dominican University (Marin County, CA); and the University of Oregon (Eugene). It is intended for people who are already running a math circle or who are thinking about organizing one. It can be used by parents to help their motivated, math-loving kids or by elementary school teachers. We also hope that bright fourth or fifth graders will be able to read this book on their own.
The main features of this book are the logical sequence of the problems, the description of class reactions, and the hints given to kids when they get stuck. This book tries to keep the balance between two goals: inspire readers to invent their own original approaches while being detailed enough to work as a fallback in case the teacher needs to prepare a lesson on short notice. It introduces kids to combinatorics, Fibonacci numbers, Pascal's triangle, and the notion of area, among other things. The authors chose topics with deep mathematical context. These topics are just as engaging and entertaining to children as typical “recreational math” problems, but they can be developed deeper and to more advanced levels.
9781470447854
QA13.5