Solving Problems in Our Spatial World (Problem Solving in Mathematics and Beyond)

✍ Scribed by Guenter Maresch, Alfred S Posamentier

• Publisher: World Scientific Publishing Co
• Year: 2019
• Tongue: English
• Leaves: 381
• Category: Library

✦ Synopsis

Immerse yourself in the fascinating world of geometry and spatial ability — either individually or in small groups, either as challenges or play problems! Here are four reasons why you should work with this book:

1. Train and improve your spatial ability in a well-balanced and structured way! The problems of the book address all subcomponents of spatial ability
2. Train spatial ability on all three levels in which we learn mathematics! The haptic way, figurative way, symbolic and mostly mental way, or a combination of all three!
3. Store geometric objects with various characteristics in the brain! This enhances your ability to solve geometric and spatial and even mathematical tasks.
4. Hours of fun! From the several thousand students and adults who worked with the problems of the book, we know that it is fun solving these problems in a variety of ways.

This book offers a very unique opportunity to enhance your spatial ability, your mathematical competence, and your logical thinking. The authors arranged 45 problems — including more than 120 tasks — in a well-balanced order, which have been tested with a variety of populations.

✦ Table of Contents

Contents
Preface
About the Authors
Four Reasons for Working with this Book
1. Pedagogical Motivation
2. Scientific Motivation
3. Neurological Motivation
4. Learning in a Very Playful Way
How to Work with the Problems of the Book
Section I Spatial World Problems
Chapter 1 Problems Addressing Visualization
Problem 1.1: Manipulating Black and White Cubes
Problem 1.2: Identifying More Nets of Cubes
Problem 1.3: Identifying the Opposite Sides of a Cube
Problem 1.4: Designing Decoration Pads
Problem 1.5: Identifying the Top View of Objects
Problem 1.6: Observations of Cube Dissections from Various Perspectives
Problem 1.7: Changing the Viewpoint
Problem 1.8: Viewing Cubes: Top View, Front View, and Side View
Problem 1.9: Rotating of a Cube
Problem 1.10: Rotating of a Rectangular Cuboid
Problem 1.11: Producing Cubic Stamps
Problem 1.12: Completing Cubic Nets
Problem 1.13: Rotating of a Die
Problem 1.14: Completing Cube Tests
Chapter 2 Problems Addressing Spatial Relations
Problem 2.1: Measuring Stacks of Cubes
Problem 2.2: Analyzing Piles of Cubes
Problem 2.3: Assembling Three-Dimensional Objects
Problem 2.4: Viewing a Pile of Colored Wooden Cubes
Problem 2.5: Analyzing Wooden Cubes
Problem 2.6: Constructing a Tower
Problem 2.7: Working with a Stack of Bricks
Problem 2.8: Cutting Objects into Two Parts
Chapter 3 Problems Addressing Mental Rotation
Problem 3.1: Finding the Odd One
Problem 3.2: Searching for the One of Four
Problem 3.3: Rotating Solids
Problem 3.4: Finding the False Object
Problem 3.5: Searching for the Wrong Solid
Problem 3.6: Playing Quartet
Problem 3.7: Rotating Objects, Which are Built of Rods and Cubes
Problem 3.8: Labeling of Vertices
Problem 3.9: Rotating an Object Around Axes
Problem 3.10: Rotating Another Object Around Axes
Problem 3.11: Playing with Colorful Cubes
Problem 3.12: Following the Red Flag
Chapter 4 Problems Addressing Spatial Orientation
Problem 4.1: Switching Between Different Town Maps
Problem 4.2: Solving the Tube in Cube Problem
Problem 4.3: Flying with a Helicopter
Problem 4.4: Taking Pictures of a Village
Problem 4.5: Helping the Photographer
Problem 4.6: Walking Around a Platonic World
Problem 4.7: Parking a Car
Problem 4.8: Searching for My Car
Problem 4.9: Standing on a Parking Area
Problem 4.10: Watching a Carousel of Basic Solids
Problem 4.11: Riding with a Cylindrical Platform
Section II Solutions and Hints
Chapter 5 Solutions and Hints of the Problems Addressing Visualization
Solution of Problem 1.1: Manipulating Black and White Cubes
Solution of Problem 1.2: Identifying More Nets of Cubes
Solution of Problem 1.3: Identifying the Opposite Sides of a Cube
Solution of Problem 1.4: Designing Decoration Pads
Solution of Problem 1.5: Identifying the Top View of Objects
Solution of Problem 1.6: Observations of Cube Dissections from Various Perspectives
Solutions of Problem 1.7: Changing the Viewpoint
Solution of Problem 1.8: Viewing Cubes: Top View, Front View, and Side View
Solution of Problem 1.9: Rotating of a Cube
Solution of Problem 1.10: Rotating of a Rectangular Cuboid
Solution of Problem 1.11: Producing Cubic Stamps
Solution of Problem 1.12: Completing Cubic Nets
Solution of Problem 1.13: Rotating of a Die
Solution of Problem 1.14: Completing Cube Tests
Chapter 6 Solutions and Hints of the Problems Addressing Spatial Relations
Solution of Problem 2.1: Measuring Stacks of Cubes
Solution of Problem 2.2: Analyzing Piles of Cubes
Solution of Problem 2.3: Assembling Three-Dimensional Objects
Solution of Problem 2.4: Viewing a Pile of Colored Wooden Cubes
Solution of Problem 2.5: Analyzing Wooden Cubes
Solution of Problem 2.6: Constructing a Tower
Solution of Problem 2.7: Working with a Stack of Bricks
Solution of Problem 2.8: Cutting Objects into Two Parts
Chapter 7 Solutions and Hints of the Problems Addressing Mental Rotation
Solution of Problem 3.1: Finding the Odd One
Solution of Problem 3.2: Searching for One of the Four
Solution of Problem 3.3: Rotating Solids
Solution of Problem 3.4: Finding the False Object
Solution of Problem 3.5: Searching for the Wrong Solid
Solution of Problem 3.6: Playing Quartet
Solution of Problem 3.7: Rotating Objects, Which are Built of Rods and Cubes
Solution of Problem 3.8: Labeling of Vertices
Solution of Problem 3.9: Rotating an Object Around Axes
Solution of Problem 3.10: Rotating Another Object Around Axes
Solution of Problem 3.11: Playing with Colorful Cubes
Solution of Problem 3.12: Following the Red Flag
Chapter 8 Solutions and Hints of the Problems Addressing Spatial Orientation
Solution of Problem 4.1: Switching Between Various Town Maps
Solution of Problem 4.2: Solving the Tube in Cube Problem
Solution of Problem 4.3: Flying with a Helicopter
Solution of Problem 4.4: Taking Pictures of a Village
Solution of Problem 4.5: Helping the Photographer
Solution of Problem 4.6: Walking Around a Platonic World
Solution of Problem 4.7: Parking a Car
Solution of Problem 4.8: Searching for My Car
Solution of Problem 4.9: Standing on a Parking Area
Solution of Problem 4.10: Watching a Carousel of Basic Solids
Solution of Problem 4.11: Riding with a Cylindrical Platform
Section III Folding Templates to be Cut Out
Chapter 9 Folding Templates of Problems Addressing Visualization
Folding Template of Problem 1.1: Manipulating Black and White Cubes
Folding Templates of Problem 1.3: Identifying the Opposite Sides of a Cube
Folding Template of Problem 1.9: Rotating of a Cube
Folding Templates of Problem 1.10: Rotating of a Rectangular Cuboid
Folding Templates of Problem 1.11: Producing Cubic Stamps
Folding Templates of Problem 1.12: Completing Cubic Nets
Folding Templates of Problem 1.13: Rotating of a Die
Folding Templates of Problem 1.14: Completing Cube Tests
Chapter 10 Folding Templates of a Problem Addressing Spatial Relations
Folding Template of Problem 2.1: Measuring Stacks of Cubes
Chapter 11 Folding Templates of a Problem Addressing Spatial Orientation
Folding Template of Problem 4.1: Switching Between Different Town Maps
Appendix A: How to Get the Interactive 3D Model on an iOS Device
Appendix B: How to Get the Interactive 3D Model on a Windows Device
Appendix C: How to Get the Interactive 3D Model on an Android Device
References