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

Description

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:Train and improve your spatial ability in a well-balanced and structured way! The problems of the book address all subcomponents of spatial ability 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! Store geometric objects with various characteristics in the brain! This enhances your ability to solve geometric and spatial and even mathematical tasks. 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. 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