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E-grāmata: Solving Problems In Our Spatial World

(City University Of New York, Usa), (Univ Of Salzburg, Austria)
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Solving Problems In Our Spatial WorldPalielināt
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Maresch and Posamentier seek to train readers to visualize three-dimensional representations in two dimensions, that is, on a planar surface. They arrange the 45 problems-including more than 120 tasks-in a very special and well-balanced order that they have tested with a variety of populations. In chapters on visualization, spatial relations, mental rotation, and spatial orientation, they present such problems as identifying the opposite sides of a cube, assembling three-dimensional objects, searching for the wrong object, and walking around a Platonic world. They include solutions and hints and folding templates to cut out. Annotation ©2019 Ringgold, Inc., Portland, OR (protoview.com)

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.

Preface v
About the Authors vii
Four Reasons for Working with this Book xi
How to Work with the Problems of the Book xxi
Section I Spatial World Problems
1(144)
Chapter 1 Problems Addressing Visualization
3(50)
Problem 1.1 Manipulating Black and White Cubes
4(4)
Problem 1.2 Identifying More Nets of Cubes
8(1)
Problem 1.3 Identifying the Opposite Sides of a Cube
9(1)
Problem 1.4 Designing Decoration Pads
10(3)
Problem 1.5 Identifying the Top View of Objects
13(5)
Problem 1.6 Observations of Cube Dissections from Various Perspectives
18(4)
Problem 1.7 Changing the Viewpoint
22(1)
Problem 1.8 Viewing Cubes: Top View, Front View, and Side View
23(2)
Problem 1.9 Rotating of a Cube
25(4)
Problem 1.10 Rotating of a Rectangular Cuboid
29(4)
Problem 1.11 Producing Cubic Stamps
33(6)
Problem 1.12 Completing Cubic Nets
39(3)
Problem 1.13 Rotating of a Die
42(7)
Problem 1.14 Completing Cube Tests
49(4)
Chapter 2 Problems Addressing Spatial Relations
53(20)
Problem 2.1 Measuring Stacks of Cubes
54(4)
Problem 2.2 Analyzing Piles of Cubes
58(2)
Problem 2.3 Assembling Three-Dimensional Objects
60(4)
Problem 2.4 Viewing a Pile of Colored Wooden Cubes
64(2)
Problem 2.5 Analyzing Wooden Cubes
66(3)
Problem 2.6 Constructing a Tower
69(1)
Problem 2.7 Working with a Stack of Bricks
70(1)
Problem 2.8 Cutting Objects into Two Parts
71(2)
Chapter 3 Problems Addressing Mental Rotation
73(28)
Problem 3.1 Finding the Odd One
74(1)
Problem 3.2 Searching for the One of Four
75(2)
Problem 3.3 Rotating Solids
77(2)
Problem 3.4 Finding the False Object
79(2)
Problem 3.5 Searching for the Wrong Solid
81(2)
Problem 3.6 Playing Quartet
83(3)
Problem 3.7 Rotating Objects, Which are Built of Rods and Cubes
86(4)
Problem 3.8 Labeling of Vertices
90(3)
Problem 3.9 Rotating an Object Around Axes
93(2)
Problem 3.10 Rotating Another Object Around Axes
95(2)
Problem 3.11 Playing with Colorful Cubes
97(2)
Problem 3.12 Following the Red Flag
99(2)
Chapter 4 Problems Addressing Spatial Orientation
101(44)
Problem 4.1 Switching Between Different Town Maps
102(3)
Problem 4.2 Solving the Tube in Cube Problem
105(12)
Problem 4.3 Flying with a Helicopter
117(3)
Problem 4.4 Taking Pictures of a Village
120(4)
Problem 4.5 Helping the Photographer
124(3)
Problem 4.6 Walking Around a Platonic World
127(3)
Problem 4.7 Parking a Car
130(3)
Problem 4.8 Searching for My Car
133(2)
Problem 4.9 Standing on a Parking Area
135(3)
Problem 4.10 Watching a Carousel of Basic Solids
138(3)
Problem 4.11 Riding with a Cylindrical Platform
141(4)
Section II Solutions and Hints
145(148)
Chapter 5 Solutions and Hints of the Problems Addressing Visualization
147(44)
Solution of Problem 1.1 Manipulating Black and White Cubes
147(3)
Solution of Problem 1.2 Identifying More Nets of Cubes
150(1)
Solution of Problem 1.3 Identifying the Opposite Sides of a Cube
151(1)
Solution of Problem 1.4 Designing Decoration Pads
152(3)
Solution of Problem 1.5 Identifying the Top View of Objects
155(2)
Solution of Problem 1.6 Observations of Cube Dissections from Various Perspectives
157(4)
Solutions of Problem 1.7 Changing the Viewpoint
161(1)
Solution of Problem 1.8 Viewing Cubes: Top View, Front View, and Side View
162(5)
Solution of Problem 1.9 Rotating of a Cube
167(2)
Solution of Problem 1.10 Rotating of a Rectangular Cuboid
169(2)
Solution of Problem 1.11 Producing Cubic Stamps
171(3)
Solution of Problem 1.12 Completing Cubic Nets
174(3)
Solution of Problem 1.13 Rotating of a Die
177(4)
Solution of Problem 1.14 Completing Cube Tests
181(10)
Chapter 6 Solutions and Hints of the Problems Addressing Spatial Relations
191(30)
Solution of Problem 2.1 Measuring Stacks of Cubes
192(5)
Solution of Problem 2.2 Analyzing Piles of Cubes
197(4)
Solution of Problem 2.3 Assembling Three-Dimensional Objects
201(4)
Solution of Problem 2.4 Viewing a Pile of Colored Wooden Cubes
205(3)
Solution of Problem 2.5 Analyzing Wooden Cubes
208(2)
Solution of Problem 2.6 Constructing a Tower
210(2)
Solution of Problem 2.7 Working with a Stack of Bricks
212(6)
Solution of Problem 2.8 Cutting Objects into Two Parts
218(3)
Chapter 7 Solutions and Hints of the Problems Addressing Mental Rotation
221(36)
Solution of Problem 3.1 Finding the Odd One
222(2)
Solution of Problem 3.2 Searching for One of the Four
224(2)
Solution of Problem 3.3 Rotating Solids
226(3)
Solution of Problem 3.4 Finding the False Object
229(2)
Solution of Problem 3.5 Searching for the Wrong Solid
231(3)
Solution of Problem 3.6 Playing Quartet
234(4)
Solution of Problem 3.7 Rotating Objects, Which are Built of Rods and Cubes
238(5)
Solution of Problem 3.8 Labeling of Vertices
243(5)
Solution of Problem 3.9 Rotating an Object Around Axes
248(2)
Solution of Problem 3.10 Rotating Another Object Around Axes
250(2)
Solution of Problem 3.11 Playing with Colorful Cubes
252(3)
Solution of Problem 3.12 Following the Red Flag
255(2)
Chapter 8 Solutions and Hints of the Problems Addressing Spatial Orientation
257(36)
Solution of Problem 4.1 Switching Between Various Town Maps
258(3)
Solution of Problem 4.2 Solving the Tube in Cube Problem
261(8)
Solution of Problem 4.3 Flying with a Helicopter
269(3)
Solution of Problem 4.4 Taking Pictures of a Village
272(4)
Solution of Problem 4.5 Helping the Photographer
276(3)
Solution of Problem 4.6 Walking Around a Platonic World
279(3)
Solution of Problem 4.7 Parking a Car
282(4)
Solution of Problem 4.8 Searching for My Car
286(1)
Solution of Problem 4.9 Standing on a Parking Area
287(3)
Solution of Problem 4.10 Watching a Carousel of Basic Solids
290(1)
Solution of Problem 4.11 Riding with a Cylindrical Platform
291(2)
Section III Folding Templates to be Cut Out
293(50)
Chapter 9 Folding Templates of Problems Addressing Visualization
299(34)
Folding Template of Problem 1.1 Manipulating Black and White Cubes
300(1)
Folding Templates of Problem 1.3 Identifying the Opposite Sides of a Cube
301(6)
Folding Template of Problem 1.9 Rotating of a Cube
307(4)
Folding Templates of Problem 1.10 Rotating of a Rectangular Cuboid
311(4)
Folding Templates of Problem 1.11 Producing Cubic Stamps
315(5)
Folding Templates of Problem 1.12 Completing Cubic Nets
320(7)
Folding Templates of Problem 1.13 Rotating of a Die
327(3)
Folding Templates of Problem 1.14 Completing Cube Tests
330(3)
Chapter 10 Folding Templates of a Problem Addressing Spatial Relations
333(4)
Folding Template of Problem 2.1 Measuring Stacks of Cubes
334(3)
Chapter 11 Folding Templates of a Problem Addressing Spatial Orientation
337(6)
Folding Template of Problem 4.1 Switching Between Different Town Maps
338(5)
Appendix A How to Get the Interactive 3D Model on an iOS Device 343(4)
Appendix B How to Get the Interactive 3D Model on a Windows Device 347(2)
Appendix C How to Get the Interactive 3D Model on an Android Device 349(4)
References 353
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