Spatial Sense Makes Math Sense - Draper, Catheryne

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Résumé :

ForewordPrefaceAcknowledgementsIntroductionPart I. Definition 1. A Perspective on Spatial Sense
Permission to Move Freely
Compositions and Decompositions of Shapes
Symmetry Is Spatial, Not One-Half
Keep in Mind
2. The Vocabulary Clues Are in the Words
Prefix Power for Polygons and Polyhedra
Vocabulary Ancestry
Keep in Mind
3. Sorting and Classifying the Symbols of Space
Arrangement-Driven Vocabulary
Measurement-Driven Vocabulary
Mixing the Arrangements and Measurements for Names
Keep in Mind
Part II. Organization 4. Ribbons, Rolls, and Rulers for the First Dimension
Transitioning from Zero Dimension to One Dimension
The Rolls of Circumferences and Perimeters
Diagonals, Diameters, Radii (Radians), and More Straight PiecesHeights, Altitudes, Apothems, and Legs
Keep in Mind
5. Angle Swings and Area Squares in Flatland
Angles Are at the Entry Gate to Flatland
Areas as Spatial Arrangements
Permission to Surround and Rearrange Shapes to Find Areas
Keep in Mind
6. Stack and Pour to Fill Volume in Spaceland
Polyhedra Nets Make Three Dimensions From Two Dimensions
Surface Areas, Polyhedra Nets, and Orange Peels
Fill 'er Up for Volume
Keep in Mind
Part III. Relationships and Patterns7. Similarity and CongruenceSimilarity Allows Stretching and ShrinkingCongruence, Transformations, and TessellationsSymmetry as a Matter of Congruence
Keep in Mind
8. Special Spatial, Yet Irrational, Patterns
Pi , ?, and 3.141592654. - From Archimedes to Supercomputers Phi , f, and 1.618. - Beauty in the Golden RatioThe Limit of e and2.71826. - A Curious Number with Curious CousinsEccentricitye - A Circle Decider Keep in Mind
9. Shape Changes and Patterns
Same Perimeters, Same Areas, Different Polygons
Similar Shapes and Side Changes Predict Areas and Perimeters
Dots, Vertices, Spaces, and Faces
Keep in Mind
Part IV. Connections10. The Influential Right Triangle
Shadows, Right Triangles, and Proportions
The Pythagorean Theorem: A Relationship of Sides
Trigonometry: A Relationship Between Sides and Angles
Keep in Mind
11. A Circle's NobilityAngles and Triangles Under Circle ControlCircle Relationships and Algebra TransformationsReturn of the Apothems for Polygon Areas
Diameters, Diagonals, and Ratios Revisited
Keep in Mind
12. From Figures to Scale Models, Then on to Calculus Connections
Shapes As Figured Numbers and Algebra
Written Geometry Through Keeping Records
Triangulation, Scale Models, and Similar Triangles
A Gentle Connection to Calculus
Keep in Mind
Conclusion: What Parents Can Do
The Best Strategy is a Team Strategy
A Visual-Spatial Parent and Child Story
Support Your Child's Strengths
Four Possible Math Profiles to Consider
Keep in Mind
Glossary
References
About the Author