Teaching Mathematics Using Interactive Mapping

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Introduction
Authors
Acknowledgments
Chapter 1 Classifying Numbers and the Distributive Law
	Chapter Outline
	Classification
		Conceptual View
		Intuitive View: Interactive Mapping Activity
	Classifying Numbers
		Natural Numbers
		Whole Numbers
		Integers
		Rational Numbers
		Irrational Numbers
		Real Numbers
		Nested Hierarchy
		Infinity
		The Number Line: Extent and Direction
		Different Classes of Numbers Positioned on the Number Line
		Absolute Value
		Prime Numbers
		Using Numbers with Maps to Analyze Demographics
	Operations
		Law of Excluded Middle
		Operations with Numbers
		Operations with Maps
	Order
		Order of Mathematical Operations
		Order of Mapping Operations
		Legend: Layers and Organization
	The Distributive Law
		Terms and Factors
		Parentheses and the Distributive Law
	Geography and Thinking Spatially in Everyday Life: Enlarging Your World!
Chapter 2 Fractions and Decimals
	Chapter Outline
	Fractions
		Adding and Subtracting Fractions with Like Denominators
		Multiplying Fractions
		The Importance of Multiplying by 1
		Adding and Subtracting Fractions with Different Denominators
		The Importance of Cancellation
		Divisibility of Numbers
		Divisibility, Prime Numbers, and Unique Factorization
		Dividing Fractions
		Fractions Larger Than One
		Fractions, Decimals, and Maps
		Arithmetic with Fractions: Rapid Mental Calculation
	Exponents and Logarithms
		Exponents
		Logarithms
	Decimals
		Convert Fractions to Decimals
		Convert Decimals to Fractions
		Adding and Subtracting Decimals
		Multiplying Decimals
		Dividing Decimals
		Rounding and Estimating
	Bases Other Than 10
		Binary
		Octal
		Hexadecimal
		Operations
	Time and Circular Measurement
		Metric
		English
		Time
		Circular Measurement
	Measuring Distances in Latitude Longitude Degrees
	Time and Longitude: Circling Back
	Looking Ahead
Chapter 3 Simple Relational Measures and Measures of Central Tendency and Variation
	Chapter Outline
	Simple Relational Measures
		Ratio
		Proportion
		Percent
		Estimation and Rounding
		Problems—Remember, "Percent" Means "per 100"
		Associated Interactive Mapping Activity: Mapping Urban Litter Proportions
	Math Word/Story Problems
		General Strategy
		Worked Problems
		Distance, Rate, Time Interactive Mapping Activity
		Deeper Thought Problem: Hope Village for Children
	Measures of Central Tendency
		Mean and Related Measures
		Median
		Mode
		Problem
		Associated Interactive Mapping Activities
	Variation
		Histogram
		Scatter Diagram
		Correlation
		Simple Linear Regression
		Associated Interactive Mapping Activity: The Histogram as a Mapping Tool
	Goodness of Fit and Statistical Significance
		Coefficient of Determination
		z-Score
		Statistical Significance
		p-Value
		Associated Interactive Mapping Activities
	Integrating Elements of this Chapter
		Fibonacci Numbers and the Golden Ratio
		Percentages, Estimation, and Rounding in the World of Sculpture
Chapter 4 Earth Measurement: Coordinate Systems and Trigonometry
	Chapter Outline
	Coordinate Systems in Common Use
		Cartesian Coordinates
		Earth Model: Sphere and Plane
		Earth Model Coordinates: Parallels and Meridians
		Earth Model Coordinates: Latitude and Longitude
		Geocoding
		Ordinal and Cardinal Directions
	Other Coordinate Systems
		Universal Transverse Mercator
		Polar Coordinates
	Trigonometry: Visual Review of Functions and Applications
		Visual Review of Trigonometric Functions
		Applications: Conceptual and Real Worlds
	Scale
		Map Scale
		Activity: Studying Map Scale with USGS Topographic Maps
		Global and Local Scale
		Activity: Determining Map Scale
		Activity: Comparing Sizes of Countries
		Map Projection
		Tissot Indicatrix
		Scale and Measurement on Mars
	Questions to Think About
Chapter 5 Data, Variables, and Thematic Maps
	Chapter Outline
	Data
		Data Scale
		Data Types
	Attributes
		Nominal Attribute
		Ordinal Attribute
		Interval Attribute
		Ratio Attribute
	Generalization
		Selection/Filtering
		Classification
		Simplification
		Symbolization
	Surveys
		Nominal Scale Survey Questions
		Ordinal Scale Survey Questions
		Interval Scale Survey Questions
		Ratio Scale Survey Questions
	Thematic Maps
		Reference Information
		Standardization of Data
		Uncertainty
	Single Variable Mapping and Data Types: Choropleth Maps
		Nominal Data Type
		Ordinal Data Types
		Interval Data Type
		Ratio Data Type
		World Earthquakes
	Exploring Data Using Bivariate Maps, Symbology and Classification
		Heat Map
		Relationship Map
	To Think About
Chapter 6 Mathematics' Foundations: Set Theory and Algebra
	Chapter Outline
	Existence and Foundational Mathematics
		Law of Excluded Middle
		The Axiom of Infinity
		The Axiom of Choice
	Set Theory
		Set Fundamentals
		Subsets
		The Empty Set and the Universal Set
		Basic Set Operations
		Venn Diagrams
		Set Theory in Hazards Analysis
	Algebra
		Fundamental Proofs
		Simple Linear Equations and Graphs; Inequalities
		A Unifying Map
		Simple Quadratic Equations and Graphs; Inequalities
	Real-World Shapes and Challenges
Chapter 7 Mathematics' Foundations: Dimension and Geometry
	Chapter Outline
	Synthetic Geometry
		Euclid: Selections
		Axioms for Euclidean Geometry in the Plane
		Selected Concepts and Theorems
		Solid Geometry
		Whole-Earth Measurements
	Transforming Dimensions: Approximations
		Area under a Curve: Approximation Techniques
		Representing Numbers as Isolines
	Dimension
		Overview
		Beyond the Usual—Fractional Dimension
		Testing the Coastline Paradox: Fractals
	Non-Euclidean Geometry
	Error Issues
		Digitizing
		Jordan Curve Theorem
	Geometric Models of the Real World?
Chapter 8 Proximity and Adjacency: Measurement
	Chapter Outline
	Overview
		Graph Theory
		Topology
	Measuring Proximity
		Graph Theory: Tracing a Walk Through Königsberg
		Proximity: Tracing Downstream
		Topology: One-Point Compactification of the Line
		Proximity Zones and Wildfire
	Measuring Adjacency
		Graph Theory: Coloring and Adjacency
		Topology
		Terrestrial Surface and Green Infrastructure
		Map Projection
Chapter 9 Measuring Hierarchies and Patterns
	Chapter Outline
	Overview
	The Dot Density Map
		Interactive View
		Conceptual Principles
		Nested and Non-Nested Hierarchies
	Non-Nested Hierarchy: The Cartogram
		Non-Contiguous Cartograms
		Contiguous Cartograms
	Hierarchical Organization Chart for this Book
References and Further Reading Suggestions
Postscript
Index