# Mathematical Reasoning for Elementary Teachers, Global Edition

## Námskeið

- STÆ0156 Stærðfræðikennsla.

## Ensk lýsing:

Long/DeTemple/Millman’s Mathematical Reasoning for Elementary Teachers presents the mathematical content needed for teaching within the context of the elementary classroom, giving future teachers the motivation they need while also showing them the bigger picture of when they will use and teach the concepts. The program also endeavors to answer the frequently-asked “Why are we learning this?” by going beyond skill explanations and showing the ways that these concepts are implemented in the future classroom and what types of questions children may ask.

Now updated to include the Common Core State Standards for Mathematics, the text imparts mathematical reasoning skills, a deep conceptual understanding, and a positive attitude to those who aspire to be elementary or middle school teachers. Teaching and Learning Experience This program will provide a better teaching and learning experience—for you and your students. Here’s how: Personalized learning with MyMathLab: MyMathLab delivers proven results in helping students succeed and provides engaging experiences that personalize learning.

## Lýsing:

Mathematical Reasoning for Elementary Teachers presents the mathematical content needed for teaching within the context of the elementary classroom, giving future teachers the motivation they need while also showing them the bigger picture of when they will use and teach the concepts. The program also endeavours to answer the frequently-asked “Why are we learning this?” by going beyond skill explanations and showing the ways that these concepts are implemented in the future classroom and what types of questions children may ask.

Now updated to include the Common Core State Standards for Mathematics, the text imparts mathematical reasoning skills, a deep conceptual understanding, and a positive attitude to those who aspire to be elementary or middle school teachers. The full text downloaded to your computer With eBooks you can: search for key concepts, words and phrases make highlights and notes as you study share your notes with friends eBooks are downloaded to your computer and accessible either offline through the Bookshelf (available as a free download), available online and also via the iPad and Android apps.

## Annað

- Höfundar: Calvin T. Long, Duane W. DeTemple, Richard S. Millman
- Útgáfa:7
- Útgáfudagur: 2015-03-05
- Blaðsíður: 872
- Hægt að prenta út 2 bls.
- Hægt að afrita 2 bls.
- Format:Page Fidelity
- ISBN 13: 9781292070155
- Print ISBN: 9781292062365
- ISBN 10: 1292070153

## Efnisyfirlit

- Title
- Copyright
- Contents
- Preface
- 1 Thinking Critically
- 1.1 An Introduction to Problem Solving
- 1.2 Pólya’s Problem-Solving Principles and the Standards for Mathematical Practice of the Common
- Guess and Check
- Make an Orderly List
- Draw a Diagram
- Pólya’s Problem-Solving Principles and the Standards for Mathematical Practice of the Common Core

- 1.3 More Problem-Solving Strategies
- Look for a Pattern
- Make a Table
- Use a Variable
- Consider Special Cases
- Pascal’s Triangle

- 1.4 Algebra as a Problem-Solving Strategy
- Use a Variable
- Use Two Variables

- 1.5 Additional Problem-Solving Strategies
- Working Backward
- Eliminate Possibilities
- The Pigeonhole Principle

- 1.6 Reasoning Mathematically
- Inductive Reasoning
- Representational Reasoning
- Mathematical Statements
- Deductive Reasoning

- Chapter 1 Summary
- Chapter 1 Review Exercises

- 2 Sets and Whole Numbers
- 2.1 Sets and Operations on Sets
- Venn Diagrams
- Relationships and Operations on Sets
- Using Sets for Problem Solving

- 2.2 Sets, Counting, and the Whole Numbers
- One-to-One Correspondence and Equivalent Sets
- The Whole Numbers
- Representingthe Whole Numbers Pictorially and with Manipulatives
- Ordering the Whole Numbers
- Problem Solving with Whole Numbers and Venn Diagrams

- 2.3 Addition and Subtraction of Whole Numbers
- The Set Model of Whole-Number Addition
- The Measurement (Number-Line) Model of Addition
- Properties of Whole-Number Addition
- Subtraction of Whole Numbers
- Take-Away Model
- Missing-Addend Model
- Comparison Model
- Number-Line Model

- 2.4 Multiplication and Division of Whole Numbers
- Multiplication of Whole Numbers
- Multiplication as Repeated Addition
- The Array Model for Multiplication
- The Rectangular Area Model for Multiplication
- The Skip-CountModel for Multiplication
- The Multiplication Tree Model
- The Cartesian Product Model of Multiplication
- Properties of Whole-Number Multiplication
- Division of Whole Numbers
- The Repeated-Subtraction Model of Division
- The Partition Model of Division
- The Missing-Factor Model of Division
- Division by Zero Is Undefined
- Division with Remainders
- Why Does Quotient with Remainder (the Division Algorithm) Work?
- Exponents and the Power Operation

- Chapter 2 Summary
- Chapter 2 Review Exercises

- 2.1 Sets and Operations on Sets
- 3 Numeration and Computation
- 3.1 Numeration Systems Past and Present
- The Egyptian System
- The Roman System
- The Babylonian System
- The Mayan System
- The Indo-Arabic System
- Physical Models for Positional Systems

- 3.2 Algorithms for Addition and Subtraction of Whole Numbers
- The Addition Algorithm
- The Subtraction Algorithm

- 3.3 Algorithms for Multiplication and Division of Whole Numbers
- Multiplication Algorithms
- Division Algorithms

- 3.4 Mental Arithmetic and Estimation
- The One-Digit Facts
- Easy Combinations
- Adjustment
- Working from Left to Right
- Estimation
- Front-End Method
- Rounding
- Approximating by Rounding

- 3.5 Nondecimal Positional Systems
- Base-Five and Base-Six Place Value Including Conversion to the Decimal System and Operations
- Addition, Subtraction, and Multiplication in Base Six

- Chapter 3 Summary
- Chapter 3 Review Exercises

- 3.1 Numeration Systems Past and Present
- 4 Number Theory
- 4.1 Divisibility of Natural Numbers
- Divides, Divisors, Factors, Multiples
- Prime and Composite Numbers
- The Divisors of a Natural Number
- Two Questions about Primes
- There Are Infinitely Many Primes
- Determining Whether a Given Natural Number Is Prime

- 4.2 Tests for Divisibility
- Divisibility of Sums and Differences
- Divisibility by 2, 5, and 10
- Divisibilityby 4, 8, and Other Powers of 2
- Divisibility by 3 and 9
- Combining Divisibility Tests
- Summary of Useful Divisibility Tests
- Applications of Divisibility
- Illustrating Factors and Divisibility with a Manipulative

- 4.3 Greatest Common Divisors and Least Common Multiples
- GCD Method 1: Greatest Common Divisors by Intersection of Sets
- GCD Method 2:Greatest Common Divisor from Prime Factorizations
- GCD Method 3: Greatest Common Divisor from the Euclidean Algorithm
- An Application of the Greatest Common Factor
- The Least Common Multiple
- LCM Method 1: Least Common Multiples by Intersection of Sets
- LCM Method 2: Least Common Multiples from Prime Factorizations
- LCM Method 3:Least Common Multiples by Using the Euclidean Algorithm
- An Application of the LCM

- Chapter 4 Summary
- Chapter 4 Review Exercises

- 4.1 Divisibility of Natural Numbers
- 5 Integers
- 5.1 Representations of Integers
- Absolute Value of an Integer
- Criteria for the Representation of the Integers
- Representing Integers with Colored Counters
- The Addition-by-0 Property with Colored Counters
- Taking Opposites with Colored Counters
- Mail-Time Representations of Integers
- Number-Line Representations of Integers

- 5.2 Addition and Subtraction of Integers
- Addition of Integers
- Addition of Integers by Using Sets of Colored Counters
- Addition of Integers by Using Mail-Time Stories
- Addition of Integers by Usinga Number Line
- Subtraction of Integers
- Subtraction of Integers with Colored Counters
- The Equivalence of Subtraction with Addition of the Opposite
- Subtraction of Integers by Using Mail-Time Stories
- Subtraction of Integers by Using the Number Line
- Ordering the Set of Integers

- 5.3 Multiplication and Division of Integers
- Multiplication of Integers
- Multiplication of Integers by Using Loops of Colored Counters
- Multiplication of Integers by Using Mail-Time Stories
- Multiplicationof Integers by Using a Number Line
- Division of Integers
- Multiplication and Division with Colored-Counter Arrays

- Chapter 5 Summary
- Chapter 5 Review Exercises

- 5.1 Representations of Integers
- 6 Fractions and Rational Numbers
- 6.1 The Basic Concepts of Fractions and Rational Numbers
- Fraction Models
- Equivalent Fractions
- Fractions in Simplest Form
- Common Denominators
- Rational Numbers
- Ordering Fractions and Rational Numbers

- 6.2 Addition and Subtraction of Fractions
- Addition of Fractions
- Proper Fractions and Mixed Numbers
- Subtraction of Fractions

- 6.3 Multiplication and Division of Fractions
- Multiplication of a Fraction by an Integer
- Multiplication of an Integer by a Fraction
- Multiplication of a Fraction by a Fraction
- Division of Fractions
- Algorithms for Calculating the Division of Fractions
- Reciprocals as Multiplicative Inverses in the Rational Numbers

- 6.4 The Rational Number System
- Properties of Addition and Subtraction
- Properties of Multiplication and Division
- Properties of the Order Relation
- The Density Property of Rational Numbers
- Computations with Rational Numbers
- Estimations
- Mental Arithmetic

- Chapter 6 Summary
- Chapter 6 Review Exercises

- 6.1 The Basic Concepts of Fractions and Rational Numbers
- 7 Decimals, Real Numbers, and Proportional Reasoning
- 7.1 Decimals and Real Numbers
- Representations of Decimals
- Multiplying and Dividing Decimals by Powers of 10
- Terminating Decimals as Fractions
- Repeating Decimals and Rational Numbers
- The Set of Real Numbers
- Real Numbers and the Number Line

- 7.2 Computations with Decimals
- Rounding Decimals
- Adding and Subtracting Decimals
- Ordering Decimals and the Real Numbers
- Multiplying Decimals
- Dividing Decimals

- 7.3 Proportional Reasoning
- Ratio
- Proportion
- Applications of Proportional Reasoning

- 7.4 Percent
- Percent
- Solving the Three Basic Types of Percent Problems
- Percentage Increase and Decrease
- Compound Interest
- The Mathematics of Growth

- Chapter 7 Summary
- Chapter 7 Review Exercises

- 7.1 Decimals and Real Numbers
- 8 Algebraic Reasoning, Graphing, and Connections with Geometry
- 8.1 Variables, Algebraic Expressions, and Functions
- Variables
- Algebraic Expressions
- Solving Equations
- Defining and Visualizing Functions
- Describing and Visualizing Functions

- 8.2 Graphing Points, Lines, and Elementary Functions
- The Cartesian Coordinate Plane
- The Distance Formula
- Slope
- Equations of Lines
- Nonlinear Functions

- 8.3 Connections between Algebra and Geometry
- Parallel and Perpendicular Lines
- Circles

- Chapter 8 Summary
- Chapter 8 Review Exercises

- 8.1 Variables, Algebraic Expressions, and Functions
- 9 Geometric Figures
- 9.1 Figures in the Plane
- Points and Lines
- Line Segments and the Distance between Points
- Rays, Angles,and Angle Measure
- Pairs of Angles and the Corresponding-Angles Theorem
- The Measure of Angles in Triangles
- Directed Angles

- 9.2 Curves and Polygons in the Plane
- Curves and Regions
- Convex Curves and Figures
- Polygonal Curves and Polygons
- Triangles
- Quadrilaterals
- Regular Polygons

- 9.3 Figures in Space
- Planes and Lines in Space
- Curves, Surfaces, and Solids
- Polyhedra
- Regular Polyhedra
- Euler’s Formula for Polyhedra
- Cones and Cylinders

- Chapter 9 Summary
- Chapter 9 Review Exercises

- 9.1 Figures in the Plane
- 10 Measurement: Length, Area, and Volume
- 10.1 The Measurement Process
- The U.S. Customary, or “English,” System of Measures
- Metric Units: The International System
- Length
- Area
- Volume and Capacity
- Weight and Mass
- Temperature
- Unit Analysis

- 10.2 Area and Perimeter
- Measurements in Nonstandard Units
- The Congruence and Addition Properties of Area
- Areas of Polygons: A Conceptual Understanding
- Length of a Curve
- The Area of a Circle

- 10.3 The Pythagorean Theorem
- Proving the Pythagorean Theorem
- Applications of the Pythagorean Theorem
- The Converse of the Pythagorean Theorem

- 10.4 Volume
- Volumes of Right Prisms and Right Cylinders
- Volumes of Oblique Prisms and Cylinders
- Volumes of Pyramids and Cones
- Volume of a Sphere

- 10.5 Surface Area
- Surface Area of Right Prisms and Cylinders
- Surface Area of Pyramids
- Surface Area of Right Circular Cones
- The Surface Area of a Sphere
- Comparing Measurements of Similar Figures

- Chapter 10 Summary
- Chapter 10 Review Exercises

- 10.1 The Measurement Process
- 11 Transformations, Symmetries, and Tilings
- 11.1 Rigid Motions and Similarity Transformations
- The Four Basic Rigid Motions
- Translations
- Rotations
- Reflections
- Glide–Reflections
- The Net Outcome of Two Successive Reflections
- The Net Outcome of Three Successive Reflections
- Classification of General Rigid Motions
- Dilations and Similarity Motions

- 11.2 Patterns and Symmetries
- What Is Symmetry?
- Reflection Symmetry
- Rotation Symmetry
- Point Symmetry
- Periodic Patterns: Figures with Translation Symmetries
- Border Patterns and Their Classification
- Wallpaper Patterns

- 11.3 Tilings and Escher-like Designs
- Tiles and Tilings
- Regular Tilings of the Plane
- Semiregular Tilings of the Plane
- Tilings with Irregular Polygons
- Escher-like Designs

- Chapter 11 Summary
- Chapter 11 Review Exercises

- 11.1 Rigid Motions and Similarity Transformations
- 12 Congruence, Constructions, and Similarity
- 12.1 Congruent Triangles
- Congruent Line Segments and Their Construction
- Corresponding Parts and the Congruence of Triangles
- The Side–Side–Side (SSS) Property
- The Triangle Inequality
- The Side–Angle–Side (SAS) Property
- The Angle–Side–Angle (ASA) Property
- The Angle–Angle–Side (AAS) Property
- Are There SSA and AAA Congruence Properties?

- 12.2 Constructing Geometric Figures
- Constructing Parallel and Perpendicular Lines
- Constructing the Midpoint and Perpendicular Bisector of a Line Segment
- Constructing the Angle Bisector
- Constructing Regular Polygons
- Mira™ and Paper-Folding Constructions
- Constructions with Geometry Software

- 12.3 Similar Triangles
- The Angle–Angle–Angle (AAA) and Angle–Angle (AA) Similarity Properties
- The Side–Side–Side (SSS) Similarity Property
- The Side–Angle–Side (SAS) Similarity Property
- Geometric Problem Solving with Similar Triangles

- Chapter 12 Summary
- Chapter 12 Review Exercises

- 12.1 Congruent Triangles
- 13 Statistics: The Interpretation of Data
- 13.1 Organizing and Representing Data
- Dot Plots
- Stem-and-Leaf Plots
- Histograms
- Line Graphs
- Bar Graphs
- Pie Charts
- Pictographs
- Choosing Good Visualizations

- 13.2 Measuring the Center and Variation of Data
- Measures of Central Tendency
- The Mean
- The Median
- The Mode
- Measures of Variability
- Box Plots
- The Standard Deviation

- 13.3 Statistical Inference
- Populations and Samples
- Population Means and Standard Deviations
- Estimating Population Means and Standard Deviations
- Distributions
- z Scores and Percentiles

- Chapter 13 Summary
- Chapter 13 Review Exercises

- 13.1 Organizing and Representing Data
- 14 Probability
- 14.1 The Basics of Probability
- The Sample Space, Events, and Probability Functions
- Experimental Probability
- Theoretical Probability
- Mutually Exclusive Events
- Complementary Events

- 14.2 Applications of Counting Principles to Probability
- The Addition Principle of Counting
- Factorials and Rearrangements of Ordered Lists
- The Multiplication Principle of Counting
- Probability Trees
- Conditional Probability
- Independent Events

- 14.3 Permutations and Combinations
- Formulas for the Number of r-Permutations
- Formulas for the Number of r-Combinations
- Solving Problems with Permutations and Combinations

- 14.4 Odds, Expected Values, Geometric Probability, and Simulations
- Odds
- Expected Value
- Geometric Probability
- Simulation

- Chapter 14 Summary
- Chapter 14 Review Exercises

- 14.1 The Basics of Probability
- Answers to Odd-Numbered Problems
- Mathematical Lexicon
- Credits
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- X
- Y
- Z

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