Mathematics for Elementary School Teachers

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  • Edition: 5th
  • Format: Paperback
  • Copyright: 1/1/2011
  • Publisher: Brooks Cole
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Intended for the one- or two-semester course required of Education majors, MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS, 5E, offers future teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect content to the hands-on activities in the corresponding Explorations Manual. Bassarear presents real-world problems, problems that require active learning in a method similar to how archaeologists explore an archaeological find: they carefully uncover the site, slowly revealing more and more of the structure. The author demonstrates that there are many paths to solving a problem, and that sometimes, problems have more than one solution. With this exposure, future teachers will be better able to assess student needs using diverse approaches.

Table of Contents

Foundations For Learning Mathematics
Getting Started and Problem Solving
Pigs and Chickens
A Coin Problem
Patterns and Communication
Sequences and Patterns
Patterns in Multiplying by 11
Pascal's Triangle
Communicating Patterns in a Magic Square
Reasoning and Proof
Does Your Answer Make Sense?
Inductive Thinking With Fractions
Deductive Reasoning and Venn Diagrams
Why is the Sum of Two Even Numbers an Even Number
Darts, Proof, and Communication
The Nine Dots Problem
How Many Games in the Tournament?
Representation and Connections
How Long Will it Take the Frog to Get Out of the Well?
How Many Pieces of Wire?
Looking Back on Chapter 1
Review Exercises
Fundamental Concepts
Classifying Quadrilaterals
Describing Sets
How Many Subsets?
Translating Among Representations
Finding Information from Venn Diagrams
Algebraic Thinking
A Variable by Any Other Name is Still a Variable
Choosing Between Functions
Matching Graphs to Situations
Developing "Graph Sense."
Looking for Generalizations
How Many Dots?
Relative Magnitude of Numbers
What if Our System was Based on One Hand?
How Well do you Understand Base Five?
Base Sixteen
Looking Back on Chapter 2
Review Exercises
The Four Fundamental Operations Of Arithmetic
Understanding Addition
Pattern in the Addition Table
Mental Addition
Children's Strategirs for Adding Large Numbers
An Alternative Algorithm
Addition in Base Five
Children's Mistakes
What Was the Total Attendance?
Estimating by Making Compatible Numbers
Number Sense with Addition
Understanding Subtraction
Mental Subtraction
Children's Strategies for Subtraction with Large Numbers
An Alternative Algorithm
Children's Mistakes in Subtraction
Rough and Best Estimations with Subtraction
Number Sense with Subtraction
Understanding Multiplication
A Pattern in the Multiplication Table
Mental Multiplication
An Alternative Algorithm
Why Does the Trick for Multiplying by 11 Work?
Multiplication in Base Five
Children's Mistakes in Multiplication
Developing Estimation Strategies for Multiplication
Using Various Strategies in a Real-life Multiplication Situation
Number Sense with Multiplication
Understanding Division
Mental Division
Understanding Division Algorithms
The Scaffolding Algorithm
Children's Mistakes in Division
Estimates with Division
Number Sense with Division
Applying Models to a Real-life Situation
Operation Sense
Looking Back on Chapter 3
Review Exercises
Number Theory
Divisibility and Related Concepts
Interesting Dates
Patterns in Odd and Even Numbers
Understanding Divisibility Relationships
Determining the Truth of an Inverse Statement
Understanding Why the Divisibility Rule for 3 Works
Divisibility by 4 and 8
Creating a Divisibility Rule for 12
Prime and Composite Numbers
The Sieve of Eratosthenes
Numbers with Personalities: Perfect and Other Numbers
Greatest Common Factor and Least Common Multiple
Cutting Squares Using Number Theory Concepts
Methods for Finding the GCF
Relationships Between the GCF and the LCM
Going Deeper into the GCF and LCM
Looking Back on Chapter 4
Review Exercises
Extending The Number System
Subtraction with Integers
The Product of a Positive and a Negative Number
Fractions and Rational Numbers
Rational Number Contexts: What Does 3/4 Mean?
Wholes and Units: Sharing Brownies
Fund-Raising and Thermometers
Partitioning with Number Line Models
Partitioning with Area Models
Partitioning with Discrete Models
Determining an Appropriate Representation
Sharing Cooking
Ordering Rational Numbers
Estimating with Fractions
Understanding Operations with Fractions
Using Fraction Models to Understand Addition of Fractions
Connecting Improper Fractions and Mixed Numbers
Estimation and Mental Arithmetic: Sums and Differences of Fractions
Estimating sums and Differences with Fractions
Understanding Multiplication of Rational Numbers
Division of Rational Numbers
Estimating Products and Quotients
When Did He Run Out of Gas?
They've Lost Their Faculty!
Beyond Integers and Fractions: Decimals, Exponents, and Real Numbers
Base 10 Blocks and Decimals
When Two Decimals Are Equal
When is the Zero Necessary and When is it Optional?
Connecting Decimals and Fractions
Ordering Decimals
Rounding with Decimals
Decimals and Language
Decimal Sense: Grocery Store Estimates
Decimal Sense: How Much Will the Project Cost?
How Long Will She Run?
Exponents and Bacteria
Scientific Notation: How Far is a Light-Year?
Square Roots
Looking Back on Chapter 5
Review Exercises
Proportional Reasoning
Ratio and Proportion
Unit Pricing--Is Bigger Always Cheaper?
How Many Trees Will be Saved?
How Much Money Will the Trip Cost?
Reinterpreting Old Problems
Using Estimation with Ratios
Comparing Rates
Is the School on Target?
Finding Information from Maps
From Raw Numbers to Rates
How Much Does That Extra Light Cost?
Who's the Better Free-Throw Shooter?
Understanding a Newspaper Article
Buying a House
What is a Fair Reason?
How Much Money Did the Bookstore Pay for the Textbook?
The Copying Machine
132% Increase
Saving for College
How Much Does that Credit Card Cost You?
Looking Back on Chapter 6
Review Exercises
Uncertainty: Data And Chance
The Process of Collecting and Analyzing Data
What is Your Favorite Sport?
How Many Siblings do you Have?
Going Beyond a Computational Sense of Average
How Many Peanuts Can You Hold in One Hand?
How Long Does it Take Students to Finish the Final Exam?
Videocassette Recorders
Fatal Crashes
Hitting the Books
Going Beyond the Basics
How Many More Peanuts Can Adults Hold Than Children?
Scores on a TeSt
Which Battery do You Buy?
Understanding Standard Deviation
Analyzing Standardized Test Scores
How Long Should the Tire be Guaranteed?
Comparing Students in Three Countries
Grade Point Average
What Does Amy Need to Bring Her GPA up to 2.5?
Concepts Related to Chance
Probability of Having 2 Boys and 2 Girls
Probability of Having 3 Boys and 2 Girls
Probability of Having at Least 1 Girl
50-50 Chance of Passing
What is the Probability of Rolling a 7?
What is the Probability of Rolling a 13 with 3 Dice?
"The Lady of the Tiger
Is this a Fair Game?
What about this Game?
Insurance Rates
Counting and Chance
How Many Ways to Take the Picture?
How Many Different Election Outcomes?
How Many Outcomes this Time?
Pick a Card, Any Card!
So You Think You're Going to Win the Lottery?
Looking Back on Chapter 7
Review Exercises
Geometry As Shape
Basic Ideas and Building Blocks
Playing Tetris
Different Objects and Their Functions
Point, Line, and Plane
Measuring Angles
Two-Dimensional Figures
Recreating Shapes from Memory
All the Attributes
Classifying Figures
Investigations 8.2d Why Triangles are so Important
Classifying Triangles
Triangles and Venn Diagrams
Congruence with Triangles
Quadrilaterals and Attributes
Relationships Among Quadrilaterals
Sum of Interior Angles of a Polygon
What are my Coordinates?
Understanding the Distance Formula
The Opposite Sides of a Parallelogram are Congruent
Midpoints of any Quadrilateral
Three-Dimensional Figures
What do you See?
Connecting Polygons to Polyhedra
Features of Three-Dimensional Objects
Prisms and Pyramids
Different Views of a Building
Isometric Drawings
Cross Sections
Looking Back on Chapter 8
Review Exercises
Geometry As Transforming Shapes
Congruence Transformations
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