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# Mathematics for Elementary School Teachers

**by**Bassarear, Tom

5th

### 9780840054630

0840054637

Paperback

1/1/2011

Brooks Cole

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## Related Products

## Summary

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 | |

Summary | |

Review Exercises | |

Fundamental Concepts | |

Sets | |

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 | |

Baby-sitting | |

Choosing Between Functions | |

Matching Graphs to Situations | |

Developing "Graph Sense." | |

Looking for Generalizations | |

How Many Dots? | |

Numeration | |

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 | |

Summary | |

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 | |

Summary | |

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 | |

Summary | |

Review Exercises | |

Extending The Number System | |

Integers | |

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 | |

Unitizing | |

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 | |

Summary | |

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? | |

Percents | |

Who's the Better Free-Throw Shooter? | |

Understanding a Newspaper Article | |

Buying a House | |

Sale? | |

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 | |

Summary | |

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 | |

Gumballs | |

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 | |

Summary | |

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 | |

Challenges | |

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 | |

Nets | |

Looking Back on Chapter 8 | |

Summary | |

Review Exercises | |

Geometry As Transforming Shapes | |

Congruence Transformations | |

Table of Contents provided by Publisher. All Rights Reserved. |