Algebra Connections

ISBN-10: 0131449281
ISBN-13: 9780131449282
Edition: 2007
List price: $117.80 Buy it from $35.36 Rent it from $27.26
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Description: For one-semester undergraduate courses in algebra for the middle grades. Strong mathematics performance in the middle grades is more important than ever-and teachers entering the field need to prepare for this endeavor in new and innovative ways.  More...

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Book details

List price: $117.80
Copyright year: 2007
Publisher: Prentice Hall PTR
Publication date: 12/2/2005
Binding: Paperback
Pages: 368
Size: 7.05" wide x 9.21" long x 0.67" tall
Weight: 2.750
Language: English

For one-semester undergraduate courses in algebra for the middle grades. Strong mathematics performance in the middle grades is more important than ever-and teachers entering the field need to prepare for this endeavor in new and innovative ways. This new approach introduces some basic concepts of number theory and modern algebra that underlie middle grade arithmetic and algebra, with a focus on collaborative learning combined with extensive in-class and out-of-class assignments. The primary goal is to help future teachers (both in-service and pre-service) gain a fundamental understanding of the key mathematical ideas that they will be teaching so that, in turn, they can help their students learn important mathematics. This text presents is designed to equip future middle grade mathematics teachers with the skills needed for teaching NCTM (National Council of Teachers of Mathematics) Standards-based curricula. Throughout the text, the reader will find a number of Classroom Connections, Classroom Discussions, and Classroom Problems. These instructional components are designed to deepen the connections between the college-level abstract algebra and number theory the students are studying now and the algebra they will teach. Other titles in the Prentice Hall Connections in Mathematics Courses for Teachers include: Geometry Connections: Mathematics for Middle School Teachers Algebra Connections: Mathematics for Middle School Teachers Data and Probability Connections: Mathematics for Middle School Teachers Calculus Connections: Mathematics for Middle School Teachers

Preface
Patterns
Classroom Connections: Representing Patterns
Reflections on Classroom Connections: Representing Patterns
Arithmetic Sequences
Classroom Connections: A Quadratic Sequence
Reflections on Classroom Connections: A Quadratic Sequence
Finite Arithmetic Sequences
Geometric Sequences
Mathematical Induction
Classroom Connection: Counting Tools
The Binomial Theorem
The Fibonacci Sequence
Arithmetic and Algebra of the Integers
A Few Mathematical Questions Concerning the Periodical Cicadas
Classroom Connections: Multiples and Divisors
Reflections on Classroom Connections: Multiples and Divisors
Multiples and Divisors
Least Common Multiple and Greatest Common Divisor
The Fundamental Theorem of Arithmetic
Revisiting the LCM and GCD
Relations and Results Concerning LCM and GCD
The Division Algorithm and the Euclidean Algorithm
Measuring Integer Lengths and the Division Algorithm
The Euclidean Algorithm
Applications of the Representation GCD (a,b) = ax + by
Place Value
Prime Thoughts
Arithmetic and Algebra of the Integers Modulo n
Classroom Connections: Divisibility Tests
Reflections on Classroom Connections: Justifying the Divisibility Tests
Clock Addition
Modular Arithmetic
Comparing Arithmetic Properties of Z and Z[subscript n]
Multiplicative Inverses in Z[subscript n]
Elementary Applications of Modular Arithmetic
Fermat's Little Theorem and Wilson's Theorem
Linear Equations Defined over Z[subscript n]
Extended Studies: The Chinese Remainder Theorem
Extended Studies: Quadratic Equations Defined over Z[subscript n]
Algebraic Modeling in Geometry: The Pythagorean Theorem and More
The Significance of Daryl's Measurements and Related Geometry
Classroom Connections: The Pythagorean Theorem
Reflections on Classroom Connections: The Pythagorean Theorem and Its Converse
Computing Distance in Two-Dimensional and Three-Dimensional Euclidean Space: The Distance Formula
An Extension of the Pythagorean Theorem: The Law of Cosines
Integer Distances in the Plane
Pythagorean Triples: Positive Integer Solutions to x[superscript 2] + y[superscript 2] = z[superscript 2]
Extended Studies: Further Investigations into Integer Distance Point Sets-A Theorem of Erdos
Extended Studies: Additional Questions Concerning Pythagorean Triples
Fermat's Last Theorem
Arithmetic and Algebra of Matrices
Classroom Connections: Systems of Linear Equations
Reflections on Classroom Connections: Systems of Linear Equations
Rational and Irrational Numbers
Systems of Linear Equations
Polynomial Curve Fitting: An Application of Systems of Linear Equations
Matrix Arithmetic and Matrix Algebra
Multiplicative Inverses: Solving the Matrix Equation AX = B
Coding with Matrices
Glossary
References
Answers to (Most) Odd-Numbered Exercises
Photo Credits
Index

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