9780131449282

Algebra Connections

by ;
  • ISBN13:

    9780131449282

  • ISBN10:

    0131449281

  • Edition: 1st
  • Format: Paperback
  • Copyright: 12/2/2005
  • Publisher: Pearson

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Summary

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.Gives both pre-service and in-service teachers 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. Directly connects college-level abstract algebra and number theory to standards-based middle grade mathematics curricula. Gives specific examples from middle-grade curricular materials to show readers the direct connections between the mathematics they are learning and the mathematics they will be teaching. Focuses on the mathematics in new reform materials. Offers Classroom Problems and Classroom Discussions that focus on discovery and collaborative learning.A useful reference for teachers of middle-grades mathematics.

Table of Contents

Preface vii
Patterns
1(62)
Classroom Connections: Representing Patterns
1(2)
Reflections on Classroom Connections: Representing Patterns
3(11)
Arithmetic Sequences
14(2)
Classroom Connections: A Quadratic Sequence
16(1)
Reflections on Classroom Connections: A Quadratic Sequence
16(5)
Finite Arithmetic Sequences
21(2)
Geometric Sequences
23(6)
Mathematical Induction
29(5)
Classroom Connection: Counting Tools
34(13)
The Binomial Theorem
47(4)
The Fibonacci Sequence
51(12)
Arithmetic and Algebra of the Integers
63(32)
A Few Mathematical Questions Concerning the Periodical Cicadas
64(1)
Classroom Connections: Multiples and Divisors
64(1)
Reflections on Classroom Connections: Multiples and Divisors
65(5)
Multiples and Divisors
70(3)
Least Common Multiple and Greatest Common Divisor
73(2)
The Fundamental Theorem of Arithmetic
75(7)
Revisiting the LCM and GCD
82(7)
Relations and Results Concerning LCM and GCD
89(6)
The Division Algorithm and the Euclidean Algorithm
95(50)
Measuring Integer Lengths and the Division Algorithm
95(7)
The Euclidean Algorithm
102(4)
Applications of the Representation GCD (a, b) = ax + by
106(4)
Place Value
110(15)
Prime Thoughts
125(20)
Arithmetic and Algebra of the Integers Modulon
145(70)
Classroom Connections: Divisibility Tests
146(1)
Reflections on Classroom Connections: Justifying the Divisibility Tests
146(2)
Clock Addition
148(3)
Modular Arithmetic
151(13)
Comparing Arithmetic Properties of Z and Zn
164(5)
Multiplicative Inverses in Zn
169(5)
Elementary Applications of Modular Arithmetic
174(14)
Fermat's Little Theorem and Wilson's Theorem
188(5)
Linear Equations Defined over Zn
193(7)
Extended Studies: The Chinese Remainder Theorem
200(3)
Extended Studies: Quadratic Equations Defined over Zn
203(12)
Algebraic Modeling in Geometry: The Pythagorean Theorem and More
215(38)
The Significance of Daryl's Measurements and Related Geometry
216(1)
Classroom Connections: The Pythagorean Theorem
217(1)
Reflections on Classroom Connections: The Pythagorean Theorem and Its Converse
217(9)
Computing Distance in Two-Dimensional and Three-Dimensional Euclidean Space: The Distance Formula
226(1)
An Extension of the Pythagorean Theorem: The Law of Cosines
227(2)
Integer Distances in the Plane
229(1)
Pythagorean Triples: Positive Integer Solutions to x2 + y2 = z2
230(7)
Extended Studies: Further Investigations into Integer Distance Point Sets---A Theorem of Erdos
237(3)
Extended Studies: Additional Questions Concerning Pythagorean Triples
240(10)
Fermat's Last Theorem
250(3)
Arithmetic and Algebra of Matrices
253(58)
Classroom Connections: Systems of Linear Equations
254(1)
Reflections on Classroom Connections: Systems of Linear Equations
255(6)
Rational and Irrational Numbers
261(7)
Systems of Linear Equations
268(14)
Polynomial Curve Fitting: An Application of Systems of Linear Equations
282(4)
Matrix Arithmetic and Matrix Algebra
286(12)
Multiplicative Inverses: Solving the Matrix Equation AX = B
298(8)
Coding with Matrices
306(5)
Glossary 311(10)
References 321(2)
Answers to (Most) Odd-Numbered Exercises 323(22)
Photo Credits 345(2)
Index 347

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