Algebra Connections by UMO University O... | WHSmith Books
Algebra Connections

Algebra Connections

By: UMO University Of Missouri (author), Ira J. Papick (author)Paperback

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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


1. Patterns1.1 Classroom connections: Representing patterns1.2 Reflections on classroom connections: Representing patterns1.3 Arithmetic sequences1.4 Geometric sequences1.5 Mathematical induction1.6 Classroom connections: counting tools1.7 The Binomial Theorem1.8 The Fibonacci sequence 2. Arithmetic and Algebra of the Integers2.1 A few mathematical questions concerning the periodical cicadas2.2 Classroom connections: multiples and divisors2.3 Reflections on classroom connections: multiples and divisors2.4. Multiples and divisors2.5 Least common multiple and greatest common divisor2.6 The Fundamental Theorem of Arithmetic2.7 Revisiting the lcm and gcd2.8 Relations and results concerning lcm and gcd 3. The Division Algorithm and the Euclidean Algorithm3.1 Measuring integer lengths and the Division Algorithm3.2 The Euclidean Algorithm3.3 Applications of the representation gcd(a, b) = ax + by3.4 Place value3.5 Prime thoughts 4. Arithmetic and Algebra of the Integers Modulo n4.1 Classroom connections: divisibility tests4.2 Reflections on classroom connections: Justifying the divisibility tests4.3 Clock addition4.4 Modular arithmetic4.5 Comparing arithmetic properties of Z and Zn4.6 Multiplicative inverses in Zn4.7 Elementary applications of modular arithmetic4.8 Fermat's Theorem and Wilson's Theorem ii4.9 Linear equations defined over Zn4.10 Extended studies: The Chinese Remainder Theorem4.11 Extended studies: Quadratic equations defined over Zn 5. Algebraic Modeling in Geometry: The Pythagorean Theorem and More5.1 The significance of Daryl's measurements and related geometry5.2 Classroom connections: The Pythagorean Theorem and its converse5.3 Reflections on classroom connections: The Pythagorean Theoremand its converse5.4 Computing distance in 2-dimensional and 3-dimensionalEuclidean space: The distance formula5.5 An extension of the Pythagorean Theorem: The law of cosines5.6 Integer distances in the plane5.7 Pythagorean triples: Positive integer solutions to x2 + y2 = z25.8 Extended studies: Further investigations into integer distance point sets - a Theorem of Erdoes.5.9 Extended studies: Additional questions concerning Pythagorean triples5.10 Fermat's Last Theorem 6. Arithmetic and Algebra of Matrices6.1 Classroom Connections: systems of linear equations6.2 Reflections on classroom connections: systems of linear equations6.3 Rational and irrational numbers6.4 Systems of linear equations6.5 Polynomial curve fitting: an application of systems of linear equations6.6 Matrix arithmetic and matrix algebra6.7 Multiplicative inverses: solving the matrix equation AX = B6.8 Coding with matrices Glossary

Product Details

  • ISBN13: 9780131449282
  • Format: Paperback
  • Number Of Pages: 368
  • ID: 9780131449282
  • weight: 520
  • ISBN10: 0131449281

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