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ESSENTIAL MATHEMATICS FOR GIFTED STUDENTS: PREPARATION FOR ALGEBRA, GRADES 4 8

ISBN 0-910609-43-8

By Francis T. Sganga, Mathematics Educator Volusia County, Florida

Cost: $18.00 + $1.80 Postage & Handling = $19.80 Total Cost.

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Parent Testimonial: "We received the math book by Francis Sganga and my eighth grade son was so sad that he didn't get to use it as an introduction to those topics (we have 2 younger children and I often teach math at a local private school). He wants you to urge Mr. Sganga to write a similar book for high school students, preparing them for calculus. Thanks."


Contains interesting and challenging problems specifically designed for gifted students

A remarkable summary of algebra concepts necessary for success in mathematics

Written by an experienced educator and former supervisor of mathematics education

A stimulating introduction to geometry and trigonometry

Clear, concise, interesting, practical, easy-to-read presentation of important topics

Hands-on activities to enhance understanding

All Sample Problems have complete detailed solutions

Includes problems related to chemistry and physics

Contains a unique Slide Rule for adding and subtracting positive and negative numbers

Can be used as a problems text in middle school geometry and algebra courses.

ABOUT THE AUTHOR

Francis (Frank) Sganga received his B.S. and M.A. degrees at the University of Florida
where, as a graduate student, he taught for two years. After working with the U.S. Corps of Engineers for two years, he succumbed to an urge to teach, and wound up spending six years
teaching at the high school level. Teachers salaries being what they were, and still are, he
decided his income was insufficient for a family of five, and moved into administration.
After three years, his superiors promoted him to the position of Mathematics Supervisor.

During his tenure as supervisor, he wrote two original competitive proposals for federal
grants (Success in Mathematics through Aural-Reading Techniques and Calculator-Assisted Mathematics for Every-day Living), that brought $1 million into the Volusia County, Florida school system. Both projects were validated by the U.S. Office of Education in Washington, D.C. for national dissemination.

In his supervisory role he spent a good deal of his time teaching gifted students at the
middle school level, as well as conducting in-service workshops for their teachers. He never allowed his penchant for teaching to lie fallow.

Also during that time he became the sole author of two major mathematics programs published by Charles E. Merrill (Bell & Howell) that were sold internationally with sales
topping $1.5 million, and invented 15 teaching aids (two patented in his name) that were
published and sold internationally by the St. Regis Paper Company.

Lastly, he wrote three articles for professional journals, which include A Bee on a Point, a Line and a Plane (NCTM's Mathematics Teacher), An Individualized Approach to Teaching Mathematics and How to Solve Word Problems, as well as six article related to education for
the local (New Smyrna Beach, Florida) newspaper, The Observer.

Currently, he is an Educational Consultant, and still tutors students from grades 4 through junior college. His current hobbies are writing, playing racquetball, and riding his 1100 cc
Honda Shadow motorcycle.

 

TABLE OF CONTENTS

 

CHAPTER 1: BASIC CONCEPTS THAT CAN LAST A LIFETIME

Inverse Operations Page 1

The Great Factor-Factor-Product Threesome Page 1

Density Page 2

A Simple Way to Work with Formulas and Equations Page 3

Activity: Discovering pi Page 6

A Cylinder Is Just a Circle with an Altitude Page 7

The World of Spheres Page 8

Formulas Are Tools Used to Get the Job Done Page 9


CHAPTER 2: ESSENTIAL TOPICS FOR SUCCESS IN MATHEMATICS

Formulas! Formulas! There's No Way to Escape them! Page 11

Einstein's Famous E = mc2 Page 12

Derivation of A = p r2 Page 13

Activity: Adding and Subtracting Integers on a Slide Rule Page 14

Multiplying and Dividing Integers Page 15

Ratios Page 16

Trigonometry and Angles Page 17

The Tangent Ratio Page 18

The Sine and Cosine Ratios Page 21

Gear Ratios, Legends on Maps and Scale Models Page 22


CHAPTER 3: SETTING UP AND USING PROPORTIONS

What Is a Proportion? Page 23

Similar Triangles Page 25


A Chemistry Equation 26

Hook's, Charles' and Boyle's Laws Page 27

Inverse Proportions Page 28


CHAPTER 4: UNDERSTANDING POINTS, LINES AND SLOPES

Rene Descartes and Analytical Geometry Page 30

Dividing a Plane into Quadrants Page 32

What Is a Slope? Page 33

Slope Formula: Rise and Run Page 34

The Graphs of Horizontal and Vertical Lines Page 37


CHAPTER 5: UNDERSTANDING LINEAR EQUATIONS AND FUNCTIONS

One and Two Variable Equations Page 38

A Linear Equation. and Its Standard Form Page 39

Inclines Are Positive; Declines Are Negative Page 41

What Is a Function? Page 43

Slope-Intercept Form of a Linear Equation Page 44



CHAPTER 6: UNDERSTANDING QUADRATIC EQUATIONS AND FUNCTIONS

Introducing Quadratic Equations Page 48

The Standard Form of a Quadratic Equation Page 49

Squares and Square Roots; Perfect Squares Page 50

The Quadratic Formula Page 51

What Getting Two Answers Means Page 53

Understanding Quadratic Function 54

Function Notation Page 55

Graphing Quadratic Functions Page 56

Finding the Vertex of a Parabola Page 60

What Is Symmetry? Page 61

The Roots of a Quadratic Equation Page 62


ABOUT THE AUTHOR Page 63

CLICK HERE FOR TWO SAMPLE PAGES IN ADOBE ACROBAT

(SWITCHING FACTORS, ABSOLUTE VALUE, OPPOSITES, ADDING AND SUBTRACTING NUMBERS ON A SLIDE RULE, ETC.)

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