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
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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.)
RETURN TO ADVANCED DIFFERENTIATED LEARNING PAGE
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