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. **

**SEND YOUR CHECK OR PURCHASE ORDER TO: GIFTED EDUCATION PRESS; 10201 YUMA COURT; P.O. BOX 1586; MANASSAS, VA 20108. TELEPHONE -- 703-369-5017.
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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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