Book Name : Discovering Geometry : An Investigative Approach
Author : Michael Serra
Edition : 4th Edition
Content :
(0) Geometric Art
(1) Introducing Geometry
(2) Reasoning in Geometry
(3) Using Tools of Geometry
(4) Discovering and Proving Triangle Properties
(5) Discovering and Proving Polygon Properties
(6) Discovering and Proving Circle Properties
(7) Transformations and Tessellations
(8) Area
(9) The Pythagorean Theorem
(10) Volume
(11) Similarity
(12) Trigonometry
(13) Geometry as a Mathematical System
စာေရးသူ၏ အမွာ
What Makes Discovering Geometry Different?
Discovering Geometry is designed so that you can be actively engaged as you
learn geometry. In this book you “learn by doing.” You will learn to use the tools
of geometry and to perform geometry investigations with them. Many of the
investigations are carried out in small cooperative groups in which you jointly
plan and find solutions with other students. Your investigations will lead you to the
discovery of geometry properties. In addition, you will gradually learn about proof,
a form of reasoning that will help you explain why your discoveries are true,
through Developing Proof group activities and exercises.
Discovering Geometry is designed so that both you and your teacher can have fun
while you learn geometry. It has a lot of “extras.” Each lesson begins with a quote
that I hope you will find funny or thought provoking. I think you’ll enjoy the
extra challenges in the Improving Your…Skills puzzles at the end of most lessons.
To solve each puzzle, you’ll need clever visual thinking skills or sharp reasoning
skills or both. I hope you will find some of the illustrated word problems
humorous. In the explorations you will build geometric solids, find the height of
your school building, and discover why elephants have big ears. In the projects you
will draw the impossible, make kaleidoscopes, design a racetrack, and create a
mural. The online Dynamic Geometry Explorations help you visualize important
geometry concepts by putting them in motion, and there are graphing calculator
projects, Fathom Dynamic Data™ projects, The Geometer’s Sketchpad
explorations, and web links that will allow you to practice and improve
your skills.
Suggestions for Success
It is important to be organized. Keep a notebook with a section for definitions,
a section for your geometry investigations, a section for discoveries, and a section
for daily notes and exercises. Develop the habit of writing a summary page when
you have completed each chapter. Study your notebook regularly.
You will need four tools for the investigations: a compass, a protractor, a
straightedge, and a ruler. Some investigations use patty paper, small squares of
waxed paper usually used between burger patties, that can be used as a unique
geometry tool. Keep a calculator handy, too.
You will find hints for some exercises in the back of the book. Those exercises are
marked with an ⓗ. Try to solve the problems on your own first. Refer to the hints
as a last resort if you can’t solve a problem. Solutions are provided for chapter
reviews so you can check your understanding and prepare for tests.
Discovering Geometry will ask you to work cooperatively with your classmates.
When you are working cooperatively, always be willing to listen to each other, to
actively participate, to ask each other questions, and to help each other when asked.
You can accomplish much more cooperatively than you can individually. And, best
of all, you’ll experience less frustration and have much more fun.
Michael Serra
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