Grade(s): 7-9
Pages: 256 (color)

Successful completion of this middle school geometry course will virtually guarantee a student’s success in high school geometry. Although the geometric concepts of perimeter, area, and volume are taught piecemeal from elementary school through middle school, many students enter high school without the skills and knowledge to succeed in high school geometry. Unfortunately, middle school students get very little education on the properties of parallelograms and the tools needed to succeed at doing geometric proofs. The result is a high number of students who struggle with high school geometry and standardized testing.

Geometry is a fundamental subject in high school standardized testing.This book teaches students an understanding of the reasoning behind the properties taught in geometry instead of merely asking them to memorize them. Students are also taught the basics of geometric proofs and coordinate geometry in a way middle school students can understand. A glossary of terms that every student in high school must master is included.

This book follows the National Math Standards in mathematics but it goes further. Use with able math students from Gr 7.

Table of Contents:
About the Author
Why Use This Book
Teaching Suggestions
Student Introduction
Glossary
Answers

Chapter 1 - Fundamentals of Geometry Reasoning
Introduction to the Student
Geometry Notation
Geometry Notation Practice
All About Lines
All About Planes
Build It!
Three Planes in Space

Chapter 2 - Uncovering All the Angles
Types of Angles
Complete the Chart
Triangle Activity
Triangle Practice
Quadrilateral Activity
Complementary and Supplementary Angles
Vertical Angles
Puzzle 1
Puzzle 2
Parallel Lines and Transversals I
Parallel Lines and Transversals II
Puzzle 3 - Find 20 Angles

Chapter 3 - Triangle Properties
Triangle Properties 1: Sum of Angle Measures
Triangle Properties 2: Exterior Angle Property
Triangle Property 3: Sum of Two Sides
Triangle Properties Practice
Triangle Property 4: Largest Angle Faces Largest Side
Property of Equilateral and Isosceles Triangles
Algebra and Geometry Practice

Chapter 4 - The Pythagorean Theorem
Exploration - What is a Theorem?
Pythagorean Triples
Practice with the Pythagorean Triples
Using the Pythagorean Theorem
Using the Pythagorean Applications
Problem Solving Strategies
Special Right Triangles

Chapter 5 - Uncovering All Polygons
Polygons – Investigation of Angles and Sides
Polygon Angles Exploration
Summary of Polygon Properties
Diagonals of a Polygon Exploration
The Number of Diagonals of a Polygon (Handshake Problem)

Chapter 6 - Quadrilateral and Parallelogram Properties
The Quadrilateral Family
Venn Diagram Activity
Parallelogram Discovery
Parallelogram Properties
Working With Parallelograms
Experimenting With Parallelograms
A Look at Trapezoids
Kite! Kite! Kite!
Critical Thinking About Quadrilaterals
Median Investigation
Using Algebra to Solve Quadrilateral Problems
Quadrilateral Matching

Chapter 7 - Metric Geometry
Perimeter and Circumference
Pi (ð) Investigation
Archimedes’ Idea for Approximating Pi
Area of Parallelograms
Parallelogram Area Activity
Area of Triangles and Trapezoids
Discovering the Area of a Trapezoid/ Area of a Trapezoid
Area of Circles
The Arbelos Problem

Chapter 8 - Geometric Constructions
A Geometric Construction
How to Bisect an Angle
How to Copy an Angle
How to Construct a Perpendicular Bisector to a Line
Finding the Median in a Triangle
Area of Triangles and Trapezoids
Geometric Construction Review
Problem Solving With Geometric Constructions
Impossible Constructions?

Chapter 9 - Geometry of Three Dimensional Shapes
3D Shapes - Prisms
The Volume of Cylinders
Volumes of Pyramids and Cones
Turn Up the Volume!
Volume of a Sphere
Surface Area of Prisms
Surface Area of a Cylinder Activity
Finding Surface Area of Prisms and Cylinders
Euler’s Formula

Chapter 10 - Symmetry and Transformations
What is Vertical, Horizontal, and Point Symmetry?
Transformations - Reflections
Transformations - Translations
Transformations - Rotations
Transformations - Dilations
Glide Reflections and Compositions
Tessellations

Chapter 11 - Proving Triangles Congruent
Introduction to Proofs - Congruency
SSS Activity
SAS Activity
ASA and AAS Activities
SSA Activity
The Essence of a Good Geometric Proof
Picture, Statement, and Reason
Finding Congruent Triangles
Two Column Proofs
Investigate Hypotenuse - Leg Theorem
Similar Figures and Introduction to Similarity Proofs
Proving Triangles Similar
Test Your Reasoning Skills

Chapter 12 - Coordinate Geometry
What is the Slope of a Line
Slope Formula
How to Write an Equation of a Line
The Midpoint Formula
The Distance Formula
Review Your Formulas
Introduction to Coordinate Proofs

Reviews:
"As a teacher I like the problem solving activities as these could be used over again or with several students in the classroom." -iParenting Reviewer
"Mathematical Reasoning presents math in a way that makes it not only simple to learn, but also practical to apply to everyday circumstance (obviously making math more meaningful to him)." -Katherine, Mississippi
"My son hated math. I saw your curriculum and gave it a try. Wow, what a great fit for my son! Your Mathematical Reasoning curriculum gave him a way to learn math that made sense to him. Thank you!" -Amy, Ontario, Canada
"For the money, the books are excellent buys and worthy supplements to any childhood students education." -Maxine, "Teaching Children Mathematics" published by NCTM
"As a math instructor, I am so happy that it looks like I may have a math-brain in my family after all! He asks to do his math school work (Mathematical Reasoning book) every day!" -Janelle, Math Teacher & Parent

Awards (earned by various titles in series):

• Dr. Toy Best Picks
• Mensa Recommended Materials for the Gifted
• iParenting Media AwardMom's Choice Awards Silver Medal for Excellence
• iParenting Media Best Products
• Creative Child Magazine Preferred Choice AwardiParenting Media Excellent Products
• Cathy Duffy Top 100 Award
• Dr. Toy Product of Excellence
• Learning® Magazine Recommended Resource for Successful Teaching
• Jenkins Group Moonbeam Children's Book Award, Silver Medal
• Mom’s Choice Awards Gold Recipient