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Mathematical Reasoning™

Bridging the Gap Between Computation and Math Reasoning

Grades: Toddler-9

Mathematics

Full Curriculum

Mathematical Reasoning™

Grades: Toddler-9

Mathematics

Full Curriculum

  •  Multiple Award Winner

Forget boring math lessons and dreaded drill sheets.  These fun, colorful books use engaging lessons with easy-to-follow explanations, examples, and charts to make mathematical concepts easy to understand.  They can be used as textbooks or comprehensive workbooks with your textbooks to teach the math skills and concepts that students are expected to know in each grade—and several concepts normally taught in the next grade.

Every lesson is followed with a variety of fun, colorful activities to ensure concept mastery.  The lessons and activities spiral slowly, allowing students to become comfortable with concepts, but also challenging them to continue building their problem-solving skills.  These books teach more than mathematical concepts; they teach mathematical reasoning, so students learn to devise different strategies to solve a wide variety of math problems.  All books are written to the standards of the National Council of Teachers of Mathematics.

Beginning 1, Beginning 2, and Level A Contents

     •  Counting
     •  Identifying
     •  Matching
     •  Ordering
     •  Position
     •  Comparing and Estimating
     •  Addition
     •  Subtraction
     •  Locating
     •  Writing
     •  Grouping
     •  Patterns
     •  Geometric Shapes
     •  Measurement
     •  Data/Probability
     •  Fractions


Level B, Level C, Level D, Level E, Level F, and Level G Contents

Mathematical Reasoning Content Chart



Understanding Pre-Algebra
This book teaches and develops the math concepts and critical thinking skills necessary for success in Algebra I and future mathematics courses at the high school level.  It was written with the premise that students cannot problem solve or take leaps of reasoning without understanding the concepts and elements that lead to discovery.  The author—with 35 years of experience teaching mathematics—is a firm believer that understanding leads to confidence and confidence gives students the resolve to succeed in higher level mathematics rather than fear it.  

It is standards-based, but what makes it different from other pre-algebra books is that it organizes concepts in a logical fashion, stressing practice and critical thinking. It avoids the mistakes—found in many other math books—of trying to teach new concepts before students receive the prerequisite skills and practice necessary for success. The concepts are presented clearly and in connection to other concepts. Math vocabulary is very important to success in higher mathematics, so this book includes easy-to-follow explanations and a user-friendly glossary.

Understanding Pre-Algebra Contents

     •  Family of Numbers
     •  Working With Integers
     •  Working With Rational Numbers
     •  Ratio, Proportion, and Percent
     •  Percent Applications
     •  Algebraic Expressions
     •  Equations and Solving Word Problems
     •  Inequalities and Applications
     •  Understanding Square Roots and Irrational Numbers
     •  Two Dimensional Geometry
     •  Understanding Volume and Surface Area
     •  Graphing on the Coordinate Plane
     •  Transformations and Congruency
     •  Understanding Functions
     •  Probability and Statistics

 



Understanding Algebra I
This is a one-year Algebra I course for Grades 7-9. Students who have a solid algebra background will have no trouble with the algebra problems from SAT and even the GRE.  This 384-page book highlights vocabulary and notation, and has examples from the history of math.

What makes this book unique and different from other algebra textbooks is that it is built from the experiences of an award-winning algebra teacher with more than 30 years of teaching experience. Many textbooks are written by a committee of authors, and many of those authors have little experience teaching beginning algebra students in middle school or high school.

Understanding Algebra I presents the most essential concepts and skills needed to fully understand and gain confidence in algebra in a step-by-step fashion, teaching students that algebra is generalized arithmetic. It helps students see the connection between mathematics that they already know and algebra, so that learning algebra becomes easier and less abstract. This book provides students with real strategies to succeed in solving word problems by using charts and translating strategies that guarantee success.

Understanding Algebra I Contents

     •  Set and Set Notation
     •  Number Lines
     •  Graphing
     •  Rationals
     •  Operations
     •  Expressions
     •  Equations
     •  Inequalities
     •  Word Problem
     •  Percent Problems
     •  Ratio Problems
     •  Motion Problems
     •  Work Problems
     •  Absolute Value
     •  Polynomials
     •  Factoring
     •  Radicals
     •  Linear Functions
     •  Slope
     •  Elimination
     •  Graphing
     •  Substitution
     •  Absolut Value
     •  Algebraic Fractions

 



Understanding Geometry
The successful completion of this colorful 272-page book 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, too many students enter high school without the skills and knowledge to succeed in high school geometry. Unfortunately, middle school students receive 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 must master is included. This book can be used as a classroom textbook in Grades 7, 8, or 9 (usually over a two-year period). In many high schools this book can also be used as a one-year high school geometry course. This book follows the National Math Standards in mathematics but it goes further.

Understanding Geometry Contents

     •  Geometry Notation
     •  Lines
     •  Planes
     •  Angles—Types and Properties
     •  Pythagorean Theorem
     •  Polygons
     •  Quadrilateral Properties
     •  Parallelogram Properties
     •  Perimeter
     •  Circumference
     •  Pi
     •  Trapezoids
     •  Geometric Constructions
     •  3D Shapes—Prism, Cylinders, Pyramids, and Cones
     •  Symmetry
     •  Transformations—Reflection, Translations, Rotations, and Dilations
     •  Tessellations
     •  Proofs
     •  Congruency
     •  Slopes


NOTE:  It is our recommendation that students complete Understanding Algebra I (see description above) before attempting Understanding Geometry.



Mathematical Reasoning™ Supplements
These supplemental books reinforce grade math concepts and skills by asking students to apply these skills and concepts to non-routine problems. Applying mathematical knowledge to new problems is the ultimate test of concept mastery and mathematical reasoning. These user-friendly, engaging books are made up of 50 theme-based collections of problems, conveniently grouped in self-contained, double-sided activity sheets that provide space for student work. Each collection contains relevant math facts at the end of the worksheet in case students need hints to solve the problems. Calculators are allowed on activity sets that have a calculator icon at the top of the front side of the set. Each activity set is accompanied by a single-sided answer sheet containing strategy tips and detailed solutions. Teachers and parents will appreciate the easy-to-understand, comprehensive solutions. These books are a wonderful enrichment tool, but also can be used to assess how well students have learned their grade level's math concepts.

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