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Mathematical Reasoning™

Bridging the Gap Between Computation and Math Reasoning

Grades: Toddler-11


Full curriculum

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Grades: Toddler-11


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.

Free Detailed Solutions are available!

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 Geometry
The successful completion of this colorful 272-page book will prepare middle schoolers for high school geometry. It covers more than 50% of the concepts taught in high school geometry using a step-by-step approach and teaches 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. Students who struggle with high school geometry usually have lower standardized test scores because it is a fundamental subject in high school standardized testing.

A glossary of terms that every student should master is included. This book can be used as a classroom textbook in Grades 7, 8, or 9 (usually over a two-year period) or as a reference for high school students. This book covers more than the National Math Standards for middle school mathematics.

Free Detailed Solutions are available!

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 Pre-Algebra (see description above) before attempting Understanding Geometry.

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

Essential Algebra for Advanced High School and SAT

Discover Essential Algebra for Advanced High School and SAT, a 241-page math book in the esteemed Mathematical Reasoning series written by award-winning author and teacher with 30 years of expertise in secondary mathematics. This powerful resource teaches the ‘essential’ connection of arithmetic and geometric concepts with algebraic concepts. Without this understanding, students tend to memorize Algebra I problem-solving steps—which is sufficient to pass Algebra I—but leaves them unprepared for math courses beyond Algebra I and the SATs.

Algebra, the essential language of all advanced mathematics, lies at the core of this book's teachings. By delving into the generalized arithmetic that underpins algebra, students develop a solid foundation in the rules governing number and fraction operations, including factors and multiples. This vital knowledge empowers students to move beyond mere memorization of Algebra I problem-solving steps and confidently tackle the complexities of math courses beyond Algebra I.

Without the knowledge and skills taught in this book, students often struggle or even fail in advanced mathematics courses and on the SATs. Imagine a good high school student who sees a problem like 3•x•y•4 and hesitates to write 12xy due to uncertainty about the rules governing multiplication. Or not understanding how to add 2x to 1/4y to combine it into a single fraction. Or why –62 is different than (–6)2. It is easy to see that not having a strong understanding of the foundational rules of algebra can stop even the smartest students from succeeding in advanced high school math courses.

Essential Algebra for Advanced High School and SAT serves as a companion to an Algebra I course or aids in post-Algebra I readiness. To ensure students’ long-term success in advanced math beyond Algebra I, this book teaches the following 'essential' mathematics skills and concepts:

  • Understanding Terms and Order of Operations
  • Understanding the Family of Real Numbers
  • Rationals and Irrationals
  • Working with Terms and Polynomials
  • Polynomial Division, Factoring, and Rational Expressions
  • Solving Equations and Inequalities
  • Ratio, Proportion, and Percent
  • How Algebra is Used in Geometry
  • Understanding Functions
  • Working With Quadratic Equations and Functions

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.

Mathematical Reasoning™

Description and Features


Description and Features

Bridges the gap between computation and mathematical reasoning for higher grades and top test scores.

All Products In This Series

Grouped product items
06913PBP Mathematical Reasoning™ Beginning 1 Toddler-PreK Paperback Book
06914PBP Mathematical Reasoning™ Beginning 2 PreK Paperback Book
06936PBP Mathematical Reasoning™ Level A K Paperback Book
06907BBP Mathematical Reasoning™ Level B 1 Paperback Book
06908BBP Mathematical Reasoning™ Level C 2 Paperback Book
06909BBP Mathematical Reasoning™ Level D 3 Paperback Book
06910BBP Mathematical Reasoning™ Level E 4 Paperback Book
06911BBP Mathematical Reasoning™ Level F 5 Paperback Book
06912BBP Mathematical Reasoning™ Level G 6 Paperback Book
06929BBP Understanding Pre-Algebra 6-8 Paperback Book
06930BBP Understanding Geometry 7-9 Paperback Book
06932BBP Understanding Algebra I 7-9 Paperback Book
06933BBP Essential Algebra for Advanced High School Math and SAT 8-11 Paperback Book
06921BBP Mathematical Reasoning™ Grades 2-4 Supplement 2-4 Paperback Book
06922BBP Mathematical Reasoning™ Grades 4-6 Supplement 4-6 Paperback Book
06924BBP Mathematical Reasoning™ Middle School Supplement 7-9 Paperback Book
EBOOK Important eBook Information
06963PEP Mathematical Reasoning™ Beginning 1 - eBook Toddler-PreK eBook
06964PEP Mathematical Reasoning™ Beginning 2 - eBook PreK eBook
06966PEP Mathematical Reasoning™ Level A - eBook K eBook
06957BEP Mathematical Reasoning™ Level B - eBook 1 eBook
06958BEP Mathematical Reasoning™ Level C - eBook 2 eBook
06959BEP Mathematical Reasoning™ Level D - eBook 3 eBook
06960BEP Mathematical Reasoning™ Level E - eBook 4 eBook
06961BEP Mathematical Reasoning™ Level F - eBook 5 eBook
06962BEP Mathematical Reasoning™ Level G - eBook 6 eBook
06979BEP Understanding Pre-Algebra - eBook 6-8 eBook
06980BEP Understanding Geometry - eBook 7-9 eBook
06982BEP Understanding Algebra I - eBook 7-9 eBook
06983BEP Essential Algebra for Advanced High School Math and SAT - eBook 8-11 eBook
06971BEP Mathematical Reasoning™ Grades 2-4 Supplement - eBook 2-4 eBook
06972BEP Mathematical Reasoning™ Grades 4-6 Supplement - eBook 4-6 eBook
06974BEP Mathematical Reasoning™ Middle School Supplement - eBook 7-9 eBook
06989CEP Understanding Pre-Algebra: Detailed Solutions PDF 6-8 eBook
06990CEP Understanding Geometry: Detailed Solutions PDF 7-9 eBook
06991CEP Understanding Algebra I: Detailed Solutions PDF 7-9 eBook
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