CONCEPTUAL MATH 1: BASIC ARITHMETIC
Student’s Version (M001)
Grades 4-6

This 170-page student text and exercise book is designed to give the student clear understanding and proficiency in basic arithmetic, including addition, subtraction, multiplication, and division. This book employs the highly motivational approach of integrating the teaching of math with the historical development of math to show why and how each arithmetic operation was invented. The student is given clear instructions on how to perform each operation and plenty of exercises to develop mastery and proficiency.

Mathematics as a science is a vast, integrated body of abstract principles derived inductively from concrete observations. Math is a marvelous human creation that began tens of thousands of years ago to satisfy certain human survival needs. Our unique approach in this book is to present math as it developed historically whereby each new idea or method can be seen to flow logically from previous discoveries and observations. For example, the student learns how addition is merely a rapid form of counting and how multiplication is merely a rapid form of addition. Our inductive approach allows the student to keep abstract concepts in math intimately tied to reality rather than as dry, floating abstractions. Furthermore, we show how each new discovery served to satisfy a human need and consequently benefited people, which makes learning math more interesting and enjoyable.

This student version is divided into two parts. Part I is the main text (80 pages) which gives some historical background for each arithmetic operation and clearly demonstrates to the student how to perform the operation. Part I contains some exercises to allow the student to immediately check if he or she understands the method. The bulk of the exercises are in Part II (84 pages) which, for each chapter of Part I, includes numerical problems, word problems, and short essay-type questions. The exercises are designed to help the student understand the concepts clearly and develop proficiency in the arithmetic operations.

In addition to the exercises in Part II, the teacher’s version of this book contains 38 timed math sheets covering all arithmetic operations. Prior to every math class the teacher will hand out one or two of the sheets for the students to complete as quickly and accurately as possible while being timed. In this manner the teacher can monitor the proficiency of the student.

This book is not intended to cover every math topic that the student is required to master as per his or her particular education district. It’s designed to build a solid, conceptual understanding of basic arithmetic. Fractions and decimals are not covered in this book. They will be covered in the next book of this series.

This book is designed so that the student can perform all the work right in the book if desired. Otherwise the work could be performed in a separate notebook that can be purchased from any local supply store. If you purchase this student's version, then we highly recommended purchasing at least one copy of the teacher’s version because it contains all the answers to the exercises. (See below.)