American Book Company, 1961

To the Teacher (excerpts)

*Basic Mathematics* is designed to promote a thorough understanding of the principles and processes of basic mathematics, and to provide for the individual needs and diverse interests found in most mathematics classes. The material in this text has been carefully selected an d presented at the student's vocabulary and experience level. Each principle is derived from facts already known to the student, and each process is developed in terms of the principles on which it depends. In addition, the subject matter is present in five cycles (units) of six topics each, to take advantage of the greater effectiveness of learning through systematic review and expansion of principles.

The organization of this text may be described in terms of five concentric rings representing the five units. Unit I, represented by the innermost circle, reviews and explains the basic concepts most essential to an understanding of the six topics: number representation, fundamental processes, common fractions, decimals, algebraic symbolism, and experimental geometry. Then each succeeding unit-ring repeats this cycle, introducing additional and broader concepts in each topic. Thus, the student's understanding of mathematical concepts increases in breadth and depth. His appreciation of the need for mathematics is also steadily increased by a different area of applications in each unit, ranging from his own experiences through the mathematics used in home and community, in business, in industry, and in government.

- Unit I: Fundamentals of Mathematics
- Understanding and Representing Numbers
- Working with Whole Numbers
- Understanding Common Fractions
- Understanding Decimal Fractions
- Using Algebraic Symbols
- Working with Measurements

- Unit II: Basic Mathematics and Its Use
- Extending the Decimal System and Graphing
- Problem Solving and Installment Buying
- Working with Fractions
- Decimals and Percentage
- Algebra at Work: Simple Equations
- Geometry at Work: Simple Constructions

- Unit III: Mathematics in Business and the Professions
- The Language of Statistics and Line Graphs
- Problem Solving and Insurance
- Using Comparisons: Ratio and Proportion
- Percentage at Work: Interest
- More about Algebra: Two and Three Step Equations
- More about Geometry: Angles and Triangles

- Unit IV: Mathematics in Industry
- Numbers with Labels and Single-Bar Graphs
- Working with Denominate Numbers
- More about Proportion
- Working with Decimals and Percentages
- Directed Numbers
- Discovering Facts about Circles

- Unit V: Mathematics in Government
- Approximate Numbers and Circle Graphs
- Working with Large Numbers: Problems of Government
- Fractions, Ratio, and Trigonometry
- More about Percentages: Taxation
- Using Algebra in More Difficult Problems
- Working with Similar Triangles