The Eclectic Manual of Methods

Grade: Kindergarten

Duration: Child-dependent


The kindergarten mathematics course provides four phases of step-by-step instructions for introducing primary-level arithmetic in preparation to begin Ray's Primary Arithmetic. Phase I teaches children to recognize groups of physical objects up to ten. Phase II drops physical objects and teaches children to combine and separate up to ten imaginary objects in their minds. In phase III, children combine and separate abstract numbers directly. Finally, in phase IV, children learn to write addition and subtraction equations. Teaching guides accompany all 56 lessons.

Ray's New Primary Arithmetic

Grade: First

Duration: Child-dependent


The Ray's New Primary Arithmetic textbook covers addition, counting, skip counting, subtraction, multiplication, division, money, and time. Teaching guides accompany all 132 lessons. Using a 10x10 abacus to demonstrate multiplication and division operations may be helpful, although it is not required. Look for one with two colors of beads (5 and 5) on each row. Inexpensive ones can be found online for around $10.00. This course changes the order of certain lessons, expands certain lessons (money and time), and removes antiquated lessons toward the end of the book.

Ray's New Arithmetic

Grade: Third

Duration: Child-dependent


As taught by teachers of bygone eras and recommended by 'The Eclectic Manual of Methods,' this course interweaves related theory and problem sets from 'Ray's New Intellectual Arithmetic,' 'Ray's Practical Arithmetic,' and 'Ray's New Test Exam.' This course expands upon the study of addition, subtraction, multiplication, and division and introduces notation, reduction, and compound numbers. This course also provides a workbook of text exercises and an answer key. Using a 10x10 abacus to demonstrate mathematical operations may be helpful, although it is not required.

Ray's New Arithmetic

Grade: Fifth

Duration: Child-dependent


As taught by teachers of bygone eras and recommended by 'The Eclectic Manual of Methods,' this course interweaves related theory and problem sets from 'Ray's New Intellectual Arithmetic,' 'Ray's Practical Arithmetic,' and 'Ray's New Test Exam.' This course continues the third-fourth grade course with factoring, fractions, decimal fractions, the metric system, and percentages. This course also provides a workbook of text exercises and an answer key.