For the old-fashioned folks, Ray's New Arithmetic are textbooks written by Joseph Ray in the first half of the 19th century, and which are becoming more popular with proponents of Charlotte Mason-style and Classical education. Just small books that resemble the McGuffey Readers, these aren't very well supported for teachers, and they certainly aren't exciting, but they are thorough and sound.

The Ray's Arithmetic books teach arithmetic in an orderly fashion, starting from rules and principles, building knowledge piece by piece, leading pupils from simple to complex. From the very first pages, Ray's Arithmetics incorporate what has become the scourge of today's math students—story problems. Students must read simple sentences which pose real life problems, decide whether to add, subtract, multiply or divide, and finally arrive at the answer—sometimes mentally—sometimes in writing.

Ray's Arithmetics students learn arithmetic, increase their reading comprehension skills, and learn to think rather than plod through page after page of addition or subtraction problems with a one-line direction at the top of each page. A student raised on Ray's will not even know he should be fearful of "story problems" because from day one every problem is posed in a sentence format.

Most early work is to be done with real objects such as fruit, counting blocks, or marbles. Later it is to be done in the head with mental images of the objects. When children are ready to think symbolically, they gradually drop their use of objects and images and learn to compute quickly with digits. Thus the child is carefully led through three growth states in arithmetic: 1) the manipulative stage, 2) the mental image stage, 3) the abstract stage.

New Primary:
This book introduces the four operations of addition, subtraction, multiplication, and division, along with counting and other basic skills. It can be used to guide your teaching for about two years—through grades 1 and 2. It goes farther than the average second grade course, but with Ray's mental system many second graders are able to do this work.

New Intellectual:
Extends work in the four operations to higher numbers and begins fractions, measurements, ratio and percentage. Can be used with many children through grades 3 and 4.

New Practical:
Reviews basic arithmetic skills and carries them to high levels. Also covers topics of measurement, factoring, decimals, percentage, ratio, proportion, powers, roots, and geometry. For grades 5 and 6. Good mastery of this book takes a child higher than a usual grade 6 level.

New Higher Arithmetic:
Includes philosophical understandings; principles and properties of numbers; and advanced study of common and decimal fractions, measurements, ratio, proportion, percentage, powers and roots, series, business math, and geometry. Has challenging work for advanced students and basic work for slower students. Can be used for grades 7 and 8, as well as for high school.

Test Examples:
A book of problems on topics in Intellectual, Practical, and Higher Arithmetic. Teachers may draw upon these for preparing tests.

Two answer keys—one for Primary, Intellectual, and Practical Arithmetic; the other for Higher Arithmetic—help parents and teachers gauge how well students are learning the material.

Finally, Ruth Beechick wrote the Mott Media Parent-Teacher Guide, which guides scheduling and planning of lessons for the Ray's texts. She shows where to adapt to the needs of slower or advanced students, making selective use of basic portions that are important for all students and higher-level portions that challenge the best students. She also describes games and activities which add variety to teaching and learning and provides a test for each unit.