Homeschool · Math
The arithmetic books generations of American children learned from, now free to read and download, with step-by-step teaching guides for the first two books.
For a young child, begin with Ray's New Primary Arithmetic. Every lesson has a guide that tells you what to get out, what to say, and which page of the book to open. Most take about fifteen minutes.
Older children, or those who have finished the Primary book, go on to Ray's New Intellectual Arithmetic: mental arithmetic, fractions, ratio and percentage, also with a guide for every lesson.
Joseph Ray (1807–1855) grew up on a farm in what is now West Virginia, studied medicine, and then spent his life teaching mathematics in Cincinnati, at Woodward High School and Woodward College. His first arithmetic came out in 1834. Over the next decades it grew into a series, from a first book for small children to a higher arithmetic for older students, and it became one of the most widely used schoolbooks in America, alongside McGuffey's Readers from the same Cincinnati publishers.
After Ray's death the series was revised and reissued in 1877 as Ray's New Arithmetics, the edition most homeschoolers use today, and the one on this page. The method is simple and thorough: count real things first, learn each table by heart, then use it straight away in short story problems, and explain every answer in a full sentence. Old prices and measures aside, the arithmetic is the same today.
In the usual order. Ages are rough guides; go by what your child can do.
Counting, reading and writing numbers to 100, then the addition, subtraction, multiplication and division tables, story problems, and the tables of money and measures. 89 short lessons with pictures.
Scanned by Google from a Harvard University copy.
Arithmetic done in the head and explained aloud: the four operations with larger numbers, fractions, and many story problems. Ray's “intellectual” means mental.
Scanned from a University of California copy.
Working on paper: long multiplication and division, fractions, decimals, measures, percentage and interest. The core book of the series.
Uploaded as a public-domain (CC0) scan.
The whole subject again in depth: number theory, ratio and proportion, powers and roots, series, and business arithmetic.
Scanned from a University of California copy.
Thousands of extra problems for review and tests, arranged to follow the other books.
Scanned from a University of California copy.
The answers and worked solutions for the Intellectual and Practical books.
Scanned printing dated 1907.
If you have heard of Ray's from the 1850s, these are the books from before the 1877 revision. They teach the same way, with older wording.
The pre-1877 Practical Arithmetic, as schoolchildren used it in the 1850s.
The earlier Intellectual Arithmetic, part of the numbered first, second and third books.
Every book here was published in the United States before 1930, so it is in the public domain there: free to read, print and share. The scans are kept by the Internet Archive, which shows them on this page and supplies the PDF downloads. The teaching guides are written for this site. Modern reprints are also sold, if you prefer a clean printed copy.