Notes on using traditional math books
All of the books I have listed on this page are available for free online from either Google Play or Archive.org. You can download the books of your choice to your computer or laptop. You can download them to an Ipad or an android tablet or a Kindle. If you choose to print the books, you’ll find that (unless you have a laser printer) you will be spending quite a bit in paper and ink. You could take the file to a place like Staples, and ask to have it printed there, but that also costs some money.
My advice is to make use of the books directly from the screen of your device.
I have had my kids open the pdf file on their tablet screen and copy the problems into a plain composition notebook. This saves printer ink and makes pdf based math programs more affordable. When I work out an example problem in the notebook I cover that page in clear contact paper to preserve it. I cover test pages that way also. Make sure each day’s work is clearly labeled with the date and lesson number.
For the younger kids
- The Number Primer by Middlesex A. Bailey and George B. Germann (1916). Nice drawings. Suitable for kindergarten or first grade.
- First Steps in Arithmetic by William Peck (1894) (Archive.org). A lovely beginner book. Exercises are written to be completed orally. This method resulted in students who did not need a calculator to answer basic arithmetic problems.
- First Steps in Number: A Primary Arithmetic by George Albert Wentworth (1895). No frills plain and practical. Suitable for first grade.
- First year in numbers by Franklin Sherman Hoyt Harriet E. Peet (1912). This is one of those rare sweet gems that are sometimes found among the vintage texts. The drawings turn the work into a pleasure. My young son enjoys working from this book.
For the elementary to middle school level student
A Common School Arithmetic by James Greenwood (1906). A truly terrifying glimpse into what arithmetic meant to children of the previous century. It is even more frightening if you read the author’s note that most of the book is meant to be done orally. A great source of word problems, because the answers are in the back of this book.
Graded Work in Arithmetic Series by S. W. Baird
(1901) These books are quite challenging and were written in a time when students were expected to be able to do quite a lot of arithmetic mentally. Fortunately for us parents, the answers are in the back of most of the books.
Graded Work in Arithmetic, First Year
Graded Work in Arithmetic, Second Year
Graded Work in Arithmetic, Third Year
Graded Work in Arithmetic, Fourth Year
Graded Work in Arithmetic, Fifth Year
Graded Work in Arithmetic, Sixth Year
Graded Work in Arithmetic, Seventh Year
Graded Work in Arithmetic, Eighth Year
School Arithmetics Series by Wentworth and Smith
(1920). Answer key in the back of the books.
School Arithmetics Book One (Grades two to four)
School Arithmetics Book Two (Grades five and six)
School Arithmetics Book Three (Grades seven and eight)
Arithmetic by Ella Maria Pierce
First Steps in Arithmetic by Ella Maria Pierce (1899) (Archive.org). Another lovely beginner book that starts with addition. The exercises, in the style of the times, are written to be asked of the child orally.
An Intermediate Arithmetic by Ella Maria Pierce (Archive.org). This book is a continuation of the above book. It is suitable to begin around third grade. The questions are written to be asked orally of the child.
The Stone-Millis Arithmetics
The Stone-Millis Arithmetics: Primary by John Charles Stone James Franklin Millis (1910). Suggested for second, third, and fourth grades.
The Stone-Millis Arithmetics: Intermediate and Advanced by John Charles Stone and James Franklin Millis (1910). Two volumes in one, suggested for fifth through eighth grade.
The new Stone-Millis arithmetics: Advanced by John Charles Stone James Franklin Millis (1920). Suggested for seventh and eighth grades. Like other books of the time, this book contains sections on practical uses of math like taxes, banking, and investments.
Ray’s Arithmetic Series
Ray’s New Primary Arithmetic for Young Learners by Joseph Ray. (1877). This is the first book in the famous Ray’s Arithmetic series, which is especially known for its emphasis on mental math. Don’t pay for a copy! Find this vintage resource free on Google Play. This book begins with counting and writing numbers up through multiplication and division. There are no answers at the back of the book.
Ray’s New Intellectual Arithmetic by Joseph Ray (1877 edition) Begins with addition (and runs through subtraction, multiplication, division, fractions, and decimals) and focuses on mental arithmetic. This book does not have the answers at the back of the book and requires an answer key. (Google Play)
Ray’s New Practical Arithmetic by Joseph Ray (1877) This book begins with addition and goes up to fractions and decimals, but also includes problems related to finance, taxes, insurance and that sort of thing. Like the others, the answers are not in the back of the book. (Google Play)
Key to Ray’s New Arithmetics, Intellectual and Practical by Joseph Ray (1879). This is the answer key to the problems in those books.
Dubb’s Arithmetical Problems by E. L. Dubbs Meant as a supplement to Ray’s Practical Arithmetic by adding practice problems. The answers are in the back. (Google Play)
Ray’s New Higher Arithmetic by Joseph Ray (1880) A more in-depth treatment of arithmetic. There are no answers in the back of the book. (Google Play)
Key to Ray’s New Higher Arithmetic by Joseph Ray (1881) The answers to problems in Ray’s New Higher Arithmetic. (Google Play)
Ray’s Algebra, First Book by Joseph Ray Fans of Dr. Ray will be happy to know that his series extends into algebra.
Ray’s Algebra, part second by Joeseph Ray.
Key to Ray’s Algebra by Joesph Ray. Contains the key to Ray’s Algebra book one and two