Option 1: Ray’s Arithmetic

 

For math, one option is to use Ray’s Arithmetic series for Levels 1 through 12. This traditional, mastery-based curriculum has been trusted for over a century, rooted in the classic one-room schoolhouse approach. Developed in the 1800s by Dr. Joseph Ray, it emphasizes mental math, practical problem-solving, and a strong foundation in arithmetic, with a natural progression to high school topics like Algebra, Geometry, and Trigonometry. Ray’s Arithmetic lets students progress at their own pace until they master each skill, building rigorous math abilities that apply directly to real-life situations. Best of all, it’s in the public domain, making it accessible and affordable for homeschool families looking for a no-nonsense, classical approach.

 

Some books cover multiple levels. Don’t be fooled by their small size—they’re full of comprehensive content. Students advance through the books at their own pace, ensuring they fully understand the material before moving on. The recommended daily math time is calculated as 5 minutes per day multiplied by the student’s age. For example, a ten-year-old would spend 50 minutes per day on math. Do not move on to the next lesson until they’ve mastered the one before.

 

Digital copies and teacher’s guides for these books are available in the public domain. For help with lesson planning, refer to The Eclectic Manual of Methods for the Assistance of Teachers by J. T. Stewart, which provides practical guidance for teaching with Ray’s series.

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Below is a breakdown of the levels and the corresponding sections per level.