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Homeschool Crew Review: Ray’s Arithmetic


I had to chuckle when I found out we were going to be reviewing Ray’s Arithmetic for the Homeschool Review Crew.  This is something we discovered about a decade ago and have used ever since for the early years of homeschooling. I love it because at the beginning Ray’s Arithmetic is entirely oral, manipulatives are encouraged, and each problem is related to real life.  That has been a great fit for my little ones through the years.

However, we got not only the basic series to review, but also many other books.  In fact, the complete Ray’s Arithmetic CD   contains 38 volumes.  This includes the basic 8 volume Ray’s Arithmetic series that we’ve had in a hard-back book version for years, as well as algebra, geometry, trigonometry, analytic geometry, calculus, and more.  Applied math books include navigation, astronomy, book keeping, physics, and logic.   For the teaching parent, there are valuable helps such as a Manual of Methods and answer keys. 

An organized, energetic teacher could conceivably teach all math from grade 1 to calculus using these books, as was done in the past.  Students would learn solid problem solving skills and gain a thorough understanding of both theory and applications of mathematics. 

In fact, this is how millions of children in America’s past did learn.  More than 100 million copies of Ray’s Arithmetic were sold in the late 1800’s, and many of these were probably shared among siblings.  An added benefit of using these texts today is the fascinating glimpse they afford into the past.  Different prices, different concepts, different ways of living, and different ways of speaking all come through in these books.  It is interesting to realize that Laura Ingalls of the Little House series and Betsy of Understood Betsy may have used these books.

Our experiences with the early grade books

The first book, Ray’s New Primary Arithmetic, meant to be studied orally, is a lot of fun.  It covers approximately the first two grades.  We did not have the Manual of Methods when we started with Ray’s and I think it would have made a difference.   The next two-year book, Ray’s New Intellectual Arithmetic has been used almost independently by my children for the first year, but the sections on fractions, ratio, and percentage required more of my time.   If a child is given a moderate amount of help, I think that the rest of the elementary program will not require an increase in mom’s weekly time, since concepts build on each other.  On the other hand, mom does have to be involved every step of the way.

Miss 7 continued her work with Ray’s New Primary Arithmetic, doing all sorts of addition and subtraction word problems.  She only occasionally uses her fingers and toes for the calculations, now. Soon no one in our family will be doing that anymore.  (Sigh!)  Because of constant practice, she can clearly translate a word problem into arithmetic.   

Here is one of the routine problems she did, “A hen had 9 chickens, but a hawk carried off 6 of them:  how many were left?”  To this the response of our little chicken-lover was, “Ohhhh!  Do we have hawks?”  She did get it right, though, once we dealt with the hawk issue. 

She also did the following addition review question, which I thought was pretty impressive, “John bought 5 pears for 6 cents, 3 pears for 4 cents, and 2 pears for 5 cents:  how many pears did he buy?  How much did they all cost?”

Miss 9 is busy with division in Ray’s New Intellectual Arithmetic, but first she did a multiplication review.  After having done exclusively word problems for the earlier lessons, she was able to manage questions like the following for the review:

“A stage starts from a certain town, and travels at the rate of 8 miles per hour:  at the same time, another starts from the same place, and travels in the same direction, at 4 miles per hour:  how far will they be apart at the end of 12 hours?”


Children are prepared for such multistep problems by doing almost all of their arithmetic in word problems, such as, “If 6 men earn $84 in 7 days, how much does each man earn in 1 day?”

Obviously, a child will not be able to complete a huge number of such problems every day.  Another thing to keep in mind is that basic fact drill helps a lot when one is studying Ray’s at this level.  When my older children used Ray’s, I tried to keep up with math drill in a variety of ways; now we use computer programs.

In the past we’ve always dropped Ray’s by the late elementary grades, mainly because the thicker upper elementary books constantly flipped shut when we used them.  Very annoying!  Obviously, anything printed from the CD will not have the flipping-shut problem. Since I think continuing with Ray’s would benefit the Little Misses, I’m considering printing out sections of the books from the CD rather than using my hardback books. 

Our experiences with higher level books

Since we haven’t used the higher levels in the past, my older children have just jumped in to study certain topics for the purposes of this review.  That was a strain on them, partly because of the choice of topics.  However, I think a child who has worked through the series and is comfortable with the old-fashioned language will have an easier time.  

Miss 12 worked on powers and roots (‘involution’ and ‘evolution’) in Ray’s New Higher Arithmetic.  Since we were jumping into the middle of the text, it was a bit of a stretch to convert Ray’s wordy explanations into mathematical ideas.   With practice, I think older children could learn to understand these explanations largely on their own, especially if they worked through a textbook from the beginning.  Since these books were written before calculators, there are detailed instructions for finding roots.  I had never seen some of this material before, and it was fascinating.

Mr. 14 began Ray’s Treatise on Geometry and Trigonometry.  Because this text begins with definitions and is almost exclusively words, it did not seem like math to my son.  He was frustrated by the axioms, theorems, and proofs, and  could not see their value.  This was largely due to the subject matter, which was entirely new to him, although the somewhat old-fashioned language contributed to his unhappiness.   The concepts, however, are clearly presented, and the book is more sensible than another geometry text we have. 

I got Miss 17 to start Ray’s Differential and Integral Calculus.  It begins with a clear description of limits, and I wanted her to be exposed to that concept as well as to basic derivatives before she begins her formal calculus studies.  Of course the new concept of limits was difficult for her, but that’s to be expected when you begin to study something radically different.  Helping my daughter understand limits also showed me a fundamental misunderstanding she’d had for quite some time, and we were able to get that sorted out.  Ray’s does a good job of introducing a young person to calculus for the first time.

Our Opinions

In an ideal world, I would teach my children math using this program almost exclusively.  The Ray’s Arithmetic CD contains a thorough, pedagogically-sound, economical math program for a child’s entire school career.  Any child who has worked through Ray’s will understand math  and will be able to think mathematically.  He or she will also be completely comfortable with word problems and real-life math.  I would still use supplementary fact drill for the younger grades and practice problems for high school geometry and trigonometry.  Some topics such as statistics would have to be added as well. 

But this is not an ideal world.  When I was surrounded by little children, I did not have the time required to use this curriculum properly for the later elementary grades.  I also did not have the helpful Manual of Methods, which would have made a huge difference. Even now, with five kids, I like self-teaching programs and Ray’s definitely requires a teacher.  We are happy with our current math curricula which are almost as thorough as Ray’s and require less of my time, and I do not think we will switch back.

If you’re considering using Ray’s, allow yourself time to read the Manual of Methods before you start your children on the texts.  Also, if your children are not comfortable with problem solving, start them with a quick review of the first book, and then move up to their level. 

Even though I expect few families will want to use this program right from the beginning to calculus, many young children would benefit hugely from the first few books.  That is what our family has done for years, and I’m expecting to go even farther with Miss 9 and Miss 7, using pages printed from the CD rather than the annoying flip-shut hardback texts we’ve used in the past.  Even though we will not switch back to Ray’s for the older children, we may use some of the texts, especially calculus, as supplements.   

I, myself, am interested in the books about astronomy, surveying, and navigation. These disciplines have influenced the world profoundly throughout history, and I know so little about them. Unfortunately, now is not a good time in my life for such self-indulgences.

To read the opinions of other homeschooling moms, please see the Homeschool Crew Review blog  (Note that some families reviewed a different set of vintage texts than we did.)  You can also get more information about the individual books on the Ray’s Arithmetic CD from this annotated book list. Sample pages are available as well.  Watch this video to see why these and other books were collected into CD form for homeschoolers. 

Disclosure Policy:   As a member of the TOS Homeschool Crew, I received the contents of the Ray’s Arithmetic CD for free.  I have also written about my past experience with Ray’s using the hardback texts from Mott Media that we bought years ago.


  1. proverbsmama says:

    I have a few days off this week, so if you give me an idea of what you want done, I will try to help you.

    When I get time, I'll try to go in and cut/paste the actual codes to a few of the pictures on my side bar so that you can see how to do them.

  2. CookieMonsterKatrina says:

    What an excellent, thorough, and helpful review!

  3. DeAnne says:

    Is the Manual of Methods in the public domain?

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