Intellectual Math (3-4)


This is the second book in the series.

(For grades 3-4)

Video lessons coming . . . 

Update (July 2018): New video lessons have been postponed for the time being until further notice.

Meanwhile, you can download the complete book here:

Ray’s New Intellectual Arithmetic

Back to Primary Math

Return to Ray’s Arithmetic Home


  1. I just discovered this website today, and as a user of Ray’s, I just wanted to say Thank You for your efforts to assist the homeschool movement. It is a priceless gift in more ways than one.

    Kimberly Beaty

  2. Hi! Thank you for all you have done. It has been a great help to my family and I. I have a child that will be beginning Ray’s Intellectual Math soon. I was hoping to continue with your wonderful videos. Do you know when they may be available? Again, thank you so much!

    • I’m glad they’ve been helpful! I’m currently developing a full year course that is based on Ray’s Intellectual Arithmetic: grade 3-4 math. So it actually covers two years: 360 lessons. It will be available first through Ron Paul Curriculum, probably in August. In the meantime, while I’m working on them I will be posting selected video lessons on YouTube from these courses (grade 3 & 4 math)… Later, when I get my free time back, I will get back to doing all the lesson pages and videos for this site. Thanks so much for your patience!

  3. Does this mean our best bet is to purchase just your math program, if allowable, through the RPC? (price??) With children needing it this fall, I’d prefer to have the aid sooner rather than later, but I am not interested in purchasing the full RPC, if that makes sense. 😊

    • Let me find out if the math course can be purchased separately through RPC as a stand-alone. I know that for members who are enrolled it’s $50.

      • Great! Thank you so much!! 😊

      • I checked with Dr. North (director of the program). To be able to purchase and access the course through RPC you’ll need to subscribe and pay the annual enrollment fee ($250 per family). The courses are available only to those who are fully enrolled.

      • Hello! I am back just to check with you – Can you tell me if there is a thorough answer key for any of the Rays available anywhere? That is my main need. I have the parent’s guide by Ruth Beechick and the little “answer key” in the series; however, they give random, minimal answers. It would be so helpful to me to have the solutions so I do not have to do the problems myself and try to stay ahead. 🙂

      • There is a complete answer key available from Mott Media. It’s for Primary, Intellectual and Practical. But be aware, there are some errors (wrong answers, incorrect units) in this! Even so, a very useful and valuable guide to have for going through the Ray’s books.

  4. Thank you so much for creating this! I have been trying to use Ray’s for about a year (kids 7, 4, 1) and continue to be sabotaged. I plan but just can’t seem to move forward and keep starting over. I am very encouraged by the simple manner in which this quality text is taught–thank you for the resource and the example! Can you update us about how/when we can get the videos for 3 and 4, etc.? Will they be available outside RPC at some point? Thanks!

    • I will be posting a few selected video lessons from Math 3 later this month, then during the summer, a few from Math 4. At some point, I will offer the courses as standalone courses separate from RPC. I’m just not sure how soon that will be. Please stay tuned.

  5. Elizabeth says:

    How are you? Hope all is well. I have a daughter who is using Saxon math 4/5
    ( she completed the stage) & is going on SaXon 5… she does her lessons &
    struggles. Her average in Saxon math is
    between a low B & C… My question to you is switching to Ray’s Arithmetic
    could possibly help her with her weakness in the lessons she is not doing so well in Saxon math?

    • Hi, Elizabeth. My apologies, apparently I didn’t get back to you with an answer to your question! I think Ray’s will probably help your daughter if she is struggling with Saxon. Give the Intellectual Math problems a try. See how she does with them.

  6. Hello,
    We just started Ray’s Arithmetic and have enjoyed it, but are stumped on the wording. My daughter started the fraction lessons, and understands the original concept, but as the problems progress, we both get lost. For example, it will start of asking 5 is what part of 7 which is 5/7. No problem. Then it moves to 3/5 of 30 is what part of 23? We get that 3/5 of 30 is 18, but don’t understand how 23 is connected to that, even if the answer is 18/23. From there is progresses even more to 3/4 of 12 is what part of 5/6 of 24? The answer being 9/20, but I just don’t understand the connection. The wording is throwing us off. Is there a different way to explain this?

    • Those types of problems are to help your student work with fractions in a sequential way, using short chains of reasoning, to help her move beyond seeing them simply as isolated “one-offs” in a given math problem — relating different quantities to one another. This will be beneficial for understanding ratios later on.

      Could you please refer me to the specific Ray’s problems that prompted your question? (Lesson NN, prob. NN) Thanks.

  7. Mark McCue says:

    I am working on problem 26 of lesson LXXX and cannot for the life of me figure out how they came up with an answer of 9%. The holder disposed of the note (face value of $50) 2 years before it was due (in 3 years) meaning he had it for one year at 6% interest, or $3.00. Even with the Key to explain the answers, I still can’t figure it out.

    • Hi, Mark. That problem is worked out in my RPC Math 4 course. Here is a link to the video for that part of Ray’s Lesson LXXX where you’ll find problem 26. Hope it helps!

      • Mark McCue says:

        Thank you so much! The explanation makes perfect sense. As I’ve discovered with several of the word problems, the issue is not so much the arithmetic as it is the English. I was not aware in this instance that the problem involved 2 people; a seller and a buyer who gets the whole three year’s interest in only two. Thanks again!

  8. Any idea what “soon” means?? 😊 No pressure, just planning our new year with hopes to utilize Ray’s! 😊

    • Hi, Kimberly. Good to hear from you again! I have had some major disruptions during the past year involving employment and place of residence and now my wife’s and my primary business had to be relocated to a different city. I think I will have to change “soon” to “postponed until further notice”. I was hoping to get back to the lessons last year after I finished the RPC courses. But right now I don’t have a suitable place to produce new videos. I am very sorry. Hoping to remedy that by early 2019.

      • Sorry to hear of your troubles!! Totally understand the need to postpone!!
        God Bless and keep you as you work out the details, and we’ll just go at it o our own! 😊

  9. Mark McCue says:

    Paul, I’m unable to follow the logic behind the solution to problem 58 of lesson LXXX in intellectual Arithmetic. There, it talks about a partnership of two men who invest $100 and $200 respectively but in the answer key it says one had $1200 for one month and the other $2400 for one month. How are those numbers, (and the solution) arrived at?

    • Mark,
      I have reviewed that problem. Now I know why I skipped it in teaching my Math 4 course! I’ll look into it further as I, too, am wondering how they arrived at the numbers they did. (A sorry situation when two grown men cannot figure out the answer to a 4th grade math problem!) If I find a suitable explanation I will post it here for you. Thanks for your question.

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