Strayer-Upton Practical Arithmetics is a series of 3 small math books published in 1934 and then reprinted in 2007, each intended to cover 2 grade levels. The first book is designed for 3rd/4th grades, then 5th/6th, and the third book is for 7th/8th grades. (Apparently, formal math lessons were not commonly taught before 3rd grade back then – something we should think about when reforming education of today!) Since these were copyrighted in 1934, they are how “math used to be taught,” which also means that not much in the way of algebra was really introduced (though there is 1 chapter in Book 3 titled “Equations”). Most people did not take algebra and other higher-level math in that generation. In fact, I think at the time many people stopped their education after 8th grade. Book 3 has, among more practice of typical middle school math topics, chapters on:
- Using Electricity and Gas
- Account and Budgets
- Putting Money to Work
- The Work of a Bank
- Thrift and Compound Interest
- Stocks and Bonds
I have the first book – actually, it’s been sitting on my shelf for 4 or 5 months with me wondering if I was really going to use it. My son is 14 years old (9th grade) but has LDs in math meaning that we were just now working through fractions (last part of last school year and starting this fall.) I knew that a lot of this book would be repetitive for him but fractions were worked on towards the end and I didn’t think it would be good to completely skip this book and jump into Book 2. I had intended to use it to work on the fractions that he was getting tired of doing in Teaching Textbooks 6 and the supplement workbook I had him working on to refresh his fractions skills from the summer memory loss. He had started dreading math every day and I knew I had to change things for him, at least a little to get him recharged again. So I pulled out this book and kind of talked to him about how many of the exercises are intended to be done orally. The book is small in width and height (about 5” X 7”) and has mostly just text written on them without a lot of pictures, so I was concerned that he might not like it at first. (Their size is easier to deal with than the Ray’s Arithmetic books, which are really narrow and hard to hold open to your page. Other than that, I cannot comment on how they differ from Ray’s in approach and flow of concepts/teaching. Ray’s Arithmetic books were written in the 1870s.) I told him we would read through the book together, do as much orally as possible (writing is also a struggle for him), and for areas that were pure review, we would pick and choose problems to do and not do all of them. So he agreed to give it a try for a few days to see how it would go.
But I still wasn’t sure where we should start in this book to make sure his skills were built up to understand fractions. Out of a 500-page book, fractions don’t start until page 447! At first, I thought I’d start here where the bulk of the fractions lessons start, but the more I looked at it, the more I realized that they had been introducing the idea of fractions back when they started introducing multiplication! They also introduced division and “single fractional parts” with the multiplication! (“Single fractional parts” being 1/n, where n is the multiplication/division fact being worked on at that time. Like 1/2, 1/3, 1/4, 1/5, etc.) The Multiplication section starts on page 86 and the first fractions introduced were on page 90. So then I thought, well, we will go back and start with the 2’s times table, do the page on division by 2’s, and then the page on what ½ is/means. Then I figured we would skip over to the 3’s and just do those pages, too. Then so on and so forth, going through all of the times tables, their introduction to division with the number, and then the introduction of the fractional part using that number as the denominator. Maybe this way, even though I think he already knows most of this, it would reinforce the relationship of multiplication, division, and fractions since they are, in fact, completely interrelated. Then I thought when we got to the fractions on page 447, and they assume he has already been working with those single fractional parts for the last 370 pages, he will be ready for the rest of the fractions lessons.
So that Wednesday we started on page 86. We got through 6.5 pages in about 30 minutes. Of course, if he were a 3rd grader, we would do 1, maybe 2, pages/day. Then we did another 6 pages on Friday. (We were only using this book 3 days/week.) I started seeing how they teach this stuff in a different order and how it makes a lot of sense and may actually help a lot of students tie the concepts together much better.
- They start by teaching what multiplication is.
- Then how to multiply by 2.
- Then they do a little practice with the 2’s times table.
- Then they turn it around and divide by 2 and show the “division table” with just 2’s.
- Then they easily extend dividing by 2 to taking 1/2 of something and relating how division by 2 and taking 1/2 is the same thing.
- Then a page of word problems and identifying the operation (+, -, X, and /.)
- Then it moves right into multiplying 2-digit numbers by 2.
- Then with carrying.
- Then with 3 digit numbers.
- Then with 0’s in the 2nd/3rd digits.
Then has lots of practice with those, which he was able to do COMPLETELY in his head as mental math using his own “self-talk” because of how it built up so incrementally! And this is a kid with working memory, visual memory, and sequential memory deficits, which is why math has been so hard for him for so long! Instead of teaching ALL of the times tables first and then moving into multi-digit multiplication where they have to use all of those times tables while they learn the process of multi-digit multiplication, they teach it as a natural extension of the very first times table they learn – the 2’s. Then they eventually add in each of the other multipliers as they learn those! What a different approach! Another benefit I found from this approach while we went through the 3’s is since all of the multi-digit multiplication problems (with carrying) in that section are all using 3 as the multiplier, he is getting constant, repetitive practice of multiplying by 3 without the rote drill of the 3’s times table drill. It’s being done as part of (slightly) more advanced math, but because he is not doing ALL of the multipliers at one time to practice the multi-digit multiplication process, he is getting focused practice on just this times table. Later (just a few pages later), they mix up the practice so he gets both the 2’s and 3’s as multipliers, but I like how it “chunks” things into small bits.
He exclaimed several times, both Wednesday and Friday, that this book makes things SIMPLE and EASY and why did they have to complicate math so much! LOL! He feels so smart when he works through these problems either all in his head or just writing the answers as he works through it in his head. He is having more great days in math now and is pushing himself farther than he has in the past. And now he seems to do better on his multiplication drills (we are using Calculadder) after spending 30 minutes in this book doing mental math. He sees it, too. He feels like his brain is just pumping out numbers by that time and gets so pumped at how well he does! Now I know (but haven’t told him more than once) that we are still in the easy problems – this is essentially a lot of review for him and so it should be relatively easy. But he is making great strides in mental math that he never had before, wanted to pick the hardest of the problems to work in his head, and even when we were almost done and he said his brain was starting to feel tired, he made a comment that he liked it because that meant he was exercising it and getting smarter! Talk about a confidence boost! He is perfectly fine working through page after page for 30 minutes, doing as many problems as necessary in each section and is happy! (So far! LOL!) In the past, if I tried to get him to do 2 Teaching Textbooks Math 6 lessons in one day, kind of compress them for particularly easy lessons, he would balk complaining about doing more than 12-13 problems/day. So I can move much faster and easier in this book without him thinking he’s doing double. LOL!
I think this book really does build up so incrementally that the students don’t even realize they are doing something new and harder than they were a few pages before. It’s kind of cool, actually. I wish we could have started it earlier. At first I felt like if we try to do this whole book that we will be “starting over AGAIN” or “backing up AGAIN”. But really, when you see this kind of transformation, are you going to take that away? By the way, because he is being so successful with this so far, and because he is able to do 5-7 pages/day without taking more than 30-40 minutes to do it, we have decided to just charge right through the book doing most of the pages/lessons all the way through rather than skipping a bunch of stuff to just do the multiplication, division, and fractions. Doing that many pages/day, we will actually be able to finish the book around Christmas time or shortly afterwards and move into Book 2. That will cover 5th/6th grade math and he will learn all of the fractions, decimals, ratios, geometry, and even measurements better than he is learning it now. If we took a year to get through that book (seems a reasonable approach since we would be moving more slowly than this first book) he should be thoroughly ready for pre-algebra, if not algebra at that time. This is about how long it would have taken with Teaching Textbooks Math 6 and Math 7 as well, so we don’t lose any ground. In fact, we might even GAIN ground if he doesn’t need a full pre-algebra program. I doubt we will do much, if any, of Book 3. It depends on how ready he is for algebra and if he needs more time with application of the fractions, decimals, percents, and ratios that Book 3 would give him with those topics.
This book (I believe they are all setup this way) has frequent reviews, diagnostic tests with annotated sections to review for missed problems, drill work (do these 100 addition problems orally in 3 minutes), and all kinds of variety! And even little “game-like” challenges that amazingly prepare them for the next incremental concept that they introduce on the next page. It’s almost like they “sneak” in little things to prepare them for the upcoming math! The book is not intended to be written in, so there is no space to “work the problems.” I have read that some people use a “sit on the couch reading together with a whiteboard in the student’s lap” approach, and others (particularly older children) use it as independent study, just writing the answers on paper for grading. We do a bit of both. A lot of reading together and doing oral problems, and now, a bit of him working problems in a notebook because he found he wanted to be able to look back and see how good a math day he had and show his Dad, which he couldn’t do when we used the whiteboard. LOL!
Here is a link to some sample pages, though many of these pages are from the very beginning of the book so are for the young beginners.
I have also inserted my scanned images of some pages below. The first several pages in that file show how they incrementally go from introducing ½ (this is right after learning to divide by 2), relating it to dividing by 2 as being the same thing as taking ½ of something, and then into multi-digit problems. Pay particular attention to the little “game” on the bottom of page 94 and how that relates to learning to carry when multiplying on page 95. If you “work through” each of these pages, you will see that no teacher book is required – the very way they lead the student through each problem guides and leads the student to the next level/step/concept. (Answers are provided in the back of the book.) You can also see on page 93 and page 95 how they “take time out” to teach how to do something before moving on through more problems. I like the “Think …” approach – it promotes good “self-talk” for the student.
The last 4 scanned pages show where the section on fractions starts late in the book and how it progresses through for a few pages. I find their approach to fractions very “common sense” style instead of math/mechanical style. For example, after the student has become very comfortable and familiar with what ¼ of something is (because they have been doing it since they were introduced to the 4 times table/division table!), they reason that if you know that ¼ of 12 roses is 3 roses, then ¾ of the 12 roses will be 3 times that many, or 9 roses. Very rational. Also, everything is constantly, and very quickly, related to real life problems rather than doing practice problems in a vacuum. AFTER they show problems in real life, THEN they will have some sections of just plain practice to get the process down. Kind of opposite of how we do things today!
I hope this review of our short experience with Strayer-Upton Practical Arithmetics Book 1 is helpful for you. I know there isn’t a lot of information on the web about this, and even fewer example pages, so I am happy to share as much as I can to spread the word about a simple, easy-to-use, and CHEAP math program that teaches math thoroughly. Enjoy!