This post will introduce a free complete math curriculum.

## “When will we ever use this?”

Isn’t that the question we all have while slaving over books filled with rocket-science math? Most of us cannot come up with a compelling answer.

I happen to enjoy working math problems. To me, it is like solving a series of complex puzzles with a long list of rules, which I think of as fun because…I’m a glutton for punishment!

And I have foisted this on my children quite often, to their dismay and my aching ears (from their laments).

But math was not always this way. There was actually a time when it was taught with an actual, practical purpose; to help people live productive and purposeful lives (not just to pass college exams and then forget it).

Imagine that!

There are all sorts of old stuff still available today, and some in print (such as Ray’s arithmetic series done by Mott Media).

But, we aren’t limited in this area, thanks to Google Books. This is where we can find arithmetic series such as the ones done by George Wentworth (and some along with David Eugene Smith)

What we call “Wentworth Arithmetic” is actually a series of books written by George Wentworth and David Eugene Smith and published by Ginn and Company in the early 1900’s.

These books are unique in our age because they were published at a time when arithmetic was becoming important in education, but before the pushes for every child to become a “rocket scientist.”

As we have been enjoying these books, we are finding that there is a unique flavor and focus to them. Here are some of the distinctives we have discovered:

- The problems take basic principles and expand them to cover every facet of living, from measuring feed for chickens to measuring lumber to make furniture and build houses. This is from the preface to Elementary Arithmetic:

…the pupil should be led to his arithmetic through paths which are interesting; that he should see that he is studying a subject which is usable in school, in his play, in his home, and in all other phases of his daily life; and that, so far as possible, the applications should be real to the pupil…It is possible to accomplish all this by arranging the work by arithmetic topics, showing the pupil the reason for studying each topic and the uses to which it can be applied.

- Instructions and tips for teachers are right on the page. No extra books required–this curriculum truly “
**open and go**.”

- Skipping problems is encouraged! The generous amount of questions are only there for extra practice.

Indeed, in general, a teacher should learn the importance of omitting exercises whenever those exercises do not relate to the experiences or probable needs of the pupils.

Preface to Book Two

- The authors present a method for solving problems, then encourage students to formulate their own methods (yes, original thinking is actually encouraged–I can hear your body hitting the floor as you faint away…).

There is so much practicality to this arithmetic that you will never have to hear the question, “When will we ever use this?”

It is gradual, it is logical, and it is thorough.

The only problem may be with children who look at the pages of problems and feel a bit overwhelmed. Reassuring them they will not have to answer every question is one way to overcome their fears. Sometimes we skip over entire sections, other times we do every odd or even problem, still other times we may skip to every third or fifth problem.

Each book covers two or more years in modern grade levels.

- Primary/Elementary covers Kindergarten through first grade

- Book Two covers grades two through four

- Book Three covers grades five through six

- Book Three covers grades seven through eight.

The third book is actually an exploration of consumer and business math. This is extremely important, but woefully neglected, in our current culture.

I know you are excited to peruse the actual files, so here are the links:

And, if you decide to print out the books, here is a free PDF of covers you can download and print out (I created these using Canva, you could easily create your own):

I love, love, love Wentworth’s series of math books and recommend them often, and I think it is wonderful that you have brought them into the spotlight! They seem to be so seldom mentioned in the groups to which I belong, which has always surprised me as I think them such gems, really! You, Sherry, are a tremendous asset to the homeschool community. I love your heart and your work.

Aww–that means so much to me, Amanda! I agree that more of us need to be utilizing these amazing books. Let’s keep spreading the word!

Thank you Sherry! Does this program come with the answer key or a solutions manual? Thank you!

Wish I could’a remembered to mention that–yes, the answers are definitely included, although there is not a solutions manual 😛

Do you think this would be good to do with another math? My children do teaching textbooks but sometimes I want them to do more of this style to fill in gaps. Thanks!

It might, but I think I would narrow down the problems so it wasn’t oppressive to get them all done 🙂

Yes…that would probably be better to narrow it down! Thank you for all the knowledge that you pass along. Blessings!

Hi, Morgan! If I may, I might have a bit of insight that could be helpful…I am not familiar with Teaching Textbooks, but I know that Kate Snow, a math educator whose opinion I trust, does have reservations about how well Teaching Textbooks develops mathematical thinking, so supplementing would likely be a good idea. Effective supplements could be as simple as using manipulatives to work through the problems (if Teaching Textbooks doesn’t require them)…the AL Abacus from RightStart (or any abacus where the ten beads on each rung are divided evenly between two colors…they used to be hard to come by in this design, but lately I have seen a few on Amazon…), or, if word problems are lacking in the curriculum, Kumon has good workbooks that focus solely on word problems, and Singapore also sells word problem books (but if you go that route you’d likely want to start a grade or two lower than that at which your children currently work, as the Singapore word problem books can be quite challenging)…Another potentially great supplement could be the logic puzzle books from Critical Thinking Company—the Mind Benders series and such (or, MEP math is a free conceptual curriculum developed in the UK based on a program from Hungary, and it includes a lot of logic-type puzzles, too, and it is a solid program in-full, but it could perhaps be used just to pull out some puzzles for supplemental work….It may be more difficult to do, because it is developed for use in classrooms, but it wouldn’t be impossible, I think…worth taking a look if cost is a factor, to be sure). If more math facts practice might be necessary, Kate Snow has a supplemental series called “Math Facts That Stick” that is game-based (they can be purchased in pdf format via the Well-Trained Mind website, which was having a 40% off sale on many products, and it might still be going on)…All that said, what “grade level” are your children currently working at? If they are working at 4th grade or lower and number sense could use more development, there is another book in Wentworth’s series that was used in conjunction with Primary Mathematics -and- School Arithmetic Book One over years/grades 1-4, and it would likely work fantastically as a supplement. If I am able to do so, I will link it here. Otherwise, though, the Wentworth series is a well-balanced blend of conceptual and procedural math (probably the most well-balanced math program I’ve come across, quite honestly; we’ve used it for a few years now, and I love it), and I agree with Sherry—you could certainly use it as a supplement, but scale way back on the problems for practice. This is the book in the Wentworth’s series that was used specifically for developing number sense, The First Steps in Number by G.A. Wentworth and E.M. Reed (there is a student “workbook,” too, that was used for practice beginning in Year/Grade 2, and I will link it as well): https://books.google.com.na/books?id=Mty9aJ4kZHcC&printsec=frontcover&source=gbs_book_other_versions_r&cad=4#v=onepage&q&f=false -and- First Steps in Number, Pupil’s Edition by G.A. Wentworth and E.M. Reed: https://books.google.com/books?id=NkM4xdwGSSYC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false .

This is great stuff–thank you for sharing your amazing knowledge with us all!

I have 4th grader and 6th grader in teaching textbooks. Thank you so much for all the resource suggestions! Blessings!

Oh! And this book, too (also by George Wentworth), could be used to good effect, I think, as a supplement for the elementary years….A Mental Arithmetic by G.A. Wentworth: https://books.google.com/books?id=DvoVAAAAYAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false .

That’s great, Amanda, thanks for the link!

What about high school years? Anything similar available with good experience?

I believe the Wentworth series does continue on with options for algebra, geometry, trigonometry, advanced arithmetic, and more.

Very interesting, I had not realized this before. I did look up the algebra and it is right there, but it was difficult to find a teacher’s edition, something that I could not live without if I was using Wentworth (which I do like a lot as I was perusing the book).

I believe the Wentworth series does continue on with options for algebra, geometry, trigonometry, advanced arithmetic, and more.

Wait, I just looked it up and, sure enough, there is a Wentworth New School Algebra, and an Answers for New School Algebra! Here are the links:

https://ia802707.us.archive.org/6/items/newschoolalgebra00wentrich/newschoolalgebra00wentrich_bw.pdf

https://books.google.com/books?id=7xMAAAAAYAAJ&pg=RA3-PT4&dq=answers+to+problems+in+wentworth%27s+school+algebra&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjzvcG9wPv3AhWsl2oFHW8ODu0Q6AF6BAgJEAI#v=onepage&q=answers%20to%20problems%20in%20wentworth's%20school%20algebra&f=false

I’m so glad you found that, I too, appreciate a teachers manual.

Sherry, thank you for sharing this, friend! I had no idea about these math books. We have been long time users of Math U See. And, although I love the approach and that the author is Christian, I do NOT love the increase in price over the years. I will take a closer look at this and consider it for my little ones.

I’m glad I could be of help to you! I so appreciate it every time I hear from you 🙂

Thank you for this post, Sherry.

Can you–or maybe one of the other readers who comment–weigh in on how these books compare to or differ from the Ray’s arithmetic books? I will delve in, myself, but thought someone might have thoughts on it, and be familiar with both sets of books.

I’m just getting started teaching my five-year-old twins. I am not a math-minded person, and a bit intimidated! But I love books of this vintage–I read lots of Gutenberg titles myself, and am reading a few to my children, as I come across any I think they will enjoy.

So I was thrilled to find vintage school books to use–although I desperately wish more would be added to Gutenberg! Scans from other sites don’t clean up the text as nicely, and aren’t as effortless to use.

I’d be grateful for any further comments.

I’ve been looking Ray’s Arithmetic and wondering the same thing!

Thanks Hannah, please note my reply to Christina 🙂

This is a great question. I have pretty good familiarity with both, and here are some of my thoughts:

The Ray’s are more simplified, and the exercises are fewer, so for some children they are less intimidating.

The Ray’s have more direct explanations, which means they are to the point and without any distracting information.

The Ray’s methods for things such as fractions have been forgotten for some reason, when they are actually genius and helped clear some things up for me.

The Ray’s depend much more on mental math exercises, give the times they were written pencil and paper were rather rare items.

The Ray’s in some places are too archaic to be practicable in our modern times.

The Wentworth’s include more actual work for the primary level, so it is easier to use for those just starting out.

The Wentworth’s are a bit more gradual, almost to the extreme of methodical, which can be great for those who are slower or those who like to move quickly and aren’t put off or distracted by loads of problems, but death to those who are easily distracted and overwhelmed.

Since these were written almost a century later than the original Ray’s, the problems have a more modern feel and are more relatable.

While they are still a bit of archaic, they are much less so.

Having said all this, I have had more than one child who did Ray’s exclusively and went on to understand Saxon Algebra pretty easily, and another child who worked through Practical Arithmetic (closely akin to Wentworth) and had the same experience with Saxon Algebra. (To be fair, we only did one-half of the algebra because they were more interested in the practical math since they were not college-bound).

Hope this gives you a better picture of the two!

Thanks so much for this Sherry, you are a star! We’ve used Hoyt’s Everyday Arithmetic in the past, thanks to your previous recommendation. Most recently we’ve been using the Good and the Beautiful’s latest maths curriculum, but my daughter is a bit fed up and bogged down with it, so we’ve talked about returning to a vintage curriculum.

I wonder if you have a preference between Wentworth vs. Everyday Arithmetic? Many thanks for your insights!

I am not certain there is a huge difference, although it is obvious there will be some variations. Since they are both free, it may do good to peruse the books yourself, perhaps even try out a lesson or two with your child to see if he/she fits well with one or the other. You could print out a few month’s worth in one and then if you have a good experience, go ahead and print the entire book.

Thanks for your thoughts Sherry. I’ve been toying with the idea of ‘splicing’ the best bits from both!

You might be interested to know that Yesterday’s Classics have Strayer-Upton available as an ebook that comes with a PDF. Currently they only have book 1 and first half of book 2, but when I emailed them a few weeks ago I had nice reply to say the second half of book 2 would be out in July, and book 3 in December, therefore getting round the difficulties of small books! https://yesterdaysclassics.com/books/mathematics/

Many thanks for all the information you share!

Thanks, Rhiannon. I was aware of the Yesterday’s Classics, but the next book coming out is terrific news! Thank you 🙂

This math looks great! Does this series include time?

Thanks!

Yep, it does!

I can download only the primary math by Wentworth, not other three. Can somebody help me to get the other three books?

Were you able to get the other books?

Hi,

A couple of years back you mentioned Hamilton Math. Is there much of a difference? Which would you recommend?

There actually is a bit of a difference. I have Hamilton’s on my bookshelf, but I cannot remember what the specifics are. You may want to look both up on Google Books and do some comparisons.

Mrs. Sherry,

If you have a child who will be 10 in December where would you start him in the Wentworth Curriculum? While flipping through the second book I’m not sure he is ready for it but is it ok to start a 10 year old in a Kindergarten/first grade book??

If I had a young boy who was 10, I think I would use something that wasn’t as grade specific, such as Wentworth’s Complete Arithmetic, so that he will not feel self conscious about grade levels in math.