Math 2

Math 2: Free Curricula

The Center for Innovation in Teaching Mathematics offers a free math teaching program for grades K/1-12. The program was developed for public schools in the UK, however there are a significant number of home-based educators using this system in North America. The program is called Mathematics Enhancement Programme (MEP) and all the necessary materials are available in PDF version online. The files can be downloaded free of charge, however you will need a password to unlock some of them. Please go to the MEP homeschool users group for both the password, and additional support in adapting this school curriculum for home use.

MEP is the only complete math curriculum I am aware of that is offered in its entirety, free of charge online. Its goal is to raise children who are thinkers. The approach taken is to make math fun, so these lessons are intended to be easy for both student and instructor. This system is a good option for those who want a hands-on approach - say, for a visual or kinesthetic learner - or for the parent who disliked math as a student and wants to offer a non-traditional program to their own children.

Very little preparation is required of the parent, as the lessons are all laid out in the teacher’s materials. If you are fond of math you will appreciate that the program teaches your kids the concepts behind their addition facts and multiplication tables. If you are not terribly sure of your own math skills you will feel more secure in teaching the MEP math, because it shows you how to teach.

To find the teaching materials, scroll down to the School Curriculum Materials section on the web site. For each primary grade level you will find a student practice book, copy masters and lesson plans. There are also colourful posters for hanging on the wall, and these are incorporated into lessons. Sometimes a textbook will be mentioned in the lesson plans, but parents who have used the system say it is absolutely not necessary to have one.

At the secondary level you’ll find the practice book and a fairly broad range of teacher support material, including lesson plans. For some grades, online interactive worksheets are available. This can be a good break, if you have kids who aren’t fond of writing or who dislike worksheets. It is also an option if you are looking for ways to incorporate ICT (information and communication technologies) into your homeschooling.

My experience with MEP thus far is rather limited, but from what I understand it doesn’t cover skills in the usual ways or sequence. Not to worry, the lesson plans look very helpful! A split page describes the activity on the left, with notes including materials you will need on the right (any manipulatives needed are usually in the teacher support materials or in the copy masters.) Skills taught for each lesson are listed, and there are diagrams and illustrations where these are needed. High school lesson plans are slightly less visual, but give the parent-educator a good bit of background to help with the teaching. If you need to prove progress I’ve been told that one lesson on so many is set up to be a test, and there are also exams available at the site.

Because the program is intended for use in British schools and begins with Kindergarten, you may not find the grade levels correspond exactly to those we use in North America. If you aren’t sure where to place your child from looking at the course content, don’t hesitate to ask the kind folks on the users group for their advice. They are a friendly lot! Canadian and American users may find they need a little help with problems that involve either measurement or currency. Again if you aren’t able to find solutions for yourself, seek out the users group.

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Ray’s Arithmetic is actually a whole series of textbooks written by Dr. Joseph Ray in the 1830’s. You may find these in different editions, but the core books of the series are: Primary Arithmetic, Intellectual Arithmetic, Practical Arithmetic, Higher Arithmetic, Elementary Algebra, and Higher Algebra. These will take you from first grade through most or all of high school.

Ray’s Arithmetic books were the most popular American math texts of the 19th century, and are still being used by homeschoolers today. If you want to use Ray’s Arithmetic you have the option to purchase the books in hard copy or on CD (see links at the bottom of this page) but because the original texts are in the public domain, they can also be downloaded free of charge from Google Books (servers located in the US only.) Some of the texts are also available free from sources that allow free downloads, regardless of the location.

Dr. Ray’s approach will be familiar to any parent who learned math in a more traditional, textbook and drill methodology. There is an early emphasis on word problems, and with added focus on mental (or intellectual) math, for which the second book is named. These skills tend to be weak areas of many more contemporary math programs, but with the epidemic of students who rely on calculators for even the simplest math problems this back to basics style of approach is regaining popularity. The so-called Singapore Math (not free but reasonably priced) follows a similar approach. It is a program recommended by a large number of homeschoolers and other educators, and the famed academic success of students taught following a Singapore styled mathematics program hints at the effectiveness of this dual focus.

Does the very idea of such an old fashioned methodology turn you off? Don’t turn away from Ray’s just yet! While you may think the 19th century math was about memorizing tables through mindless repetitive drills, I find it striking that in the earlier books so many of the problems are followed with the challenge for the student to answer, “Why?”

Other programs use diagrams and blocks to help students visualize how adding is just quick counting, multiplication quick adding of same numbered groups, and so on. If you really look at it, Ray’s is teaching the same way - minus the manipulatives. As the titles of some versions hint, it works through induction and analysis. The process involves building one skill upon another, and leading the student to draw conclusions from information he already knows. No concept is ever introduced until the proper foundation has been laid, and the whole process teaches the student to think logically.

The Ray’s Arithmetic user group says that this approach to teaching math helps to increase verbal comprehension skills, and to eliminate the phenomenon of the dreaded word problem. From the very beginning each problem is phrased as a word problem, so children using Ray’s never know there is any other kind of problem until they are well beyond thinking to fear word problems.

Especially in the lower grades, Ray’s is a good choice for a student who is an aural learner. It has few illustrations, and I believe the earlier texts were meant to be read aloud by the teacher who would ask the questions in a drill format, calling upon students for the answers to the questions posed. This means you don’t even need to print out the texts: simply read the lessons aloud with your children directly from your computer if you are on a tight printing budget.

Before you cringe at the thought of doing lessons orally, give some of the simpler lessons a try. There are benefits to oral lessons! You may find that your children, like mine, are keen on being quizzed orally. I suspect they enjoy both the competition of trying to answer first, and the fact that they never know how many more questions are coming (it can’t be overwhelming if they don’t see how many more are coming!) Oral lessons increase interaction between you and your kids, and they give you a chance to deal with any errors or difficulties immediately, before your child has made a whole series of errors of the same type. (If you’ve ever had a child misunderstand the directions on a worksheet & do the entire thing wrong because of it, you’ll appreciate the ability to nip things in the bud!)

Ray’s Primary Arithmetic is sometimes recommended as a text for grades 1 & 2. It introduces the four basic arithmetic operations (+, - , x, ÷) and takes an extensive look at both American and British currency, as well as measurements. Ray’s Intellectual Arithmetic (roughly grades 3 & 4) reviews the arithmetic operations and introduces fractions - speaking of them first as “parts of numbers.”

By the time you reach Ray’s Practical Arithmetic (grades 5 & 6) you will be teaching a much broader range of concepts including place value, Roman numerals, factoring, the metric system and progressions. Extra examples can be had through Dubbs’ Arithmetical Problems, of which Dr. Ray was a co-author, and Test Problems for Practical Arithmetic. Higher Arithmetic is recommended for grades 7 & 8, and possibly 9 depending on the student. Follow up with algebra when ready. There are later books for geometry, trigonometry, and even calculus if you wish to continue using the Ray’s series through the later years of high school.

Ray’s books place a certain emphasis on business-related concepts (interest, discount, taxes, insurance - even bankruptcy.) The word problems in the first two books focus on farming and commerce for the most part, and the later books teach the more specific skills that would be needed to run a farm or shop. Measurements introduced are far more detailed than anything studied today, including the difference between Troy, Avoirdupois and Apothecaries weight, dry and liquid measure, long measure, square measure and circular measure.

Currencies and measurements are taught as tables of equivalences (so many pennies to a nickel, so many nickels to a dime, so many dimes to a dollar, etc.) that include a great number of terms not commonly used today. You may wish to study these more from a historical perspective, teaching your children why it was important for people in Dr. Ray’s time to know these conversions. Some practical experience (e.g. through reading recipes or perhaps canning fruits or jam) might be helpful when it comes to teaching dry and liquid measures, and weights.

Time is introduced in Ray’s, but not telling time per se. As with the measurements and currencies, the approach is to memorize a table of equivalences. You may find you need to supplement with clock worksheets or some similarly visual method for telling time.

Since I have seen some folks asking on forums whether the keys or teacher’s editions are necessary, I should say that a few of the answers are stated or worked out in the actual texts for those who need them. Although not really needed for the primary book, there is a solution manual for the mental and practical arithmetic. It is called Key to Ray’s Arithmetic.

Teachers editions for the four core books are available on the aforementioned CD. Ruth Beechick’s Parent-Teacher Guide (one book, covers four core books) is also used by some parents for scope & sequence, scheduling, games, and other ideas on how to use the original books. There is also a set of workbooks written by Dr. Rudy Moore, which are keyed to the series but provide much more visual interest. They also include quizzes, for those who want to use them. Four workbooks are available per grade, for grades one through four.

Where to Download Ray’s Arithmetic Free of Charge
I’ve listed several versions of the books, in case of download problems and for those trying to match a key to a text. Bold links can be used anywhere in the world. Non-bold links are for US downloads, though you may be able to view the items from other locations without the download option. Most texts are in PDF format, though other versions may also be available. If you need a PDF reader there is a list at Wikipedia. If you have links to other internationally available versions, or to books you don’t find in this list such as the geometry, trigonometry or calculus books, please feel free to post them in a comment. I’ll add them to the list!

Ray’s New Primary Arithmetic for Young Learners (1877)

Ray’s Arithmetic, Second Book : Intellectual Arithmetic, by Induction and Analysis (1860)

Ray’s New Intellectual Arithmetic (1877) or Ray’s New Intellectual Arithmetic (1877)

The Principles of Arithmetic : Analyzed and Practically Applied : For Advanced Students (circa 1856) or

Practical Arithmetic, by Induction and Analysis (circa 1857) or Ray’s New Practical Arithmetic (circa 1877) or

Ray’s New Practical Arithmetic (1877) or Ray’s Arithmetic, by Induction and Analysis (1885)

Ray’s New Test Examples in Arithmetic (circa 1883) or Ray’s New Test Examples in Arithmetic (1883)

Dubbs’ Arithmetical Problems : To Supplement Ray’s New Practical Arithmetic (1893)

Ray’s New Higher Arithmetic (circa 1880)

Key to Ray’s New Higher Arithmetic (1881)

Ray’s Algebra, Part First : On the Analytic and Inductive Methods of Instruction (184

Ray’s Algebra, Part Second : An Analytical Treatise (circa 1852) or Ray’s Algebra, Part Second : An Analytical Treatise (1857)

A Key to the New Higher Algebra, by Benjamin Greenleaf (1865)

 

 

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Resources:

Ray’s Arithmetic on CD - $59 USD for 26 books, including all the core books plus teachers editions

Complete 8-Book Set - $84.99 at ChristianBook.com

Beechick’s Parent-Teacher Guide - $10.99 USD at McGuffey Readers World, or $99.99 USD for the complete 8-book set

Workbooks - $9.95 USD each at McGuffey Readers World

Printables for Ray’s Arithmetic - includes flash cards, math fact sheets, etc.

This work was created by Ruby of Freehold 2, and is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 2.5 Canada License.

Excerpts copyright quoted authors. Please visit their sites to read more, and respect the terms of their copyrights. Thanks!