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CCH’s Online Catalog: Grammar Stage Math - Grades 1-6

This page last revised:
June 2001

Copyright 1997-2001




Grammar Stage Math:
Grades 1-6



Using the Online Catalog


Option 1: Ray’s Arithmetic
For 1st-6th, 7th, or 8th grades. Ray’s Arithmetic were the texts used in 19th century America, before its jettison of the classical tradition in education and the dumbing down of our schools, and because of its excellent approach, is CCH’s top choice for arithmetic instruction in the grammar stage.

Option 2: Math-U-See Arithmetic
For 1st-6th grades. Ray’s Arithmetic were the texts used in 19th century America, before its jettison of the classical tradition in education and the dumbing down of our schools, and because of its excellent approach, is CCH’s top choice for Arithmetic instruction in the grammar stage.

Option 3: Professor B’s Mathematics
For beginning or remedial arithmetic students and up. Professor B’s unique, non-graded approach to arithmetic is perfect for older children just beginning formal mathematics study, or those who have had a bad experience with math in public or private school and are in need of some relearning and remediation, or those who are math-phobic or who have a failure mentality about math. It is also perfect for parents who want to teach themselves arithmetic so they can teach it to their children.

Option 4: Saxon Math
For 3rd-6th grades. My personal experience with Saxon Math has been less than satisfactory. I would recommend either Ray’s, Math-U-See, or Professor B’s before recommending Saxon. However, there are some students and parents who take to Saxon’s incremental approach like a duck to water. This option is for them.


Ray’s Arithmetic Series

Ray’s ArithmeticRay’s Arithmetic Set
Joseph Ray, M.D.

For 1st-6th, 7th, or 8th grades. Ray’s Arithmetic were the texts used in 19th century America, before its jettison of the classical tradition in education and the dumbing down of our schools. Over 120 million copies were sold in its heyday. Ray’s teaches arithmetic in its logical progressive order of concrete - mental - symbolic arithmetic, just as Harvey’s taught grammar in its logical progressive order of letters (orthography) - words (etymology) - sentences (syntax). Most early work is done with real objects--blocks, marbles, buttons, etc. Later the work shifts to mental arithmetic with mental images of concrete objects. Then it proceeds to symbolic arithmetic, gradually dropping the use of objects and images and proceeding to computation quickly with digits. In this way the child is led carefully through the three progressive stages in arithmetic: concrete (manipulative), mental, and symbolic. The Ray’s Arithmetic Set includes all seven books listed below, plus the Parent-Teacher Guide for Ray’s Arithmetic by Dr. Ruth Beechick. Again, the suggested grade levels are just that--suggestions only. Once the material in each text is mastered, the child is ready to go on to the next text. Children do not have to be held back to conform to suggested grade level guidelines.

Primary Arithmetic
For 1st and 2nd grade. Primary Arithmetic introduces the four operations along with counting and other basic skills. This text focuses on the concrete or manipulative stage of arithmetic development. It will not take two years to complete this text; CCH recommends proceeding to Intellectual Arithmetic when it has been completed.

Intellectual Arithmetic
For 3rd and 4th grade. Intellectual Arithmetic extends the work in the four operations into higher numbers, as well as introducing fractions, measurements, ratio, and percentage. This text focuses on the mental stage of arithmetic development. It will not take two years to complete this text; CCH recommends proceeding to Practical Arithmetic when it has been completed.

Practical Arithmetic
For 5th and 6th grade. Practical Arithmetic extends basic arithmetic skills to higher levels, as well as providing work on factoring, decimals, percentage, ratio, proportion, powers, roots, and geometry. This text focuses on the symbolic stage of arithmetic development. CCH recommends proceeding to Higher Arithmetic when Practical Arithmetic has been completed.

Test Examples in Arithmetic
For use with Practical Arithmetic; containing additional problems on all topics covered in Practical Arithmetic. The book can be used for additional computation practice in these topics, or for parents to prepare test material.

Key to Primary, Intellectual, and Practical Arithmetic
Contains all the answers for all the problems in the Primary, Intellectual, and Practical Arithmetic texts.

Higher Arithmetic
For 7th and 8th grade, or earlier for those children completing the previous texts prior to the start of 7th grade. Higher Arithmetic includes philosophical understandings; principles and properties of numbers; and advanced study of common and decimal fractions, measurements, ratio, proportion, percentage, powers and roots, series, business math, and geometry. Students that complete this text will have a greater understanding and ability in arithmetic than most of today’s high school graduates, and will be well-prepared for algebra, geometry, and advanced mathematics in the dialectic and rhetoric stages, or even in college. A knowledge of the arithmetic taught in Ray’s was enough to proceed to Harvard and other classical colleges in America’s colonial days.

Key to Higher Arithmetic
Contains the answers for all the problems in the Higher Arithmetic text.

Parent-Teacher Guide for Ray’s Arithmetic
By respected educator and homeschooling author Dr. Ruth Beechick. The Guide includes lesson plans for all the texts, from Primary through Higher Arithmetic, how to adapt the material for slower or faster students, tests for each Ray’s unit in all the texts, games and activities to enhance concept teaching, and more.

Ray’s Arithmetic Workbooks
The workbooks are not part of the Ray’s Arithmetic Set. The workbooks are also not necessary, as plenty of exercises are included in the texts. But they are available for use with the Primary and Intellectual Arithmetic texts for those who wish to use them. The above texts and the Parent-Teacher Guide, as well as the workbooks, can be purchased separately (rather than in one set) by contacting the publisher, Mott Media.


Math-U-See Arithmetic Series

Math-U-See ArithmeticMath-U-See Arithmetic
Steve Demme

The Math-U-See program utilizes systematic review over an extended period of time, and manipulatives, to establish the link between seeing math and understanding math in children. The program provides the interlocking, colorful blocks and fraction overlays to teach math, along with the curriculum to provide the systematic practice and reinforcement of concepts. The goal of Math-U-See instruction is not only to teach a student how to do math, but to also simultaneously understand the concepts of math. Because of its design, this program also provides teaching and practice in the grammatical work of translation from one type of mathematical representation to another; i.e., 2 blocks and 7 blocks makes 9 blocks, and 2 + 7 = 9. One final note: the suggested grade levels are just that--suggestions only. Once the material in each course is mastered, the child is ready to go on to the next course. Children do not have to be held back to conform to suggested grade level guidelines.

Foundations of Mathematics
For 1st and 2nd grade. The child who can count to nine and write their numbers is ready for this stage of the curriculum. Topics range from place value through measurement, and cover operations through an introduction to multiplication. The teacher’s manual includes instructions, examples, practice problems, answer keys to the student text, extra word problems, and tests with answer keys. The student text has four worksheets for each lesson. You will need: the Foundations lesson by lesson instruction video, teacher’s manual, and student text, and the manipulatives (they only have to be purchased once for the entire 6-year curriculum). Also recommended is the Skip Count Tape and Coloring Book, which helps students learn the math facts, and the fraction overlays. While the initial cost may seem high, the Foundations series covers two years of instruction, and the manipulatives, fraction overlays, and skip count tape and coloring book do not need to be purchased again in subsequent years. 37 lessons. Foundations can also be used in 3rd grade with children whose formal mathematics instruction has been delayed until after the mastery of phonics, reading, and penmanship. Take the Foundations Placement Test to see if your child needs this course or if he ready to move on to Intermediate Mathematics.

Intermediate Mathematics
For 3rd and 4th grade. The child who has mastered the addition, subtraction, and multiplication facts, and understands the underlying concepts, is ready for this stage of the curriculum. The course begins with a review of concepts learned in Foundations, and proceeds from reading & writing numbers to one million through probability, graphing, and map reading. Along the way the child learns division, fractions, decimals, percentages, and more. The teacher’s manual includes instructions, examples, extra problems, and answer keys. The student text has four worksheets for each lesson. You will need: the Intermediate lesson by lesson instruction video, teacher’s manual, and student text, fraction overlays, and the manipulatives. Also recommended is the Intermediate tests & word problems, and the supplementary blocks for use in this stage of the math curriculum. 41 lessons. Intermediate Mathematics can also be used in 4th grade with children whose formal mathematics instruction has been delayed. Take the Intermediate Placement Test to see if your child needs this course or if he is ready to move on to Advanced Mathematics.

Advanced Mathematics
For 5th and 6th grade. (Their website says for 7th and 8th grades, but a Math-U-See representative made it clear to me that this is not because children in 5th and 6th grade cannot do the work with the proper preparation (the previous Math-U-See courses), but because most modern math curricula teach these concepts in 7th and 8th grades. The concepts in Advanced Mathematics are still arithmetic concepts, for the most part, proper for the grammar stage, allowing children to go on to algebra and geometry in the dialectic, which is proper for the dialectic stage.) The child who understands and can perform all the basic operations with whole numbers and fractions is ready for this stage of the curriculum. Topics range from changing fractions and decimals to percents through positive and negative numbers and probability. Along the way he learns operations with polynomials, basic geometry, ratio and proportion, squares and square roots, and more. The teacher’s manual includes instructions, examples, extra problems, selected solution pages, and answer keys. The student text has four worksheets for each lesson. You will need: the Advanced lesson by lesson instruction video, teacher’s manual, and student text, algebra & decimal inserts, manipulatives, and fraction overlays. Also recommended is the Advanced tests & word problems. 36 lessons. Advanced Mathematics can also be used in 5th and 6th grades with children whose formal mathematics instruction has been delayed. Take the Advanced Placement Test to see if your child needs this course or if he is ready to move on to Algebra.


Professor B’s Mathematics Series

Professor B’s MathematicsProfessor B’s Mathematics
Everard Barrett

For beginning or remedial arithmetic students and up. Professor B (Everard Barrett) takes the subject material of arithmetic, which in modern public and private education is traditionally spread over seven to eight years of expensive textbook/workbook materials and instruction, and presents that material in three texts, three workbooks, and a charts book. The concepts are presented contextually, as a developmental flow, like a continuing story. These developmental steps are like the rungs of a ladder; mastery at previous rungs provides readiness for the next connection. “Arithmetic can be effectively taught as an upward, progressive climbing of the ladder without gaps,” rather than as a spiral review (the incremental approach). Professor B’s texts, Mathematics Power Learning for Children, restructure the traditionally disconnected, fragmented content of arithmetic and inform parents how to consistently tell the truth simply in all the operations on the whole numbers, fractions, and decimals, from basic to advanced levels of skill. This truth-telling approach to arithmetic stimulates and activates a child’s natural capacities for mastery of mathematics, reduces mental tension related to math, teaches math as a contextual story that makes sense, enables rapid and thorough understanding, eliminates remediation and sole rote learning, and allows sustained mastery of skills.

Texts have 150 to 160 pages each, and are non-consumable; they can be used for each child in the family as often as needed. The consumable workbooks contain the student’s practice exercises, and each child should have their own workbook. The workbooks have 131 to 144 pages each. The charts book -- a single non-consumable book containing all the charts needed for the concepts introduced in Book One -- contains detailed instructions for speed practice; counting to one hundred and beyond; doubling numbers mentally; acquiring strong skills in column addition; and maintaining mastery of the multiplication facts.

There are three levels in Professor B Mathematics. Your child may go on to the next level when he has satisfactorially completed each level, regardless of grade. Professor B Mathematics has been designed to allow children to proceed at their own pace, whether slow or fast, it matters not. Level One includes the non-consumable text, Mathematics Power Learning for Children Book One, the consumable Workbook Level One (one per child), and the non-consumable Chart Book. Level Two includes the non-consumable text, Mathematics for Power Learning for Children Book Two, and the consumable Workbook Level Two (one per child). Level Three includes the non-consumable text, Mathematics for Power Learning for Children Book Three, and the consumable Workbook Level Three (one per child). Professor B has produced videos which correspond to each of the three levels. These videos do not contain material that is left out of the texts, but they were produced to help math-phobic parents learn to teach math to their children. They are not necessary, but helpful for those that would like the security of a little extra hand-holding. When a child has completed all three levels he may go on to Algebra, but if he is still in the grammar stage, CCH recommends going on to Ray’s Higher Arithmetic to learn business math, powers and roots, and all other higher arithmetic practice, or Math-U-See’s Advanced Mathematics (which does not include the business math), before beginning Algebra.

Professor B’s is excellent for those children who have struggled with traditional mathematics instruction (90% of the students in America), or are transferring to homeschooling from public or private school, and are either behind in math, or have been taught the wacky and confusing new-new math or some other such experimental and damaging program, or who have already developed a “failure mentality” or phobia about math. There is no such thing as a student who “can’t do math,” just as there is no such thing as a student who cannot read or write. There are just students who have been poorly taught. The best instructional program in any subject is the one that illuminates the subject and makes it clear for every human being. Professor B’s Mathematics is such a program. I have found that it is also an excellent program for those students in the dialectic stage who have done Saxon Math all through their career, who can do arithmetical computations but who do not understand the *concepts* of arithmetic, which in turn is keeping them from understanding algebraic concepts. It is not traditionally structured and there are no grade levels, so an older grammar stage or even dialectic or rhetoric stage child can begin in Level One (or Two, if math facts have been solidly mastered) and work his way through the entire program in a summer, if he so desires, before going on to Algebra. A parent who is terrified of the prospect of teaching her children math because it was not her strong suit in school can go through the program herself and finally learn arithmetic without the frustration. Professor B’s Mathematics may not be for everybody, and it certainly is not a traditional grade 1-6 series, but as a remedial course or for those who have delayed mathematics instruction until phonics, reading, and handwriting has been firmly established (and that is not a bad idea, and something I would do if I could begin all over again with my children), it is an excellent, excellent choice.


Saxon Math: An Incremental Development

Saxon Math: An Incremental DevelopmentSaxon Math: An Incremental Development
Stephen Hake and John Saxon

For 3rd-6th grades. The Saxon philosophy of instruction is based on the concept of incremental development: the introduction of topics in easily understandable pieces (increments), permitting the assimilation of one facet of a concept before the next facet is introduced. Both facets are then practiced together until another is introduced. The incrementalization of topics is combined with continual review, wherein all previously learned material is reviewed in every lesson for the entire year. Topics are never dropped but are instead increased in complexity and practiced every day, providing the time required for concepts to become totally familiar. Familiarization of topics and skills with constant review allows students to internalize and automate arithmetic operations, the goal of the grammar stage. A further benefit is that the books are non-consumable texts: the child does his math by copying the problems out of the book and solving them on notebook paper. The obvious advantage for families with more than one child is clear - the materials need only be purchased once.

Math 54.
For 3rd or 4th grade. This text begins at the beginning with arithmetic instruction: addition, counting patterns, digits, place value, writing both cardinal and ordinal numbers, and so on through subtraction, adding and subtracting two-and three-digit numbers, simple word problems, beginning multiplication and division, beginning decimals and fractions, measurements, and time and money. The home-study kit includes time tests for facts memorization, an important focus of this year’s curriculum. Continue to use manipulatives (buttons, pennies, etc. - not included) to reinforce old concepts (sets, addition) and introduce new ones such as double digit addition or subtraction, multiplication or decimals. 142 lessons.

Math 65.
For 4th or 5th grade. Reviews numbers, counting sequences, place value, reading and writing both cardinal and ordinal numbers, addition, subtraction; and emphasizes memorization of multiplication and division facts, multiplication and division word problems, number lines, very basic geometry, multiplying and dividing money, adding, subtracting, multiplying and dividing fractions and decimals, conversions, introduction to percentage, etc. Continue to use manipulatives as needed to illustrate new concepts. 140 lessons.

Math 76.
For 5th or 6th grade. Reviews operations with numbers, and emphasizes operations with fractions and decimals, expanded notation, least common multiple and greatest common denominator, factorization, percentages, ratio and proportion, exponents and squared numbers and roots, more word problems and geometry, unit conversions, etc. 140 lessons.

Math 87.
For 6th or 7th grade. Reviews all topics in arithmetic, such as operations, word problems, fractions, factorization, decimals, average, ratio, graphs, proportions, exponents, square roots, rates, percentages; and explores more thoroughly scientific notation, measures, variables, order of operations, signed numbers, equations, mean, median, mode, range, interest, probability, and more word problems and geometry. Math 87 reviews and goes deeper into most of the concepts covered in Math 76. If 76 was a breeze for your child, 87 could be skipped and the year better spent on Algebra 1/2. If Math 76 required your child to expend time and effort to grasp the concepts, Math 87 will provide the review and practice toward automation and internalization. 135 lessons.

Algebra 1/2.
For 6th or 7th grade. This text covers all topics normally taught in prealgebra, as well as additional topics from geometry and discrete mathematics. Students completing the Saxon program through Algebra 1/2 should be well-versed in: fractions, decimals, mixed and signed numbers, base two numbers, arithmetic operations, order of operations, percentages, proportions, ratio, divisibility, rounding, place value, conversions, scientific notation, and word problems, as well as geometric concepts of classifiction of polygons and solids, area and perimeter of planar figures, and volume and surface area of geometric solids. 137 lessons. A Saxon Algebra 1/2 Tutorial is also available with Escondido Tutorial Service.

My personal opinion of pre-algebra is that it is a waste of a year of math instruction. Arithmetic is the proper preparation for algebra, and every algebra program worth its salt contains the instruction included in pre-algebra texts. If a 7th grader is not ready for algebra, he needs remedial arithmetic instruction, and not pre-algebra. Please see Professor B’s Mathematics for remedial arithmetic instruction.

Because of the style of presenting the material, through drill and review using concrete rather than analytical presentation methods, CCH does not recommended continuing the Saxon program into the dialectic stage, for Algebra and Geometry, unless the student is taking Algebra with Escondido Tutorial Service.


Using the Online Catalog

This online catalog is made possible through an association with Amazon.com. Clicking on the book cover will take you to Amazon’s information page about that book. You can look at its price, availability, any discounts currently taken for that title, reviews of the book, and other information, as well as order it if you decide to purchase the book. You can even place books in your shopping cart and save them for purchase at a later time. You can continue to add or delete books from your shopping cart until you are satisfied with your order and ready to purchase. Clicking on your browser’s “Back” button will bring you back to this catalog.

Sometimes books go out of print, or the publisher runs out of stock. Any book not available from Amazon.com for any reason can be searched using AddAll.com, a book shopping site which will scan Amazon as well as Barnes and Noble, Powell’s Books, Book Close Outs and many other new and used book sites. Be sure to also check BookFinder.com for out of print book searches.

Still have questions? Ask me!

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