If a student has mastered addition and subtraction in Foundations, I recommend he move to Gamma. There will be review of single digit multiplication facts and skip counting, and you will see this when you compare the scope and sequence of each book. But, after studying the new material in Gamma and comparing it with Foundations, I am persuaded that a lot more than 1/3 of the book is new. I hope the following explanation helps.

In Gamma there are word problems for area and perimeter, money, skip counting, single digit and multiple digit multiplication throughout the book. There are none in the Foundation Student text. The ones that were added later in the Teacher Text are all of the same kind on one page. When you see the Gamma Student you will see the significant improvement. In fact, there are word problems in all the books.

Measurement, which was presented in "Special Lessons", (inches in a foot, pints in a quart, etc.) is now not just in a special lesson or two, but reviewed and used in applications throughout. This is a major improvement, as this is one of the best ways to apply math skills being taught in multiplication.

As a former high school math teacher, I saw that if there were two areas most students were weak in, they were multiplication and fractions. (As an aside, I have also counseled many, many Math·U·See graduates of Foundations who were in the Intermediate Text and still skip counting). So, while I understand that there is an overlap of concepts in Gamma and Foundations, there is a lot more than the material covered in lessons 21-30 that is new. I didn't know how else to write the curriculum and have room for all of the improvements. With all that has been enumerated in points 1-3, I would estimate at least half of the book will be new, challenging and beneficial to students coming from Foundations.

I can see that if a student finished Foundations and had really mastered all of the material, that only about half of Gamma would be new, but I think most students will find it worthwhile and profitable to do the Gamma after finishing Foundations.

Intermediate to Epsilon

When comparing the Scope and Sequences of Intermediate (classic) and Epsilon, you will notice a review of basic fraction concepts. The Epsilon does review these concepts, but it also teaches reducing fractions, prime factorization, mixed numbers, improper fractions, converting to decimals and percents, and more linear measure. Over half of the topics in Epsilon are completely new topics.

In addition to the new topics, Epsilon contains word problems that are much improved over Intermediate, and the student that has studied simple fractions will be challenged by the applications of fractions found there. Multiple digit multiplication and division are also reviewed and employed in the application story problems, as well as the systematic review pages.

When all of these factors are considered, roughly 2/3 to 3/4 of Epsilon will be new to the Intermediate grad. (And when you do Epsilon you will understand how much 2/3 of a book really is!)

As a former high school math teacher, I found that the two critical areas of need for my students were knowing and understanding multiplication and fractions. So, I would encourage students to be proficient in the foundational math abilities of multiplication and fractions before attempting decimals, percents, and Pre-Algebra. For most students, my recommendation upon finishing Intermediate would be to study Epsilon.

Advanced to Algebra 1

If a student has mastered the advanced material and feels comfortable with what he has learned, then proceed to Algebra 1.

If the student needs more review of the algebra concepts in Advanced, you might consider doing Pre-Algebra next.