Primary Mathematics, for grades 16, is designed to integrate adult supervision with independent student practice. The goal is to establish a mental foundation on which to build more advanced math competency. Singapore does this by introducing key concepts with concrete examples and pictures before moving logically to treatment of the abstract concept.
How Do These Work?
Each grade level is divided into two semesters, A and B. At the core of each semester is a student textbook and a workbook, accompanied by a teacher's guide (or home instructor guide). Intensive practice books supplement each semester level; extra practice and challenging word problem books are available for each grade level. The student textbook and workbook are the only essential elements for each semester, though Singapore educators insist the consistent success of their students in the fields of math and science is due to extensive practice.
The Primary Math series balances repetitive drill and creative problem solving. It moves students more quickly and rationally toward mastery of abstract concepts than most math curricula. Compared to U.S. materials that cover a large number of topics fairly superficially, PM focuses on core math concepts that will best prepare students for higher math. There is an emphasis on homework and practice, and an effective mix of word problems, drills and mental calculation.
Teachers should guide students through the textbook lessons. While many students could conceivably work through the majority of the material on their own, to really grasp the information they will need assistance. Because of the concretetoabstract method implemented by the series, teachers are encouraged to illustrate important ideas using handson activities and manipulatives. By contrast, the workbooks are designed to be completed by the students without assistance, but adult interaction will strengthen the process. An emphasis is laid on developing communication skills within the language of mathematics.
Instruction can be paced to the needs of individual students. In most cases two or three pages from the textbooks will be sufficient for each day. The accompanying section from the workbook should be completed independently by the student. The series is suitable for both classroom and home school instruction.
The average U.S. student is behind the Singapore scope and sequence, so you may need to start with a level lower than you think you need—use the placement tests (see below) to evaluate this.
Our Honest Opinion:
Primary Mathematics has proven very popular with people wanting to supplement other math curricula, and in that case, you'll want to choose the books that best meet your need. But if you're just beginning and want to use it as a full curriculum, start with a "Semester Pack": one each of the Textbook, Workbook and Home Instructor Guide. Don't buy a whole year's worth at first—take the time to find out which pieces you will use. After you've used it for one semester, and want to go on...

If you never used a particular book, don't buy it again! A number of our customers have told us they use only the textbook or only the workbook, but their recommendations have not been consistent so we leave the "either/or/both?" decision to you.

If you used the Home Instructor Guide only for the answers, consider the fact that there are just two inexpensive answer keys for the entire series (one for grades 1A3B and one for 4A6B)!

If your student needs a little extra practice, buy the Extra Practice book for the whole year.

If he needs a lot of extra practice with a variety of extra challenges, add the Intensive Practice books for each semester.

If he needs more of a brain stretcher, consider the Challenging Word Problems books.
Additional Information:
Comparison of Scope & Sequence for Standards & U.S. editions(through 6th grade)
Comparison of Scope & Sequence for Standards, Common Core & U.S. editions(through 5th grade)
If you're ready for the next step, you may want to use the Dimensions Math or the New Elementary Math series.
Singapore Math recommended this as the best one for us to carry as a follow up, though they offer others. Some customers who have used the Primary Mathematics series have liked it, others have not, so evaluate before you go on!
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