Saxon Math already has a series of book for kindergarten through third grade, and another series that begins with Math 54 for fourth grade and continues up through Calculus. So why this Intermediate series for grades 3, 4, and 5? For the lower levels, at least part of the answer lies in the differences between the Saxon Math program for K-3 and the rest of the Saxon books from Math 54 up through Calculus. The K-3 program is completely different from the other Saxon books. They were written by a different author, incorporate manipulatives, and have a very teacher-intensive form of lesson presentation.
Math 54 and all the texts beyond that were written by John Saxon, Stephen Hake or both of them together. Saxon Math Intermediate 3, 4, and 5 were written by Stephen Hake and, consequently, are more similar to the upper level books than the K-3 series. Those just starting into Saxon Math at third grade level should probably go with Math Intermediate 3 since it ensures a more comfortable transition into Math 54. Those who have been using the Saxon K-3 series up through second grade can go either way, perhaps deciding based on a preference for manipulatives used in the K-3 courses or a preference for the less teacher-intensive Intermediate 3 course. For older students, you need to choose between Math Intermediate 4 and Math 54, and between Math Intermediate 5 and Math 65.
The Saxon Math Intermediate courses differ some from the Math 54 and up courses in layout, and they require a little more teacher involvement. Parents might need to work through presentation of new concepts with students in each lesson, but some students should be able to work independently through most or all of many lessons.
There are four components to the homeschool kit for each level: the student text, a solutions manual, Power Up Workbook, and Homeschool Testing Book.
Each lesson begins with “Power Up” activities. These are a bit more involved than the “Warm Up” activities that begin each lesson in Math 54 and Math 65. Power Up activities include four categories of problems each time: math fact review, count aloud or “jump start,” mental math, and problem solving. Math Intermediate 3 labels the second category “jump start.” Whatever the label, this second category might include oral counting by increments, drawing hands on a clock, thermometer reading, writing a fact family for three numbers, etc. The count aloud category is dropped from some of the Power Up sections in Math Intermediate 4 and 5 since by fourth and fifth grades students should be able to skip count fairly proficiently and will need only occasional review. The separate Power Up Workbook is used for the written activities for the Power Up section of each lesson with one page to accompany each lesson. The top half of each page is for math fact review problems. Then sections for each of the other three type activities might each contain some content (e.g., clock face in jump start) or simply provide blank space for students to write their responses. I suspect that some students will need assistance in completing some of these activities, especially at the beginning of the school year.
After the Power Up activities, a new concept is introduced along with sample problems that are completely worked out. The series includes some work on conceptual understanding as new skills and concepts are taught. However, concepts are taught with written or pictorial explanations rather than manipulatives (aside from fraction manipulatives used a few times in fourth grade), and conceptual development is not as strong as in Singapore Math or Math-U-See. After the new concept is presented, some lesson practice problems provide students with practice only on the new concept. “Written Practice” problems follow with 15 to 20 problems per lesson for third grade that review previously taught concepts. The number of written practice problems increases to 30 per lesson in fourth and fifth grades.