Saxon K-3 is in a very easy-to-use, scripted format.
Each lesson begins with a "meeting", where the child practices things like recognizing a daily pattern, counting coins, skip-counting, fact memorization, charting the day's weather, etc.
After the meeting, there is a lesson that contains the day's new material. Everything is scripted for the parent, which is very helpful if you're a new homeschooler or not totally comfortable teaching math. It isn't stilted or unnatural to read the scripts, though once you're more experienced you might read the lesson yourself and put it into your own words instead.
The worksheets which follow the lesson (not present in K) are two-sided. Because of Saxon's incremental format, each worksheet contains practice on what was just learned, as well as a review of everything covered so far. This constant review is amazingly helpful. Things that are learned are not forgotten. You can do both sides of the worksheet at once, or do one half during math and the other half later in the day.
The meetings CAN get tedious for the adult. The practice is very good for the child, but after 4 grades of repeating patterns it's totally understandable if you want to throw the meeting book through the nearest window. I admit I did stop charting the weather after a while. But....
Do not skip things! The real beauty of Saxon is in the way it's planned so meticulously. You don't just learn a new skill one day, each skill is built up to with careful planning. The flow is so gentle and natural, resulting in lessons that feel "easy" and there are not a lot of discouraging wrong answers. Everything in Saxon has a purpose, even if you don't see it at the time. A complex skill, like, say, long division, is the culmination of smaller skills that have been learned and practiced over a long period of time. So y the time you finally learn the actual long division, the child fully understands not only how to perform the function, but also how and why it works.
In Saxon 5/4 the format changes to a more traditional text book that is written to the student rather than to the parent. You can still very easily sit with your child and go through the lesson together. Or a more independent student can do the lesson completely unassisted. I do suggest keeping up with the lessons, though, in case the child needs help with something. It's good to be familiar with exactly where they are in the process of learning those bigger skills, and to know the particular vocabulary the lessons have been using.
Starting in Saxon 5/4 there is no more meeting. Rejoice! It's replaced by a section called "mental math", in which there are a handful of problems meant to be calculated mentally and recorded on the special recording sheets (I personally redesigned the recording sheets, as I didn't like theirs as much https://greencarrot.wordpress.com/wp-admin/upload.php?item=393 ).
Every day there is a times fact sheet (master sheets in school texts, pre-printed in homeschool versions). You're supposed to time the student for 5 minutes while he does the sheet, but many people count up instead, or don't use a timer at all. It depends entirely on how that particular student responds to pressure and self-competition. Some love it, some hate it.
After mental math there is the short lesson introducing the new material. This is almost always very easy, as Saxon takes things in small steps rather than throwing a difficult skill at them all at once. Following that there is a small number of problems directly related to the lesson. Then there is a longer section of review problems, which practice everything learned previously. VERY useful, so don't skip these! Some people suggest doing only odds or evens in the review set, but I have found that doing so results in poorer retention, as a lot of things end up never being practiced.
Please, don't skip! The time invested in this review pays off, big time.
Saxon will take your child from Kindergarten up through high school. If one year is spent on the extra pre-algebra work, you will get through Algebra 2. If not, there is an "advanced mathematics" book that is for very mathy students who are going to pursue college work in math or engineering. We are currently in the 7th grade book (8/7) which includes a lot of pre-algebra and algebraic concepts.
Grade levels used
Strong foundation, traditional math, no gimmicks, incremental development