This was the book that started it all for us. We had been using another algebra book that I just wasn't happy with because I didn't feel like it covered enough algebra topics. I went to a homeschooling conference and heard the author, Stan Schmidt, give a talk about what math should be like and I was sold.
Much to the horror of my eldest daughter, I came home with the Beginning Algebra book and presented it to her as her next math book. "You mean I have to do algebra over again?" she asked. "Yes," I replied, "but this time you'll actually learn it.
After I explained the concept of Fred to the kids, they all wanted to get their hands on the book to read the story and see what it was all about. My daughter dove into the book and finished it before the end of the school year. Ever since then this has been our "go-to" algebra book.
Beginning Algebra is the first book to come with a Home Companion. This is definitely worth getting as it breaks down the main book into 188 lessons. Not only does it give the day-to-day break down, it also gives additional problems for the student to work on.
Life of Fred Beginning Algebra covers:
numbers and sets, integers, equations, solving for unknowns, exponents, motion and mixture, factoring (everyone's favorite!), fractions, square roots, quadratic equations, functions and slope and inequalities and absolute value.
All of this is covered in a day in the life of Fred, a five year old math professor at KITTENS University in Kansas. His tone is very conversational, which makes learning the math a lot more enjoyable. For example we learn about linear equations in the context of Fred helping a chaplain write a sermon about ten young girls waiting at night to meet an important dignitary :)
I have been very please with this set of algebra books as I believe it to be a very thorough coverage of beginning algebra. If you would like to read more about Fred or to order any of the Fred books, you can go to my website.