Math is one thing that I can rely on. Math is math, and regardless of what the common core constituents might say, it doesn't change. That means you can use the same math
Note: This post is a little outdated now, as the years have gone by and I've chosen different options for my younger kids. But I still see these resources as very solid choices, and maybe our experience with them will help you as you make decisions for your own kids.
At the beginning, when the eldest was starting kindergarten and first grade, the big item on my wish list was the Saxon manipulatives set to go along with their math
But guess what? That manipulative set was stinkin' expensive! Woo howdy! I didn't have the triple-digit sum they wanted me to shell out for that thing – and this was 15 years ago; it must be even worse now. So I bought something else (see below) and made do for awhile. Amazingly enough, over time (as I was never able to save up enough money for that manipulative set, lol), I discovered that we could make do with a few items around the house. And most of the other things, we didn't really need, anyway. And I came to the conclusion that using manipulatives for math is an over-rated concept.
Our Homeschool Math
Grades K-3: Abeka Math Workbooks. Guess what – these are very reasonably priced, especially if you don't buy the accompanying teacher's materials. Who needs them at this level? I think we can all add the numbers in our head at this stage in order to check our child's work. Abeka may very well offer manipulatives, but I never bought them. We used Legos or dried beans when necessary, which wasn't very often. These workbooks are cute and colorful. There is plenty of space for young hands to write big numbers. Kids can even work independently, because there are age-appropriate explanations of each new skill. There is also repetition and review sufficient to keep the child proficient at prior skills.
Grades 4-8: Saxon 5/4, 6/5, 7/6, 8/7, and Algebra ½. I think in the homeschool world you either love Saxon or you hate it. I happen to love it – although for these years only. Before these levels, you have to do the whole manipulative thing. After these levels, Saxon does something weird with Geometry and Algebra by combining them into the same course. I don't like the way that looks on a high school transcript. But for the later elementary and middle school years, Saxon is the bomb, in my opinion. John Saxon was one of the pioneers of the perpetual review concept, which now is considered fairly standard, I think. It makes sense that you would keep a child practicing everything he has done before – but it didn't used to be that way. In my public school classroom we would finish a chapter on fractions and go on to decimals — and never see the fractions again. In the Saxon
The other thing I LOVE about Saxon is that it is NOT a workbook. The child must show their work on a separate piece of paper. I think this is VERY important when learning math, y'all. Kids need to learn how to line up numbers before adding them. Kids need to learn how to copy problems correctly, to write numbers without mixing up the digits. Kids need to learn how to do math NEATLY, how to organize a page of work, how to show the answer clearly. These are important skills – almost as important as the actual math itself – and these years are the perfect time to learn them.
And yes, we do both Saxon 8/7 and Algebra ½ (which is considered to be a pre-algebra text, from what I understand). I've read that they are very similar and so it is not necessary to do both – I say give the kid as much opportunity to solidify general math concepts as possible before moving on to real Algebra or Geometry. They need to have those procedures in their head so thoroughly that they don't have to think about them any more, so that the very new and abstract concepts of Algebra and Geometry can be given their full attention. It is very difficult to learn Algebra if you still struggle with general math.
Depending on your child, you may be finished with the sequence up to here by the end of either seventh grade or eighth grade. In our family, we skipped the Abeka Kindergarten math book and went straight to the first grade book while still in kindergarten. That meant that my kids were ready for Algebra I in eighth grade. If your child is taking Algebra I in ninth grade, that is totally fine. Many colleges do not require four full years of high school math, anyway. For more about that, see my post about How to KNOW What Your Teen Needs to Get Into College.
Related Reading: 7 Honest Homeschool Math Curriculum Reviews from Susan Landry of A Sparrow's Home. She touches on several that we've never tried.
Grade 8 or 9: Elementary Algebra, by Harold R. Jacobs. This is an engaging book with explanations that kids can follow, which means it works great for independent learning. My kids loved the comics at the front of many of the lessons (whatever it takes, right?). This is a solid Algebra I textbook. It is not cheap, but if you are going to use it for multiple children over the years it is fairly reasonable. I have no doubt that it is no more expensive than other math curriculums (curriculi?) that are not as thorough nor understandable. Besides, unless you agree with core
Related Reading: Online Math Curriculum: CTC Math vs. Aleks
Grade 9 or 10: Geometry, by Harold R. Jacobs. Why mess with a good thing? The Jacobs Geometry is just as great a textbook as the Algebra one. Again, the kids used this mostly independently; they asked me when they had a question or couldn't understand something. But that did not happen very often, which tells me that these two textbooks did their job. I don't have the time to sit with my kids and learn every lesson with them. Buying a textbook like this means that I don't have to — which is why I say that homeschooling high school is not as hard as many people think it's going to be.
Related Reading: Homeschool High School Math Online with Mr. D Math
Grade 10 or 11: Intermediate Algebra, by Lial, Hornsby, and McGinnis. This textbook was written to be used at community colleges. Hence it is written to the student, with thorough explanations, practice problems, and even tests built in. We tried a fancy-dancy intellectual Algebra 2 textbook first and hated it. This textbook is down-to-earth and easy to understand. DO NOT buy a recent edition — no need to waste your money. Find the cheapest older one (in decent condition) that you can get. The math is still the same!! As the homeschool mom, YOU determine what is required in your math courses. No need to bow to the pressure of having to be “current.”
Related Reading: Teaching Textbooks 3.0 Homeschool Math Curriculum Review
Grade 11 or 12: Precalculus, by Lial, Hornsby, and Schneider. We had such success with the Lial Algebra 2 that we used her textbook for Precalc also. As the student reads the explanation for each lesson, there are guided problems to solve. Then a full exercise set for independent practice. My kids worked through EVERYTHING independently; then I graded their tests. We also purchased the Student's Solutions Manual so they hardly ever had to ask me much of anything. Pretty handy! Again, get an older edition that fits your budget.
None of my kids has made it to Calculus in high school. I did find a copy of Saxon's Calculus at a