For math, I use a spiral-approach for our spine, and use other resources as supplements.
I like Saxon Math because it's a spiral approach, the lessons are thorough, the problems are challenging, and it offers lots of practice. It's a classic. It's been working great for homeschoolers for 25 years.
Measuring a line. In Saxon, concepts are taught initially in a lesson and then problems reviewing that concept keep appearing on the worksheets for a long time, allowing the concept to solidify and become easy. Eventually, the textbook spirals back and builds upon that concept... like then measuring a line in centimeters after learning how to measure in inches, and then comparing inches to centimeters, etc.
I was one of those homeschool students who switched to Saxon (from a mastery approach) in 6th or 7th grade. The problems were hard. The workload seemed massive. I was getting terrible scores. The concepts were easy ... baby stuff ... things I'd learned years ago ... but I couldn't remember how to do them. I was embarrassed.
The reason Saxon felt hard, is because I had kinda been cheating. I would master a new concept, and look over my worksheet of 25 nearly-identical problems repeating that concept ad nauseum. I didn't have to learn the math. I could just employ my short term memory for one of the problems and fill in the pattern for the rest.
Ten lessons later, I had caught up. I was spending 3 times as much time studying math as I had been using the mastery approach, but I should have been spending more time all along. I was reviewing now, and therefore keeping everything fresh. My accuracy improved, and so did my confidence. Confidence is a big thing when it comes to math.
Confidently graphing our family's shoes as part of a Saxon lesson. Papa could probably use a few more.
A lot of parents look at the huge Saxon textbooks and think, "Ew, text. Why would I do that to my Kindergartner?" It's important to realize that with the early grades, they aren't even looking at the textbook (that's a script for the teacher). They are manipulating concrete objects before manipulating numbers on paper. A lot of other math programs do this as well, but it's something that is important to me and I'm glad Saxon does that.
Playing with pattern blocks during a Saxon lesson.
Now that I've given a speech on the merits of a spiral approach, you can laugh at me while I explain all the parts we take out.
Playing "store" during a Saxon math lesson. The kids can't get enough of this game, especially when I let them use the barcode scanner app on my cell phone. It beeps when it scans, so they get to pretend they're actually checking out at the register. Of course, they have to add up the prices themselves, but that's the whole point.
I skip the Meeting Book. (It's too repetitive, and geared to a classroom setting.) I don't buy the manipulative kit either. I skip all the assessments, because I already know how they're doing and which problems are tricky for them. There, that's getting better. I skip almost 30 lessons at the beginning of the textbook, because they are refreshers and we don't need them (our summer breaks are shorter for sanity's sake). I skip duplicate fact sheets, because drilling on a worksheet is awfully mundane, and not as interesting as Khan Academy, or games, or even flashcards. I skip whole lessons if I'm confident they've already got it down, or if it's the day after Halloween and we have candy to do math with.
"Look Mama! An ABAB pattern ..."
"Challenge problem: if you wanted to make your candy last for a whole month, how many pieces should you allow yourself to eat each day?" (Challenge problem answer: Loads and loads on day 1, and then the stash mysteriously disappears due to poor behavior...)
Reflections on odd and even numbers
After paring Saxon down, (there's still plenty to go around, I promise) I have a cushy schedule to fill up with delectable math supplements. I prefer this to advancement to the next grade, generally. Adding depth and complexity and agility is more important to me than racing ahead.
Singapore Textbook and pan balance
Supplement 1: Singapore
Singapore Math has been a wonderful companion to Saxon, because it has different strengths. It is mastery-based, *best of both worlds* so they can have that experience of really digging into a concept and sticking with it until you can accomplish something fancy. These are good just to have as a reference if they need something explained differently. I also love them when we need a fresh face to math.
He did it. Now he knows exactly how many Unifex cubes his "so-soft" weighs.
Their workbooks are prettier (some are in full color) and switching to Singapore for a few weeks can give them a second wind. Their workbooks are good if you would rather avoid worksheets, but still want to habituate them to the occasional page of problems. Maybe you're going on a road trip and want something they can do independently. My favorite Singapore resource is their Intensive Practice workbooks, designed to give you interesting and challenging problems once you already grasp the basic concepts.
I've been putting one of the "challenge problems" up on the board each week for each of them. It's a chance to pass on the great feeling of solving a problem, rather than simply doing a problem.
Supplement 2: Flashcards
I mentioned that I skip some fact sheets. I make this up by playing a flashcard game at the end of the year (after they finish their mathbooks and we burn them in effigy), that we call "Break My Record."
Basically, I use a box-full of laminated fact flashcards and drill them with a timer, keeping track of their "record-breaking times." The following year, they have to break those records-- they have to be even faster. Even an adult can benefit from drilling 17 minus 9 as quickly as possible, and it's fun. They beg to do it in the middle of the school year. Saxon teaches facts in families (like all the doubles [such as 12+12] together), and I drill them in those families with a grand cumulative finale of "all the facts you've learned so far." I'm a fan of competing against yourself. I spend a few minutes a day for about a week playing "Break my Record," but this is the only time we drill for speed. Here is an article explaining why. I also love what it says about making mistakes: "We now know that making math mistakes grows your brain. MRI scans of people taking math tests find that every time the test-taker makes a mistake, a synapse fires in their brain. There are actually two possible synapses; the first one comes from people making a mistake, and the second one comes from noticing they've made a mistake."
Supplement 3: Math-U-See
I don't have this curriculum, but I borrowed my mom's old manipulatives, and they're awesome. We use them as needed to explain concepts concretely.
Supplement 4: Khan Academy
What a cool, free resource! While I don't rely on this for math (too much screen time), it's perfect for those occasional days when they're fighting the very idea of school and I need to trick them into it.
Supplement 5: Games
A simple printable math game for numeral recognition.
I'm really glad I made the decision this year to take one day a week playing math games instead of learning lessons and solving problems. It's a sacrifice, but I believe it pulls it's own weight. We play board games and card games; most of the time they're real games, but they certainly teach real math.
Clue teaches logic, Chutes and Ladders teaches subtraction, Sorry teaches one-to-one correspondence, Battleship teaches graphing, War teaches number sense, Life teaches place value, and Monopoly teaches you how be the dictator of a small country. We've often come to a lesson and my kids will say, "Oh, I already know how to do that from playing ________." I love game day.
Supplement 6: Tasks
I just discovered this link to "visual, engaging math tasks" this week, so I can't say I've explored the idea long, but I really liked the day we spent doing it. They're math puzzles, essentially, and they're creative, and challenging, and group-oriented. My dad would love them :)
Here's another link to more math tasks. I'm excited to try these.
Supplement 7: Euclid
Math is beautiful.