Here's the short answer: you don't!
Say what?!?!
Yep, that's right. You don't finish an entire curriculum! Your kids will be fine, and you can relax a little. Read on for some tips to at least get closer to finishing, as well as my reasoning for why you shouldn't worry about completing the entire curriculum.
First, do your kids really need to do every lesson in the curriculum? Probably not. As you go through, you will likely find lessons that are redundant - things your child already knows, or lessons that don't fit what you think your child needs to learn. It is perfectly ok to skip those lessons! Public and private school teachers do this all the time.
Second, no one anywhere in the world will ever learn everything there is to learn. There will always be gaps in what is taught, learned, and even simply what material is available. Don't worry about cramming it all in. Some of those gaps will be filled in later, and some never will be filled in. That is just fine! Think back on your education - to all of the things you did learn, wanted to learn, should have learned, and filled in later. Most of us have a mix of "did/wanted/should have/filled in later" learning. I can't think of anyone that doesn't have this mix.
Third, go to any public (or even private) school, and see how many of the teachers there finish every lesson of every bit of curriculum. I have yet to meet a single teacher able to accomplish this. There are simply too many subjects, not enough hours, and too many other things that get in the way. The best teachers I know skip around in the curriculum, focus on the class's strengths and weaknesses, and adjust along the way. As a homeschooling parent, I do the same thing.
My son is turning 14 in August, and for his math and social studies curriculums (well, for all of his subjects actually) we skip around, just touch on some lessons, do some lessons in their entirety, and skip some lessons outright. As you think about your child's curriculum, and find yourself panicking about how many lessons there are in each subject, and how many weeks to get through it, with how many hours there are in a day, RELAX.
Skim through the first six weeks of each bit of curriculum. Are there lesson that your child is already familiar with? Yes? Either just touch on them for a refresher, or skip those entirely.
For math, if there is a lesson my son already knows, I might give him 10 out of 30 problems, just to keep in practice. So, if he's suppose to do 30 graphing problems today, but he already knows the material, I will ask him to do 10 problems to check that he has indeed learned the material previously, and then I will give him tomorrow's lesson today. Do this several times, and eventually you've cut out an entire week, or even month, of lessons during the course of the school year. Eventually you'll get closer to finishing the curriculum, even if you don't actually make it to the very end. Last year, for math we actually covered 1 1/2 math curriculums by using this method. We skipped several chapters entirely, and just touched on a few. We cut out several weeks of study on integers and single-variable equations. Later in the year, we cut several weeks on certain types of word problems and some graphing. Will my son be at a disadvantage because of it? No. The parts we skipped were material he already knew, or material that is covered in his science curriculum, or is material he has learned himself through his interest in computer programing and video game physics. Not only that, but because he learned them in a context that was interesting to him, and in which he had a practical application, he actually understands those bits of his math curriculum far better than if we'd only focused on the curriculum itself. Look for those places where the curriculum overlaps your child's interests or other subjects. Then, decide if you can just lightly touch on those areas or skip over them entirely. You'll save a lot of time which you can then devote to other subjects and activities. Plus, you also save time that can later be applied to more difficult lessons.
For world history, my son already knows a huge amount about the major wars of the last few centuries. When we get to those time periods, we'll touch on these events, but we won't study them in depth because my son already knows more about them than our curriculum actually covers! Again, that is weeks cut off of the curriculum. This is an area that fits my son's wanted to learn. Because he wanted to learn about war and military history, he's covered a huge portion of world history on his own with no curriculum, and no formal teaching/learning. Your children will do the same with their own individual passions.
Don't worry about finishing an entire curriculum. Your child will be perfectly fine, even if you don't finish all of the material. They might even be better off if they are learning in a relaxed environment rather than an environment in which there is a stress over following the plan completely. After all, what is important isn't the calendar and making sure lessons #1 through #32 are all completed. What is important is that your child is LEARNING. If you do 15 lessons, and your child has learned a substantial amount, isn't that better than doing all 32 lessons and having your child only remember the barest of details?
Focus on the LEARNING, not the calendar and curriculum plan.
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Updated: Thank you so much for the fantastic comments! And, so many within just a few hours of posting this!