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  1. I think having a story in mind helps to make sense of the steps of long division. You might enjoy this blog post: The Cookie Factory Guide to Long Division
  2. For this reason, it's a good idea to choose a homeschool curriculum based on which one best helps the parent understand math, not which one is most attractive to the child. But I also think that one of the great things about homeschooling is how we parents grow and learn along with our kids, especially on the topics we didn't quite get during our own school days.
  3. Awhile back, I wrote a series of blog posts expanding on what Jackie and Farrar are talking about. There are two very different ways to look at learning and understanding math, and the perspective you choose will make a world of difference to your child's future. If you're interested, you can find my articles here: Understanding Math: A Cultural Problem. While I said earlier that you can teach mathematical understanding with any curriculum, there are some that make it easier than others.
  4. You've gotten a lot of good advice so far. Here are a few more things you may want to think about... (1) Your son is only eight years old. He has plenty of time to learn math. Things he doesn't get now will be much easier after he's matured a bit. This age is a great time to take breaks and follow rabbit trails. You can come back to your curriculum between the breaks, but don't feel bound to it. Here are some ideas for blending math adventure with ongoing practice. See also How to Talk Math with Your Kids. (2) You don't have to change curriculum, unless you decide you want to. You can use any curriculum in a way that builds mathematical thinking, if you do it the "buddy math" way. (3) Games are often better than worksheets for providing lots of practice to develop mastery of a topic. Kids enjoy them and don't realize how much math they're doing as they play. I've posted lots of games on my blog that require nothing other than what you already have around the house: cards, dice, pencil and paper, etc. See also Learning the Math Facts. (4) Math is a much wider and wilder country than the "tame" bits included in a curriculum. And often, kids find those wild, unexplored areas much more interesting than basic arithmetic. Math that captures a child's imagination can make the tedious stuff seem more bearable. Living math books are a great way to explore. (5) With or without a curriculum, your son will have gaps in his knowledge. That's the human condition. But if he learns to enjoy learning, then gaps can be filled as needed, when he discovers them, even in high school or adulthood. The main thing now is for him to learn that math is "figure-out-able."
  5. Your Bundle War is a great math war variation. I love the idea! Here are some other multiplication games your group might enjoy: Multiplication Models The Product Game Contig
  6. I always found those word problem books to be great practice for my kids when I used the levels a year or two "behind" their current grade level. Here are a couple of sample problems, to show what I mean. I think these problems would be appropriate for most 7th-grade students. From a "5th grade" level book A "6th grade" level problem I also have a blog post on how to think your way through middle- and high-school level math problems. Your son might find it helpful: The Case of the Mysterious Story Problem And the MathCounts program is an excellent source for middle school practice problems, too. You don't have to do the competition itself, but it is fun to get some friends together and try the Club program. How to Translate Word Problems (A sample video, on my blog) More Problem-Solving Tips Videos Problem of the Week Archive Practice Plans Order more practice problems Or try the previous year competition puzzlers Best wishes!
  7. I have posted a wide variety of math games on my blog, from preschool level to middle school (or beyond). This post lists them all: I've also written several books on homeschooling math in a playful way, but the games on my blog will take you far, no purchase required.
  8. I agree with Farrar. Before you think about switching curriculum, try taking a break from the work and just playing with ideas for awhile. There are so many interesting things to do with math beyond the regular textbook work, and it will give his brain a chance to recharge. Here are a couple of posts from my blog that may help: My Favorite Math Games Trouble Finding the Right Math Program
  9. She might enjoy some of the challenges on these websites:
  10. A change in notation often signals an increase in abstraction. Along with that increase in abstraction comes the power to talk about whole new classes of number relationships. For example, in elementary school, we deal with just-plain-number equations. Simple, single relationships, like 2+3=5. In middle school, we step up the ladder of abstraction to deal with a whole class of number relationships all at once. We are not really interested in specific numbers, but on broader relationships between numbers. The equation "x+3=y" gives us a collection of numbers that are all related to each other because "This is three more than that." In high school, we step up the ladder again. Now we are less interested in any particular equation. Instead, we are looking at whole classes of equation-relationships. Not just the one equation x+3=y, but all of the x+n=y type of functions. Or even more broadly, any function where we take in an x and output a related value f(x). In this new level of abstraction, often we are not trying to solve a particular equation. Instead we are looking at what a whole class of equation-relationships has in common, and how they are different from this other class of equation-relationships. Or at what happens when we combine functions --- put a value into one function and then take the output and dump it into another function --- and does it matter which order we do the functions? Or can we find a way to go backwards --- if we know the output, can we figure out what the original input would have been? In the early days of working with functions, it can seem like not much has changed except the notation. And so it can seem like a ridiculous thing to do. Why change something that's not broken? But as the student moves on, the power of the new notation will become more important because it gives them a way to think about bigger ideas.
  11. If you like to supplement your math program with games, I'm running a book giveaway at my math blog (7/15 through 7/17/2019):
  12. My favorite is the (free) sticks and shadows series of lessons at
  13. Ooooh, the idea of a number chart reminds me of this game. Use a blank chart, and choose a large starting number, like maybe 180, so the numbers that go in the blanks flow past 200. Or play several times, with different starting numbers, gradually increasing to build up to 200 and beyond.
  14. If you'd like some more combination puzzles, I've enjoyed these from You probably wouldn't want to give her the worksheets straight, but just pick out a puzzle that sounds interesting to explore. And if you're looking for math card games, I've shared several on my blog. You may find something there she'll enjoy.
  15. Your daughter's struggle may also mean that she's moved a bit too far ahead in the math books, and her mind needs some time to catch up, to consolidate her understanding. Learning often happens in spurts and plateaus, so perhaps she's ready for a plateau. When her mind goes blank on a specific problem, you can try the Socratic approach of asking questions. What do those marks on the paper mean to her? How does she think about them? Can she imagine any situation that might use those numbers in real life? Does she know that the answer in a subtraction problem is called the "difference"? What does that make her think about? How different are these two numbers? (Incidentally, "difference" is a more fruitful, less limited way to understand subtraction than "take away." Come back to the idea of "difference" over and over throughout her elementary years, and she'll have a much easier time when she gets to algebra.) Can she think of an answer that would be way too low (5?) or too high (3 million?) --- and how does she know those silly answers can't be true? Could she make up a problem of her own that is similar to the troublesome one, for you to solve? (My kids always liked trying to stump Mom.) Math is not the marks on the paper. Math is what happens in our heads as we reason about ideas. You don't want to teach her how to manipulate the symbols, but how to think about the ideas. And also, while she's in the plateau, you can keep playing games. Math games are a great way to consolidate learning. For example, Snugglenumber is a great (and free!) game for thinking about place value. Or check out the other math games on my blog.
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