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  1. Check out these free resources on my blog: My Favorite Math Games (played with stuff you have around the house) Math Adventures for All Ages (internet links) Elementary and Middle School Fun Stuff (internet links)
  2. Have you considered going to a local community college for an Associates degree? In our area, the SAT/ACT is totally optional because the community college gives its own untimed placement test --- you can even pause the test and come back to finish it another day. And after you've earned an Associate's degree, you've proven you can do college-level work, so the big colleges don't require the SAT/ACT when you transfer in. The rules may be different where you live, but it's worth looking into --- and as a bonus, you save a ton of money going the community college route.
  3. Math problems in high school are challenging because there are so many "moving parts" --- so many things to think about. There is rarely an easy, straight path to the answer. So your son needs a way to focus his thoughts on the problem and feel his way through the darkness. And he needs to be comfortable with the idea of dead ends, that he may have to try several different things before he discovers the approach that will work for that problem. Part of that is what they're calling these days a "growth mindset" --- the willingness to keep trying in the face of failure, trusting that you can figure it out. And part of it is learning to develop a systematic way to think about complex situations. I wrote a blog post about how to solve story problems that you and your son might find useful: How to Solve Math Problems I later expanded that into a short pdf book that you can pick up free at my newsletter site: free 24-page problem-solving booklet. (No subscription necessary!)
  4. A few more options for a creative break between textbook levels: Nrich has a wide selection of puzzle and games for all ages. Browse, play, enjoy. SolveMe puzzles are a fun and accessible intro to algebraic thinking. More ideas from my blog's internet math resources page.
  5. Language is inherently vague, at least as compared to math. This discussion shows that the same words can mean quite different things to different people. My vote for the meaning of "increase by a factor of 1.75" would go with the addition crowd, because this reminds me of computing interest. Your principal increases by a factor we call the interest rate, and the equation looks like: New amount = Principal x (1 + rate) But of course, whoever originally made the statement may mean 1.75 to be the "1 + rate" in that equation, which would put him in the multiplication camp. If you're dealing with a textbook question, answer according to how the author is interpreting the words, if you can figure that out from context.
  6. 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
  7. 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.
  8. 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.
  9. 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."
  10. 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!
  11. 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: https://denisegaskins.com/2017/01/07/my-favorite-math-games/ 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.
  12. 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
  13. She might enjoy some of the challenges on these websites: http://www.estimation180.com/ http://www.wyrmath.com/
  14. 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.
  15. 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): https://denisegaskins.com/2019/07/15/giveaway-lets-play-math-sampler/
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