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)

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.

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!)

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.

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we call the interest rate, and the equation looks like: New amount = Principal x (1 + rate) But of course, whoever originally made the statement may mean 1.75 to be the "1 + rate" in that equation, which would put him in the multiplication camp.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.

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

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.

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.

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."

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!

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.

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

She might enjoy some of the challenges on these websites: http://www.estimation180.com/ http://www.wyrmath.com/

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.

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/

My favorite is the (free) sticks and shadows series of lessons at https://catcode.com/trig/trig01.html

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.

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.

One thing that makes math worse is when kids (and the rest of us—this is a cultural problem) view math as a performance subject. Every problem feels like a mini-test, and every wrong answer is perceived as a failure. The standard approach to math homework tends to reinforce this performance notion. The student works on problems, then the teacher/parent checks the answers and points out every flaw. If your daughter has any tendency at all toward perfectionism, then the “I hate math” response is completely natural. After all, she will make mistakes. If she could get everything right, that would mean she was working at too low a level. As an extreme example: If you gave her a first-grade book, she could probably do it all without a single error (unless her mind wandered from sheer boredom), but there would be no point to that. She won’t learn anything unless she works at a level where she makes fairly frequent mistakes. As parents, one of our biggest challenges is to convince kids that mistakes are good. They are a sign that points to opportunity: My mistake tells me, “I can learn something here.” Sometimes what I need to learn is a math concept, other times it’s simply to pay attention to details—but there’s always something. I found a lot more success with my math-hating daughter when we switched to the buddy system. It let me continually reinforce the idea that math is a puzzle -- something that might stump her temporarily, but that she could learn to figure out.

As one of my favorite mathematicians-turned-teacher says, "Fractions are hard!" The pamphlet Tanton wrote isn't for students, but for parents and teachers to help us understand some of the reasons our students struggle. Highly recommended! In the meantime, the most important thing about math is that it's supposed to make sense. If your daughter can't make sense of fractions at this time, perhaps the best thing to do is put them away for awhile and do some other type of math. There are plenty of interesting things to study. No reason to beat your head against a brick wall when you could turn left and discover a fascinating nature trail. [For example: One of my favorite middle-school math sidetracks is to explore discrete math with Agmath.com's Counting and Probability units.] And then in a few months, when she comes back to fractions refreshed after the break, she may find that her mind has been working in the subconscious all along and that things make more sense to her. At least, that's how it often worked for my kids.

Math anxiety (or any other kind of stress) affects working memory, which makes it much harder to learn and remember math facts. Since you've been working on this so long with so much frustration, I would suggest dropping it -- at least for now. Let your daughter release the stress by giving her a major change of pace. Think about what you really want your daughter to learn. Is your long-term goal a girl who can whiz through multi-digit pencil-and-paper calculations? Or is it that she understands and can use math in her real life? Memorizing the math facts is vital for developing speed with pencil-and-paper calculations, but not very important in building real-life understanding. A great way to build understanding is to do a lot of story problems where you let her use a calculator (yes, really!) for the final calculation. Her focus should be on making sense of the story situation and figuring out what to do with the numbers, not on the mechanics of carrying, borrowing, and partial products. The ability to analyze and make sense of a situation will give her a strong foundation for algebra. This is not a case of "easing off" on her progress in math or letting her fall behind, but of refocusing her efforts onto the more important part of the problem. If your curriculum doesn't provide enough story problems for this sort of focus, then you might spend some time with an Edward Zaccaro book. In my family's more than a quarter-century of homeschooling, we took several breaks from our regular curriculum, going on side-tracks like this through other areas of math, just to give the kids a change from whatever topic had become a stress-point. It refreshes the brain, and when we went back to the curriculum later, they usually found the tough topic much easier than it had been before.

I wrote a blog post recently with lots of links for math journaling. You may find it useful. Math Journals for Elementary and Middle School [The post starts with a very short description of my self-published journals, since I wrote it to announce when those first came out, but you can skip down to the activity ideas.]

I like to think visually, so what helps me most in problems like this is to draw a decision tree. A decision tree has a branch for each possible thing that could happen. At the end of the branches, you can see all the possible outcomes. To find the probability of a specific outcome, you multiply the probability of the series of branches that lead to it. If you are interested in something that happens on more than one branch, you add the probabilities of each branch. For example, the probability of rain on Tuesday is the sum of the probability of rain ONLY on Tuesday AND the probability that it rains both days --- because both of those outcomes fit the question. I made a sketch of how I would think through the calculations. If you prefer a higher-res pdf, you can find it at this link.

Here are some tips I wrote out for my math team, back in the day: https://denisegaskins.com/2008/12/17/mathcounts-ready-or-not/

The (free) Numberless Word Problem resources at this site are a great way to help kids start thinking math problems through: https://bstockus.wordpress.com/numberless-word-problems/ After you read a few of their links, you'll be able to use the same approach on any problems in your child's math book, or whatever additional resources you try.