Singapore math uses bar model diagrams (also known as strip models or tape models, or in Singapore they just call them "models"). This is a type of visual algebra that lets the student solve problems by manipulating virtual blocks (like Legos-of-the-mind). I have a series of posts on my blog that explain bar modeling from simple to challenging. They might give you the foundation you need to understand what the math book has in mind: Elementary Problem Solving: Review

You might find this explanation from my blog helpful. Number bonds are a valuable teaching tool, even if you don't use Singapore math: Number Bonds = Better Understanding

I'll play the curmudgeon here. Why are you worrying about number facts? The important thing for this age level is to work on building number sense. Number facts are abstract, isolated little bites of data. Number sense is a whole web of inter-connected relationships that tie the numbers together and help kids think their way through math problems. Take a look at these articles: Build Number Sense The Power of Subitizing

There are MANY "right" ways to do multiplication, and it sounds like your daughter has invented a version of the lattice method. There's no reason why she shouldn't continue to use her method. The fact that she knows to add on the slant shows an understanding of place value. One of the freedoms of homeschooling is to let kids do things in ways that make sense to them, without forcing each unique peg into the standard schoolish hole. We each have to choose our battles. There are some things we must insist our children do the standard way, and others where we can give them freedom. If her method bothers you enough that you want to fight a Do-It-My-Way battle, that's for you to decide. But her method is sound, as long as she keeps place value in mind.

Do you know any other homeschoolers using Singapore math? If you can get a look at the Home Educator Guide, I think you will find it's not as hard to teach as you expect it to be. And the Singapore focus on teaching by concrete --> visual --> abstract sounds like a good match for your daughter.

A few points, in no particular order: (1) Liping Ma's book is great, for what it does. It will not show you why the Singapore Math subtraction model is necessary. Its purpose is much more general, namely to open the readers' eyes to the fact that elementary arithmetic is deeper and richer than most of us realize. (2) On 45 - 7: If you had 4 dimes and a nickel, and you wanted to buy a piece of candy for 7 cents, what would you do? Wouldn't you hand the clerk one dime, and then put the change back with the other money still in your pocket? That's all the Singapore method is asking you to do! The most important key to mental math is to make the problem simpler. Children make mistakes in subtraction much more often than in addition, so this "making change" method turns the subtraction problem into a simpler addition. Very few children will make a mistake when adding 35 + 3, but many will get confused trying to borrow and subtract 45 - 7. (3) Subtraction is one of those stumbling-block topics that causes trouble for lots of kids. With three out of my five children, we had to walk away from subtraction for weeks or even months, doing other math in the meantime. It's not worth the tears (from mom or kids), when there are plenty of other interesting things to do and subtraction will still be waiting when we come back. That's one of the joys of homeschooling -- the freedom to do things out of order, to follow rabbit trails, without worrying about an artificial schedule imposed by textbook writers. Flip ahead to the fractions chapter, or geometry, or bar graphs, or whatever topics are waiting later in the book. We usually found the Singapore math B semester books more interesting than the A semester (which tended to focus on basic arithmetic). Or take time out for living math with library books. Enjoy your break, and come back to subtraction one of these days.... (4) When I was teaching mental math to my kids, and we ran into a new method they found confusing, we divided the lesson. In the textbook part, which we did orally, they were supposed to try at least a few problems by the new method. In the workbook, though, they could use any method they wanted. I mention several useful thinking strategies for mental math in my PUFM post on subtraction: PUFM 1.4: Subtraction(5) Making tens (ten bonds, the pairs of numbers that add up to ten) are super important. Another good game for practicing those is Concentration/Memory. Fun for all ages: Game: Tens Concentration

I have a series of articles on my blog that walk through bar models from the beginning (2nd grade problems) to 5th grade, using word problems from children's books: Word Problems from LiteratureBar models are basically a visual form of algebra. They can be very helpful in ratio and proportion problems, which confuse many students. Or any time that you face a textbook story problem and don't know where to start.

This happens to everyone, adults included. When the teacher (or pastor or inspirational speaker) says something, it seems to make sense, but we only see the surface level. But later when we try to apply the equation (or the life principle, or whatever), then we find out that we didn't understand after all -- or at least we didn't get it as well as we thought we did.

I'm not familiar with the Dolciani books, but since you have no other answers, I'll weigh in with my opinion. YMMV! Exponents are vitally important. But it seems weird to focus on them so early in a pre-algebra course. They will almost surely be covered again later (check the table of contents?) and revisited in even more depth when she gets to algebra. Sometimes seeing a different presentation can help with tricky math topics. Your daughter might like the Math is Fun page on exponents, which is a quick overview/review using numbers only (no variables). Or the more detailed Purplemath pages, designed for algebra students. I don't think you need to stop and camp out on exponents. Have her make a reminder sheet summarizing the exponent rules and let her use that as needed with future homework. Eventually, she will get used to how exponents work, just from sheer repetition, but the rules are not intuitive to beginners.

I don't know what the earlier thread was, but these might work for you: CorbettMaths 5-a-Day: daily practice problems for several levels of elementary through middle school math Daily Math Review: focus on middle school I can't believe I missed getting the CorbettMaths page on my blog's resource list. I must find time to update that!

Sixth grade math is hard! One thing that makes it worse, though, 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. If your son has any tendency at all toward perfectionism, then the "I'm terrible at math" response is completely natural. No matter how good he really is, he will make mistakes. If he could get everything right, that would mean he was working at too low a level. As an extreme example: If you gave him a first-grade book, he could probably do it all without a single error (unless his mind wandered from sheer boredom), but there would be no point to that. He won't learn anything unless he works at a level where he makes fairly frequent mistakes. As parents, one of our big 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. The standard approach to math homework tends to reinforce the performance notion. The student works on problems, then the teacher/parent checks the answers and points out every failure. I found a lot more success in homeschooling math when I switched to the buddy system, which let me continually reinforce the idea that math was a puzzle -- something that might stump us temporarily, but that we could learn to figure out.

We do a LOT of informal mental math and play a lot of math games. But the only things we work at memorizing are the multiplication facts, and we don't start trying to memorize until about 4th grade. By then, all but the hardest facts have been absorbed through regular use, and memorizing the last few doesn't take too much effort. We don't stress over it, but the kids need to be fast enough (by memory or by using strategies like Noreen described) by 5th grade that it doesn't hinder their other work. If they are still lagging, we'll take time out then and focus on multiplication, using the strategies I describe in this blog post series.

Here is an video modeling the multiplication with Legos.

Your daughter sounds a lot like mine, except my dd is a writer, not an artist. Understands math, is good at it, but has very little interest in school math work. Plenty of tears, often due to perfectionist angst --- not wanting to do something new if she couldn't do it perfectly. We did a variety of things when she was younger, including Singapore Math. Never the same curriculum for very long, though, and often broken up with stretches where number games were our only formal math practice while we wandered around in recreational math topics. (Many of those games are available [free] on my blog.) When we used Singapore Math (and later Math Mammoth), we always worked in several chapters at once. She could never handle very much of straight calculation practice at once, and Primary Math always started the school year with lots of that. So we did Buddy Math through a little bit of arithmetic each day, then skipped to a more interesting topic to round out our math time. I loved doing Buddy Math with her, because her mind works so differently from mine. It was fascinating to hear how she approached problems. I didn't try to stay on "grade level", so she was advanced on some topics (algebra in first grade) and behind on others. We weren't trying to rush to calculus (though we did some of Don Cohen's activities), just to build a solid foundation of understanding and to play with interesting ideas along the way. Some of the things she liked: Eric Zaccaro books, Penrose the Math Cat (or anything with cats), Danica McKellar books (though she was never a girly-girl), logic puzzles of all sorts, Competition Math for Middle School (just for the puzzles, NOT actual competitions), getting together with friends for math club activities, James Tanton's G'Day Math courses... Now she's a senior in high school, doing well in her college algebra (dual credit) class, still building on that solid framework of understanding. She won't get all the way to calculus before she graduates, but the tears are (mostly) in the past --- and she just published her third novel. I'll count that as a homeschooling success. :) So I guess my recommendation would be not to fear the tears, but recognize that the textbook is pushing her into a place of emotional stress. Back off a bit --- either skipping completely away from the text for awhile, or just doing smaller chunks at a time --- and add some variety for balance. Don't avoid difficult math, because mastering a challenge is satisfying. Explore some of the wonderful resources online when she needs a break from textbook work.

From my math blog: Snugglenumber is good for all ages. Target Number and Contig both focus on building multistep mental math skills. My Closest Neighbor reinforces several fraction concepts. And they might enjoy the Odd-Even-Prime Race or a Factoring Game.

Blogging is a great way to share her writing with friends and family. (They can subscribe to get her new stories in their email automatically.) My daughter started blogging when she was 8yo, and it was a good way to practice her writing skills. Kitten's blog, as an exampleAnd the kids' version of NaNoWriMo can be great fun. Kids get to set their own target word count, and they can change it if needed. My daughter started Nano when she was 10yo, and has done it every year since. The last year or two (mid-teens), she's been able to hit the adult-level goal of 50,000 words. (And one of the books she started in Nano became her first published novel, at age 13!) NaNoWriMo Young Writers Program

I don't know if there's any particular "right" way, other than to pay attention to meaning. The meaning of the words, the meaning of the story situation in the word problem, and the meaning of the numbers --- what they are doing in the story. Here are some ideas from my blog that might help: Tell Me a (Math) Story: informal word problems as a family game Talking Math with Your Kids: my short review of a wonderful resource Elementary Math Problem Solving Tools: intro to the Word Problems from Literature series Word Problems from Literature: printable worksheets with links to the original posts where I explain how to teach them Be wary of the keyword strategy. Some keywords are helpful, especially the ones that are actual math words like area or product. But even those can be used in ways that fool an impatient child who isn't paying attention to meaning. For instance, the following puzzle contains two key words: "What shall we add to 7 to obtain 9 as the sum?"If your children are trained to look for key words, they may be tricked into answering "16." Keywords work best with simplistic, textbooky problems that are meant to be cranked through with little thought. They're no help at all in real life. But paying attention to the meaning of the situation, and the meaning of the numbers within that situation, and learning to use what you know to figure out what you don't know --- those are important life skills for us all.

I liked Jacob's book and used it with all my older kids. (Hadn't heard of AoPS in those days.) But youngest daughter and I worked through a couple of the AoPS books together and thoroughly enjoyed it. Plenty of challenging, thought-provoking puzzles. She is a good reader, but she didn't like the books as much when she just read them on her own. Working through together buddy style made it more fun for us both.

Aw, thank you! :blushing:

Math fiction that features a homeschooling family. Not books (yet), but still fun: The Mathematical Adventures of Alexandria Jones

Great book!

I think I have about thirty math games on my blog now. Many of them deal with math facts.

Factors to consider, remembering that "your mileage may vary": Fourth grade math is hard. There are a lot of new ideas, or old ideas that come together in a new way, in fourth grade math. Whenever children (or humans in general) wrestle with new things like that, their minds naturally tend to glitch out on earlier concepts. In upper elementary school, they make silly addition mistakes. In middle school they make silly addition and multiplication mistakes. In high school, the silly mistakes expand to include fractions. And calculus students always make silly algebra mistakes. Memory aids can hurt. When the mind is juggling so many concepts (see point above), do you really want to add an extra weight of "remember the cute math fact story"? Human brains, like camel backs, may give out when overloaded. Memory tends to fail at the most inconvenient time. Like on a test, or in the middle of a long division problem. Therefore, even more important than memorizing facts, we need to give our kids tools for figuring out the things they forget. So judge your options and make decisions primarily based on whether the tool (flashcards, abacus, phone app, or whatever) strengthens your son's ability to reason things out when memory fails him. Thinking strategies can help. Teach your son mental math strategies that will work with all sorts of numbers, not just the elementary math facts. That will give him a stronger foundation to master whatever his math program throws at him this school year. For specific examples of the most useful strategies at his level, check out my Profound Understanding blog posts: PUFM 1.3 Addition PUFM 1.4 Subtraction

Does your child dream of becoming an author? My kids have all enjoyed writing stories, and for years we've used their novels as a primary component of our homeschool language program. Most of them never got to the point of publication, of course -- in fact, three of the five never finished a complete manuscript. They still learned a lot, though, and had fun doing it. But my youngest got hooked on Nanowrimo at age 10 and published her first novel at 13yo. Now she's 17 and still writing. Her third book will come out next month, if all goes well, and she'll complete the 4-book series before she graduates from high school. Cool! If your kids want to follow in her footsteps, Teresa is offering a free 50-page booklet of short stories and writing tips called Where Do Writers Get Ideas? It's the sign-up bonus for her email newsletter list, but you can just take the booklet without subscribing to the newsletter, if you want. Get Your Free Writing BookletAnd if you or your kids enjoy fantasy quest stories, the first installment of her serial adventure is free for the month of July at Smashwords. Use the promo code SFREE at checkout. Banished (The Riddled Stone, Book One)

Mental math method: The tanks differ by 940 - 400 = 540 liters of water. Every minute, the fuller tank loses 45 and the emptier tank gains 45, so they move closer together at 90 liters/minute. They will be even in 540/90 = 6 mins. Not what the algebra book wants you to do, but it makes a good common-sense check.