I loved that book, but it's heavy on "inspiration" and not so great on practical suggestions. You should check out her new website, where she's been putting up some more practical stuff. And if you get a chance to take her free course on How to Learn Math (I forget the exact title), go for it! YouCubed.orgAnother excellent resource for learning to think mathematically is Christopher Danielson's blog: Talking Math With Your KidsAnd the primary thing to keep in mind as you teach homeschool math is this: math is just common sense. If you find yourself teaching stuff that doesn't make sense, just to follow the steps, then you really aren't teaching math. Following steps that we don't understand is the human equivalent of dog tricks. For it to be real math, it has to make sense.

Do you have a budding writer? Here's some inspiration: Homeschool teen Teresa Gaskins' fantasy adventure novel is free for Kindle now through Monday. Banished: The Riddled Stone, Book OneShe wrote this book when she was 13yo. Now she's 15, and just finishing up Book Two of the series, which is scheduled for publication in spring 2015. Teresa also writes a blog (occasionally), and your kids may enjoy reading her older stories there. She started by writing much shorter tales and gradually worked her way up to full novels: Kitten’s Purring — Stories for a Cozy Lap

Do you have a budding writer? Here's some inspiration: Homeschool teen Teresa Gaskins' fantasy adventure novel is free for Kindle now through Monday. Banished: The Riddled Stone, Book OneShe wrote this book when she was 13yo. Now she's 15, and just finishing up Book Two of the series, which is scheduled for publication in spring 2015. Teresa also writes a blog (occasionally), and your kids may enjoy reading her older stories there. She started by writing much shorter tales and gradually worked her way up to full novels: Kitten’s Purring — Stories for a Cozy Lap

Some of the documents on Scribd are uploaded by individuals, and they occasionally play loose with copyright laws. But the books in their lending library are legit, uploaded through a contract with the publisher or author, or through an official distributor like Smashwords. As an independently-published author, I think it's a cool way for readers to find things they can't get at their normal bookstore or library. My math book for homeschoolers is also available through Scribd, if you're interested. Lots of playful, no-preparation ideas for math activities and games, flavored with teaching tips and what-is-math-really-all-about advice: Let's Play Math: How Homeschooling Families Can Learn Math Together, and Enjoy ItAnd my teen daughter's novel will be there next year, after its exclusive contract with Amazon runs out. They also have Claudia Zaslavski's Math Games & Activities from Around the World, and a lot of other great books for homeschoolers. Wonderful resource!

I wonder if it would help to move away from answer-getting math for awhile and play with math that doesn't have a specific right answer. Where the focus is more on explaining what you think and why. Like these websites: Estimation 180 Would You Rather? Math Arguments 180

That story is from my blog: The Cookie Factory Guide to Long Division

You might also look into some non-curriculum math. My two go-to sites for preschool and early-elementary are: Moebius Noodles (activity ideas for exploring advanced concepts at a kid's level) Talking Math with Your Kids (tips for using everyday conversation to encourage mathematical thinking)

I agree with TheAttachedMama. We used an earlier version of Singapore Math, but the reviews and end-of-section stuff always seemed much harder than the regular lessons. Also, no matter what curriculum you use, 4th grade takes a huge jump in difficulty of material. It's an adjustment for most kids---certainly was for all five of mine---and they usually need a lot more reminders than I think they should. So I wouldn't panic or switch math programs over this, unless you were planning to switch anyway. Build in supplements and reviews to your regular schedule, using the Math Mammoth or Singapore challenge supplements you already have. Don't try to coordinate the review with current lessons, just do 2-4 problems a day until the skills become more automatic. Sometimes for my kids I made 4-a-day practice pages by folding a piece of paper in half both ways and then copying a different type of review problem into each quarter. (They liked to check their answers themselves, using a calculator.) It was easy to adjust the difficulty level or type of problems I included, based on the student's needs. Math Mammoth would be a good source for these, because you can make a few weeks' worth of 4-a-days at once. Pick four or more topics he needs practice in. Find and bookmark the appropriate MM worksheets. Then fold up a bunch of papers. Copy one problem into each section of paper, making a balanced mix of problems.

Here's how we do it, posts from my math blog: Focus on understanding first, with the Multiplication Models Card Game (printable) Learn mental methods for figuring things out when memory fails (blog post series appears in reverse order, scroll down to get the beginning) Play multiplication games for review

Counting on fingers is not a horrible habit, it is a crutch. Please think for a moment about the purpose of crutches --- when do you use them? The blasted things are uncomfortable and a real nuisance, but there are times when you just can't get anywhere without them. And if you are in one of those times, it would do you no good at all to have a friend insist that you put the crutches down and crawl along without them. That is how your daughter feels right now about her fingers. Mental math is a tough adjustment, and this is her first year homeschooling, and the little kids can do it, and Mom is frustrated. Her confidence is broken, in a cast, and needs time for healing. So she falls back on what she knows she can do, counting up the answer. This is a *good* thing. It means she still believes that math should make sense, that understanding what she is doing is more important than merely guessing at an answer, even if Mom gets mad. You *want* her to value sense-making, because otherwise she will try to memorize her way through middle school and high school math, and that is the road to disaster. What you describe above is the problem of transfer, and it is one of the huge, unsolved problems of education. It's fairly easy to teach someone to do a simple, limited task like answering flash cards. But how can we get that knowledge to sink in deeply, so they can use it in all sorts of different situations? No one has really figured that out. There is no easy solution. It requires patience, and providing a variety of experiences, and patience, and pointing out connections, and asking the student to think of connections, and lots more patience. I have a few suggestions that might help: Consider trying Buddy Math (it's a method you can use on your current curriculum, not a new program). I know you are busy, but this can make a world of difference for a struggling student. Even if you don't do the whole buddy method, consider spending more time on each problem. Do fewer math problems in a day, so you have time to work more deeply on each one. Talk together about the different ways you might solve it. Make it a challenge: can we think of three totally different ways to do it? In math, even if there is only one right solution to a problem, there is *never* only one way to get there! Thinking about alternatives will help her develop that transfer of skills. Pick up some workbooks that target mental math methods. This series looks fun and will help her master the techniques your younger kids picked up without realizing: Mental Math in the Primary Grades, and then Mental Math in the Middle Grades. It may still take her longer to do a calculation than what you are used to with the other kids, but these books will give her a boost in recognizing the types of mental tools she can use. Go to YouCubed and explore some of the ideas, or even sign up to take Jo Boaler's free online class on how to learn math. Do it together, as a shared adventure in learning. I suppose it's possible that your daughter has a slight LD. Most of us do, I think. We all have one area (or several) where we struggle more than we think we should. But from the things you describe above and in your other post, I would guess the trouble is mostly that you're asking your daughter to do something new to her. Jumping into mental math in fourth grade is a big adjustment for a child who wasn't taught that way. It's worth fighting for, IMO, because those mental math techniques are based on the fundamental properties of numbers, and those same properties are also fundamental to understanding algebra. But the main goal is for her to understand and talk intelligently about her options, not that she be able to do each calculation as fast as possible. And be very sure that she no longer needs those crutches before you try to take them away.

Two things really helped my children at this age: telling stories, and playing games. Stories give their minds something to work on, thus helping them to visualize and understand math better than numbers alone. And games are low-stress review, always a good thing. Here are some of my favorite math ideas for this age, from my blog: Tell Me a (Math) Story Game: Tens Concentration How Crazy Can You Make It? Math Game: What Number Am I?

The classic book on this topic is How to Solve It by George Polya. He teaches students to ask general questions that can apply to any problem. Here is a pdf of his questions. In another book, Polya described the process of solving a problem as trying to find a path through an unknown wilderness. You have a starting place, and you can try different routes from there, based on your initial information. If you get stuck, you can switch to looking at your destination and working backward from there, trying to find paths that would end at the goal. By working at the problem from both ends like that, you eventually (we hope!) find a path that connects the whole distance. Here is a 4-step approach based on Polya's "connecting paths" metaphor which might help your son, though I wrote it with younger students in mind. Page 1 is for quick reference, and page 2 lists the steps in more detail: How To Solve a Tough Math ProblemAnd here is a quote by Polya that may not make sense at first, but after you think about it for awhile, you can see that it summarizes his problem-solving approach: “If you can't solve a problem, then there is an easier problem you can solve: find it.†― George Pólya Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving, Volume I

I saw the same pattern your son did and got the same answer, 4624 blocks. The difference in the sides is not just perspective. The pattern is very different, depending on which angle you look at. I tried to confirm our answer by calculating from the other perspective, but I couldn't quite visualize what the blocks were doing from that side. At first, I thought it was just a straight sum of squares, but that came out with almost double the number of blocks, so I looked again and realized it was more complicated than that, and I didn't want to take the time to build a model and figure it out.

Oh, right! I forgot Beast Academy isn't all out yet. Since my kids are all past that stage, I haven't been following it that closely.

I wouldn't worry or change anything. IMO, the current cultural rush to do algebra and high school math earlier and earlier is detrimental to true learning. Much better to take one's time and really understand the upper-elementary and middle school topics that are so foundational to everything that follows. I have never cared whether my kids make it to calculus in high school or not, but I definitely care that they thoroughly master fractions, ratios, and proportional thinking.

Her answers are definitely valid, and I would count them for full credit unless the question specified a certain form. The first answer is fully simplified, too. The second answer can be written as a monomial, which might be considered "simplified," but there are certain problems in algebra (such as geometric series in algebra 2 or precalculus) where the form that she gave would actually be *more* helpful in seeing the pattern of the solution.

The answers are equivalent, and since the book did not specify a certain form to use, your daughter's answers are perfectly fine. In fact, I prefer her answer in the second one over what the book gave because mixed numbers are almost never used in algebra and beyond. Be warned: The problem of recognizing equivalent or equally valid answers will only get worse in high school math. The answer key is a help, but not an absolute authority!

[Cross-posted from the General Education board.] The Math Teachers at Play blog carnival features some of the best math preK-12 education posts each month by homeschoolers, classroom teachers, math ed profs, and more: games, activities, lesson ideas, teaching tips, recreational puzzles, and soooo much fun. Check out this month's edition: Math Teachers at Play #79I have to say, I think this carnival has a higher percentage of my "personal favorite" posts than any of them I've hosted so far. Really worth a visit!

The Math Teachers at Play blog carnival features some of the best math preK-12 education posts each month by homeschoolers, classroom teachers, math ed profs, and more: games, activities, lesson ideas, teaching tips, recreational puzzles, and soooo much fun. Check out this month's edition: Math Teachers at Play #79

No significant difference at all.

Echoing everyone else, this is a development question. It's much easier for young children to figure out what to do in a problem where stuff is moving, where we are putting things together or taking things apart. The comparison aspect is much more difficult---but you don't want to sidestep the issue, because it's important for them to learn. Therefore, rather than teaching them to memorize "key words" which will have a tendency to trip them up later in other, more complex situations (comparing and distance are NOT always subtraction, especially in middle school and beyone), I prefer to help them analyze the story: MaryAnnA's suggestion: Get some blocks, pennies, or whatever to represent each person's stuff. See how many blocks you can match up and how many extras don't match. Eventually the child will be able to imagine the items without something tangible. Or ask: Who has fewer? How many would we have to give them to make it even? The one thing you DON'T want to do is to see this as an example of "story problems are too hard" and start focusing only on number calculations. For young children, story problems are mental manipulatives that lead them to conceptual understanding. Abstract, number-only calculations lead to rote procedures (follow the steps and get it over with). Both types of math are useful, but if you had to choose one, word problems are by far the more important.

How about something totally non-schooly, playing with big mathematical ideas? Moebius Noodles Math Pickle Math Cats

I was going to suggest the Ed Zaccaro books, but Kiana already mentioned them. So I'll add Creative Problem Solving in School Mathematics and the Math Olympiad Contest Problems books by George Lenchner and Richard Kalman. Oh, and Math Pickle is wonderful: http://www.mathpickle.com/K-12/Videos.html

Moebius Noodles: http://www.moebiusnoodles.com/

Something the math books often forget to tell you (or just assume you already know) is that the fraction line acts like automatic parentheses around the whole top and the whole bottom. Every fraction line, all the time, but it usually doesn't make much difference until we get to algebra.