I recently ran a series on my blog about learning the multiplication facts conceptually, through conversation and with a bare minimum of memory work. Perhaps that would resonate with her? How to Conquer the Times Table, Part 1

Can he do it if you put away the worksheet and just ask him a real-life problem: "I have a sack for cookies. I put my two cookies into the sack, and then I give it to you. When you look into the sack, there are two cookies there. How many cookies were in the sack at the beginning, before I put my cookies in?" Young children often find word problems ever so much easier than abstract, numbers-only problems. They can make a mental image and imagine doing things with it, so the words of the problem act like a mental manipulative. (You can also teach him to act out problems with real manipulatives.) I would definitely not worry about getting math facts into his head until he can reliably solve word problems. Here are a couple articles from my blog that you might find helpful: Elementary Problem Solving: The Early Years : "One of the best mental math games relies on adult/child conversation, a proven method for increasing children’s reasoning skills. As soon as your child can count past five, give him simple, oral story problems to solve..." Penguin Math: Elementary Problem Solving 2nd Grade

Here is a baby-steps method for word problems (from my blog) that might help your daughter: Algebra: A Problem in Translation In the process of solving a word problem, the student must work her way through three steps: Translate the words into a mathematical calculation or algebraic equation. Do the calculation or solve the equation. Interpret the resulting number in the context of the original problem. When a student struggles with solving problems, most of the time it is step one that gives her trouble. She does not know how to translate the problem from English into “mathish.†If we want to help our students with their math problems, we need to teach them how to do this sort of translation.

I second this! I've tried several grammars, though by no means all of them, and KISS Grammar is the only one I will ever recommend: The Primary KISS Difference — A Grammar with an End

Pubescent brain fog happens to girls, too. It's not just a boy thing!

I would say that one needs to study grammar until one can look at a passage of college-level writing (or other complex prose or poetry) and explain what each word is doing within the passage --- how it is adding to the meaning --- and how the independent and subordinate clauses connect together to communicate the author's point. And until one can use such knowledge to talk intelligently about style and logic in writing, to explain why grammatical errors are wrong (NOT because they break some "rule", but to explain how they prevent the reader from understanding what is written), and to adjust the complexity of one's own writing to the appropriate level for the given audience (including college professors, as necessary). I don't think most traditionally-taught grammar ever reaches this goal. This is why I love KISS Grammar: The Primary KISS Difference — A Grammar with an End

I shared this problem on my blog, and a friend reminded me of something I forgot to say: Because x is in the denominator of one of the exponents, we have to note in our answer that it can't equal zero.

I see you have little ones, so this might be difficult, but I've found that by far the most efficient way to do math (with any curriculum) at this easily-distracted age is to use Buddy Math. It cuts down on silly mistakes (or lets you nip them in the bud) and keeps the student from staring out the window or doodling when he should be working. And best of all, it gives you a really solid understanding of how much your student knows and doesn't know. My daughter and I worked through quite a bit of MM4 that way, and we are still using it with her pre-algebra work in 7th grade.

If you teach these as "tricks" to memorize and apply, then you are adding a HUGE cognitive load and making math more difficult than it has to be. But if you take time to play with these tricks and see why they work -- like, the reason you use the "one less" number in the Magic 9s trick is because the 9 has taken 1 for itself, in order to become a 10 -- then you are deepening the student's understanding. I still might not want to do too many of the tricks, but I don't think they would be harmful. For instance, can your student see that "Number in the Middle" will work for ANY two numbers you want to add? If you want to add 10 + 20, that is the same as double 15. Or 40 + 60 is the same as double 50. All you are doing is taking the extra amount on the bigger number and sharing it between the two numbers. A lot of Singapore Math word problems will use a similar trick: "May had 70 stickers and her brother Joey had 40. She gave him some stickers, and then they both had the same amount. How many stickers did May give Joey?"

Here are a few articles from my blog that might help: Percents: Key Concepts and Connections Percents: The Search for 100% Trouble with Percents (be sure to click through and read the articles and comments at MathNotations as well!)

Whenever you need an alternate explanation to help you understand something in algebra, Purplemath is a great place to start. Here is their page on exponent rules. And then just remember: All exponents follow the same rules, even if they are fractions. And multiplying or adding or doing anything with fractions will work the same way it always does, even if the fractions are exponents. As for this problem, since even the instructor found it hard to interpret, I would forget about it and focus on whatever comes next. And if you run into trouble again, feel free to ask a new question. I'm sure any of us "mathy moms" would be glad to help!

Well, most of what you listed there (all but geometry) fall under the category of Arithmetic -- that is, working with numbers. That is what the bulk of "school math" is, but it is really only a tiny corner of Mathematics. There are plenty of fascinating math topics that never even get mentioned in school. "School math" is about as lifeless as if you gave your kids only a series of grammar workbooks and told them that was language arts (and never even let them see an actual book). And then fed them broccoli-flavored ice cream for desert. If you really want a new perspective, take a few weeks away from your math book and try some of the activities here: http://moebiusnoodles.posterous.com/#!/ Your kids will have a chance to explore mathematical ideas like symmetry, fractals, and functions. And you yourself will begin to see math in more places than you ever imagined!

I would use Moebius Noodles: http://moebiusnoodles.posterous.com/#!/ It's not a curriculum, but a series of guided activities to explore math concepts. They are developing a book, forum, and resource gallery, but I haven't heard what the address will be. For now the discussion board linked above is the best place I know to find ideas.

Sounds like a good informal rule for avoiding misunderstanding, but there's no official rule. (Sort of like how some people put slashes through their 7's and 0's, to make them clearly different from 1's and O's.) Harold Jacobs' Geometry is full of polygons where the vertices spell words, and I'm sure he used plenty of I's and O's.

On the other hand, the new expression doesn't simplify nicely at all: ((x^3/2x)*x/9 * (x^9/15)* 5/18)^3 = {(5/162) * x^[(3/2x) + 1 + (9/15)]}^3 = (125/4,251,528) x^[(144x + 135)/30x] That is the simplest I can figure out how to make it look. In my experience, Alcumus isn't that mean!

Are you SURE about this correction? Because the expression as you typed it originally simplified down to just plain x, which is the way I would expect an Alcumus problem to behave. This one is much nastier! Let me explain the original expression, one piece at a time: [(x^3/2x)^x/9 * (x^9/15)^5/18]^3 You have to use the order of operations: Work on the stuff inside the square brackets first, and simplify the exponents before you try to mess with the multiplication. The first piece is (x^3/2x)^x/9, which uses the exponent rule that (x^a)^b = x^(ab). The two fractions are exponents, and because you have a power raised to another power, the exponents get multiplied. And then, of course, you have to put the resulting fraction into lowest terms: (3/2x)(x/9) = (3x/18x) = 1/6. Therefore, this first messy piece simplifies to x^(1/6). The second piece is (x^9/15)^5/18, which uses the same exponent rule. Power raised to another power, so the exponents again get multiplied. This also simplifies to x^(1/6). The third piece is the product inside the square brackets, which is now x^(1/6) * x^(1/6). It uses the rule x^a * x^b = x^(a+b), and simplifies to x^(1/3). Finally, we apply the cube that is outside the square brackets, which simplifies our final answer to just plain x.