My kids hated Calculadder. They hated feeling rushed, and they hated feeling like failures when they couldn't finish the page in the recommended time. I found MUCH more success in two things: Not worrying about math facts Playing number games For students at your daughter's age, this is probably the best game to start with: Tens Concentration

Here are a few resources I've used for high school. None of them are enough for a complete course, but they make good fillers or short lessons: Raymond Smullyan puzzles Lewis Carroll puzzles The Wason Selection Task A wonderful content-free logic puzzle The Monty Hall Problem Some fun quotations

You might find this series of blog posts helpful in wrapping your own brain around the idea of the bar model method: Elementary problem solving series

Whatever math program you end up using, you may want to consider Danica McKeller's supplement series. My daughter has thoroughly enjoyed them, to the point that we now pre-order each book as soon as it's listed at Amazon. Here are my reviews of the first two books, and another blog post where I taught my daughter an idea from the second book: Review: Kiss My Math Review: Math Doesn’t Suck Prime Numbers Are like Monkeys

Thank you for the encouraging words! :001_smile:

Personally, I've changed our math program nearly every year. I don't think it hurts, as long as you teach for meaning (relationally, rather than instrumentally). But at least part of your son's problem is that he sees math instrumentally --- he can follow calculation recipes to perfection, but he can't figure out what to do when he doesn't have the recipe. So no matter what math program you end up using, part of your goal needs to be opening his eyes to see the relationships between math ideas, how they interconnect. Mental math is a good way to build up understanding, but you don't have to use Singapore Math. (Though I do love Singapore Math, and if it fits your family's learning style, I'd say go for it.) For instance, I wrote a blog post on mental addition, but many of those methods also apply in other situations. Or here's a good workbook series: primary, upper-elementary, older students. But whatever mental math tricks you learn, be sure to emphasize how important it is that your son learn WHY it works as well as HOW to do it. Similarly, there are many ways to learn and practice solving word problems. I have a series on my blog using Singapore-style bar diagrams, and here's a great book that covers a wide variety of other approaches, and this one is also excellent. And a great way to encourage creative math thinking is by finding math books he will read on his own. Worth much more than the cost of a new curriculum!

I am clearly in the minority here, but I think getting stressed out over a 12yo (especially a boy) not showing his work is like the king who stood on shore and commanded the tide not to come in. Your real problem is that he is making a lot of mistakes and can't explain what he is doing. The mistakes may be due to plain carelessness, or to pre-adolescent mental fugue, or to deep gaps in his understanding. How can you tell? The only way I know to really find out what your student understands and doesn't understand is to do the work with him: Try Buddy Math. My recommendation would be to get the targeted worksheets on the subjects that seem his weakest (like the Math Mammoth workbooks) and sit down together. Alternate problems buddy-style down the page. Don't make him do anything that you don't do. When you work your problem, model the type of explanation you want from him. When he works a problem, if you don't understand what he's doing, ask him to explain again -- and here's something important: Listen carefully! Often our children think differently from the way we think, so just the fact that he does it differently does not in itself mean he's wrong. ALL of my children have done things differently than me, and I have learned a lot by trying to understand their point of view. (Yes, even about math. People think it's cut-and-dried, but it's not! There are many different, valid ways to approach almost any problem. For example: Mental Addition. Or for a more recent example: these two posts.) If/when your son makes a mistake, try asking Socratic questions to get him to rethink the problem. And on the chance that pre-adolescence is part of his problem, be prepared for temper tantrums over mistakes and especially over being corrected. I personally have trouble being patient with such tantrums, but I've learned that my impatience only makes it worse. I went through it myself at that age, didn't you? Whenever my daughter hits a really bad tantrum, we just put the math up. Everything's usually fine when we come back to the same math problem fresh the next day.

That depends on the pdf and on the printer. Most printers have very specific guidelines about the pdf you submit: minimum margin allowances, bleed area, picture specs, etc. And you have to make sure that all your fonts are embedded in the pdf. If that paragraph sounds like nonsense to you, then odds are you're not ready to send a pdf straight to a printer. You might try a company like Create Space, which (I think) has a way to take a Word document and convert it to something they can print. That way, you won't have to learn a whole new vocabulary and set of technical skills. If you are wanting to sell your book (rather than just print something for your own use), I strongly suggest you read a whole bunch of posts on the Book Designer blog. TONS of valuable information there!

Not exactly together, but in very close company. Division is intimately connected to multiplication, and teaching them in concert helps to reinforce that fact. Multiplication asks, "This times that equals what?" Division asks, "What times this equals that?" Division is "backwards" multiplication.

It's great if you want to explore ideas and learn wherever they take you. I prefer the worksheets over the original little book (which is such a tiny, awkward size). You can get a pretty good feel for the book by exploring these activities: Don Cohen's Map to Calculus Start with Infinite Series, because a lot of the other activities build on that one.

We did this with my older kids. It worked well. Aside from library books and whatever math came up in life, we mostly played the oral story problem game: Elementary Problem Solving: The Early Years And resisted formal arithmetic until about 4th grade. By the time my younger kids came along, I had discovered Miquon and Singapore Math, and I enjoyed those enough myself that we added them to our schoolwork. But we still did it mostly orally and didn't put much emphasis on formal arithmetic until later.

Not a curriculum recommendation, but here's something for you and her that will help you get through middle school math and beyond. My daughter loves this book series: Review: Math Doesn’t Suck Review: Kiss My Math

BTW, if you're reading the hobbit with an mid- to upper-elementary student, you may enjoy this blog post: Hobbit Math: Elementary Problem Solving 5th Grade

I'll jump in on the opposite side of the question. I read Lord of the Rings first, and loved it. When I read Hobbit, I was very disappointed. The Hobbit is a kid's bedtime story. The Lord of the Rings is an adult morality tale, in the very best sense. The Hobbit is popcorn and soda. The Lord of the Rings is a feast of literature. If you're in the mood for light reading, go with The Hobbit. If you're in the mood for a *real* story, with real characters and real temptations and real conflict and pain and joy, go with Lord of the Rings. It is dark in many places (as is life) and beautiful and full of grace, too.

Spring Fever?

A couple of sample pages from the Math Mammoth book on ratios and proportions: Problem Solving with Diagrams, Part 1 Ratio Problems and Bar/Block Models 2 There are a couple of ratio problems solved with diagrams in my blog post: Hobbit Math: Elementary Problem Solving 5th Grade And lot and lots of practice here: Thinking Blocks Interactive Ratio Problems

The fraction line acts like an implied set of parentheses: fraction = (everything on top) / (everything on bottom) So that's why you have to simplify the top and bottom separately. The numerator and denominator are each within their own set of invisible parentheses.

No! "On the level" means as you are working that level of PEMDAS. 1st level = P = Parentheses. Simplifying whatever is in parentheses. If the stuff in parentheses is complicated enough, you will need to apply PEMDAS within them. 2nd level = E = Exponents (and Roots, but usually students do Order of Operations before they learn about roots). Simplify all the powers and roots, before you do anything else. 3rd level = MD = Multiplication and Division. These are on the same level and must be done all at the same time, before any adding or subtracting. Don't pay any attention to the M being written before the D. Multiplication and Division have the exact same priority and must be worked at the same time. Here is the first place you really might have to pay attention to the "left to right" rule. As long as everything is multiplication, you can do it in any order, but beware: with division, the order matters! So to be sure you don't mess up a complicated calculation, work from left to right. (Or, before you start, turn all divisions into multiplying by the reciprocal. Then you can multiply everything without worrying about order.) 4th level = AS = Addition and Subtraction. Again, these are on the same level. Don't pay any attention to the A being written before the S. Addition and Subtraction have the exact same priority and must be worked from left to right. (Or, before you start, you can turn all the subtractions into adding a negative number. Once you get everything as adding, you can do it in any order you like -- just keep the negative signs with the correct numbers.) In many cases, the "left to right" rule won't matter, but when there is division or subtraction, it might. Order matters for division and for subtraction.

Concrete, specific recommendations... How do I learn math myself? First, examine what it means to understand math. Read this article. Your goal must be to improve your own relational understanding of math. Second, reassure yourself that elementary math is hard to understand, so it's not strange that you get stuck on how to explain things. Get Liping Ma's book from the library, or order a used copy of the first edition. Don't rush through Liping Ma's book. Read it slowly. As mwntioned above, there are four open-ended questions, each given at the beginning of a chapter, and then the teachers' answers are described and analyzed. The best way to read it is to read each question and then close the book and think about how you would answer it yourself --- even write out a few notes, if you want. And then, after you decide what you would have said, read the rest of the chapter. When you run into something you don't understand in your Math Mammoth book, check out the Math Mammoth YouTube channel. Maria has made a lot of videos! If you can't find what you need there, email her and ask. She's always helpful. The Parker & Baldridge textbook is excellent (and it's available used for about half price), even if you're not using Singapore math. But if you don't have the Singapore books to look at, you will miss some of the value, since the textbook refers to the Singapore books to analyze exercises for homework. Even so, I wouldn't buy the Singapore books just to use them with P&B, unless you can get a good deal on used copies. [sample sections of the Parker & Baldridge book, so you can decide if it might help you learn math: Section 1.6, Section 7.1.] I have not used Kitchen Table Math or Arithmetic for Parents, but I've heard very good reviews of them. [sample excerpts are available at these links, so you can decide if they might be better at helping you learn math.] How do I keep everything organized in my mind? Did you read the article about understanding math? As you move from memorizing steps to learning math concepts relationally, you will find it easier to connect things in your mind and to learn new ideas. Keep a math journal and write down the things you learn. Writing them down will help you remember, even if you never look back at the journal. But when your mind goes blank and you think, "I know I studied that recently", the journal gives you a quick way to glance back. Make your journal even easier to flip back through by writing the topic you are studying in the top margin of the page. When you run into a new vocabulary word, draw a Frayer Model Chart (more examples) in your journal and fill in all the sections. Don't forget the Non-examples! If you find something that's really helpful (perhaps a list of steps for solving word problems?), you may want to flip to the back page of your journal and start an easy-reference section. How can I add depth to our math studies? Join the Living Math Forum. You will find plenty of good ideas -- not all of which will work for you, but some will. Check out the I Love Math books or other math readers from your library. Read some of them aloud, and leave others lying around for your kids to discover. If Math Mammoth is working for you, I'd be hesitant to switch programs. Many people take years to find a math program that works well for their families, so moving away from one that does work is rarely wise. On the other hand, adding in extra (such as Hands-On Equations or Beast Academy) can add depth, since different math programs explain things differently -- as long as you don't let it overwhelm you! When I've done multiple math programs with my students, I have sometimes switched back and forth (finish a unit or two in one program, then switch to the other for variety, and skip anything that is too repetitive), and sometimes let the child choose each day which book she was in the mood for.

Actually, her method is the most efficient way to manage a timed test -- except that she should have circled and numbered each answer as she worked. For instance, if she solved question 5 and her answer matched B, she would circle it and write 5B on her paper. And then she should pause about every 5-7 problems (or perhaps before turning a page in the test booklet) and transfer those answers to the bubble sheet. To bubble each problem as you go means you waste too much time looking back and forth between the test book, scratch sheet, and answer sheet.

KISS doesn't teach diagramming (though you are welcome to add it yourself, if you wish), because the sentences used in KISS Grammar get wa-a-a-a-ay to complicated:

I recently published a series of posts on how to approach math facts in a conceptual, mental-math manner: "Let's Play Math!" blog: Times Table Series And here are a few games that might help: Times Tac Toe Contig Game: Master Your Math Facts Multiplication Bingo Target Number (or 24) Free Rice Multiplication The Game That Is Worth 1,000 Worksheets (Math War)

One thing we've tried (rather inconsistently) is to make Friday a free day. Math still must be done, but it can be more creative, living-math-style stuff, with library books and games. You don't have to buy that many games. There are plenty of ideas online: http://letsplaymath.net/best-of-the-blog/#activities I've found that I'm more consistent with that sort of thing if we invite friends over to play: http://letsplaymath.net/2007/06/18/how-to-start-a-homeschool-math-club/ Also, it's not so much the cartoons and characters that make math fun. It's the thinking. Math that is just following a recipe someone else has given you (standard textbook math) is drudgery. Math that lets you think and figure things out is fun. That's why living books are so great for math. Try Family Math, or The "I Hate Mathematics!" Book, or The Man Who Counted, or the Murderous Maths series, or ... http://livingmath.net/ReaderLists/tabid/268/language/en-US/Default.aspx

KISS Grammar is a very solid program that does not use diagramming. The author explains why in this article: Diagramming Sentences within the KISS Approach Here are a couple forum posts on KISS Grammar, if you are interested in reading more: www.welltrainedmind.com/forums/showthread.php?p=3326468#poststop www.welltrainedmind.com/forums/showthread.php?t=336032

Everyone should be a team, even the individuals. That is, you practice together and solve problems out loud and explore ideas and share tips and solutions. And sometimes you break into smaller groups and race each other to solve problems, and sometimes you even practice individually. Then, in January, you use the "school" competition to choose the 4 students who will officially represent your group at the regional competition. In our region, we can also take an alternate (who competes as an unofficial individual (that is, he can't advance, and some years the alternate's answers were not scored -- I think it depended on the number of volunteers they had), unless someone is sick and then he moves onto the team). And then if you want to pay to take extra, official individual competitors, that is up to you. (We never had enough students for that -- sometimes we're begging kids to come on the team, and one year I had to draft my son.) After the school competition and selection of the official team, we usually have several practices together before the regional meet. In addition to solving problems, we talk about strategies -- for instance, my gang didn't like to work together on the Team Round problems, but prefer to each call out the number of the problem he wanted to tackle and share the work that way. At the regional competition, there are two individual rounds: Sprint (shorter, non-calculator problems) and Target (longer word problems with calculators allowed). There should be a short break between rounds. Then the third round is the Team Round, where the team members are allowed to talk together and share the work however they wish. At our regional, the alternates were grouped into sets of 4 to do the Team Round, but that's not nearly as much fun as working with your friends. The MathCounts resources are good, but they are not organized in any logical manner, so they are not as useful for learning new material as for random practice. Check out the wonderful resources at the AGMath site. I especially like his Introduction to Counting, which later became part of his excellent book Competition Math for Middle School. Alcumus, at the AoPS website, is also great practice. And be sure to go over old tests, and review the sometimes-quirky way that MathCounts wants their answers written. These blog posts are a little old, since I haven't had a team recently (for instance, they were written before I discovered agmath.com): MathCounts — Ready or Not, Here It Comes Math Club: Counting 101