The complicated problems in CWP are purely algebra problems. The bar diagrams are a visual form of algebra. Some students who understand math fairly well can do an instinctive form of algebra in their heads (with a little help from scratch paper), at least for simpler problems. It sounds to me like your daughter is in the latter group. For many students, the visual tool of the bar diagrams makes thinking through an algebra problem easier. But students have been learning algebra for hundreds of years without bar diagrams, and students who have that instinctive "I get it" way of thinking usually don't have too much trouble learning it. So I'd say it's entirely up to you whether you want to put effort into getting your daughter to master the other half of the bar diagram problems, the ones that she doesn't get instinctively. The bar diagrams will give her one more tool for thinking through algebraic problems, but they may not really be that necessary for her. If you do want to teach it, you probably don't need to go all the way back to CWP 2. You could try working through the levels of my Word Problems from Literature series with her, having her draw and explain the simple diagrams and then discuss how the diagrams change as the problems get more complex: Elementary Problem Solving: The Tools Penguin Math: Elementary Problem Solving 2nd Grade Ben Franklin Math: Elementary Problem Solving 3rd Grade Narnia Math: Elementary Problem Solving 4th Grade Hobbit Math: Elementary Problem Solving 5th Grade

I'm not sure what you mean by factoring first in a problem like this. If it had been 5/9 of 27, then I could see TT mentioning that one could divide out the 9s. Either way, if the factoring idea doesn't help, she can just multiply all the fractions out and then put her answer in simplest form at the end. There's no reason that she has to divide out factors ahead of time --- it's just that most people prefer to work with smaller numbers whenever possible. As for understanding this type of problem, the other posts are right on the mark. First find out what ONE part would be --- say, 1/9 of 27 --- and then after she's found that (and put it in simplest form, if possible), then she can think about what 5 of the parts (5/9) would be. It's a common sense approach. Don't try to jump to an efficient technique (like factoring at the start) if it doesn't make sense, because a human brain will not remember things that don't make sense. She might be able to remember it for a test, but she'll forget it (or it will get jumbled up in her mind) as soon as the test is past. First learn the common sense method. After that is mastered, then she can try to learn the more efficient way, and compare them, and see if she can figure out how they are the same.

I don't know how you do math, but at this stage I like to sit right with my student and do everything together. We take turns on the problems: I will do one, while my daughter listens and checks me, and then it's her turn to do one. I describe the method in this blog post: Buddy Math As for the word problems, since they are always a struggle, I would not expect him to do a single one on his own. Make them a work-together project until he feels more comfortable. In Singapore math 3A, you have two basic types of story problems, so the first thing to do is figure out which type you are dealing with: (1) A whole is made up of parts. There are two or more parts that make up a whole thing, or a whole set of things. Food: one part was eaten and the other was left. Store: some things were sold Saturday and the others were sold Sunday. Money: we have part and the other part we still need to earn. People: part are adults and the other part are children. etc. (2) One thing is compared to another. One thing is bigger than, or smaller than, or heavier than the other thing. One person has more money or fewer stickers or whatever than the other person. etc. Each of these basic problems has its own basic diagram. The whole-and-parts diagram is one long bar divided into pieces, with a bracket over the whole thing. The comparison diagram is two bars, one longer than the other, with the difference marked by a bracket. Draw the diagram that goes with the type of problem that you have. Later in the book, drawings get more complicated, with extra brackets or bars divided into special pieces. But you should start with the simple ones. Next, start to label the things in your story where they fit on the diagram. If it's a whole-and-parts, then which thing is the whole and which are the parts? Which is the big set, and which are the sub-sets? If it's a comparison, which thing is bigger/smaller/more/less, and by how much? You may have to read the story several times to figure out where each name and number goes. After you have labeled all the pieces of your diagram that you can, decide which piece represents what you are trying to find. (Ideally, it will be the only piece without a number attached. But in a more complicated problem, there may be other unknown parts that you have to figure out first.) Label it with a question mark. It might pay for you and your son to go back through all the story problems in the 3A book and just practice this part: identify the type of problem, and draw & label the diagram. No calculations! When I do this with my kids, they like the feeling that they are "getting off easy", but I like the fact that they are doing all the thinking. Finally, think about how you can use the things you know to figure out what you don't know. This is a basic, algebraic question. Don't let your son fall into the trap of thinking he's dumb because he doesn't instantly know how to figure this out, because it's an algebra question. It's not always obvious how to do it! That's what makes the bar diagram so powerful -- it is a pictorial type of algebra.

My daughter loved Ko's Journey, but she could have gone through it without really understanding the math because the program refuses to let you make a mistake. Still, it was lots of fun, and it gave her a chance to practice math in a non-workbooky way. She also thoroughly enjoyed Beast Academy and read through the books even before I had a chance to. She learned things from them, and she's in 8th grade. Of course, the multiplication she already knew. And we do a lot of mental math, so while that part might have been new to another student, it wasn't new to her. But she loved the rep-tiles, a type of puzzle she hadn't seen before. And the perfect square sails lesson has been really useful to her in our pre-algebra lessons this semester. So you shouldn't necessarily dismiss BA because it's "just" a 3rd grade book.

In Level 1 we almost always could finish an exercise in 20 minutes or less. In Level 2, at least by the end, we were often splitting an exercise in half and doing it over two days. This year, doing Level 3 in the 6th grade book, the sentences are usually long enough that we only do two sentences each day: one for me to analyze, and the other for my daughter. (We buddy-up her school work that way, so she doesn't do everything on her own.) 20 minutes seems like a good amount of time. Much longer than that, and my daughter would wear out and not be able to focus. We do not do grammar every day, either, just 2-3 times per week. She does a lot of writing and has a fairly good "feel" for language, so the grammar lessons primarily serve to help her understand and be able to explain what she has already learned instinctively through learning to talk and to read.

:thumbup: My daughter's book just got a five-star review on the Home School Book Review blog: http://homeschoolblogger.com/homeschoolbookreview/788010/

"Knowing the facts cold" is great until your mind goes blank in the middle of a standardized test. If your child is relying only on memory, and memory fails, he is left with nothing but wild guessing. I have known too many students like that! Much better to learn ways to think things through that don't rely on memory. And also practice memorization, but don't trust it too much. The only addition/subtraction facts I make my children memorize are the doubles and the pairs that make 10. You can figure all the others out from those. What I meant by "numbers getting bigger" is the sort of problem I explain in Mental Math: Addition. It is a fairly typical 2-digit addition problem, and I demonstrate four different ways a student could think his way through the problem.

Word problems are mental manipulatives. They are concrete, living, real-world math, in contrast to the abstraction of plain calculation problems. Plain calculations are not really problems at all, just the answers to some forgotten problem. A "linear function" or even a "direct variation" is meaningless to a student, but a car or train traveling at constant speed is something we can visualize --- it has meaning. "When we teach children to solve problems in school, we do not expect them to meet exactly and literally the same problems in later life. Mathematical education would be next to useless if its only use were literal. We want much more, we want to teach children to solve problems in general. In this respect traditional word problems are especially valuable, because to solve a word problem, you have to understand what is said there. This function of word problems is very poorly understood in America." --- Andre Toom, Word Problems in Russia and America "As important as mathematics is, it is a distant second to the need for good reading comprehension. We teachers so often hear students summarize a course by saying, ‘I could do everything except the word problems.’ Sadly, in the textbook of life, there are only word problems." --- Herb Gross, quoted by Jerome Dancis in Reading Instruction for Arithmetic Word Problems

More important than speed is logic. MUCH more important. I recommend that you take the worksheet and sit down with him and discuss how many different ways you can think of to figure out each calculations WITHOUT counting and without memorizing. For instance, for your example of 9 + 7: 9 is almost 10, so if you imagine each number as a pile of blocks, you could "move" one block from the 7 pile to the 9 pile. Then you would have 10 + 6. Or you could imagine moving 3 blocks from the 9 pile over to the 7 pile. Or you could think about 9 being 2 more than 7, so 7 + 9 is the same as 7 + 7 + 2 extra (since most kids learn the doubles before the odd numbers). Make it a creative game. Take turns inventing ways to figure out the problems, simplifying them to use things you do know. No finger-counting allowed, because the focus is on logic! He may still use finger counting during his normal school work, but as he learns to reason things out this way, I think you will notice the fingers get less use over time. Logic is more reliable, especially as numbers get bigger.

It's partly the vague-ness of language that causes the problem. In regular, informal conversation, someone might say "5 times more" and mean the same thing as "5 times as many" --- they just use the word "more" because they want to emphasize the size of the amount. Singapore math is making a somewhat artificial distinction between the two phrases, in order to make the word problem work. If you pay attention to word problems, you will probably notice other ways they are like an artificial world all their own, which our students need to learn how to navigate. One thing that really bothers me (and that I teach my children to notice) is that rate problems always assume (but almost never state it directly) that people work at the same rate for hours on end without getting tired or getting in each other's way, or taking a coffee break and wandering off into discussion, or whatever.

You might try "word algebra" with your ds, instead of the bar diagrams. My Word Problems from Literature series explains word algebra and works through several examples: Elementary Problem Solving: The Tools Penguin Math: Elementary Problem Solving 2nd Grade Ben Franklin Math: Elementary Problem Solving 3rd Grade Algebra: A Problem in Translation You could probably work through your CWP books using word algebra, if you think your son would take to it.

Good for him! Mature writers know that EVERY writer needs an editor. None of us can see our own work clearly, so we desperately need the input of others in order to improve. And good for you, that you have been encouraging him. Continue to point out the good things he is doing -- but now also add in one (so it doesn't seem overwhelming) constructive comment on how to improve. If you don't know much about writing, one of the best things to do is simply tell him where you get confused in his story. Which part is hard to follow, or where are you not quite sure what he means? A few free resources on fiction writing: The NaNoWriMo young writer's program The Junior Secret Noveling Club and instructions on teaching it planning worksheets writing comic books

I don't think the changes would matter unless you were specifically thinking of putting a child into a classroom school the next year. One of the primary goals of Common Core is to make a standard progression across the country, so that children who change schools (as is so common in our mobile society) don't get lost because one school taught something in 2nd grade and the other left it until third. But most classroom schools haven't changed over to Common Core yet, so don't worry about it!

In KISS, you start at Level 1 and work your way up through the levels, no matter your student's age or grade level. At each KISS Level, the grade-level books (or the online pages, for people who want to use those) have the SAME lessons and instructions. The exercises have longer and more challenging sentences at the higher grade levels, but the concept that the student is practicing in each exercise is the same. The second grade book is different from the others, for young students who need a gentler introduction to the grammar work. One thing I really appreciated about the 2nd grade book was that it did NOT teach the different types of complements. All complements (predicate adjective, predicate noun, indirect object, and direct object) were marked with a "C". That gave my daughter plenty of time to master the concept of a complement before adding the idea that there were different types and learning to distinguish them.

On a publishing blog, I read today that Amazon cleared out several of the old classic books that had been on Kindle for free. Has anyone heard that, or noticed it when searching for books? I just went looking for Augustine's Confessions, and I had to get it from Project Gutenberg --- which is fine, except that it's a minor nuisance to have to transfer it by hand.

KISS is the only grammar my daughter has ever used. She started it in 2nd grade, and is now in 8th grade (and wrote the book in my signature). We take our time working through the books, because we're not in any hurry to finish. As long as we're learning, that's great. We used the 2nd grade book off and on for a couple of years, then used the 3rd grade book on and off for a couple more, and then used several of the miscellaneous pages on the website. At the beginning, we could whip through a lesson in one sitting very easily. Now we're working in the 6th grade book (Levels 3/4), doing about 6 sentences a week --- two sentences a day on MWF. KISS is a great program! But don't be in a hurry to finish any book in a set amount of time. Much better to be laid back about it, keep the pressure low, and enjoy yourselves.

All of my five have done book plotting and writing as a major part of their English courses through junior high and high school. The youngest is the first to have actually finished and edited her book to the point of being publishable -- see my signature. She has done the Young Writer's Program of NaNoWriMo for several years. It's a great program, and I recommend it. Do download their planning workbooks and let your children do some planning ahead of time (though they aren't supposed to start the actual writing until November). She also enjoyed The Junior Secret Noveling Club, which she worked through with friends in a homeschool co-op a few years ago.

As you look ahead, you might find this blog helpful. It is by a friend of mine whose daughter is a dancer, very artistic. They have been doing Ambleside high school for a couple of years now (they started with a quick review of pre-7), and the blog follows their weekly schedule, with associated links and adaptations. College Prep with a Charlotte Mason Education

I have some explanations and lots of examples on my blog. Start with: Elementary Problem Solving: The Tools and then work through the grade levels in order, starting with the easy ones: Elementary problem solving series

When my daughter and I started the Grade 6 book, it was a shock how much more difficult the sentences seemed. We have switched to just doing two sentences a day: one that I mark, discussing my thoughts out loud, and one that she does the same. There is almost always at least one thing in those two sentences that we aren't sure about, so we mark our best guess and then check the AK. Sometimes, the sentences seem a little bit easier, and I try to talk my dd into doing four of them (two for me and two for her). But whenever she gives in, it turns out to be a mistake --- at least one of the extra sentences will prove difficult enough to cause a meltdown. If you are trying to do a whole page at once, then I'm not surprised you feel challenged!

My older kiddos went straight into Jacobs Elementary Algebra, and it always seemed pretty conceptual to me. It doesn't assume your student had pre-algebra, so it starts with the basics and builds from there. My girls were able to do it independently, but my son was too careless at that age and needed me to keep his attention from wandering.

We also enjoyed CS101. I love Keith Devlin's work and am looking forward to Introduction to Mathematical Thinking, and my daughter is considering a few of the programming courses that work with Python...

My daughter enjoyed it for awhile, but got frustrated because of errors or missing information. She is now using this: http://inventwithpython.com/ But I'll also be checking out the other links...

I really like KISS Grammar. It uses literature, and the price is great. We do it about 5-10 minutes a day, which keeps the previous skills sharp (you use all the old stuff continuously) and lets us make slow progress. I'm not trying to finish quickly, just to keep learning and practicing.

Diagramming is just one tool for thinking logically about how sentences are put together. The main thing is the logic, not the tool. Personally, I don't like diagramming, because it HIDES the logical connections for me. I can understand a sentence when I read it, but when I look at a diagram I'm not sure where to start. I much prefer the KISS parsing method --- but that's what I'm used to. Use the tool that helps you think about the logic of the sentence, because that's what is really important.