Ok, thank you! That's helpful!

OK, I understand. We haven't run into that, but I'm sure other people have! Hopefully they'll chime in! I wonder, though, if it might be that he is still in a more concrete stage of thinking so it's hard for him to wrap his mind around the fact that the bars might not be exactly proportional. Maybe that will change with time? How old is he?

Why can't you draw them proportionately? Or are you saying in the videos (the Thinking Blocks ones, right?) they're not proportionate? It definitely helps to see them at least close to being proportionate!

And your kids didn't complain about having to do both?

Mental Math: Try these videos. (I'll be redoing the subtraction ones within the next week or two, though, because I've discovered a better way to teach it to kids who are slower at picking up math concepts.) Learning mental math this way is what opened up my eyes to truly understand our number system. I got A's in school but never really understood what I was doing. Now I do. Bar diagrams: Try this website for a good intro. I highly recommend learning to do these. They made everything so much more clear to me than algebra ever did! Juggling Books: If I were in your position, I'd try doing just the Textbook and Challenging Word Problems book as our main program. This is kind of what I'll be doing with my 8yo this year. Then add in a bunch of fun stuff like Beast Academy, living math books, Life of Fred, Penrose books, Sir Cumference books, Primary Grade Challenge Math, Mathematicians Are People, Too, Family Math, .... whatever looks good and you can afford. For a kid who is math intuitive, I think it would be worth a try to just use the textbook (Standards edition as it has more review in the textbooks than the U.S. edition) and CWP would go over the topics again in a more challenging way. Another note - if you do decide to go to Singapore, go through my mental math videos with your dd FIRST and practice for a few weeks before she takes the placement test. She will test further along that way and you won't waste as much money on books where you don't need half the info.

My first thought was Singapore. Why do you think you wouldn't do well with it? The mental math? The bar diagrams? All the books to juggle? Knowing the reason would help us advise you better! My kids are the same way - they could do it on their own many times but they like having me right there with them. I just view it as quality time. So, we often do math side by side on the couch. We do Beast Academy this way, Primary Grade Challenge Math, Singapore Textbook, read living math books together. At the table we do Miquon, Singapore Workbook, and CWP. And we also do work at the white board sometimes, which they seem to like a lot - this is more for exploring new topics and trying to figure out how to do really hard problems together. I think Singapore would be the best fit. Math Mammoth is meant to be self-taught, though I suppose you could sit there with her and read it to her, but it also goes slowly - probably too slowly for a gifted math student (unless you're willing to cross out a lot). Miquon is great, but it's only through 3rd/4th grade, though I wouldn't hesitate to use it as a supplement for an older child. I haven't used MEP, so can't help there! I have Life of Fred Apples and Fractions (and I've gone through half the Trig book).... and wasn't super impressed - it was just... alright - but you'll find people who swear by it. Singapore doesn't have a lot of repetition so it sounds like the best fit to me.

Several of my fractions videos are based off of this book! The book is very slooooooow and step-by-step. Some kids might need that, though. C-rods have been a WONDERFUL tool to help my kids understand fractions. I don't see the misunderstandings in them that I do in the kids I'm tutoring this summer, and I'm pretty positive C-rods are why. I totally agree about checking the basics. I am tutoring one child this summer specifically for fraction help. He's a bright kid, knows more than he thinks he does, but has lost confidence because of confusion in the area of fractions. All the rules get jumbled up in his head and he doesn't know what to do. After a few sessions, I finally discovered one of the big problems - he was confused about what the top number and bottom number mean. He'd say something like, "2/5? 5/10? Wait, 1/2?" So, of course, if that's confusing the rest is going to be. The thing is, if I drew a circle or rectangle and divided it up and shaded some pieces, he could tell me what fraction was shaded - I'm assuming that's because he'd done that in school a lot - but he struggled within harder problems. Using C-rods, bar diagrams, and doing some number line work has helped. Oh, and we're going through Math Mammoth Fractions, too, and I really like it so far!

They helped ME because I had to draw out each step and I could see what was happening in each step. It's very possible that it's because I'm a visual learner that it clicked so well. With algebra (and elementary math, too), I just followed the rules without understanding why I was doing what I was doing. Like, when you want to find 2/5 of 250, I knew you had to divide by the denominator and multiply the numerator, but I couldn't tell you WHY. The bar diagrams make it easy to see why. Bar diagram videos are a great idea! I'm just not sure I understand it well enough to TEACH it yet (well, to anyone besides my kids! I can stumble through it with them and they don't mind!). I'll have to work on that!

Why didn't I think of doing a bar diagram first? Maybe that's what we'll do. I'm still a bit worried, though, that they'll want to skip the diagrams because algebra would be easier.... Hmmm..... That's kinda sorta my plan for my almost 9yo. She hasn't done any Singapore 3 yet, but with what I've taught her with the C-rods over the past few months, I think she'll fly through it. We may even skip most of it. Not sure yet.... We'll also do MM Fractions, PGCM, and iPad apps. Shhhhh, don't tell her that's more than most people do for math!!!

Do you think teaching variables in BA 3C would conflict with the teaching of bar diagrams? Variables are more abstract than bar diagrams. I'm just concerned that my girls will not want to do the bar diagrams if they already know how to do it using algebra, and I think it's important to understand the bar diagram method. It actually makes it clear what is happening in the problem. Algebra doesn't. At least, that's my personal experience (though, I was taught procedurally instead of conceptually, so maybe that's the problem). I could turn a word problem into algebra and then follow the steps to figure it out, but I didn't understand what I was doing even though I got the right answers. Once I went through the CWP books (3 and 4) last year I truly understood what was happening because I could SEE IT. This is also why I'm hesitant about doing HOE and Dragon Box. And it's why I haven't added any more algebra videos to what we have online so far (see link in my siggy) - because I'm not sure it would be beneficial to my kids to learn algebra right now. So, opinions? Personal experiences? Anyone taught their kids algebra before bar diagrams and still found the diagrams useful? (My oldest has only gone through CWP 2, if that matters....)

Yes, Singapore will help him understand higher math better because it focuses on conceptual understanding instead of ONLY procedural understanding. I am tutoring about 15 people this summer (1st-9th grades + their parents, too!) who are in public school and they are all doing great with my "Singapore-like" way of teaching. They are all making connections and starting to actually understand math instead of trying to memorize a bunch of seemingly unrelated pieces of information. It's very encouraging to see! I would suggest going through my mental math videos linked below and teaching it to your child. Practice with him for a while and THEN have him take the Singapore placement test. It is usually the mental math that children haven't learned and makes them score lower on the placement tests. That's why I suggest that you teach that first. HTH!

From what I've read, yes, that would be too much. Saxon is very spiral and so you can't just skip over concepts the child already knows like you could in a mastery program. (Plus it DOES NOT focus on conceptual understanding which, IMO, is VERY important.) Math in Focus (again, from what I've read on here) is basically the same as Singapore Primary Mathematics, but it is meant for public schools and is more expensive. Have you looked at Singapore PM? We've used that and have been very happy with it! I'm sure someone will come along who has actually used both programs to help you more than I have!

:iagree::iagree::iagree: I'd suggest moving to Miquon. It is about $20ish dollars per year and it's strength is teaching concepts using Cuisenaire Rods. Click the link in my siggy to see how to teach the "Miquon way." Math Mammoth would be another good option. Or MEP (though I haven't personally used it. It gets great reviews by people who understand the importance of conceptual understanding.)

Try this. In case you're not familiar with Cuisenaire Rods, each color represents a number. The whites are 1 and are 1 cm long. The reds are 2 and are 2 cm long. Etc....

I agree that taking a break would be a good idea. I'd just let him play around with Cuisenaire Rods, no instruction or anything, just let him build. Then eventually teach him the number names and the concepts should "be there" without much effort at all. C-rods make it all pretty intuitive - fact families, commutative property, etc.

You're welcome! I love knowing I've been able to help so many people!!!

That's totally something my oldest would do! I'm glad my videos helped! I believe that in the original classrooms back in the 60's (I think?) they first introduced the rods without the number names attached to them. So in Kindergarten they would learn about addition and subtraction, but it would look like w+r=g instead of 1+2=3. I'm pretty sure that was so that kids would see the rods as more of an abstract relationship and, therefore, have an easier time naming them various things. I'm not sure if it actually worked or not. It does take a certain level of mental maturity, I believe, for kids to do fractions with the rods. The ability to switch names of the rods around at will is pretty abstract.

It's always best to teach something conceptually before teaching the algorithm/shortcut, but that doesn't mean you can't go backwards. I'm tutoring lots of kids this summer who have memorized the algorithms in PS, but have no idea what they are actually doing. So, I'm taking them backwards, starting with mental addition and subtraction within 20, and then moving them forward from there. The hardest thing is convincing them that it actually is important and will be helpful. Several of them balked at doing 1st grade level math when they are heading into jr. high or high school, but they got over that quickly once we were able to move on to long multiplication, square numbers, etc. and they could see why it was helpful to start where we did. So, I guess, what I'm saying is that if I were you I would probably backtrack and build my kids' conceptual framework. I'd probably keep doing the other regular stuff, too, so they don't forget it but maybe just once or twice per week.

You're very welcome! Here's the link! Here's another resource you might like, too, if you don't already know about it. We've done the Miquon/Singapore combo and I've been VERY happy with it and thought it was "enough," though we do more stuff for fun, too! But I'd be totally satisfied with just those two.

Maybe I should have clarified better. They don't work for LARGE multiplication and division done the way Crewton Ramone (and I think also MUS?) teaches. They can be used for smaller multiplication and division as shown in Miquon. But they really are a great tool for teaching the multiplication algorithm and long division!

There's nothing wrong with that set, but they are plastic which don't work well for multiplication and division. The wood ones work better for that!

Also, this may help! http://www.thinkingblocks.com/index.html

Have you just read through or have you actually worked out the problems? That might make the difference. I went through the CWP books 2-4 before I started with my dd on CWP 2. Could you and your ds figure it out together? Instead of you teaching it, maybe it could be the two of you working as a team to figure it out. That might be good motivation for him, too. Maybe if you give a few specific examples, some of us could help you figure out the answers to your questions....

Hi! Just thought I'd pop in to answer this question... The videos include much of what is taught in Miquon math. That is where I initially learned about how to use C-rods. Once my older daughter graduated from the last book, I went in search of more ways to use the C-rods to teach conceptually for the higher levels. I couldn't find anything all in one place, so I decided to make a resource for others like me who wanted this info but didn't want to spend all the time researching that I have. So, most of the K-3rd info on my site is based off of Miquon (though Miquon has much MORE to it like number line stuff and order of operations, etc.) and then it has stuff I've gleaned from Singapore, RightStart, Liping Ma's book, Math Mammoth Fractions, some really old books on Cuisenaire Rods, Crewton Ramone's videos, and other random things I've seen online. HTH!

Interesting. This is basically how we teach it with Cuisenaire Rods. I learned it from the Miquon curriculum.