So many people have given to such great encouragement. I find a lot of it encouraging to, since my kids are (or will be in a few months) 8,6,4,2. I just have two more thoughts to consider: first, as good as it is to get great ideas from others, really think about what works for you and what doesn't. For instance, I tried for two or three years to do the "school mornings, rest during afternoon quiet times" thing that works so well for many. Time and time again, I found myself frustrated and ready to the in the towel. Eventually, I figured out that myth sanity is helped more by spending an hour of afternoon time whiner littles nap to clean my kitchen, prepare dinner, and do the little bit of bookwork needed with my older kids while they sat on the kitchen counter and talked with me. I wasn't rushing them, I wasn't in a hurry since I was doing something else with my hands but they had all my mental focus still, and our mornings were much more enjoyable when we could all be together instead of trying to school while my littles wanted my attention or got into trouble. It turns out that even thought I thought having time to myself was the answer, it was much better for me to skip my me-time and instead have more relaxed time with my kids. My second thought is that I let kids do as much as they can independent as soon as they can And I cover"extras" likes science, history, etc only in passing out by checking out fun library books for them to look at. I make sure they do math and reading 3-4 times a week, and I'm happy. Everything else is up to then to pursue at this point. Also, sending a 3/4 year old to preschool for a year when they're "almost" old enough for school (not napping super well anymore but I'm not really up d for starting K yet... ) has always been a blessing for us. :)

One progression that really helped my kids get in the language-mindset I wanted was the following: 1) Take all favorite or well known movies, and watch them in minority language. Several times. 2) Rip audio of minority language track on movie and burn to CDs or Ipod for car trips or listening to while cooking/cleaning/walking/etc. 3) Register with the minority language audible site (e.g., audible.fr) and start purchasing audio versions of her favorite books. Many mp3 players can play things slower if she would like to slow the audiobook down to help her register more of what is being said. 4) Transition to audiobooks that are more advanced and originally written in minority language (instead of translations of favorites that were presumably written in English still). When I want to stretch myself, I even (quickly) repeat the audiobook (i.e., it says a line, I repeat line under my breath, repeat).

Ummm. Reading through this thread (at least near the end) was a bit depressing... SO my thoughts on the original question are that most people don't know how to talk about math, and if you want your child to be able to talk about math competently (regardless of whether it's math she learned today or math she learned last month), you need to first model what it looks like to talk about math. This may sound stupidly obvious, but I'm not sure it is in a homeschooling environment, since there may not be a teacher doing the teaching verbally and visually in front of the child (perhaps the child is reading or being read to, but that's different than having a mathematical conversation, imo) and thereby demonstrating what it is you would like. So I'm totally in agreement with the above posts about leading the child in what you expect and desire and modelling precisely what you would have her do. Perhaps, initially, that looks like you reading together, and you giving a summary/explanation of the material the way you would like her to and doing a sample problem for her. Then slowly involve her more in the process (let her come up with the sample problem, let her work out your sample problem, start to discuss the topic and then ask her to finish, etc. - whatever works for you!).

So I don't have a kid there yet, but my own experience with IB is this: good program, a few good friends, most of us got a year or more of college credit, but still not very challenging for very accelerated students. It was a great track for hard workers and bright students, but definitely not for *very* bright students. I can look at my kids right now (oldest is only 7, and certainly not as advanced as many of the kids discussed on this forum) and already see that it wouldn't be a good fit for them academically (at least the way my school did it, but I think the nature of the program is to have a lot of structure so that the educations can be relatively uniform), though the bonding with hard-working peers (some of them, at any rate) was good for me. Most of the IBers I knew also took 2-3 AP classes on top of the IB load each year or were involved with a sport or music that required practice an additional 3-5 hours a day.

Thank you! :)

I think it's easier to imagine if you just think of factors as grouping items. If you can group a items into x groups of d (i.e. d divides a) and you can group b items into y groups of d (d being the GCD), then you can look at a-b (assuming a>b) as taking the y groups away from the x groups (since a>b implies y>x and all groups have the same size d). What you have left is obviously still in groups of d, so it's clear that d must also be a divisor of a-b. It doesn't have to be fancy, I don't think, and might help if there is any lingering confusion (though I know you said she already got it by thinking of number lines and skip counting- sometimes an alternative way of thinking about it can just really solidify a concept, I feel! :) )

Ah, this might answer a lot of my questions regarding the offerings at the Y, when your experience seems so different from anything I've seen or heard of. I didn't realize the "levels" in formal gymnastics had any correlation to the "levels" in Y gymnastics, and none of the Y's in my area have anything beyond level 3 (one doesn't have gymnastics at all, one has only level 1 and the one we're at has up to level 3).

We love the Y! The prices are great and I love having my kids be able to do everything in one place (one kid does swimming, one does gymnastics, one does martial arts, all while I work out! ) But I feel like the quality of instruction our kids have gotten from them (in swimming, dance, and gymnastics) is much, much inferior to the quality they've gotten other places, even just basic cheer/tumbling places. I'm not trying to diss the Y itself - I had no idea that they had their own national gymnastics programs. But most of our classes are taught by 15-18 year olds with no real competitive experience themselves (most, but not all - a few are really good). For the price point, we still like the program, but I'm under no illusion that it the same as working with trained coaches. I'll definitely look into what you're saying, because I'd be really excited if there were options like this (maybe one of the other local Y's is the "main" gymnastic one around, and I never knew it?)! I just assumed that what we are offered at our nearest Y (which is the largest one in our city) was standard procedure. But I would absolutely love it if the Y could be what we're looking for here!

I really appreciate everybody's input so far! I know I don't always say things as well as I should, but I appreciate being able to sound here without having to worry too much about saying things just right or getting criticized. :) I'm definitely a verbal processor and so just hearing everyone else's thoughts and experience is really helpful for me to get a big picture view of things. I know that I really need to simultaneously just live in the moment (don't their interests change so quickly anyway?) but also set some boundaries with regards to what we are or aren't willing to do ahead of time, so that we don't get carried away in the moment (a tendency I've felt pulling at me when I see how they love stuff). Right now, I'm not anxious or worried or stressed (though I realize it may sound that way). But I also feel like I'm doing a lot of waffling and being in limbo on some things that really should just be decided (even if we re-evaluate again in a year).

But wouldn't it be nice if life came with a "how to" manual? lol. It's exactly this balance that I'm trying to find, and I'll probably find it right in time for my kids to change interests and we'll start over again! :) I love this, and I think it's really what I want for my kids! So maybe it's asking to much that I'd rather spend our time and money on activities and hobbies that they could carry into their adult lives. (At least when it's a bigger commitment in terms of time, finances, etc.) Music falls into that category for me, because lots of adults continue music just because they love it. Hiking, biking, swimming and rock climbing all fall into that category. My son started Taekwondoe, and I feel like it, too, falls into that category (the studio has a wide variety of ages, from 6 up to 60s). And I'm open to recreational, light-hearted pursuits of things that probably won't be life-long endeavors (so we do stuff like dance, gymnastics, etc. in the very laid back environment of the ymca), because it's not a huge investment for me there. But it doesn't ease my inner turmoil that says "Do more! They're so good! Competitive gymnastics, here we come!" on the one hand, and "Whoa, crazy lady! You know we don't to spend that kind of time, money, and energy on something so (relatively) short-lived!"

I realize that what I'm about to say may sound counter-culture and extreme, but it seems to me that we (in our country) generally place to much value on sports. Rare is the young person who makes a career out of it, though I recognize there are other benefits (teamwork, sportsmanship, etc.). So with that in mind, I really struggle to decide on the value we want to put on athletics and sports with my kids. They want to be involved in all sorts of stuff. So far, we let them try things out a bit at the YMCA and go a little deeper when they want (e.g., my 5 yo wanted ballet after a short class, so she's now in a year-long ballet class). They're pretty good little sportsters, in their respective activities. I feel this constant pull between wanting to let them go further, wanting to invest so they can pursue what they love, and the much more pragmatic piece of me that says that it's unlikely to develop into a life-long hobby, and thus there's not a huge reason to throw all our time and money into right now when they could just do it leisurely some place like the YMCA and when I think there are a LOT of other very important things for kids to be learning/doing/spending their time on (relaxed time with family, free play, learning to serve the poor and needy, etc.) How do you handle this pull, or am I the only one who really struggles with it? I was so proud when my little 3 yo passed her Kindergarten gymnastics skills, and I when I think about it, I think, "Yes! Let's keep pursuing this!" She just loves it! I was so frustrated when my 5 yo was being taught incorrect gymnastics forms by teens who aren't even gymnasts themselves, and I think "No way! Move her to a better place!" But better is more expensive and too high strung for us (dance this year has been far to competitive for our tastes). If I'm not willing to be serious down the road (i.e., if I don't think we'd want to do competing things with lots of travel), should I not even let me kids start exploring down that road? Or let them, and draw those boundaries later? Maybe this is just an issue where I need to do some deeper soul-searching. But any thoughts are welcome. ETA we do live active lifestyles with lots of time outdoors (hiking, biking, walking, etc). But I think I'm having a hard time feeling like the life I feel is best for our family will somehow deprive my kids or that they'll resent me for lack of opportunities when they were young. Also, it seems that the Y by us doesn't have all the same offerings of some other Y's, so our options, currently, at least seem to be limited to either very basic Y classes (where the teens aren't aware of the fact that a 3 yo shouldn't be bridging in gymnastics, for instance) or a private place that does want lots of time and money.

We're in the process of doing some testing. I don't know exactly what all we'll end up having tested. His is part of a neuro-psych eval. It will end up being 3-5 sessions of 2-3 hours each. Both our primary and secondary insurance cover it without pre-authorization, but he does have ASD and SPD and tested high for ADHD (though not as a formal dx since the psychologist feels that SPD often causes ADHD-like symptoms even without actual ADHD), so I don't know if they would've covered it without that ASD dx.

Then what? I used to have this grand long-term plan about how homeschooling was going to go. And then I had four kids and they're 2e and things haven't gone at all to plan. So the last year has just been flying by the seat of our pants and focusing on reading, writing, and math with lots of free time to run and play and be kids. But just in the last three months, my 7 yo has started reading relatively fluently in our minority language (German), and I've been left wondering where to go with him now. Would you just have him focus on reading for a while, taking in whatever he wants and strengthening his skills that way? Would you start right in on normal age/level appropriate native curriculum? A bit of both? FWIW, we have no access to German books unless we buy them, so it's a bit harder (and more expensive!) to expose him to the variety of literature that we have access to in English.

Could you link to (or just copy and paste) Quark's list? Do you mean her big long math thread? I didn't mean to double up on something that's already been done! It's so hard to keep track of everything and still keep my head on my shoulders with my four kiddos! lol. :)

I was thinking about the books folks were recommending for fun math reading, and wondered if we could get a list going of good subject books for accelerated kids in various fields. I'm thinking mostly of stuff like math and science, but would gladly expand as people provide their suggestions! :) My kiddo loves to read and I would much rather give him interesting science books at this age than do any formal science with him. He's already read stuff like LOF and BA just for fun with math, but I'm not really looking for curricula or textbooks. One of my personal favorites is The Code Book, by Simon Singh. The math is straight-forward but it's gets people interested while covering a good bit of history too. I'll be honest that my kiddo loves the "Magic School Bus presents...." books as well (different than the normal Magic School Bus in that they don't have much of the fictional side to them). Way more full of information than a typical picture book, but he's still very enamored with bright, colorful pictures! lol. What are your favorites? ETA: Maybe mention any questionable content or advanced knowledge needed (e.g., if a book assumes a working knowledge of trig or number theory or something).

I've been looking for Christian biographies to read in the evenings with my kids. I've come across Trailblazers, Christian Heroes then and Now, and Lightkeepers (seem like they may not be real stories, but it's unclear). I'm wondering if folks here can recommend something else or if you can strongly recommend one of these over the others? I'd really like some picture book options as well as short chapter books!

I just wanted to respond to this and point out that the NSA (not NASA, but National Security Agency) recruits HEAVILY at all upper level math events, because they are the largest employer of mathematicians in the country. While spending a summer interning there (and it's nice, bc you get the same salary as permanent employees at your education/experience level) we also got tours of the CIA and several other notable places that recruit mathematicians pretty heavily, and they work as mathematicians. They can't tell you how *many* they employ, because that's classified... But they can tell you that they hire more than anyone else in the US. :) (Caveat: that was 10 years ago that I worked there, so it's possible they're no longer the largest employer of mathematicians in the country.)

Well insurance ended up covering it, but now I want to bang my head against a wall. Lady gave him the Wisconsin card sorting test, and he thought it was just a long game like paper, rock , scissors. Kept getting eight or nine right and then the next one wrong. I asked him about it in the car afterwards, and he just responded that she'd doneso many the same, he thought she'd be ready to switch already. I don't feel like it tasted his ability to adapt at all. Sigh. He's such a black and white thinker, I wonder if all the tests will be this frustrating? I really wanted to say something, just to help him understand that she's not just choosing answers randomly and it's about finding the pattern, but was afraid of messing up the results. What would you have done?

Good to know about the show. I only watched bits and pieces, so I may not recommend it again (and am thankful that this was my first time). :)

Love that list, too! I just thought I'd also chip in to add my own encouragement to the OP to do lots of fun stuff and explore a lot. There's math everywhere, and so much if it is cool. I usually have more ideas than people actually want to hear (***needs to get better at reading social cues that she's geeking out on math***), but one idea for a girl of that age off the top of my head is (if she hasn't already) that she could watch the Bletchley Circle series (dramatized, but still kinda cool) and do a study on cryptography. Look into the Enigma. What did these ladies actually do? Look at the history of cryptography (maybe read the Code Book and other similar ones). Study modern cryptography. What is RSA and why/how does it work? Why are primes so important? Branch off into number theory. Why are large primes so hard to find? Learn basic coding and program a few of her own programs to find prime numbers or determine if a number is prime. Time them and see which ones run more quickly. Look into large of numbers her programs can actually handle - how do other people handle much larger numbers (e.g., 200 digit numbers). Introduce her to simple, but rigorous, proofs in the context of basic number theory theorems regarding prime numbers. What sorts of cryptography is used by things she uses (banks, email, etc.)? Is it all RSA or do some actually use other techniques? What does the government use or what has it used in the past? Just keep going deeper and further into any little subarea that she finds interesting! :) When you've exhausted this trail, start over with another interesting topic. You don't have to scratch very hard to find math under whatever you want to talk about in life (though some are more of them will have more interesting math than others, of course). Another one I love talking about with kids that age would be kinds of infinity and how the numbers we usually work with are a negligibly small subset of the entire set of real numbers (compare countable and uncountable sets and classify integers, rationals, irrationals, transcendentals, etc. as one or the other), even though they're certainly not negligible in terms of their importance or usage. Ok. I'm turning off my inner geek now. :)

Thanks! :) Bump for other ideas?

Ha ha ha! This is so not what I meant! Sorry for the confusion and thank you for the thought! :) Though maybe I SHOULD see if he's interested in juggling.... lol.

This reassures me some, bc my guy is nowhere near as quick as your guy (he's 7.5 but only finishing up 4A right now), so it looks like it'll take a fair while to get through all the aops stuff. So if we do just spend some time finishing BA whenever he's done with SM, then maybe pre-alg will be a good fit for him. The books certainly look long enough to spend a LONG time in each one!

This is my boy. And I've considered nixing the CWP, except that I've gotten so much advice about advanced learners going deep and not just fast, and I don't want to do him a disservice. I'm really on the fence about continuing it because I am loathe to continue something that may turn him off to his current love of math.

My kiddo is nowhere near that fast, so we've got a bit of time yet, I think. :) How old was your older when he finished up SM then? I'm just curious how long the pre-alg through pre-calc took him.