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Cake and Pi

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About Cake and Pi

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    Hive Mind Queen Bee

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  1. I laid out 5 tally sticks, 4 parallel to each other and the 5th across and on top of the other 4. He's learned that this is 5. So I asked him how many there were and he answered "five." I took the top stick off and moved it a few inches to the side as he was watching, then asked again how many there were, but this time he said "six." I put it back and he said there were 5 again. I told him I was just moving the stick, directed him to watch closely, and put it off to the side again, and again he said there were 6. I asked him to count them, which he did and then told me there were 5. I tried va
  2. ... It's 7 big cubes, 7 square flat thingys, 4 bars, and 5 tiny cubes. 😄 Obviously that doesn't count as a formal definition mathematically speaking, but that's how the number exists in my mind in it's most basic form -- no trading involved. Now, trading absolutely starts happening when I try to manipulate 7745 on a larger scale, by, say adding or subtracting 2153. But if I'm just adding or subtracting a 1- or 2-digit number I'll be zoomed into that vertical number line jumping up or down it, and there's no trading there either. Yep. I was pretty floored. I sincerely thought he h
  3. I think so? Yes? I think our mental models are reversed, though. It goes the opposite direction in my head with trading flowing from place value instead of the other way around. Both models accomplish the same thing and seem to contain the same components. Maybe it's just a difference in how we each first made sense of quantity in our early days? Except... I go straight to trading when working in other bases... which again may be because that's the way I first understood other bases. Different mental models in different bases. Very inconsistent, lol. It sounds like you are working
  4. All of this 100% fits my observations with DS 7. Both, they're interrelated. Just google HIE. CP is a pretty misleading term for his condition, honestly. It's probably better to just stick with encephalopathy. Whole exome sequencing was clear. He has ASD and ADHD and probably SLDs, but so do some or all of the older three. The only difference between them and him is the encephalopathy. No, he's not really there yet. He's close, though. He can count on with with smaller quantities in context. Like he knows when his brothers have 3 slices of pizza and he only has 1 and can even
  5. My older three kids never did counting on at all. They also never did the pre-skill to counting-on that counting-on replaces and is more effeciciant than: counting up from 1. So, when I gave them an expression like 4+3 or a group of 4 and 3 more objects, they never counted up from one like "I have 1, 2, 3, 4... 5, 6, 7" to get the sum and they also never counted on like "I already have 4, so 5, 6, 7." I taught them to subitize 0-10 as five-and-something first, absolutely no counting. Then they automatically regrouped with 5s instead of counting. So, 4+3 was "Move 1 from the 3 to the 4. Now I h
  6. Unfortunately, this did not work. 😞 It was a great idea! I tried getting the sample on this version of iTunes and got "This book sample requires an iPad with the latest version of iOS and Apple Books installed and Automatic Downloads enabled." Our charter funds roll over in April, after which I'll have a fresh $1,800 at my disposal for technology and curriculum for DS 7. I may end up just buying an iPad at that point. This is not the first time I've felt like we really needed one for something.
  7. Oh, I don't. I would think that if he was going to get it any time soon, though, he would understand *some* portion of all of that, not all of it. I was just illustrating that that he doesn't have any understanding at all. None of the pieces are there. I think @Kanin might be right about DS 7 thinking the trading game is hilarious precisely because it makes no sense to him and he thinks it's funny that such an obviously unfair trade (to him) is being promoted by me. No idea, really. Right now I can't even get him to associate 23 with 2 yellows and 3 greens, though, and I'm not sure I r
  8. Okay. So just for fun, I decided to ask the numerate members of my immediate family about their mental models for numbers. DH: He says he sees just the digits of a number, the way one would write the number, in his mind with an implicit understanding that the digits are multiplied by powers of ten, and that's it unless he is given context. With context he switches to visualizing quantities, quite accurately, so it sounds like he uses a quantity model. He gave me some examples that I'm not going to remember correctly. Something like one cubic foot of concrete is a cube *this* big (holds
  9. If I give him two 10-chips and three 1-chips he cannot name, write, or point to the number/quantity represented, neither can he represent the quantity with any other manipulative (ie. on abacus, with base-ten blocks, etc). If I show him the written number "23" or say it or build 23 with abacus/base-10 manipulatives he cannot choose two 10-chips and three 1-chips to represent it. There is really zero understanding. He just knows that he can exchange ten 1-chips for a 10-chip (but again, not the other way around). Honestly, it means about as much as if I'd trained him to always exchange 7 tooth
  10. Nope. The chip trading is just a memorized rule. He's memorized that he can trade the ten 1-chips for a 10-chip (but not vice versa) and that's exactly where the meaning ends. What would that look like? How would you present such a model? Would my home-made c-rods (that essentially show a quantity of glued-together cm cubes) fit in that model, or do you think they are more likely to cause confusion in a quantity-based model?
  11. Maybe! I have place value chips. Each place value has its own color, and on one side the units all have "1" the tens all have "10" etc. He understands trading. I've played games with him where he can trade me ten yellow 1 chips for a green 10 chip, and he gets that and thinks its hilarious for some reason. But I haven't gotten him to connect that back to physical representations of numbers, like base-ten blocks, the abacus, or c-rods, or to written (or place-value card) two-digit numbers. And we have and play Tiny Poka Dot! No, I don't think we can get our hands on an apple devic
  12. I cannot figure out how to buy or view her ebooks. We only have Android devices, and I can't find an Apple book reader for my phone or PC. 😞 Not at the moment; we're trying to get speech up and going again. Other than the four-month gap in services we're currently in, he's had 1-4 hours of speech therapy per week pretty much continuously since 16mo, though. Hopefully we'll get through the wait list here soon. He sequences pictures like a pro, just not words. He can't tell you (and doesn't understand) a short verbally delivered story. But if you give him pictures of an event th
  13. Average as of last testing, but it keeps going up as he gets older. This could be related to his brain slowly remodeling after perinatal injury, or maybe they just haven't been able to accurately measure his IQ all along because of his communication (esp. low receptive) difficulties. I don't either! It seems to affect every part of him, though. He technically has super mild CP (the rare, non-spastic low-tone kind), growth problems, learning and processing struggles, and I presume his unusual memory stuff is also a direct result. We have a strong family history of giftedness and autism
  14. I'm trying to decide what direction to go with my 7.5yo (2nd grade age) SN learner and would love your opinions and input. I'm using a mashup of Right Start 1st edition level A, ST Math kindergarten level, MUS Primer, and my own inventiveness with a variety of other materials and manipulatives. I have a strong math background and already successfully taught my three older kids all of this stuff already, but he's his own animal. Nothing I thought I knew applies. Altogether it took him 6-7 months to master (90% accuracy or so) subitizing and counting with 1-to-1 correspondence 0-10 alo
  15. My DS 9 loves EMF. He calls it "magical meep math," lol. In all seriousness, though, it's good math, just as solid as AoPS, but with a different emphasis. The two are so incredibly different that a kid could probably do all/most of EMF and then restart near the beginning of AoPS and vice versa. The "pre-algebra" courses cover much more than pre-algebra and in a way that is dramatically different from AoPS. My DS 9 did the first 5 EMF courses off and on in between AoPS Geometry and Intermediate Algebra assignments and it was new and interesting enough to keep him going back for more. He sp
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