Thanks all, especially for the comments about enthusiasm. Â Yes, dh and I enjoy math, though probably not as much as the girls do. Â Of course, they have not had any school to make some parts seem like a drudgery.

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I did have one thought after I posted, and that is that dd1 already has a clear concept on multiplication, something she has understood for years. Â She hasn't worked out every combination, but she understands what's happening perfectly. Â I shouldn't be so down on times tables at this point, then, and she could even explore multiplication further if I mention creating a table for herself. Â She already did something very mathematical with her rainbow Sharpies when she first brought them home-- she drew dresses in every color combination. Â First a black top and purple skirt, then every combination with Â black top. Â Then a purple top, and onward and etcetera. Â I'm sure she could come up with a times table, especially if it involves her beloved Sharpies (I wish I had never introduced those--the fumes!)

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I'm not sure she's 100% clear on place value yet. We do the occasional "100+80+1" as suggested. Â I see inklings of understanding when we talk about it--yes, we really do talk about this stuff randomly! Â Crazy! Â This was never dinner-table conversation when I was growing up! Â Thankfully, dh has not tried teaching her "carrying" or whatever the proper mathematical name for it is. Â And I'm a bit nitpickity when one of them says "14+20 is 34 because 1+2 is 3 and 4+0 is 4." Â I feel compelled to say "you do understand that it's really because 10+20=30 and 4+0=4?" Â Perhaps it's time for an abacus around the house? Â They'd have fun with that!

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The funny thing is, I wish I understood this Base 10 system we have--really grokked it (Hey! My Spellcheck recognized that word!). Â Why "10" is not represented as some other random symbol, more like Roman numerals. Â I'd really like to hear the history of the number system we use. Â That would help me clarify the brilliance of place value and the elegance of the system. Â I suppose even Roman numerals had special symbols for 5 and 10, 50, 100, etc. Â Interesting that humans seem to place particular importance on the number 10.

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6.5yo dd2 tells me "But you have to understand me when I say 2+2=22." Â "I get it, Boo Bear. Â You mean that a 2 and 2 written together make the number 22." Â "Yes. Â People should understand that." Â "I do, Boo Bear. Â I do!"

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