Right now, she can write from 0 to 99, and can tell
predecessor and succesor of any number.

One night, instead of story, i taught her summation,
like if you have 3 toffee, and I give you 2 more,
how many will you have ... etc.

in couple of days she was able to do all single-digit
addition and subtraction mentally, using finger beyound
1 digit.

I never could have told her 2 + 2 = 4, since she can't
associate symbols 2 , + and = with anything.

Now i'm trying to find a good example for multiplication,
some thing related to increase and decrease in area, that
kid can relate to ..

Hope That Helps

https://www.cut-the-knot.org/pythagoras/12MatchesAreaPuzzle.shtml

may be too much for a little kid, but it does give an idea of possible manipulations.

To stick with your toffees, maybe "you have 3 friends, and each friend has 2 toffees, how many do they have together..."

We were very surprised that he figured it out all on his own.

I am not a teacher (I'm an engineer) but I am wondering if it would be beneficial to consider some practical project that would be of interest to young people, but requires some math to get it done.

For example, when I was about 9 or 10 years old (many, MANY years ago), I was interested in developing secret codes to communicate with friends and play mates. That was back in the days when TV programs like "The Man From U.N.C.L.E." were popular. Anyway, I think I might have been motivated to learn the number theory behind public key cryptography, if it had been discovered by then (well, it had not been discovered in North America yet by Diffie, Hellman, et. al. but it had been discovered and kept secret much earlier by Brit'sh cryptologers, so it was not available then).

Anyway, my point is that, if there is some activity that would be of interest to young people, and could be used to illustrate math principles, then it might pique their interest in using math to solve the poblem at hand.

Another example for older (high-school?) students might be the classical problem of cuttig out the largest possible semi-circular table top from a sheet of rectangular material (such as plywood or plastic or some such) or the more complicated problem of cutting out TWO congruent semi-circles (to make a circular table top) from a rectangular sheet of material. (Here, a math teacher could collude with an industrial arts - or what we used to call "shop" - teacher to make this into something like a "unit study".)

Would these kinds of "practical" problems be of interest in teaching math principles?

Regards,

anXZMouse
(which is equivalent to aNonYMouse, unless, of course, the XZ mouse happens to be at the origin ;-).