[Bob]

And what about 10 times 10? Do we actually multiply that?

Probably not. Most people don't need to even think about calculating it.

Calculating 10 times 10 can be done, though, by two different methods:

You can append a zero to any number to multiply it by 10. This is a shortcut which is only available for the base of the number system. (I work with hexadexcimal, base 16, a lot. I know that I can multiply a hex number by 16 by simply appending a zero to it.)

You can also multiply it out longhand as you would do with any other multi-digit numbers.

   1 0
   x 1 0
   -----
     0 0
+1 0
  -----
  1 0 0

I am not sure there is any difference in not multiplying 9 times 9 and not multiplying 10 times 10.

What steps can you follow to multiply 9 times 9? How would you teach someone how to do it?

You can either:

1) Count up by 9s until you reach 81. (This is actually addition, not multiplication.)

or

2) Multiply 9 times 10 by adding a 0 and then subtract 9 from the result. (This is just a shortcut for adding up the 9s.)

or

3) Remembering that it's 81 from having memorized the multiplication tables.

[NCLaw441]

I agree with you completely, except for the conclusion from your prior post. Just as we get 9x9=81 from memorized multiplication tables, we do the same regarding 10x10. So, instead of using the numbers given and then applying the multiplication table, we change the numbers and THEN apply the multiplication table. Neither is really estimating, it seems to me.