Two Digits with Numerals (2)
What To Look For In This Video
- I started with a problem (79 - 21) that does not require an exchange of a ten. The student was able to solve the problem without recording any intermediate results.
- Even for this simple problem, I wanted to hear an explanation (in other words, a proof that the result is correct). Notice how she proved that since 3 + 4 = 7 then 7 - 2 must be 5.
- The next problem (72 - 23) is harder and I wanted the student to explain why it is harder.
- Even here, with a small mistake, she was able to solve the problem “in her head” - that is, without recording anything but the answer.
- Notice that her strategy is different from the one that she had been using previously. (Instead of taking 3 ones from one of the tens, she took the 2 ones that she started with and then 1 additional one from one of the tens. Of course this also is not the standard algorithm.) To me, this is even more evidence that she is thinking logically about the problem and not mindlessly following some mechanical procedure.