See the math problems that set off a New York DJ’s anti-Common Core rant ==> http://twitchy.com/2014/03/02/see-the-math-problems-that-set-off-this-ny-djs-anti-common-core-rant/
(https://scontent-b-ord.xx.fbcdn.net/hphotos-ash3/t1/1920068_10153883193810084_1890319477_n.png)
See the math problems that set off a New York DJ’s anti-Common Core rant ==> http://twitchy.com/2014/03/02/see-the-math-problems-that-set-off-this-ny-djs-anti-common-core-rant/
(https://scontent-b-ord.xx.fbcdn.net/hphotos-ash3/t1/1920068_10153883193810084_1890319477_n.png)
That's actually a nice little visual diagram illustrating - literally - what we mean when we say things like "carry the one" or "borrow from the tens".
At the top, we're dealing with subtracting 52 from 134; unfortunately we can't just subtract down each column because, for example, 5 is greater than 3. So what to do, what to do? We "borrow" a couple of units from the next higher position in the number 134, we "add" those extra 10 units to the 3 - which gives us 13, btw - and now we can do the actual subtraction.
Visually, that subtraction is accomplished by x-ing out one dot for each unit of value contained in the number being subtracted. So, in the middle column, the student first "added" in those extra 10 units - shown by the 10 dots at the bottom (5 of which are x-ed out) - and then we x out 5 of those 13 dots, representing the subtraction of 5 from 13. That gives us the result - 8 - which the student has written at the bottom of the middle column. On the right-hand column we do the same thing, we have four dots representing the 4 in the ones place in 134 and we x out 2 of them to represent the subtraction of 2 from 4. That gives us the result - 2 - which the student has written at the bottom of the right-hand column. For the left-hand column we need do nothing further since there is nothing in the hundreds place of the number being subtracted; however, we need to note that the student correctly x-ed out one unit from the hundreds position in 134 to represent the unit that was borrowed and converted into 10 units in the tens column. Since there are no dots remaining in the hundreds column, there is nothing to write down. Consequently, the answer, as visually demonstrated by the graphic the student drew, is that 134 minus 52 is 82. Checking on my calculator confirms that.
The second question simply calls for the student to abstract that principle and apply it twice, once to a borrowing from the hundreds to the tens, and again as a borrowing from the tens to the ones.
Again, that's a pretty nifty pedagogical tool there. I wish I'd thought of it when I was trying to help my daughter figure this part of subtraction out.