The math problem I gave the boys was that they had $462 and had to give me $58.
First I had them use our place value cards and count out $462.
OK...they both have the $462. But now HOW do they give me $58? I expected Douglas, 8, to have the solution quickly as he has been doing subtraction with borrowing for a couple years. However, we had not used these cards in a long time and he had forgotten how to use them. I had brought them out to make Charles, 6, do some thinking. So for the moment they are both stumped.
Charles gives me the $50, but has no idea where or how to get the $8.
To help them, I keep pointing to the extra cards, referring to them as a "bank."
Charles simply takes the extra six 1s he needs from the bank.
So Douglas follows suit. Problem solved, right? Hmmmmmmmmm. I tell them there is just one problem. I am going to have to have them arrested for robbing the bank. They laugh, but put the money back.
They keep thinking and moving the cards around, but are finding no solution.
About this time, Charles remarks, "This is the hardest problem ever!"
I remind them again that this is a bank....Charles says, "I got it!" and he told Douglas his idea. He could give the bank one of his $10 and get some $1s.
Douglas immediately sees what he had been missing. He could "borrow" and he knew how to do that.
Now they still have $462, just with different denominations. So...
...it is now easy to give me $58.
And the answer is $404. $462 minus $58 equals $404. PROBLEM SOLVED!
And a new concept has been introduced. We went on to work the problem out on paper and it made complete sense to him. He worked several problems with borrowing...both using the cards and on paper.