Did everyone get it wrong? The pitfall of 240-160
"You have 240 yen in your wallet. You bought a snack for 160 yen. How much change will you get?"
I encountered this problem at a workshop a while ago. At first glance, it looks like a very ordinary subtraction word problem. However, when I thought about it carefully, I felt it was a very good problem.
So, I immediately gave it to the children in my class.
Then, without hesitation, all the children wrote the equation:
240-160
They then looked satisfied, with expressions that said, "I did it!"
So I asked them back, "Is this really the only equation?"
The atmosphere in the classroom changed.
"What if you pay with 200 yen?"
"You could also pay with 210 yen, right?"
"If you had exactly 160 yen, there would be no change."
As they said this, the children began to write the following equations:
240-160
210-160
200-160
160-160
What this makes us realize is that children have a tendency to try to form equations by using the numbers written in the problem text exactly as they are when they see a word problem.
However, what about in actual shopping?
Even if you have 240 yen in your wallet, it does not necessarily mean you will hand over all 240 yen at the register. If you are buying a 160 yen snack, you might hand over exactly 160 yen, or you might hand over 200 yen or 210 yen.
In other words, there are three possible ways to pay in this problem: 160 yen, 200 yen, or 210 yen. (Handing over 240 yen exactly is unlikely in normal shopping.)
The interesting thing about this problem is whether or not one can realize that the "amount of money in the wallet" and the "amount of money actually paid" are not necessarily the same.
Once you understand the mechanism, it is not difficult. However, for children who try to form equations by looking only at the numbers in the problem text, isn't this truly an eye-opening problem?
What is truly important in word problems is not just looking at the numbers, but concretely imagining the problem situation in your head.
That is precisely why I want children to encounter many such "good problems that cannot be solved without imagining the problem situation." The ability to think while picturing real-life situations, rather than just numbers, is the foundation for solving word problems.