Milk has been on sale at our local gas station/convenience store. Griffin and I walked up there the other day to buy some milk. Two percent milk for the kids and me; skim for Mommy.
Me: Griff, the milk we just bought was $5.50 for two gallons. How much was each gallon?
Griffin (9 years old): With tax included? Or not included? I don’t do tax problems.
Note: I weep for the loss of 4% and 5% sales tax rates. They were so easy to compute mentally, and such a nice introduction to the financial world for elementary age children. Minnesota’s sales tax rate is presently 
Me: No worries about taxes. There is no tax on milk.
G: OK. Two twenty-five. Er…no that’d be $4.50.
So…
$2.75!
Me: How did you do that?
G: Well, I thought it would be $2.25, but that’s half for $4.50, so there’s an extra dollar. So I split that dollar in half, which is 50 cents, put that with the $2.25, which is $2.75.
Me: Nice. I could see that thinking in your first answer; when you said $2.25. I was curious whether you used that first wrong answer or started over from scratch.
When I thought about it, I did it differently. I thought that half of $5.00 is $2.50, then I need to add half of 50 cents. Same answer, though. $2.75.
So what do we learn?
I called in to a Minnesota Public Radio program on math education last week. One of the pervasive questions in such conversations is about how kids are learning to do arithmetic in modern American schools, and it arose in this program.
The thinking Griffin is doing here is lovely, and modern math curriculum is trying to encourage more of it than in the past. He is splitting 
This thinking is not closely related to the standard long division algorithm. One of the big challenges in school curriculum is relating mental math strategies such as Griffin’s to efficient algorithms that are more useful for complicated computations. I have a few resources parents may find helpful over at Sophia.org.
Starting the conversation
Anytime you find yourself wondering about such things, ask your child to think along with you. I wanted to know whether the gas station price for a gallon of milk was a good one. This required me knowing what the price was for each gallon. Not a hard problem for me, but I had to think for a moment. So then I asked Griffin. Do the same at the grocery store, the convenience store, the hardware store; anyplace where things are priced in groups.
If your kid needs a challenge, ask about gasoline. I paid x for y gallons yesterday. How much per gallon? This one will likely require estimation skills!