Grant Wiggins has posted a dialog between himself and some middle school mathematicians. Here is an excerpt from one of the letters they sent to him.
With that problem conquered, we moved on to the three-rock episode. Drew didn’t like our chances here. With all his experience in adjusting the four rocks to the perfect weights, using just three didn’t look good. We then remembered an earlier part of your email when you commented that future texts should leave out material to make problems more interesting. Were you doing that to us here, we wondered? Probably so. Therefore, we assumed that we had poetic license to create a little backstory for Farmer John.
So Farmer John has his rocks returned from Farmer Joe and is, at first, heartbroken to see that his forty-pound rock has become a one-pound rock, a three-pound rock, and a thirty-six pound rock. The original rock was used to measure the perfect amount of hay, and can still do that as a trio… and now the rocks are now a bit more portable, for those days that are hard on the back. So, things are looking up.
Farmer John also realizes that he now has the capability to measure other weights of hay. Using both sides of the balance, he can accurately measure hay in the amounts compiled by Kelsey, Aidan, Kirby, Jon, and Kyle and shown on the next page…
The letter is an excellent example of students thinking mathematically, as they ponder some of the various ways they can adjust the problem given to make it more interesting. It seems clear from this exchange that a pro-tip when teaching mathematics is to let students modify the problems to explore other possible interpretations.