“I would eat the extra meatball.”

Simon Terrell recaps his lesson study trip to Japan with Akihiko Takahashi, who was the subject of Elizabeth Green’s American math article last week:

In one case, a teacher was teaching a lesson about division with remainders and the example was packaging meatballs in pack of 4. When faced with the problem of having 13 meatballs and needing 4 per pack, one student’s solution was “I would eat the extra meatball and then they would all fit.” It was so funny and joyful to see that all thinking was welcomed and the teacher artfully led them to the general thinking that she wanted by the end of the lesson.

I can trace my development as a teacher through the different reactions I would have had to “I would eat the extra meatball,” from panic through irritation to some kind of bemusement.

BTW. The comments here have been on another level lately, team, including Simon’s, so thanks for that. I’ve lifted a bunch of them into the main posts of Rand Paul Fixes Calculus and These Tragic “Write An Expression” Problems.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. More here.


  1. I love your observation about your development as a teacher, Dan. Spot on! For me, the fourth phase has been “Finally! I was ready to say it if no one else did!”

  2. I can confirm that eating the meatball would fit best with my personal ‘real life’ ;-)

  3. Hooray for the student who admitted what most of us would think, but even more kudos for the teacher who created the environment where the student felt valued enough to feel he could answer in that way.

  4. I’d then ask, what other number of meatballs would leave you with one for you to eat . . . two . . . three . . . or extra hungry, four.

  5. I run into this same kind of thinking when we answer “Which is the better buy?” Problems. A student will occasionally say “But I don’t need 32 oz I’d just buy the smaller one.” Sometimes it’s hard to argue with that logic. You can’t buy Costco sized packaging for everything. I have learned not to just laugh those kind of answers off, but to just make them part of the conversation. I would not have done that in my first year of teaching.