What’s the mistake? Can you figure out how this happened?

If we’re nice then maybe Nico Rowinsky will slip into the comments and let us know what happened with this kid.

• Missed the 7 when s/he used the calculator? Didn’t think of reasonableness, before or after.

• Sounds like a good guess to me. Since there is no student work, the student either did the calculation elsewhere and copied the answer here, or they solved it on a calculator and made the mistake you suggest.

Regardless of how this mistake came to be, it’s obvious the student does not have the habit of mind to look at his/her answer and ask, “Does this answer make sense? Is it reasonable?” This is a habit that is supposed to be fostered throughout a student’s career in school. It looks like that didn’t happen with this student and the teacher needs to encourage that thinking from the students.

I wouldn’t be surprised if other students in class have this same issue. Even if they’re calculating the correct answer, that doesn’t mean they’re verifying for themselves that the answer is reasonable.

• l hodge

They think minutes is spelled m e a n (joke). That suggests to me that they were not really thinking about minutes and how long the pupils took on the logic puzzle. The student is not really engaged with the question. They also might not have a good intuitive understanding of mean. I don’t know what went on in class, but the handout highlights the computational definition for mean without giving a clear sense of what that actually tells you about the times or other data you are looking at.

• Could be doing a faulty partial products division: figure out how many 20’s in 340 (or how many 2’s in 34), put that in the 10’s place (that’s the faulty part), figure out how many 7’s in 0, put that in the 1’s place.

Personally, it was harder for me to see how unreasonable this answer is — place value mistakes don’t blare out at me the way other mistakes do, and it’s easy for me to be casually off by an order of magnitude before I stop and think. It’s easier for me to realize that the average time taken can’t be 170 minutes if most of the data is in the teens. And I might check that the 340 is right before I check the division!