How long will it take Marie to saw another board into 3 pieces? So this is supposed to be really simple, and it's taken from the following picture:



Text-only:


  It took Marie $10$ minutes to saw a board into $2$ pieces. If she works just as fast, how long will it take for her to saw another board into
  $3$ pieces?


I don't understand what's wrong with this question.  I think the student answered the question wrong, yet my friend insists the student got the question right.

I feel like I'm missing something critical here. What am I getting wrong here?
Haha! The student probably has a more reasonable interpretation of the question.

Of course, cutting one thing into two pieces requires only one cut! Cutting something into three pieces requires two cuts!  


  -------------------------------  0 cuts/1 piece/0 minutes 
  ---------------|---------------  1 cut/2 pieces/10 minutes 
  ---------|-----------|---------  2 cuts/3 pieces/20 minutes 


This is a variation of the "fence post" problem: how many posts do you need to build a 100 foot long fence with 10 foot sections between the posts?  

Answer:  11  You have to draw the problem to get it...See below, and count the posts!

|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----| 
0-----10----20----30----40----50----60----70----80----90---100
Something is wrong, certainly. Several answers have debated the question of whether it was the student or the teacher who was wrong. I see another possibility: the question is wrong.

The student's been taught, in a maths lesson, about proportions or "rule of three" or something similar. So it's natural for the student to assume that the question's purpose is to test the student's ability to use that technique. And also to assume that the question is sound, and that the student isn't responsible for looking for errors in it and dealing with them (if any). So even if the student spots the out-by-one error, they might assume that that is merely an error in the way the question was presented, and then go on to answer the proportions question that they think was intended.

"15 minutes" and "20 minutes" are both reasonable responses to a question which was unsound in what the circumstances seem to be. The correct thing would've been to present the underlying proportions question in a different way.