How long will it take Marie to saw another board into 3 pieces?
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
Well, the information is incomplete, so they're both right and wrong. Since the question is for $3^{rd}$ graders the correct answer should be $20$ minutes ($2$ cuts $\times$ $10$ min), though the teacher is right if you do cut it like this (first red, then green):
The problem is that the question doesn't say anything about how you have to cut it, so the blue cut would have been good enough too. That cut should only have taken a few seconds.
The student was correct:
Sawing a board into two pieces requires exactly one cut to be made. Sawing the board into three pieces requires exactly two cuts...
Hence, if it took $\bf 10$ minutes to make one cut, then cutting a board twice, at the same pace, would take $\;2 \times 10 = \bf 20$ minutes.
The instructor should receive tutoring from the student, I'm afraid.