[QuantumRoar]

There are just too many assumptions in this article. It says: Use the repeated addition strategy to solve 5x3. That is clearly what the student did.

The argument about bundles and bananas is besides the point. But even then it works because

3x(5 bananas) = (3x5) bananas = 5 x (3 bananas)

Of course, if I define my own special multiplication, then 3x5 != 5x3. If I put enough concepts on top of it an operate in obscure mathematical domains, sure, I'll need to be careful about things being accidentally equal but not equivalent. But I bet the student expected that multiplication behaves just like the multiplication an elementary student knows. Or do you expect them to define the operations they're working with?

When I grade the work of students, I will accept any answer that is in accordance with the question. Who cares how often they commute things that commute, or if they picked an entirely different approach that was never even discussed. If it says solve X using Y and they solved X using Y, they deserve the points.

If the teacher didn't make it clear enough in his question, then it's not the student's fault.

[jonsen]

  3 bundle x 5 banana/bundle =
  5x3 bundlexbanana/bundle =
  5 bundle x 3 banana/bundle =
  15 banana