Maths problems

Someone posed me a maths problem the other day, one that their sixth-grade son had had difficulty with. Turns out he’d had difficulty, too. It struck me that simple arithmetic and unit conversion are handy skills to have.

The question was along these lines:

You’re in a large 70 metre squared room. You drop a big bag of tiny marbles on the floor. You see that 3 marbles fit in 1 square centimetre. If you assume that the marbles cover the rest of the room in the same proportion, how many marbles are in the room?

Okay, so it’s a ludicrous setup. But they’re looking for understanding. And you need to understand two main things here:

  1. That the term “squared” means the room is square and 70m on each side.
  2. That there are 100cm in 1m.

So if the room is 70m by 70m, then it’s also 7000cm by 7000cm. That means its area is 49,000,000cm². If each of those square centimetres has 3 marbles in it, then there are 147,000,000 marbles in the room.

The question the young man was posed had three multiple choice answers. None of the answers was close to what I just calculated. I’d like to see the teacher show her work.