# Is 5 x 3 5 times 3 or 3 times 5?

A plot of land marked 5m x 20m has a different shape than 20m x 5m, similar to a plot of land measuring 100m2.

A few days ago, the teacher mismarked a third-grader’s problem solving the ferry problem “6 x 4 = 24.” Many have argued about this. I see that the problem is not really new, it’s that we haven’t learned and understood the nature and conventions of multiplication.

A parent in the US once said it was wrong for teachers to use machines when grading student work. The problem is as follows: Ask the students to do the calculation 5 x 3, while interpreting the calculation as the sum of the numbers.

The student answered 5 + 5 + 5, but the teacher mistyped it and pointed out that the answer should be 3 + 3 + 3 + 3 + 3. So in your opinion was the teacher right or wrong?

The essence of multiplication is repeated addition. In Vietnam and some countries around the world (like the US), the convention is to write the number of iterations first.

The answer is true in the US, but false in Japan. In Japan, on the contrary, the calculation of 5 x 3 will be analyzed as follows: the first written number 5 is the unit, taken 3 times, so it should be understood as 5 + 5 + 5.

In commutative multiplication, of course, 5 x 3 is the same as 3 x 5, but the essence is quite different. If the same area is 100 m2, for example, 5m x 20m or 20m x 5m is not specified, although the area is the same, the shape of the land is very different.

Going back to the ferry problem, in a third grade environment, I think the teacher wanted to overemphasize the nature of the problem, so it caused a lot of controversy.

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