Stop saying "Just add zeros"!

I wish primary school teachers would stop teaching students that you just add zeros when multiplying by multiples of 10. It often leads to confusion when students start using decimals and also when they begin dividing by multiples of 10.

When students learn they layer their new learning onto their existing knowledge and the language of just add zero makes no sense. When you add zero you do not change the size of the number!

Yes, you do physically “put place holder zeros on the end of whole numbers” when multiplying by multiples of 10, however the more important concept is that the place value of each digit moves. Each digit moves up one place value for x10, up two place values for x100 and up three place values for x1000 and so on. Then for division by multiples of 10, the digits all move so that the number gets smaller by so many place values.

The add zeros to the end instruction leads to 0.035 x 100 = 0.03500 which is clearly incorrect. Instead, the concept of each digit moving up two place values is correct reasoning so that 0.035 x 100 = 3.5

Division is the inverse (opposite) operation to multiplication so division will “undo” multiplication and multiplication with “undo” division. Logically, it makes sense so that when dividing by multiples of 10 the number get smaller because each digit moves back to where it would have been before it was multiplied by the same multiple of 10.

Recently I have had a lot of correcting students way of thinking in this area, and after a bit of a struggle to unlearn what they had been thinking, they give a little “Aha” and I give a little "Hoorah"!