Read aloud the following number:
Now mentally answer this question: What is the value of the 8 in this number?
I see two correct ways of stating this:
Eighty thousand, and
And I’m trying to decide whether I care about the difference between these. I’m not sure that I do.
So now I do what I always do to test ideas. I ask, What if? Specifically, What if we looked to the right of the decimal point? What would this question look like there?
So consider the number 0.0008.
If you said Zero-point-zero-zero-zero-eight, then I’ve got a lot more work to do with you.
Place value language matters in math classrooms.
And the sentence in the picture below is confusing.
No, I’m guessing we would all agree that this is eight ten-thousandths, which is not at all the same as eighty-thousandths (although it is the same as eighty hundred-thousandths).
So now I see that my What if? question has muddied the waters, rather than clarified them.
What can we conclude?
I suppose that the major conclusion is this:
We need to stop pretending that decimal place value (i.e. to the right of the decimal point) behaves exactly like whole-number place value (i.e. to the left of the decimal point).
In the abstract, this is certainly true. But composing units is not conceptually (or linguistically) equivalent to partitioning them.
Like I was saying here: