Tenths vs Tens…Hundredths vs Hundreds. Problematic for many students. I believe this is a conceptual problem. This post provides an approach to unpack the concepts through money in a scaffolded handout.
Overview
Money is likely prior knowledge for many if not most students, and is a relevant context. This handout attempts to leverage interest or knowledge of money to unpack decimal place values. In the first page, the concept of “tenth” is addressed with dimes as 1/10 of a dollar. Similarly, “hundredth” is addressed with pennies as 1/100 of a dollar. A key point to consider is that US monetary system base unit is a dollar. More on that in the other pages.
Hundreds to Hundredths
The handout aligns each place value with the appropriate currency. This is followed by writing each number in numeric form and then word form with the place value table as a guide. To enhance the word part, you can highlight the each place value in money, digit, and word in the same color (e.g., the “2” in yellow).
Also, note the shading. The dollar as the base unit is in the center and shaded the darkest. The tens and tenths are shaded the same as they are a factor of 10 from ones. (I don’t reference the term with students.) Same for hundreds and hundredths.
Thousandths
The last page addresses thousandths.
Access to Handout
here is a link to the handout.
I’m going to repeat a question i was asked, I’d like to find a better way to address it instead of ‘that’s just the way it is’.
The question, ‘why isn’t there a oneth?’
When one names the place values one might expect, but doesn’t get, symmetry. …hundreds, tens, ones, (oneth), tenth, hundredth….
One can look to the place value exponents and recover the symmetry, …10^2, 10^1, 10^0, 10^-1, 10^-2….
But it doesn’t explain why the decimal point goes where it goes. Moreover, place value comes before exponents are taught.
So, please, a model response to ‘why isn’t there a oneth?’
Interesting. So I alluded to this in my point about the dollar bill being the base unit of currency. 1 or “oneth” is the foundation and all other values or place values, or currency units are relative to the 1. 1/10 is relative to the 1. Tens is ten ones.
A Google search revealed a teacher that challenged her class to answer the question. They answered, after some time to work on it, that a oneth part of a whole would be a whole, so it would be redundant to have a ones place and a oneth place. This answer is along the lines of yours as well.
It still feels clumsy but I shall move on, thanks for your good work.