There are several skills with fractions that will make understanding of decimals easier. These should be consolidated and explored before starting decimals.
1. Parts of a fraction have to be the same size
This is another reason why I frequently like to have students make their own fraction and decimal manipulatives. After several tries of cutting a strip into tenths, they’re much more likely to remember this point.
2. How many fractional pieces make a whole
It’s critical for decimals that students understand it takes ten tenths to make a whole, but this is just an extension of earlier fraction work. However many pieces the whole is subdivided into, it takes that many to make a whole. This seems pretty straightforward to us, but students need to experience and see this themselves for different fractional parts.
3. Iterative notion of fractions
This is understanding what the two numbers in a fraction mean.
a. The bottom number tells you the size of your piece – you have thirds, or fifths, etc.
b. The top number tells you how many pieces you have.
This understanding helps you realize that 2/7 is conceptually no different than 2 apples. You’re dealing with sevenths, and you have two of them.
4. Improper Fractions
Working with multiple representations of decimals will be a lot smoother if students have already had a chance to experience converting improper fractions.
This is a short (5 question) fraction diagnostic that I think is a fair representation of what students need to bring to the table to move fluidly into decimals.