In grade 4, students explore decimals to tenths and add & subtract them using intuitive methods. This is really a foundational year for understanding decimals.
In grade 4 decimals, there are several critical understandings that students need to explore and understand.
In grade 4, students need to understand that the first decimal place is just where we put one kind of fractions – tenths. They should be able to move flexible between recording a number as 3 1/10 and 3.1
This is the general principle that in our number system, you need ten pieces or a group of ten to make one of the unit to the left. That is, 10 tens make a hundred, 10 singles make a ten, 10 tenths make a whole, etc. Conversely, the pieces get 10 times smaller as you move right.
1.7 can be represented as 1 whole and 7 tenths, but students also need to see that it could be thought of as 17 tenths. The Toss a Decimal activity below is a good way to practice this.
Additionally, students need to move flexibly between concrete, visual oral, and decimal and fractional expressions of decimal numbers.