In this lesson, students continue to use base-ten diagrams and vertical calculations to add and subtract decimals to thousandths.

First, students reason about the zeros in a decimal and whether a statement such as "” is true. Then, students have an opportunity to practice adding decimals in an optional activity.

In the main activity, students recall that a base-ten unit can be decomposed into another unit that is its size. For example, 1 tenth can be decomposed into 10 hundredths. They use this idea to subtract a larger value from a smaller value that is in the same base-ten place. Take for instance. Decomposing the 1 hundredth in 0.012 as 10 thousandths makes it easier to subtract 7 thousandths.

Students see that decimals can also be written in several equivalent ways. Because 0.4 can be viewed as 4 tenths, 40 hundredths, 400 thousandths, or 4,000 ten-thousandths, it can be written as 0.40, 0.400, 0.4000, and so on. The additional zeros at the end of the decimal do not change its value. Students use this idea to subtract a number with more decimal places from one with fewer decimal places (such as ). These calculations encourage students to make use of the structure of base-ten numbers (MP7).

As in an earlier lesson, students create visual representations of base-ten units here. Consider providing access to physical base-ten blocks (if available), or using paper cutouts of base-ten representations  from the blackline master as alternatives to drawing.

Some students might find graph paper helpful for aligning the digits for vertical calculations. Consider making graph paper accessible for activities that involve addition and subtraction of decimals.