Lesson 3
Adding and Subtracting Decimals with Few NonZero Digits
Lesson Narrative
As with addition, prior to grade 6 students have used various ways to subtract decimals to hundredths. Baseten diagrams and vertical calculations are likewise used for subtracting decimals. “Unbundling,” which students have previously used to subtract whole numbers, is a key idea here. They recall that a baseten unit can be expressed as another unit that is \(\frac{1}{10}\) its size. For example, 1 tenth can be “unbundled” into 10 hundredths or into 100 thousandths. Students use this idea to subtract a larger digit from a smaller digit when both digits are in the same baseten place, e.g., \(0.012  0.007\). Rather than thinking of subtracting 7 thousandths from 1 hundredth and 2 thousandths, we can view the 1 hundredth as 10 thousandths and subtract 7 thousandths from 12 thousandths.
Unbundling also suggests that we can write a decimal in several equivalent ways. Because 0.4 can be viewed as 4 tenths, 40 hundredths, 400 thousandths, or 4,000 tenthousandths, it can also 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. They use this idea to subtract a number with more decimal places from one with fewer decimal places (e.g., \(2.5  1.028\)). These calculations depend on making use of the structure of baseten numbers (MP7).
The second activity is optional; it gives students additional opportunities to practice summing decimals.
Learning Goals
Teacher Facing
 Add or subtract decimals, and explain the reasoning (using words and other representations).
 Comprehend the term “unbundle” means to decompose a larger baseten unit into 10 units of lower place value (e.g., 1 tenth as 10 hundredths).
 Recognize and explain (orally) that writing additional zeros or removing zeros after the last nonzero digit in a decimal does not change its value.
Student Facing
Let’s add and subtract decimals.
Required Preparation
Students draw baseten diagrams in this lesson. If drawing them is a challenge, consider giving students access to:
 Commercially produced baseten blocks, if available.
 Paper copies of squares and rectangles (to represent baseten units), cut outs from copies of the blackline master of the second lesson in the unit.
 Digital applet of baseten representations https://ggbm.at/zqxRkhMh.
Some students might find it helpful to use graph paper to help them align the digits for vertical calculations. Consider having graph paper accessible for these activities: Representing Decimal Subtraction and Enough to Subtract?
Learning Targets
Student Facing
 I can tell whether writing or removing a zero in a decimal will change its value.
 I know how to solve subtraction problems with decimals that require “unbundling” or “decomposing.”
Print Formatted Materials
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Additional Resources
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