# Lesson 4

Adding and Subtracting Decimals with Many Non-Zero Digits

### Lesson Narrative

This lesson strengthens students’ ability to add and subtract decimals, enabling them to work toward fluency. Students encounter longer decimals (beyond thousandths), find missing addends, and work with decimals in the context of situations. They decide which operation (addition or subtraction) to perform and which strategy to use when finding sums and differences. They also reinforce the idea that we can express a decimal in different but equivalent ways, and that writing additional zeros after the last non-zero digit in a decimal does not change its value. Students use this understanding to practice subtracting numbers with more decimal places from those with fewer decimal places (e.g., $$1.9 - 0.4563$$).

To solve these problems, students must lean heavily on their understanding of base-ten numbers (MP7). Given problems such as $$7 - {?} = 3.4567$$ and $$0.404 + {?} = 1$$, they need to think carefully about the meaning of each place value, the meaning of addition and subtraction, and potential paths toward the solution. Along the way, they also begin to see patterns in the calculations, which enables them to become increasingly fluent in finding sums and differences (MP8).

### Learning Goals

Teacher Facing

• Add or subtract decimals with multiple non-zero digits, and explain (orally) the solution method.
• Interpret a description (in written language) of a real-world situation involving decimals, and write an addition or subtraction problem to represent it.
• Recognize and explain (orally) that vertical calculation is an efficient strategy for adding and subtracting decimals, especially decimals with multiple non-zero digits.

### Student Facing

Let’s practice adding and subtracting decimals.

### Required Preparation

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 the Decimals All Around activity.

### Student Facing

• I can solve problems that involve addition and subtraction of decimals.