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 nonzero 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 baseten 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).
Lesson Overview
 4.1 Warmup: The Cost of a Photo Print (5 minutes)
 4.2 Activity: Decimals All Around (15 minutes)

4.3 Activity: Missing Numbers (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 4.4 Cooldown: Taller and Farther (5 minutes)
Learning goals:
 Add or subtract decimals with multiple nonzero digits, and explain (orally) the solution method.
 Interpret a description (in written language) of a realworld 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 nonzero digits.
Learning goals (student facing):
 Let’s practice adding and subtracting decimals.
Learning targets (student facing):
 I can solve problems that involve addition and subtraction of 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.
Glossary:
 Access the complete Grade 6 glossary.
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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