This lesson is optional. Prior to grade 6, students have added and subtracted decimals to the hundredths using a variety of methods, all of which focus on understanding place value. This lesson reinforces their understanding of placevalue relationships in preparation for computing sums and differences of any decimals algorithmically.
In this lesson, students use two methods—baseten diagrams and vertical calculations—to find the sum and differences of decimals. Central to both methods is an understanding about the meaning of each digit in the numbers and how the different digits are related. Students recall that we only add the values of two digits if they represent the same baseten units. They also recall that when the value of a baseten unit is 10 or more we can express it with a different unit that is 10 times higher in value. For example, 10 tens can be expressed as 1 hundred, and 12 hundredths can be expressed as 1 tenth and 2 hundredths. This idea is made explicit both in the diagrams and in vertical calculations.
Lesson overview
 2.1 Warmup: Changing Values (5 minutes)

2.2 Optional Activity: Squares and Rectangles (15 minutes)
 There is a digital applet in this activity.

2.3 Optional Activity: Finding Sums in Different Ways (15 minutes)
 Includes "Are you Ready for More?" extension problem.
 There is a digital applet in this activity.

2.4 Optional Activity: Representing Subtraction (15 minutes)
 There is a digital applet in this activity.
 Lesson Synthesis
 2.5 Cooldown: Why or Why Not? (5 minutes)
Learning goals:
 Compare and contrast (orally and in writing) vertical calculations and baseten diagrams that represent adding and subtracting decimals.
 Explain (in words and through other representations) that adding and subtracting decimals requires combining digits that represent like baseten units.
 Interpret and create diagrams that represent 10 like baseten units being composed into 1 unit of higher place value, e.g., 10 tenths as 1 one, and comprehend the word “bundle” to refer to this concept.
Learning goals (student facing):
 Let’s represent addition and subtraction of decimals.
Learning targets (student facing):
 I can use diagrams to represent and reason about addition and subtraction of decimals.
 I can use place value to explain addition and subtraction of decimals.
 I can use vertical calculations to represent and reason about addition and subtraction of 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.
 Print and cut up the Squares and Rectangles blackline master. Prepare one copy for every student. These tools will be useful throughout the unit, so consider printing on card stock and organizing them for easy reuse.
 Digital applet of baseten representations (an assignable version of the digital applet is in the Additional Materials section of this lesson).
Some students might find graph paper helpful for aligning the digits for vertical calculations. Consider having graph paper accessible for these activities: Finding Sums in Different Ways, Representing Subtraction, and Why or Why Not?
Required Materials:
 Graph paper
 Preprinted slips, cut from copies of the blackline master
Glossary:
 Access the complete Grade 6 glossary.
Standards
 This lesson builds on the standards: CCSS.5.NBT.A.1CCSS.5.NBT.B.7MS.5.NBT.1MS.5.NBT.7
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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