# Lesson 2

Using Diagrams to Represent Addition and Subtraction

### Lesson Narrative

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 place-value relationships in preparation for computing sums and differences of any decimals algorithmically.

In this lesson, students use two methods—base-ten 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 base-ten units. They also recall that when the value of a base-ten 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.

### Learning Goals

Teacher Facing

• Compare and contrast (orally and in writing) vertical calculations and base-ten 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 base-ten units.
• Interpret and create diagrams that represent 10 like base-ten 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.

### Student Facing

Let’s represent addition and subtraction of decimals.

### Required Preparation

Students draw base-ten diagrams in this lesson. If drawing them is a challenge, consider giving students access to:

• Commercially produced base-ten 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 base-ten representations https://www.geogebra.org/m/FXEZD466.

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?.

### 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.

Building On