In Module 4, Topic B, students apply their understanding of place value strategies to the addition algorithm, moving from horizontal to vertical notation. Their understanding of vertical addition starts with concrete work with number disks, moving to pictorial place value chart drawings, and ending with abstract calculation. Consistent use of number disks on a place value chart strengthens students’ place value understanding and helps them to systematically model the standard addition algorithm including the composition of a ten. It is important to note that the algorithm is introduced at this level and is connected deeply to the understanding of place value. However, fluency with the algorithm is a Grade 3 standard and is not expected at this level. In Lesson 6, students use number disks on a place value chart to represent the composition of 10 ones as 1 ten with two-digit addends. The use of manipulatives reminds students that they must add like units (e.g., 26 + 35 is 2 tens + 3 tens and 6 ones + 5 ones). Lesson 7 builds upon this understanding as students relate manipulatives to a written method, recording compositions as new groups below in vertical form (as shown at right). As they move the manipulatives, students use place value language to express the action as they physically make a ten with 10 ones and exchange them for 1 ten. They record each change in the written method, step by step. In Lesson 8, students move from concrete to pictorial as they draw unlabeled place value charts with labeled disks to represent addition (as shown at right). As they did with the manipulatives, students record each action in their drawings step by step on the written method. In Lessons 9 and 10, students work within 200, representing the composition of 10 ones as 1 ten when adding a two-digit addend to a three-digit addend. This provides practice drawing three-digit numbers without the complexity of composing a hundred. It also provides practice with adding like units. As student understanding of the relationship between their drawings and the algorithm deepens, they move to the more abstract chip model, in which place value disks are replaced by circles or dots (as shown below right). It is important to note that students must attend to precision in their drawings. Disks and dots are drawn in horizontal arrays of 5, recalling student work with 5-groups in Kindergarten and Grade 1. This visual reference enables students to clearly see the composition of the ten. While some students may come into this topic already having learned vertical addition, including carrying above the tens, the process of connecting their understanding to the concrete and pictorial representations develops meaning and understanding of why the process works, not just how to use it. Therefore, students will be less prone to making place value errors.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 2

12. Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.

a. Explain that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.2.10 Using vocalization, sign language, augmentative communication, or assistive technology, identify the meaning of the + sign (add, plus, put together) and the sign (subtract, take away, take from) and the = sign (equal, the same as); compose and decompose numbers up to 20 using objects, pictures, drawings, or numbers.

Mathematics MA2019 (2019) Grade: 2

14. Explain why addition and subtraction strategies work, using place value and the properties of operations.

Note: Explanations may be supported by drawings or objects.

Tags:

1000, add, models, operations, place value, strategy, subtract, threedigit