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.

Unpacked Content

Evidence Of Student Attainment:

Students:

add and subtract within 1000.

explain their reasoning using concrete models or drawings, or using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

relate the strategy used to a written method (symbolic and numeric recording of the steps used).

Teacher Vocabulary:

Compose

Decompose

Knowledge:

Students know:

how to count to 1,000.

how to identify hundreds, tens, and ones.

how to compose numbers.

how to decompose two digit numbers.

how to record strategies for solving addition and subtraction problems.

Skills:

Students are able to:

add and subtract within 1000.

model addition problems using visual models.

record strategies for solving addition problems.

communicate the relationship between models and symbolic (numeric) representations.

Understanding:

Students understand that:

relationships between models of addition/subtraction problems and written strategies of those models can be used to justify solutions.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.2.12.1: Define regrouping, total, sum, difference and solve.
M.2.12.2: Add and subtract two two-digit numbers with and without regrouping.
M.2.12.3: Determine the value of the number in the ones, tens, hundreds and thousands place using concrete models or drawings and strategies based on place value.
M.2.12.4: Match the number in the ones, tens, hundreds and thousands position to a pictorial representation or manipulative of the value.
M.2.12.5: Model written method for recording horizontal and vertical addition and subtraction problems.
M.2.12.6: Represent two- and three-digit numbers with multiple models.
Examples: models—base ten blocks, number lines, linking cubes, straw bundles.
M.2.12.7: Recall single-digit addition and subtraction facts.
M.2.12.8: Add and subtract within 20, e.g., by using objects or drawings to represent the problem.

Prior Knowledge Skills:

Notice same/different and some/all.

Recognize numerals from 1-50.

Add one to a set of objects (up to 10 objects).

Given small groups of objects, create larger groups by combining the small groups.

Understand ten and 1 (ten 1's =10).

Put together two small groups of objects to create a larger group.

Subtract one from a set of objects (up to 10 objects).

Given a group of objects (20 or less), divide the group into smaller groups in various ways.

Take away objects from a large group to create two smaller groups.

Understand number words.

Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.

Rote count to 10.

Understand amount words, such as more, less, and another.

Begin to understand that parts of an object can make a whole.

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.

Unpacked Content

Evidence Of Student Attainment:

Students:

solve addition and subtraction problems using objects, pictures, words and numbers. Explain and justify strategies for adding and subtracting.

Teacher Vocabulary:

Properties of operations

Knowledge:

Students know:

strategies for finding sums and differences.

physical (manipulative) models and pictorial models (place value blocks, lines and dots, bundles and sticks, etc.) for representing numbers using place value concepts.

Skills:

Students are able to:

use logical reasoning, place value concepts and vocabulary, and properties of numbers and operations to justify strategies for finding sums and differences.

Understanding:

Students understand that:

relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and strategies.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.2.14.1: Explain addition and subtraction problems using concrete objects, pictures.
M.2.14.2: Use multiple strategies to add and subtract including counting on, counting back and using doubles.
M.2.14.3: Recall single-digit subtraction facts.
M.2.14.4: Recall single-digit addition facts.
M.2.14.5: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Prior Knowledge Skills:

Match numerals to objects or drawings.

Identify numerals 1 to 10.

Count from 0 to 10.

Add and subtract numbers within 20 using objects, pictures and fingers.

Take a smaller set out of a larger set.

Combine two sets to make a larger set up to twenty.

Count items in a set up to twenty.

Establish one-to-one correspondence between numbers and objects.

Understand one less than a number 2 through 20.

Understand one more than a number 1 through 20.

Understand positional terms with equal signs.

Tags:

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