Module 4, Topic C parallels Topic B, as students apply their understanding of place value strategies to the subtraction algorithm, moving from concrete to pictorial to abstract. 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. In Lesson 11, students use number disks on a place value chart to subtract like units (e.g., 76 – 43 is 7 tens – 4 tens and 6 ones – 3 ones). They practice modeling the standard subtraction algorithm within 100 without decompositions and then progress to problems that require exchanging 1 ten for 10 ones (e.g., in 76 – 47 students must recompose 7 tens 6 ones as 6 tens 16 ones). The use of manipulatives allows students to physically experience the renaming and understand the why behind recomposing a quantity. Lesson 12 builds upon this understanding as students relate manipulatives to a written method, recording recompositions in vertical form. In subtraction, a common error is for students to switch the top and bottom digits in a given place when renaming is necessary. They perceive the digits as a column of unrelated numbers, rather than part of a larger total, and simply subtract the smaller from the larger. Hence, many students would solve 41 – 29 as 28, instead of understanding that they can take 9 ones from 41 ones. To prevent this error and aid students in seeing the top number as the whole, students use a “magnifying glass” to examine the minuend. They draw a circle around the top number and add a handle. Before subtracting, they look inside the magnifying glass at the whole number and determine if each digit is big enough to subtract the number below it. If not, they decompose one of the next larger units to make ten of the unit they need. In Lesson 13, this is used in conjunction with the chip model; students record each change they make to their model simultaneously on the algorithm. In Lessons 14–15, students move to the more abstract dot drawings on their place value charts and follow the same procedure for decomposing a ten and relating it to the written method. Here, however, students subtract a two-digit subtrahend from a three-digit minuend (e.g., 164 – 36). This provides practice working with and drawing three-digit numbers without the complexity of decomposing a hundred. As in Topic A, Topic C closes with a lesson that focuses on one- and two-step word problems within 100. Students apply their place value reasoning, mental strategies, and understanding of compositions and decompositions to negotiate different problem types with unknowns in various positions. Because two different problem types (i.e., add to, take from, put together/take apart, compare) are often combined in two-step word problems, some quantities will involve single-digit addends, especially when students are working with the more challenging comparison problems. They are encouraged to be flexible in their thinking and to use drawings and/or models to explain their thinking. Students continue to use tape diagrams to solve word problems, relating the diagrams to a situation equation (e.g., 8 + ____ = 41) and rewriting it as a solution equation (e.g., 41 – 8 = ___), thus illustrating the relationship between operations. Students find success when using their mental strategies of making a multiple of 10 and counting on (e.g., 9, 10, 20, 30 40, 41) as they experience the relationships between quantities within a context.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 2

1. Use addition and subtraction within 100 to solve one- and two-step word problems by using drawings and equations with a symbol for the unknown number to represent the problem.

Unpacked Content

Evidence Of Student Attainment:

Students:

solve a variety of addition and subtraction problems, using concrete and pictorial representations.

explain and justify solutions using connections among a variety of representations (e.g., manipulatives, drawings, and equations with a symbol for the unknown number).

write equations that represent the work they have shown.

Teacher Vocabulary:

One-step word problems

Two-step word problems

Knowledge:

Students know:

addition and subtraction strategies to solve one- and two-step word problems within a 100.

Skills:

Students are able to:

represent quantities and operations (addition & subtraction) physically, pictorially, or symbolically.

strategically use a variety of representations to solve addition and subtraction word problem.

use informal and mathematical language to communicate the connections among addition and subtraction.

accurately compute sums and differences.

use symbols to represent unknown quantities in equations.

Understanding:

Students understand that:

addition is both putting together and adding to.

subtraction is taking apart, taking from, and comparisons.

mathematical problems can be solved using a variety of strategies, models, representations.

variables represent unknown quantities when representing mathematical situations algebraically.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.2.1.1: Solve one-step addition and subtraction word problems with an unknown by using drawings and equations with a symbol for the unknown number to represent the problem.
M.2.1.2: Understand key words in addition and subtraction word problems.
Examples: adding to, taking from, putting together, taking apart, sum, difference, all together, how many more, how many are left, in all.
M.2.1.3: Locate the unknown regardless of position.
Examples: start unknown, change unknown, and result unknown.
M.2.1.4: Apply signs +, -, = to actions of joining and separating sets.
M.2.1.5: Add and subtract within 50, e.g., by using objects or drawings to represent the problem.
M.2.1.6: Solve addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects or drawings to represent the problem.
M.2.1.7: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
M.2.1.8: Represent numbers with objects or drawings.

Prior Knowledge Skills:

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Understand key words in addition and subtraction word problems. Examples: sum, difference, all together, how many more, how many are left, in all.

Define subtraction as separating groups of objects, taking from, or taking apart.

Define addition as combining groups of objects, adding to, or putting together.

Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Represent numbers with objects or drawings.

Use objects to combine and separate groups.

Define how many, all together, and in all.

Count to 20 by ones.

Demonstrate 1:1 correspondence.

Mimic counting objects in sequential order arranged in a line, circle, or array.

Count no more than 5 objects in a scattered configuration.

Mimic counting no more than 5 objects in a scattered configuration.

Count to 10 by ones.

Count in sequential order.

Mimic counting in sequential order.

Demonstrate one to one correspondence.

Make purposeful marks such as lines and circles.

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:

100, 1000, add, addition, operations, place value, strategy, subtract, subtraction, word problem