**Addition and Subtraction Within 200 with Word Problems to 100**

**Students develop place value strategies to fluently add and subtract within 100; they represent and solve one- and two-step word problems of varying types within 100; and they develop conceptual understanding of addition and subtraction of multi-digit numbers within 200. Using a concrete to pictorial to abstract approach, students use manipulatives and math drawings to develop an understanding of the composition and decomposition of units, and they relate these representations to the standard algorithm for addition and subtraction.**

**Video - 2nd Grade Addition & Subtraction Strategies - Pictorial Representation with Place Value Chart**

**Video - 2nd Grade Addition & Subtraction Strategies - Arrow Method**

**Video - 2nd Grade Addition & Subtraction Strategies - Place Value Chart****Topic A:**In Topic A, students build upon their understanding of the base ten system and their prior knowledge of place value strategies presented in Module 3. In Lesson 1, students relate 10 more and 10 less and 1 more and 1 less to addition and subtraction. They recognize that they must add and subtract like units, and that the digit in the tens place changes when adding and subtracting 10, just as the digit in the ones place changes when adding or subtracting 1. Students see numbers in terms of place value units; 54 – 10 is 5 tens 4 ones minus 1 ten. They learn to record the addition and subtraction of multiples of 10 using arrow notation. In Lesson 2, students apply place value understanding to add and subtract multiples of 10 before counting on by tens. For example, when adding 20 to 43, they may count 53, 63. Students also develop flexibility in using related addition problems. For example, to solve 92 – 60, one student might think 9 tens – 6 tens is 3 tens, plus 2 is 32, while another starts at 60, adds on 3 tens and then 2 ones to reach 92, so 32.

__Math News Parent Resource - Courtesy of Lafayette Schools____Lesson 1: Relate 1 more, 1 less, 10 more, and 10 less to addition and subtraction of 1 and 10.__

**Video: Module 4 Lesson 1**__Lesson 2: Add and subtract multiples of 10 including counting on to subtract.__

__Lesson 3: Add and subtract multiples of 10 and some ones within 100.__

__Video: Module 4 Lesson 3__

__Lesson 4: Add and subtract multiples of 10 and some ones within 100.__

Video: Module 4 Lesson 4

__Lesson 5: Solve one- and two-step word problems within 100 using strategies based on place value.__

Topic B: In 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.

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__Lesson 6: Use manipulatives to represent the composition of 10 ones as 1 ten with two-digit addends.____Video: Module 4 Lesson 6____Lesson 7: Relate addition using manipulatives to a written vertical method.____Video: Module 4 Lesson 7____Lesson 8: Use math drawings to represent the composition and relate drawings to a written method.____Video: Module 4 Lesson 8__

Lesson 9: Use math drawings to represent the composition and relate drawings to a written method.Lesson 9: Use math drawings to represent the composition and relate drawings to a written method.

__Video: Module 4 Lesson 9____Lesson 10: Use math drawings to represent the composition when adding a two-digit to a three-digit addend.____Video: Module 4 Lesson 10__**Topic C:**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.

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__Lesson 11: Represent subtraction with and without the decomposition of 1 ten as 10 ones with manipulatives.__

__Video: Module 4 Lesson 11____Lesson 12: Relate manipulative representations to a written method.____Lesson 13: Use math drawings to represent subtraction with and without decomposition and relate drawings to a written method.____Video: Module 4 Lesson 13____Lesson 14: Represent subtraction with and without the decomposition when there is a three-digit minuend.__

__Video: Module 4 Lesson 14____Lesson 15: Represent subtraction with and without the decomposition when there is a three-digit minuend.__

__Lesson 16: Solve one- and two-step word problems within 100 using strategies based on place value.__

**Video: Module 4 Lesson 16****Topic D:**In Lesson 17 of Topic D, students extend the base ten understanding developed in Topic A to numbers within 200. Having worked with manipulatives to compose 10 ones as 1 ten, students relate this to composing 10 tens as 1 hundred. For example, students might solve 50 + 80 by thinking 5 ones + 8 ones = 13 ones, so 5 tens + 8 tens = 13 tens = 130. They use place value language to explain when they make a new hundred. They also relate 100 more from Module 3 to + 100 and mentally add 100 to given numbers. In Lesson 18, students use number disks on a place value chart to represent additions with the composition of 1 ten and 1 hundred. They use place value language to explain when they make a new ten and a new hundred, as well as where to show each new unit on the place value chart. In Lesson 19, students relate manipulatives to a written method, recording compositions as new groups below in vertical form. As they did in Topic B, students use place value language to express the action as they physically make 1 hundred with 10 tens disks and 1 ten with 10 ones disks. Working in partners, one student records each change in the written method step by step as the other partner moves the manipulatives. In Lessons 20 and 21, students move from concrete to pictorial as they use math drawings to represent compositions of 1 ten and 1 hundred. Some students may need the continued support of place value drawings with labeled disks, while others use the chip model. In both cases, students relate their drawings to a written method, recording each change they make to their model on the numerical representation. They use place value language to explain these changes. Lesson 22 focuses on adding up to four two-digit addends with totals within 200. Students now have multiple strategies for composing and decomposing numbers, and they use properties of operations (i.e., the associative property) to add numbers in an order that is easiest to compute. For example, when solving 24 + 36 + 55, when adding the ones, a student may make a ten first with 4 and 6. Another student may decompose the 6 to make 3 fives (by adding 1 to the 4).

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__Lesson 17:____Use mental strategies to relate compositions of 10 tens as 1 hundred to 10 ones as 1 ten.____Video: Module 4 Lesson 17____Lesson 18: Use manipulatives to represent additions with two compositions.____Video: Module 4 Lesson 18____Lesson 19: Relate manipulative representations to a written method.____Lesson 20: Use math drawings to represent additions with up to two compositions and relate drawings to a written method.____Video: Module 4 Lesson 20____Lesson 21: Use math drawings to represent additions with up to two compositions and relate drawings to a written method.____Lesson 22:____Solve additions with up to four addends with totals within 200 with and without two compositions of larger units.__**Topic E:**Topic E begins with an extension of mental math strategies learned in first grade, when students learned to subtract from the ten by using number bonds. In Lesson 23, they return to this strategy to break apart three-digit minuends and subtract from the hundred. For example, in first grade students solved 14 – 9 by restating the problem as 10 – 9 + 4. In second grade, students use the same strategy to restate 143 – 90 as 100 – 90 + 43. In Lesson 24, students use number disks on a place value chart to represent subtraction and develop an understanding of decomposition of tens and hundreds. This concrete model helps students see the answer to the question, “Do I have enough ones?” or, “Do I have enough tens?” When they do not, they exchange one of the larger units for ten of the smaller units. Repeated practice with this exchange solidifies their understanding that within a unit of ten there are 10 ones, and within a unit of a hundred there are 10 tens. This practice is connected to the strategies they learned with tens and ones; they learn that the only real difference is in place value. The strategies are also connected to addition through part–whole understanding, which is reinforced throughout. In Lesson 25, students move towards the abstract when they model decompositions on their place value chart while simultaneously recording the changes in the written form. Students draw a magnifying glass around the minuend, as they did in Topic C. They then ask the question, “Do I have enough ones?” They refer to the place value disks to answer and exchange a ten disk for 10 ones when necessary. They record the change in the written form. Students repeat these steps when subtracting the tens. Students use math drawings in Lesson 26 as they move away from concrete representations and into the pictorial stage. They follow the same procedure for decomposing numbers as they did in Lesson 25 with the number disks, but now they may use a chip model or number disk drawing. They continue to record changes in the written form as they work with their models. Topic E closes with the special case of subtracting from 200. Using number disks on a place value chart, students review the concept that a unit of 100 is comprised of 10 tens. They then model 1 hundred as 9 tens and 10 ones and practice counting to 100 both ways (i.e., 10, 20, 30…100 and 10, 20…90, 91, 92, 93…100). Next, they model the decomposition of a hundred either in two steps (as 10 tens then decomposing 1 ten as 10 ones) or one step (as 9 tens and 10 ones) as they represent subtractions from 200 (see image to the right). Students use this same reasoning to subtract from numbers that have zero tens. For example, to subtract 48 from 106, students model the decomposition of 106 as 10 tens 6 ones and as 9 tens 16 ones. Throughout the lesson, students relate their models to a written form step by step.

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__Lesson 23: Use number bonds to break apart three-digit minuends and subtract from the hundred.____Video: Module 4 Lesson 23____Lesson 24: Use manipulatives to represent subtraction with decompositions of 1 hundred as 10 tens and 1 ten as 10 ones.____Video: Module 4 Lesson 24____Lesson 25: Relate manipulative representations to a written method.____Video: Module 4 Lesson 25____Lesson 26: Use math drawings to represent subtraction with up to two decompositions and relate drawings to a written method.____Video: Module 4 Lesson 26____Lesson 27: Subtract from 200 and from numbers with zeros in the tens place.____Video: Module 4 Lesson____27____Lesson 28: Subtract from 200 and from numbers with zeros in the tens place.__**Topic F:**Module 4 culminates with Topic F, in which students think about and discuss the multiple strategies they have learned to represent and solve addition and subtraction problems. They share their reasoning as they link their drawings to two written methods, and discuss the similarities, differences, and efficacy of each approach. In Lesson 29, students learn the totals below written method. Throughout Grades 1 and 2, students decompose numbers into expanded form to recognize place value and to understand that they must add like units. These problems are written horizontally. Here, students use this prior learning to solve addition problems in a similar way. They decompose two- and three-digit numbers, then add like units and record the totals horizontally (see image below). They then transition into the vertical form of the method when they decompose the numbers mentally, add like units, and record the totals below. The totals below method gives students the option of adding from left to right or from right to left. Students explain how each step of their math drawing relates to this written method. In Lesson 30, students represent and solve problems using both the totals below and the new groups below methods (students used the latter method throughout the module). They relate both methods to their math drawings and discuss the differences and similarities between the two. In Lesson 31, students apply knowledge of addition and subtraction strategies to solve two-step word problems. Students are challenged to make sense of more complex relationships as they are guided through more difficult problem types, such as comparison problems. These problems will involve smaller numbers and will be scaffolded to address the heightened level of difficulty.

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__Lesson 29: Use and explain the totals below written method using words, math drawings, and numbers.____Lesson 30: Compare totals below to new groups below as written methods.____Video: Module 4 Lesson 30____Lesson 31:____Solve two-step word problems within 100.__