Grade: 2 UNIT 4: Addition and Subtraction of Numbers to 200 with Word Problems to 100

Grade: 2 UNIT 4: Addition and Subtraction of Numbers to 200 with Word Problems to 100 Suggested Range: 35

Essential Question / Key Concepts / Cross Curricular Connections
How can I use place value, counting and comparison of numbers to 200? / A.Sums and differences within 100
B.Strategies for composing a Ten
C.Strategies for decomposing a Ten*
D.Strategies for composing Tens and Hundreds
E.Strategies for decomposing Tens and Hundreds
F.Student explanation of Written Methods** / Social Studies: Communities located on a map, the 50 states, three branches of government, two senators per state. Determine how many senators total. Discuss leaders elected, presidential election and electoral votes.
Unit Vocabulary
Equation Minuend
New groups below
Place value chart
Place value or number disk
Subtrahend Totals below
Assessments
*Mid-Module Assessment: After Session C (2 days, included in Unit Instructional Days)
**End of Module Assessment: After Session F (2 days, included in Unit Instructional Days)
Mathematical Practices
MP.1 Make sense of problems and persevere in solving them. Students solve two-step word problems, and are challenged to make sense of more complex relationships within situations. They flexibly solve problems with a variety of strategies at their disposal, sometimes finding many ways to solve the same problem.
MP.2 Reason abstractly and quantitatively. Students reason abstractly when they represent two-step problems and harder problem types with drawings such as tape diagrams and when they relate those drawings to equations. As the Module progresses, students move back and forth between concrete, pictorial, and abstract work to make sense of quantities and their relationships in problem situations.
MP.3 Construct viable arguments and critique the reasoning of others. Students construct viable arguments when they use place value reasoning and properties of operations to explain why their addition and subtraction strategies work, and when they use that reasoning to justify their choice of strategies in solving problems. They critique the reasoning of others when they use those same concepts to disprove or support the work of their peers.
MP.4 Model with mathematics. Students model with mathematics when they write equations to solve two-step word problems, make math drawings when solving a vertical algorithm, or when they draw place value charts and disks to represent numbers.
MP.6 Attend to precision. Students attend to precision when they label their math drawings and models with specific place value units. They calculate accurately and efficiently when adding numbers within 200 and they use the relationship between addition and subtraction to check their work.
Unit Outcomes (Focus)
Unit 4 is devoted to three major areas of work. The first two are building fluency in two-digit addition and subtraction within 100 (2.NBT.5) and applying that fluency to one- and two-step word problems of varying types within 100 (2.OA.1). Students’ increasing fluency with calculations within 100, begun in Grade 1, allows word problems to transition from being mere contexts for calculation into opportunities for students to see and analyze the relationships between quantities (MP1 and 2). Daily application problems and specific objectives in Section A, C, and F provide students with guided and independent practice as they negotiate a variety of problem types, including the more complex comparison problems. Note that most two-step problems involve single-digit addends, and do not involve the most difficult comparison problem types. The third major area of work is developing students’ conceptual understanding of addition and subtraction of multi-digit numbers within 200 (2.NBT.7, 2.NBT.9) as a foundation for work with addition and subtraction within 1000 in Unit 5.

UNIT3 SECTION A: Sums and differences within 100 Suggested Number of Days: 5

Essential Question
How can I use strategies to solve addition and subtractionword problems?
How can Iadd and subtract three-digit numbers?
How can I add and subtract tens and hundreds in my head? Explain why? / Key Objectives

• Relate 1 more, 1 less, 10 more, and 10 less to addition and subtraction of 1 and 10.
• Add and subtract multiples of 10 including counting on to subtract.
• Add and subtract multiples of 10 and some ones within 100.
• Solve one- and two-step word problems within 100 using strategies based on place value.

Comments / Standard No. / Standard
 Major Standard  Supporting Standard  Additional Standard / Priority
Begins at Grade 3
In Section A, students work with place value strategies to fluently add and subtract within 100 (2.NBT.5). The final objectives of unit 3 (finding 1 more, 1 less, 10 more, 10 less) transition into mental addition and subtraction of 1 and 10 (2.NBT.8). Students mentally add and subtract 100 in Topics D and E, as well as during fluency activities throughout the module, as they did in Unit 3. This knowledge is then extended and used to solve problems. / 2.OA.1
2.NBT.5
2.NBT.8
2.NBT.9 / Use 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, drawings, and equations with a symbol for the unknown number to represent the problem.
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
Explainwhyadditionandsubtractionstrategieswork,usingplacevalueandthepropertiesofoperations.(Explanationsmaybesupportedbydrawingsorobjects.)

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UNIT 3 SECTIONB: Strategies for Composing a Ten Suggested Number of Days: 5

Essential Question
How can I add and subtract with regrouping and explain why? / Key Objectives

• Use manipulatives to represent the composition of 10 ones as 1 ten with two-digit addends.
• Relate addition using manipulatives to a written vertical method.
• Use math drawings to represent the composition and relate drawings to a written method.
• Use math drawings to represent the composition when adding a two-digit to a three-digit addend.

Comments
In Section 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. / Standard No. / Standard
 Major Standard Supporting Standard Additional Standard / Priority
Begins at Grade 3
2.NBT.7
2.NBT.9
2.OA.1
2.NBT.5 / 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. Understand 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.
Explain why addition and subtraction strategies work, using place value and the properties of operation.(Explanations may be supported by drawings or objects.)
Use addition and subtraction within 100 o solve one--‐ and two--‐step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction

UNIT 3 SECTION C: Strategies for Decomposing a Ten Suggested Number of Days: 6

Essential Question
How can I use strategies to solve addition word problems?
How can I add and subtract with regrouping and explain why? / Key Objectives

• Represent subtraction with and without the decomposition of 1 ten as 10 ones with manipulatives.
• Relate manipulative representations to a written method.
• Use math drawings to represent subtraction with and without decomposition and relate drawings to a written method.
• Represent subtraction with and without the decomposition when there is a three-digit minuend.
• Solve one- and two-step word problems within 100 using strategies based on place value.

Comments / Standard No. / Standard
 Major Standard  Supporting Standard  Additional Standard / Priority
Begins at Grade 3
Section C parallels Section 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. / 2.OA.1
2.NBT.7
2.NBT.9
2.NBT.5 / Use 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, drawings, and equations with a symbol for the unknown number to represent the problem.
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. Understand 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.
Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

UNIT 3 SECTION D: Strategies for Composing Tens and Hundreds Suggested Number of Days: 6

Essential Question
How can I add more than two big numbers with regrouping? / Key Objectives

• Use mental strategies to relate compositions of 10 tens as 1 hundred to 10 ones as 1 ten.
• Use manipulatives to represent additions with two compositions.
• Relate manipulative representations to a written method.
• Use math drawings to represent additions with up to two compositions and relate drawings to a written method.
• Solve additions with up to four addends with totals within 200 with and without two compositions of larger units.

Comments / Standard No. / Standard
 Major Standard  Supporting Standard  Additional Standard / Priority
Begins at Grade 3
In Section D, students extend the base ten understanding developed in Section 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 Unit 3 to + 100 and mentally add 100 to given numbers. / 2.NBT.6
2.NBT.7
2.NBT.8
2.NBT.9 / Add up to four two-digit numbers using strategies based on place value and properties of operations.
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. Understand 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.
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
Explain why addition and subtraction strategies work, using place value and the properties of operations.

UNIT 3 SECTION E: Strategies for Composing Tens and Hundreds Suggested Number of Days: 6

Essential Question
How can I add and subtract with regrouping and explain why? / Key Objectives

• Use number bonds to break apart three-digit minuends and subtract from the hundred.
• Use manipulatives to represent subtraction with decompositions of 1 hundred as 10 tens and 1 ten as 10 ones.
• Relate manipulative representations to a written method.
• Use math drawings to represent subtraction with up to two decompositions and relate drawings to a written method.
• Subtract from 200 and from numbers with zeros in the tens place.

Comments / Standard No. / Standard
 Major Standard  Supporting Standard  Additional Standard / Priority
Begins at Grade 3
Section 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 the first objective, 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. / 2.NBT.7
2.NBT.9 / 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. Understand 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.
Explain why addition and subtraction strategies work, using place value and the properties of operations

UNIT 3 SECTION F: Student Explanation of Written Methods Suggested Number of Days: 3

Essential Question
How can I use strategies to solve addition and subtraction word problems with regrouping? Explain why? / Key Objectives

• Use and explain the totals below written method using words, math drawings, and numbers.
• Compare totals below to new groups below as written methods.
• Solve two-step word problems within 100.

Comments / Standard No. / Standard
 Major Standard  Supporting Standard  Additional Standard / Priority
Begins at Grade 3
Unit 4 culminates with Section 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. / 2.OA.1
2.NBT.7
2.NBT.9 / Use 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, drawings, and equations with a symbol for the unknown number to represent the problem.
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. Understand 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.
Explain why addition and subtraction strategies work, using place value and the properties of operations. 3 NOTE: Explanations may be supported by drawings or objects.

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POSSIBLE ACTIVITIES
ADD/SUBTRACT WITHIN 1,000: Create a worksheet with squares representing vertical four-digit addition and subtraction problems. Students fill in the square based on teacher direction, the roll of a die, drawing of a number card, etc. Once the numbers are filled in, they calculate the answer. The use of squares reinforces place value and helps to keep the numbers alignment. Addition and subtraction worksheets can be found online (see Resources, below).
BIG ADDITION: The hundreds chart can be used to start students adding numbers that would normally be too big to handle in normal calculations. Give a problem like 31+25. Have students put a counter on the first number. First add tens by moving the counter down that many places. From 31, students would move down 2 rows going from 31, to 41, to 51; then look at the ones place (5) and move the counter to the right five times, counting: 52, 53, 54, 55, 56. 31+25 = 56 (see Resources, below).
BIG SUBTRACTION: This is played just like Big Addition (see above), but students learn to start on the bigger number, move up by tens, and then move to the left by ones to solve subtraction problems. Additional subtraction practice can be found online (see Resources, below).
DEEP SEA DUEL: (partner activity) Students attempt to be the first to choose three cards that add up to the target number specified by the teacher.
Extension: students can use 4, 5, or 6 cards to reach a larger target number. The activity and examples can be found online (see Resources, below).
KRYPTO: The rules of Krypto are simple: Combine five number cards using two arithmetic operations (+, –) to arrive at a "target" number. You can create a random target number. A deck of cards with the face cards removed can be used in place of number cards.
INTRODUCE SUDOKU: Sudoku puzzles allow second grade students to practice their reasoning skills and can be found online (see Resources, below).
PROBLEM SOLVING ACTIVITIES: Combine students in groups and go through the problem-solving process (use the practice standards as reference). Additionalproblems are available online (see right).
Ex: A set of 10 cards, each showing one of the digits from 0 to 9, is divided up between five envelopes so that there are two cards in each envelope. The sum of the cards inside it is written on each envelope (see below). What numbers could be inside the 8 envelope? (Sample answer: 0 and 8)
PROBLEM SOLVING ACTIVITIES: Finding the right “problem” is the hardest task of problem-solving. Remember, students should not be able to solve the problemeasily….that would be an exercise! Allow students to work in groups or pairs to solve the following problems. Remind students to attempt multiple strategies, useconcrete models to help conceptualize as well as represent these problems using equations with a letter standing for the unknown quantity. Additional problems can befound online (see right).
Ex: In Bird Hotel, there are 46 nests for guests. Bird families stop in for a rest on their way south. Big Bird wants to know how many empty nests there are inthe hotel today. Here are the clues his workers gave; not all of the nests are empty today; more than 40 nests are empty; an even number of nests areempty; the empty nests could be counted by fours, with none left over. How many of the nests in Bird Hotel are empty today? Write to help explain your best thinking using words, numbers, or pictures. (Answer: 44)
RESOURCES
Online addition/subtraction practice can be found at Click on Resources and select Math Magician Addition/Subtraction (level 2 is facts within 20, level 1 is facts within 10).
Addition and subtraction worksheets can be found at dadsworksheets.com. Click on Addition and/or Subtraction on the right side of the menu.
Deep Sea duel can be found at illuminations.nctm.org. Click on Activities, select 3rd-5th, and scroll down until you find Deep Sea Duel.
You can find Sudoku puzzles at printactivities.com. Scroll down the bottom of the page until you see Sudoku for Kids, click, and select level.
CROSSWORD PUZZLES: Crossword puzzles for addition and subtraction can be found at mathinenglish.com. Click on Crossword Puzzle and select Addition or subtraction. MAZES: Worksheet mazes to print out or play online are located at Click on the Maze link from the menu bar.
Additional Websites:
Math Class Games:
Common Core Specific Questions:
Multi-Step Word Problems:
Common Core Specific Questions:
Topic Specific Practice:
Topic Specific Practice:
Library of Virtual Manipulatives:
Apps:
Arithmetic Invaders Express: Grade K-2 Math Facts – Defend the solar system by solving counting, addition, subtraction, and multiplication problems.
My Math Flash Cards App - My Math Flash Cards App is for mastering basic elementary math facts. It’s an easy to use and customizable application to enable focused learning.
Speedo Math - Here the students practice all aspects of math, including addition, subtraction, multiplication, and division. The game contains multiple levels and an instant results chart. So, if you can make it within the given seconds, you are a great champion in the order of operations.
For more problem-solving examples go to nrich.maths.org.
For additional problems check out Click on Schools, select Dry Creek Elementary School. Click on the Dry Creek Elementary School Website! Select Family Resources at top and then Math WASL Prompts.
Additional Websites:
Math Class Games:
Common Core Specific Questions:
Multi-Step Word Problems:
Common Core Specific Questions:
Topic Specific Practice:
Topic Specific Practice:
Library of Virtual Manipulatives:

Archdiocese of New YorkPage 12014 – 2015