Catholic Schools in the Archdiocese of New York



Grade: 2 UNIT 1: Sums and Differences to 20 Suggested Number of Days: 10

|Essential Question |Key Concepts |Cross Curricular Connections |

|How can I use mental math strategies to add and subtract quantities |Foundations for Addition and Subtraction Within 20 |Religion/Social Studies: Using a number line and comparing it |

|within 20? |Mental Strategies for Addition and Subtraction within 20 |to a timeline of historical events. |

| |Strategies for Addition And Subtraction within 100** | |

|Unit Vocabulary | | |

|Make ten and subtract from ten | | |

|Decomposing a number | | |

|Ten plus Counting on | | |

|Number bond Leading to a ten | | |

|Say Ten counting Sum | | |

|Making ten Place value | | |

| |Assessments | |

| | | |

| |**End of Module Assessment: After Session C ( 2 days, included in Unit | |

| |Instructional Days) | |

|Mathematical Practices |

|MP1.  Make sense of problems and persevere in solving them. Students make math drawings and use recomposing strategies to reason through the relationships in word problems. They write equations and word sentences to|

|explain their solutions. |

|MP2. Reason abstractly and quantitatively. Students decompose numbers and use the associative property to create equivalent but easier problems, e.g., 25 + 6 = 20 + 5 + 5 + 1. They reason abstractly when they relate|

|subtraction to addition and change 13 – 8 = ___ into an unknown addend, 8 + ___ = 13, to solve. |

|MP3. Construct viable arguments and critique the reasoning of others. Students explain their reasoning to prove that 9 + 5 = 10 + 4. They communicate how simpler problems embedded within more complex problems enable|

|them to solve mentally, e.g., 8 + 3 = 11, so 68 + 3 = 71. |

|MP7. Look for and make use of structure. Students use the structure of ten to add and subtract within 20, and later, within 100. E.g., 12 – 8 = 10 – 8 + 2 = 2 + 2, and 92 + 3 = 90 + 2 + 3 = 90 + 5. |

|Unit Outcome (Focus) |

| |

|Unit 1 sets the foundation for students to master the sums and differences to 20 (2.OA.2) and to subsequently apply these skills to fluently add one-digit to two-digit numbers at least through 100 using |

|place value understandings, properties of operations and the relationship between addition and subtraction (2.NBT.5). In Grade 1, students worked extensively with numbers to 10 and they developed Level 2 |

|and Level 3 mental strategies to add and subtract within 20 (1.OA.1) and 100 (1.NBT.4-6). |

|For example, to solve 12 + 3 students might make an equivalent but easier problem by decomposing 12 as 10 + 2 and composing 2 with 3 to make 5. Students can use this knowledge to solve related problems such|

|as 92 + 3. They also apply their skill using smaller numbers to subtract problems with larger numbers: 12 – 8 = 10 – 8 + 2 = 2 + 2, just as 72 – 8 = 70 – 8 + 2 = 62 + 2. |

|Daily fluency activities provide sustained practice to help students attain fluency within 20. This fluency is essential to the work of later modules and future grade levels, where students must fluently |

|recompose place value units to work adeptly with the four operations. Activities such as Say Ten counting and Take from 10, and the use of ten-frame cards and Hide Zero cards, solidify student fluency. |

|Because the amount of practice required by each student to achieve mastery will vary, a motivating, differentiated fluency program needs to be established in these first weeks to set the tone for the rest |

|of the year. |

|Throughout the Unit, students will represent and solve one-step word problems through the daily Application Problem (2.OA.1). Application problems can precede an objective to act as the lead-in to a |

|concept, allowing students to discover through problem-solving the logic and usefulness of a strategy before that strategy is reviewed. Or, they can follow the concept development so that students connect |

|and apply their learning to real-world situations. This latter structure can also serve as a bridge between teacher-directed work and students solving problems independently on activity worksheets and at |

|home. In either case, problem-solving begins as a guided activity, with the goal being to move students to independent problem- solving, wherein they reason through the relationships of the problem and |

|choose an appropriate strategy to solve. In Unit 1, application problems follow concept development. |

UNIT 1 SECTION A: Foundations for Addition and Subtraction within 20 Suggested Number of Days: 2

| Essential Question |Key Objectives |

| | |

|How can I use mental math strategies to add and|Make number bonds of ten. |

|subtract quantities within 20? |Make number bonds through ten with a subtraction focus and apply to one-step word problems. |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard |Begins at |

| | | |Grade 3 |

|Section A reactivates students’ Kindergarten |2.OA.1 |Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting| |

|and Grade 1 learning, as they practice | |together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the | |

|prerequisite skills for Level 3 decomposition | |unknown number to represent the problem. | |

|and composition methods: partners to 10 and | | | |

|decompositions for all numbers within 10. | |Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | |

|Students move briskly from concrete to |2.OA.2 | | |

|pictorial to abstract as they remember their | |Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each | |

|“make ten” facts. They use ten-frame cards to | |decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | |

|visualize 10, and they write the number bonds |K.OA.3 | | |

|of 10 from memory. They use those facts to see | |For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record| |

|relationships in larger numbers (e.g., 28 needs| |the answer with a drawing or equation. | |

|how many to make 30.) The number bond is also | |Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each | |

|used to represent related facts within 10. |K.OA.4 |composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and | |

| | |one, two, three, four, five, six, seven, eight, or nine ones. | |

| | |Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on making ten | |

| |K.NBT.1 |(e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the | |

| | |relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier | |

| | |or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 = 1 = 12 + 1 = 13). | |

| |1.OA.6 | | |

UNIT 1 SECTION B: Mental Strategies for Addition and Subtraction within 20 Suggested Number of Days: 3

|Essential Question |Key Objectives |

| | |

| |Make a ten to add within 20. |

| |Make a ten to add and subtract within 20. |

| |Decompose to subtract from a ten when subtracting within 20 and apply to one-step word problems. |

|How can I use mental math strategies to add and | |

|subtract quantities within 20? | |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard |Begins at Grade 3 |

|Section B also moves from concrete to pictorial to |2.OA.1 |Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from,| |

|abstract, as students use decomposing strategies to | |putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a | |

|add and subtract within 20. By the end of Grade 1, | |symbol for the unknown number to represent the problem. | |

|Unit 2, students learned to form ten as a unit. | | | |

|Hence, the phrase make ten now transitions to make a | |Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit | |

|ten. Students use the ten-structure to reason about | |numbers. | |

|making a ten to add to the teens, and they use this |2.OA.2 | | |

|pattern and math drawings to solve related problem | | | |

|sets (e.g., 9 + 4, 9 + 5, 9 + 6). Students reason | | | |

|about the relationship between problems such as 19 + | | | |

|5 and 20 + 4 to 9 + 5 and 10 + 4. They use place | | | |

|value understanding to add and subtract within 20 by | | | |

|adding to and subtracting from the ones. The section | | | |

|ends with a lesson in which students subtract from | | | |

|10. The goal in making a 10 and taking from 10 is for| | | |

|students to master mental math. | | | |

UNIT 1 SECTION C: Strategies for Addition and Subtraction within 100 Suggested Number of Days: 3

|Essential Question |Key Objectives |

| | |

|How can I use mental math strategies to add and subtract |Add and subtract within multiples of ten based on understanding place value and basic facts. |

|quantities within 100? |Add within 100 using properties of addition to make a ten. |

| |Decompose to subtract from a ten when subtracting within 100 and apply to one-step word problems. |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard |Begins at Grade|

|Section C calls on students to review strategies to add | | |3 |

|and subtract within 100 (1.NBT.4–6) to set the foundation | | | |

|for Grade 2’s work towards mastery of fluency with the | | | |

|same set of problems (2.NBT.5). They use basic facts and | | | |

|place value understanding to add and subtract within | | | |

|multiples of 10 without crossing the multiple (e.g., 7 – 5| | | |

|= 2, so 47 - 5 = 42.) This segues into the use of basic | | | |

|facts and properties of addition to cross multiples of 10 | | | |

|(e.g., 26 + 9 = 20 + 6 + 4 + 5). In the final objectives, | | | |

|students decompose to make a ten, and then to subtract | | | |

|from numbers that have both tens and ones. | | | |

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| |2.OA.1 |Use addition and subtraction within 100 to 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 | |

| |2.NBT.5 |between addition and subtraction. | |

| | |Fluently add and subtract within 20 using mental strategies. (See standard 1.OA.6 for a list of mental strategies.) By end of | |

| | |Grade 2, know from memory all sums of two one-digit numbers. | |

| |2.OA.2 | | |

| | |Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, | |

| | |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 and explain the reasoning used. Understand that in adding | |

| |1.NBT.4 |two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | |

| | |Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.| |

| | | | |

| | |Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), 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 and explain the reasoning used. | |

| | | | |

| |1.NBT.5 | | |

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| | | | |

| |1.NBT.6 | | |

|Possible Activities |

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|ADD/SUBTRACT WITH DICE: Create a worksheet with four squares representing vertical two-digit addition and subtraction problems. Students roll a die and place the number rolled in any of the four boxes. Once the four |

|boxes of a problem are filled in the student works with a partner to solve the problem. They may encounter difficulty with subtraction. They can discuss and “discover” why some problems do not work. |

|BIG CARDS ______+________= ______: Give a group of children large cards or pieces of paper with the numbers 0–9. The single digit cards can be combined to make two digit numbers. The group is also given a card with a |

|plus sign, minus sign, and an equal sign. They are challenged to come up with equations that are true. They are to list as many combinations as they can find with the group of numbers they are given. |

|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 Deep Sea duel can be found at illuminations.. Click on Activities, select 3rd-5th, and |

|scroll down until you find Deep Sea Duel. |

|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. You can find Sudoku puzzles at . Scroll down the bottom of the page until you |

|see Sudoku for Kids, click, and select level. |

|MEASUREMENT WITH TOOLS: (partners) Give students a basket of various tools: ruler, yardstick, meter stick, measuring tape. Have them choose an appropriate object to measure with each tool and explain why they chose the |

|object. |

|MEASUREMENT CONVERSATIONS: Have students measure items in the classroom using multiple units. Discuss the measurements as a class. |

|Ex: A student measured the length of a desk in both feet and inches. She found that the desk was 3 feet long. She also found out that it was 36 inches long. Ask: “Why do you think there are two different numbers for the|

|same desk?” Provide additional examples to prompt conversations on how students can measure an object using two different units and get different numbers. |

|MEASUREMENT WORD PROBLEMS: Additional word problems can be found online see Resources, below. |

|Ex: A snail and a turtle both started out on Monday toward a pond 32 inches away. An owl was watching them and told them how far they were at the beginning of each day of the race. By Tuesday both the snail and the |

|turtle had gone 1 inch. By Wednesday the snail had traveled 2 inches, and the turtle had crawled 7 inches. By Thursday the snail was 4 inches from the start, and the turtle was 13 inches from the start. By Friday the |

|snail was 8 inches from the start, and the turtle was 19 inches from it. If the snail and the turtle kept moving in the same ways, on what day will each animal reach the pond? All answers should be expressed as |

|equations and modeled on a number line. |

|(Answer: Snail on Monday; turtle on Tuesday.) |

|Activities (con’t) |

|PROBLEM SOLVING ACTIVITIES: Finding the right “problem” is the hardest task of problem-solving. Remember, students should not be able to solve the problem easily….that would be an exercise! Allow students to work in |

|groups or pairs to solve the following problems. Remind students to attempt multiple strategies, use concrete models to help conceptualize as well as represent these problems using equations with a letter standing |

|for the unknown quantity. Additional problems can be found online (see Resources, below). 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 in the 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 are empty; 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) |

|HOW MUCH BIGGER IS IT? (stations) Provide two objects of different length at each station and have students measure them to the nearest whole unit (centimeter, inches,etc.). Ask the students to explain which object |

|is bigger using a subtraction problem. The students will record all measurements before going to the next station. Have students use their data to make a graph. Allow students to share and compare graphs. |

| |

|HOW BIG IS A FOOT? Read the book How Big is a Foot? by Rolf Myller and discuss the issues the king had when the bed was not measured correctly. Challenge students to measure themselves and make a list of the |

|measurements using both centimeters and inches. Discuss the difference in the units and how important it is to be consistent with units. Extend: Have students display their measurements in a table or graph and |

|compare with other students. Note: This activity can still be completed without reading the book. |

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|GET TO ZERO: (2 player game) Reinforces addition and subtraction by instructing students start with the number 999 on the top of a piece of paper and roll three dice. Arrange the dice in any order and subtract that |

|number from 999. Each student should “do the math” to check each other’s work. The students take turns rolling the dice and subtracting. At any time a student can choose to roll only one or two dice instead of all |

|three dice. The first student who gets to zero (exactly) wins the game. If students cannot subtract the number rolled, they skip their turn. Game sheets can be created or found online (see Resources, below).Ex: If a |

|student rolls a 3, 5, and 6. They can subtract 536 or 635 etc. from 999. |

|Resources |

|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. |

|Butterfly Math Addition – This app works on number recognition and addition. |

|Math Express – This is a fun educational math game designed for girls and boys ages 4-7, combining engaging math exercises and fresh graphics. The game includes exercises to help visualizations and counting|

|of numbers. |

|Math Puppy – This app features both Bingo and Challenge modes. Its animated math calculator and subtraction module are included in the free app; other modules may be purchased. |

|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. |

|Additional measurement word problems can be found at . Click on Schools tab and choose Dry Creek Elementary. Click on Dry Creek Website. Select Family Resources at top 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: |

| |

|Apps: |

|Reading the Ruler – Easy way for kids to learn to read inches and Metric rulers. |

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