2: Q I know all of the Simple and Complex Learning Goals and my understanding goes beyond the grade level target.

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1 Topic Proficiency Scale Domain: Operations and Algebraic Thinking Topic: Addition and Subtraction (without regrouping) Critical Area: Addition and Subtraction within I know all of the Simple and Complex Learning Goals and my understanding goes beyond the grade level target. 3.0 I know all of the Simple and Complex Learning Goals. C1: Use addition and subtraction (without regrouping) within 100 to solve simple one-step word problems using drawings and equations with a symbol for the unknown number. (2.OA.1) C2: Use strategies (based on place value, properties of operations, and/or the relationship between addition and subtraction) to fluently add and subtract within 100. (2.NBT.5) C3: Use mental strategies to fluently add and subtract within 20 (2.OA2) - making ten - doubles/doubles plus one - compose/decompose leading to a 10 - relationship between addition and subtraction 2.5 I know all of the Simple Learning Goals plus some of the Complex Learning Goals. 2.0 I know all of the Simple Learning Goals. S1: Determine whether the sum or difference of an equation will be even or odd based on the numbers in its expression. (2.OA.3) S2; Determine a group of objects as odd or even. (2.OA.3) S3: Represent whole-number sums and differences within 100 on a number line diagram. (2.MD.6) Academic Vocabulary: V1: sum V2: difference V3: odd V4: even 1.0 I know some of the Simple Learning Goals. 0.5 Not applicable. 0.0 No evidence of knowing the Learning Goals.

2 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. 2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. 2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 2. NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram. Topic Proficiency Scale Domain: Operations and Algebraic Thinking Topic: Addition and Subtraction (without regrouping) Critical Area: Addition and Subtraction within I know all of the Simple and Complex Learning Goals and my understanding goes beyond the grade level target. 3.0 I know all of the Simple and Complex Learning Goals. C1: Use addition and subtraction (without regrouping) within 100 to solve simple one-step word problems using drawings and equations with a symbol for the unknown number. (2.OA.1) C2: Use strategies (based on place value, properties of operations, and/or the relationship between addition and subtraction) to fluently add and subtract within 100. (2.NBT.5) C3: Use mental strategies to fluently add and subtract within 20. (2.OA2) - making ten - doubles / doubles plus one - compose/decompose leading to a 10 - relationship of addition and subtraction 2.5 I know all of the Simple Learning Goals plus some of the Complex Learning Goals. 2.0 I know all of the Simple Learning Goals. S1: Determine whether the sum or difference of an equation will be even or odd based on the numbers in its expression. (2.OA.3) S2: Determine a group of objects as odd or even. 2.OA.3) S3: Represent whole-number sums and differences within 100 on a number line diagram. (2.MD.6) Academic Vocabulary: V1: sum V2: difference V3: odd V4: even 1.0 I know some of the Simple Learning Goals. 0.5 Not applicable. 0.0 No evidence of knowing the Learning Goals. Introduce concepts and continually monitor. Assess and report in a later quarter.

3 Success Criteria Domain: Operations and Algebraic Thinking Critical Areas : Place Value Mathematical Practices: MP2 - Reason abstractly and quantitatively MP6 - Attend to precision MP7 - Look for and make use of structure MP8 - Look for and express regularity in repeated reasoning Complex Goal: Use addition and subtraction within 100 to solve one-step word problems using drawings and equations with a symbol for the unknown number. (2.OA.1) Guiding Questions: How is related to? What is the relationship of the quantities? Explain how you know that your answer is correct. What mathematical language can you use to explain? Can we put this problem in context to make it make sense? What do you already know that will help you solve this problem? How does this problem connect to other concepts you ve learned? What is happening in this situation? How would you prove that? Mastery: Students will be able to independently solve one- and two-step word problems involving addition and subtraction. 2.OA.1 calls for students to add and subtract numbers within 100 in the context of one and two step word problems. Students should have ample experiences working on various types of problems that have unknowns in all positions, including: This standard also calls for students to solve one- and two-step problems using drawings, objects and equations. Students can use place value blocks or hundreds charts, or create drawings of place value blocks or number lines to support their work. Two step-problems include situations where students have to add and subtract within the same problem. It is important to attend to the difficulty level of the problem situations in relation to the position of the unknown. Result Unknown, Total Unknown, and Both Addends Unknown problems are the least complex for students. The next level of difficulty includes Change Unknown, Addend Unknown, and Difference Unknown The most difficult are Start Unknown and versions of Bigger and Smaller Unknown (compare problems). This standard focuses on developing an algebraic representation of a word problem through addition and subtraction. The intent is NOT to introduce traditional algorithms or rules, but to make meaning of operations. Second graders should work on ALL problem types regardless of the level of difficulty. Mastery is expected in second grade. Students can use interactive whiteboard or document camera to demonstrate and justify their thinking.

4 Use strategies (based on place value, properties of operations, and/or the relationship between addition and subtraction) to fluently add and subtract within 100. (2.NBT.5) Making ten (e.g., = = = 14) Composing / Decomposing a number leading to a ten (e.g., 13-4 = = 10-1 = 9) Using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12-8 = 4) Doubles / Doubles plus one (Creating equivalent but easier or known sums) (e.g., adding by creating the known equivalent = = 13). 2.NBT.5 mentions the word fluently when students are adding and subtracting numbers within 100. Fluency means accuracy (correct answer), efficiency (basic facts computed within 4-5 seconds), and flexibility (using strategies such as making 10 or breaking numbers apart). This standard calls for students to use pictorial representations or strategies to find the solution. Students who are struggling may benefit from further work with concrete objects (e.g., counting manipulatives, place value blocks). Example: = Example: =

5 continued... Adding and subtracting fluently refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently. Students should have experiences solving problems written both horizontally and vertically. They need to communicate their thinking and be able to justify their strategies both verbally and with paper and pencil. Addition strategies based on place value for may include: Adding by place value: = 70 and = 15 and = 85. Incremental adding (breaking one number into tens and ones); = 58, = 68, = 78, = 85 Compensation(making a friendly number): 48+2=50,37 2=35,50+35=85 Subtraction strategies based on place value for may include: Adding up (from smaller number to larger number): 37+3=40,40+40=80,80+1= 81, and = 44. Incremental subtracting: = 71, = 61, = 51, 51 7 = 44 Subtracting by place value: 81 30=51,51 7=44 Properties that students should know and use are: Commutative property of addition (Example: = 5 + 3) Associative property of addition (Example: (2 + 7) + 3 = 2 + (7+3) ) Identity property of 0 (Example: = 8) Students in second grade need to communicate their understanding of why some properties work for some operations and not for others. Commutative Property: In first grade, students investigated whether the commutative property works with subtraction. The intent was for students to recognize that taking 5 from 8 is not the same as taking 8 from 5. Students should also understand that they will be working with numbers in later grades that will allow them to subtract greater numbers from smaller numbers. This exploration of the commutative property continues in second grade. Associative Property: It is difficult for students to recognize that the associative property does not work for subtraction at this grade level because it is a challenge to determine all the possibilities. Properties are only used as strategies. Students do not need to name or identify the specific properties, only how to apply them and which property works best in equation situations. Use mental strategies to fluently add and subtract within 20. (2.OA2) - making ten - doubles / doubles plus one - compose/decompose leading to a 10 - relationship of addition and subtraction Students will be able to use mental strategies to solve addition and subtraction equations within 20

6 2.OA2 mentions the word fluently when students are adding and subtracting numbers within 20. Fluency means accuracy (correct answer), efficiency (within 4-5 seconds), and flexibility (using strategies such as making 10 or breaking apart numbers). Research indicates that teachers can best support students memorization of sums and differences through varied experiences making 10, breaking numbers apart and working on mental strategies, rather than repetitive timed tests. Mental strategies help students make sense of number relationships as they are adding and subtracting within 20. The ability to calculate mentally with efficiency is very important for all students. Mental strategies may include the following: Counting on Making tens (9 + 7 = ) Composing / Decomposing a number leading to a ten ( 14 6 = = 10 2 = 8) Relationship between addition and subtraction (8 + 5 = 13 is the same as 13-8 = 5) Doubles Doubles plus one (7 + 8 = ) The use of objects, diagrams, or interactive whiteboards, and various strategies will help students develop fluency. A 15 minute, daily Number Talk will provide opportunity for students to develop these skills. Example: 9 + 5= Example: 13-9 = (Doubles / Doubles plus one) District Resources: My Math - Chapters 1-7 Number Talks

7 Exemplar Samples Example: In the morning there are 25 students in the cafeteria. 18 more students come in. After a few minutes, some students leave. If there are 14 students still in the cafeteria, how many students left the cafeteria? Write an equation for your problem. Student 1 Step 1: Step 2:

8 Step 3: Since I have two tens I need to trade a ten for 10 ones. Step 4: Step 5: Student 2 Step 1: I used a number line. I started at 25 and needed to move up 18 spots so I started by moving up 5 spots to 30, and then 10 spots to 40, and then 3 more spots to 43. Then I had to move backwards (red arrows) until I got to 14 so I started by first moving back 20 spots until I got to 23. Then I moved to 14 which were an additional 9 places. I moved back a total of 29 spots. Therefore there were a total of 29 students left in the cafeteria. My equation is = 14 (See the number line representation on the following page)

9 Student 3 Step 1: I used a hundreds board. I started at 25. I moved down one row which is 10 more then moved to the right 8 spots and landed on 43. This represented the 18 more students coming into the cafeteria. Step 2: Now starting at 43, I know I have to get to the number14 which represents the number of students left in the cafeteria so I moved up 2 row which is 20 less then moved to the left until I land on 14, 9 spaces. I moved back a total of 29 spots. That means that 29 students left the cafeteria. Step 3: My equation to represent this situation is = 14.