Formative instructional & assessment tasks for the common core state standards in mathematics 
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GRADE 2 PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education  Department of Public Instruction Formative Instructional & Assessment Tasks for the Common Core State Standards in Mathematics Word Document versions of the documents http://commoncoretasks.wikispaces.com/ STATE BOARD OF EDUCATION The guiding mission of the North Carolina State Board of Education is that every public school student will graduate from high school, globally competitive for work and postsecondary education and prepared for life in the 21st Century. NC DEPARTMENT OF PUBLIC INSTRUCTION June St. Clair Atkinson, Ed.D., State Superintendent 301 N. Wilmington Street :: Raleigh, North Carolina 276012825 In compliance with federal law, NC Public Schools administers all stateoperated educational programs, employment activities and admissions without discrimination because of race, religion, national or ethnic origin, color, age, military service, disability, or gender, except where exemption is appropriate and allowed by law. Inquiries or complaints regarding discrimination issues should be directed to: Dr. Rebecca Garland, Chief Academic Officer :: Academic Services and Instructional Support 6368 Mail Service Center, Raleigh, NC 276996368 :: Telephone: (919) 8073200 :: Fax: (919) 8074065 Visit us on the Web :: www.ncpublicschools.org WILLIAM C. HARRISON Chairman :: Fayetteville WAYNE MCDEVITT Vice Chair :: Asheville WALTER DALTON Lieutenant Governor :: Rutherfordton JANET COWELL State Treasurer :: Raleigh Jean W. Wolard Plymouth REGINALD KENAN Rose Hill KEVIN D. HOWELL Raleigh SHIRLEY E. HARRIS Troy CHRISTINE J. GREENE High Point JOHN A. TATE III Charlotte ROBERT “TOM” SPEED Boone MELISSA E. BARTLETT Roxboro PATRICIA N. WILLOUGHBY Raleigh M0910 Table of Contents 1. Common Core State Standards ........................................................................................................................................ 1 2. Administration Manual ....................................................................................................................................................... 3 3. Operations & Algebraic Thinking ................................................................................................................................ 15 4. Number and Operations in Base Ten ........................................................................................................................ 126 5. Measurement and Data .................................................................................................................................................. 158 6. Geometry .............................................................................................................................................................................. 203 7. Student Record Keeping Forms ................................................................................................................................. 221 NOTE: The separate Word document versions of each section can be found online at http://commoncoretasks.wikispaces.com/ . Common Core State Standards Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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. (Note: See Glossary, Table 1.) Add and subtract within 20. 2.OA.2 Fluently add and subtract within 20 using mental strategies. (Note: See standard 1.OA.6 for a list of mental strategies). By end of Grade 2, know from memory all sums of two onedigit numbers. Work with equal groups of objects to gain foundations for multiplication. 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.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Number and Operations in Base Ten Understand place value. 2.NBT.1 Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens – called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2.NBT.2 Count within 1000; skipcount by 5s, 10s, and 100s. 2.NBT.3 Read and write numbers to 1000 using baseten numerals, number names, and expanded form. 2.NBT.4 Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Use place value understanding and properties of operations to add and subtract. 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.NBT.6 Add up to four twodigit numbers using strategies based on place value and properties of operations. 2.NBT.7 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 threedigit 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. 2.NBT.8 Mentally add 10 or 100 to a given number 100900, and mentally subtract 10 or 100 from a given number 100900. 2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Note: Explanations may be supported by drawings or objects.) Measurement and Data Measure and estimate lengths in standard units. 2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Relate addition and subtraction to length. 2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 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 wholenumber sums and differences within 100 on a number line diagram. Second Grade – Standards 1. Extending understanding of baseten notation – Students extend their understanding of the baseten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students understand multidigit numbers (up to 1000) written in baseten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones). 2. Building fluency with addition and subtraction – Students use their understanding of addition to develop fluency with addition and subtraction within 100. They solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of whole numbers in baseten notation, using their understanding of place value and the properties of operations. They select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds. 3. Using standard units of measure – Students recognize the need for standard units of measure (centimeter and inch) and they use rulers and other measurement tools with the understanding that linear measure involves iteration of units. They recognize that the smaller the unit, the more iterations they need to cover a given length. 4. Describing and analyzing shapes – Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two and threedimensional shapes, students develop a foundation for understanding attributes of two and threedimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades. Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 1 Work with time and money. 2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? Represent and interpret data. 2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in wholenumber units. 2.MD.10 Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple put together, takeapart, and compare problems using information presented in a bar graph. (Note: See Glossary, Table 1.) Geometry Reason with shapes and their attributes. 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. (Note: Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 2.G.2 Partition a rectangle into rows and columns of samesize squares and count to find the total number of them. 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. 2 Administration Manual K2 Assessment in North Carolina In response to North Carolina legislative and State Board requirements, the NC Department of Public Instruction provides Local Education Agencies with statedeveloped assessments to be implemented for Kindergarten, First and Second Grades. These assessments are to include documented, ongoing individualized assessments throughout the year and a summative evaluation at the end of the year. These assessments monitor proficiency of the standards in the North Carolina Standard Course of Study: Common Core State Standards for Mathematics. Assessments may take the form of these state developed materials, adaptations of these materials, or unique assessments adopted by local school boards. The intended purposes of these assessments are: • To provide information about progress of each student for instructional adaptations and early interventions. • To provide nextyear teachers with information about the status of each of their incoming students. • To inform parents about the status of their children relative to gradelevel standards at the end of the year • To provide the school and school district information about the achievement status and progress of groups of students in grades K, 1, and 2. The North Carolina Department of Public Instruction is committed to continued development of quality teaching and ongoing classroom assessment as essential preparation for the students to master rigorous standards as defined by the NC Standard Course of Study: Common Core State Standards and Essential Standards. We believe the strategies that engage students in selfassessment, greater ownership of their learning, communicating, reasoning, problem posing and problem solving result in longterm growth and learning. Therefore, the Formative Instructional and Assessment Tasks for Mathematics are designed to clarify the bond that links quality assessment and effective teaching and subsequently effective schools. Learning takes place one student at a time, and quality teaching and assessment is essential in ensuring that every public school student will graduate from high school, globally competitive for work and postsecondary education and prepared for life in the 21st Century. These statedeveloped assessment materials are aligned with the Common Core State Standards for Mathematics and may be adopted or modified as appropriate for individual school districts. As you use them with students, add to and adapt the materials in order to make them useful for each school’s unique situation. The North Carolina Department of Public Instruction appreciates any suggestions and feedback, which will help improve upon this resource. Feedback may be sent to NCDPI Elementary Mathematics Consultant Amy Scrinzi (Amy.Scrinzi@dpi.nc.gov). 3 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION The Purpose of the Formative Instructional and Assessment Tasks The Formative Instructional and Assessment Tasks are provided as tools to use to assess Kindergarten, First Grade and Second Grade students’ mathematical understanding as specified in the NC Standard Course of Study: Common Core State Standards for Mathematics (CCSSM). Mathematical Concepts Assessed The Formative Instructional and Assessment Tasks are designed to reveal the extent to which a student knows and understands specific concepts. Moving beyond only whether an answer is right or wrong, the tasks focus attention on the thinking and processes that all students use in solving the tasks, with opportunities to demonstrate his or her knowledge, skill, and understanding. Therefore, the tasks assess the Common Core State Standards and highlight Standards for Mathematical Practice that may emerge as students explore the tasks. The Continuum for Understanding specifically addresses the conceptual understandings indicated in the CCSSM. The Standards for Mathematical Practice that are likely to emerge are indicated in bold for each task. Types of Tasks When assessing young children, it is important to remember that they frequently know more than they can record in traditional, symbolic formats. “Age, fluency with language, and experiences influence how successful students are likely to write a strong explanation or offer an explanation orally” (Joyner & Muri, 2011). Therefore interviews, as well as written responses, are provided. Interview: The teacher asks a series of questions to one student and carefully listens to the student’s responses and observes the student’s strategies and thinking as the student works. Written Response: The teacher presents a problem to one or more students and asks the students to use pictures, numbers, and words to show their thinking and explain their reasoning. Since both correct answers and appropriate processes are valued in mathematics, teachers find that observing students and talking with them are ways to provide students with opportunities to demonstrate what they know and can apply in new situations. Thus, the teacher is encouraged to ask the student clarifying questions during the assessment or after the assessment to gain a more accurate picture of what the student knows and understands. Insight into children’s thinking helps teachers build on what students understand, not just what they can do by memorizing processes. “Without the conversations or written explanations, we have no clue as to the students’ logic behind their wrong answers.” (Joyner & Muri, 2011, p. 250) 4 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION The Role of the Classroom Teacher The classroom teacher uses the tasks in a formative manner. As defined by North Carolina Department of Public Instruction, formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to help students improve their achievement of intended instructional outcomes. Therefore, a teacher may use these tasks to: • Determine prior knowledge regarding a concept that is about to be taught. • Assess understanding throughout an instructional sequence to gain an understanding of how to best meet the needs of all of the students in an ongoing basis. • Determine if the student is Developing Understanding of a particular concept or if the student has Complete Understanding, demonstrating proficiency. • Assess understanding after the instructional sequence to determine if all students are proficient with that concept and are ready to move forward. The teacher may administer the tasks to a whole class, small group of children, or an individual student, depending on the purpose for collecting data. For example, the teacher may decide that s/he would like to gain awareness of the entire class’ understanding of a particular concept. Thus, the task(s) selected would then be administered to all of the students in the class. Other times the teacher may need to determine what a particular student, or small group of students, understands in order to plan the most effective mathematical experiences. Thus, the task(s) selected would then be used with the selected student(s). Therefore, the assessment tasks can be used in multiple ways with the purpose of informing instructional planning and practice. The Role of the Local Education Agency (LEA) A school district may decide to use the assessment tasks to create benchmark assessments, aligning a collection of tasks to their unique pacing guide to be administered districtwide at several points throughout the year. The classroom teacher scores the quarterly benchmark assessments, sees students’ answers, observes misconceptions, and uses the data gathered to inform further instruction and plan interventions or enrichments as needed (Joyner & Muri, 2011). The district uses the data from the benchmark assessments to gain a global view of how students are performing within particular domains or clusters, determine which additional instructional materials and resources may be needed, and discern particular topics and concepts that teachers may need additional support or growth and work with principals and teachers to plan professional development and coaching opportunities accordingly. These statedeveloped assessment tasks are aligned with the North Carolina Standard Course of Study: Common Core State Standards for Mathematics and may be adopted or modified as appropriate for individual school districts. As they are used with students, please add to and adapt the materials in order to make them useful for each school’s unique situation. The North Carolina Department of Public Instruction appreciates any suggestions and feedback, which will help improve upon this resource. 5 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION The Components of the Formative Instructional & Assessment Tasks The Formative Instructional and Assessment Tasks are composed of four parts: 1. Assessment Tasks 2. Student Forms 3. Blackline Masters 4. Class/Student Summaries 1. Assessment Tasks The assessment tasks inform the classroom teacher of a) the Mathematical Concepts addressed, b) the materials needed, c) the assessment task directions, the d) Continuum of Understanding, and the e) Standards for Mathematical Practice. a.) Mathematical Concepts: Designate the domain, cluster, and standard assessed. There may be some tasks that assess multiple concepts. Domain: Large group of related standards. Include: Counting and Cardinality (K), Operations and Algebraic Thinking, Number and Operations in Base Ten, Measurement and Data, and Geometry. Cluster: Groups of related standards. Standard: Define what students should understand and be able to do. b.) Materials: Student and teacher materials needed to complete the task. Materials may include: Blackline Master (BLM), Student Form (SF) or classroom materials. Provide additional materials or substitute materials with those that students use during regular mathematics lessons as needed. c.) Task: Directions for the administering the task. May include “Teacher Talk”: dialogue for the teacher to say to the student(s) while administering the task. Indicated in italics. d.) Continuum of Understanding: Designates indicators: specific behaviors and skills that signify if the student is Developing Understanding or demonstrates Complete Understanding. Indicators: Specific behavior or skill within the continuum noted by a bullet. Developing Understanding: If the student exhibits one OR more of the indicators listed, then the student’s understanding is still evolving. Complete Understanding: If the student exhibits ALL of the indicators listed, then the student has demonstrated proficiency with that particular skills or concept on that one particular task. Other tasks may be needed in order to confirm proficiency in that overall skill or concept. 6 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION In addition, there may be specific behaviors, strategies, concepts, or skills for which the teacher is to observe. These are located to the right of the indicators. Answers to the tasks are also provided in this area. e.) Standards for Mathematical Practice: Describe processes and dispositions that mathematically proficient students exhibit. Practices that are likely to emerge as a result of completing the task are noted in BOLD. The teacher is encouraged to note which practices were observed during the tasks as well as during daily instruction to gain a global picture of the mathematical processes and dispositions that the student exhibits. 7 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION The Formative Instructional and Assessment Tasks are composed of three additional parts: 1. Assessment Tasks 2. Student Forms 3. Blackline Masters 4. Class/Student Summaries 2. Student Forms Student forms are provided as an option to use for all tasks that require a written response from the student. These forms are located with the appropriate task and are designated as “SF”. Teachers may copy, edit, or revise the forms as needed. 3. Blackline Masters If a task requires a particular illustration or specific materials, then a blackline master is included. These forms are located with the appropriate task and are designated as “BLM”. Teachers may copy, edit, or revise forms as needed. 4. Class/Student Summaries Class and Student Summaries are provided to help the classroom teacher collect and organize data. These forms are located with the appropriate Domain/Cluster. These forms are provided as Word documents allowing the teacher to type information as desired, change the size of the space provided, or add additional columns or categories as needed. Teachers may copy, edit, or revise the forms as needed. 8 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION Selecting an Assessment Task The Formative Instructional and Assessment Tasks are placed with the corresponding Domain(s), Cluster(s), and Standard(s) on the common core assessment wiki. When searching for a task, simply click on the domain and cluster of interest. Tasks will be located with each standard assessed. In addition, each grade is provided with a comprehensive list of assessment tasks and the standards to which they align. NOTE: Some tasks assess multiple standards. Therefore, tasks are placed with the primary standard assessed and additional standards assessed are noted in the table and with the task directions. When selecting a task, consider the following: 1. Designate a learning target. What skill or concept do you want students to know? 2. Identify the student(s). Are you curious about all of the students, a handful of students, or one student in particular? Thinking about the student(s), what are you most interested in learning that is related to the learning target? 3. Review and select the tasks. Locate tasks that are aligned with the learning target and address your questions about the student(s). 4. Read the tasks carefully. Which tasks would best uncover student understanding for the particular learning target? Does it need to be a new task or one previously administered? Depending on the task and the learning target, the same task could be administered multiple times over the course of the year. 5. Decide on an amount of tasks. To gain a more accurate view of student knowledge, one task may not be enough. Perhaps one task, along with classroom evidence, will provide an appropriate picture of the student’s understanding. Perhaps more than one task is needed. 6. Decide how the tasks and materials will be presented. Will all students be assessed on a task at the same time? If so, what will students who finish earlier/later than others do as other students work? Will students move from one station to another? If so, what will they do if they have questions about the task? Will students need access to optional materials? If so, how will they be provided? “Knowing what is to be learned is the starting point for instructional planning. This knowledge is also the starting point for determining what is to be assessed and how it will be measured.” (Joyner & Muri, 2011, p. 55) 9 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION Assessing Students During classroom instruction, the teacher facilitates learning by providing rich tasks, asking probing questions, observing students, and scaffolding learning as appropriate. However, during classroom assessment, the classroom teacher wants to learn what a student knows and is able to do without the support typically provided during instruction. In order to help the classroom teacher gather the best information possible from the tasks, the teacher’s role becomes that of an observer. Refraining from any coaching, prompting, or targeted questioning, the teacher only reads the assessment task to the student as many times as needed and encourages the student to solve the problem to the best of his/her ability. On occasion, a word provided in the directions may not make sense to the student and an alternative word is provided as determined by the teacher. However, the classroom teacher is very careful not to provide additional information that could cover up what the student does or doesn’t understand. The goal of assessment is to uncover student thinking so that instruction can best meet his/her needs. As the classroom teacher carefully observes students at work, s/he is finding out as much as possible about what students are thinking and how they go about working on tasks. The teacher may take notes on student strategies and behaviors, ask clarifying questions, or restate the problem as needed. For example, do students work with confidence on the task or are there some aspects that seem more difficult? Which ones? Can you determine why and make notes for adjustments next time this happens? Oftentimes, the observation provides the most information about student thinking. Because young children frequently know more than they can record in traditional, symbolic formats, it is important for the teacher to gather as much information about student understanding as students work on the various tasks. As the teacher circulates, s/he asks additional questions to learn as much as possible about students’ thinking. For example, the teacher might say, “Tell me more about the picture you have drawn.” or “Tell me what you are doing with the counters.” or “Tell me more about your thinking.” The teacher makes notes about students’ responses. Consider using the following clarifying questions to help understand student thinking: • Tell me more about that. • Can you show me? • Why do you say that? • What else can you tell me? • How do you know? • Why do you think that happened? • Do you think this will happen every time? 10 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION The assessment tasks can be administered individually, in small groups, or as a whole class, depending on the purpose for the assessment task. Oftentimes, if a task is presented in a whole class setting, the task requires the student to provide a written response. In this situation, the teacher is unable to observe all children carefully to learn about their thinking. Therefore, if the teacher has questions about a student’s work, the teacher is encouraged to ask follow up questions, clarifying what the student wrote and gaining better insight into the student’s thinking. When administering a task, consider the following: 1. Prepare the materials. Gather the materials needed for the task. All Blackline masters and Student Forms are located next to the task. Additional materials from the general classroom supplies may be needed. Will you need enough for the entire class or just one or a few students? 2. Read through the task directions. The language that the teacher is to use when administering a task is provided in italics. This ‘teacher talk’ is provided to help the classroom teacher ask questions and provide information without guiding thinking. Comments and notes to the teacher are not in italics. These comments provide prompts or reminders to the teacher as the task is administered. 3. Read the Continuum for Understanding indicators. Much of the administration of an assessment task is spent carefully observing children as they work. Read over the indicators to know what you are looking for as the students solve the problem. 4. Observe the students carefully. How are the students solving the problem? What are they using? Are they counting everything over and over or are they counting on? Do they know 10 more or 10 less fluently, or are they counting up or back to figure it out? Keep a clipboard, tablet, or other documentation devices to take notes as students work. Oftentimes, the observation provides the most information about student thinking. 5. What’s Next? After a student has completed a task, will s/he head back to Math Stations? Move on to the next item on his/her contract? Get his/her snack and join the others on the carpet or on the playground? Use the limited time you have wisely and refrain from having students wait for one another by planning “what’s next”. 11 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION Interpreting Data and Making Inferences The primary purpose of an assessment is to discern student understanding and then use this knowledge to plan instruction and teach students according to their needs. Because the tasks that are provided are considered assessments rather than evaluations, proficiency scores are not provided. Thus, an item is not simply marked as “correct” or “incorrect” or “proficient” or “not proficient”. Instead, the Continuum of Understanding is provided to help inform the teacher about the depth to which the student demonstrates understanding. As student responses are reviewed, the teacher uses the Continuum of Understanding to determine which strategies, skills, and understanding the student exhibits. Pay particular attention to what the student DOES understand and what the student does NOT. Both are equally important in determining the next instructional steps. The overall goal is that by the end of the year, all students will have become proficient with the mathematics described for their grade level. Proficient means that they can model and explain the concepts, they can use the mathematics appropriately and accurately, and they are fluent and comfortable in applying mathematics. Giving meaning to students’ words and actions is not a simple task, but it is critical that the interpretations are as accurate as possible. Because decisions about students and teaching arise from the interpretations, teachers must think carefully about the mathematics they are teaching, the continuum of understandings and skills related to the learning targets, and the information they have learned from the assessment. When interpreting data and making inferences, consider the following: 1. Ask Questions: If a student response is unclear or additional questions are needed to gain clarification about student thinking, have a discussion with the student. Share the work with the student and ask questions that will uncover the student’s thinking. Remember, this is not a time to teach the student something s/he may have answered incorrectly. This is a time to better understand the student’s thinking so that future instruction can meet his/her needs. 2. Types of Mistakes: Look beyond whether an item’s answer was correct or incorrect by looking carefully at the types of mistakes that were made. Some mistakes that children make come from a lack of information. At other times mistakes reflect a lack of understanding. Remember that there is logic behind students’ answers. The teacher must look for the reasons for the responses, dig deep and identify any misconceptions that may exist. Ask questions or seek clarification if needed. “Without the conversations or written explanations, we have no clue as to the students’ logic behind their wrong answers.” (Joyner & Muri, 2011, p. 250) “Unless we take the time to analyze incorrect responses, we may have no clue as to why students miss questions.” (Joyner & Muri, 2011, p. 123) 12 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION 3. Note Strategies Used: The Continuum of Understanding provides strategies of particular interest as well as additional skills and knowledge that the student may exhibit. Carefully note how the student solves the problem present in the task. What strategies does the student use? Does the student continually use a counting strategy rather than moving forward to making tens? Are there strategies that are never used? What strategies need to be highlighted during future instruction? 4. Organize Data: How will you capture the notes made about the student work? Will data be recorded by individual student, on class summary sheets, or both? Some teachers may wish to make notes on the task direction sheet for each student and staple it to the student work. Other teachers may want to use the individual student recording form provided to capture notes, using the task direction sheet to guide the structure of the notes. Teachers may also want to compile class data on the class summary sheets to gain a global perspective of the class as a whole, determine small groups, and determine next instructional steps. Assigning meaning to students’ words, actions, and products is perhaps the most difficult part of assessment. However, teachers must deal with students’ misconceptions as well as their strengths if students are going to be successful. If decisions are made from too little evidence or misleading evidence teachers may not plan the necessary classroom experiences for the students to refine their thinking. Therefore, it is important to note that these assessment tasks will provide only a part of the evidence of students’ knowledge and understanding and will be combined with other information the teacher has gathered about the student. These assessments are not intended to provide a complete picture of a student’s mathematics understandings. These assessments and additional student products and anecdotal information will need to be combined to gain the most accurate picture of student’s ability and understanding of mathematics. References: Joyner, J. & Muri, M. (2011). INFORMative assessment: Formative assessment to improve math achievement. Sausalito, CA: Math Solutions. “When we do not have an opportunity to see the steps or procedures that students use in determining answers or if students do not explain their thinking, the correct answers may be the results or informed guesses rather than solid understanding.” (Joyner & Muri, 2011, p. 122) 13 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION A Special ThankYou The development of the NC Department of Public Instruction K2 Formative Instructional and Assessment Tasks was a collaborative effort with a diverse group of dynamic teachers, coaches, administrators, university faculty, and NCDPI staff. We are very appreciative of all of the time, support, ideas, and suggestions made in an effort to provide North Carolina with quality formative assessment items for Kindergarten, First, and Second Grade. The North Carolina Department of Public Instruction appreciates any suggestions and feedback, which will help improve upon this resource. Please send all correspondence to Barbara Bissell (barbara.bissell@dpi.nc.gov) and Amy Scrinzi (amy.scrinzi@dpi.nc.gov). K2 Assessment Committee The K2 Assessment Committee led the work of the K2 Assessments. With support of their school and district, they volunteered their time and effort to develop the K2 Formative Instructional and Assessment Tasks. Jill Burke, First Grade Teacher, Chapel HillCarrboro City Schools Leanne Daughtry, District Office, Johnston County Schools Andi Greene, First Grade Teacher, Edgecombe County Schools Tery Gunter, Second Grade Teacher, Durham County Schools Tesha Isler, Teaching/Learning Coach, Wayne County Schools Patty Jordan, Second Grade Teacher, Wake County Schools Rebecca Kidd, Kindergarten Teacher, Asheboro City Schools Loryn Morrison, District Lead Teacher, Davidson County Schools Becky Pearce, Kindergarten Teacher, Guilford County Schools Kitty Rutherford, NCDPI Elementary Consultant Amy Scrinzi, NCDPI Elementary Consultant District Support In a true collaborative effort, districts in North Carolina that had begun implementing the Common Core State Standards during the 20112012 school year voluntarily shared their assessment efforts with the K2 Assessment Committee. Many of the final tasks presented are a direct result of this collaborative support. Cabarrus, CharlotteMecklenburg, Cleveland, Currituck, Davidson, IredellStatesville, Kannapolis, and Union Critical Friends Our Critical Friends carefully reviewed the assessment tasks, offered specific feedback, and provided suggestions for additional tasks as needed. Their feedback guided the final development of the assessment tasks. Melanie Burgess, Jeanette Cox, Donna Dalke, Ana Floyd, Sharon Frost, Royanna Jackson, Jeane Joyner, Rendy King, Carol Midgett, Drew Polly, Wendy Rich, Karen Young, and Pam Zelando 14 Operations & Algebraic Thinking Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 1a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Daniel had some stickers. His brother gave him 5 more stickers. Now Daniel has 18 stickers. How many stickers did Daniel have to start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 13 stickers • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 18  5 = *; * + 5 = 18). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 15 OA Task 1a Name ____________________________________ 2.OA.1 Add ToStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Daniel had some stickers. His brother gave him 5 more stickers. Now Daniel has 18 stickers. How many stickers did Daniel have to start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ stickers 16 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 1b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Jayden has some baseball cards. His friend gave him 28 more baseball cards. Now Jayden has 95 baseball cards. How many baseball cards did John start with? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 67 baseball cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts • Equation is accurate (e.g., 95 – 28 = *; 28 + * = 95). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 17 OA Task 1b Name ____________________________________ 2.OA.1 Add ToStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Jayden has some baseball cards. His friend gave him 28 more baseball cards. Now Jayden has 95 baseball cards. How many baseball cards did Jayden start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ baseball cards 18 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 1c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Alice has some pennies. Her dad gave her 48 more pennies. Now Alice has 83 pennies. How many pennies did Alice start with? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 35 pennies • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., * + 48 = 83; 83 – 48 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 19 OA Task 1c Name ____________________________________ 2.OA.1 Add ToStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Alice has some pennies. Her dad gave her 48 more pennies. Now Alice has 83 pennies. How many pennies did Alice start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ pennies 20 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 1d Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Nevaeh had some jewels. She gave 11 jewels to her sister. Now Nevaeh has 79 jewels. How many jewels did Nevaeh have to start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 90 jewels • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 48  11 = *; * + 11 = 48). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 21 OA Task 1d Name ____________________________________ 2.OA.1 Add ToStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Nevaeh had some jewels. She gave 11 jewels to her sister. Now Nevaeh has 79 jewels. How many jewels did Nevaeh have to start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ jewels 22 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 2a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Some baseball cards were on the table. Sam took 42 baseball cards. Then there were 26 baseball cards on the table. How many baseball cards were on the table before? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 68 baseball cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., *  42 = 26; 26 + 42 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 23 OA Task 2a Name ____________________________________ 2.OA.1 Take FromStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Some baseball cards were on the table. Sam took 42 baseball cards. Then there were 26 baseball cards on the table. How many baseball cards were on the table before? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ baseball cards 24 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 2b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Some players are on the basketball court. 14 players left. Then there were 16 players on the basketball court. How many players were on the basketball court before? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 30 players • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., *  14 = 16; 14 + 16 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 25 OA Task 2b Name ____________________________________ 2.OA.1 Take FromStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Some players are on the basketball court. 14 players left. Then there were 16 players on the basketball court. How many players were on the basketball court before? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ players 26 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 2c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Some fish are swimming in the stream. 23 fish swam away. Then there were 31 fish swimming in the stream. How many fish were swimming in the stream before? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 54 fish • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g. 23 + 31 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 27 OA Task 2c Name ____________________________________ 2.OA.1 Take FromStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Some fish are swimming in the stream. 23 fish swam away. Then there were 31 fish swimming in the stream. How many fish were swimming in the stream before? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ fish 28 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 2d Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: There were some Legos in a bucket. 50 Legos spilled out of the bucket. Then there were 33 Legos in the bucket. How many Legos were in the bucket before? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 83 Legos • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 50 + 33 = *; *  50 = 33). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 29 OA Task 2d Name ____________________________________ 2.OA.1 Take FromStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE There were some Legos in a bucket. 50 Legos spilled out of the bucket. Then there were 33 Legos in the bucket. How many Legos were in the bucket before? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ Legos 30 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 3a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Smaller Unknown: More, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Daniella has 9 more bracelets than Katie. Katie has 22 bracelets. How many bracelets does Daniella have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 31 bracelets • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 9 + 22 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 31 OA Task 3a Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Compare Smaller Unknown: More, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Daniella has 9 more bracelets than Katie. Katie has 22 bracelets. How many bracelets does Daniella have? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ bracelets 32 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 3b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Smaller Unknown: More, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Carlos has 13 more comic books than his friend David. Carlos has 30 comic books. How many comic books does David have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 43 comic books • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 30 + 13 = *; 13 + * = 30). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 33 OA Task 3b Name ____________________________________ 2.OA.1, 2.NBT.5, 2.NBT.9 Compare Smaller Unknown: More, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Carlos has 13 more comic books than his friend David. Carlos has 30 comic books. How many comic books does David have? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ comic books 34 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 3c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Smaller Unknown: More, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Kevin has 23 more shiny rocks than his friend Matthew. Kevin has 27 shiny rocks. How many shiny rocks does Matthew have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 4 shiny rocks • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 27  23 = *; 23 + * = 27). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 35 OA Task 3c Name ____________________________________ 2.OA.1, 2.NBT.5, 2.NBT.9 Compare Smaller Unknown: More, Onestep Formative Instructional and Assessment Tasks Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Kevin has 23 more shiny rocks than his friend Matthew. Kevin has 27 shiny rocks. How many shiny rocks does Matthew have? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ shiny rocks 36 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 3d Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Smaller Unknown: More, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Makayla has 22 more mini mystery books than her sister Brittany. Makayla has 40 mini mystery books. How many mini mystery books does Brittany have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 62 mini mystery books • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 22 + * = 40; 40  22 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 37 OA Task 3d Name ____________________________________ 2.OA.1, 2.NBT.5, 2.NBT.9 Compare Smaller Unknown: More, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Makayla has 22 more mini mystery books than her sister Brittany. Makayla has 40 mini mystery books. How many mini mystery books does Brittany have? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ mini mystery books 38 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 4a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Bigger Unknown: Fewer, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Luke has 5 fewer books than Josh. Luke has 7 books. How many books does Josh have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 2 books • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., *  5 = 7; 5 + 7 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 39 OA Task 4a Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Compare Bigger Unknown: Fewer, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Luke has 5 fewer books than Josh. Luke has 7 books. How many books does Josh have? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ books 40 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 4b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Bigger Unknown: Fewer, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: The 2nd grade class has 9 fewer students than the 3rd grade class. The 2nd grade class has 22 students. How many students are in the 3rd grade class? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 31 students • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 9 + 22 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 41 OA Task 4b Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Compare Bigger Unknown: Fewer, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE The 2nd grade class has 9 fewer students than the 3rd grade class. The 2nd grade class has 22 students. How many students are in the 3rd grade class? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ students 42 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 4c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Bigger Unknown: Fewer, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: There are 36 fewer apples in the box than apples on the ground. There are 50 apples in the box. How many apples are on the ground? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 86 apples • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 36 + 50 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 43 OA Task 4c Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Compare Bigger Unknown: Fewer, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE There are 36 fewer apples in the box than apples on the ground. There are 50 apples in the box. How many apples are on the ground? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ apples 44 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 4d Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Bigger Unknown: Fewer, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: There are 11 fewer cinnamon candies than chocolate candies. There are 30 cinnamon candies. How many chocolate candies are there? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 41 chocolate candies • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 30 + 11 = *; 11 = *  30) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 45 OA Task 4d Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Compare Bigger Unknown: Fewer, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE There are 11 fewer cinnamon candies than chocolate candies. There are 30 cinnamon candies. How many chocolate candies are there? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ chocolate candies 46 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 5a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToResult Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: John collected 67 baseball cards. His friend gave him 28 more baseball cards. How many cards does John have now? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 95 baseball cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 67 + 28 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 47 OA Task 5a Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add ToResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE John collected 67 baseball cards. His friend gave him 28 more baseball cards. How many cards does John have now? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ baseball cards 48 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 5b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToResult Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Val has 26 butterflies for the Science Fair. Sam brought 38 more butterflies for the Science Fair. How many butterflies did they take to the science fair? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 64 butterflies • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 26 + 38 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 49 OA Task 5b Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add ToResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Val has 26 butterflies for the Science Fair. Sam brought 38 more butterflies for the Science Fair. How many butterflies did they take to the science fair? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ butterflies 50 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 5c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add To Result Unknown, Twostep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Ana brought 6 DVDs to a party. Mark brought 7 DVDs to the party. Steve brought 8 DVDs to the party. How many DVDs do they have for the party? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 21 DVDs • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 6 + 7 + 8 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 51 OA Task 5c Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add ToResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Ana brought 6 DVDs to a party. Mark brought 7 DVDs to the party. Steve brought 8 DVDs to the party. How many DVDs do they have for the party? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ DVDs 52 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 5d Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add To Result Unknown, Twostep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Benjamin has 7 baseball cards. Kyle gave Benjamin 8 baseball cards. Jim gave Benjamin 3 more baseball cards. How many cards does Benjamin have now? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 18 baseball cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 7 + 8 + 3 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 53 OA Task 5d Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add ToResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Benjamin has 7 baseball cards. Kyle gave Benjamin 8 baseball cards. Jim gave Benjamin 3 more baseball cards. How many cards does Benjamin have now? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ cards 54 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 6a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add To: Change Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Lucas had 67 baseball cards. His friend gave Lucas some more baseball cards. Now Lucas has 95 baseball cards. How many baseball cards did his friend give Lucas? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 28 baseball cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 67 + * = 95) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 55 OA Task 6a Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add To: Change Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Lucas had 67 baseball cards. His friend gave Lucas some more baseball cards. Now Lucas has 95 baseball cards. How many baseball cards did his friend give Lucas? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ baseball cards 56 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 6b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add To: Change Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Jalen had 30 marbles. When he cleaned out his closet he found some more marbles. Now Jalen has 58 marbles. How many marbles did Jalen find? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 28 marbles • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 30 + * = 58; 58 – 30 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 57 OA Task 6b Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add To: Change Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Jalen had 30 marbles. When he cleaned out his closet he found some more marbles. Now Jalen has 58 marbles. How many marbles did Jalen find? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ marbles 58 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 6c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Add To: Change Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Pam has 17 cards of animals from Africa. She has some cards from other continents. All together she has 90 cards. How many cards are from other continents? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 73 cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., * = 90 – 17; 90 = * + 17) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 59 OA Task 6c Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add To: Change Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Pam has 17 cards of animals from Africa. She has some cards from other continents. All together she has 90 cards. How many cards are from other continents? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ cards 60 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 7a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve oneand twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromResult Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: 60 apples were on the shelf. 23 apples were sold. How many apples are on the shelf now? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Basic Facts Creates easier or known sums Doubles Other: Complete Understanding • Correctly solves the problem: 37 apples • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 60 – 23 = *; 23 + * = 60) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 61 OA Task 7a Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Take FromResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE 60 apples were on the shelf. 23 apples were sold. How many apples are on the shelf now? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ apples 62 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 7b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Take From Result Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Mrs. Hope’s class saw 76 butterflies in the garden. Some of the butterflies flew away. Now there are 49 butterflies in the garden. How many butterflies flew away? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 27 butterflies • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 76 – 49 = *; 76 = 49 + *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 63 OA Task 7b Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Take FromResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Mrs. Hope’s class saw 76 butterflies in the garden. Some of the butterflies flew away. Now there are 49 butterflies in the garden. How many butterflies flew away? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ butterflies 64 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 7c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve oneand twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromResult Unknown, Twostep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Avi drew 5 pictures to enter in the school art contest. Erick drew 7 pictures. Avi spilled water on 2 of his pictures and ruined them. How many pictures will Avi and Erick enter in the contest? Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 10 pictures • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 65 OA Task 7c Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Take FromResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Avi drew 5 pictures to enter in the school art contest. Erick drew 7 pictures. Avi spilled water on 2 of his pictures and ruined them. How many pictures will Avi and Erick enter in the contest? Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ pictures 66 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 8a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve oneand twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Take From Change Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: The principal had 38 balloons. Some balloons popped. Then the principal had 19 balloons. How many balloons popped? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 19 balloons • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 38  * = 19; 19 + * = 38) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 67 OA Task 8a Name ____________________________________ 2.OA.1 1.NBT.5, 1.NBT.9 Take From Change Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE The principal had 38 balloons. Some balloons popped. Then the principal had 19 balloons. How many balloons popped? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ balloons 68 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 8b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve oneand twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Take From Change Unknown, Twostep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: 12 children were on the baseball field. Some children left the baseball field to play on the swings. Then 2 more children came to the baseball field. Now there are 8 children on the baseball field. How many children left to play on the swings? Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 6 children left the baseball field • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 69 OA Task 8b Name ____________________________________ 2.OA.1 1.NBT.5, 1.NBT.9 Take From Change Unknown, Twostep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE 12 children were on the baseball field. Some children left the baseball field to play on the swings. Then 2 more children came to the baseball field. Now there are 8 children on the baseball field. How many children left to play on the swings? Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ children 70 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 8c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve oneand twostep 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.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between ad
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Title  Formative instructional & assessment tasks for the common core state standards in mathematics 
Other Title  Common core state standards in mathematics 
Date  2012 
Description  Grade 2 
Digital CharacteristicsA  3.91 MB; 236 p. 
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Related Items  http://worldcat.org/oclc/857589738/viewonline 
Pres File NameM  pubs_formativeinstructionalmathematicsgrade2201210.pdf 
Full Text  GRADE 2 PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education  Department of Public Instruction Formative Instructional & Assessment Tasks for the Common Core State Standards in Mathematics Word Document versions of the documents http://commoncoretasks.wikispaces.com/ STATE BOARD OF EDUCATION The guiding mission of the North Carolina State Board of Education is that every public school student will graduate from high school, globally competitive for work and postsecondary education and prepared for life in the 21st Century. NC DEPARTMENT OF PUBLIC INSTRUCTION June St. Clair Atkinson, Ed.D., State Superintendent 301 N. Wilmington Street :: Raleigh, North Carolina 276012825 In compliance with federal law, NC Public Schools administers all stateoperated educational programs, employment activities and admissions without discrimination because of race, religion, national or ethnic origin, color, age, military service, disability, or gender, except where exemption is appropriate and allowed by law. Inquiries or complaints regarding discrimination issues should be directed to: Dr. Rebecca Garland, Chief Academic Officer :: Academic Services and Instructional Support 6368 Mail Service Center, Raleigh, NC 276996368 :: Telephone: (919) 8073200 :: Fax: (919) 8074065 Visit us on the Web :: www.ncpublicschools.org WILLIAM C. HARRISON Chairman :: Fayetteville WAYNE MCDEVITT Vice Chair :: Asheville WALTER DALTON Lieutenant Governor :: Rutherfordton JANET COWELL State Treasurer :: Raleigh Jean W. Wolard Plymouth REGINALD KENAN Rose Hill KEVIN D. HOWELL Raleigh SHIRLEY E. HARRIS Troy CHRISTINE J. GREENE High Point JOHN A. TATE III Charlotte ROBERT “TOM” SPEED Boone MELISSA E. BARTLETT Roxboro PATRICIA N. WILLOUGHBY Raleigh M0910 Table of Contents 1. Common Core State Standards ........................................................................................................................................ 1 2. Administration Manual ....................................................................................................................................................... 3 3. Operations & Algebraic Thinking ................................................................................................................................ 15 4. Number and Operations in Base Ten ........................................................................................................................ 126 5. Measurement and Data .................................................................................................................................................. 158 6. Geometry .............................................................................................................................................................................. 203 7. Student Record Keeping Forms ................................................................................................................................. 221 NOTE: The separate Word document versions of each section can be found online at http://commoncoretasks.wikispaces.com/ . Common Core State Standards Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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. (Note: See Glossary, Table 1.) Add and subtract within 20. 2.OA.2 Fluently add and subtract within 20 using mental strategies. (Note: See standard 1.OA.6 for a list of mental strategies). By end of Grade 2, know from memory all sums of two onedigit numbers. Work with equal groups of objects to gain foundations for multiplication. 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.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Number and Operations in Base Ten Understand place value. 2.NBT.1 Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens – called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2.NBT.2 Count within 1000; skipcount by 5s, 10s, and 100s. 2.NBT.3 Read and write numbers to 1000 using baseten numerals, number names, and expanded form. 2.NBT.4 Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Use place value understanding and properties of operations to add and subtract. 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.NBT.6 Add up to four twodigit numbers using strategies based on place value and properties of operations. 2.NBT.7 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 threedigit 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. 2.NBT.8 Mentally add 10 or 100 to a given number 100900, and mentally subtract 10 or 100 from a given number 100900. 2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Note: Explanations may be supported by drawings or objects.) Measurement and Data Measure and estimate lengths in standard units. 2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Relate addition and subtraction to length. 2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 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 wholenumber sums and differences within 100 on a number line diagram. Second Grade – Standards 1. Extending understanding of baseten notation – Students extend their understanding of the baseten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students understand multidigit numbers (up to 1000) written in baseten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones). 2. Building fluency with addition and subtraction – Students use their understanding of addition to develop fluency with addition and subtraction within 100. They solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of whole numbers in baseten notation, using their understanding of place value and the properties of operations. They select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds. 3. Using standard units of measure – Students recognize the need for standard units of measure (centimeter and inch) and they use rulers and other measurement tools with the understanding that linear measure involves iteration of units. They recognize that the smaller the unit, the more iterations they need to cover a given length. 4. Describing and analyzing shapes – Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two and threedimensional shapes, students develop a foundation for understanding attributes of two and threedimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades. Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 1 Work with time and money. 2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? Represent and interpret data. 2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in wholenumber units. 2.MD.10 Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple put together, takeapart, and compare problems using information presented in a bar graph. (Note: See Glossary, Table 1.) Geometry Reason with shapes and their attributes. 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. (Note: Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 2.G.2 Partition a rectangle into rows and columns of samesize squares and count to find the total number of them. 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. 2 Administration Manual K2 Assessment in North Carolina In response to North Carolina legislative and State Board requirements, the NC Department of Public Instruction provides Local Education Agencies with statedeveloped assessments to be implemented for Kindergarten, First and Second Grades. These assessments are to include documented, ongoing individualized assessments throughout the year and a summative evaluation at the end of the year. These assessments monitor proficiency of the standards in the North Carolina Standard Course of Study: Common Core State Standards for Mathematics. Assessments may take the form of these state developed materials, adaptations of these materials, or unique assessments adopted by local school boards. The intended purposes of these assessments are: • To provide information about progress of each student for instructional adaptations and early interventions. • To provide nextyear teachers with information about the status of each of their incoming students. • To inform parents about the status of their children relative to gradelevel standards at the end of the year • To provide the school and school district information about the achievement status and progress of groups of students in grades K, 1, and 2. The North Carolina Department of Public Instruction is committed to continued development of quality teaching and ongoing classroom assessment as essential preparation for the students to master rigorous standards as defined by the NC Standard Course of Study: Common Core State Standards and Essential Standards. We believe the strategies that engage students in selfassessment, greater ownership of their learning, communicating, reasoning, problem posing and problem solving result in longterm growth and learning. Therefore, the Formative Instructional and Assessment Tasks for Mathematics are designed to clarify the bond that links quality assessment and effective teaching and subsequently effective schools. Learning takes place one student at a time, and quality teaching and assessment is essential in ensuring that every public school student will graduate from high school, globally competitive for work and postsecondary education and prepared for life in the 21st Century. These statedeveloped assessment materials are aligned with the Common Core State Standards for Mathematics and may be adopted or modified as appropriate for individual school districts. As you use them with students, add to and adapt the materials in order to make them useful for each school’s unique situation. The North Carolina Department of Public Instruction appreciates any suggestions and feedback, which will help improve upon this resource. Feedback may be sent to NCDPI Elementary Mathematics Consultant Amy Scrinzi (Amy.Scrinzi@dpi.nc.gov). 3 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION The Purpose of the Formative Instructional and Assessment Tasks The Formative Instructional and Assessment Tasks are provided as tools to use to assess Kindergarten, First Grade and Second Grade students’ mathematical understanding as specified in the NC Standard Course of Study: Common Core State Standards for Mathematics (CCSSM). Mathematical Concepts Assessed The Formative Instructional and Assessment Tasks are designed to reveal the extent to which a student knows and understands specific concepts. Moving beyond only whether an answer is right or wrong, the tasks focus attention on the thinking and processes that all students use in solving the tasks, with opportunities to demonstrate his or her knowledge, skill, and understanding. Therefore, the tasks assess the Common Core State Standards and highlight Standards for Mathematical Practice that may emerge as students explore the tasks. The Continuum for Understanding specifically addresses the conceptual understandings indicated in the CCSSM. The Standards for Mathematical Practice that are likely to emerge are indicated in bold for each task. Types of Tasks When assessing young children, it is important to remember that they frequently know more than they can record in traditional, symbolic formats. “Age, fluency with language, and experiences influence how successful students are likely to write a strong explanation or offer an explanation orally” (Joyner & Muri, 2011). Therefore interviews, as well as written responses, are provided. Interview: The teacher asks a series of questions to one student and carefully listens to the student’s responses and observes the student’s strategies and thinking as the student works. Written Response: The teacher presents a problem to one or more students and asks the students to use pictures, numbers, and words to show their thinking and explain their reasoning. Since both correct answers and appropriate processes are valued in mathematics, teachers find that observing students and talking with them are ways to provide students with opportunities to demonstrate what they know and can apply in new situations. Thus, the teacher is encouraged to ask the student clarifying questions during the assessment or after the assessment to gain a more accurate picture of what the student knows and understands. Insight into children’s thinking helps teachers build on what students understand, not just what they can do by memorizing processes. “Without the conversations or written explanations, we have no clue as to the students’ logic behind their wrong answers.” (Joyner & Muri, 2011, p. 250) 4 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION The Role of the Classroom Teacher The classroom teacher uses the tasks in a formative manner. As defined by North Carolina Department of Public Instruction, formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to help students improve their achievement of intended instructional outcomes. Therefore, a teacher may use these tasks to: • Determine prior knowledge regarding a concept that is about to be taught. • Assess understanding throughout an instructional sequence to gain an understanding of how to best meet the needs of all of the students in an ongoing basis. • Determine if the student is Developing Understanding of a particular concept or if the student has Complete Understanding, demonstrating proficiency. • Assess understanding after the instructional sequence to determine if all students are proficient with that concept and are ready to move forward. The teacher may administer the tasks to a whole class, small group of children, or an individual student, depending on the purpose for collecting data. For example, the teacher may decide that s/he would like to gain awareness of the entire class’ understanding of a particular concept. Thus, the task(s) selected would then be administered to all of the students in the class. Other times the teacher may need to determine what a particular student, or small group of students, understands in order to plan the most effective mathematical experiences. Thus, the task(s) selected would then be used with the selected student(s). Therefore, the assessment tasks can be used in multiple ways with the purpose of informing instructional planning and practice. The Role of the Local Education Agency (LEA) A school district may decide to use the assessment tasks to create benchmark assessments, aligning a collection of tasks to their unique pacing guide to be administered districtwide at several points throughout the year. The classroom teacher scores the quarterly benchmark assessments, sees students’ answers, observes misconceptions, and uses the data gathered to inform further instruction and plan interventions or enrichments as needed (Joyner & Muri, 2011). The district uses the data from the benchmark assessments to gain a global view of how students are performing within particular domains or clusters, determine which additional instructional materials and resources may be needed, and discern particular topics and concepts that teachers may need additional support or growth and work with principals and teachers to plan professional development and coaching opportunities accordingly. These statedeveloped assessment tasks are aligned with the North Carolina Standard Course of Study: Common Core State Standards for Mathematics and may be adopted or modified as appropriate for individual school districts. As they are used with students, please add to and adapt the materials in order to make them useful for each school’s unique situation. The North Carolina Department of Public Instruction appreciates any suggestions and feedback, which will help improve upon this resource. 5 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION The Components of the Formative Instructional & Assessment Tasks The Formative Instructional and Assessment Tasks are composed of four parts: 1. Assessment Tasks 2. Student Forms 3. Blackline Masters 4. Class/Student Summaries 1. Assessment Tasks The assessment tasks inform the classroom teacher of a) the Mathematical Concepts addressed, b) the materials needed, c) the assessment task directions, the d) Continuum of Understanding, and the e) Standards for Mathematical Practice. a.) Mathematical Concepts: Designate the domain, cluster, and standard assessed. There may be some tasks that assess multiple concepts. Domain: Large group of related standards. Include: Counting and Cardinality (K), Operations and Algebraic Thinking, Number and Operations in Base Ten, Measurement and Data, and Geometry. Cluster: Groups of related standards. Standard: Define what students should understand and be able to do. b.) Materials: Student and teacher materials needed to complete the task. Materials may include: Blackline Master (BLM), Student Form (SF) or classroom materials. Provide additional materials or substitute materials with those that students use during regular mathematics lessons as needed. c.) Task: Directions for the administering the task. May include “Teacher Talk”: dialogue for the teacher to say to the student(s) while administering the task. Indicated in italics. d.) Continuum of Understanding: Designates indicators: specific behaviors and skills that signify if the student is Developing Understanding or demonstrates Complete Understanding. Indicators: Specific behavior or skill within the continuum noted by a bullet. Developing Understanding: If the student exhibits one OR more of the indicators listed, then the student’s understanding is still evolving. Complete Understanding: If the student exhibits ALL of the indicators listed, then the student has demonstrated proficiency with that particular skills or concept on that one particular task. Other tasks may be needed in order to confirm proficiency in that overall skill or concept. 6 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION In addition, there may be specific behaviors, strategies, concepts, or skills for which the teacher is to observe. These are located to the right of the indicators. Answers to the tasks are also provided in this area. e.) Standards for Mathematical Practice: Describe processes and dispositions that mathematically proficient students exhibit. Practices that are likely to emerge as a result of completing the task are noted in BOLD. The teacher is encouraged to note which practices were observed during the tasks as well as during daily instruction to gain a global picture of the mathematical processes and dispositions that the student exhibits. 7 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION The Formative Instructional and Assessment Tasks are composed of three additional parts: 1. Assessment Tasks 2. Student Forms 3. Blackline Masters 4. Class/Student Summaries 2. Student Forms Student forms are provided as an option to use for all tasks that require a written response from the student. These forms are located with the appropriate task and are designated as “SF”. Teachers may copy, edit, or revise the forms as needed. 3. Blackline Masters If a task requires a particular illustration or specific materials, then a blackline master is included. These forms are located with the appropriate task and are designated as “BLM”. Teachers may copy, edit, or revise forms as needed. 4. Class/Student Summaries Class and Student Summaries are provided to help the classroom teacher collect and organize data. These forms are located with the appropriate Domain/Cluster. These forms are provided as Word documents allowing the teacher to type information as desired, change the size of the space provided, or add additional columns or categories as needed. Teachers may copy, edit, or revise the forms as needed. 8 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION Selecting an Assessment Task The Formative Instructional and Assessment Tasks are placed with the corresponding Domain(s), Cluster(s), and Standard(s) on the common core assessment wiki. When searching for a task, simply click on the domain and cluster of interest. Tasks will be located with each standard assessed. In addition, each grade is provided with a comprehensive list of assessment tasks and the standards to which they align. NOTE: Some tasks assess multiple standards. Therefore, tasks are placed with the primary standard assessed and additional standards assessed are noted in the table and with the task directions. When selecting a task, consider the following: 1. Designate a learning target. What skill or concept do you want students to know? 2. Identify the student(s). Are you curious about all of the students, a handful of students, or one student in particular? Thinking about the student(s), what are you most interested in learning that is related to the learning target? 3. Review and select the tasks. Locate tasks that are aligned with the learning target and address your questions about the student(s). 4. Read the tasks carefully. Which tasks would best uncover student understanding for the particular learning target? Does it need to be a new task or one previously administered? Depending on the task and the learning target, the same task could be administered multiple times over the course of the year. 5. Decide on an amount of tasks. To gain a more accurate view of student knowledge, one task may not be enough. Perhaps one task, along with classroom evidence, will provide an appropriate picture of the student’s understanding. Perhaps more than one task is needed. 6. Decide how the tasks and materials will be presented. Will all students be assessed on a task at the same time? If so, what will students who finish earlier/later than others do as other students work? Will students move from one station to another? If so, what will they do if they have questions about the task? Will students need access to optional materials? If so, how will they be provided? “Knowing what is to be learned is the starting point for instructional planning. This knowledge is also the starting point for determining what is to be assessed and how it will be measured.” (Joyner & Muri, 2011, p. 55) 9 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION Assessing Students During classroom instruction, the teacher facilitates learning by providing rich tasks, asking probing questions, observing students, and scaffolding learning as appropriate. However, during classroom assessment, the classroom teacher wants to learn what a student knows and is able to do without the support typically provided during instruction. In order to help the classroom teacher gather the best information possible from the tasks, the teacher’s role becomes that of an observer. Refraining from any coaching, prompting, or targeted questioning, the teacher only reads the assessment task to the student as many times as needed and encourages the student to solve the problem to the best of his/her ability. On occasion, a word provided in the directions may not make sense to the student and an alternative word is provided as determined by the teacher. However, the classroom teacher is very careful not to provide additional information that could cover up what the student does or doesn’t understand. The goal of assessment is to uncover student thinking so that instruction can best meet his/her needs. As the classroom teacher carefully observes students at work, s/he is finding out as much as possible about what students are thinking and how they go about working on tasks. The teacher may take notes on student strategies and behaviors, ask clarifying questions, or restate the problem as needed. For example, do students work with confidence on the task or are there some aspects that seem more difficult? Which ones? Can you determine why and make notes for adjustments next time this happens? Oftentimes, the observation provides the most information about student thinking. Because young children frequently know more than they can record in traditional, symbolic formats, it is important for the teacher to gather as much information about student understanding as students work on the various tasks. As the teacher circulates, s/he asks additional questions to learn as much as possible about students’ thinking. For example, the teacher might say, “Tell me more about the picture you have drawn.” or “Tell me what you are doing with the counters.” or “Tell me more about your thinking.” The teacher makes notes about students’ responses. Consider using the following clarifying questions to help understand student thinking: • Tell me more about that. • Can you show me? • Why do you say that? • What else can you tell me? • How do you know? • Why do you think that happened? • Do you think this will happen every time? 10 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION The assessment tasks can be administered individually, in small groups, or as a whole class, depending on the purpose for the assessment task. Oftentimes, if a task is presented in a whole class setting, the task requires the student to provide a written response. In this situation, the teacher is unable to observe all children carefully to learn about their thinking. Therefore, if the teacher has questions about a student’s work, the teacher is encouraged to ask follow up questions, clarifying what the student wrote and gaining better insight into the student’s thinking. When administering a task, consider the following: 1. Prepare the materials. Gather the materials needed for the task. All Blackline masters and Student Forms are located next to the task. Additional materials from the general classroom supplies may be needed. Will you need enough for the entire class or just one or a few students? 2. Read through the task directions. The language that the teacher is to use when administering a task is provided in italics. This ‘teacher talk’ is provided to help the classroom teacher ask questions and provide information without guiding thinking. Comments and notes to the teacher are not in italics. These comments provide prompts or reminders to the teacher as the task is administered. 3. Read the Continuum for Understanding indicators. Much of the administration of an assessment task is spent carefully observing children as they work. Read over the indicators to know what you are looking for as the students solve the problem. 4. Observe the students carefully. How are the students solving the problem? What are they using? Are they counting everything over and over or are they counting on? Do they know 10 more or 10 less fluently, or are they counting up or back to figure it out? Keep a clipboard, tablet, or other documentation devices to take notes as students work. Oftentimes, the observation provides the most information about student thinking. 5. What’s Next? After a student has completed a task, will s/he head back to Math Stations? Move on to the next item on his/her contract? Get his/her snack and join the others on the carpet or on the playground? Use the limited time you have wisely and refrain from having students wait for one another by planning “what’s next”. 11 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION Interpreting Data and Making Inferences The primary purpose of an assessment is to discern student understanding and then use this knowledge to plan instruction and teach students according to their needs. Because the tasks that are provided are considered assessments rather than evaluations, proficiency scores are not provided. Thus, an item is not simply marked as “correct” or “incorrect” or “proficient” or “not proficient”. Instead, the Continuum of Understanding is provided to help inform the teacher about the depth to which the student demonstrates understanding. As student responses are reviewed, the teacher uses the Continuum of Understanding to determine which strategies, skills, and understanding the student exhibits. Pay particular attention to what the student DOES understand and what the student does NOT. Both are equally important in determining the next instructional steps. The overall goal is that by the end of the year, all students will have become proficient with the mathematics described for their grade level. Proficient means that they can model and explain the concepts, they can use the mathematics appropriately and accurately, and they are fluent and comfortable in applying mathematics. Giving meaning to students’ words and actions is not a simple task, but it is critical that the interpretations are as accurate as possible. Because decisions about students and teaching arise from the interpretations, teachers must think carefully about the mathematics they are teaching, the continuum of understandings and skills related to the learning targets, and the information they have learned from the assessment. When interpreting data and making inferences, consider the following: 1. Ask Questions: If a student response is unclear or additional questions are needed to gain clarification about student thinking, have a discussion with the student. Share the work with the student and ask questions that will uncover the student’s thinking. Remember, this is not a time to teach the student something s/he may have answered incorrectly. This is a time to better understand the student’s thinking so that future instruction can meet his/her needs. 2. Types of Mistakes: Look beyond whether an item’s answer was correct or incorrect by looking carefully at the types of mistakes that were made. Some mistakes that children make come from a lack of information. At other times mistakes reflect a lack of understanding. Remember that there is logic behind students’ answers. The teacher must look for the reasons for the responses, dig deep and identify any misconceptions that may exist. Ask questions or seek clarification if needed. “Without the conversations or written explanations, we have no clue as to the students’ logic behind their wrong answers.” (Joyner & Muri, 2011, p. 250) “Unless we take the time to analyze incorrect responses, we may have no clue as to why students miss questions.” (Joyner & Muri, 2011, p. 123) 12 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION 3. Note Strategies Used: The Continuum of Understanding provides strategies of particular interest as well as additional skills and knowledge that the student may exhibit. Carefully note how the student solves the problem present in the task. What strategies does the student use? Does the student continually use a counting strategy rather than moving forward to making tens? Are there strategies that are never used? What strategies need to be highlighted during future instruction? 4. Organize Data: How will you capture the notes made about the student work? Will data be recorded by individual student, on class summary sheets, or both? Some teachers may wish to make notes on the task direction sheet for each student and staple it to the student work. Other teachers may want to use the individual student recording form provided to capture notes, using the task direction sheet to guide the structure of the notes. Teachers may also want to compile class data on the class summary sheets to gain a global perspective of the class as a whole, determine small groups, and determine next instructional steps. Assigning meaning to students’ words, actions, and products is perhaps the most difficult part of assessment. However, teachers must deal with students’ misconceptions as well as their strengths if students are going to be successful. If decisions are made from too little evidence or misleading evidence teachers may not plan the necessary classroom experiences for the students to refine their thinking. Therefore, it is important to note that these assessment tasks will provide only a part of the evidence of students’ knowledge and understanding and will be combined with other information the teacher has gathered about the student. These assessments are not intended to provide a complete picture of a student’s mathematics understandings. These assessments and additional student products and anecdotal information will need to be combined to gain the most accurate picture of student’s ability and understanding of mathematics. References: Joyner, J. & Muri, M. (2011). INFORMative assessment: Formative assessment to improve math achievement. Sausalito, CA: Math Solutions. “When we do not have an opportunity to see the steps or procedures that students use in determining answers or if students do not explain their thinking, the correct answers may be the results or informed guesses rather than solid understanding.” (Joyner & Muri, 2011, p. 122) 13 K2 ASSESSMENT IN NORTH CAROLINA NC DEPARTMENT OF PUBLIC INSTRUCTION A Special ThankYou The development of the NC Department of Public Instruction K2 Formative Instructional and Assessment Tasks was a collaborative effort with a diverse group of dynamic teachers, coaches, administrators, university faculty, and NCDPI staff. We are very appreciative of all of the time, support, ideas, and suggestions made in an effort to provide North Carolina with quality formative assessment items for Kindergarten, First, and Second Grade. The North Carolina Department of Public Instruction appreciates any suggestions and feedback, which will help improve upon this resource. Please send all correspondence to Barbara Bissell (barbara.bissell@dpi.nc.gov) and Amy Scrinzi (amy.scrinzi@dpi.nc.gov). K2 Assessment Committee The K2 Assessment Committee led the work of the K2 Assessments. With support of their school and district, they volunteered their time and effort to develop the K2 Formative Instructional and Assessment Tasks. Jill Burke, First Grade Teacher, Chapel HillCarrboro City Schools Leanne Daughtry, District Office, Johnston County Schools Andi Greene, First Grade Teacher, Edgecombe County Schools Tery Gunter, Second Grade Teacher, Durham County Schools Tesha Isler, Teaching/Learning Coach, Wayne County Schools Patty Jordan, Second Grade Teacher, Wake County Schools Rebecca Kidd, Kindergarten Teacher, Asheboro City Schools Loryn Morrison, District Lead Teacher, Davidson County Schools Becky Pearce, Kindergarten Teacher, Guilford County Schools Kitty Rutherford, NCDPI Elementary Consultant Amy Scrinzi, NCDPI Elementary Consultant District Support In a true collaborative effort, districts in North Carolina that had begun implementing the Common Core State Standards during the 20112012 school year voluntarily shared their assessment efforts with the K2 Assessment Committee. Many of the final tasks presented are a direct result of this collaborative support. Cabarrus, CharlotteMecklenburg, Cleveland, Currituck, Davidson, IredellStatesville, Kannapolis, and Union Critical Friends Our Critical Friends carefully reviewed the assessment tasks, offered specific feedback, and provided suggestions for additional tasks as needed. Their feedback guided the final development of the assessment tasks. Melanie Burgess, Jeanette Cox, Donna Dalke, Ana Floyd, Sharon Frost, Royanna Jackson, Jeane Joyner, Rendy King, Carol Midgett, Drew Polly, Wendy Rich, Karen Young, and Pam Zelando 14 Operations & Algebraic Thinking Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 1a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Daniel had some stickers. His brother gave him 5 more stickers. Now Daniel has 18 stickers. How many stickers did Daniel have to start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 13 stickers • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 18  5 = *; * + 5 = 18). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 15 OA Task 1a Name ____________________________________ 2.OA.1 Add ToStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Daniel had some stickers. His brother gave him 5 more stickers. Now Daniel has 18 stickers. How many stickers did Daniel have to start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ stickers 16 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 1b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Jayden has some baseball cards. His friend gave him 28 more baseball cards. Now Jayden has 95 baseball cards. How many baseball cards did John start with? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 67 baseball cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts • Equation is accurate (e.g., 95 – 28 = *; 28 + * = 95). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 17 OA Task 1b Name ____________________________________ 2.OA.1 Add ToStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Jayden has some baseball cards. His friend gave him 28 more baseball cards. Now Jayden has 95 baseball cards. How many baseball cards did Jayden start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ baseball cards 18 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 1c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Alice has some pennies. Her dad gave her 48 more pennies. Now Alice has 83 pennies. How many pennies did Alice start with? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 35 pennies • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., * + 48 = 83; 83 – 48 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 19 OA Task 1c Name ____________________________________ 2.OA.1 Add ToStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Alice has some pennies. Her dad gave her 48 more pennies. Now Alice has 83 pennies. How many pennies did Alice start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ pennies 20 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 1d Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Nevaeh had some jewels. She gave 11 jewels to her sister. Now Nevaeh has 79 jewels. How many jewels did Nevaeh have to start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 90 jewels • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 48  11 = *; * + 11 = 48). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 21 OA Task 1d Name ____________________________________ 2.OA.1 Add ToStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Nevaeh had some jewels. She gave 11 jewels to her sister. Now Nevaeh has 79 jewels. How many jewels did Nevaeh have to start with? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ jewels 22 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 2a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Some baseball cards were on the table. Sam took 42 baseball cards. Then there were 26 baseball cards on the table. How many baseball cards were on the table before? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 68 baseball cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., *  42 = 26; 26 + 42 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 23 OA Task 2a Name ____________________________________ 2.OA.1 Take FromStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Some baseball cards were on the table. Sam took 42 baseball cards. Then there were 26 baseball cards on the table. How many baseball cards were on the table before? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ baseball cards 24 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 2b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Some players are on the basketball court. 14 players left. Then there were 16 players on the basketball court. How many players were on the basketball court before? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 30 players • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., *  14 = 16; 14 + 16 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 25 OA Task 2b Name ____________________________________ 2.OA.1 Take FromStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Some players are on the basketball court. 14 players left. Then there were 16 players on the basketball court. How many players were on the basketball court before? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ players 26 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 2c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Some fish are swimming in the stream. 23 fish swam away. Then there were 31 fish swimming in the stream. How many fish were swimming in the stream before? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 54 fish • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g. 23 + 31 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 27 OA Task 2c Name ____________________________________ 2.OA.1 Take FromStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Some fish are swimming in the stream. 23 fish swam away. Then there were 31 fish swimming in the stream. How many fish were swimming in the stream before? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ fish 28 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 2d Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromStart Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: There were some Legos in a bucket. 50 Legos spilled out of the bucket. Then there were 33 Legos in the bucket. How many Legos were in the bucket before? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 83 Legos • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 50 + 33 = *; *  50 = 33). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 29 OA Task 2d Name ____________________________________ 2.OA.1 Take FromStart Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE There were some Legos in a bucket. 50 Legos spilled out of the bucket. Then there were 33 Legos in the bucket. How many Legos were in the bucket before? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ Legos 30 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 3a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Smaller Unknown: More, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Daniella has 9 more bracelets than Katie. Katie has 22 bracelets. How many bracelets does Daniella have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 31 bracelets • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 9 + 22 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 31 OA Task 3a Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Compare Smaller Unknown: More, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Daniella has 9 more bracelets than Katie. Katie has 22 bracelets. How many bracelets does Daniella have? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ bracelets 32 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 3b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Smaller Unknown: More, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Carlos has 13 more comic books than his friend David. Carlos has 30 comic books. How many comic books does David have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 43 comic books • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 30 + 13 = *; 13 + * = 30). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 33 OA Task 3b Name ____________________________________ 2.OA.1, 2.NBT.5, 2.NBT.9 Compare Smaller Unknown: More, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Carlos has 13 more comic books than his friend David. Carlos has 30 comic books. How many comic books does David have? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ comic books 34 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 3c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Smaller Unknown: More, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Kevin has 23 more shiny rocks than his friend Matthew. Kevin has 27 shiny rocks. How many shiny rocks does Matthew have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 4 shiny rocks • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 27  23 = *; 23 + * = 27). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 35 OA Task 3c Name ____________________________________ 2.OA.1, 2.NBT.5, 2.NBT.9 Compare Smaller Unknown: More, Onestep Formative Instructional and Assessment Tasks Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Kevin has 23 more shiny rocks than his friend Matthew. Kevin has 27 shiny rocks. How many shiny rocks does Matthew have? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ shiny rocks 36 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 3d Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Smaller Unknown: More, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Makayla has 22 more mini mystery books than her sister Brittany. Makayla has 40 mini mystery books. How many mini mystery books does Brittany have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 62 mini mystery books • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 22 + * = 40; 40  22 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 37 OA Task 3d Name ____________________________________ 2.OA.1, 2.NBT.5, 2.NBT.9 Compare Smaller Unknown: More, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Makayla has 22 more mini mystery books than her sister Brittany. Makayla has 40 mini mystery books. How many mini mystery books does Brittany have? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ mini mystery books 38 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 4a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Bigger Unknown: Fewer, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Luke has 5 fewer books than Josh. Luke has 7 books. How many books does Josh have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 2 books • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., *  5 = 7; 5 + 7 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 39 OA Task 4a Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Compare Bigger Unknown: Fewer, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Luke has 5 fewer books than Josh. Luke has 7 books. How many books does Josh have? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ books 40 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 4b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Bigger Unknown: Fewer, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: The 2nd grade class has 9 fewer students than the 3rd grade class. The 2nd grade class has 22 students. How many students are in the 3rd grade class? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 31 students • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 9 + 22 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 41 OA Task 4b Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Compare Bigger Unknown: Fewer, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE The 2nd grade class has 9 fewer students than the 3rd grade class. The 2nd grade class has 22 students. How many students are in the 3rd grade class? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ students 42 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 4c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Bigger Unknown: Fewer, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: There are 36 fewer apples in the box than apples on the ground. There are 50 apples in the box. How many apples are on the ground? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 86 apples • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 36 + 50 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 43 OA Task 4c Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Compare Bigger Unknown: Fewer, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE There are 36 fewer apples in the box than apples on the ground. There are 50 apples in the box. How many apples are on the ground? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ apples 44 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 4d Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Compare Bigger Unknown: Fewer, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: There are 11 fewer cinnamon candies than chocolate candies. There are 30 cinnamon candies. How many chocolate candies are there? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 41 chocolate candies • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 30 + 11 = *; 11 = *  30) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 45 OA Task 4d Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Compare Bigger Unknown: Fewer, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE There are 11 fewer cinnamon candies than chocolate candies. There are 30 cinnamon candies. How many chocolate candies are there? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ chocolate candies 46 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 5a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToResult Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: John collected 67 baseball cards. His friend gave him 28 more baseball cards. How many cards does John have now? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 95 baseball cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 67 + 28 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 47 OA Task 5a Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add ToResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE John collected 67 baseball cards. His friend gave him 28 more baseball cards. How many cards does John have now? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ baseball cards 48 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 5b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add ToResult Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Val has 26 butterflies for the Science Fair. Sam brought 38 more butterflies for the Science Fair. How many butterflies did they take to the science fair? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 64 butterflies • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 26 + 38 = *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 49 OA Task 5b Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add ToResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Val has 26 butterflies for the Science Fair. Sam brought 38 more butterflies for the Science Fair. How many butterflies did they take to the science fair? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ butterflies 50 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 5c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add To Result Unknown, Twostep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Ana brought 6 DVDs to a party. Mark brought 7 DVDs to the party. Steve brought 8 DVDs to the party. How many DVDs do they have for the party? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 21 DVDs • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 6 + 7 + 8 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 51 OA Task 5c Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add ToResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Ana brought 6 DVDs to a party. Mark brought 7 DVDs to the party. Steve brought 8 DVDs to the party. How many DVDs do they have for the party? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ DVDs 52 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 5d Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add To Result Unknown, Twostep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Benjamin has 7 baseball cards. Kyle gave Benjamin 8 baseball cards. Jim gave Benjamin 3 more baseball cards. How many cards does Benjamin have now? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 18 baseball cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 7 + 8 + 3 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 53 OA Task 5d Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add ToResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Benjamin has 7 baseball cards. Kyle gave Benjamin 8 baseball cards. Jim gave Benjamin 3 more baseball cards. How many cards does Benjamin have now? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ cards 54 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 6a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add To: Change Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Lucas had 67 baseball cards. His friend gave Lucas some more baseball cards. Now Lucas has 95 baseball cards. How many baseball cards did his friend give Lucas? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 28 baseball cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 67 + * = 95) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 55 OA Task 6a Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add To: Change Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Lucas had 67 baseball cards. His friend gave Lucas some more baseball cards. Now Lucas has 95 baseball cards. How many baseball cards did his friend give Lucas? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ baseball cards 56 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 6b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Add To: Change Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Jalen had 30 marbles. When he cleaned out his closet he found some more marbles. Now Jalen has 58 marbles. How many marbles did Jalen find? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 28 marbles • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 30 + * = 58; 58 – 30 = *) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 57 OA Task 6b Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add To: Change Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Jalen had 30 marbles. When he cleaned out his closet he found some more marbles. Now Jalen has 58 marbles. How many marbles did Jalen find? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ marbles 58 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 6c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Add To: Change Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Pam has 17 cards of animals from Africa. She has some cards from other continents. All together she has 90 cards. How many cards are from other continents? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 73 cards • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., * = 90 – 17; 90 = * + 17) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 59 OA Task 6c Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Add To: Change Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Pam has 17 cards of animals from Africa. She has some cards from other continents. All together she has 90 cards. How many cards are from other continents? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ cards 60 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 7a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve oneand twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromResult Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: 60 apples were on the shelf. 23 apples were sold. How many apples are on the shelf now? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Basic Facts Creates easier or known sums Doubles Other: Complete Understanding • Correctly solves the problem: 37 apples • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 60 – 23 = *; 23 + * = 60) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 61 OA Task 7a Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Take FromResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE 60 apples were on the shelf. 23 apples were sold. How many apples are on the shelf now? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ apples 62 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 7b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve one and twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Take From Result Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Mrs. Hope’s class saw 76 butterflies in the garden. Some of the butterflies flew away. Now there are 49 butterflies in the garden. How many butterflies flew away? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 27 butterflies • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 76 – 49 = *; 76 = 49 + *). • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 63 OA Task 7b Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Take FromResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Mrs. Hope’s class saw 76 butterflies in the garden. Some of the butterflies flew away. Now there are 49 butterflies in the garden. How many butterflies flew away? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ butterflies 64 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 7c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve oneand twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Take FromResult Unknown, Twostep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: Avi drew 5 pictures to enter in the school art contest. Erick drew 7 pictures. Avi spilled water on 2 of his pictures and ruined them. How many pictures will Avi and Erick enter in the contest? Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 10 pictures • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 65 OA Task 7c Name ____________________________________ 2.OA.1 , 2.NBT.5, 2.NBT.9 Take FromResult Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE Avi drew 5 pictures to enter in the school art contest. Erick drew 7 pictures. Avi spilled water on 2 of his pictures and ruined them. How many pictures will Avi and Erick enter in the contest? Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ pictures 66 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 8a Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve oneand twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Take From Change Unknown, Onestep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: The principal had 38 balloons. Some balloons popped. Then the principal had 19 balloons. How many balloons popped? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Equation is inaccurate. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 19 balloons • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Equation is accurate (e.g., 38  * = 19; 19 + * = 38) • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 67 OA Task 8a Name ____________________________________ 2.OA.1 1.NBT.5, 1.NBT.9 Take From Change Unknown, Onestep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE The principal had 38 balloons. Some balloons popped. Then the principal had 19 balloons. How many balloons popped? Write an equation that represents this problem. Use a symbol for the unknown number. Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ balloons 68 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 8b Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve oneand twostep 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.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.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Take From Change Unknown, Twostep Materials SF, Pencil, Paper, counters and base ten materials available Task Provide materials to the student. Read the problem to the student: 12 children were on the baseball field. Some children left the baseball field to play on the swings. Then 2 more children came to the baseball field. Now there are 8 children on the baseball field. How many children left to play on the swings? Solve the problem and use words, numbers or pictures to explain your reasoning. Continuum of Understanding Developing Understanding • Incorrectly solves the problem. • Relies on counting as primary strategy for solving problem. • Explanation is lacking in detail or nonexistent. Strategy(ies) Used: Counting All Counting On Makes Tens Basic Facts Creates easier or known sums Doubles Doubles +/ 1, 2 Other: Complete Understanding • Correctly solves the problem: 6 children left the baseball field • Successfully uses strategies such as making tens, creates easier or known sums, and basic facts. • Explanation is clear. Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning. 69 OA Task 8b Name ____________________________________ 2.OA.1 1.NBT.5, 1.NBT.9 Take From Change Unknown, Twostep Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE 12 children were on the baseball field. Some children left the baseball field to play on the swings. Then 2 more children came to the baseball field. Now there are 8 children on the baseball field. How many children left to play on the swings? Solve the problem. Use words, numbers or pictures to explain your reasoning. __________________ children 70 Formative Instructional and Assessment Tasks NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE OA Task 8c Domain Operations and Algebraic Thinking Number and Operations in Base Ten Cluster Represent and solve problems involving addition & subtraction. Use place value understanding and properties of operations to add and subtract. Standard(s) 2.OA.1 Use addition and subtraction within 100 to solve oneand twostep 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.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between ad 
OCLC number  857589738 