Common Core State Standards Math Workgroup Training

1. Includes information from OSPI, ESDs, NCTM, Ohio Department of Education and other sources Math Common Core State Standards Dr. Marci Shepard Orting School District CCSS Math Workgroup April 2012 Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

2. Did you miss previous sessions? http://www.orting.wednet.edu/education/components/layout/default.php?sectionid=374& Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

3. Office of Superintendent of Public Instruction Randy I. Dorn , State Superintendent Common Core State Standards The Big Ideas in MATH

4. Focusing on the Foundation… Washington’s Implementation Timeline & Activities 2010-11 2011-12 2012-13 2013-14 2014-15 Phase 1: CCSS Exploration Phase 2: Build Awareness & Begin Building Statewide Capacity Phase 3: Build Statewide Capacity and Classroom Transitions Phase 4: Statewide Application and Assessment Ongoing: Statewide Coordination and Collaboration to Support Implementation CCSS Webinar Series Part 2: Mathematics 4 January 2012

5. http://www.youtube.com/watch?v=dnjbwJdcPjE&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=5&feature=plcp Orting School District * Teaching, Learning and Assessment * 2012

6. Content Progressions and Major Shifts January 2012 CCSS Webinar Series Part 2: Mathematics 6 Major Shifts Focus Fewer big ideas --- learn more Learning of concepts is emphasized Coherence Articulated progressions of topics and performances that are developmental and connected to other progressions Application Being able to apply concepts and skills to new situations

7. Structural Comparison: WA Standards vs. CCSS Mathematics WA Mathematics Standards Common Core State Standards Presentation of Standards Grade K-8, high school standards presented in traditional and integrated pathways. Grades K-8, high school standards presented through six mathematical domains including specially noted STEM standards - denoted by (+) symbols . Organization Grade-level standards are broken into core content areas, additional key content, and mathematical processes. Grade-level standards are broken into clusters of learning under several domains and all have Standards for Mathematical Practice. Examples Standards are accompanied by explanatory comments and examples. Standards have occasional examples in italics. Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 Transition for Algebra I | Transition for Geometry | Integrated Math I | Integrated Math II

8. Reading Literacy Standards Grades 6-8 Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

9. What does literacy look like in the mathematics classroom? Learning to read mathematical text Communicating using correct mathematical terminology Reading, discussing and applying the mathematics found in literature Researching mathematics topics or related problems Reading appropriate text providing explanations for mathematical concepts, reasoning or procedures Applying readings as citing for mathematical reasoning Listening and critiquing peer explanations Justifying orally and in writing mathematical reasoning Representing and interpreting data Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

10. Organization of the Standards Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

11. CCSS Design and Organization Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

12. Format of K-8 Standards Grade Level Domain Standard Cluster Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

13. Grade Level Introduction Critical Area of Focus Cross-cutting themes Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

14. Grade Level Overview Grade 4 Overview Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. Gain familiarity with factors and multiples. Generate and analyze patterns. Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations—Fractions Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal fractions. Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Represent and interpret data. Geometric measurement: understand concepts of angle and measure angles. Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Mathematical Practices Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

15. CCSS for High School Mathematics Organized in “Conceptual Categories” Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability Conceptual categories are not courses Additional mathematics for advanced courses indicated by (+) Standards with connections to modeling indicated by ( ★ ) Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

16. Format of High School Standards Domain Cluster Standard Advanced Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

17. Format of Standards Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

18. Conceptual Category Introduction Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

19. Conceptual Category Overview Domain Cluster Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

20. High School Mathematical Pathways Two main pathways: Traditional: Two algebra courses and a geometry course, with statistics and probability in each Integrated: Three courses, each of which includes algebra, geometry, statistics, and probability Both pathways: Complete the Common Core in the third year Include the same “critical areas” Require rethinking high school mathematics Prepare students for a menu of fourth-year courses Typical in U.S. Typical outside U.S. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

21. Two Main Pathways Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

22. Pathway Overview Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

23. Course Overview: Critical Areas (units) Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

24. Course Detail by Unit (critical area) Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

25. Questions 1-4 Understanding the Math Common Core State Standards Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

26. Content Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

27. Grade Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K–2 Addition and subtraction, measurement using whole number quantities 3–5 Multiplication and division of whole numbers and fractions 6 Ratios and proportional reasoning; early expressions and equations 7 Ratios and proportional reasoning; arithmetic of rational numbers 8 Linear algebra Critical Areas in Mathematics Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

28. Activity 2: K-8 Critical Areas of Focus HS Critical Areas Read a K-8 grade level’s Critical Areas of Focus or HS Critical Area What are the concepts? What are the skills and procedures? What relationships are students to make? Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

29. Concepts, Skills and Procedures Concepts B ig ideas U nderstandings or meanings S trategies R elationships Understanding concepts underlies the development and usage of skills and procedures and leads to connections and transfer. Skills and Procedures Rules Routines A lgorithms Skills and procedures evolve from the understanding and usage of concepts. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

30. Concepts , Skills and Procedures Grade 4 Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right . For example, recognize that 700  70 = 10 by applying concepts of place value and division. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

31. Activity 2 Critical Areas Read the grade level Critical Areas of Focus or HS Critical Areas What are the concepts? What are the procedures and skills? What relationships are students to make? Look at the domains, clusters and standards for the same grade(s) or High School Course How do the Critical Areas inform their instruction? Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

32. Critical Areas of Focus Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

33. Digging into the Standards…. Focusing on the Domain Read using a highlighter to identify language someone might have difficulty with Develop parent friendly language and/or examples for 2 nd column of template Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

34. Question 5 Understanding the Math Common Core State Standards Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

35. Progressions Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

36. Progressions Progressions Describe a sequence of increasing sophistication in understanding and skill within an area of study Three types of progressions Learning progressions Standards progressions Task progressions Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

37. Learning Progression for Single-Digit Addition From Adding It Up: Helping Children Learn Mathematics , NRC, 2001. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

38. Learning Progressions Document for CCSSM http://ime.math.arizona.edu/progressions/ Narratives Typical learning progression of a topic Children's cognitive development The logical structure of mathematics Math Common Core Writing Team with Bill McCallum as Creator/Lead Author Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

39. Standards Progressions Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

40. CCSS Domain Progression K 1 2 3 4 5 6 7 8 HS Counting & Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number & Quantity Number and Operations – Fractions The Number System Operations and Algebraic Thinking Expressions and Equations Algebra Functions Functions Geometry Geometry Measurement and Data Statistics and Probability Statistics & Probability Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

41. Standards Progression: Number and Operations in Base Ten Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

42. Use Place Value Understanding Grade 1 Grade 2 Grade 3 Use place value understanding and properties of operations to add and subtract. 4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 6. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding and properties of operations to add and subtract. 5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 6. Add up to four two-digit numbers using strategies based on place value and properties of operations. 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 three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. 9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Use place value understanding and properties of operations to perform multi-digit arithmetic. 1. Use place value understanding to round whole numbers to the nearest 10 or 100. 2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

43. High School Pathways The CCSSM Model Pathways Two models that organize the CCSSM into coherent, rigorous courses NOT required. The two sequences are examples, not mandates Pathway A: Consists of two algebra courses and a geometry course, with some data, probability and statistics infused throughout each (traditional) Pathway B: Typically seen internationally that consists of a sequence of 3 courses each of which treats aspects of algebra, geometry and data, probability, and statistics. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

44. Flows Leading to Algebra Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

45. Task Progression (later in presentation) Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

46. QuestionS 6-14 Understanding the Math Common Core State Standards Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

47. Practices Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

48. 8 CCSSM Mathematical Practices Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning Standards for Mathematical Practice Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

49. Standards for Mathematical Practices Graphic Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

50. Standards for Mathematical Practices Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

51. Take a moment to examine the first three words of each of the 8 mathematical practices … what do you notice? Mathematically Proficient Students… Standards for Mathematical Practices Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

52. Consider the verbs that illustrate the student actions each practice. For example, examine Practice #3: Construct viable arguments and critique the reasoning of others . Highlight the verbs. Discuss with a partner : What jumps out at you? Standards for Mathematical Practices Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

53. Mathematical Practice #3: Construct viable arguments and critique the reasoning of others Mathematically proficient students understand and use stated assumptions , definitions , and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions , communicate them to others, and respond to the arguments of others . They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments , distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings , diagrams , and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense , and ask useful questions to clarify or improve the arguments. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

54. Mathematical Practice #3: Construct viable arguments and critique the reasoning of others Mathematically proficient students: • understand and use stated assumptions, definitions, and previously established results in constructing arguments. • make conjectures and build a logical progression of statements to explore the truth of their conjectures. • analyze situations by breaking them into cases, and can recognize and use counterexamples. • justify their conclusions, communicate them to others, and respond to the arguments of others. • reason inductively about data, making plausible arguments that take into account the context from which the data arose. • compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. • construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. • determine domains to which an argument applies. • listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

55. Mathematical Practice #3: Construct viable arguments and critique the reasoning of others Mathematically proficient students: • understand and use stated assumptions, definitions, and previously established results in constructing arguments. • make conjectures and build a logical progression of statements to explore the truth of their conjectures. • analyze situations by breaking them into cases, and can recognize and use counterexamples. • justify their conclusions, communicate them to others, and respond to the arguments of others. • reason inductively about data, making plausible arguments that take into account the context from which the data arose. • compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument- explain what it is. • construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. • determine domains to which an argument applies. • listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

56. Observations What do you notice? What will students be doing differently? What will teachers be doing differently? Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

57. The Standards for [Student] Mathematical Practice On a scale of 1 (low) to 6 (high), to what extent is your school/our district promoting students ’ proficiency in Practice 3? Evidence for your rating? Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

58. The Standards for [Student] Mathematical Practice SMP1: Explain and make conjectures… SMP2: Make sense of… SMP3: Understand and use… SMP4: Apply and interpret… SMP5: Consider and detect… SMP6: Communicate precisely to others… SMP7: Discern and recognize… SMP8: Notice and pay attention to… Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

59. Standards for Mathematical Practice …describe the thinking processes, habits of mind and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics; in this sense they are also a means to an end SP1. Make sense of problems “….they [students] analyze givens, constraints , relationships and goals. ….they monitor and evaluate their progress and change course if necessary. …. and they continually ask themselves “Does this make sense ?” Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

60. Standards for Mathematical Practice AND…. describe mathematical content students need to learn SP1. Make sense of problems “……. students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.” Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

61. Buttons Task Gita plays with her grandmother’s collection of black & white buttons. She arranges them in patterns. Her first 3 patterns are shown below. Pattern #1 Pattern #2 Pattern #3 Pattern #4 1. Draw pattern 4 next to pattern 3. 2. How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how you figured this out. 3. How many buttons in all does Gita need to make Pattern 11? Explain how you figured this out. 4. Gita thinks she needs 69 buttons in all to make Pattern 24. How do you know that she is not correct? How many buttons does she need to make Pattern 24? Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

62. Buttons Task 1. Individually complete parts 1 - 3. 2. Then work with a partner to compare your work and complete part 4. (Look for as many ways to solve parts 3 and 4 as possible.) Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

63. Buttons Task Gita plays with her grandmother’s collection of black & white buttons. She arranges them in patterns. Her first 3 patterns are shown below. Pattern #1 Pattern #2 Pattern #3 Pattern #4 1. Draw pattern 4 next to pattern 3. 2. How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how you figured this out. 3. How many buttons in all does Gita need to make Pattern 11? Explain how you figured this out. 4. Gita thinks she needs 69 buttons in all to make Pattern 24. How do you know that she is not correct? How many buttons does she need to make Pattern 24? 15 buttons and 18 buttons 34 buttons 73 buttons Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

64. Buttons Task Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

65. Buttons Task Which mathematical practices are needed complete the task? Indicate the primary practice. 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. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

66. Standards for [ Student ] Mathematical Practice “Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking .” Stein, Smith, Henningsen , & Silver, 2000 “ The level and kind of thinking in which students engage determines what they will learn .” Hiebert , Carpenter, Fennema , Fuson , Wearne, Murray, Oliver, & Human, 1997 Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

67. The Nature of Tasks Used in the Classroom … …Will Impact Student Learning! Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

68. But, WHAT TEACHERS DO with the tasks matters too! The Mathematical Tasks Framework Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000) Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

69. http :// www.insidemathematics.org/index.php/classroom-videovisits/public-lessons-numerical-patterning/218-numerical-patterninglesson-planning?phpMyAdmin=NqJS1x3gaJqDM-1-LXtX3WJ4e8 Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

70. Learner A Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

71. Learner B Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

72. Buttons Task Revisited What might a teacher get out of using the same math task two days in a row, rather than switching to a different task(s )? – Address common misconceptions – Support students in moving from less to more sophisticated solutions Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

73. Buttons Task Revisited Which of the Standards of Mathematical Practice did the students engage in when they revisited the task ? Indicate the primary practice. 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. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

74. But, WHAT TEACHERS DO with the tasks matters too! The Mathematical Tasks Framework Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000) Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

75. The 8 Standards for Mathematical Practice – place an emphasis on student demonstrations of learning… Equity begins with an understanding of how the selection of tasks, the assessment of tasks, the student learning environment creates great inequity in our schools… Standards for [ Student ] Mathematical Practice Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

76. To what extent do all students in your class, school or our district have the opportunity to engage in tasks that promote attainment of the mathematical practices on a regular basis? Please rate on a scale of 1 (low) to 6 (high). Standards for [ Student ] Mathematical Practice Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

77. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

78. Content and Practices Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

79. Cognitive Complexity Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

80. Depth of Knowledge Levels Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

81. Sorting Activity Categorize tasks into level 1, 2, 3, or 4 using Cognitive Complexity Levels. Record your responses on the provided worksheet. Share results and come to consensus at your table. One person will record results on the “master” copy. Share results and review criteria groups used for low and high levels. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

82. Sorting questions to ponder… How did you determine between levels 2 & 3? Does a task presented as a word problem always have a high level of cognitive complexity? If a task requires an explanation, does it have a high level of cognitive complexity? Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

83. Changing the Cognitive Complexity Level Pick out a task that was placed in level 1 or 2. Determine how you would modify your task to be a level 3 task. Share task out with whole group. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

84. Cognitive Complexity and Mathematical Practices Which levels of cognitive complexity allow students to develop the mathematical practices? Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

85. Task Progression A rich mathematical task can be reframed or resized to serve different mathematical goals Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

86. Are there various levels of Cognitive Complexity in your instructional materials? Review several types of problems/tasks found in your instructional materials. What level of cognitive complexity are these tasks? Level 1 (recall) Level 2 (skill/concept) Level 3 (strategic thinking) Level 4 (extended thinking) Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

87. Are there various levels of Cognitive Complexity in your instructional materials? Share the types of problems/tasks you found. What are the prevalent levels of complexity in your instructional materials? How will this impact meeting the standards for mathematical practice? Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

88. Gas Mileage Problem With scaffolding Without scaffolding Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

89. Who’s Doing the Work? TEDtalk : Dan Meyer Video http://www.youtube.com/watch?v=BlvKWEvKSi8 Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

90. Video Debrief How much is too much support; how much is too little? How does scaffolding interfere/promote standards for mathematical practice? Compare/contrast Gas Mileage activities Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

91. Appendix A Questions 15-22 Understanding the Math Common Core State Standards Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

92. Tables Understanding the Math Common Core State Standards Question 23 Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

93. Transition Plans Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

94. Three-Year Transition Plan for Common Core State Standards for Mathematics by Grade Level Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

95. Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

96. State Resources for Transition Grade-level transition documents describe: What standards to continue What standards to remove What standards to move to Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

97. OSD Resources Math Common Core State Standards Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

98. OSD Teaching, Learning and Assessment Website: Common Core State Standards: http://www.orting.wednet.edu/education/components/scrapbook/default.php?sectiondetailid=3910& Common Core State Standards for Math: http://www.k12.wa.us/CoreStandards/Mathematics/pubdocs/CCSSI_MathStandards.pdf Designing High School Mathematics Courses (Appendix A): http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf Illustrative Math: http://illustrativemathematics.org/ Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

99. Mathematical Practices by Grade Level: http://www.azed.gov/standards-practices/files/2011/10/2010mathglossary.pdf 3-Year Transition Plan: http://www.k12.wa.us/CoreStandards/pubdocs/Three-YearDomainImplementation.pdf Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

100. Transition Plans by Grade Level: Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 Transition for Algebra I | Transition for Geometry | Integrated Math I | Integrated Math II Progressions Documents: http://ime.math.arizona.edu/progressions/ Videos on CCSS-M: http://www.youtube.com/playlist?list=PLD7F4C7DE7CB3D2E6&feature=plcp Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012

101. It is time to recognize that standards are not just promises to our children, but promises we intend to keep.” 1 Students need to meet the standards, and in order to do that, what they must learn is not standards but mathematics. 2 1 CCSS, 2010, p. 5 2 PARCC – Draft Content Framework - 2011 Dr. Marci Shepard  Orting School District  Teaching, Learning & Assessment  2012