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- 1. Math Common Core State Standards Dr. Marci Shepard Orting School District CCSS Math Workgroup April 2012Includes information from OSPI, ESDs, NCTM, Ohio Department of Education and other sources 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. Common Core State Standards The Big Ideas in MATH Office of Superintendent of Public Instruction Randy I. Dorn, State Superintendent
- 4. Focusing on the Foundation… Washington’s Implementation Timeline & Activities 2010-11 2011-12 2012-13 2013-14 2014-15Phase 1: CCSS ExplorationPhase 2: Build Awareness & BeginBuilding Statewide CapacityPhase 3: Build Statewide Capacityand Classroom TransitionsPhase 4: Statewide Application andAssessmentOngoing: Statewide Coordinationand Collaboration to SupportImplementation January 2012 CCSS Webinar Series Part 2: Mathematics 4
- 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 ShiftsMajor ShiftsFocus Coherence Application• Fewer big ideas --- • Articulated progressions of topics • Being able to apply learn more and performances that are concepts and skills to• Learning of concepts developmental and connected to new situations is emphasized other progressions January 2012 CCSS Webinar Series Part 2: Mathematics 6
- 7. Structural Comparison: WA Standards vs. CCSS Mathematics WA Mathematics Standards Common Core State Standards Grades K-8, high school standards presented through six mathematical Presentation of Grade K-8, high school standards presented domains including specially noted Standards in traditional and integrated pathways. STEM standards - denoted by (+) symbols. Grade-level standards are broken into Grade-level standards are broken into core clusters of learning under several Organization content areas, additional key content, and domains and all have Standards for mathematical processes. Mathematical Practice. Standards are accompanied by explanatory Standards have occasional examples Examples comments and examples. in italics.Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 |Grade 8Transition 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. Cross-cuttingGrade Level Introduction themes Critical Area of Focus Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 14. Grade Level OverviewGrade 4 Overview Mathematical PracticesOperations and Algebraic Thinking 1. Make sense of problems and Use the four operations with whole numbers to solve problems. persevere in solving them Gain familiarity with factors and multiples. 2. Reason abstractly and Generate and analyze patterns. quantitativelyNumber and Operations in Base Ten 3. Construct viable arguments and Generalize place value understanding for multi-digit whole numbers. critique the reasoning of others Use place value understanding and properties of operations to perform multi-digit arithmetic. 4. Model with mathematicsNumber and Operations—Fractions 5. Use appropriate tools Extend understanding of fraction equivalence and ordering. strategically Build fractions from unit fractions by applying and extending previous 6. Attend to precision understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal 7. Look for and make use of fractions. structureMeasurement and Data 8. Look for and express regularity Solve problems involving measurement and conversion of in repeated reasoning 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. 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 StandardsDomainClusterStandardAdvanced Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 17. Format of StandardsDr. 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 OverviewDomainCluster Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 20. High School Mathematical Pathways Typical• Two main pathways: in U.S. – 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 Typical outside U.S.• 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 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 OverviewDr. 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. Understanding the Math Common Core State Standards QUESTIONS 1-4 Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 26. ContentDr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 27. Critical Areas in Mathematics Priorities in Support of Rich Instruction andGrade Expectations of Fluency and Conceptual Understanding Addition and subtraction, measurement usingK–2 whole number quantities Multiplication and division of whole numbers3–5 and fractions Ratios and proportional reasoning; early 6 expressions and equations Ratios and proportional reasoning; arithmetic 7 of rational numbers 8 Linear algebra 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 ProceduresConcepts• Big ideas• Understandings or meanings• Strategies• RelationshipsUnderstanding concepts underlies the development and usage of skills and procedures and leads to connections and transfer.Skills and Procedures• Rules• Routines• AlgorithmsSkills and procedures evolve from the understanding and usage of concepts. Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 30. Concepts, Skills and ProceduresGrade 4 Number and Operations in Base TenGeneralize 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 2nd column of template Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 34. Understanding the Math Common Core State Standards QUESTION 5 Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 35. Progressions Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 36. • 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 AdditionFrom Adding It Up: Helping Children Learn Mathematics, NRC, 2001. Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 38. Learning Progressions Document for CCSSMhttp://ime.math.arizona.edu/progressions/• Narratives• Typical learning progression of a topic• Childrens 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. Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 40. CCSS Domain Progression K 1 2 3 4 5 6 7 8 HSCounting &Cardinality Ratios and Proportional Number and Operations in Base Ten Relationships Number & Number and Operations – Quantity The Number System Fractions Expressions and Equations Algebra Operations and Algebraic Thinking Functions Functions Geometry Geometry Statistics & Measurement and Data Statistics and Probability 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 UnderstandingGrade 1 Grade 2 Grade 3Use place value understanding and Use place value understanding and Use place value understanding andproperties of operations to add and properties of operations to add and properties of operations to performsubtract. subtract. multi-digit arithmetic.4. Add within 100, including adding a 5. Fluently add and subtract within 100 1. Use place value understanding totwo-digit number and a one-digit using strategies based on place value, round whole numbers to the nearest 10number, and adding a two-digit number properties of operations, and/or the or 100.and a multiple of 10, using concrete relationship between addition and 2. Fluently add and subtract within 1000models or drawings and strategies based subtraction. using strategies and algorithms based onon place value, properties of operations, 6. Add up to four two-digit numbers place value, properties of operations,and/or the relationship between using strategies based on place value and/or the relationship betweenaddition and subtraction; relate the and properties of operations. addition and subtraction.strategy to a written method and explain 7. Add and subtract within 1000, using 3. Multiply one-digit whole numbers bythe reasoning used. concrete models or drawings and multiples of 10 in the range 10–90 (e.g.,Understand that in adding two-digit strategies based on place value, 9 × 80, 5 × 60) using strategies based onnumbers, one adds tens and tens, ones properties of operations, and/or the place value and properties ofand ones; and sometimes it is necessary relationship between addition and operations.to compose a ten. subtraction; relate the strategy to a5. Given a two-digit number, mentally written method. Understand that infind 10 more or 10 less than the number, adding or subtracting three digitwithout having to count; explain the numbers, one adds or subtractsreasoning used. hundreds and hundreds, tens and tens,6. Subtract multiples of 10 in the range ones and ones; and sometimes it is10-90 from multiples of 10 in the range necessary to compose or decompose10-90 (positive or zero differences), tens or hundreds.using concrete models or drawings and 8. Mentally add 10 or 100 to a givenstrategies based on place value, number 100–900, and mentally subtractproperties of operations, and/or the 10 or 100 from a given number 100–relationship between addition and 900.
- 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. (later in presentation)TASK PROGRESSION Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 46. Understanding the Math Common Core State Standards QUESTIONS 6-14 Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 47. PracticesDr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 48. 8 CCSSM Mathematical Practices Standards for Mathematical Practice – 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
- 49. Standards for Mathematical PracticesGraphic 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. Standards for Mathematical PracticesTake a moment to examine the first three wordsof each of the 8 mathematical practices… whatdo you notice? Mathematically Proficient Students… Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 52. Standards for Mathematical Practices• 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? Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 53. Mathematical Practice #3: Construct viablearguments and critique the reasoning of othersMathematically proficient students understand and use stated assumptions,definitions, and previously established results in constructing arguments. They makeconjectures and build a logical progression of statements to explore the truth of theirconjectures. They are able to analyze situations by breaking them into cases, and canrecognize and use counterexamples. They justify their conclusions, communicate themto others, and respond to the arguments of others. They reason inductively aboutdata, making plausible arguments that take into account the context from which thedata arose. Mathematically proficient students are also able to compare theeffectiveness of two plausible arguments, distinguish correct logic or reasoning fromthat 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 asobjects, drawings, diagrams, and actions. Such arguments can make sense and becorrect, even though they are not generalized or made formal until later grades. Laterstudents learn to determine domains to which an argument applies. Students at allgrades 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 viablearguments and critique the reasoning of othersMathematically proficient students:• understand and use stated assumptions, definitions, and previously established results inconstructing arguments.• make conjectures and build a logical progression of statements to explore the truth of theirconjectures.• 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 contextfrom which the data arose.• compare the effectiveness of two plausible arguments, distinguish correct logic or reasoningfrom 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 madeformal until later grades.• determine domains to which an argument applies.• listen or read the arguments of others, decide whether they make sense, and ask usefulquestions to clarify or improve the arguments. Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 55. Mathematical Practice #3: Construct viablearguments and critique the reasoning of othersMathematically proficient students:• understand and use stated assumptions, definitions, and previously established results inconstructing arguments.• make conjectures and build a logical progression of statements to explore the truth of theirconjectures.• 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 contextfrom which the data arose.• compare the effectiveness of two plausible arguments, distinguish correct logic or reasoningfrom 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 madeformal until later grades.• determine domains to which an argument applies.• listen or read the arguments of others, decide whether they make sense, and ask usefulquestions 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 districtpromoting 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 anddispositions that students need to develop adeep, flexible, and enduring understanding ofmathematics; in this sense they are also a means to anendSP1. Make sense of problems“….they [students] analyzegivens, constraints, relationships and goals. ….theymonitor and evaluatetheir progress and change course if necessary. …. andthey continually ask themselves “Does this make sense?” Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 60. Standards for Mathematical PracticeAND…. describe mathematical content students need to learnSP1. Make sense of problems“……. students can explain correspondences betweenequations, verbal descriptions, tables, and graphs ordraw diagrams of important features andrelationships, graph data, and search for regularity ortrends.” Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 61. Buttons TaskGita 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 #41. 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? Explainhow you figured this out.4. Gita thinks she needs 69 buttons in all to make Pattern 24. How doyou know that she is not correct? How many buttons does she need tomake Pattern 24? Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 62. Buttons Task1. Individually complete parts 1 - 3.2. Then work with a partner to compare yourwork and complete part 4. (Look for as manyways to solve parts 3 and 4 as possible.) Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 63. Buttons TaskGita 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 #41. Draw pattern 4 next to pattern 3. 15 buttons and 18 buttons2. How many white buttons does Gita need for Pattern 5 and Pattern 6?Explain how you figured this out. 34 buttons3. How many buttons in all does Gita need to make Pattern 11? Explainhow you figured this out. 73 buttons4. Gita thinks she needs 69 buttons in all to make Pattern 24. How doyou 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
- 64. Buttons Task Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 65. Buttons TaskWhich mathematical practices are needed completethe 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 differenttasks will provoke different levels and kindsof student thinking.”Stein, Smith, Henningsen, & Silver, 2000“The level and kind of thinking in whichstudents engage determines what theywill 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 FrameworkStein, 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 RevisitedWhat might a teacher get out of using the samemath task two days in a row, rather thanswitching 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 RevisitedWhich of the Standards of Mathematical Practice did thestudents 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 FrameworkStein, Grover & Henningsen (1996)Smith & Stein (1998)Stein, Smith, Henningsen & Silver (2000) Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 75. Standards for [Student] Mathematical PracticeThe 8 Standards for Mathematical Practice –place an emphasis on student demonstrationsof 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… Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 76. Standards for [Student] Mathematical Practice To what extent do all students in your class, school or our district have the opportunity to engage in tasks thatpromote attainment of the mathematical practices on a regular basis? Please rate on a scale of 1 (low) to 6 (high). 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 PracticesWhich levels of cognitive complexity allowstudents to develop the mathematicalpractices? 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 CognitiveComplexity 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 CognitiveComplexity 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 AUnderstanding the Math Common Core State Standards Questions 15-22 Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012
- 92. TablesUnderstanding 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 TransitionGrade-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 RESOURCESMATH 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.pdfDesigning 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.pdf3-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 IIProgressions 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. 1 CCSS, 2010, p. 5 Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 20122 PARCC – Draft Content Framework - 2011

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