1. Alum Rock Union Elementary School District CCSS-Mathematics Grade 5 March 2014

2. WELCOME AND INTRODUCTION

3. Outcomes Understand the background, rationale and organization of the Common Core State Standards-Mathematics (CCSS-M). Increase understanding of number talks and how they can be implemented in the third grade classroom. Identify how the new mathematics assessment will measure student understanding

4. Outcomes (continued) Become familiar with the CCSS-M instructional shifts

5. Agenda Welcome and Introduction CCSS Overview CCSS Standards for Mathematical Practice CCSS Mathematics Content Standards Assessment Instructional Shifts in Mathematics Mathematics Discourse Closing and Feedback

6. Norms “No one is as smart as all of us are together.” Respect Individual think time Everyone participates Everyone helps Leave no one behind Take responsibility Be positive Technology courtesy (cell phones and computers)

7. CCSS-M OVERVIEW Overview and Structure of the CCSS Mathematics Content Standards

8. States that have Adopted the Common Core State Standards http://www.corestandards.org/in-the-states

9. Why the Common Core State Standards? Ensure that our students are:  Meeting college and work expectations;  Provided a vision of what it means to be an academically literate person in the twenty-first century;  Prepared to succeed in our global economy and society; and  Provided with rigorous content and applications of higher knowledge through higher order thinking skills.

10. Benefits of the CCSS  Internationally benchmarked  Evidence and research-based  Expectations clear to students, parents, teachers, and the general public  Costs to the state reduced  Consistent expectations for all— not dependent on a zip code

11. Common Core State Standards San Jose Common Core Tech

12. STANDARDS FOR MATHEMATICAL PRACTICE Common Core State Standards

13. Underlying Frameworks National Council of Teachers of Mathematics 5 Process Standards Problem Solving Reasoning and Proof Communication Connections Representations NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

14. Strands of Mathematical Proficiency Strategic Competence Adaptive Reasoning Conceptual Understanding Productive Disposition NRC (2001). Adding It Up. Washington, D.C.: National Academies Press. Procedural Fluency Underlying Frameworks

15. Standards for 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.

16. CCSS Standards for Mathematical Practice Please examine the first three words of each of the 8 mathematical practices…what do you notice? Mathematically Proficient Students…

17. CCSS Standards for [Student] Mathematical Practice What are the verbs that illustrate the student actions for your assigned mathematical practice? Circle, highlight or underline them for your assigned practice. Please select a spokesperson.

18. Notetaking Guide Standards for Mathematical Practice

19. 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…

20. Rigor of the Standards Revised Bloom’s Taxonomy

21. CCSS Mathematical Practices OVERARCHING HABITS OF MIND 1. Make sense of problems and persevere in solving them 6. Attend to precision REASONING AND EXPLAINING 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

22. Standards for Mathematical Practice  Each group will be assigned to read one of the Standards for Mathematical Practice.  What will your classroom look like/sound like as this standards is being implemented  Use your note taking guide to capture shared ideas. Jigsaw

23. Website: Inside Mathematics For classroom videos of the CCSS Standards for Mathematical Practice in action.

24. CCSS-M CONTENT STANDARDS

25. Common Core State Standards for CA DOMAINS California Standards Grades K-7 STRANDS K-5 Counting and Cardinality (K only) Operations and Algebraic Thinking Number and Operations in Base 10 Number and Operations-Fractions Measurement and Data Geometry 6-8 Ratio and Proportional Relationships (grade 6-7) The Number System Expressions and Equations Functions (Grade 8) Geometry Statistics and probability Number Sense Algebra and Functions Measurement and Geometry Statistics, Data Analysis and Probability Mathematical Reasoning California Comparison 25

26. CCSS Domains and Conceptual Categories K12345678HS 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 EquationsAlgebra Functions Geometry Measurement and DataStatistics and Probability Statistics & Probability Findwell, Bradford & Foughty, Zachary. “”Preparing to Implement the Common Core State Standards for Mathematics. Indiana Department of Education and Ohio Department of Education. March 30, 2011

28. Overview Page- Fifth Grade

29. Content Standards 29

30. Reviewing CCSS-M Structure Domain Cluster Heading Cluster Standards Mark and label your standards. CCSS First Grade Overview

31. ASSESSMENT

32. Assessment: What We Know Assessments will be given to students as a field test in 2013-2014 Students will receive scores in 2014-15. California is a governing state in the SMARTER Balanced Assessment Consortium. Assessments will include: – Computer Adaptive Assessments (interim & summative) – Selected Response – Performance Assessments (interim & summative) Technology Enhanced Constructed Response Performance Task Extended Performance Event

33. SBAC’s Four Major Claims #1 Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. #2 Students can frame and solve a range of complex problems in pure and applied mathematics #3 Students can clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others. #4 Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

34. Smarter Balanced: New Website http://www.smarterbalanced.org/

35. Traditional Selected Response CST Example A company has 6 big trucks. Each truck has 18 wheels. How many wheels is this in all? A 24 B 96 C 108 D 116 2009 California Standards Test Released Test Question pg. 14, #34

36. Non-Traditional Selected Response

37. Non-Traditional Selected Response Rubric

38. Performance Task

39. Performance Task Rubric

40. The main point in mathematics teaching is to develop the tactics of problem solving. George Polya

41. CCSS-M Assessments (Claim 4) View the Tasks. What skills will students need in order to complete the task?

42. INSTRUCTIONAL SHIFTS IN MATHEMATICS Common Core State Standards

43. Focus Shift 1: Focus Coherence Shift 2: Coherence Rigor Shift 3: Fluency Shift 4: Deep Understanding Shift 5: Application Shift 6: Dual Intensity Instructional Shifts Combined

44. Shift #1: Focus Strongly where the Standards Focus Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom. Focus deeply on what is emphasized in the standards, so that students gain strong foundations.

45. Grade Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K–2 Addition and subtraction - concepts, skills, and problem solving and place value 3–5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving 6 Ratios and proportional reasoning; early expressions and equations 7 Ratios and proportional reasoning; arithmetic of rational numbers 8 Linear algebra; linear functions Key Areas of Focus in Mathematics

47. Focus Using a highlighter, please highlight the standards that are in direct alignment with your grade level’s focus.

48. Shift #2: Coherence: Think Across Grades, and Link to Major Topics Within Grades Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years. Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

49. Coherence: Think Across Grades K12345678HS 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 EquationsAlgebra Functions Geometry Measurement and DataStatistics and Probability Statistics & Probability Findwell, Bradford & Foughty, Zachary. “”Preparing to Implement the Common Core State Standards for Mathematics. Indiana Department of Education and Ohio Department of Education. March 30, 2011

50. The CCSSM require a balance of:  Procedural skill and fluency  Solid conceptual/deep understanding  Application of skills in problem solving situations Pursuit of all three requires equal intensity in time, activities, and resources. Rigor

51. Fluency (Shift 3) The standards require speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts Rigor

52. Required Fluencies in K-6 GradeStandardRequired Fluency KK.OA.5Add/subtract within 5 11.OA.6Add/subtract within 10 2 2.OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100 3 3.OA.7 3.NBT.2 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within 1000 44.NBT.4Add/subtract within 1,000,000 55.NBT.5Multi-digit multiplication 66.NS.2,3 Multi-digit division Multi-digit decimal operations

53. Fluency Please underline the standards that are in direct alignment with your grade level’s fluency standards.

54. Deep Understanding (Shift 4) Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives Students are able to see math as more than a set of mnemonics or discrete procedures Conceptual understanding supports the other aspects of rigor (fluency and application) Rigor

55. 55

56. Application (Shift 5) Students can use appropriate concepts and procedures for application even when not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS. Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content. Rigor

57. Shift 6: Dual Intensity Students are practicing and understanding. – Both occur with intensity – Fluency Practice – Extended application of math concepts – Driven by specific mathematical content; varies throughout the year. Rigor

58. It Starts With Focus The current U.S. curriculum is "a mile wide and an inch deep." Focus is necessary in order to achieve the rigor set forth in the standards. Remember Hong Kong example: more in-depth mastery of a smaller set of things pays off.

59. MATHEMATICS DISCOURSE

60. Norms “No one is as smart as all of us are together.” Respect Individual think time Everyone participates Everyone helps Leave no one behind Be positive

61. Hand Signals Solution Strategy I agree

62. Hand Signals Agree Solution Strategy

63. Number Talks and Time Number Talks (about 10 minutes) Mini-lesson(10 to 20 minutes) Lesson (more than 20 minutes)

64. Socio-mathematical Norms Errors are gifts, they promote discussion. Share a second sentence to connect your thoughts. The answer is important, but it is not the math. Build on the thinking of others. Ask questions until ideas make sense. Think with language and use language to think.

65. Math Talk Examples Mental Math Number Strings Dilemmas True/False Statements What’s My Rule?

66. Mental Math 32 x 15

67. Number Talk Classroom Example Fifth grade students solving the same problem.

68. Number String (Mental Math) ½ + 1 1 ½ + ½ 2 + ½ 2 ½ + ½

69. True/False 24 x 11=24 x 10 +24 True or False? Why?

70. True/False 2/5 + 2/3=4/8 True or False? Why?

71. Dilemma Explain the mathematical reasoning that both Kirsten & David used to solve for the unknown above. Kirsten says that 2/3 + 5/4 = 9/7 Davis says that 2/3 + 5/4=33/20

72. What’s My Rule? InOut 15321532 37543754

73. What’s My Rule? InputOutput 15321532 37543754

74. What’s My Rule? XY 15321532 37543754

75. Standards for Mathematical Practice 1. Make sense of problems & persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments & 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.

76. Number Talks Online Resources http://goo.gl/ylgKi for K-2 Resources http://goo.gl/ylgKi http://goo.gl/F58uB for 3-5 Resources http://goo.gl/F58uB

77. CLOSING

78. Closing Please complete the evaluation and reflection form. Contact information: Kirsten_sarginger@sccoe.org