1. North Carolina Department of Public Instruction Curriculum and Instruction Division “FOCUS” on CCSS-M Spring 2012 RESA K-5 Mathematics

2. Introductions 10/4/2015 page 2 Microsoft

3. Agenda Assessment Overview Professional Development Three Mathematical Shifts: Focus –Major Work of the Grade –Mile Wide and an Inch Deep Mathematical Task Navigating through Navigations

4. Norms Listen as an Ally Value Differences Maintain Professionalism Participate Actively 10/4/2015 10/4/2015 page 4

5. Parking Lot 10/4/2015 page 5 TechnologySession Materials Breaks cc: Microsoft.com

6. K-2 ASSESSMENT

7. K-2 State Assessment Requirements State Statute(115C-174.11): (a) Assessment Instruments for First and Second Grades. – The State Board of Education shall adopt and provide to the local school administrative units developmentally appropriate individualized assessment instruments consistent with the Basic Education Program for the first and second grades, rather than standardized tests. Local school administrative units may use these assessment instruments provided to them by the State Board for first and second grade students, and shall not use standardized tests except as required as a condition of receiving federal grants.

8. K-2 State Assessment Requirements The State Board of Education requires that schools and school districts implement assessments at grades K, 1, and 2 that include documented, on-going individualized assessments throughout the year and a summative evaluation at the end of the year. These assessments monitor achievement of benchmarks in the North Carolina Standard Course of Study. They may take the form of the state-developed materials, adaptations of them, or unique assessments adopted by the local school board.

9. K-2 State Board Requirements Intended purposes of these assessments: (1)to provide information about the progress of each student for instructional planning and early interventions; document growth over time (2)to inform parents about the status of their children relative to grade-level standards (3)to provide next-year teachers with information about the status of each of their incoming students (4)to provide the school and school district information about the achievement status and progress of groups of students in K, 1, and 2

10. K-2 Assessment 2012 K-2 Assessment Committee –Identify Assessment Critical Components. –Write K-2 Assessment Items. –Re-design the K-2 Observation Profile. –Create a “How To” resource for assessment implementation. Completion & Distribution: June 15* *Final date subject to change

11. K-2 Assessment On-Going Assessment –Bank of Items 1-3 items per cluster/standard –Mostly consists of Performance Tasks Summative Assessment –Focuses on the Critical Areas –Mostly consists of Performance Tasks –Is in similar format to current summative assessment –Distributed only to each LEA K-2 Math Administrator

14. 3-5 ASSESSMENT

15. YearStandards To Be TaughtStandards To Be Assessed 2011 – 20122003 NCSCOS 2012 – 2013CCSSCCSS (NC) 2013 – 2014CCSSCCSS (NC) 2014 – 2015CCSSCCSS (SBAC) Common Core State Standards Adopted June, 2010

16. Technology and Testing Content of the North Carolina assessments is aligned to the CCSS-M; however, the technology will not be as sophisticated as in assessments created by the Smarter Balanced Assessment Consortium (SBAC).

17. Let’s look at a familiar problem…

18. Which of the following represents ? a. b. c. d.

19. Same problem- a new twist…

20. For numbers 1a – 1d, state whether or not each figure has of its whole shaded. 1a. 1b. 1c. 1d. ο Yes ο No

21. Turn and Talk This item is worth 0 – 2 points (depending on the responses). –What series of Yes and No responses would a student earn 2 points? 1 point? 0 points?

22. For numbers 1a – 1d, state whether or not each figure has of its whole shaded. 1a. 1b. 1c. 1d. ο Yes ο No

23. 2 points: YNYN 1 point: YNNN, YYNN, YYYN 0 point: YYYY, YNNY, NNNN, NNYY, NYYN, NYNN NYYY, NYNY, NNYN, NNNY, YYNY, YNYY Or numbers 1a - 1d, state whether or not each figure has of its whole shaded.

24. Let’s Do Some Math!

25. Sample Open-Response Question In the barnyard is an assortment of chickens and pigs. Counting heads I get 13; counting legs I get 46. How many pigs and chickens are there ? - Bill McCallum, 2012

27. 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. Standards for Mathematical Practices

28. http://www.k12.wa.us/smarter/

29. Shifting Gears…. How did you become an effective teacher?

30. PHI DELTA KAPPA International Research Bulletin “ If we spend more money on traditional form of professional development, such as workshops, conferences, presentations, and courses remotely related to the daily challenges of teaching, we can expect little return on our investments.” http://www.pdkintl.org/research/rbulletins/resbul27.htm http://www.pdkintl.org/research/rbulletins/resbul27.htm

31. Key Points Professional development should involve teachers in the identification of what they need to learn and, when possible, in the development of the learning opportunity and/or process. Phi Delta Kappan, 2005

32. Professional development should be primarily school based and integral to the school operations. Key Points Phi Delta Kappan, 2005

33. Professional development should provide opportunities to engage in developing a theoretical understanding of the knowledge and skills to be learned. Phi Delta Kappan, 2005 Key Points

34. “Despite virtually unanimous criticism of most traditional forms of professional development, these ineffective practices persist.” Phi Delta Kappan, 2005

35. Horizon Research After a one year study on the traditional model of Professional Development, the study found… –Impact on teachers’ use of instructional practices to elicit student thinking

36. “But NO Impact on….” Teacher content knowledge Teachers’ use of representations in instruction Teachers’ focus on mathematics reasoning in instruction Student achievement Garet et al., 2010

37. What Works? Effective Teacher Development –Collaboration » PLCs –Coaching Steve Leinwand, 2012

38. Turn and Talk Take a moment to: –Reflect on the information about effective teacher development. –Share strategies for supporting teacher development.

39. 39

41. Three Mathematical Shifts Focus Coherence Rigor

42. Coleman & Zimba (2012) www.achievethecore.org

43. PLC for Today Norm –Keep a focus on the students Goal –Know and articulate the major work of your grade level or course.

45. A focus on “FOCUS” In your PLC: –Discuss the three topics provided for each grade level. –Decide which of the three should not receive intense focus at the indicated grade.

46. Table of Contents

47. Time to Reflect 10/4/2015 page 47

48. Major Work 48

51. In Your Grade Level Groups Identify clusters/standards as: –major work of the grade level –supporting work of the grade level –additional work of the grade level Major Work of the Grade –Greater emphasis; Intense focus: The depth of the ideas/learning The time that they take to master Their importance to future mathematics

54. First Grade Example 54

55. Let’s Get Started! Identify clusters/standards as: –major work of the grade level –supporting work of the grade level –additional work of the grade level Please sit with the grade level groups of 3-5 people. www.ncdpi.wikispaces.net

56. LUNCH

57. Let’s Get Started! Identify clusters/standards as: –major work of the grade level –supporting work of the grade level –additional work of the grade level Please sit with the grade level of your choice. www.ncdpi.wikispaces.net

58. Time to Reflect

59. Digging Deeper

62. Turn and Talk How are the handouts different from one another?

63. Mile Wide, Inch Deep? Make true equations. Write one number in every space. Draw a picture if it helps. 63

64. First Grade 2003 NC Standard Course of Study Common Core State Standards Build understanding of place value (ones, tens). Understand place value. 2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones — called a “ten.” The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). 3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 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.

65. Second Grade 2003 NC Standard Course of Study Common Core State Standards Use a variety of models to build understanding of place value (ones, tens, hundreds).. Understand place value. 1. Understand that the three digits of a three-digit 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: 100 can be thought of as a bundle of ten tens — called a “hundred.” 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. Count within 1000; skip-count by 5s, 10s, and 100s. 3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 4. Compare two three-digit 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. 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. 1

66. Time to Reflect

67. What can be more fundamental in mathematics than numbers and operations, yet numbers and arithmetic are so familiar to most of us that we run the risk of underestimating the deep, rich knowledge and proficiency that these standards encompass? Chapin & Johnson, 2006

68. Let’s Do Some Math!

69. 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. Standards for Mathematical Practices

70. Overarching habits of mind of a productive Mathematical Thinker

71. Spin to Win

72. 72

73. What strategies did you use to create the largest number? What strategies did you use to create the smallest number?

74. Record Your Thoughts What content standards & Mathematical Practices did this task address? How could this task be altered to meet the needs of different learners? 74

75. Let’s Do Some More! 1.Tell Me – Show Me/ Compare –Number Name, Place Value, & Expanded Form 2.Human Number Line 3.Race for a Square 4.Make a Square Disappear 5.Close to 100!

76. Your Turn In your small group: – Read & explore your task. – Discuss and write your thoughts on the Record Your Thoughts handout – Be prepared to teach the rest of your table your task. 76

77. Teach Your Table At your table: – Teach your task. After all tasks have been taught, discuss: –What content standards & Mathematical Practices did this task address? –How could this task be altered to meet the needs of different learners? 77

78. Tell Me, Show Me & Be Sure to Compare Number Name, Place Value Name, and Expanded Form

79. 79

80. 80

81. Human Number Line

82. 82

83. Race for a Square

84. Make a Square Disappear

85. Close to 100!

86. Place Value How would you define place value? What is the distinguishing characteristic of the base-ten number system? Why do you think we use a base-ten number system rather than different base? 86

87. What Do Students Think? At your tables, Review the student work example. Answer the following questions together: What does this student understand about place value? What questions would you ask to gain a better understanding of student place value knowledge and/or to reflect on his/her thinking? What questions/task would you provide next? Be prepared to share your table’s thoughts with the whole group.

88. 88 1

89. 89 2

90. 90 3

91. 91 4

92. 92 5

93. 93 6

94. Turn and Talk Discuss at your table: –Why would it be important for students to have a firm foundation of place value before introducing decimals?

95. Before considering decimal numerals with students, it is advisable to review some ideas of whole number place value. One of the most basic of these ideas is the 10 to 1 relationship between the value of 2 adjacent positions. 95 Chapin & Johnson, 2006

96. Exploration Stations: Decimals Spin to Win/Compare Tell Me – Show Me Number Line Make a Square & Race for a Square Make a Square Disappear

97. Exploration Stations With your partner, visit each of the different stations. Explore each task. Record ideas, extensions and additional explanations you want to remember. Be prepared to share your thoughts & experiences at the end of the session.

99. Exploration Stations: Reflection 99

100. 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. Standards for Mathematical Practices

101. 101

102. 102

103. 103

104. 104

105. Turn and Talk Discuss at your table: –What are your thoughts about introducing decimals through place value?

106. 106 Glasgow, et al. (2000). The Decimal Dilemma, NCTM.

107. 107 Glasgow, et al. (2000). The Decimal Dilemma, NCTM.

108. 108 Glasgow, et al. (2000). The Decimal Dilemma, NCTM.

109. Time to Reflect

111. CCSS for Reading Standards Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events. Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language. 111

113. Finding Rich Tasks- It’s a Process 113

114. Navigate through Navigations Decide on a grade band: K-2 or 3-5 Form groups of 3-4 people within your grade band – Select a Navigations book – Choose 3-5 lessons – Use the template located on the wiki to record the CCSS alignment: 114 www.ncdpi.wikispaces.net

115. Navigation Alignment

116. What are Features of a Good Task? It begins where the students are; accessible to wide range of learners. It is seen as something to make sense of. It requires justifications and explanations for answers and methods. The focus is on making sense of the mathematics involved and thereby increasing understanding. Van de Walle, 2004

117. What are Features of a Good Task? It challenges the learners to think for themselves. It offers different levels of challenge. It encourages collaboration and discussion. It has the potential for revealing patterns or leading to generalizations. It invites children to make decisions. nrich.maths.org

118. Altering the Lesson: Place Value in Whole Numbers & Decimals Changed the sequence of tasks Omitted some tasks Added an additional task Extended some tasks Used small group & stations rather than whole group instruction Altered the recording sheets

119. Alter Your Lesson In your small group: –Choose 1 lesson –Discuss how this lesson may be altered To align with the CCSS and Mathematical Practices. To meet the needs of different learners. To exhibit features of a “Good Task”. –Be Prepared to share your ideas with the whole group 119

120. Food for Thought NCTM’s Navigation Series Until we meet again Performance metrics

122. Time to Reflect

123. www.ncdpi.wikispaces.net 10/4/2015 123

124. DPI Contact Information Kitty Rutherford Elementary Mathematics Consultant 919-807-3934 kitty.rutherford@dpi.nc.gov Amy Scrinzi Elementary Mathematics Consultant 919-807-3839 amy.scrinzi@dpi.nc.gov Robin Barbour Middle Grades Mathematics Consultant 919-807-3841 robin.barbour@dpi.nc.gov Johannah Maynor Secondary Mathematics Consultant 919-807-3842 johannah.maynor@dpi.nc.gov Barbara Bissell K – 12 Mathematics Section Chief 919-807-3838 barbara.bissell@dpi.nc.gov Susan Hart Program Assistant 919-807-3846 susan.hart@dpi.nc.gov