1. Systems of Professional Learning Module 4 Grades K–5: Focus on Designing Learning

2. By the end of this session you will have: Strengthened your working relationships with peer Core Standards Coaches Explored the structure of the Standards and the Progressions documents on which the Standards were developed Created effective learning targets for use in planning lessons Described a process and strategies for conducting informal needs assessment in order to identify student needs 2

3. By the end of this session you will have: Identified elements that need to be considered when designing and implementing CCS-Math lessons Designed and/or modified CCS-Math lessons in order to meet the needs of all students Made plans for next steps in your CCS-Math implementation 3

4. Morning Session Welcome and Introductions Sharing Implementation Experiences Creating Learning Targets Identifying an Entry Point into the Mathematics Afternoon Session Designing CCS-Math Lessons Reflecting on the Lesson Design Supporting Teachers Post-Assessment, Session Evaluation, & Wrap Up 4

5. Please complete the Pre-Assessment 5 Page 4

6. Section 1 Page 6

7. In Module 3 you: Articulated a common understanding of UDL. Identified the importance of incorporating UDL Principles into lessons. Described the alignment of instructional practices and learning expectations of the CCS-Math. Planned for implementing UDL strategies within classroom lessons. 7

8. UDL is a set of three principles developed for providing all individuals equal opportunities to learn. 8 CAST (2014) Principle 1: Provide Multiple Means of Representation Principle 2: Provide Multiple Means of Action and Expression Principle 3: Provide Multiple Means of Engagement

9. Universal Design for Learning Principles include guidance on: Providing flexibility; Reducing barriers; Providing appropriate accommodations, supports, and challenges; and Setting expectations for all students. AND….. 9 CAST (2014)

10. 10 UDL can support teachers’ implementation of the CCS-Math Standards. The strategies that have been discussed for implementing the CCS-Math Standards overlap with the strategies that can be used to meet the UDL Principles. Think about, plan for, and implement the UDL Principles strategically. Begin with those that will have the greatest impact on YOUR students.

11. In Module 3 you: Developed a shared understanding of the four attributes of the formative assessment process. Reflected on the role of students in the formative assessment process. Explored strategies for supporting teachers as they make changes to their classroom practices. Made plans for next steps in your CCS-Math implementation. 11

12. 12 Assessment OF Learning Assessment FOR Learning

13. 13 (SBAC)

14. Activating students as learning resources for one another Activating students as owners of their own learning Wiliam, D. (2011) 14

15. 15 Sharing Implementation Experiences 1.Each participant will discuss with their table group one positive highlight, one question that they have as coaches, and one ongoing need for teachers from their personal implementation of the CCS-Math thus far. 2.Each table group will then determine two positive highlights, two questions, and two ongoing needs that they will present to the larger group. 3.Participants will record notes and “New Ideas” generated from the discussion. Guide Pages 8-9 Positive Highlights Questions Ongoing Needs Pages 6-7

16. Section 2 Page 9

17. The CCS-Math embodies a core shift in teaching and learning. Three Shifts: Focus, Coherence, and Rigor Standards for Mathematical Practice Problem Types Accessibility Key Classroom Practices Formative Assessment Process 17

18. In order to design learning experiences that align with the CCS-Math, teachers must develop a deep understanding of the structure of the Standards. 18

19. “Mathematics does not break down into lesson- sized pieces.” - Phil Daro 19 Daro, P. (2013)

20. “…individual statements of what students are expected to understand and be able to do are embedded within domain headings and cluster headings designed to convey the structure of the subject.” “The Standards” refers to all elements of the design – the wording of domain headings, cluster headings, and individual statements; the text of the grade level introductions and high school category descriptions; the placement of the standards for mathematical practice at each grade level.” 20 Daro, McCallum, & Zimba (2012)

21. Fewer topics allow for focusing on the major work for each grade. Focus http://www.corestandards.org/ 21

22. 22 Provides the critical areas for the grade level. Describes key ideas that students should learn in relation to each of the critical areas. http://www.corestandards.org/

23. 23 Domains Cluster Headings http://www.corestandards.org/

24. 24 http://www.corestandards.org/

25. “…the Standards were crafted to reward study on multiple levels: from close inspection of details, to a coherent grasp of the whole.” “Specific phrases in specific standards are worth study and can carry important meaning; yet this meaning is also importantly shaped by the cluster heading in which the standard is found. At higher levels, domain headings give structure to the subject matter of the discipline, and the practices’ yearly refrain communicates the varieties of expertise which study of the discipline develops in an educated person.” 25 Daro, McCallum, & Zimba (2012)

26. “Mathematics does not break down into lesson- sized pieces.” - Phil Daro 26 “Fragmenting the Standards into individual standards, or individual bits of standards, erases all these relationships and produces a sum of parts that is decidedly less than the whole.” Daro, P. (2013)

27. Why is paying attention to the structure important? Why not just focus on the individual standard statements? How were the major work, critical areas, cluster headings, and individual standard statements determined? 27

28. 28 Part 2 Examine your assigned domain across the K-5 grade band and record five general observations about the progression and two observations about the relationship between the Content and Practice Standards. 2.NBT.1 Understand that 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. K.NBT.1 Compose and decompose numbers from 11to19 into ten ones and some further ones e.g. by using objects, drawings, and record each composition or decomposition by a drawing or equation. 1.NBT.2a Understand that numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

29. 29 Access the CCS-Math Progressions here: http://ime.math.arizona.edu/progressions/. http://ime.math.arizona.edu/progressions/ Click on the first bulleted item under the heading: Draft Front Matter. Within the Draft Front Matter, scroll down to page 9 which begins the section titled: Organization of the Common Core State Standards for Mathematics.

30. 30 What information do the Progressions documents provide? Why is this information important? How can this information be useful to teachers? Guide Pages 14-15 Page 11

31. 31

32. How do we use the structure of the Standards and the information in the Progressions documents to determine the learning targets of day-to-day lessons if the Standards themselves are not broken down into lesson-sized pieces? Why do we need to focus on learning targets, why not just focus on the individual standards themselves? 32

33. 33 Learning targets: Focus on what students will learn, not what they will do. Success Criteria: Observable and measurable behaviors to be reached.

34. 34 Grade 3 Introduction http://www.corestandards.org/Math/Content/3/introduction/ http://www.corestandards.org/Math/Content/3/introduction/ Mathematics Grade 3 In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two- dimensional shapes.

35. Grade 3 Critical Area #2 developing understanding of fractions, especially unit fractions (fractions with numerator 1) 35 Grade 3 Introduction http://www.corestandards.org/Math/Content/3/introduction/ http://www.corestandards.org/Math/Content/3/introduction/

36. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators. 36 Grade 3 Introduction http://www.corestandards.org/Math/Content/3/introduction/

37. 37 (1) Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division. Grade 3 Introduction http://www.corestandards.org/Math/Content/3/introduction/ http://www.corestandards.org/Math/Content/3/introduction/

38. 38 3) Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle. Grade 3 Introduction http://www.corestandards.org/Math/Content/3/introduction/ http://www.corestandards.org/Math/Content/3/introduction/

39. 39 2) Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators. Grade 3 Introduction http://www.corestandards.org/Math/Content/3/introduction/ http://www.corestandards.org/Math/Content/3/introduction/

40. 40 4) Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole. Grade 3 Introduction http://www.corestandards.org/Math/Content/3/introduction/ http://www.corestandards.org/Math/Content/3/introduction/

41. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators. 41 Grade 3 Introduction: Key Ideas of Critical Area #2 http://www.corestandards.org/Math/Content/3/introduction/ http://www.corestandards.org/Math/Content/3/introduction/

42. Students view fractions in general as being built out of unit fractions, 42 Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. Students are able to use fractions to represent numbers equal to, less than, and greater than one.

43. With your group, do the following: 1.Choose a grade level and critical area for which you will focus on designing learning throughout the remainder of this Module. 2.Identify the key ideas that support the critical area. 3.As you work, complete Part 1 of the Learning Target Planning Template 43 Page 12

44. 44 Students view fractions in general as being built out of unit fractions. “Mathematics does not break down into lesson- sized pieces.” - Phil Daro Daro, P. (2013)

45. 45 “Fragmenting the Standards into individual standards, or individual bits of standards, erases all these relationships and produces a sum of parts that is decidedly less than the whole.” – Daro, P. (2013) Critical Area Key Idea Lesson(s)

46. 46 Students view fractions in general as being built out of unit fractions. Cluster: Develop understanding of fractions as numbers. Associated Standard 3.NF.A.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

47. With your group, do the following: 1.Explore the domain Progressions document that aligns with your identified critical area. 2.Determine which key idea your group will use as the focus for your first lesson(s) within this critical area. 3.Identify the cluster headings and individual standard(s) that support your selected key idea. 4.Complete Part 2 of the Learning Target Planning Template. 47 Page 13

48. 48 Students view fractions in general as being built out of unit fractions. Cluster: Develop understanding of fractions as numbers. Associated Standard 3.NF.A.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Access the CCS-Math Progressions here: http://ime.math.arizona.edu/progressions/. http://ime.math.arizona.edu/progressions/

49. If I want my students to be able to understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Students will understand that fraction notation consists of the numerator and the denominator. Students will _______________________________. 49

50. With your group, do the following: 1.Create the lesson level learning targets for the general entry point lessons into the mathematics of the identified critical area. 2.Place your critical area, key idea, standard(s), and learning targets on chart paper. Additional resource: http://commoncoretools.me/wp- content/uploads/2014/02/Elaborations.pdf 50 Page 14

51. With your group, review the work of others who worked at your same grade level. Using sticky notes, provide your peers with questions to consider, suggestions on additional learning targets, and any general feedback that would be helpful in developing out their lesson design. 51

52. 52 The major work for each grade level provides the critical areas and supporting key ideas that students should explore at each grade level. Every lesson and resource should be designed and considered for the impact it will make on students’ understanding those key ideas. The progression of the mathematics is an important part of the design process.

53. 53

54. Section 3 Page 16

55. …you find that your students have gaps in their content knowledge? 55

56. Scaffolding Open Questions Parallel Tasks 56

57. Determining the prior knowledge: Use the learning target information that you created in Section 2 and the information from the Progressions documents to identify what students should already know and be able to do prior to the work at the current grade level. Be sure to identify prior knowledge based on both the Content and the Practice Standards. 57 Guide Page X Page 16

58. 58 3.NF.A.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Prior Knowledge 2.G.3: Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

59. 59 What will be assessed: 2.G.3 – Can students partition shapes into two, three, or four equal shares? 2.G.3 – Do students recognize that equal shares of identical wholes need not have the same shape? MP4 – Can students draw a picture of circles and rectangles and partition the shape in their drawing into halves, thirds, and or fourths? MP6 – Do students use the words halves, thirds, and fourths? Can students label their models with the correct fraction notation?

60. Determining the prior knowledge: Use the learning target information that you created in Section 2 and the information from the Progressions documents to identify what students should already know and be able to do prior to the work at the current grade level. Be sure to identify prior knowledge based on both the Content and the Practice standards. 60 Guide Page X Page 16

61. Was there anything interesting or surprising about what you found? How did you determine where students should be with their development of the Practice Standards? 61

62. 62 (SBAC)

63. Decisions to be made: How will you elicit evidence? Formally: pre-tests, diagnostic assessment Informally: questions, tasks, student work When will you elicit evidence? Prior to planning the upcoming lessons Fractions Example: Activities built into Geometry lessons in the unit that precedes the work with fractions. 63

64. With your group, determine how you will assess students’ prior knowledge. Be prepared to talk about your assessment decisions. 64 Page 17

65. 65 (SBAC)

66. …you find that your students have gaps in their content knowledge? 66

67. “The natural distribution of prior knowledge in classrooms should not prompt abandoning instruction in grade level content, but should prompt explicit attention to connecting grade level content to content from previous learning.” “Much unfinished learning from earlier grades can be managed best inside grade level work when the progressions are used to understand student thinking.” 67 Daro, McCallum, & Zimba (2012)

68. With your group, brainstorm ideas for addressing gaps in prior knowledge that you will work into your lesson plan in Section 4. Mix, Mingle, and Share When prompted, find two other people with whom you will share your ideas. When time is called, return to your table group and share any new ideas gained from your one- on-one discussions. 68 Page 18

69. Section 4 Page 20

70. What are the ingredients? Example: Formative assessment practices are used throughout the lesson. 70

71. 71 Page 21

72. Use the template to design a lesson that will address: The learning targets you identified in Section 2. The needs of all students through the pre- assessment data you created in Section 3. 72

73. Illustrative Mathematics – http://www.illustrativemathematics.org http://www.illustrativemathematics.org Achieve the Core – http://achievethecore.org http://achievethecore.org Smarter Balanced – http://smarterbalanced.org http://smarterbalanced.org Mathematics Assessment Project – http://map.mathshell.org/materials/index. php http://map.mathshell.org/materials/index. php 73 Page 24

74. Now that you have used it – How will the regular use of a template like this affect classroom instruction in your setting? Is there anything you would change about the template? 74 Page 24

75. 75 …Be back in 10 minutes

76. Section 5 Page 26

77. Use the following tools to evaluate the lesson you created/modified: EQuIP rubric (introduced in Module 1) UDL Principles (introduced in Module 3) Record your observations and modifications on page 27. 77 Page 27

78. What were the strengths of your lesson design? What areas of your lesson design were deficient? Which of the evaluation tools did you find most helpful in finding these deficiencies? 78

79. Section 6 Page 29

80. What do you want to know? Create the questions you want to answer around teachers’ readiness, prior knowledge, and understanding of the structure of the Standards and how to design learning that is aligned to the CCS-Math. How will you find out? Conduct observations? Attend grade level meetings? Talk one-on-one? What will you do with your findings? 80 Pages 29-30

81. 81 Page 32

82. By the end of this session you will have: Strengthened your working relationships with peer Core Standards Coaches Explored the structure of the Standards and the Progressions on which the Standards were developed Created effective learning targets for use in planning lessons Described a process and strategies for conducting informal needs assessment in order to identify student needs 82

83. By the end of this session you will have: Identified elements that need to be considered when designing and implementing CCS-Math lessons Designed and/or modified CCS-Math lessons in order to meet the needs of all students Made plans for next steps in your CCS-Math implementation 83

84. Where Are You Now? Assessing Your Learning. Please complete an online Session Evaluation. Your feedback is very important to us! The survey is located here: 84 http://surveys.pcgus.com/s3/CT-Math-Module-4-K-5

85. achievethecore.org americaachieves.org ctcorestandards.org engageny.org 85