1. All information in this Power Point is located on www.engageny.orgwww.engageny.org Dr. Elizabeth Frangella January 2013 1

2. - A Story of Units O Each Unit tells the story of concepts on their grade level. O Layout for each – Introduction O Sequence of Grade- Modules Aligned to Standards O Summary for the year O Key areas of Focus O Required Fluency O http://engageny.org/sites/default/files/reso urce/attachments/a-story-of-ratios-a- curriculum-overview-for-grades-6-8.pdf http://engageny.org/sites/default/files/reso urce/attachments/a-story-of-ratios-a- curriculum-overview-for-grades-6-8.pdf NEW! 2

3. To Find the Major, Supporting and Additional work of each grade O http://engageny.org/sites/default/files/reso urce/attachments/nys-math-emphases-k- hs.pdf http://engageny.org/sites/default/files/reso urce/attachments/nys-math-emphases-k- hs.pdf 3

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14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Instructional Shifts (went from 6 to 3) 14

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Curriculum Map 15

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17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points: 17 A Story of Units is being written in alignment with the Instructional Shifts required by the CCLS. All standards for each grade have been carefully included in the module sequence. The P-5 modules are designed with deliberate coherence to capitalize on the learning progressions that are embedded in the CCLS. The activities promote a careful balance of fluency practice, conceptual understanding, and application, which aligns with the instructional shift, rigor.

18. Standards for Math Practice (part of the Common Core) O Like the Instructional Shifts, each Standard for Mathematical Practice is integrated into the design of A Story of Units. 18

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Standards for Mathematical Practice 19 “… describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.”

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Standards for Mathematical Practice 20 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.

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Indicators of Quality in Instructional Materials and Tools for Mathematics 21 Problems in the materials are worth doing. Assignments aren’t haphazardly designed. Exercises are given to students in intentional sequences. The modules contain different types of problems that are presented in a simple to complex format. There is variety to what students produce in response to prompts.

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Indicators of Quality in Instructional Materials and Tools for Mathematics 22 There are separate teacher materials that support and reward teacher study. The use of manipulatives follows best- practices. The visual design isn’t distracting or chaotic. Support for English language learners and members of other special populations is provided.

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Point 23 A Story of Units adheres to the guidelines established in the Publishers’ Criteria and benefits from on-going feedback from Student Achievement Partners throughout the writing process.

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Three Types of PARCC Assessments PARCC Type I Tasks 24 Assess concepts, skills and procedures Include a balance of conceptual understanding, fluency, and application Can involve any or all mathematical practice standards Are machine-scored including innovative, computer- based formats

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units PARCC Type I Tasks 25

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units PARCC Type II Tasks 26 Assess ability to express mathematical reasoning Call for written arguments/justifications, critique of reasoning, or precision in mathematical statements (MP.3, MP.6) and can involve other mathematical practice standards Are hand-scored, or machine-scored with innovative computer-based formats, or a combination

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units PARCC Type II Tasks 27

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units PARCC Type III Tasks 28 Assess modeling/applications Call for modeling/application in a real-world context or scenario (MP.4) and can also involve other mathematical practice standards Are hand-scored, machine-scored with innovative computer-based formats, or a combination

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units PARCC Type III Tasks 29 Sample Grade 4 Problem Jim has three times as much money as Sally. If Jim has $14 more than Sally, how much money do they have altogether?

30. Assessments O PARCC? O New York State? O Computer based? O All unknown at this time 30

31. Draft of CC Sample Questions O Have you looked at the Draft of the New York State Testing Program documents?New York State Testing Program O Let’s look at some other sample math questions the state has used in the Network Training. Please take them out now. 31

32. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Turn and Talk 32 How do the new PARCC assessments compare with previous assessments? Did you notice the SHIFTS What did you notice about the RIGOR ? (anything else?)

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34. VOCABULARY O http://www.graniteschools.org/depart/teac hinglearning/curriculuminstruction/math http://www.graniteschools.org/depart/teac hinglearning/curriculuminstruction/math The following slides are from the Granite School Math Department presentation on the Common Core. 34

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38. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Instructional Shifts 38

39. Shift 1: Focus O —“…focus deeply on only the concepts that are prioritized in the standards...” 39

40. Shift 2: Coherence O —“Principals and teachers carefully connect the learning within and across grades so that… students can build new understanding onto foundations built in previous years.” 40

41. Shift 3: Rigor O —“…pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding, procedural skill and fluency, and applications.” 4 consolidated shifts 41

42. Fluency O —“Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions...” O One or two fluencies are required for each grade level and fluency suggestions are included in most lessons. Implementation of effective fluency practice is supported by the lesson structure. 42

43. SPRINTS and CHORALS O DO NOW- O Let’s take a minute to see what fluency is all about. SPRINTSPRINT- written practice for speed and accuracy CHORAL-CHORAL- Skip counting aloud This example is by fractions~ forward and backward http://engageny.org/resource/nti-november-2012-rigor- breakdown-skip-counting-by- fractions#.UOjPB6s8YbU.email 43

44. Conceptual Understanding O —“Students deeply understand and can operate easily within a math concept before moving on. They learn more than the trick to get the answer right. They learn the math.” 44

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47. Application— O “Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so.” 47

48. Dual Intensity— O “Students are practicing and understanding. There is more than a balance between these two things in the classroom—both are occurring with intensity.” 48

49. Rigor in the Assessments O Each assessment utilizes a combination of problems that build from simple to complex O procedural skill, O fluency, and O conceptual understanding. O Multiple-choice questions will be representative of PARCC Type I and II tasks. 49

50. RIGOR continued O Application problems including multi-step word problems are always part of the assessments. O Constructed response questions, will typically involve more complex tasks that require students to explain their process for solving a problem—i.e., Type II and III tasks. 50

51. Rigor continued O For these problems, answers alone are insufficient. Students must be able to thoroughly explain their thought processes. O Handout and discuss how to make questions more rigorous- Can you do it? 51

52. Let’s try one O Take a few minutes to do this assessment task- O The EVOO problem is a Grade 6 Problem 52

53. Do Now- A problem with “teeth” O Elaine bought 6 lbs 4oz of EVOO for 16.80. The container leaked and she lost some of the oil. She quickly sold the remaining oil to George, at a per ounce price 3/7 higher than she paid for it. Altogether she made a profit of $ 3.60. What percentage of oil was lost in the leak? 53

54. A Lesson Structure (others on site) Fluency Practice15 minutes Concept Development20 minutes Application Problems15 minutes Student Debrief10 minutes Total Time60 minutes O.O. 54

55. Common Language Addition and Subtraction, Grade 1Multiplication and Division, Grade 3 Represent and solve problems involving addition and subtraction. Represent and solve problems involving multiplication and division. Apply properties of operations as strategies to add and subtract. Apply properties of operations as strategies to multiply and divide. Understand subtraction as an unknown- addend problem. Understand division as an unknown-factor problem. Add and subtract within 20.Multiply and divide within 100. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. Determine the unknown whole number in a multiplication or division problem relating three whole numbers. Use place value understanding and properties of operations to add and subtract. Use place value understanding and properties of operations to perform multi-digit arithmetic. 55

56. Student needs 56

57. Some Connections 57

58. MAP O Let’s take a few minutes to look at the standards and how they progressstandards and how they progress O ROLLOUT- Standards Map 58

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60. Some good “stuff” inside O http://engageny.org/sites/default/files/resource/att achments/grade-5-math-guide_0.pdf http://engageny.org/sites/default/files/resource/att achments/grade-5-math-guide_0.pdf O From: Educator Guide to the 2013 Grade 5 Common Core Mathematics Test (time frame for teaching- what is taught AFTER the test) 60

61. Emphasis and Sequencing Teach after the test 61

62. WHAT ABOUT TEACHERS? O I HAVE TO BE COMFORTABLE WITH MATH! O Let’s say that together- O I HAVE TO BE COMFORTABLE WITH MATH! 62

63. Cluster Emphases for Instruction and the 2013 Grade 8 Common Core Mathematics Test 65–75% 70–80% 15–25% 10–20% 5–15% 5–10% Cluster EmphasisRecommended Instructional Time Approximate Number of Test Points MajorSupportingAdditional 63

64. Looking at how to use the mapped standards O 6.NS.4- This standard refers to greatest common factor- a staple of in-class worksheets. Note the second sentence and the example given: O Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor with a multiple as a sum of two whole numbers with no common factor. For example, express 36 +8 as 4(9 + 2) 64

65. The example given is to express 36 + 8, a sum of two numbers with a common factor, as 4 (9 + 2), a multiple of a sum of two numbers with no common factor. This example sends a signal about how ―greatest common factor can be piped into the main flow of ideas leading to algebra. For example, consider what we do when we express ax + a as a(x + 1). We are using the distributive property to express a sum of terms with a common factor as a multiple of a sum of terms with no common factor (6.EE.3,4). Standard 6.NS.4 is a kind of rehearsal for this, with numbers instead of variables. 65

66. Think about the student mistakes that COULD happen, and plan appropriately. Answer a question with another question- make them think DON’T TOUCH THE MANIPULATIVES! For Teachers: Anticipate the Errors 66

67. Resources O https://mathreasoninginventory.com/Home/Index EXCELLENT FREE ASSESSMENT SITE from Scholastic magazine- TOO OLD TO LEARN? https://mathreasoninginventory.com/Home/Index O National Library of Virtual Manipulatives http://nlvm.usu.edu/ http://nlvm.usu.edu/ O Mathematics Assessment Project http://map.mathshell.org/materials/index.php http://map.mathshell.org/materials/index.php O Maths Dictionary for Kids http://amathsdictionaryforkids.com/ http://amathsdictionaryforkids.com/ O Thinkingblocks.com http://thinkingblocks.com/ http://thinkingblocks.com/ O Laying the foundation- http://www.ltftraining.org/ http://www.ltftraining.org/ O Commoncore.pearson.ed.com/ http://commoncore.pearsoned.com/index.cfm?locator=PS1c O9 http://commoncore.pearsoned.com/index.cfm?locator=PS1c O9 O Ilustrative Mathematics http://illustrativemathematics.org/standards/k8 http://illustrativemathematics.org/standards/k8 67

68. Don’t Forget O Download the most recent PARRC model frameworks O http://www.parcconline.org/parcc-model- content-frameworks http://www.parcconline.org/parcc-model- content-frameworks O Check out the Network Training information for November on www.engageny.orgwww.engageny.org O Check out this link for math resources- especially for High School O http://www.mrlsmath.com/20-free-resources- for-high-school-math-teachers/ http://www.mrlsmath.com/20-free-resources- for-high-school-math-teachers/ 68