1. JANEL JOHNSON MIDDLE SCHOOL MATHEMATICS OFFICE OF STANDARDS AND LEARNING JULY 2015 South Carolina College- and Career- Ready Standards for Mathematics Session 1 Good Morning! Please sign-in and get 1 of each handout off the table by the door.

2. Agenda – Session 1 July 2015 Office of Standards and Learning 2 9:30 – 9:45 a.m.Logistics Introductions and Norms Edmodo Groups Accessing the Standards 9:45 – 10:00 a.m.Overview of the SCCCR-M 10:00 – 10:30 a.m.Mathematical Process Standards 10:30 – 11:00 a.m.Profile of the South Carolina Graduate 11:00 – 11:30 a.m.Middle Grades Overview 11:30 a.m. – 12:30 p.m.Lunch 12:30 – 3:30 p.m.6 th Grade Mathematics Standards Support Document

3. Session Outcomes July 2015 Office of Standards and Learning 3 Know how to access resource and support materials for the new South Carolina College- and Career-Ready Standards for Mathematics Understand the format and structure of the new South Carolina College- and Career-Ready Standards for Mathematics Explain and investigate the Profile of the SC Graduate, its relationship to the standards, and its potential for transforming education in South Carolina Explain and understand the content of and relationship among the standards in 6 th Grade Mathematics

4. Office of Standards and Learning July 2015 4 Logistics

5. July 2015 Office of Standards and Learning 5 Questions Raise your hand and ask questions during the session. Parking Lot – questions not directly related to the session Breaks Morning Break and Afternoon Break Lunch (45 min) Technology Feel free to take notes on your computer or tablet Cell phones on silent Session Materials Supplies Will be posted on SCDE website and Edmodo Group Photos: microsoft.com

6. Introductions and Norms July 2015 Office of Standards and Learning 6 Norms Listen as an Ally Value Differences Maintain Professionalism Actively Participate Good Morning! My name is… I (teach) (grade level) at (school) in (district). Describe your summer using 1 word.

7. Join our Edmodo Groups July 2015 Office of Standards and Learning 7 SCDE Mathematics Team: https://edmo.do/j/snmcixhttps://edmo.do/j/snmcix 1. Create an account. (If you have an account, log in.) 2. Enter URL above.

8. Join our Edmodo Groups July 2015 Office of Standards and Learning 8 Office of Standards and Learning: https://edmo.do/j/fu7i2y https://edmo.do/j/fu7i2y 1. Create an account. (If you have an account, log in.) 2. Enter URL above.

9. Accessing the Standards and Resources July 2015 Office of Standards and Learning 9 www.ed.sc.gov

10. Accessing the Standards and Resources July 2015 Office of Standards and Learning 10

11. Accessing the Standards and Resources July 2015 Office of Standards and Learning 11

12. What is your current level of comfort with the new South Carolina College- and Career-Ready Standards for Mathematics? July 2015 Office of Standards and Learning 12 Developing Awareness Building Knowledge Transforming Practice Building Capacity Go to www.poll.si  Enter poll's ID ivpx

13. PAGES 5-6 Office of Standards and Learning July 2015 13 Overview of the South Carolina College- and Career-Ready Standards

14. Mathematics Standards Overview July 2015 Office of Standards and Learning 14 Content Standards  Grade Level (K – 8)  High School Standards Process Standards  Grades K-12

15. Format of Mathematics Content Standards July 2015 Office of Standards and Learning 15

16. Format of Mathematics Content Standards July 2015 Office of Standards and Learning 16 In grades K – 8:  GradeLevel.KeyConcept.Standard Number (e.g., K.NS.1) or, if applicable,  GradeLevel.KeyConcept.Standard NumberStandardLetter (e.g., K.NS.4a) In courses:  CourseName.KeyConcept.StandardNumber (e.g., A1.AREI.1) or, if applicable,  CourseName.KeyConcept.StandardNumberStandardLetter (e.g., A1.AREI.6a)

17. Terms July 2015 Office of Standards and Learning 17 Including references content that must be mastered, while e.g. references possible illustrative examples. The phrase i.e. references the only examples or terms that should be used.

18. Terms July 2015 Office of Standards and Learning 18 Fluently and fluency describe a student’s ability to compute with accuracy, flexibility, and efficiency (Kilpatrick, Swafford, & Findell, 2001). Real-world refers to authentic contexts through which students engage in mathematics and should serve as a stepping-stone for thinking about important mathematical concepts.

19. PAGES 7-8 Office of Standards and Learning July 2015 19 Mathematical Process Standards

20. Purpose of the Mathematical Process Standards July 2015 Office of Standards and Learning 20 The Mathematical Process Standards: demonstrate the ways in which students develop conceptual understanding of mathematical content and apply mathematical skills drive the pedagogical component of teaching and serve as the means by which students should demonstrate understanding of the content standards

21. Mathematical Process Standards 1.Make sense of problems and persevere in solving them. 2.Reason both contextually and abstractly. 3.Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4.Connect mathematical ideas and real-world situations through modeling. 5.Use a variety of mathematical tools effectively and strategically. 6.Communicate mathematically and approach mathematical situations with precision. 7.Identify and utilize structure and patterns. July 2015 Office of Standards and Learning 21

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23. NASCAR July 2015 Office of Standards and Learning 23 Take out a copy of the Mathematical Process Standards A Tagxedo will be displayed with the words from the Mathematical Process Standards. Read it carefully! When your group knows which Mathematical Process Standards is being displayed, send your runner to GRAB a notecard with that Mathematical Process Standard. Pick a runner for your table group! START YOUR ENGINES!!!!!!!

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28. Mathematical Process Standards Gallery Walk July 2015 Office of Standards and Learning 28 Group 1Group 2Group 3Group 4Group 5Group 6Group 7 SherrieAlvaJasmineTiashaLynnTimothy P.Bridget Kimberly Whetsine Christine L.JasonLisaShannonSarahHeather Tim N.JohnMike P.Kim ClarkBeckyChristy M.Rebecca M. LuannSarahTawanaJill B.FrankieTammyRebecca S. JulieAndrewAshleeAnnetteMike W.Jill S.Thomas KellieRoryKim NoeMickiJenniferKalaSandra JerryDionneSeanRechelKristinaGrahamDonna LauraErieCherylBetty Kimberly McGaha JuliaCathy DeborahCindy

29. Mathematical Process Standards Gallery Walk July 2015 Office of Standards and Learning 29 Read the Mathematical Process Standard that matches your group number. Make a poster that shows how this standard would sound and look in the classroom. (5-7 minutes) Pick a speaker to remain at your group’s poster. Gallery Walk! (1-2 minutes per poster)

30. PAGE 9 Office of Standards and Learning July 2015 30 Profile of the South Carolina Graduate

31. July 2015 Office of Standards and Learning 31

32. Process Standards and the Profile of the SC Graduate July 2015 Office of Standards and Learning 32 In the new mathematics standards, the needed world class mathematical  knowledge is supported by the rigorous K – 12 grade level and course content standards,  skills are identified in the SCCCR Mathematical Process Standards, and  life and career characteristics are identified in the South Carolina Portrait of a College- and Career-Ready Mathematics Student.

33. Linking the SC Profile and Mathematical Process Standards July 2015 Office of Standards and Learning 33 Personal Response  Choose one “World Class Skill” and one “Life and Career Characteristic” on which to focus throughout the rest of this engagement.  Identify standards that support your chosen skill and/or characteristic and mark them with the appropriate acronym(s).

34. Mathematical Process Standards Observation Tool July 2015 Office of Standards and Learning 34

35. Mathematical Process Standards Observation Tool Probe deeper into student understanding.  Ask questions which build on what you observed about what the children said:  What do you suppose Billy was thinking when he said....  Ask questions which connect the teacher’s actions and the mathematical ideas of the lesson:  How would you respond if...  In clarifying Sara’s thinking, why...  What mathematical ideas do you think students were grappling with in this lesson? July 2015 Office of Standards and Learning 35

36. PAGE 38 Office of Standards and Learning July 2015 36 Middle Grades Overview

37. Key Concepts July 2015 Office of Standards and Learning 37 6 th Grade7 th Grade8 th Grade Number System Ratios and Proportional Relationships Functions Expressions, Equations, and Inequalities Geometry and Measurement Data Analysis and StatisticsData Analysis, Statistics, and Probability

38. Terms July 2015 Office of Standards and Learning 38 Specific vocabulary is used throughout grades 6 – 8 standards to indicate various levels of understanding. The only terminology defined is terminology that could be misinterpreted.

39. Investigate and Explore July 2015 Office of Standards and Learning 39 The words investigate and explore indicate the initial understanding of a concept.  7.DSP.6: Investigate the relationship between theoretical and experimental probabilities for simple events.  8.EEI.3: Explore the relationship between quantities in decimal and scientific notation.

40. Apply July 2015 Office of Standards and Learning 40 Once students have an initial understanding, they are asked to apply this knowledge, often in real-world and mathematical situations.  7.DSP.7: Apply the concepts of theoretical and experimental probabilities for simple events.  8.EEI.4: Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems.

41. Extend July 2015 Office of Standards and Learning 41 When standards expand upon the previous knowledge of students, the standard indicates that students will extend their knowledge. For these standards, educators should assist students in building upon previous knowledge to enrich their understanding of the interconnectedness of mathematics.  6.NS.8: Extend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers.

42. Discover July 2015 Office of Standards and Learning 42 The word discover in a standard indicates that students will be given the opportunity to determine a formula through the use of manipulatives or inquiry-based activities.  6.GM.2: Use visual models (e.g., model by packing) to discover that the formulas for the volume of a right rectangular prism (V=lwh, V=Bh) are the same for whole or fractional edge lengths. Apply these formulas to solve real-world and mathematical problems.

43. Translate Among/Translate Between July 2015 Office of Standards and Learning 43 The phrases translate among and translate between are often associated with multiple representations of a concept and indicate that given representations a and b, students must be able to convert from a to b and vice versa.  7.GM.1: Determine the scale factor and translate between scale models and actual measurements (e.g., lengths, area) of real-world objects and geometric figures using proportional reasoning.

44. Terms Activity July 2015 Office of Standards and Learning 44 REVIEW Review the term assigned to your table. FIND Identify the 6 th Grade standards where your assigned term is used. POST Write the code for the standard on a sticky note and place it on the poster.

45. Lunch July 2015 Office of Standards and Learning 45

46. Office of Standards and Learning July 2015 46 6 th Grade Mathematics Standards

47. Alignment of the SCCCR-M and CCSS-M July 2015 Office of Standards and Learning 47 Please go to http://scdemsmath.weebly.com http://scdemsmath.weebly.com Click on “6 th Grade” Scroll down to “ SCCCR-M and CCSS-M Alignment Document for 6th Grade Mathematics”

48. Alignment of the SCCCR-M and CCSS-M July 2015 Office of Standards and Learning 48 Read through each alignment document. What differences do you notice in the following standards?  6.NS.9  6.RP.2  6.GM.2

49. Support Document July 2015 Office of Standards and Learning 49 Course Coversheet organizes the middle school course standards into possible instructional units and provides links to specific middle school course Units. Each middle school course Unit contains:  Clarifying notes related to the standards within the unit  New academic vocabulary in the unit  Prior and subsequent knowledge related to the unit  Description of the relationship between the standards in the unit  Potential instructional strategies and lessons  Resources for the unit  Sample formative assessment tasks and questions

50. Course Coversheet July 2015 Office of Standards and Learning 50 Unit 1Unit 2Unit 3Unit 4Unit 5Unit 6Unit 7 Number System Ratios and Rates Graphing and Rational Numbers ExpressionsEquationsStatisticsGeometry Standards 6.NS.1 6.NS.2 6.NS.3 6.NS.4 6.NS.9 6.RP.1 6.RP.2 6.RP.3 6.NS.5 6.NS.6 6.NS.7 6.NS.8 6.EEI.1 6.EEI.2 6.EEI.3 6.EEI.4 6.EEI.5 6.EEI.6 6.EEI.7 6.EEI.8 6.EEI.9 6.DS.1 6.DS.2 6.DS.3 6.DS.4 6.DS.5 6.GM.1 6.GM.2 6.GM.3 6.GM.4

51. Support Documents July 2015 Office of Standards and Learning 51 Please go to http://scdemsmath.weebly.com http://scdemsmath.weebly.com Click on “6 th Grade” Scroll down to “SCCCR-M Support Document for 6th Grade Mathematics”

52. Relationship Among Standards Standards in this Unit July 2015 Office of Standards and Learning Standards in this unit are all necessary to develop computational skills necessary for work with positive rational numbers. 6.NS.1 6.NS.2 6.NS.3 6.NS.4 6.NS.9 52 Unit 1 – Number System

53. July 2015 Office of Standards and Learning 53 SectionQuestions (10-20 minutes) Clarifying notes related to the standards within the unit New academic vocabulary in the unit Prior and subsequent knowledge related to the unit How long do you think it would take to teach this unit? What would you teach first? Potential instructional strategies and lessons Resources for the unit What additional strategies and/or resources can be used in this unit? Sample formative assessment tasks and questions Complete pages 2-4 of The Dream Team task

54. Relationship Among Standards Standards in this Unit July 2015 Office of Standards and Learning Standards in this unit will establish an understanding of relationships that exist among quantities of similar and different units. 6.RP.1 6.RP.2 6.RP.3 54 Unit 2 – Ratios and Rates

55. July 2015 Office of Standards and Learning 55 SectionQuestions (10-20 minutes) Clarifying notes related to the standards within the unit New academic vocabulary in the unit Prior and subsequent knowledge related to the unit How long do you think it would take to teach this unit? What would you teach first? Potential instructional strategies and lessons Resources for the unit What additional strategies and/or resources can be used in this unit? Sample formative assessment tasks and questions Complete the Longest Matches in NHL Playoff History task

56. Unit 3 – Graphing and Rational Numbers July 2015 Office of Standards and Learning 56 Standards in this Unit 6.NS.5 6.NS.6 6.NS.7 6.NS.8

57. 6.NS.5 July 2015 Office of Standards and Learning 57 Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation. In your groups, brainstorm a list of real-world situations with integers. Include the meaning of zero for each situation.

58. Real-World Situations of Integers July 2015 Office of Standards and Learning 58

59. Unit 4 - Expressions July 2015 Office of Standards and Learning 59 Standards in this Unit 6.EEI.1 6.EEI.2 6.EEI.3 6.EEI.4

60. 6.EEI.3 and 6.EEI.4 July 2015 Office of Standards and Learning 60 6.EEI.3 Apply mathematical properties (e.g., commutative, associative, distributive) to generate equivalent expressions. 6.EEI.4 Apply mathematical properties (e.g., commutative, associative, distributive) to justify that two expressions are equivalent. In your groups, brainstorm a list of properties students should have knowledge of.

61. Properties of the Number System July 2015 Office of Standards and Learning 61 Source: Robert FantRobert Fant

62. Properties of the Number System July 2015 Office of Standards and Learning 62 Source: Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8

63. Conjecture Creation July 2015 Office of Standards and Learning 63 Source: Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8 2 × 5 + 5 = 3 × 5 Could I trade 5 for another number and still have a true statement?

64. Unit 5 - Equations July 2015 Office of Standards and Learning 64 Standards in this Unit 6.EEI.5 6.EEI.6 6.EEI.7 6.EEI.8 6.EEI.9

65. 6.EEI.8 July 2015 Office of Standards and Learning 65 6.EEI.8 Extend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations. a. Write an inequality of the form > or < and graph the solution set on a number line. b. Recognize that inequalities have infinitely many solutions.

66. Hershey Park Inequalities July 2015 Office of Standards and Learning 66 Please go to http://scdemsmath.weebly.com/  Click on “6 th Grade”  Scroll down to “6.EEI.8 - Hershey Park Inequalities” Read the lesson in its entirety. What changes would you make to the lesson? How could the lesson be modified if students did not have access to technology? Could this lesson be used to fully teach standard 6.EEI.8?

67. Unit 6 - Statistics July 2015 Office of Standards and Learning 67 Standards in this Unit 6.DS.1 6.DS.2 6.DS.3 6.DS.4 6.DS.5

68. 6.DS.5d July 2015 Office of Standards and Learning 68 6.DS.5 Describe numerical data sets in relation to their real- world context. d. Find measures of variability (interquartile range, mean absolute deviation) using a number line.

69. Mean Absolute Deviation July 2015 Office of Standards and Learning 69 Mean Absolute Deviation The mean absolute deviation (MAD) of a set of data is the average distance between each data value and the mean. The MAD helps determine whether the set's mean is a useful indicator of the values within the set. The larger the MAD, the greater variability there is in the data (the data is more spread out). The larger the MAD, the less relevant is the mean as an indicator of the values within the set.

70. Number of Hours Spent Playing Sports or Outside July 2015 Office of Standards and Learning 70 The data below is the number of hours 6 th graders spent playing sports or playing outside over the weekend. 0 0 0 1 3 4 4 4 5 5 5 5 6 6 7 8 8 9 10 10 The mean is 5. What is the deviation or difference from the mean? Source: Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8

71. Number of Hours Spent Playing Sports or Outside July 2015 Office of Standards and Learning 71 The data below is the number of hours 6 th graders spent playing sports or playing outside over the weekend. 0 0 0 1 3 4 4 4 5 5 5 5 6 6 7 8 8 9 10 10 0 -50 -50135 -5-4-2012345 012345678910 What is the absolute value of the deviation? Source: Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8

72. Number of Hours Spent Playing Sports or Outside July 2015 Office of Standards and Learning 72 The data below is the number of hours 6 th graders spent playing sports or playing outside over the weekend. 0 0 0 1 3 4 4 4 5 5 5 5 6 6 7 8 8 9 10 10 0 510 510135 5421012345 012345678910 What is the mean absolute deviation? Source: Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8

73. Number of Hours Spent Playing Sports or Outside July 2015 Office of Standards and Learning 73 The data below is the number of hours 6 th graders spent playing sports or playing outside over the weekend. 0 0 0 1 3 4 4 4 5 5 5 5 6 6 7 8 8 9 10 10 5+5+5+4+2+1+1+1+0+0+0+0+1+1+2+3+3+4+5+5 20 48 20 2.4 hours The average distance from the mean number of hours is 2.4 hours. Source: Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8

74. Using the Mean Versus the MAD July 2015 Office of Standards and Learning 74 Robert is trying to decide whether to move to New York City or to San Francisco based on temperature. Which city should he choose if he loves hot weather and really dislikes cold weather? Mean = 63° MAD = 14° Mean = 64° MAD = 3.5° Source: EngageNY

75. Unit 7 - Geometry July 2015 Office of Standards and Learning 75 Standards in this Unit 6.GM.1 6.GM.2 6.GM.3 6.GM.4

76. 6.GM.2 July 2015 Office of Standards and Learning 76 6.GM.2 Use visual models (e.g., model by packing) to discover that the formulas for the volume of a right rectangular prism ( = ℎ, = ℎ ) are the same for whole or fractional edge lengths. Apply these formulas to solve real-world and mathematical problems.

77. Finding the Volume of a Fractional Rectangular Prism July 2015 Office of Standards and Learning 77 Would the approach modeled in the video benefit some learners more than others? How so? What misconceptions may students have with this standard?

78. Session Outcomes July 2015 Office of Standards and Learning 78 Know how to access resource and support materials for the new South Carolina College- and Career-Ready Standards for Mathematics Understand the format and structure of the new South Carolina College- and Career-Ready Standards for Mathematics Explain and investigate the Profile of the SC Graduate, its relationship to the standards, and its potential for transforming education in South Carolina Explain and understand the content of and relationship among the standards in 6 th Grade Mathematics

79. Resources July 2015 Office of Standards and Learning 79 SCDE Math Webpage Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8 by John A. Van de Walle, Jennifer M. Bay-Williams, Lou Ann H. Lovin, and Karen S. Karp

80. Certificates of Attendance After BOTH sessions, a survey will be sent to you via e-mail. Once complete, your certificate will be sent to you via e-mail within 7-10 business days. July 2015 Office of Standards and Learning 80

81. Agenda – Session 2 July 2015 Office of Standards and Learning 81 Graduation Standards in Middle School 7 th Grade Standards  Support Document 8 th Grade Standards  Support Document Compacted Curriculum for Accelerated Classes

82. Future Resources July 2015 Office of Standards and Learning 82 Additional Support Documents for Units 3-7 Vertical Articulation Document

83. Feedback Form July 2015 Office of Standards and Learning 83 Please go to http://scdemsmath.weebly.com/ Click on “Session 1 Feedback Form” List at least 2 things you will take back and use in your school or district. What suggestions do you have for the Grade 6 Mathematics Support Document? How can this session be improved?

84. Questions July 2015 Office of Standards and Learning 84 Photo: microsoft.com

85. Contact Information Janel E. Johnson Ed. Associate - Middle School Mathematics E-mail: jejohnson@ed.sc.govjejohnson@ed.sc.gov P: 803.734.7814 F: 803.734.8388 July 2015 Office of Standards and Learning 85