1. Mathematics Rigor with Common Core State Standards CCSA Conference March, 2012 Kitty Rutherfordkitty.rutherford@dpi.nc.govkitty.rutherford@dpi.nc.gov Robin Barbour robin.barbour@dpi.nc.govrobin.barbour@dpi.nc.gov

2. www.corestandards.org

3. Critical Areas Critical Area Focal Points

4. 10/10/2015 page 4 Mathematical Practices Grade Level Overview

5. Grade Level DomainDomain Standards ClusterCluster

6. High School Themes Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability

7. High School Standards Notation Perform operations on matrices and use matrices in applications. 6. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs of incidence relationship in a network. 11.Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y =g(x intersect are the solutions of the equations f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. ★

8. K-8 Domains DomainsK12345678 Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Measurement and Data Geometry Number and Operations - Fractions Ratios and Proportional Relationships The Number System Expressions and Equations Statistics and Probability Functions

10. 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

12. Mathematical practices describe the habits of mind of mathematically proficient students… Who is doing the talking? Who is doing the thinking? Who is doing the math? 10/10/2015 page 12

13. Instructional Task What rectangles can be made with a perimeter of 30 units? Which rectangle gives you the greatest area? How do you know? What do you notice about the relationship between area and perimeter?

14. Compared to…. 5 10 What is the area of this rectangle? What is the perimeter of this rectangle?

15. 10/10/2015 page 15

16. 10/10/2015 page 16 Make sense of problems and preserve in solving them.

17. When planning, ask “What task can I give that will build student understanding?” rather than “How can I explain clearly so they will understand?” Grayson Wheatley, NCCTM, 2002 10/10/2015 page 17

18. Types of Math Problems Presented How Teachers Implemented Making Connections Math Problems

19. Lesson Comparison United States and Japan The emphasis on skill acquisition is evident in the steps most common in U.S. classrooms The emphasis on understanding is evident in the steps of a typical Japanese lesson Teacher instructs students in concept or skill Teacher solves example problems with class Students practice on their own while teacher assists individual students Teacher poses a thought provoking problem Students and teachers explore the problem Various students present ideas or solutions to the class Teacher summarizes the class solutions Students solve similar problems 19

20. What do you see? 404 102 304 20

21. Predict some additional data. 404 102 304 21

22. How close were you? 404 102 304 203 22

23. All the numbers – so? 454 253 152 404 102 304 203 23

24. Where are you? Roller Coaster454 Ferris Wheel253 Bumper Cars152 Rocket Ride404 Merry-go-Round102 Water Slide304 Fun House203 24

25. Fill in the blanks. Ride??? Roller Coaster454 Ferris Wheel253 Bumper Cars152 Rocket Ride404 Merry-go-Round102 Water Slide304 Fun House203 25

26. The Amusement Park RideTimeTickets Roller Coaster454 Ferris Wheel253 Bumper Cars152 Rocket Ride404 Merry-go-Round102 Water Slide304 Fun House203 26

27. The Amusement Park The 4 th and 2 nd graders in your school are going on a trip to the Amusement Park. Each 4 th grader is going to be a buddy to a 2 nd grader. Your buddy for the trip has never been to an amusement park before. Your buddy want to go on as many different rides as possible. However, there may not be enough time to go on every ride and you may not have enough tickets to go on every ride. 27

28. The bus will drop you off at 10:00 a.m. and pick you up at 1:00 p.m. Each student will get 20 tickets for rides. Use the information in the chart to write a letter to your buddy and create a plan for a fun day at the amusement park for you and your buddy. 28 The Amusement Park

29. 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

30. 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

31. Mathematics Claims The Smarter Balanced Assessment Consortium has released a document outlining four claims about what mathematically proficient students can do. The claims are a synthesis of the Standards for Mathematical Practice, and form the guiding principles to be used in creating assessments.

32. Mathematics Claim 1 & 2 Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Students can frame and solve a range of complex problems in pure and applied mathematics.

33. Mathematics Claim 3 & 4 Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

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

40. Which of the following represents 2/5? a. b. c. d.

41. For numbers 1a – 1d, state whether or not each figure has 2/5 of its whole shaded. 1a. 1b. 1c. 1d. ο Yes ο No

42. Scoring Rubric Responses to this item will receive 0 – 2 points, based upon the following: 2 points: YNYN 1 point: YNNN, YYNN, YYYN 0 point: YYYY, YNNY, NNNN, NNYY, NYYN, NYNN, NYYY, NYNY, NNYN, NNNY, YYNY, YNYY

43. RIGOR Conceptual Understanding Application Skills and Procedures

44. Rigor through Standards

45. Rigor though Standards 6 th Grade Critical Area: Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems.

46. Skipping material will create gaps in learning which jeopardizes foundational content needed to maximize the likelihood of success in High School Mathematics Content Acceleration Compacting 3 years of content into 2 is supported by research; 2 years into 1 is considered too challenging Considering high school courses is essential when making middle school recommendations

47. 6 th Grade7 th Grade8 th Grade 100 % 100% 7 th grade??% 8 th grade Math 1 Standards Option 1: Option 2: 6 th Grade7 th Grade8 th Grade 100 % 6 th gradeRemaining 7 th grade Remaining 8 th grade Math 1 Standards ??% 7 th grade??% 8 th grade High School Courses in Middle School Getting Students Ready

48. 10/10/2015 page 48 Integer Exponents (8.EE.1) Multiplication and Division with Scientific Notation (8.EE.4) Solving Systems by Substitution (8.EE.8) Volume of Pyramids, Cones and Spheres (7.G.6, 8.G.9) Surface Area of Pyramids (6.G.4, 7.G.6) At A Glance Instructional Implications High School

49. 10/10/2015 page 49 Angles (7.G.5, 8.G.5) Using Pythagorean Theorem in 3-D Figures (8.G.7) Mean Absolute Deviation (6.SP.5c) Two-way Tables (8.SP.4) Qualitative Graphs (8.F.5) Graphing Proportional Relationships (7.RP.2a, b, c, d, 8.EE.5) At A Glance Instructional Implications Math One

50. www.ncdpi.wikispaces.net 10/10/2015 50

51. www.ncdpi.wikispaces.net 10/10/2015 51

52. Grade Band Pages 10/10/2015 52

53. Crosswalk Documents 10/10/2015 page 53 The crosswalks reflect a comparison between the Common Core State Standards and the North Carolina Standard Course of Study. They inform educators about how the current standards align with the CCSS Standards.

54. Mathematics Crosswalk

55. CAUTION!! 10/10/2015 page 55 CONTENT APPEARING TO BE THE SAME MAY ACTUALLY BE DIFFERENT!! The CCSS Requires CLOSE Reading!!!

56. Unpacking Documents 10/10/2015 page 56 The purpose of the Unpacking Documents is to increase student achievement by ensuring educators understand the new standards. The “unpacking” of the standards done in these documents is an effort to answer a simple question “What does this standard mean that a student must know and be able to do?” and to ensure the description is helpful, specific and comprehensive for educators.

57. Unpacking – At a Glance 10/10/2015 page 57

58. 10/10/2015 page 58 Unpacking – Standards for Mathematical Practice

59. Unpacked Content 10/10/2015 page 59

60. Common Core Glossary Table 1. Common multiplication and division situations

63. K-5 Units Students learn mathematics by exploring mathematically-rich tasks and sharing strategies, ideas, and approaches with one another. (practices) K Adding and Subtraction 1 st Exploring Two-Digit Numbers 2 nd Two- & Three-Digit Addition & Subtraction 3 rd Unit on Area and Perimeter 4 th Fractions 5 th Fractions 10/10/2015 page 63

64. Format of the Lessons The phases of the lesson: Engage - Brief opening activity Explore - Mathematically-rich task Explain - Discussion of task and concepts Elaborate - Follow-up activity Evaluate - description of formative and summative assessments 10/10/2015 page 64

65. Additional Wiki Information

66. YearWho Can Apply Nomination Deadline Application Deadline 2012 Elementary Teachers Grades K - 6 April 1, 2012May 1, 2012 2013 Secondary Teachers Grades 7 - 12 April 1, 2013May 1, 2013 www.paemst.org Presidential Awards for Excellence in Mathematics and Science Teaching

67. Elementary Mathematics Add-on Licensure 18-hour Graduate program (6 courses) Participating Universities –East Carolina University –Appalachian State University –NC State University –UNC Chapel Hill –UNC Charlotte –UNC Greensboro –UNC Wilmington Dr. Sid Rachlin (rachlins@ecu.edu)rachlins@ecu.edu

68. Webinars Archived Webinars: -November 17 th : CCSS and Math I Standards -January 10 th : K-12 Getting Started: Organization Tools and Instructional Planning Model -February 9 th : Making Mathematics Accessible (K-12) -March 8 th : K – 2 Assessment and Calendar Time

69. http://illustrativemathematics.org/ http://commoncoretools.wordpress.com K, Counting and Cardinality; K–2, Operations and Algebraic Thinking K, Counting and Cardinality; K–5, Operations and Algebraic Thinking K–3, Categorical Data; Grades 2–5, Measurement Data* (data part of the Measurement and Data Progression) 3-5, Number and Operations – Fractions 6-7, Ratio and Proportional Relationships 6-8, Progression for Statistics and Probability 6–8, Expressions and Equations ADDITIONAL RESOURCES:

70. QUESTIONS COMMENTS

71. Kitty Rutherford kitty.rutherford@dpi.nc.gov Robin Barbour robin.barbour@dpi.nc.gov Contact Information Website: www.ncdpi.wikispaces.net