1. From NECAP to the Common Core Mathematics and New Assessments April 26, 2011 1

2. AGENDA From NECAP to the Common Core Mathematics and New Assessments  Introduction and background information  Transition Timeline (NECAP to the Common Core and New assessments)  Overview of Mathematics CCSS Design and Organization Similarities/Differences between CCSS & GLEs/GSEs  Time for Questions and Answers  Next Steps 2

3. Introduction and Background Information State-led and developed common core standards for K-12 in English/language arts and mathematics Focus on learning expectations for students, not how students get there. 3

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5. Why Now?  Disparate standards across states  Student mobility  Global competition  Today’s jobs require different skills 5

6. Why Important?  Prepares students with the knowledge and skills they need to succeed in college and work  Ensures consistent expectations regardless of a student’s zip code  Provides educators, parents, and students with clear, focused guideposts 6

7. From NECAP to the Next Generation Assessment Systems Transition / Timeline 7

8. So what? Implications & Impact in NH  Adoption State Board adopted the CCSS “in principle” and is committed to a thoughtful, orderly transition process for implementation and assessment  Alignment Process began this summer to look at gaps and matches and grade differentials DOE putting together a broad view to post & distribute Focus groups currently meeting to review analysis  Implementation TAKE IT SLOW! NECAP in place for at least three years Toolkit for administrators & curriculum leaders in development 8

9. Now what? Transition Timeline 2010-2011 – NECAP as usual  Begin review of standards-Use Toolkit  NECAP Management Team releases plan to principals in April 2011 2011-2012 – NECAP as usual 2012 2013 – NECAP ( with transitional items) 2013 2014 – final NECAP (best possible transitional test) 2014-2015 – no fall NECAP test  NECAP Science remains  New assessments based CCSS 9

10. Curriculum and Assessment Timeline for New Hampshire (adjusted format) 10 2010-20112011-20122012-20132013-20142014-2015 NH Curriculum Standards for English language arts and mathematics* NH Curriculum Frameworks for ELA and Math NH Curriculum Frameworks for ELA and Math (supplemented with some differences) NH Common Core Standards in English language arts and mathematics in use Common Core State Standards for ELA and mathematics Begin Review Using Toolkit – The goal is to familiarize Continue Review, using NH Toolkit – Begin implementation of K-2 standards Begin to seriously map the grade level differences between NH and CCSS to plan for SY13-14 First year for new standards to be used in classrooms CCSS with NH specific enhancements fully implemented in classrooms State Assessment in Reading, Writing, Mathematics NECAP (fall) New SBAC Adaptive Test (spring) State Assessment in Science NECAP (spring) *NH Curriculum Standards in all other content areas remain in place http://www.education.nh.gov/spotlight/k12_ccss.htm A place to start:

11.  Fewer and more rigorous.  Aligned with college and career expectations  Internationally benchmarked  Rigorous content and application of higher- order skills.  Builds on strengths and lessons of current state standards.  Research based Mathematics Common Core Standards 11

12. Review of Major Components of the Mathematics CCSS Presentation for the NH Department of Education 12

13. Intent of the Common Core  The same goals for all students  Coherence  Focus  Clarity and Specificity 13

16. 16 Key Features: Mathematics  Learning progressions that follow how students learn concepts  Understanding the mathematics AND procedural skill are equally important  “processes and proficiencies” from the NCTM process standards & Adding It Up  8 mathematical practices are the same throughout the grades  Standards for content vary by grade  Mastery of standards through grade 7 prepares students for algebra in grade 8  Appendix: Designing HS Mathematics Courses [http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf ] 16

17. Common Core State Standards  Introduction  Application of CCSS for ELLs  Application to Students with Special Needs  Mathematics Standards Standards for Mathematical Practice Grade levels/strand introductions Domains, Clusters and Standards  Appendix A: Model Pathways for High School Courses [http://www.corestandards.org/assets/CCSSI_Mathematics_A ppendix_A.pdf ] 17

20. Standards for Mathematical Practice 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 20 [ Explain and make conjectures…] [ Make sense of...] [ Understand and use…] [ Apply and interpret…] [ Consider and Detect] [ Communicate precisely to others…] [Discern and recognize…] [Notice and pay attention to….]

21. Key Advances  Properties of operations: Their role in arithmetic and algebra  Mental math and “algebra” vs. algorithms  Operations and the problems they solve  Units and unitizing Unit fractions Unit rates  Quantities-variables-functions-modeling  Number-expression-equation-function  Modeling  Practices 21

22. Common Core Format High School Conceptual Category Domain Cluster Standards K-8 Grade Domain Cluster Standards (There are no preK Common Core Standards) 22

23. Mathematics Standards: 23

24. Mathematics K-8 : Design & Organization Introduction Page  Highlights: 2-3 Critical Areas  Provides: Emphasis of Content Overview Page  Provides: Domains Cluster Headings Mathematical Practices

25. DOMAIN CLUSTER HEADINGS Standards within the CLUSTER FOOTNOTES Components: K-8 grade level Mathematics Standards

26. Grade Level Domains High School Conceptual Categories K – 5 Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations – Fractions Measurement and Data Geometry 6-8 Ratios and Proportional Relationships The Number System Expressions and Equations Functions Geometry Statistics and Probability  Number and Quantity  Algebra  Functions  Modeling  Geometry  Statistics and Probability Standards for Mathematical Content 26

27. Distribution of the Domains (K-8) 27

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29. Overview: Mathematics Grades K - 5 Introduction at earlier grade  Addition, subtraction, multiplication, and division of whole numbers and other rational numbers Introduction at later grade  Statistics & probability is introduced as a domain in Grade 6  Expressions & Equations is introduced as a domain in Grade 6 More specificity  Focus on operations with whole numbers, fractions, and decimals as the foundation for more demanding math concepts and procedures 29

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31. Overview : Mathematics Grades 6 – 8 Introduction at earlier grade  Percent increase and decrease and interest rate  Histograms, box plots, quartiles and inter-quartile range Introduction at later grade  Functions as a domain is introduced in grade 8 More specificity  Grades 6 & 7 standards: ramp up to algebraic concepts in Gr. 8  Grade 8 standards focus is on linear equations and functions 31

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33. Grade Level Domains High School Conceptual Categories K – 5 Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations – Fractions Measurement and Data Geometry 6-8 Ratios and Proportional Relationships The Number System Expressions and Equations Functions Geometry Statistics and Probability  Number and Quantity (N)  Algebra (A)  Functions (F)  Modeling (*)  Geometry (G)  Statistics and Probability (S) Standards for Mathematical Content 33

34. High School Standards Conceptual Categories – Cross course boundaries – Span high school years Standards – “Core” for common mathematics curriculum for all students to be college and career ready – “College Ready” for entry level credit bearing course – (+) Additional mathematics that students should learn in order to take courses such as calculus, discrete mathematics, or advanced statistics.

35. Components: High School Mathematics Standard DOMAIN CLUSTER HEADING Standards within the CLUSTER *Modeling The STAR indicates Modeling is expected to demonstrate proficiency and may be indicated at the DOMAIN, CLUSTER, CLUSTER HEADING or STANDARD level. Students are expected to demonstrate proficiency of this Cluster by applying their knowledge within a real word application.

36. Conceptual Categories: Domains Number and Quantity  The Real Number System  Quantities  The Complex Number System  Vector and Matrix Algebra  Seeing Structure in Expressions  Arithmetic with Polynomials & Rational Functions  Creating Equations  Reasoning with Equations and Inequalities Functions  Interpreting Functions  Building Functions  Linear, Quadratic, & Exponential Models  Trigonometric Functions 36

37. Conceptual Categories: Domains (continued) Modeling Geometry  Congruence  Similarity, Right Triangles, and Trigonometry  Circles  Expressing Geometric Properties with Equations  Geometric Measurement & Dimension  Modeling with Geometry Statistics and Probability  Interpreting Categorical and Quantitative Data  Making Inferences and Justifying Conclusion  Conditional Probability and Rules of Probability  Using Probability to Make Decisions 37

38. Overview: Mathematics High School Introduction at earlier grade  Complex numbers  Quadratic, logarithmic, & trigonometric functions  Logarithmic identities Specificity  Reflects four years of instruction  1 st three years prepare students for college or career  4 th year allows for course of choice  STEM standards (+)  Modeling is integrated throughout all the domains (*) 38

39. Traditional Integrated  ALGEBRA I  GEOMETRY  ALGEBRA II  4 th Year Mathematics Course  MATHEMATICS I  MATHEMATICS II  MATHEMATICS III  4 th Year Mathematics Course Model Course Pathways in Mathematics COMPACTED: Grades 7 & 8 Standards + Algebra I Standards OR Mathematics I Standards Instruction occurs over 2 years (during Grades 7 & 8) 39

40. Cracking the High School Mathematics “Code” High School Number and Quantity The Real Number SystemN-RN QuantitiesN-Q The Complex Number SystemN-CN Vector and Matrix N-VM Algebra Seeing Structure in ExpressionsA-SSE Arithmetic with Polynomials & Rational FunctionsA-APR Creating EquationsA-CED Reasoning with Equations and InequalitiesA-REI N.RN N.Q N.CN N.VM A.SSE A.APR A.CED A.REI PATHWAYS

41. Cracking the High School Mathematics “Code” (continued) Functions Interpreting FunctionsF-IF Building FunctionsF-BF Linear, Quadratic, & Exponential ModelsF-LE Trigonometric FunctionsF-TF Modeling* Geometry CongruenceG-CO Similarity, Right Triangles, and TrigonometryG-SRT CirclesG-C Expressing Geometric Properties with EquationsG-GPE Geometric Measurement and DimensionG-GMD Modeling with GeometryG-MG F.IF F.BF F.LE F.TF G.CO G.SRT G.C G.GPE G.GMD G.MG PATHWAYS

42. How to read a Common Core High School Mathematics Standard A-SSE.1b Letter & Number indicating the Standard within the Cluster Conceptual Category ALGEBRA Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1.Interpret expressions that represent a quantity in terms of its context.* b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. Domain

43. How to read a Common Core High School PATHWAYS Mathematics Standard (+)N.CN.4,5,6 Numbers indicating the Standards within the Cluster Heading Conceptual Category Domain Number & Quantity The Complex Number System Represent complex numbers and their operations on the complex plane. 4. (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a give complex number represent the same number. 5. (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i) 3 = 8 because (-1 + √3 i) has modulus 2 and argument 120 0. 6. (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. Indicates: STEM standard

44. CONCEPTUAL CATEGORY DOMAIN Standards within the CLUSTER CLUSTER HEADING

45.  For grades preK-8, a model of implementation can be found in NCTM’s Curriculum Focal Points  For the secondary level, please see NCTM’s Focus in High School Mathematics: Reasoning and Sense Making  See Handout w/additional resources www.nctm.org/cfp www.nctm.org/FHSM Additional Information 45

46. Reflections: Now What? What actions will you take based upon what we worked on today? What do you need to learn? Who will you work with? What do you need to integrate into your practice? Who will support you? 46

47. Want to know more?  NH DOE Website: http://www.education.nh.gov/spotlight/k12_ccss.htm  Maine Department of Education http://www.maine.gov/education/lres/math/standard s.html http://www.maine.gov/education/lres/math/standard s.html  NCSM November 30 2010 Webinar on CCSS http://www.carnegielearning.com/webinars/getting- started-with-the-common-core-state-standards-first- steps-for-mathematics-education-leaders/ http://www.carnegielearning.com/webinars/getting- started-with-the-common-core-state-standards-first- steps-for-mathematics-education-leaders/  Rhode Island Department of Education http://www.ride.ri.gov/Instruction/CommonCoreMate rials.aspx#HowToReadPPT http://www.ride.ri.gov/Instruction/CommonCoreMate rials.aspx#HowToReadPPT 47