1. CCSSI FOR MATHEMATICS “STANDARDS OF PRACTICE” Collegial Conversations GRADES 4 – 5

2. Today’s Goal To explore the Standards for Content and Practice for Mathematics Begin to consider how these new CCSS Standards are likely to impact your classroom practices

3. What are the Common Core State Standards? Aligned with college and work expectations Focused and coherent Included rigorous content and application of knowledge through high-order skills Build upon strengths and lessons of current state standards Internationally benchmarked so that all students are prepared to succeed in our global economy and society Research and evidence based State led- coordinated by NGA Center and CCSSO

4. Focus Key ideas, understandings, and skills are identified Deep learning of concepts is emphasized –That is, time is spent on a topic and on learning it well. This counters the “mile wide, inch deep” criticism leveled at most current U.S. standards.

5. Benefits for States and Districts Allows collaborative professional development based on best practices Allows development of common assessments and other tools Enables comparison of policies and achievement across states and districts Creates potential for collaborative groups to get more economical mileage for: –Curriculum development, assessment, and professional development

6. Common Core Development Initially 48 states and three territories signed on As of November 29, 2010, 42 states have officially adopted Final Standards released June 2, 2010, at www.corestandards.org Adoption required for Race to the Top funds

7. Michigan’s Implementation Timeline Held October and November of 2010 rollouts District curricula and assessments that provide a K-12 progression for meeting the MMC requirements will require minimal adjustments to meet CCSS Curriculum and assessment alignment in SY10-11 Implementation SY11-12 New assessment 2014-15 (Smarter Balanced Assessment Consortium or SBAC – replaces MEAP and MME)

9. Background

10. Each State that is a member of the Consortium in 2014– 2015 also agrees to do the following: Adopt common achievement standards no later than the 2014–2015 school year, Fully implement the Consortium summative assessment in grades 3–8 and high school for both mathematics and English language arts no later than the 2014–2015 school year, Adhere to the governance requirements, Agree to support the decisions of the Consortium, Agree to follow agreed-upon timelines, Be willing to participate in the decision-making process and, if a Governing State, final decisions, and Identify and implement a plan to address barriers in State law, statute, regulation, or policy to implementing the proposed assessment system and address any such barriers prior to full implementation of the summative assessment components of the system. Responsibilities of States in the Consortium

16. Technology Approach SBAC Item Bank Partitioned into a secure item bank for summative assessments and a non-secure bank for the interim/benchmark assessments: Traditional selected-response items Constructed-response items Curriculum-embedded performance events Technology-enhanced items (modeled after assessments in use by the U.S. military, the architecture licensure exam, and NAEP)

17. Domains are large groups of related standards. Standards from different domains may sometimes be closely related. Look for the name with the code number on it for a Domain. HOW TO READ THE GRADE LEVEL STANDARDS

18. Common Core Format Clusters are groups of related standards. Standards from different clusters may sometimes be closely related, because mathematics is a connected subject. Clusters appear inside domains.

19. Common Core Format Standards define what students should be able to understand and be able to do – part of a cluster. They are content statements. An example content statement is: “Find all factor pairs for a whole number in the range 1 – 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 – 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 – 100 is prime or composite,” 4.OA.4. The “OA” stands for “Operations and Algebraic Thinking”. Please refer to page three in your grade level appropriate Common Core document. Progressions of increasing complexity from grade to grade

20. Common Core - Clusters May appear in multiple grade levels in the K-8 Common Core. There is increasing development as the grade levels progress What students should know and be able to do at each grade level Reflect both mathematical understandings and skills, which are equally important

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

22. Format of K-8 Standards Grade Level DomainDomain

23. Format of K-8 StandardsClusterCluster ClusterCluster StandardStandard StandardStandard

24. Mathematics » Grade 4 » Introduction In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. 1.Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context. 2.Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number. 3.Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.

26. Mathematics » Grade 5 » Introduction In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume. 1.Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.) 2.Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately. 3.Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.

28. DomainsGrade Levels Counting and CardinalityK only Operations and Algebraic Thinking 1-5 Number and Operations in Base Ten 1-5 Number and Operations - Fractions 3-5 Measurement and Data1-5 Geometry1-5 K – 5 DOMAINS

29. DomainsGrade Levels Ratio and Proportional Relationships 6-7 The Number System6-8 Expressions and Equations6-8 Functions8 Geometry6-8 Statistics and Probability6-8 MIDDLE GRADES DOMAINS

30. Michigan GLCE vs. CCSS

31. MAJOR SHIFTS K - 5 Numeration and operation intensified, and introduced earlier Early place value foundations in Kindergarten Regrouping as composing/decomposing in Grade 2 Decimals to hundredths in Grade 4 All three types of measurement simultaneously Non-standard, English and metric Emphasis on fractions as numbers Emphasis on number line as visualization/structure

32. HOW IS THERE LESS? Backed off of algebraic patterns K – 5 Backed off of statistics and probability in K – 5 Delayed content like percent and ratios and proportions

33. Fractions, Grades 3–6 3. Develop an understanding of fractions as numbers. 4. Extend understanding of fraction equivalence and ordering. 4. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4. Understand decimal notation for fractions, and compare decimal fractions. 5. Use equivalent fractions as a strategy to add and subtract fractions. 5. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 6. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

34. CCSSM Mathematical Practices The Common Core proposes a set of Mathematical Practices that all teachers should develop in their students. These practices are similar to NCTM’s Mathematical Processes from the Principles and Standards for School Mathematics. THE REASON WHY WE ARE HERE TODAY!

35. Design and Organization Mathematical Practice – expertise students should acquire: (Processes & proficiencies) NCTM five process standards: Problem solving Reasoning and Proof Communication Connections Representations

36. NCTM Process StandardsCCSS Mathematical Practices Problem SolvingMake sense of problems and persevere in solving them. Use appropriate tools strategically Reasoning and ProofReason abstractly and quantitatively. Critique the reasoning of others. Look for and express regularity in repeated reasoning CommunicationConstruct viable arguments ConnectionsAttend to precision. Look for and make use of structure RepresentationsModel with mathematics. NCTM Process Standards and the CCSS Mathematical Practice Standards

37. Design and Organization Mathematical proficiency ( National Research Council’s report Adding It Up) – Adaptive reasoning – Strategic competence – Conceptual understanding (comprehension of mathematical concepts, operations, relations) – Procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently, and appropriately) – Productive disposition (ability to see mathematics as sensible, useful, and worthwhile

38. Mathematics/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

39. Mathematics/Standards for Mathematical Practice “The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.” CCSS, 2010 Standards for Mathematical Practice Carry across all grade levels Describe habits of a mathematically expert student Standards for Mathematical Content K-8 presented by grade level Organized into domains that progress over several grades Grade introductions give 2-4 focal points at each grade level High school standards presented by conceptual theme (Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability

40. Standards of Mathematical Practice 1.Choose a partner at your table and “Pair Share” the Standards of Practice between you and your partner. 2. When you and your partner feel you understand generally each of the standards, discuss the following question: What implications might the standards of practice have on your classroom?

41. Transition from Current State Standards & Assessments to New Common Core Standards Develop Awareness Needs Assessment/Gap Analysis Planning Capacity Building Job-embedded Professional Development

42. Transition Planning Next Steps: Alignment of CCSS with curriculum Gap analysis (content and skills that vary from the MEAP and MME) What instructional practices will facilitate the transition? What new assessment strategies will be needed? Professional development needs?

43. Transition Planning Gather in teams from your schools and discuss – What are your immediate needs as a classroom teacher being asked to implement the CCSS? – What professional development is needed? – What initial gaps come to mind and how do you address these gaps? – As a school team, look at the eight Standards for Mathematical Practice. What do they look like? Sound like? What will students need in order to implement them? What will teachers need? What are the implications for assessment and grading? Select a recorder, time keeper and someone to report out for your group.

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