Common Core Standards College- and Career-readiness Standards

1. Florida’s Plan for Implementation Common Core StandardsCollege- and Career-readiness Standards Fall 2011 North East Florida Educational Consortium

2. Learning Goals • Teachers will know the design and organization of the Mathematics Common Core Standards. • Teachers will understand that the Mathematical Practices and Mathematic Content Standards describe varieties of expertise that mathematics educators should seek to develop in their students. • Teachers will be able to integrate the Mathematical Practices and Mathematic Content Standards when developing student learning goals. • Your Personal Goal Essential Question: How can you develop learning goals for your students using the Common Core Mathematic Standards?

3. Mathematic Standards 3

4. 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.

5. Mathematical Practices: Focus on “Processes and Proficiencies” Process standards Proficiency standards • problem solving, • reasoning and proof, • communication, • representation, and • connections • adaptive reasoning, • strategic competence, • conceptual understanding, • procedural fluency, and • productive disposition

6. Mathematics/Standards for Mathematical Practice • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning

7. Small Group Activity – Unpacking What students should know and be able to do. • Read the Mathematical Practice (pgs. 6-8) • Highlight: Know what? / Demonstrate how? • Reflect on how the practices will: • help in teacher role in the classroom? • impact instruction? • appear in the classroom? • help inform professional development needs? • Prepare to share out

8. Group Sorting Activity • Activity: Connect Practice Standards to Fraction Lesson • Materials: • Mathematical Practices Sorting Mat • Teacher Action sorting cards • Match the learning activity to the best Mathematical Practice that will be demonstrated by students

9. Mathematics Format • Domains • Larger 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.

10. Mathematics Format • Clusters • Groups of related standards. • Standards from different clusters may sometimes be closely related, because mathematics is a connected subject. • Clusters appear inside domains.

11. Mathematics Format • Standards • Define what students should be able to understand and be able to do. • Standards are part of a cluster.

12. Common Core Format K-8 High School • Conceptual Category • Domain • Cluster • Standards • Grade • Domain • Cluster • Standards 12

13. K-8 Grade Level Overview Domain Standard Grade Page K 9 1 13 2 17 3 21 4 27 5 33 6 39 7 46 8 52 Cluster

14. Common Core – Domain • Domains are overarching big ideas that connect topics across the grades • Descriptions of the mathematical content to be learned elaborated through clusters and standards

15. 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

16. Common Core – Standards • Standards are content statements. An example content statement is: “Use properties of operations to generate equivalent expressions.” • Progressions of increasing complexity from grade to grade

17. Format of High School Standard Domain Conceptual Page Category 58 Number & Quantity 62 Algebra 67 Functions 72 Modeling 74 Geometry 79 Statistics & Probability Cluster

18. Format of High School Standards Regular Standard STEM Modeling

19. Domains K-8 / HS Conceptual Categories

20. Coding Key for Math Standards CCMA.K12.MP.# = Mathematical Practice Grades K-5 Key CCMA.K.CC.# = Counting and Cardinality CCMA.K.OA.# = Operations and Algebraic Thinking CCMA.K.NBT.# = Number and Operations on Base Ten CCMA.K.NF.# = Number and Operations – Fractions CCMA.K.MD.# = Measurement and Data CCMA.K.G.# = Geometry Grades 6-8 Key CCMA.6.RP.# = Ratios and Proportional Relationships CCMA.6.NS.# = The Number System CCMA.6.EE.# = Expressions and Equations CCMA.6.F.# = Functions CCMA.6.G.# = Geometry CCMA.6.SP.# = Statistics and Probability

21. Conceptual Categories CCMA.K12.MP.# = Mathematical Practice • Number and Quantity • Algebra • Functions • Modeling • Geometry • Statistics and Probability CCMA.(CC).(D).#

22. Highlight your grade level & the one directly below & above. Progression of Skills Select a domain for your grade level. What do you notice about the progression? Highlight the verbs within the cluster content statements & standards

23. Small Group Activity – Unpacking • Find your Grade Level in the CCSS Document • Look through the Domains & Standards • Complete the Unpacking handout; identify concepts that are: • New • The Same • Not Included • Located in another grade level

24. Article Reading Read the article and highlight two sentences and two words that you think is particularly important. First Round: (1 minute each person) Each person shares one sentence and why significant. Identify location with group – page/paragraph – read sentence out loud; share reason selected Second Round: (1 minute each person) Each person shares the word and why significant. Third Round: (10 minutes total) Group discussion about what they heard.

25. Connecting Mathematical Practices w/ Content Standards • Small Group Activity pg. 1 • Find the first page for your grade level, locate the instructional focus “critical areas”, and list the key concepts for each area. • Follow the next set of directions • Small Group Activity pg. 2 • Follow directions for the activity. • You find a different standard for each mathematical practice

26. Rubric

27. Rubric /Lesson Plan

28. Regularly encourage students to demonstrate and deepen their understanding of numbers and operations by solving interesting, contextualized problems and by discussing the representations and strategies they use.

29. Key Advances Focus and coherence • Focus on key topics at each grade level. • Coherent progressions across grade levels. Balance of concepts and skills • Content standards require both conceptual understanding and procedural fluency. Mathematical practices • Foster reasoning and sense-making in mathematics. College and career readiness • Level is ambitious but achievable.

30. Mathematical Proficiency “HOW” THE MATHEMATICS WORK Computational & Procedural Skills “WHERE” THE MATHEMATICS WORK Problem Solving DOING MATH “WHY” THE MATHEMATICS WORK Conceptual Understanding