COMMON CORE STANDARDS C OLLEGE - AND C AREER - READINESS S TANDARDS North East Florida Educational ConsortiumFall 2011 F LORIDA ’ S P LAN FOR I MPLEMENTATION

Learning Goals 2  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?

Mathematic Standards 3

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. 4

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

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 6

Small Group Activity – Unpacking What students should know and be able to do. 1.Read the Mathematical Practice (pgs. 6-8) 2.Highlight: Know what? / Demonstrate how? 3.Reflect on how the practices will:  help in teacher role in the classroom?  impact instruction?  appear in the classroom?  help inform professional development needs? 4.Prepare to share out 7

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 8

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. 9

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. 10

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

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

K-8 Grade Level Overview 13 GradePage K

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 14

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 15

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 16

Format of High School Conceptual PageCategory 58Number & Quantity 62Algebra 67Functions 72Modeling 74Geometry 79Statistics & Probability

Format of High School Standards

19 Domains K-8 / HS Conceptual Categories

Coding Key for Math Standards 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 CCMA.K12.MP.# = Mathematical Practice

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

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

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

Article Reading 24 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.

Connecting Mathematical Practices w/ Content Standards 25  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

Rubric 26 Rubric Evaluation Level 4.0 In addition to score 3.0, teacher can explain how the Mathematics Practices and Mathematics Content Standards interconnect with each other and why both are necessary for Mathematics instruction. Level 3.0 Target The teacher can explain the design and organization of the MCCS and can integrate the Mathematics Practices and Content Standards when developing unit goals. Level 2.0 Teacher can explain the how the MCCS is organized but needs assistance in integrating the Mathematical Practices and Concept Standards when developing unit goals. Level 1.0 With help, teacher can explain the design of the MCCS and can integrate the Mathematical Practices and Concept Standards when developing unit learning goals. Level 0.0 Even with help, no understanding of the Mathematics CCS or the Mathematical Practices and Mathematic Content Standards is demonstrated.

Rubric /Lesson Plan 27 Course NameMathematics / Grade 1 Standard(s): MACC.1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Note: See Table 1 Learning Goal(s)/ Objective(s) The student will understand and/or be able to solve addition and subtraction problems within 20 that involve comparing, with unknowns in all positions, using models, explanation, and equations. Essential Question(s) How can you solve addition and subtraction problems that involve comparing with unknowns in all positions? Rubric/EvaluationLevel 4.0 In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught the student is able to:  Create and solve their own original addition and subtraction problems within 20 that involve comparing, with unknowns in all positions, using models, explanation, and equations. Level 3.0 Target The student understands and is able to:  Solve addition and subtraction problems within 20 that involve comparing, with unknowns in all positions, using models, explanation, and equations. The student exhibits no major errors or omissions Level 2.0 With help, a partial understanding of some of the simpler details and processes as the student is able to:  Solve addition and subtraction problems within 20 that involve comparing, with unknowns in two of three positions, using two or three strategies included in the Score 3.0 target. However, the student exhibits major errors or omissions regarding the more complex ideas and processes. Level 1.0 With help, a partial understanding of some of the simpler details and processes as the student is able to:  Solve addition and subtraction problems within 20 that involve comparing, with unknowns in one of three positions, using models. Level 0.0Even with help, no understanding or skill demonstration

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. 28

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. 29

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