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Making Sense of The CT Mathematics Standards (Common Core State Standards) Grades 9-12 ATOMIC Conference November 29, 2011 Shelbi Cole – CSDE Sharon Heyman- UCONN Peggy Neal-CREC

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Goals Provide a brief tour of the Standards – Standards for Mathematical Practice – Mathematical Content Standards – Critical Areas of Focus – Layout Explain the CSDE Unit Template Development Process Review Sample Units Q & A

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10/12/20143 Mathematics Common Core Document

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STANDARDS FOR MATHEMATICAL PRACTICE Making Sense of the CT Mathematics Standards

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The standards for mathematical practices are located in the front of the mathematics standards and within the “nature of mathematics” section at each grade level. The standards for mathematical practice illustrate the connection between 21 st century skills and mathematical content and instruction. The standards for mathematical practices should be considered when creating curricula, assessments, and professional development for teachers, and administrators. Standards for Mathematical Practice

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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

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SMP 1: Make sense of problems and persevere in solving them. Mathematically Proficient Students: Explain the meaning of the problem to themselves Look for entry points Analyze givens, constraints, relationships, goals Make conjectures about the solution Plan a solution pathway Consider analogous problems Try special cases and similar forms Monitor and evaluate progress, and change course if necessary Check their answer to problems using a different method Continually ask themselves “Does this make sense?” Gather Information Make a plan Anticipate possible solutions Continuously evaluate progress Check results Question sense of solutions

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SMP 2: Reason abstractly and quantitatively Decontextualize Represent as symbols, abstract the situation Contextualize Pause as needed to refer back to situation x x P 5 ½ Mathematical Problem

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SMP 3: Construct viable arguments and critique the reasoning of others Use assumptions, definitions, and previous results Make a conjecture Build a logical progression of statements to explore the conjecture Analyze situations by breaking them into cases Recognize and use counter examples Justify conclusions Respond to arguments Communicate conclusions Distinguish correct logic Explain flaws Ask clarifying questions

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SMP 4: Model with mathematics Images: asiabcs.com, ehow.com, judsonmagnet.org, life123.com, teamuptutors.com, enwikipedia.org, glennsasscer.comhttp://tandrageemaths.wordpress.com Problems in everyday life… Mathematically proficient students make assumptions and approximations to simplify a situation, realizing these may need revision later interpret mathematical results in the context of the situation and reflect on whether they make sense …reasoned using mathematical methods

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SMP 5: Use appropriate tools strategically Proficient students are sufficiently familiar with appropriate tools to decide when each tool is helpful, knowing both the benefit and limitations detect possible errors identify relevant external mathematical resources, and use them to pose or solve problems

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SMP 6: Attend to precision Mathematically proficient students communicate precisely to others use clear definitions state the meaning of the symbols they use specify units of measurement label the axes to clarify correspondence with problem calculate accurately and efficiently express numerical answers with an appropriate degree of precision Comic:

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SMP 7: Look for and make use of structure Mathematically proficient students look closely to discern a pattern or structure step back for an overview and shift perspective see complicated things as single objects, or as composed of several objects

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SMP 8: Look for and express regularity in repeated reasoning Mathematically proficient students notice if calculations are repeated and look both for general methods and for shortcuts maintain oversight of the process while attending to the details, as they work to solve a problem continually evaluate the reasonableness of their intermediate results

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MATHEMATICS CONTENT STANDARDS Making Sense of the CT Mathematics Standards

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Mathematics | Kindergarten In Kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with sets of objects; (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics. (1) Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as = 7 and 7 – 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away. (2) Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as three-dimensional shapes such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes. Each grade level section of the Common Core contains Critical Areas of Focus A description of the key areas where instruction & learning time should be focused. Critical Areas of Focus

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10/12/ Mathematics Common Core Layout

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10/12/ Mathematics Common Core Layout

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10/12/ Mathematics Common Core Layout

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10/12/ Mathematics Common Core Layout

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10/12/201421

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Common Core State Standards K-12 Mathematics Learning Progressions Kindergarten HS Counting and Cardinality Number and Quantity Number and Operations in Base TenThe Number System Number and Operations: Fractions Ratios and Proportional Relationships (6 and 7) Operations and Algebraic ThinkingExpressions and Equations Algebra Functions Geometry Measurement and DataStatistics and Probability Statistics And Probability

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Grade Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K–2 Addition and subtraction, measurement using whole number quantities 3–5 Multiplication and division of whole numbers and fractions 6 Ratios and proportional reasoning; early expressions and equations 7 Ratios and proportional reasoning; arithmetic of rational numbers 8Linear algebra Priorities in Mathematics

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GradeRequired Fluency KAdd/subtract within 5 1Add/subtract within 10 2 Add/subtract within 20 Add/subtract within 100 (pencil and paper) 3 Multiply/divide within 100 Add/subtract within Add/subtract within 1,000,000 5Multi-digit multiplication 6 Multi-digit division Multi-digit decimal operations 7Solve px + q = r, p(x + q) = r 8 Solve simple 2 2 systems by inspection KeyFluencies Key Fluencies

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10/12/ The high school standards specify the mathematics that all students should learn in order to be college and career ready. The standards are not defined by grade levels, rather they are defined by conceptual category. The high school standards also describe additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics. Organizational Notes for High School Standards

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Appendix A in the Common Core shows two paths in course design: Traditional - Algebra, Geometry, Algebra II Integrated - Math I, Math II, Math III

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THE DESIGN PROCESS Making Sense of the CT Mathematics Standards

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Team Structure Grade bands K HS

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Rigorous Curriculum Design Model Providing a frame for district curriculum work Prioritized standards Curriculum Units of study With prioritized and supporting standards Pacing Calendar Unit Planning Organizer

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Process Identified grade band standards as Priority or Supporting – Based on critical areas of focus and overall continuum of learning Considered grade band progression of conceptual understanding and skill acquisition – ALL standards are important – Example: CC.9-12.N.RN.2 CC.9-12.N.RN.1 Aligned K-12 Standards – All teams joined for the continuum gallery walk – Consensus reached on status of standards (priority or supporting)

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Geometry Units of Study Pacing Unit TitlePacingStandards 1. Transformations and the Coordinate Plane 4 weeks G.CO.1, G.CO.4, G.GPE.5 G.CO.2, G.CO.3, G.CO.5 G.SRT.2, G.GPE.4, G.GPE.6, G.GPE.7 2. Congruence, Proof and Constructions 5 weeks G.CO.7, G.CO.8, G.CO.9 G.CO.6, G.CO Polygons 4 weeks G.CO.10, G.CO.11 G.CO Similarity, Proof and Trigonometry 5 weeks G.SRT.5, G.SRT.8 G.MG.3, G.SRT.1, G.SRT.2 G.SRT.3, G.SRT.4, G.SRT.6, G.SRT.7 5. Circles and other Conic Sections 4 weeks G.C.2, G.C.5, G.GPE.1 G.C.1, G.C.3, G.GPE.2, G.GPE.4 6. Extend to Three Dimensions 4 weeks G.GMD.3 G.GMD.1, G.GMD.4, G.MG.1, G.MG.2 7. Applications of Probability 3 weeks S.CP.1, S.CP.3, S.CP.6 S.CP.2, S.CP.4, S.CP.5 S.CP.7

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SDE Unit Planning Organizer C:\Documents and Settings\pneal\Desktop\ALG I -For Web Posting\HS-ALGI-UNIT 1.doc C:\Documents and Settings\pneal\Desktop\ALG I -For Web Posting\HS-ALGI-UNIT 1.doc

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Transitioning to CCSS K-8 Transition Guide HS needs to fully implement in grade 9 during followed by grade 10

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Web Links CCSS link State website

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QUESTIONS

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