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Shelbi Cole – CSDE Sharon Heyman- UCONN Peggy Neal-CREC

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

2 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

3 Mathematics Common Core Document
The Common Core State Standards document begins with an introduction that captures the authors’ motivation and focus for building a common vision for understanding mathematics. The document itself includes an Introduction, The 8 Standards for mathematical Practice, the Content Standards for each grade level (K-8) and the high school standards by standard area (Number and uantity, Algebra, Functions, Modeling, Geometry, Statistics and Probability) At the end of the introduction is a guide entitled, “How to read the grade level standards.” 4/6/2017 3

Making Sense of the CT Mathematics Standards STANDARDS FOR MATHEMATICAL PRACTICE

5 Standards for Mathematical Practice
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 21st 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. Supporting the development of expertise in students of all ages that is described in these eight practices should be as much a goal of the mathematics curriculum as the learning of specific content.

6 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

7 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

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

9 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 Distinguish correct logic Communicate conclusions Explain flaws Justify conclusions Ask clarifying questions Respond to arguments

10 SMP 4: Model with mathematics
Problems in everyday life… …reasoned using mathematical methods 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 Images:,,,,,,

11 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

12 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:

13 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

14 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

15 Mathematics content Standards
Making Sense of the CT Mathematics Standards Mathematics content Standards

16 Critical Areas of Focus
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. 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. East Hartford Public Schools slide

17 Mathematics Common Core Layout
Notice the terminology used in the Common Core State Standards document. 4/6/2017 17

18 Mathematics Common Core Layout
In grades Kindergarten through five - NUMBER is grouped into four domains (Counting and Cardinality; Operations and Algebraic Thinking; Number Operations in Base Ten; and, Number Operations – Fractions) while - in grades six through eight – NUMBER is grouped into two different domains (Ratios and Proportional Relationships; and, The Number System). These Domains mark the beginning and end of a learning progression with NUMBER. Therefore the diverse category titles are designed to reflect a clear, specific, and more narrow focus on the content. An abbreviation system has been developed that uses the grade level and content domain initials. 4/6/2017 18

19 Mathematics Common Core Layout
4/6/2017 19

20 Mathematics Common Core Layout
These standard bullets are also grouped into “Clusters” based on related concepts. In this slide, “Use place value understanding and properties of operations to perform multi-digit arithmetic”, is the concept that joins standards bullets 1, 2, and 3, into a “Cluster”. 4/6/2017 20

21 The third and final major component is a list of each Domain with the related clusters and standards for that grade level designed to describe all the student learning objectives for the grade. (Pause) 4/6/2017 21

22 Common Core State Standards K-12 Mathematics Learning Progressions
Kindergarten 1 2 3 4 5 6 7 8 HS Counting and Cardinality Number and Quantity Number and Operations in Base Ten The Number System Number and Operations: Fractions Ratios and Proportional Relationships (6 and 7) Operations and Algebraic Thinking Expressions and Equations Algebra Functions Geometry Measurement and Data Statistics and Probability Statistics And Probability

23 Priorities in Mathematics
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 8 Linear algebra

24 Key Fluencies K Add/subtract within 5 1 Add/subtract within 10 2
Grade Required Fluency K Add/subtract within 5 1 Add/subtract within 10 2 Add/subtract within 20 Add/subtract within 100 (pencil and paper) 3 Multiply/divide within 100 Add/subtract within 1000 4 Add/subtract within 1,000,000 5 Multi-digit multiplication 6 Multi-digit division Multi-digit decimal operations 7 Solve px + q = r, p(x + q) = r 8 Solve simple 22 systems by inspection

25 Organizational Notes for High School Standards
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 (page 57) 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. 4/6/2017 25

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

27 Making Sense of the CT Mathematics Standards

28 Team Structure Grade bands K-2 3-5 6-8 HS

29 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

30 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 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) Read example aloud

31 Geometry Units of Study Pacing
Unit Title Pacing Standards 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.12 3. Polygons G.CO.10, G.CO.11 G.CO.13 4. Similarity, Proof and Trigonometry 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 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 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

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

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

34 Web Links CCSS link State website


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