1. GRADES K – 2 ATOMIC CONFERENCE NOVEMBER 29, 2011 Kathy St. Onge Ann Spinelli Mary Santilli Marcia Ferreira Making Sense of The CT Mathematics Standards (Common Core State Standards)

2. Intent of the Common Core  Same goals for all students  Coherence  Focus  Clarity, rigor and specificity  Opportunities for broadening the discussion about the teaching and learning of mathematics

3. 45 states have adopted (as of December 2011)

4. CCSS Assessment Projects  SBAC SMARTER Balanced Assessment Consortium  30 states - http://www.k12.wa.us/smarter/ http://www.k12.wa.us/smarter/  PARCC (Partnership for the Assessment of Readiness for College and Careers)  25 states - http://www.achieve.org/PARCChttp://www.achieve.org/PARCC

5. “These Standards are not intended to be new names for old ways of doing business.” CCSSM, p. 5

6. Organization of the CCSS Standards for Mathematical Practice Math Content Standards  Domains  Clusters  Standards

7. Connecting the Practices to the Content  Math content standards describe what students should understand and be able to do.  Math practices describe ways in which students should interact with mathematics.  Curricula, assessment and professional development should be focused on connecting the mathematical practices and the content standards. (CCSS p. 8)

8. Standards for Mathematical Practices  8 Mathematical Practices  Related to the NCTM Process Standards (2000) and the Strands of Mathematical Proficiency (Adding It Up, 2001)

9.  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

10. “…describe the varieties of expertise that mathematics educators at all levels should seek to develop in their students.” Standards for Mathematical Practice

11. Mathematically Proficient Students Will… Adapted from Inside Mathematics

12. Standards for Mathematical Practice 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 1.Make sense of problems and persevere in solving them 6. Attend to precision Overarching habits of mind of a productive mathematical thinker. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning 4. Model with mathematics 5. Use appropriate tools strategically Reasoning and explaining Modeling and using tools Seeing structure and generalizing

13. 1. Make Sense of Problems and Persevere in Solving Them Engage in problem solving on a regular basis Foster a “productive disposition” - build success early on Involve students in sharing solutions, methods, and reasoning Frame the class environment to encourage student interaction and conversation – math discourse Allow students to “struggle” with the mathematical tasks – avoid rescuing too soon to diminish the cognitive load Emphasize equivalent representations of a given situation or mathematical relationship

14. 2. Reason Abstractly and Quantitatively Teach concepts in context – symbols have meaning Base instruction on making sense and select practice that involves the application of concepts being learned Emphasize reasoning as opposed to only learning procedures Allow students to develop a representation of mathematical problems on a regular basis Mathematical Problem x x 4 Decontextualize Represent as symbols, abstraction Refer back to the situation Contextualize 5 2 =?

15. 3. Construct Viable Arguments and Critique the Reasoning of Others Encourage interaction and conversation on a regular basis Use problem-based activities – rich tasks Practice the language of “argument,” conjecture, and discourse while students are engaged in mathematical tasks Facilitate student discourse – “talk moves” * Encourage taking risks, defending solutions Have students present solutions and ideas on a regular basis *Classroom Discussions: Using Math Talk to Help Students Learn, 2 nd edition, Grades K-6 by Suzanne Chapin, Catherine O’Connor and Nancy Anderson, Math Solutions, 2009.

16. 4. Model with Mathematics Use physical objects, drawings and physical gestures to represent math situations Encourage student verbal descriptions Encourage representing the same situation in different ways Guide students to see similarities in different ways to represent the same situations Problems in everyday life…

17. 5. Use Appropriate Tools Strategically Provide mathematical tools in the classroom Ensure that students know how to use the appropriate tools effectively Discuss criteria to help make a decision as to when to use a mathematical tool Encourage students use their rationale for using a tool in their explanation of their solution

18. 6. Attend to Precision Make mathematical tools available in the classroom Display and provide instruction on mathematical vocabulary – interactive word wall Hold students accountable for using vocabulary in discussion and written explanations Embed instruction about math symbols (7, +, =, >,  ) Discuss answers in terms of the context of the problems to give students experience with the idea of a “reasonable” answer Review processes for computational skills; include error analysis and feedback to develop accuracy and proficiency

19. 7. Look for and Make Use of Structure Encourage students to always look for patterns to help develop conceptual understanding Provide opportunities for students to generalize Use mental math to practice patterns in our number system Provide opportunities to work on tasks that generate data that can be used to develop a generalization Foster a class environment that values and encourages student reasoning as opposed to teacher “telling”

20. 8. Look for and Express Regularity in Repeated Reasoning Encourage students to always look for patterns or an opportunity to generalize about computational skills Use mental math to practice patterns in our number system that can be used to develop more efficient computation methods Incorporate lessons and activities that use pattern or structure to help develop conceptual understanding Foster a class environment that values and encourages student reasoning as opposed to teacher “telling” what to notice or how to do a skill The Leadership and Learning Center Seminar- “Digging Deeper into the Common Core State Standards”

21. Incorporating the Practice Standards…  Examine the math problems.  Think about the Mathematical Practices that students would engage in when solving the problems.  Share with someone next to you your reasoning.

22. Summary All Standards for Mathematical Practice will not be demonstrated with every math exercise given, but multiple standards should be evident in every mathematics lesson.

23. Common Core State Standards K-12 Mathematics Learning Progressions Kindergarten 12345678HS 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 http://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspx?page=3&TopicRelationID=1704&ContentID=83475&Content=102764

24. 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 Priorities in Mathematics http://commoncoretools.wordpress.com/

25. 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 1000 4Add/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 http://commoncoretools.wordpress.com/

26. K-2 Content Standards

27. Grade Level Overview

28. 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 5 + 2 = 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. A description of the key areas where instruction & learning time should be focused. Critical Areas of Focus

29. Format of Pre-K-8 Standards Standard 2.NBT.1 (code) Domain Grade Level 2.NBT (code) Cluster

30. Process Used to Develop Framework for District Curriculum Work Grade Level Band Teams K – 2 3 – 5 6 – 8 High School

31. Prioritized Standards Vertical Alignment Named Units & Assigned Standards Developed Unit Pacing Plan Created Sample Assessment Items Developed a Suggested Sequence of Instruction A Frame for District Curriculum Work

32. ALL Standards are Important KINDERGARTEN Counting and Cardinality Know number names and the count sequence. 1. Count to 100 by ones and by tens. 2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). 3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). SECOND GRADE Number and Operations in Base Ten Understand place value. 1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. 2. Count within 1000; skip-count by 5s, 10s, and 100s. 3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

33. Kindergarten Units Counting and Matching Numerals 0-5 with Comparing Counting and Matching Numerals 6- 10 with Comparing Counting and Matching Numerals 11-20 Teen Numbers (11-19) & Counting to 100 Fluency with Addition & Subtraction within 5 Exploring Addition & Subtraction within 10 Identify & Describe 2D & 3D Shapes Compare, Analyze and Compose 2D & 3D Shapes Measurement by Direct Comparison Units of Study Priority Standards Supporting Standards Critical Areas of Focus: Key areas where instruction & learning time should be focused.

34. FIRST GRADE Suggested Unit SequencePacing 1 Fluency with Addition & Subtraction within 105 weeks 2 Exploring Addition & Subtraction within 204 weeks 3 Counting & Place Value5 weeks 4 Exploring Addition and Subtraction within 1005 weeks 5 Defining Attributes of 2D & 3D Shapes2 weeks 6 Partitioning Circles & Rectangles2 weeks 7 Measuring Length with Non-Standard Units2 weeks 8 Time to the Hour and Half-Hour2 weeks Mapped out year using school calendars Developmentally appropriate Critical Areas of Focus for grade level Time to Process & Practice Suggested Pacing Timeframe

35. Unit Planning Organizer Development of Unit Planning Organizer (in process) Mathematical Practices Domain & Standards Overview Priority & Supporting CCSS Explanations & Examples Concepts Students Need to Know Skills Students Need to Be Able to Do Bloom’s Taxonomy Levels Unit Assessment Items

36. Transition Guide

37. Transition Guide: Displaced Grade Level Concepts

38. Assessment Test Mode: Administer one on one Rote Count Teacher: Count out loud starting at 1 and count as high as you can. Record highest number student accurately counts to. Ex: Child counts from 1-15 accurately, then skips 16. Stop student and record last correct number stated. Grade Level Band Teams Assessment Items Based on CCSS Unit Planning Organizer Items for use during instruction when appropriate Kindergarten Assessment Items Unit 1 - Counting and Matching Numerals 0 – 5 with Comparing

39. Match Numerals Preparation: In advance, teacher puts out groups of objects (ex: counters, unifix cubes or bears) and numeral cards 0-10. Objects should be arranged in groups of 3, 5, 8 and 10. Teacher: Give students the shuffled set of numeral cards. Count each group. Put the matching numeral card next to each set. Observe and record (  or - ) if student correctly matches all four sets. Unit 2 - Counting and Matching Numerals 6 – 10 with Comparing Kindergarten Assessment Items

40. Unit 4 - Fluency with Addition and Subtraction within 5 There are 5 apples in a bowl. Some apples are red. Some apples are green. How many of each color apple could be in the bowl? ___ red apples ___ green apples Find a different answer. ___ red apples ___ green apples

41. Constructed Response Write a number sentence and solve the problem. Use manipulatives (base-ten blocks, hundreds chart, number lines) or a drawing to show how to solve this problem. Grade 1 - Assessment Items Unit 4 - Exploring Addition and Subtraction within 100 Mrs. Jones needs 42 cupcakes for the class picnic. She has 32 cupcakes. How many more cupcakes does she need to buy? Mrs. Jones needs 42 cupcakes for the class picnic. She has 32 cupcakes. How many more cupcakes does she need to buy? This is how Joe found the answer to 29 + 30 + 1 29 + 30 + 1 = 30 + 30 = 60 What did Joe do to solve the problem? This is how Joe found the answer to 29 + 30 + 1 29 + 30 + 1 = 30 + 30 = 60 What did Joe do to solve the problem?

42. Multiple Choice Grade 2 - Assessment Items Unit 2 - Place Value to 1,000 Circle all the statements that are equal to this number. 823 a) 8 hundreds and 23 tens b) 823 ones c) 7 hundreds, 12 tens and 3 ones d) 82 tens and 3 ones e) 8 hundreds and 23 ones f) 7 hundreds and 23 tens What is another way to show 729? 700 + 2 + 90 700 + 20 + 9 70 + 200 + 9 7 + 20 + 900

43. Constructed Response Grade 2 - Assessment Items Unit 3 - Fluency with Addition and Subtraction within 100 Solve the problem. 54 - 29 Show or explain how to find the answer two different ways. Write an equation for this problem. Solve the equation to find the answer. The teacher is 70 inches tall. The student is 47 inches tall. How much taller is the teacher than the student?

44. QUESTIONS