1. 2005 Connecticut Mathematics Curriculum Framework: Building Understanding Across the Grades November 9, 2005

2. Your Presenters… Roseanne Hornyak Consultant Connecticut Academy for Education rhornyak@ctacad.org **** Marlene A. Megos 9 - 12Mathematics Consultant Connecticut State Department of Education marlene.megos@po.state.ct.us **** Charlene Tate Nichols PK – 8 Mathematics Consultant Connecticut State Department of Education charlene.tate.nichols@po.state.ct.us

3. By the end we hope you: become familiar with the 2005 Connecticut Mathematics Curriculum Framework; become familiar with the 2005 Connecticut Mathematics Curriculum Framework; understand how certain concepts build across the grades; and understand how certain concepts build across the grades; and learn how the framework can be implemented through effective instruction. learn how the framework can be implemented through effective instruction.

4. The 2005 Connecticut Mathematics Curriculum Framework A two-fold purpose… To articulate the mathematical understandings that all Connecticut students should have. To articulate the mathematical understandings that all Connecticut students should have. To influence the way mathematics is taught and assessed. To influence the way mathematics is taught and assessed.

5. The 2005 Connecticut Mathematics Curriculum Framework Supporting Documents 1998 Framework 1998 Framework NCTM Principles and Standards for School Mathematics NCTM Principles and Standards for School Mathematics CSDE Goals 2000 Curriculum CSDE Goals 2000 Curriculum

6. The 2005 Connecticut Mathematics Curriculum Framework Supporting Documents NAEP Standards NAEP Standards Third International Mathematics and Science Study (TIMSS) – Third International Mathematics and Science Study (TIMSS) – Mile wide/Inch Deep Mile wide/Inch Deep Implementation of Rich Problems Implementation of Rich Problems Program for International Student Assessment (PISA) Program for International Student Assessment (PISA) Relevant resources related to content Relevant resources related to content

7. What’s New? Grade by grade concept development Grade by grade concept development Pre-Kindergarten – Grade 12 Pre-Kindergarten – Grade 12 Core and extended high school standards Core and extended high school standards

8. 1998/2005 Mathematics Frameworks Crosswalk (p. 4) 19982005 8: Patterns 9: Algebra and Functions 1: Algebraic Reasoning: Patterns and Functions 1: Number Sense 2: Operations 3: Estimation and Approximation 4: Ratio, Proportion and Percent 2: Numerical and Proportional Reasoning 5: Measurement 6: Spatial Relationships and Geometry 3: Geometry and Measurement 7: Probability and Statistics 10: Discrete Mathematics 4: Working with Data

9. Organization of Framework Consists of four Content Standards with guiding questions: (p. 5) 1. Algebraic Reasoning: Patterns and Functions – Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? 2. Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies. How are quantitative relationships represented by numbers?

10. Organization of Framework Consists of four Content Standards with guiding questions: 3. Geometry and Measurement – Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. How do geometric relationships and measurements help us to solve problems and make sense of our world? 4. Working with Data: Probability and Statistics – Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. How can collecting, organizing and displaying data help us analyze information and make reasonable and informed decisions?

11. 2005 Mathematics Framework - Matrix Students should… Pre-KKindergartenGrade 1Grade 2 1.1 Understand and describe patterns and functional relationships. a. Sort and classify objects by an attribute. b. Describe and extend patterns using the attributes of various objects. a. Sort and classify objects using attributes. b. Identify a pattern and describe the rule using the physical attributes or position of objects in a sequence. a. Examine attributes of objects and describe the relationships. a. Describe and extend patterns. b. Analyze change in terms of quantity and quality using patterns. 1.2 Represent and analyze quantitative relationships in a variety of ways. a. Represent the result of counting, combining and separating sets of objects using number sentences. a. Represent real-life situations using number sentences. 1.3 Use operations, properties, and algebraic symbols to determine equivalence and solve problems. a. Identify quantities as equivalent or non- equivalent. a. Represent quantities that have the same value with an equal sign.

12. Framework Companion Document The Content Standards provide the foundation for all grades Pre-K to 12. The Content Standards provide the foundation for all grades Pre-K to 12. The Performance Standards are developmentally sequenced grade level expectations. The Performance Standards are developmentally sequenced grade level expectations. The Expected Performances define The Expected Performances define what students should be able to do what students should be able to do related to the Performance related to the Performance Standards & provide a basis Standards & provide a basis for CMT/CAPT for CMT/CAPT

13. Kindergarten ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies. How do patterns and functions help us describe data and physical phenomena and solve a variety of problems? Students should… Performance StandardsExpected Performances 1.1 Understand and describe patterns and functional relationships. a. Sort and classify objects using attributes. (1) Sort and classify objects by size, shape, color, texture, use, position and orientation and describe the reason for the action. b. Identify a pattern and describe the rule using the physical attributes or position of objects in a sequence. (1) Recognize, copy and extend patterns of sounds, colors, shapes, textures and numbers in a variety of contexts and describe the rule of the pattern. (2) Make comparisons and describe qualitative and quantitative changes of a given pattern (more, less, bigger, smaller, longer, one more, one less). (p. 10)

14. (p. 8)

15. Framework Coding A complete code for a performance expectation includes 5 characters. 2:1.3a (1) refers to: 2 - Grade 2 1.3 - Algebraic Reasoning content standard supportive concept 3 a - performance standard a (1) – expected performance 1 1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems. a. Represent quantities that have the same value with an equal sign. (1) Demonstrate understanding of the = sign as an equality symbol. Coding (p. 7), Actual Standard (p. 12)

16. Using the 2005 Mathematics Framework Progressive development of essential concepts and skills Progressive development of essential concepts and skills Deep conceptual understanding facilitated through emphasis on the NCTM Process Standards: Deep conceptual understanding facilitated through emphasis on the NCTM Process Standards: Problem solving Problem solving Reasoning and proof Reasoning and proof Communication Communication Connections Connections Representation. Representation.

17. Using the Mathematics Framework in Your District… CSDE CMT/CAPT Assessment of selected concepts and skills in Grades 3-8 and 10. DISTRICT Curriculum, Instruction and Assessment Guidelines STUDENT LEARNING CSDE FRAMEWORK Guide for mathematics content and instruction in grades PreK- 12. DISTRICT Curriculum, Instruction and Assessment Guidelines STUDENT LEARNING CSDE FRAMEWORK CSDE CMT/CAPT

18. Connecting the Framework to the CMT AND CAPT The Framework outlines: what concepts and skills should be taught what concepts and skills should be taught how and to what extent the concepts and skills should be taught at the grade level indicated how and to what extent the concepts and skills should be taught at the grade level indicated

19. Connecting the Framework to the CMT and CAPT The CMT and CAPT assess selected skills and concepts at the grade levels indicated The CMT and CAPT assess selected skills and concepts at the grade levels indicated The mathematics concepts and skills assessed on the CMT and CAPT reflect what students have learned-not just at the grade levels when the tests are administered The mathematics concepts and skills assessed on the CMT and CAPT reflect what students have learned-not just at the grade levels when the tests are administered

20. CMT Changes Generation 4 Testing for each grade, 3-8. Spring testing beginning 2006. There are no separate answer booklets. Students can underline and highlight in booklets. There are no grid-in items for Grades 3 and 4. Grade-appropriate rulers are provided. A formula sheet is provided for Grade 8, other grades should know formulae and conversions. Number of multiple-choice items decreases while constructed- response items increases as the grade level increases. There will be 2 strand 25 questions at each grade level. Both questions will be on the same session. Care has been taken to balance the work required on that session. There will be 2 strand 25 questions at each grade level. Both questions will be on the same session. Care has been taken to balance the work required on that session.

21. Reporting Format 25 content strands organized by the four standards: numerical and proportional reasoning; geometry and measurement; working with data: probability and statistics; and algebraic reasoning: patterns and functions. The CMT scores will continue to be reported by strand. CMT Handbook (p. 1)

22. Handbook Available on the CSDE website, on CD and in limited quantity in hard copy. Will be periodically updated. Information is organized by grade level. Vocabulary lists are cumulative. New vocabulary at a grade level is in bold print. CMT Handbook (p. 1)

23. Rulers For Use During The Connecticut Mastery Test CMT Handbook (p. 2) Rulers for Grades 3 & 4 Ruler for Grades 5, 6, 7 & 8

24. Connecting CMT and CAPT Grade 8 Formula Sheet CMT Handbook (p. 3)

25. Preparing students for the Connecticut Mastery Test (CMT ) should be an ongoing process. A sound K-8 mathematics program embeds these strategies into all instructional planning. Strategy 1: Asking “Why?” Strategy 2: Embed In Context, Present As A Problem CMT Handbook (p. 10)

26. Sample Lessons and Activities by Standard and Grade Level (p. 15) NUMERICAL and PROPORTIONAL REASONING PreK-2 Page Let's Count to 10 17 Do It with Dominoes 17 How Many More Fish? 17 Grades 3-5 Estimation 17 Fun With Estimation 17 Parking at the Mall 17 Grades 6-8 A Conceptual Model for Solving Percent Problems (5-8) 17 Shops at the Mall 17 Developing Number Sense 18

27. Sample Lesson and Activity Descriptions NUMERICAL AND PROPORTIONAL REASONING Let's Count to 10 – Grades PreK-2 – http://illuminations.nctm.org/index_o.aspx?id=147 Do It with Dominoes – Grades PreK-2 – http://illuminations.nctm.org/index_o.aspx?id=47 CMT Handbook p. 17

28. Mathematics Grade 3 Vocabulary List CMT Handbook (p. 40) This list, while not exhaustive, includes vocabulary with which all teachers and students should be familiar.

29. Mathematics Grade 3 Content CMT Handbook (p. 31)

30. CAPT Mathematics Generation 3 Direct alignment between Framework Expected Performances and CAPT Items Direct alignment between Framework Expected Performances and CAPT Items Solving Problems in Context Solving Problems in Context Reported by the 4 Content Standards Reported by the 4 Content Standards Categorized by the Components of the Standard { 1.1, 1.2, 1.3, 2.1, 2.2,…} Categorized by the Components of the Standard { 1.1, 1.2, 1.3, 2.1, 2.2,…}

31. CAPT Mathematics Generation 3 Formula Sheet Formula Sheet Handbook out “early” next year Handbook out “early” next year 12 points per content standard 12 points per content standard 2 open ended 2 open ended 6 grid ins 6 grid ins

32. Scavenger Hunt Work with a partner with expertise at a different grade level to “hunt” for the answers.

33. Algebraic Reasoning: Patterns and Functions Following the Developmental Path

34. Jigsaw Move to one grade level table to do the given activity: Grade 1 – Follow the Number Roads Grade 3 – The Ups and Downs of Patterns Grade 5 – What’s the Best Deal Grade 7 – Bouncing Tennis Balls Grade 9 – Modeling Orbital Debris, Activity 2 Source: Navigating through Algebra & Illuminations, NCTM

35. Algebraic Reasoning: Patterns and Functions Decide what students have to know & do to have success with the given activity Decide what students have to know & do to have success with the given activity Pick out expected performances In Algebraic Reasoning that apply from the given grade level– chart your 3 main EP’s Pick out expected performances In Algebraic Reasoning that apply from the given grade level– chart your 3 main EP’s Next …

36. Jigsaw Move to mixed groups to: share your activity share your activity share your 3 main Expected Performances; and share your 3 main Expected Performances; and answer the focus question. answer the focus question. How does the development of Algebraic concepts build through the grades?

37. Integrating the Standards Work with a team with varied grade level experiences. Activities: Grade 1- Find the Picture Grade 7 – Land Use Project What instruction would one have to do in order to lead up to these activities? What strategies would you use? What expected performances are assessed through the use of the performance tasks?

38. Using the Mathematics Framework in Your District… What will YOU do?

39. Moving On From Here… Ideas, questions, comments?

40. For more information… CSDE Mathematics Page - http://www.state.ct.us/sde/dtl/curriculum/currm ath.htm CSDE Mathematics Page - http://www.state.ct.us/sde/dtl/curriculum/currm ath.htm http://www.state.ct.us/sde/dtl/curriculum/currm ath.htm http://www.state.ct.us/sde/dtl/curriculum/currm ath.htm Implementing the Standards - http://illuminations.nctm.org/index.asp Implementing the Standards - http://illuminations.nctm.org/index.asp http://illuminations.nctm.org/index.asp Project Interactive - http://www.shodor.org/interactivate/index.html Project Interactive - http://www.shodor.org/interactivate/index.html http://www.shodor.org/interactivate/index.html Performance Assessments – http://ctcurriculum.org/ Performance Assessments – http://ctcurriculum.org/ http://ctcurriculum.org/

41. Thanks and have a great day! Roseanne Hornyak rhornyak@ctacad.org **** Marlene A. Megos marlene.megos@po.state.ct.us **** Charlene Tate Nichols charlene.tate.nichols@po.state.ct.us