Welcome teachers from CFN 609!

1. Please sit with your team ensuring there is representation of 3-5 in your triad. As you are waiting scan the room and posters. Contribute to any of the posters using a post it or with a marker. Welcome teachers from CFN 609!

2. Constructing a viable unit plan in MathematicsHow can we approach instruction from the Instructional Shifts, the Mathematical Practices and Common Core Learning Standards using GoMath as our main resource and support? 3-5 Session 1 November 22, 2013 Presented and compiled by: Karen Cardinali, Achievement Coach CFN 609 kcardinali@schools.nyc.gov

3. Welcome • Instructional shifts: • What are the shifts and how do tare we addressing them in out unit plan and instruction? • Standards for Mathematical Practice: • How do they develop across grades? • Unpacking content standards, strategies and models: Operations and Algebraic Thinking Domain: • What will do teachers and students need to know and be able to do and how will teachers help them students get there? • Performance based assessment: • Is there evidence of the Shifts, Practices and Standards on the PBA that are being developedin the unit? • Lunch • Enjoy and rejuvenate • Unit planning: • What is the background work that goes into planning for a coherent unit of study? • Action Plan/Reflections/Bridge to Practice How will this information be shared back at school incorporated into your practice and how will we prepare for our next session together? AGENDA Compiled by Karen Cardinali

4. How can we approach instruction from the shifts, the practices and standards using GoMath as our main resource and support? What mathematics will my students encounter during a specific unit of study and what strategies, models and resources will help them develop their understanding during this unit? Where do these experiences and practices fit in my students’ progression of learning? How can we create a viable unit plan that emphasizes the depth and intent of the Common Core Learning Standards? Guiding Questions li

5. PARKING LOT… For the successes, challenges and questions that have arisen as a result of delivering instruction using the GoMath Program and at what levels these can be addressed.(Norms)(Reflections)

6. In order to prepare students for life in the twenty- first century, the focus of education needs to be on learning to learn, create, innovate, communicate, and discern. In order for teachers to facilitate robust learning habits in their students they need to practice these learning habits themselves. To upgrade instruction we need to focus on the underpinning concepts in a domain as well as attend to the development of skill within that domain. Therefore, teachers need to have deep and flexible knowledge about the content they teach and about how people learn that content. Agents of Change: West and Cameron

7. How do we guide and measure our work? Compiled by Karen Cardinali

8. The CCLS requires 3 Instructional Shifts in Mathematics Revised from a similar doc on Engageny

9. SHIFT #1: Focus

10. Teaching math in a more coherent way. • Allowing time for reasoning practice and to integrate each new idea into a growing knowledge structure. • Spending more time, more effort, more energy with higher expectations around fewer ideas. • As teachers we need to take advantage of time. Focus leads to: • Strong foundational knowledge. • Deep conceptual understanding of core concepts. • Ability to transfer understanding across concepts and grades. Focus means: Compiled by Karen Cardinali

11. Shift #2: Coherence: Think across grades, and link to major topics within grades. Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years. Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. Math instruction is not a checklist of topics to cover but a set of interrelated and powerful ideas that connect to each other. What is initially complex becomes more simple and elegant over time. Compiled by Karen Cardinali

12. Demonstration of coherence: over the course of three years students build on previous knowledge 4.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Grade 4 5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Grade 5 6.NS. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Grade 6 Compiled by Karen Cardinali

13. http://vimeo.com/44524812 While listening: Add to your definition of Focus, Coherence and Rigor. (Deep understanding, Fluency and Application). Jot down any salient points or examples that have deepened your understanding about how to incorporate the shifts into your practice. After video: Discuss with schoolmates the challenges/opportunities of incorporating the shifts and how the shifts reveal themselves in our lessons and assessments Video: Jason Zimba, co-founder, Student Achievement Partners and writer, Common Core State Standards for mathematics discusses the shift of Rigor Compiled by Karen Cardinali

14. Mark each equation true or false: 8x 9=80-9 8 x 3 = 4 x 6 49/7=56/8 • Compute each of the following: 357 + 17,999 +1 357 +17,999 37 x 25 x 4 1001 x 20 Examples of Fluency Compiled by Karen Cardinali

15. Write 4 fractions that are all equal to 5. • Which number is least and which is greatest? How do you know? ¾,2,4/4,3/5 • Amber didn’t know what 7 X 5 equals, but she knew 5 X 5= 25 and 2 x 5 = 10. Use drawings, words and/or equations to explain why Amber can add 25 and 10 to find what 7 X 5 equals. Examples of Deep/Conceptual understanding: Compiled by Karen Cardinali

16. 9 Large trucks are carrying1/2 ton of lumber each. 7 small trucks are carrying ¼ ton of lumber each. How many total tons are being carried by all of the trucks? • A student performs the following steps when solving an equation:… … Is the solution correct? If yes, explain why. If no, explain what was wrong with the student’s reasoning. Examples of Application Compiled by Karen Cardinali

17. Where and how does the program support shifting instruction to meet the demands of the CCLS? • Focus • Coherence • Rigor: • Deep understanding • Fluency • Application How might we compliment and enhance? GoMath! Compiled by Karen Cardinali

18. From the video: “Rigor is about creating an environment where each student is expected to learn at high levels, each student is supported so he can learn at high levels and each student demonstrates learning at high levels”. How will we create this environment? Creating an Environment of Rigor Compiled by Karen Cardinali

19. Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning Standards for Mathematical Practice

20. Triads count off by 8. • Read the practice as per your grade level (2 minutes). • Talk to one another, unpack the practice. Starting with Grade 3, what is the expectation for this practice and how can teachers support student development? How does this expectation build from Grade to Grade? • Create a poster to help your triad present the practice. Be prepared to share out with the group. What do these practices look like on your grade? Compiled by Karen Cardinali

21. Before leaving the room, please take your things and move to your grade level table. Thank you and enjoy a short break, we will start back promptly at ______ 10 Minute Break Compiled by Karen Cardinali

22. Take 5-10 minutes to individually read over the highlighted content standards that are associated with the chapter your grade level will be planning today. (Read at least the NF.1 and NF.2 standards) Jot down your thoughts on the problems, strategies and models you might use or see when teaching towards these standards. Which standards do you need more support with? Standards addressed in the chapter: Stop and Jot Compiled by Karen Cardinali

23. 3- Read pgs: 3-5 4- Read pgs: 6-9 (stop at decimals) 5-Read pgs: 11(-14) ___________________ Use the talking points to guide your discussion. • Be prepared to present to the group the mathematics students at your grade level will be experiencing with fractions and the models to help with the development of that understanding. Progressions Number and Operations- Fractions, 3-5 Compiled by Karen Cardinali

24. What is the mathematics students will grapple with in Grade 3 when learning about fractions? What are the models student are using to begin to understand fractional parts? Use these to demonstrate the meaning of ¾. What is the relationship between unit fractions and the number 1? How are third graders beginning to reason about equivalent fractions? Grade 3 Talking points Compiled by Karen Cardinali

25. : • What is the mathematics students will grapple with in grade 4 when learning about fractions? • How can we use visual models such as a number line and area model to support students developing understanding of equivalent fractions? • Use an area model and number line to show that 2/3 =4x2/4x3. • How is the meaning of addition the same for both fractions and whole numbers. Can you use a model to explain? Grade 4 Talking Points… Compiled by Karen Cardinali

26. What is the mathematics students will grapple with in grade 5 while learning about fractions? • Describe a visual model that can support the work of finding like denominators when adding fractions with unlike denominators. • How can estimation help students with the reasonableness of their answers? • Explain how 5/3 =1/3 of 5. Can you use a visual model to explain your thinking? c/ b x d? Grade 5 talking points Compiled by Karen Cardinali

27. How does the mathematics develop across grades? (Share out Posters grade 3-5) After each grade shares: What do you think students might struggle with? What is your comfort level in that area? What are the important pre-requisites for each grade? Which models are developed and what is the trajectory from concrete to abstract? Whole Group Process Compiled by Karen Cardinali

28. Take 5-10 minutes to re-visit what you jotted down How has your thinking about these standards been enhanced by reading the Progressions documents? Which standards do you need more support with? Re-Visit Stop and Jot Compiled by Karen Cardinali

29. You will find unpacking standards documents to support teachers in their understanding of the common core and essential standards. The unpacking documents demonstrate at a granular level the knowledge and skills students are expected to master at a particular grade. http://www.dpi.state.nc.us/acre/standards/common-core-tools/ MATH “UNPACKED” STANDARDSPublic Schools of North Carolina Compiled by Karen Cardinali

30. Work through the PBA. Think about the strategies you might see students using. Scan the end of chapter tests. Begin to think about: • Which standards are being addressed? • In what way do the assessments address the shift of Rigor? Chapter tests and Performance Based Assessments Compiled by Karen Cardinali

31. Enjoy your Lunch We will start back in one hour promptly Compiled by Karen Cardinali

32. Planning? Structures? Challenges? Solutions? Units of study/Chapters Compiled by Karen Cardinali

33. Created by Karen Cardinali

34. Created by Karen Cardinali

35. Meet in grade level groups to begin to plan the unit of study using the template Grade 3: Chapter 8 Grade 4: Chapter 6 Grade 5: Chapter 6 Unit Planning Compiled by Karen Cardinali

36. Were the shifts acknowledged throughout the unit? Were there opportunities for Rigor in the unit/lessons as a whole? • How well did you find the standards addressed and the models used to support student understanding? • On a scale of 1-10 (1 being least)what is your comfort level with the content and underpinnings of this chapter to move forward with your own lesson planning? • Reflect on the process. Debrief Compiled by Karen Cardinali

37. How will you relay the information to the principal? How will you share this information with your grade level teacher team? Which aspects of today’s workshop resonated with you as something that could support your team in providing coherent instruction across the classrooms? ACTION PLAN Compiled by Karen Cardinali

38. Choose one “GoMath” inspired lesson from the unit of study that was planned today (or current chapter-Grade 3) and plan it in detail. -Bring in 5 copies of the lesson plan with the task or samples of student work that will be used to assess understanding. -If the lesson was taught, kindly prepare to reflect on how the plan impacted the lesson. ***Please bring a copy of the unit plan that you worked on and continued with your team. You will not be judged on your lesson or unit plan, it is purely for a reflective and collaborative purpose Bridge to PracticeBetween now and session 2 on January 13, 2014, Please prepare the following Compiled by Karen Cardinali

39. Please take 10 minutes to reflect on your learning today. • What questions do you have about anything we discussed today (Shifts, standards, unit planning…)? • What ideas resonated with you (Shifts, standards, unit planning…)? Please be specific. • What will you bring back to your classroom to use? How will you use it? Please be specific. • Optional: Name and School __________________________________ Reflections School____ Compiled by Karen Cardinali

40. www.604and609.org; Network website www.engageny.org: State curriculum, materials and updates www.achievethecore.org www.illustrativemathematics.org; Sample problems for each standard and links to other helpful websites http://ime.math.arizona.edu/progressions/: Progressions Documents www.commoncoretools.me www.corestandards.org http://www.dpi.state.nc.us/acre/standards/common-core-tools/ http://parcconline.org/parcc-content-frameworksMajor, supporting and additional work of the grade http://schools.nyc.gov/Academics/CommonCoreLibraryDOE website, links, resources, Program specific information http://www.p12.nysed.gov/assessment/math/ccmath/parccmcf.pdf http://vimeo.com/44524812: Video clip on the instructional Shifts www.Thinkcentral.com : Online Resource for GoMath http://www.ode.state.or.us/wma/teachlearn/commoncore/math-practice-posters-in-student-language.pdf MP Posters Important Links Compiled by Karen Cardinali

41. Enjoy your afternoon. Thank you for your attention and participation. CFN 609 Compiled by Karen Cardinali