1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Application and Concept Development in Practice

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives Revisit Module 1 in order to further examine the lesson components of Application Problems and Concept Development in preparation to: Model, teach, and practice the instructional routines that will support implementation of A Story of Units. Differentiate according to the needs of diverse learners and varied student populations in any given district, school, or classroom. 2

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 3

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Application Problems and Concept Development From our previous sessions, what do you recall about the role of Application Problems and Concept Development in A Story of Units? 4

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Application Problems 5 Application involves using relevant conceptual understandings and appropriate strategies even when not prompted to do so. Time allotted to application varies, but is commonly 10-20 minutes of the lesson. The Read, Draw, Write (RDW) process is modeled and encouraged through daily problem solving.

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Concept Development 6 Constitutes the major portion of instruction and generally comprises at least 20 minutes of the total lesson time. Builds toward new learning through intentional sequencing within the lesson and across the module. Often utilizes the deliberate progression from concrete to pictorial to abstract, which compliments and supports an increasingly complex understanding of concepts. Accompanied by thoughtfully sequenced problem sets and reproducible student sheets.

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Application Problems and Concept Development: Getting Started “I do my application problems in the morning, as part of my morning work and share them during morning meeting or debrief.” “Hearing about all of the components, I can see how I can incorporate this into my current centers structure.” “Watching students complete the application problems can really help me implement the concept development in a way that meet kids where they are.” 7

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Application Problems and Concept Development: Getting Started What solutions can you implement in order to overcome anticipated obstacles? “My math block is only 40 minutes. I want to include application problems. How can I do this?” “I have students with significant cognitive disabilities in my classroom. How can I use the materials to meet these students’ needs as well?” 8

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 9

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Modeling and Practice: Application Problems 10 Materials Space Systems for sharing Time management Beginning of the year

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Modeling and Practice: Application Problems 11 Dora found 5 leaves that blew in through the window. Then she found 2 more leaves that blew in. Draw a picture and use numbers to show how many leaves Dora found in all.

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Modeling and Practice: Application Problems 12 With a partner, choose another Lesson 1 from the set provided and consider the instructional choices you might make. Role play an introduction to the Application Problem based on the lesson you selected.

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Modeling and Practice: Concept Development 13

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Modeling and Practice: Concept Development 14 With a partner, examine the remaining portion of the Concept Development. What choices will you make as you introduce students to A Story of Units?

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Reflection What have you learned by modeling and practice of the Application Problem and Concept Development? 15

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 16 Successful implementation of both Application Problems and Concept Development in A Story of Units requires the support of well-established instructional routines. Carefully introducing students to tools and strategies such as the RDW process at the beginning of the school year is an investment in their success throughout the year.

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 17

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Differentiation in Application Problems and Concept Development 18 Student NeedsSolution to Address the ChallengeMultiple Means of….? Fine motor difficultiesApplication Problem: Use materials and take a picture Representati on English Language Learners Application Problem: Work with a partnerAction & Expression Students struggling with visual focusing Concept Development: Paper or card stock to help focus on embedded numbers Engagement Students who do not have mastery of subitizing Concept Development: “How many did you count? Repeat that total. (Repeat several times, helping them to focus on seeing the quantity.)” Action & Expression Students who do not have consistent 1:1 correspondence Concept Development: “Grab and lift the objects from the carton as you count.” Action & Expression

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Differentiation in Application Problems and Concept Development 19 Chose from the set of Lesson 1 materials provided. With your table, discuss how you might adapt the Application Problem or Concept Development. Develop your own sample dialogue for either the Application Problem or Concept Development, keeping in mind the needs of a specific student population.

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Differentiation in Application Problems and Concept Development What did you learn about differentiating these lesson components? 20

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 21 Multiple means of representation, action and expression, and engagement will support the wide variety of learners in our classrooms and enhance their ability to develop and apply procedural skills and conceptual understanding. As with all the lesson components, teachers should make instructional choices that are best suited to the needs of the learners they serve, using sample vignettes and suggested tools as models rather than mandates.

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Reflection on Preparation and Implementation Take 2 minutes to reflect on what you have learned about using Application Problems and Concept Development to meet the needs of the diverse learners that you serve. How will you use what you have learned today as you prepare to implement A Story of Units? 22