1. A Story of Units Overview

2. Session Objectives
Examine the rationale and alignment of A Story of Units to the CCLS, Learning Progressions, Instructional Shifts, Publishers’ Criteria, PARCC, Major Content Emphases, and the Pre-Post Math Standards.
Explore the How to Implement A Story of Units document as a tool for facilitating effective implementation of the Common Core Math Standards aligned curriculum.
Prepare for redelivery of this information to teachers and other colleagues by identifying key tools and resources provided.

4. The Shape of Math in A+ Countries
Mathematics topics intended at each grade by at least two-thirds of A+ countries
Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states

5. “To meet the realities of the 21st century global economy and maintain America’s competitive edge into the future, we need students who are prepared to compete not only with their American peers, but with students from all across the globe for the jobs of tomorrow.”
“Benchmarking for Success: Ensuring U.S. Students Receive a World-Class Education”

6. AGENDA
Examine Alignment with the Instructional Shifts Examine Alignment with the Mathematical Practices Examine Alignment with the Publishers’ Criteria Examine PARCC Type I, II, and III Tasks Examine Alignment with the Major Content Emphases and the Pre-Post Math Standards Watch a Video Clip of A Story of Units in the Classroom

7. Instructional Shifts

8. Turn and Talk
What have your districts/schools found to be most engaging about CCLS and the Instructional Shifts?
What have your schools done to move toward implementing the Instructional Shifts in the mathematics classroom?
What is the general reaction from administrators, educators, and students?

9. Curriculum Map

10. A Story of Units Aligned to the Learning Progressions
Coherence Across the Grades Grade 2: 3 tens or 3 units of 10 (Grade 2 OA Standards) Grade 3: 3 fours or 3 units of/groups of four (Grade 3 OA Standards) Grade 4: 3 fourths or 3 units of one-fourth (Grade 3 NF Standards)

11. A Story of Units Aligned to the Learning Progressions
Coherence Across the Grades Learning 12 tens = tenths = 1.2 Learning 4 thirds 4/3 = 1 1/3 or even 4 threes = 12

12. A Story of Units Aligned to the Learning Progressions
Grade 3
Grade 4
Grade 5
Number and Operations in Base Ten Standards (NBT)
Counting up and down by ones, tens and hundreds, both with the number line and place value chart are essential from Grade 3 forward to rounding and mental math.
Meaningful understanding of all operations with base-ten whole numbers
Understanding place value’s extension into decimal fractions and operations

13. Turn and Talk
How do these examples of the Instructional Shifts in A Story of Units compare with evidence of coherence in your current curriculum?

15. Number Line Model

16. Number Line Model

17. Key Points:
A Story of Units is being written in alignment with the Instructional Shifts required by the CCLS.
All standards for each grade have been carefully included in the module sequence.
The P-5 modules are designed with deliberate coherence to capitalize on the learning progressions that are embedded in the CCLS.
The activities promote a careful balance of fluency practice, conceptual understanding, and application, which aligns with the instructional shift, rigor.

18. AGENDA
Examine Alignment with the Instructional Shifts Examine Alignment with the Mathematical Practices Examine Alignment with the Publishers’ Criteria Examine PARCC Type I, II, and III Tasks Examine Alignment with the Major Content Emphases and the Pre-Post Math Standards Watch a Video Clip of A Story of Units in the Classroom

19. Standards for Mathematical Practice
A Story of Units Overview
Standards for Mathematical Practice
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.

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

21. Focus Standards for Mathematical Practice

22. Mathematical Practice Brought to Life
Lessons 2 and 3 include examples of MP.7, “Look for and make use of structure,” because, in counting, students make use of the structure provided by multiples of ten and a hundred. Students think in terms of “getting to a ten” or “getting to a hundred.”

23. Mathematical Practice in Lessons

24. Name this Math Practice
“Giving students opportunities to practice counting using ones and bundles of tens and hundreds while asking them to identify benchmark numbers will cue them to the ease and efficiency of skip-counting.” MP.7 – Look for and make use of structure.

25. Mathematical Practices
At your table count off from 1 to 8.
Take two minutes to read your math practice.
Highlight the key phrases of the math practice.
Share with your table examples of how each math practice is integrated into the A Story of Units curriculum.

26. Table Talk
Share with members of your table, examples of how the Standards for Mathematical Practice are brought to life in A Story of Units. Person 1 shares MP.1, person 2 shares MP.2, etc.

27. Key Point
A Story of Units brings the Standards for Mathematical Practice to life. Although all practices are integrated throughout the curriculum, individual lessons may highlight one or two practices specifically to facilitate educators in developing these habits of mind in their students.

28. AGENDA
Examine Alignment with the Instructional Shifts Examine Alignment with the Mathematical Practices Examine Alignment with the Publishers’ Criteria Examine PARCC Type I, II, and III Tasks Examine Alignment with the Major Content Emphases and the Pre-Post Math Standards Watch a Video Clip of A Story of Units in the Classroom

29. The Publishers’ Criteria
Focus, Coherence, and Rigor in the CCSSM
Criteria for Materials and Tools Aligned to the Standards
Appendix: “The Structure is the Standards”

30. Focus, Coherence, and Rigor
At any given grade level 75% of the year should be spent on major areas of work.
The first half of the year should predominantly cover major areas of work.

31. Criteria for Materials and Tools

32. Criteria for Materials and Tools
Examples of Student Reasoning in A Story of Units
Sally did some counting. Look at her work. Explain why you think Sally counted this way.
177, 178, 178, 190, 200, 210, 211, 212, 213, 214

33. Criteria for Materials and Tools
Examples of Student Reasoning in A Story of Units
Whisper the numbers as you count:
Count by 1s from 367 to 375.
Skip-count by 10s from 422 to 492.
Skip-count by 100s from 156 to 856.
Count by 1s from 269 to 261.
Skip-count by 10s from 581 to 511.
Skip-count by 100s from 914 to 314.
I found letter ____ to be challenging, because ________.

34. “The Structure is the Standards”
You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece a day in an envelope for the next year…
Standards for a Grecian Urn

35. Indicators of Quality in Instructional Materials and Tools for Mathematics
Problems in the materials are worth doing.
Assignments aren’t haphazardly designed. Exercises are given to students in intentional sequences.
The modules contain different types of problems that are presented in a simple to complex format. There is variety to what students produce in response to prompts.

36. Indicators of Quality in Instructional Materials and Tools for Mathematics
There are separate teacher materials that support and reward teacher study.
The use of manipulatives follows best-practices.
The visual design isn’t distracting or chaotic.
Support for English language learners and members of other special populations is provided.

37. Key Point
A Story of Units adheres to the guidelines established in the Publishers’ Criteria and benefits from on-going feedback from Student Achievement Partners throughout the writing process.

38. AGENDA
Examine Alignment with the Instructional Shifts Examine Alignment with the Mathematical Practices Examine Alignment with the Publishers’ Criteria Examine PARCC Type I, II, and III Tasks Examine Alignment with the Major Content Emphases and the Pre-Post Math Standards Watch a Video Clip of A Story of Units in the Classroom

39. PARCC Type I Tasks Assess concepts, skills and procedures
Include a balance of conceptual understanding, fluency, and application
Can involve any or all mathematical practice standards
Are machine-scored including innovative, computer-based formats

40. PARCC Type I Tasks

41. PARCC Type II Tasks Assess ability to express mathematical reasoning
Call for written arguments/justifications, critique of reasoning, or precision in mathematical statements (MP.3, MP.6) and can involve other mathematical practice standards
Are hand-scored, or machine-scored with innovative computer-based formats, or a combination

42. PARCC Type II Tasks

43. PARCC Type III Tasks Assess modeling/applications
Call for modeling/application in a real-world context or scenario (MP.4) and can also involve other mathematical practice standards
Are hand-scored, machine-scored with innovative computer-based formats, or a combination

44. PARCC Type III Tasks
Sample Grade 4 Problem Jim has three times as much money as Sally. If Jim has $14 more than Sally, how much money do they have altogether?

45. Turn and Talk
How do the new PARCC assessments compare with current and previous assessments?

46. Key Point
The problems woven throughout the modules, as well as the Mid-Module and End-of-Module Assessment Tasks, are aligned with the PARCC Type I, Type II, and Type III problems/tasks.

47. AGENDA
Examine Alignment with the Instructional Shifts Examine Alignment with the Mathematical Practices Examine Alignment with the Publishers’ Criteria Examine PARCC Type I, II, and III Tasks Examine Alignment with the Major Content Emphases and the Pre-Post Math Standards Watch a Video Clip of A Story of Units in the Classroom

48. Major Content Emphases

51. Pre-Post Math Standards
Select a testing grade and review the Standards that are expected to be taught before and after the state test.
Which Standards will be addressed after the test?

52. Pre-Post Math Standards
Grade 3
Grade 4
Grade 5
3.MD.4
3.MD.8
3.G.1
4.NF.5
4.NF.6
4.NF.7
4.MD.1
4.MD.2
5.OA.3
5.G.1
5.G.2

53. Key Point
A Story of Units is being written in alignment with the Major Content Emphases. Each grade focuses only on the appropriate math and prioritizes the major work of the grade. For Grade 3 through Grade 5, the standards identified on the Pre-Post Math Standards as those which should be taught after the state test in April, have been intentionally aligned with the final modules of those grades.

54. AGENDA
Examine Alignment with the Instructional Shifts Examine Alignment with the Mathematical Practices Examine Alignment with the Publishers’ Criteria Examine PARCC Type I, II, and III Tasks Examine Alignment with the Major Content Emphases and the Pre-Post Math Standards Watch a Video Clip of A Story of Units in the Classroom

55. Video Clip – Subtraction with Renaming
Guiding Questions:
What resonates with you as it relates to our transition to teaching the CCLS?
What do you notice about the interaction between the students and the teacher?
Where do you see evidence of the Instructional Shifts and the Standards of Mathematical Practice?

56. Video Clip – Subtraction with Renaming
This video is posted in the video library on EngageNY:

57. Video Clip – Subtraction with Renaming
Guiding Questions:
What resonates with you as it relates to our transition to teaching the CCLS?
What do you notice about the interaction between the students and the teacher?
Where do you see evidence of the Instructional Shifts and the Standards of Mathematical Practice?

58. Key Points A Story of Units
aligns with the Instructional Shifts required by the CCLS.
brings the Standards for Mathematical Practice to life.
adheres to the Publishers’ Criteria.
includes PARCC Type I, Type II, and Type III problems/tasks.
aligns with Major Content Emphases and the Pre-Post Math Standards.

59. Next Steps
What are your next steps in introducing components of this curriculum to your school(s)/district(s)?
How can you use your expertise as a leader and as an educator of mathematics to share your support of this curriculum?

60. Overview Follow Up

61. Team Time – Major Content Emphases
How are the major content emphases for your grade(s) reflected in the Curriculum Overview?
How much time is devoted to the major content emphases?
When are the ‘post’ standards addressed?

62. Team Time – Mathematical Models
Which mathematical models are relevant for your grade(s)?
In what ways will these models impact instruction?

63. Team Time – Publishers’ Criteria
In what ways does A Story of Units meet the expectations established in the Publishers’ Criteria?