1. By Cheri Modeen, Necia Marchetti, Amy Hibbard & Eric Vaillancourt
Red Creek CSD 2013 Summer Math Academy August 5, 2013 Day 1, Grades PK-12 AM Session By
Cheri Modeen, Necia Marchetti,
Amy Hibbard & Eric Vaillancourt

2. Agenda
Dan Meyer video – Discussion of PK-12 Mathematical Shifts & Mathematical Practices
Vertical Coherence of the PK-12 Curriculum – A glance at the Curriculum Maps
Overview of Math Modules
Overview of a Lesson

3. Dan Meyer – TED talk http://www.youtube.com/watch?v=BlvKWEvKSi8
California teacher & doctoral candidate at Stanford.
International speaker & consultant.
Named one of Tech & Learning’s 30 “Leaders of the Future.”
AMTNYS 2013 Keynote St. John Fisher.

4. Mathematical Shifts Focus – Learn more about less.
Coherence – Build skills across grade levels.
Fluency – Develop speed & accuracy.
Deep Understanding – Really know it. Really do it.
Application – Use it in the real world.
Dual Intensity – Think fast AND solve problems.

5. Session 1 - A Story of Units
May 2013
Network Team Institute
TIME ALLOTTED FOR THIS SLIDE:
3 minutes
MATERIALS NEEDED: X
Instructional Shifts
Start with the standards… why…
The authors of the Common Core State Standards tell us that the “standards are not intended to be new names for old ways of doing business. They are a call to take the next step.” (CCSSM, page 5) Student Achievement Partners, the writers of the Common Core State Standards, has described some examples of the “old ways of doing business,” articulating the kind of instruction to avoid.
In order to move away from these old ways, a new approach to mathematics education was needed. This new plan was articulated in the form of the Instructional Shifts, which describe how to implement the Standards as they were intended so that all students will be career and college ready when they leave high school.
NOTE TO FAILITATOR: If your audience is not familiar with these Instructional Shifts, take time to discuss each one.
These shifts have been a driving force in creating A Story of Units.
Each grade-level focuses on the major work.
Material is organized into coherent topics, emphasizing natural connections that exist both within and across grades.
A balance of rigor is maintained in the daily lesson components as well as in the assessments.
Practice standards are meaningfully connected to the content standards.

6. Which shifts did you see in Dan’s video?
Turn & Talk
Why are these important?

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

8. Which practices did you see in Dan’s video?
Turn & Talk
Why are these important?

9. NYS Math Modules PK-12 Curriculum with 3 Stories:
Grades PK-5 – The Story of Units
Grades 6-8 – The Story of Ratios
Grades 9-12 – The Story of Functions
Each has a Curriculum Map
Curriculum Maps show the PK-12 Coherence

10. Session 1 - A Story of Units
May 2013
Network Team Institute
TIME ALLOTTED FOR THIS SLIDE:
1 minutes
MATERIALS NEEDED: X
A Story of Units
Slides 10-13, Facilitator will describe the tight alignment to the Standards, the progression of mathematics, and intentionality that support and unify the P-5, 6-8, and 9-12 curricula being developed by the Common Core, Inc. team.
Facilitate a discussion about this progression from A Story of Units to A Story of Ratios to A Story of Functions.

11. Session 1 - A Story of Units
May 2013
Network Team Institute
TIME ALLOTTED FOR THIS SLIDE:
1 minutes
MATERIALS NEEDED: X
A Story of Ratios
Slides 10-13, Facilitator will describe the tight alignment to the Standards, the progression of mathematics, and intentionality that support and unify the P-5, 6-8, and 9-12 curricula being developed by the Common Core, Inc. team.
Facilitate a discussion about this progression from A Story of Units to A Story of Ratios to A Story of Functions.

12. Session 1 - A Story of Units
May 2013
Network Team Institute
TIME ALLOTTED FOR THIS SLIDE:
1 minutes
MATERIALS NEEDED: X
A Story of Functions
Slides 10-13, Facilitator will describe the tight alignment to the Standards, the progression of mathematics, and intentionality that support and unify the P-5, 6-8, and 9-12 curricula being developed by the Common Core, Inc. team.
Facilitate a discussion about this progression from A Story of Units to A Story of Ratios to A Story of Functions.

13. Session 1 - A Story of Units
May 2013
Network Team Institute
TIME ALLOTTED FOR THIS SLIDE:
1 minutes
MATERIALS NEEDED: X
PK-12 Coherence
Slides 10-13, Facilitator will describe the tight alignment to the Standards, the progression of mathematics, and intentionality that support and unify the P-5, 6-8, and 9-12 curricula being developed by the Common Core, Inc. team.
Facilitate a discussion about this progression from A Story of Units to A Story of Ratios to A Story of Functions.

14. Philosophy and Workflow of A Story of Units
Session 1 - A Story of Units
May 2013
Network Team Institute
TIME ALLOTTED FOR THIS SLIDE:
3 minutes
MATERIALS NEEDED: X
Philosophy and Workflow of A Story of Units
Elementary Mathematics
Common Core Standards: The Progressions
A Story of Units: Curriculum Map
Module Overviews and Assessments
Topic Openers
Lesson Objectives
From the field of mathematics, learning progressions have been clearly defined for us in the Common Core Learning Standards. From those, we developed a framework for the P-5 curriculum. This is illustrated in the curriculum map and articulated in the accompanying grade-level descriptions of the Curriculum Overview. From this established sequence of modules, overview and assessments are created. Each topic is then fully developed to include daily objectives that describe a teaching sequence towards mastery.

15. What’s in a Module?

16. Module Parts: Module Overview Mid-Module & End-Of-Module Assessments
Table of Contents (with Lessons listed)
Focus & Foundational Standards
Terminology
Suggested Tools
Mid-Module & End-Of-Module Assessments
Rubrics for Assessments
Topics with Topic Openers for each Topic
Lessons with Specific Objectives

17. Module Focus Grade K—Module 5
February 2013
Network Team Institute
What information do you know from the table of contents?
Look at the Table of Contents on the first page of Grade K and Grade 3—Module 5. You have both on your desk – thumb thru one or the other as I have both up here.
What information do you know from the Table of Contents? Some of the same: 5th Module, Title, but also:
The module begins with a module overview and ends with the module assessments.
The K module is comprised of five topics, A through E; the page numbering system restarts at 1 for each topic.
The 3 module is comprised of six topics, A through F; the page numbering system restarts at 1 for each topic.

18. Module Focus Grade K—Module 5
Take two minutes to read the section individually. As you read the module, identify at least three key points from your reading. After two minutes, I’ll ask you to share your key points with others at your table who have read a different grade module.
February 2013
Network Team Institute
Following the Table of Contents is an Overview Narrative describing the math of the module - intended to provide teachers with any background information they might need prior to beginning instruction.
Take two minutes to read the section individually. As you read the module, identify at least three key points from your reading. After two minutes, I’ll ask you to share your key points with others at your table who have read a different grade module.
This module builds on students’ understanding of the numbers to 10.
Understanding of 10 ones is a crucial foundation for developing understanding of 1 ten.
Students will explore teen numbers as 10 ones and some more ones using concrete objects, pictures, number bonds, and Hide Zero cards.
Students will decompose teen numbers.
Students will solve “how many” questions involving teen numbers.
Show pre-written ideas on chart paper.

19. Module Focus Grade K—Module 5
February 2013
Network Team Institute
Following the Overview narrative, is a diagram illustrating the Distribution of Instructional Minutes to clearly communicate the carefully balanced and rigorous instruction of the module.
How many lessons are in this K module on the left? (24) 3 module on the right? (30)
How are the lessons structured?
Most - though not all - are comprised of four lesson components: Fluency Work, Conceptual Development, Application Problems, and Student Debrief
Amount of time spent on each of these components varies by lesson - Lessons 23 and 24 (K) and Lesson 30 (3) do not include Application Problems
Amount of time spent on each of the lesson components is driven by the rigor emphasized in the standard(s) addressed in any given lesson
Order of the components may vary
Which Mathematical Practices are addressed in this module?
K- MP.2, 3, 4, and 7
3- MP.2, 3, 6, and 7
Emphasize – this does not mean others are not present – these are just prime situations that one can be practiced until it becomes Habit of Mind
Following the Distribution of Instructional Minutes diagram, are the Standards associated with this module.
Curriculum Overview also has Standards but in a year overview-big picture-this is by module.

20. Module Focus Grade K—Module 5
February 2013
Network Team Institute
Take a minute to read this section and review the Standards, and then discuss with table partner how they relate to the overview narrative that we’ve already read and discussed.
Which standards are the focus of this module? (This module focuses on the first two clusters of standards in the Counting and Cardinality domain, as well as the first standard from the Number and Operations in Base Ten domain.) These CC standards are addressed in GK—M19 (look at curriculum map) with numbers up to 10; this module is an extension of that work. K.CC4 also has a 4th part which is addressed in the final module. This is the only module in which K.NBT.1 is a focus.
Which Mathematical Practices are addressed in this module? (MP.2, 3, 4, and 7. This corresponds with the information we saw in the Distribution of Instructional Minutes diagram.) While it is certainly hoped that teachers will continue to promote all practices on a regular basis as opportunities arise, these four practices are particularly appropriate for the lessons in this module. In addition to the information provided in this list, activity-specific suggestions are provided in the lessons themselves.
Show above on chart paper.

21. Module Focus Grade K—Module 5
February 2013
Network Team Institute
Turn the page and refer to the Overview of Module Topics and Lesson Focus chart.
The module is comprised of five topics, A through E, which we also saw in the Table of Contents.
The lesson titles are included by topic. For example, five lessons are listed under Topic A, and Lesson 6 is the beginning of Topic B.
The left-hand column identifies the standard(s) per topic. Focus standards are bold.
The number of instructional days is included per topic in the right-hand column.
Instructional days are also allotted for the mid-module and end-of-module assessments.
The final line of the chart, at the bottom of the second page, gives the total number of instructional days intended for this module. This matches the map and grade-level description in the Curriculum Overview document.

22. Module Focus Grade K—Module 5
February 2013
Network Team Institute
After the overview chart, you will find Terminology and Suggested Tools and Representations.
“How does the information in these sections inform instruction / how do you envision using this information?”
teachers can use this section as a quick review of what students already know coming in to this module (Familiar Terms and Symbols)
what they will be learning for the first time in this module
look for evidence that participants understand these three aspects of how the information is presented:
The terminology is listed in two parts: New or Recently Introduced Terms, and Familiar Terms and Symbols.
Examples are provided for each term. This lets teachers know what terms will be used in the module. It is also a resource for them to ensure appropriate/accurate use of vocabulary.
The list of Suggested Tools and Representations gives teachers an idea of how the content will be communicated as well as what materials will be needed during the module.

23. Module Focus Grade K—Module 5
February 2013
Network Team Institute
Following the Suggested Tools and Representations, there is a statement regarding Scaffolds.
How to Implement A Story of Units document includes scaffolds for English language learners, students with disabilities, students performing above grade level, and students performing below grade level.
Strategically-placed margin notes within each lesson elaborate and demonstrate the use of specific scaffolds at specific times.
The last component of the Module Overview is an Assessment Summary chart, indicating which standards are addressed in each of the assessments.
This is the end of the Module Overview; Topic A begins on the next page.

24. Module Focus Grade K—Module 5
February 2013
Network Team Institute
This is the topic opener for Topic A:
The relevant standards (K.NBT.1, K.CC.1, K.CC.2, K.CC.4abc, K.CC.5) are included under the topic title; the focus standards (K.NBT.1, K.CC.1) are bold.
The language of the focus standard, as it appears in the CCLS, is also provided.
The number of instructional days (5) is provided.
Coherence links from/to are provided to help teachers understand how this module fits in the scope of the curriculum. We can see that this instruction is building on GPK—M5 and prepares students for G1—M2.
The five lessons in this topic are sequenced toward mastery of counting 10 ones and some ones.
Note the page number in the bottom, right corner. The pages of the module overview are numbered using roman numerals. This page number, 5.A.1, indicates that this is the first page of Topic A in Module 5. The next page will be numbered 5.A.2, and this format will continue with all pages for the four lessons in Topic A numbered sequentially. The topic opener for Topic B will restart at one, 5.B.1. This will continue for all topics throughout the module.

25. What’s in a Lesson?

26. Lesson Parts Many similar lesson parts PK-12.
PK-5 & 6-12 use slightly different lesson formats & names for lesson parts.
Definition of “problem set” is different in PK- 5 vs
PK-5 have fluencies; 6-12 do not at this time.

27. Grades PK-5 & 6-12 Lesson Parts
Objective
Fluency Practice
May include Sprints
Application Problem
Concept Development
Includes Activities or Problems
Includes Problem Set (which is a timed task during lesson)
Student Debrief
Includes Exit Ticket
Homework
Grades 6-12
Student Outcome
Classwork
With Discussions, Examples, & Exercises
Closing
Exit Ticket
Problem Set
Which is the Homework

28. Module Focus Grade K—Module 5
February 2013
Network Team Institute
Lesson 1 begins on the next page.
Following the lesson title, each lesson provides a Suggested Lesson Structure including a pie chart to show the information at a glance. It reiterates the information, lesson by lesson, that was provided in the Distribution of Instructional Minutes diagram in the module overview. Note that this lesson includes all four lesson components, and so each lesson component will be described in the order in which they appear in the Suggested Lesson Structure. (Allow 3 minutes for participants to read and discuss the lesson.)
“NOTES ON” boxes are included down the right-hand margin. In various lessons, notes are provided for teachers on scaffolding English language learners, students with disabilities, students performing above grade level, and students performing below grade level.
Following the lesson plan, are the reproducible student pages: Lesson 1 Worksheet(s), Lesson 1 Exit Ticket, and Lesson 1 Homework. Note that the student pages are provided in the order in which they are intended to be used.

29. Fluency Videos Grade K-1 Counting Exercise (8 min)
november-2012-rigor-breakdown-counting- exercises-for-k-1
Ten Frame Flash - 2 minutes
november-2012-rigor-breakdown-ten-rame- flash
Skip Counting by Fractions
november-2012-rigor-breakdown-skip- counting-by-fractions

30. Fluency Drill Fluency Practice
Skip Count forward and backwards by three’s two times starting at 0.
(up to 30)

31. Personal Boards
Write out the skip counting by 3’s on your personal boards starting at 0.
Underline the multiples of 6.

32. Fluency Drill
Skip Count forward and backwards by sixes. (up to 30)

33. Multiplication by 3 and 6
What do you notice? Write your observations on your personal board.
2 x 3 = 6 2 x 6 = 12
3 x 3 = 9 3 x 6 = 18
4 x 3 = x 6 = 24

34. Application Problem
Amy needs to cut a piece of paper into 6 equal parts. Draw at least three pictures to show how Amy can cut her paper so that all the parts are equal. (Early finishers can do the same thing with halves, fourths, or eighths.)
n-core-video-series-grade-3-module-5- mathematics-application-example

35. Grade 3 Module 5
Lesson #2 video-series-grade-3-module-5-mathematics- example-of-instruction
Janice Fan, a writer for A Story of Units, is a 3rd grade teacher at Folk Arts Cultural Treasures School in Philadelphia, PA. In the video clip you will see her students engaging in one of the lessons from the beginning of this module.
Common Core Video Series: Grade 3 Mathematics ~ use fraction strips Length (min:sec): 7:11
Reflection:
What do you notice about the students’ experiences in this lesson?
How does it compare to your past experiences with fractions lessons?

36. What is a SPRINT?

37. Rigor Breakdown – Procedural Skill and Fluency for Grades 3-5
February 2013
Network Team Institute
Sprint Design
A Sprint has two parts (Sprint A and Sprint B) with closely related problems on each.
Students are given 60 seconds for each Sprint.
Every student should get at least 25% right.
Ideally, no student will finish within the 60 seconds.
A typical 4th or 5th grade Sprint has 44 problems, younger students need fewer problems.
The problems on Sprint A should be almost identical to the problems on Sprint B without actually being identical. Sprint B should be neither harder nor easier than Sprint A.
Your goal in writing the Sprint is that every student should get at least 25%
Younger students need fewer problems, perhaps as few as

38. Rigor Breakdown – Procedural Skill and Fluency for Grades 3-5
February 2013
Network Team Institute
Sprint Design
Problems on the Sprint start easy and get progressively more complex (perhaps in quadrants).
Problems should be patterned in such a way as to encourage MP.8, “Look for and express regularity in repeated reasoning.”
Intelligent design and delivery makes the Sprint superior to computer-generated worksheets.
You don’t want students skipping around while working a Sprint in hopes of finding the easiest problems to work – that only slows them down and takes their concentration off doing the problems and on finding easy ones.
If you are not familiar with the delivery of a Sprint, please refer to the How to Implement A Story of Units document and read about the Sprint routine.

39. Lunch Break Module Focus July 2013 Network Team Institute
When we return from lunch, we will explore the Topic Openers and lessons. Please sit at one of the tables that is designated for your professional group.
NOTE TO FACILITATOR: During lunch, place a sign on each table to direct participants where to sit by professional role, and assign topics openers to each table. Also, make sure to review the sticky note questions during lunch and plan to address the questions with the group or individuals in the last half of the session.