A Story of Units- Coherence Across the Grades

Number and Operations in Base Ten Progression

Sequence of SessionsOverarching Objectives of this May 2013 Network Team Institute

Participants will understand the focus of each module presented, the instructional path, and the student outcomes; and be ready to teach and/or prepare their colleagues to teach these modules.

Participants will examine the K–5 progressions documents and the sequence of standards foundational to developing an understanding of Number and Operations in Base Ten, thereby enabling participants to enact cross-grade coherence of NBT development in the classroom and to train their colleagues to do the same.

Participants will understand the purpose and implementation of Fluency, Problem Sets, Student Debriefs, Exit Tickets, Application Problems and Conceptual Development within A Story of Units. They will practice these components and be prepared to use them as tools through which to meet the needs of diverse learners.

Participants will examine formal and informal assessment within the Modules and develop an understanding of how to use the data generated to make instructional decisions.

High-Level Purpose of this Session

Participants will understand the sequence of standards that comprise the Numbers and Operations-Base Ten domain in order to understand the content in the first module of each grade level .

Participants will review examples of concrete and pictorial models to develop basic foundational understanding. Participants will review the algorithms employed in A Story of Units in order to understand how the mathematics develop. Participants will examine the K-5 Number and Operations- Base Ten Progressions document in order to further understand

the sequence of content development.

Related Learning Experiences

The Coherence Session begins Day 2 and was preceded on Day 1 with a half day training on the specific math content of Module 1 and how to implement the Module.

The Coherence Session will be followed a three-part series enabling participants to understand and practice the instructional

routines of fluency, application problems and concept development, and problem sets, student debriefs and exit tickets. Each of these sessions will focus on how to differentiate the instructional component according the needs of diverse learners in any given classroom.

Key Points• While work in NBT is dependent on understanding of the meanings and properties of operations, it also fosters a deeper

understanding of them.• The NBT standards include a deliberate trajectory from reasoning about quantities, the base-ten system, and the meanings of

operations to mastery of standard algorithms.• Content knowledge directed by the standards and Progressions document supports the implementation of coherence in the

classroom.

Session Outcomes

What do we want participants to be able to do as a result of this session?

How will we know that they are able to do this?

In order to be prepared to teach or train your colleagues to implement the modules, participants will:

Understand the sequence of standards in NBT

Develop a foundational knowledge base of concrete and pictorial models

Review the algorithms found in NBT and their coherence across the grades

Review the NBT Progression document and identify key ideas

Participants will articulate how the standards are organized in K-5 and continue on into 6-8

Participants will articulate or model various concrete and pictorial models

Participants will articulate the deliberate trajectory from reasoning about quantities, the base-ten system, and the meanings of operations to mastery of standard algorithms

Share key ideas with colleagues

Session Overview 8:45-10:15Section Time Overview Prepared Resources Facilitator Preparation

Session Introduction 8:45-8:49

Frame session, referencing workshop agenda.

Introduce objectives and sequence for this session.

• Session PowerPoint• Review session notes and

PowerPoint presentation

NBT Across the Grades:

A Progression of Standards

8:49-9:06 Review progression standards• Numbers and Operations – Base

Ten Progressions Document• Review Progressions document

A Progression of Concrete and Pictorial Models

9:06-9:21 Review concrete and pictorial

models

• Prepared bag of words and phrases for NBT

• Curriculum map

Video

Prepare word and phrase cards

Video

A Progression of Algorithms

9:21-9:30 Review coherence of algorithms

Videos Highlighters, Assorted colors Card sort of NBT phrases and

words

Preview videos

The Progressions Documents-Number and Operations-Base Ten

9:50-10:15 Progression study and discussion

Key takeaways

Session RoadmapSection: Introduction Time: 8:45-8:49

[4 minutes] In this section, you will…

• Frame session, referencing the agenda to outline what will be covered in the session.

• Introduce objectives and sequence the session to focus participant learning.

Materials used include:

• Session PowerPoint• Number and Operations in Base Ten Progression

Time Slide #/ Pic of Slide Script/ Activity directions GROUP

3 min Slide 1 Turnkey Materials Provided in Addition to PowerPoint:

• Card Sort

Additional Suggested Resources:

• Progression on Number and Operations in Base Ten

This session is the beginning of Day 2 of the NTI. Day 1 provided an overview of the curriculum, an examination of assessment in the curriculum, and Module Focus sessions on the beginning of the school year. Following this session, there will be a three-part series on implementation of the curriculum, during which participants will explore instructional choices in response to their students’ needs.

Respond to feedback from Day 1. Encourage participants to reflect on the Module Focus lesson and share big-picture comments

Whole group

with the group.

1 min Slide 2 Our objectives for this session are:• Examine the sequence of standards that

comprise the Number and Operations—Base Ten domain.

• Examine the sequence of base ten models employed in A Story of Units.

• Examine and practice the algorithms employed in A Story of Units.

Section: A Progression of Standards Time: 8:49-9:06

[ 17 minutes] In this section, you will…

Reflect on the Progression of Standards for Number and Operations- Base Ten in order to ensure basic knowledge

Materials used include:

Session PowerPoint Prepared bag of words and phrases for NBT Curriculum map

Time Slide #/ Pic of Slide Script/ Activity directions GROUP

2 min.

Slide 3

Let’s start by reflecting on the progression of standards across the Number and Operations—Base Ten domain.

Whole group

8 min. Slide 4 In your zip bag, you will find a collection of words and phrases that pertain to the NBT domain. Clear space on your table. Using your current knowledge of the NBT domain, work as a team to organize the cards according to the learning progression that exists in the domain. For example, in what grade do students “use place value understanding to round multi-digit whole

numbers to any place?” What skills/understandings lead up to that? What subsequent skills/understandings rely on this?

Allow about 5 minutes for this challenge, then encourage volunteers to share observations with the group. Have participants leave their arrangements on their tables for reference later in the session

1 min Slide 5 The slide shows three of the standards that are included in the cards you sorted. They are an example of the coherence that exists in the NBT domain. Facilitate a discussion about this learning progression. CLICK TO ADVANCE STANDARDSHave participants show a thumbs-up if they recognized this sequence in their sort.

2 min. Slide 6 The slide shows three of the standards that are included in the cards you sorted. They are an example of the coherence that exists in the NBT domain. Facilitate a discussion about this learning progression. CLICK TO ADVANCE STANDARDSHave participants show a thumbs-up if they correctly identified this sequence in their sort.

1 min Slide 7 As you know, this is a map of the A Story of Units curriculum, showing the breakdown of modules, grade by grade. In this version, however, modules that focus on Number and Operations—Base Ten standards are shaded in light blue; modules that focus on Number and Operations—Fractions standards are shaded in dark blue.

2 min. Slide 8 Refer to your copy of the curriculum map. Take 1 minute to turn and talk with others at your table. Share your observations and ask them to do the same. Allow 1 minute for participants to turn and talk, and then encourage volunteers to share their thoughts with the group.

1 min Slide 9 But that emphasis on Number and Operations—Base Ten doesn’t really end in 5th grade. The NBT standards, along with the NF standards, provide a strong foundation for the NS standards in middle school. Consequently, mastery of these concepts and skills is crucial to success in Algebra.Facilitate a discussion about this learning progression

1 min. Slide 10 The misconception that could occur in looking at this sequence, is that NBT is restricted in its application in MS and HS to solely the NS and Algebra strands, respectively, whereas it is applied throughout all domains.

We saw in the presentation yesterday, a different perspective… through the coherence of units to ratios to functions.

These are the curriculum maps for A Story of Units, A Story of Ratios, and A Story of Functions. Again, you see the shaded the

modules that focus on NBT and NF in A Story of Units. On the second map, showing A Story of Ratios, modules focused on the Number System domain are shaded in blue. On the third map, showing A Story of Functions, modules focused on Algebra are also shaded. As you can see, the progression plays an important role from Grade 1 through Grade 12. This is a large part of students’ career and college readiness.

Section: A Progression of Visual Models Time: 9:06-9:21

[ 15 minutes] In this section, you will…

• Examine the progression of visual models in order to understand the coherence of model development in K-5

Materials used include:

• Session PowerPoint• Video of Session 5 NBT Progression- Demonstration of Visual Models

Time Slide #/ Pic of Slide Script/ Activity directions GROUP

1 min. Slide 11 Now that we’ve reflected on the progression of standards across the Number and Operation—Base Ten domain, let’s examine the progression of visual models used in A Story of Units.

Whole group

10 min. Slide 12 << For turnkey purposes, a video of the NTI presentation of this portion of the session will be available. >>

Let’s take a look at a video that talks about and demonstrates how this progression builds.

Slide 13

4 min. Slide 14 Take 2 minutes to turn and talk with others at your table. Share your observations and ask them to do the same. Allow 2 minutes for participants to turn and talk, and then facilitate a discussion.

Section: A Progression of Algorithms Time: 9:21-9:50

[ 29 minutes] In this section, you will…

• Examine the progression of algorithms in K-5 in order to understand the development of algorithms from K to 5 th grade.

Materials used include:

• Session PowerPoint • Video-Demonstration –A Progression of Algorithms

Time Slide #/ Pic of Slide Script/ Activity directions GROUP

1 min. Slide 15 Now let’s examine the progression of algorithms used in A Story of Units Whole group

15 min.

Slide 16 << For turnkey purposes, a video of the NTI presentation of this portion of the session will be available. >>

5 min. Slide 17 Take 2 minutes to turn and talk with others at your table. Share your observations and ask them to do the same. Allow 2 minutes for participants to turn and talk, and then facilitate a discussion.

Section: The Progressions Document for Number and operations-Base Ten

Time: 9:50-10:15

[25 minutes] In this section, you will…

• Review and discuss progression documents to identify the sequence of instruction.

• Reflect on takeaways, key points and next steps to solidify understanding and develop a plan for implementation.

Materials used include:

• Session PowerPoint• NBT Progressions Document• Highlighters, Assorted colors• Card sort of NBT phrases and words

Time Slide #/ Pic of Slide Script/ Activity directions GROUP

1 min. Slide 18 For this final portion, you will need to have a printed copy of the Number and Operations—Base Ten progression document. During the last NTI, we shared three strategies for reading and digesting the Progressions.

Whole Group

8 min. Slide 20 Today we will employ a new technique. Start with the grade on which your work is most focused. If you are a classroom teacher, this will likely be an easy choice. If you work across multiple grades, perhaps you might select the grade which you find to be most challenging. Turn to the section of the progressions document that addresses the grade you’ve selected. As you read, look for and highlight evidence in support of the visual models and the algorithms we’ve shared.

Then turn to the previous grade and do the same using a new color. If you have time, turn to the subsequent grade and do the same using a third color.

For example, if you teach 3rd grade, you might highlight evidence relevant to 3rd grade in green, highlight evidence relevant to 2nd grade in blue, and highlight evidence of 4th grade in yellow. This will help you focus

your attention on the work of your grade while being attentive to the coherence across grades.

Take 6 minutes to read and highlight independently, and then you’ll have an opportunity to share your observations with others at your table.

Allow 6 minutes for participants to read independently.

4 min. Slide 21 Take 2 minutes to turn and talk with others at your table.

Allow 2 minute for participants to turn and talk, and then facilitate a discussion

5 min. Slide 22 Take 3 minutes to look back at your card sort. Talk with others at your table. Is there anything that you’d like to move? If so, why. Use your Progressions document, as well as this morning’s demonstrations as evidence to guide your decisions.

Allow about 3 minutes for this challenge, then encourage volunteers to share observations with the group.

2 min. Slide 23 As we end this session, take a moment to reflect, either privately or with your colleagues, on these next steps:

• How will this information impact instruction in your classroom/school/district?

• How will you continue to use the Progressions documents as you implement A Story of Units?

• How can you initiate a study of the Progressions with your colleagues?

5 min. Slide 24 Let’s review key points of this session:

• While work in NBT is dependent on understanding of the meanings and properties of operations, it also fosters a deeper understanding of them.

• The NBT standards include a deliberate trajectory from reasoning about quantities, the base-ten system, and the meanings of operations to mastery of standard algorithms.

• The Standards and Progressions provide valuable insight that

enables educators to meet their students’ needs in a way that also maintains coherence across the curriculum.

We will continue to explore these points in sessions later today. In particular, the last point is the focus of the three-part series that follows this session. We’ll examine instructional choices that enable educators to successfully implement this curriculum and make informed decisions in response to their students’ needs.

NOTE TO FACILITATOR: Have participants select a grade-level on which to focus during the In Practice sessions. As you dismiss to break, encourage participants to locate the Lesson 1s in their binders.

Use the following icons in the script to indicate different learning modes.

Video Reflect on a prompt Active learning Turn and talk

Turnkey Materials Provided PowerPoint Handouts

Additional Suggested Resources How to Implement A Story of Units