A Story of Units- Coherence Across the Grades
Number and Operations in Base Ten Progression
Sequence of Sessions
Overarching 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?
In order to be prepared to teach or train your colleagues to
implement the modules, participants will:
How will we know that they are able to do this?

Participants will articulate how the standards are organized in
K-5 and continue on into 6-8

Understand the sequence of standards in NBT


Develop a foundational knowledge base of concrete and
pictorial models
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

Review the algorithms found in NBT and their coherence
across the grades

Review the NBT Progression document and identify key ideas
Session Overview 8:45-10:15
Section
Time
Overview
Prepared Resources
 Frame session, referencing
workshop agenda.
Session Introduction
8:45-8:49
NBT Across the
Grades:
8:49-9:06

A Progression
of Standards

A Progression
of Concrete
and Pictorial
Models
9:06-9:21
•
 Introduce objectives and
sequence for this session.
 Review progression standards
 Review concrete and pictorial
models
•
Session PowerPoint
Review session notes and
PowerPoint presentation
•
Numbers and Operations – Base •
Ten Progressions Document
Review Progressions document
•
Prepared bag of words and
phrases for NBT

Curriculum map

Prepare word and phrase
cards
Video

Preview videos
•


A Progression
of Algorithms
9:21-9:30

The
Progressions
DocumentsNumber and
OperationsBase Ten
9:50-10:15

 Review coherence of algorithms 

 Progression study and discussion
 Key takeaways
Facilitator Preparation
Video
Videos
Highlighters, Assorted colors
Card sort of NBT phrases and
words
Session Roadmap
Section: Introduction
Time: 8:45-8:49
[4 minutes] In this section, you will…
Materials used include:
•
•
Frame session, referencing the agenda to outline what will be
covered in the session.
Introduce objectives and sequence the session to focus participant
learning.
•
•
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:
Whole group
•
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
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…
Materials used include:

Reflect on the Progression of Standards for Number and OperationsBase Ten in order to ensure basic knowledge
Time
2 min.
Slide #/ Pic of Slide



Session PowerPoint
Prepared bag of words and phrases for NBT
Curriculum map
Script/ Activity directions
GROUP
Let’s start by reflecting on the progression of standards across the
Number and Operations—Base Ten domain.
Whole group
Slide 3
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 STANDARDS
Have 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 STANDARDS
Have 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
th
really end in 5 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…
Materials used include:
•
Examine the progression of visual models in order to understand
the coherence of model development in K-5
•
•
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…
Materials used include:
•
Examine the progression of algorithms in K-5 in order to
understand the development of algorithms from K to 5 th grade.
•
•
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
Slide 16
<< For turnkey purposes, a video of the NTI presentation of this portion of
the session will be available. >>
Slide 17
Take 2 minutes to turn and talk with others at your table. Share your
observations and ask them to do the same.
15 min.
5 min.
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…
Materials used include:
•
•
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.
•
•
•
•
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
Turnkey Materials Provided


PowerPoint
Handouts
Additional Suggested Resources

How to Implement A Story of Units
Active learning
Turn and talk