A Story of Units- Module Practice Grades 3-5
Application Problems and Concept Development
Sequence of Sessions
Overarching Objectives of this May 2013 Network Team Institute
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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, Worksheets, Student Debriefs, Exit Tickets, Application
Problems and Conceptual Development within A Story of Units. They will be prepared to use these components 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
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Additional modeling, teaching and practice of the instructional routines of Application Problems and Concept Development
Understand and articulate how to use Application Problems and Concept Development routines for differentiating instruction
Related Learning Experiences
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This session builds upon the session presented earlier that reviewed all of the components of the Module in anticipation of the deeper
study of specific components.
This Module Applicaton and Concept Development Practice Session will be followed by a session on Assessment
After that there will be a session on Module 1 for each grade level K, 1, 2, 3, then be an opportunity for participants to meet with the
curriculum writes to ask questions in an extended Q&A session that concludes the two day training.
Key Points
•
Successful implementation of both Application Problems and Concept Development in A Story of Units requires the support of wellestablished 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.
Session Outcomes
What do we want participants to be able to do as a result of
How will we know that they are able to do this?
this session?
 Model, teach and practice the Application Problem and
 Participants will identify key ideas of the Application Problem
Concept Development components to support implementation
and Concept Development components.
of Module 1
 Participants will be able to articulate how to implement the
 Understand and demonstrate application problems and
components in Module 1 for a particular grade level (GK-5),
concept development and how they are to be used for
thereby preparing participants to teach and/or prepare their
differentiating instruction to meet the diverse needs of
colleagues to teach these Modules.
learners..
 Participants will articulate the function of curricular
components Application Problems and Concept Development
and how they can be used to differentiate instruction.
Session Overview
Section
Time
Session Introduction
11:3011:32
Implementation of
Application Problems
and Concept
Development
11:3211:43
Modeling and Practice
11:4312:08
Differentiation in
Application Problems
and Concept
Development
12:0812:26
Overview
 Frame session, referencing
workshop agenda.
 Introduce objectives and
sequence for this session.
 Discuss concerns and best
practices
Model and practice
 Application Problems
 Concept Development
 Discuss how to use Application
Problems and Concept
Development to differentiate
instruction
Prepared Resources
Facilitator Preparation
•
Review session notes and
PowerPoint presentation
•
Review appropriate module
•
Session PowerPoint
•
•
Session Powerpoint
Module 1 for each grade level
,3,4,and 5
•
Session Powerpoint
Module 1 for each grade level
,3,4,and 5
Review appropriate module
Session Powerpoint
Module 1 Grade 4
Review appropriate module
•
Reflection on
Preparation and
Implementation
12:2612:30
 Reflect on what has been learned
Session Roadmap 11:30-12:30
Section: Introduction
Time: 11:30 a.m.-11:32 p.m.
[2 minutes] In this section, you will…
Materials used include:
•
Review the agenda to frame the session for participants.Introduce
objectives and sequence the session to identify the focus of the
session
•
•
Session PowerPoint
Lesson 1 in Module 1 from each grade level
Time
Slide #/ Pic of Slide
Script/ Activity directions
GROUP
30 secs.
Slide 1
NOTE THAT THIS SESSION IS DESIGNED TO BE 60 MINUTES IN LENGTH
Grade
band-K2,or 3-5
Additional Suggested Resources to have available:
• A Story of Units: A Curriculum Overview for Grades P-5
• How to Implement A Story of Units
This session, Application and Concept Development in Practice, follows a
session on Fluency in Practice. It is one session in a three-part series in which
we look at Lesson 1 in order to model, teach, and practice the instructional
routines that will support implementation of A Story of Units. These sessions
also include discussion and practice on ways to differentiate according to the
needs of diverse learners and varied student populations in any given district,
school, or classroom
1 min.
Slide 2
Our objectives for this session are to revisit the modules we explored
yesterday 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
In this session, we will specifically be returning to the lesson components of
Application Problems and Concept Development. As in the previous session,
our examples will be drawn from Lesson 1 in K-5. While we’ll look at some
examples as a group, you will also have the opportunity to engage with
Lesson 1 of the grade level of your choice.
NOTE TO FACILITATOR: CHOOSE ONE OF THE PROVIDED SET, LESSON 1—
MODULE 1, GRADES K–5. BEFORE BEGINNING THE SESSION, LET THE
PARTICIPANTS KNOW THAT YOU’LL BE MODELING FROM GRADE X
THROUGHOUT THE LESSON. INSTRUCT THEM TO LOCATE THEIR COPY OF
GRADE X—LESSON 1 AT THIS TIME SO THEY CAN FOLLOW ALONG LATER.
30 secs.
Slide 3
We’ll begin with a discussion of concerns and best practices associated with
implementing the lesson components of Application Problems and Concept
Development. Later in the session, we’ll model and practice these
components, discuss how we can differentiate to support varied learners,
then take some time to reflect and plan.
Section: Implementation of Application Problems and
Concept Development
Time: 11:32-11:43
[11 minutes] In this section, you will…
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Materials used include:
Review what was learned in the previous Lesson Study about Application Session PowerPoint
Problems and Concept Development to link this session to previous
Module 1
learning and set the stage for this session
Identify concerns about implementation and plan for response to
facilitate implementation of the module.
Discuss potential solutions that could be used
Time
Slide #/ Pic of Slide
Script/ Activity directions
GROUP
2 mins.
Slide 4
As we begin, let’s take a minute to highlight what we learned in our
previous Lesson Study. What do you recall about the role of Application
Problems and Concept Development in A Story of Units? Take a minute
to share with a partner at your table.
Grade
band-K2,or 3-5
We know that many of you have expressed concerns about the length of
the lessons. Many of you also agree that all four of the components are
extremely important. Since we’re focusing on application problems and
concept development, let’s talk about why those are so critical to the
lessons structure. What purposes do they serve?
• Application problems:
• Students jog their memories
• Apply those concepts – how are kids doing this?
• What might they need to work on next?
• Concept Development:
• Jump into the objective of the lesson
• Where we have a shared learning experience, guided by
the teacher, in order to develop student conceptual
understanding
Allow 1 minute for participants to turn and share their understandings of
Application Problems and Concept Development in A Story of Units. Then
ask for participants to share aloud with the table group (one for each
lesson component).
Click to advance to the next slide.
30 secs.
Slide 5
Let’s quickly review some of the key points we learned in the Lesson
Study yesterday that are captured on the slide.
Highlight the ones that were missed by the participants.
30 secs.
Slide 6
Let’s quickly review some of the key points we learned in the Lesson
Study yesterday
Highlight anything that was missed earlier.
5 mins.
Slide 7
As you prepare to begin A Story of Units, it is important to recognize your
concerns about implementation and plan proactively in order to achieve
success. Let’s surface some of the concerns you have specifically
regarding Application Problems and Concept Development.
Here are some Ah-Ha’s that have been shared previously about Concept
Development and Application Problems.
NOTE TO FACILITATOR: Prepare this slide in advance based on the
concerns that are submitted during the Lesson Study. Be prepared to
address the concerns with thoughtful solutions. Share a few examples
before you have them share their concerns and hold the table discussion.
Open the floor for participants to voice their concerns. Allow 3 minutes
for open sharing. As this time of open sharing draws to a close, click to
advance summary. Point out the most frequent concerns if they have not
already been voiced during this period.
Now let’s consider how you might address the concerns that have been
shared by the group. Take 2 minutes to brainstorm at your table. As you
anticipate potential roadblocks, think about how you might navigate
through them successfully.
Allow 2 minutes for brainstorming, then click to the next slide.
3
mins.
Slide 8
Lead a whole-group discussion of potential solutions to the obstacles that
might be encountered in implementing these lesson components. If it is
not voiced by the group, be sure to point out that just as fluency routines
must be taught, so must teachers and students learn the routines
associated with Application Problems and Concept Development.
Modifications:
Move the application problem to the morning routine
Use Centers to teach a variety of levels in the classroom
Pinpoint problems that low performing students must solve for each
Problem Set, instead of intentions to completing the entire worksheet
(Reference the Debrief for Problems that intend to be discussed in the
Debrief.)
Adaptations:
Continue use of concrete materials when necessary.
--Use the concrete materials (number disks) in Problem 1 of Lesson 4.
Problem 4 models 10 times 2 ones, and repeats with 10 times 4 tens.
Instead repeat with 10 times 2 tens, or 10 times 3 tens. Notice what is
intentional (the units, and what can be adapted to the needs of your
students.)
Use smaller numbers (2x3) in the Application Problem, especially if you
choose to model with square tiles.
**Read the Note in the Application Problem.
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?”
Section: Modeling and Practice
Time: 11:43-12:08
[25 minutes] In this section, you will…
Materials used include:
•
•
Model how to introduce the Application Problems and Concept
Development components to develop teaching skills
Reflect on how to introduce Application Problem and Concept
Development components to colleaguesto prepare for
•
•
Session PowerPoint
Lesson 1 from Grade 4-Module 1
•
implementation
Plan the instructional strategies to use for introducing a
preselected Concept Developemnt
Time
Slide #/ Pic of Slide
Script/ Activity directions
GROUP
30 secs.
Slide 9
Now that we’ve spent some time discussing your concerns about Application
Problems and Concept Development and brainstorming potential solutions,
we’re going to take a few minutes to model some ways that you might introduce
these lesson components in your classrooms and give you time to plan the
instructional strategies you want to use to introduce one of the lesson concepts
to your class or colleagues.
Grade
band-K2,or 3-5
5 mins.
Slide 10
LOCATE THEIR COPY OF GRADE 4—LESSON 1 APPLICATION PROBLEM SO YOU
CAN FOLLOW ALONG.
As I model an introduction to the Application Problem, remember that with this
lesson component, you have the opportunity to make some instructional choices
about how you’ll use this problem in your classroom. I’m simply modeling one
way that you might approach this problem.
No matter which instructional choices you make, remember that the RDW
approach is an important tool in helping your students. In Grade K, students use
the Listen, Draw, Say process to solve problems. In Grade 1, teachers formally
introduce the RDW process in Module 2, but informally use the process with
simple math drawings in Module 1. In Grade 2, students formally use the RDW
process daily, given the fact that students will have had practice with this in
Grade 1.
If this approach is unfamiliar to you and your students, becoming comfortable in
this process will be a priority at the beginning of the school year. Teaching this
process to your students will take some time, but this investment will pay off as
they develop the ability to apply their conceptual understandings and
procedural skills.
Lead the participants through the Application Problem from your selected
Lesson 1, modeling the introduction of the application problem/RDW process. Be
sure to demonstrate the type of support you would provide to students who are
inexperienced with this process – lots of questions, prompts, cues, wait time,
feedback and praise – even though the adult learners in your session could
navigate this without your assistance.
NOTE TO FACILITATOR: Be prepared to discuss various possible instructional
choices in the lesson. How did you choose to approach this problem, and what
other equally valid choices might you have made?
Participants solve as normal.
Low levels come to Doc Camera with square tiles
2 high performers go to the board to solve, using their solutions to debrief the
AP.
5 mins
Slide 11
Now, 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. You have 5 minutes
for this activity.
NOTE TO FACILITATOR: Be prepared to discuss various possible instructional
choices in the lesson. How did you choose to approach this problem, and what
other equally valid choices might you have made?
In my class…
• Space to share thinking and solve problems
• Folder (pre-filled)
• Read it aloud
• When to share strategies – right then, or later in the day
• Show your picture to an assigned partner (not expecting a high level of
conversation yet)
• “think aloud” sharing strategies
• Routine for cleaning up
5 mins.
Slide 12
Now let’s continue with the next lesson component, Concept Development. To
do this, let’s return to Grade 4—Lesson 1. (Use the same lesson you selected to
model the Application Problem.)
As we noted during our Lesson Study, the Concept Development elaborates on
the “how-to” of delivery through models, sample vignettes, and dialogue. All of
these tools provided are intended to give teachers a snapshot of what the
classroom might look and sound like at each step of the way. However, no part
of the lesson should be considered a mandate. Your word choice may be
different from that in the vignettes, and you should use what works from the
suggested talking points, along with knowledge of your students’ needs, to write
sample vignettes of your own.
Teach Problem 1 to the whole group and time it.
Release to participants to write script for Problem 2 for 2 minutes. Then practice
with a partner.
Continue working through the rest of this Concept Development.
NOTE TO FACILITATOR: Be prepared to discuss various possible instructional
choices in the lesson.
5 mins.
Slide 13
Now, with your partner, continue working through the rest of this Concept
Development. Keep in mind, what choices will you make as you introduce your
students to A Story of Units?
NOTE TO FACILITATOR: Be prepared to discuss various possible instructional
choices in the lesson.
2 mins.
Slide 14
What, for you, is the biggest takeaway from our modeling and practice of the
Application Problem and Concept Development? Take 2 minute to discuss this at
your table.
Allow 2 minutes for discussion at the tables, then advance to the next slide.
2 mins.
Slide 15
Here are a few key points we want to take away from this activity:
• 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.
Section: Differentiation in Application Problems and
Concept Development
Time: 12:08-12:26
[18 minutes] In this section, you will…
Materials used include:
•
•
Engage in deep study of how to use these components to
differentiate instruction
Study and practice from Module 1 how to adapt Application
Problems and Concept Development components to model
differentiation
•
•
•
Module 1
Preselected Application Problem and Concept Development lesson
components
Session PowerPoint
Time
Slide #/ Pic of Slide
Script/ Activity directions
GROUP
30 secs.
Slide 16
Now that we’ve taken some time to focus on implementing the instructional
routines that support Application Problems and Concept Development in A
Story of Units, let’s consider how we can differentiate these lesson components
to meet the needs of various student populations.
Grade
band-K2,or 3-5
7 mins.
Slide 17
Examples of differentiation include:
-Application Problem:
Fine motor issues- use materials and take a picture
English Language Learner- Work with a partner
-Concept Development:
UDL boxes can spark some of your considerations.
Students who may struggle with visual focusing- Paper or card stock to help look
for embedded numbers by covering other quantities
May jot down additional questions, anticipating students’ needs:
-for those that might not have mastery subitizing 3 or 4
-for those who might not have consistent 1 to 1 correspondence
MAKE THIS REALLY SHORT!!!
In our previous discussion of differentiation and Fluency Practice, we looked at
the scaffolding suggestions in A Story of Units. Remember that these are
organized according to the UDL framework, not according to specific
populations. Notes within the lessons point out opportunities for multiple
means of representation, action and expression, and engagement.
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.
Let me take a minute to share some example of how I might have adapted the
Application Problem or Concept Development in Grade X Lesson 1 to meet the
needs of various students.
NOTE TO FACILITATOR: Complete this slide prior to the session, reflecting on the
Application Problem and Concept Development that you selected for use in the
modeling and practice.
• Provide specific examples of how you might have differentiated
those lesson components by using alternate means of
representation, action and expression, or engagement.
• How specifically would those choices have supported the needs of
various student populations?
7 mins.
Slide 19
J Just as we practiced implementing instructional routines associated with
Application Problems and Concept development, let’s take a few minutes here
to practice differentiation of these lesson components.
THINK ABOUT 5 THINGS THAT KIDS MIGHT DAY OR DO/WHAT MIGHT YOU DO
OR SAY TO HELP THAT CHILD.
THINK ABOUT DIFFERENT STRUCTURES AND/OR SYSTEMS THAT ALLOW FOR
DIFFERENTIATION – CAN YOU DO SMALL GROUPS? CAN YOU DO MORE
INDEPENDENT PRACTICE?
Chose from the set of Lesson 1 materials provided. With partner, discuss how
you might adapt the Application Problem or Concept Development. Develop
your own sample dialogue for one of these lesson components, keeping in mind
the needs of a specific student population. If you complete this activity before
our time is up, look at another example of this lesson component and consider
other ways to differentiate these materials.
Allow 6 minutes for this activity. Participants may choose a lesson component to
consider during this activity, or you may assign certain tables to look at either the
Application Problem or Concept Development.
Advance to the next slide.
3 mins.
Slide 19
Now take a minute to reflect on your experience in this activity. Did anything
surprise you? What did you learn?
Facilitate a brief whole-group conversation to allow participants to share their
experiences in this practice session.
1 min.
Slide 20
Let’s review some key points of this session:
• 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 both
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.
Section: Reflection on Preparation and Implementation
Time: 12:26-12:30
[3 minutes] In this section, you will…
Materials used include:
•
Reflect on takeaways, key points and next steps
•
Session PowerPoint
Time
Slide #/ Pic of Slide
Script/ Activity directions
GROUP
3 min.
Slide 21
As we approach the end of this session, take 2 minutes to reflect silently on what Grade
band-Kyou have learned about Application Problems and Concept Development in A
2,or 3-5
Story of Units. How will you use what you have learned today as you prepare to
implement A Story of Units?
(Allow 2 minutes for silent reflection.)
As we close this session, remember that the lesson components in A Story of
Units all work together to achieve balanced, rigorous instruction. In our next
session, we’ll revisit the Student Debrief, including another look at the Problem
Set and Exit Ticket.
Use the following icons in the script to indicate different learning modes.
Video
Reflect on a prompt
Turnkey Materials Provided
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PPT
Facilitators Guide
Handouts
Additional Suggested Resources
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Progressions documents
How to Teach A Story of Units
Active learning
Turn and talk