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A Story of Units- Module Practice Grades 3-5

Application Problems and Concept Development

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, 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 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 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 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.

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?

Model, teach and practice the Application Problem and Concept Development components to support implementation of Module 1

Understand and demonstrate application problems and concept development and how they are to be used for differentiating instruction to meet the diverse needs of learners..

Participants will identify key ideas of the Application Problem and Concept Development components.

Participants will be able to articulate how to implement the components in Module 1 for a particular grade level (GK-5), thereby preparing participants to teach and/or prepare their colleagues to teach these Modules.

Participants will articulate the function of curricular components Application Problems and Concept Development and how they can be used to differentiate instruction.

Session OverviewSection Time Overview Prepared Resources Facilitator Preparation

Session Introduction 11:30-11:32

Frame session, referencing workshop agenda.

Introduce objectives and sequence for this session.

• Session PowerPoint• Review session notes and

PowerPoint presentation

Implementation of Application Problems and Concept Development

11:32-11:43

Discuss concerns and best practices

• Session Powerpoint• Module 1 for each grade

level ,3,4,and 5• Review appropriate module

Modeling and Practice 11:43-12:08

Model and practice Application Problems Concept Development

• Session PowerpointModule 1 for each grade level ,3,4,and 5

Review appropriate module

Differentiation in Application Problems and Concept

12:08-12:26

Discuss how to use Application Problems and Concept Development to differentiate

• Session PowerpointModule 1 Grade 4

Review appropriate module

Development instruction Reflection on Preparation and Implementation

12:26-12:30

Reflect on what has been learned

Session Roadmap 11:30-12:30Section: Introduction Time: 11:30 a.m.-11:32 p.m.[2 minutes] In this section, you will…

• Review the agenda to frame the session for participants.Introduce objectives and sequence the session to identify the focus of the session

Materials used include:• 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 LENGTHAdditional 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

Grade band-K-2,or 3-5

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 classroomIn 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… Review what was learned in the previous Lesson Study about

Application Problems and Concept Development to link this session to previous learning and set the stage for this session

Identify concerns about implementation and plan for response to facilitate implementation of the module.

Materials used include:Session PowerPointModule 1

Discuss potential solutions that could be used


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.

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 routineUse Centers to teach a variety of levels in the classroomPinpoint 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…

• 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 implementation

• Plan the instructional strategies to use for introducing a preselected Concept Developemnt

Materials used include:• Session PowerPoint• Lesson 1 from Grade 4-Module 1


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.


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 tiles2 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…• 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

Materials used include:• Module 1 • Preselected Application Problem and Concept Development lesson

components• Session PowerPoint


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.


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


3 min. Slide 21 As we approach the end of this session, take 2 minutes to reflect silently on what you have learned about Application Problems and Concept Development in A 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 Active learning Turn and talk

Turnkey Materials Provided PPT Facilitators Guide Handouts

Additional Suggested Resources Progressions documents

How to Teach A Story of Units

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