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Module Focus: Grade K – Module 5 Sequence of Sessions

Overarching Objectives of this May 2014 Network Team Institute Module Focus sessions for K-5 will follow the sequence of the Concept Development component of the specified modules, using this narrative as a tool

for achieving deep understanding of mathematical concepts. Relevant examples of Fluency, Application, and Student Debrief will be highlighted in order to examine the ways in which these elements contribute to and enhance conceptual understanding.

High-Level Purpose of this Session Focus. Participants will be able to identify the major work of each grade using the Curriculum Overview document as a resource in preparation for

teaching these modules. Coherence: P-5. Participants will draw connections between the progression documents and the careful sequence of mathematical concepts that

develop within each module, thereby enabling participants to enact cross- grade coherence in their classrooms and support their colleagues to do the same.

Standards alignment. Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the module addresses the major work of the grade in order to fully implement the curriculum.

Implementation. Participants will be prepared to implement the modules and to make appropriate instructional choices to meet the needs of their students while maintaining the balance of rigor that is built into the curriculum.

Related Learning Experiences● This session is part of a sequence of Module Focus sessions examining the Grade K curriculum, A Story of Units.

Key Points● Students look for and make use of structure in the counting sequence.● Writing teen numbers is not taught in isolation, but rather in conjunction with the composition of teen numbers, through the support

of “Hide Zero” or place value cards.● To compare teen numbers, students decompose them as 10 and some ones, and then compare the ones 1-9.● Students extend their work with Number Bonds represent teen numbers as addition sentences.● Students gain foundations in Place Value.● Scaffolding Focused: Amplify Language● Scaffolding Focused: Move from Concrete to Representation to Abstract● Scaffolding Focused: Give Specific Guidelines for Speaking, Reading, Writing, or Listening

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?

Focus. Participants will be able to identify the major work of each grade using the Curriculum Overview document as a resource in preparation for teaching these modules.

Coherence: P-5. Participants will draw connections between the progression documents and the careful sequence of mathematical concepts that develop within each module, thereby enabling participants to enact cross- grade coherence in their classrooms and support their colleagues to do the same. (Specific progression document to be determined as appropriate for each grade level and module being presented.)

Standards alignment. Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the module addresses the major work of the grade in order to fully implement the curriculum.

Implementation. Participants will be prepared to implement the modules and to make appropriate instructional choices to meet the needs of their students while maintaining the balance of rigor that is built into the curriculum.

Participants will be able to articulate and demonstrate the key points discussed.

Session Overview

Section Time Overview Prepared Resources Facilitator Preparation

Introduction Overview

20 minIntroduces A Story of Units and instructional strategies and scaffolding

• Grade K Module 5 PPT• Facilitator Guide

Review Grade K Module 5

Module Introduction 57 min Introduces Grade K Module 5• Grade K Module 5 PPT• Facilitator Guide


Topic A: Count 10 Ones and Some Ones

26 minExplores counting objects to ten and some ones using the Say Ten way


Review Topic A

Topic B: Compose Numbers 11-20 from 10 and Some Ones; Represent and Write Teen Numbers

40 min

Explores advancing work with teen numbers by using manipulatives and working in reverse to gain understanding at more abstract level


Review Topic B

Topic C: Compose Numbers 11-20 from 10 and Some Ones; Represent and Write Teen Numbers

11 minExplores understanding the teen number structure using number towers and stairs


Review Topic C

Topic D: Extend the Say Ten and Regular Count Sequence to 100

15 minExplores leading students beyond teen numbers to 100


Review Topic D

Topic E: Extend the Say Ten and Regular Count Sequence to 100

19 min

Explores using what students have learned about teen numbers to apply it to addition sentences, part-part whole relationships, and comparison of number


Review Topic E

Review 13 minReviews the key points and reinforces the Progression Documents as a framework



Session Roadmap

Section: Introduction Overview Time: 20 minutes

In this section, you will be introduced to A Story of Units and components of the curriculum.

Materials used include:• Grade K Module 5 PPT• Grade K Module 5 Facilitator Guide• Grade K Module 5 Module Overview• Grade K Module 4 Module Overview

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

1 min 1. NOTE THAT THIS SESSION IS DESIGNED TO BE 3 HOURS 15 MINUTES IN LENGTH.

Welcome! In this module focus session, we will examine Grade K – Module 5.

1 min 2. Our objectives for this session are to:• Examination of the development of mathematical

understanding across the module using a focus on Concept Development within the lessons.

• Introduction to mathematical models and instructional strategies to support implementation of A Story of Units.

• As an overall theme of this NTI, we’ve been asked to pay special attention to the ways in which we can provide scaffolds to support specific student needs. Before we begin our examination of the mathematics in this module, let’s take a few minutes to review some of the principles we can use to support learning.

1 min 3. The mathematics modules were created based on the premise that scaffolding must be folded into the curriculum in such a way that it is part of its very DNA. The instruction in these modules is intentionally designed to provide multiple entry points for students at all levels.

Teachers are encouraged to pay particular attention to the manner in which knowledge is sequenced in the curriculum and to capitalize on that sequence when working with special student populations. Most lessons move from simple to complex allowing teachers to locate specific steps where students are struggling or need a challenge.That said, there are specific resources to highlight and enhance strategies

that can provide critical access for all students.

In developing the scaffolds already contained in the curriculum, Universal Design for Learning (UDL) has provided a structure for thinking about how to meet the needs of diverse learners. Broadly speaking, that structure asks teachers to consider multiple means of representation; multiple means of action and expression; and multiple means of engagement. These dimensions promote engagement of students and provide multiple approaches to the same content.

Individual lessons contain marginal notes to teachers (in text boxes) highlighting specific UDL information about scaffolds that might be employed with particular intentionality when working with students. These tips are strategically placed in the lesson where the teacher might use the strategy to the best advantage.

Let’s now examine additional strategies that can be considered.In this module study, we will focus on three key ideas for developing scaffolds that can be adapted for your classroom to meet the needs of your students.

Explicit focus on the language of mathematics, using the development from concrete to representation to abstract in the building of concepts, and communicating clear expectations in instructions are areas that can provide multiple entry points for students and can be used to promote student learning.

1 min 4. Much of what we share in the mathematics classroom with students is embedded in language that is specific. Students learn casual language before academic language. This means they may sound comfortable and fluent, but may need additional support in their writing and speaking in an academic environment.

Presenters should stress that academic language is an essential component of closing the achievement gap and providing access to grade level content and beyond.

Students may have a preconceived or informal idea of the meaning of a mathematical term. Be specific in the definition or meaning that will be used.

Be cautions of words with multiple meanings that might be confusing• a garden plot and the request to plot points on a coordinate plane

Words with multiple meaning must be anticipated and then addressed, and teachers must also be prepared to pause and provide explanations when students identify words the teacher has not anticipated. Whenever possible, words with multiple means should be avoided on assessments, particularly when the meanings may be close enough to be confusing.

Make sure that Language is internally consistent (if practice problems ask students to solve, the assessments should use the same term). If language is not internally consistent, then different terms are highlighted and taught.• add, plus, sum, combine, all mean the same thing• prism, a rectangular prism, box, package all reference the same figure

in G6M5_L11

1 min 5. The more concrete and visual these ideas can be in foundational stages, the better!• Use contexts that are familiar to students in your classroom.• Use graphic organizers or other means for students to visually

organize thinking.

Note: Teachers should be thoughtful and purposeful about which graphic organizers they select. Are teachers introducing a new concept with a need to organize notes or are they connecting ideas comparing and contrasting? The goal is always to help students make those connections and not use a graphic organizer just for the novelty of it.• Consider using non-verbal displays of mathematical relationships in

your scaffolding.• Use multiple representations and multiple approaches in explaining

problems and allowing students to express solutions.• Use pictures/ visuals/ illustrations are used to make content clearer.

1 min 6. Each day needs structured opportunities for students to speak and write in English.• Students can chorally repeat key vocabulary or phrases• Have them “turn to a neighbor and explain”

Clearly set expectations by the explicit instructions in student-friendly language.

Use visuals in your instructions.

Be direct about language.• Pause to discuss a vocabulary term and discuss how it may be used in

the lesson. Have students repeat the word chorally so that they can all hear and practice.

Provide sentence frames for anyone who may benefit.• “The volume of my prism is ___units cubed. I found this by ______.• “My idea is similar to _____’s because ____.”

Generic/ universal sentence frames may remain posted in the classroom throughout the year. These might include:• “I agree with ____ because ___” or “I think the answer is _____

because...”

2 min 7. Let’s review some key points of scaffolding instruction.

As we study the module for this session, be thinking about specific scaffolds that might be most helpful for your classroom. We will pause at various points in the session to intentionally examine and discuss suggestions for scaffolds.

8. Note to presenter:Insert this slide at appropriate points in the module study for an in-depth look at scaffolds. You may highlight a scaffold that already exists and discuss it or locate a point where a student might encounter difficulty and explore options.

Delete the slide from this current sequence after you’ve inserted it in appropriate places throughout your session.

Note to presenter: When you have inserted the slide, list several suggestions for scaffolds that would address the situation.

Possible scaffolds:

9. Note to presenter:If applicable, insert this slide at an appropriate point in the module study for an in-depth examination of a problem or task for multiple entry points through the principles of the Universal Design for Learning (UDL). Delete this slide from this current sequence after you’ve used it elsewhere as needed.

REPRESENTATION: The “what” of learning.How does the task present information and content in different ways?How students gather facts and categorize what they see, hear, and read.How are they identifying letters, words, or an author's style?

In this task, teachers can ...Pre-teach vocabulary and symbols, especially in ways that build a connection to the learners’ experience and prior knowledge by providing text based examples and illustrations of fields. Integrate numbers and symbols into word problems.

ACTION/EXPRESSION: The “how” of learning.How does the task differentiate the ways that students can express what they know?How do they plan and perform tasks?How do students organize and express their ideas?

In this task, teachers can...

Anchor instruction by pre-teaching critical prerequisite concepts through demonstration or models (i.e. use of two dimensional representations of space and geometric models).

ENGAGEMENT: The “why” of learning.How does the task stimulate interest and motivation for learning?How do students get engaged?How are they challenged, excited, or interested?

In this task, teachers can...Optimize relevance, value and authenticity by designing activities so that learning outcomes are authentic, communicate to real audiences, and reflect a purpose that is clear to the participants.

If available, reviewing student work would provide participants with the opportunity to deeply understand the benefits of students sharing their thinking in working the problem. Assessments in the module have rubrics that clearly outline expectations and could be used in the discussion.

1 min 10. • We will begin by exploring the module overview to understand the purpose of this module. Then we will dig in to the math of the module.

• We’ll lead you through the teaching sequence, one concept at a time. You’ll have the opportunity to practice using models that support the concept development.

• Along the way, we’ll also examine the other lesson components and how they function in collaboration with the concept development.

• Finally, we’ll take a look back at the module, reflecting on all the parts as one cohesive whole.

1 min 11. • The fifth module in Grade K is Numbers 10-20 and Counting to 100. The module includes 24 lessons, one of which is optional because of its exploratory nature, yet highly encouraged. Module 5 is allotted 30 instructional days, including 6 for interview-style assessments.

• This module builds on understandings established in Module 4, preparing students to extend their knowledge of whole-part relationships to teen numbers.

• At this point in the year, students have a strong foundation in Numbers to 10, and have practiced complex counting exercises to 30 in Fluency preparing them to extend the counting sequence to 100.

3 min 12. Before moving on, some information into the background of the development of this curriculum is needed.• As we tour the Module today, you may notice some discrepancies.

There are now exit tickets, but no Sprints, or Core Differentiated Fluency Practice Sets, for example.

• Some above grade level concepts are taught but not assessed (e.g. writing numerals to 100) and are explicitly mentioned in the Module Overview.

• Those implementing the curriculum may perceive this as a “disconnect,” but should not be concerned. By this point in the year, teachers are familiar enough with the curriculum to make wise decisions for their class based on their students’ needs.

• We are continually revising this curriculum to improve it. As always, your feedback is welcome, and know that it is an integral part of our revisions process.

2 min 13. Exit tickets are included in Module 6 also. So, if teachers decide to introduce the procedure, they will be able to continue it into the next Module.

Alternatively, Exit Tickets could be omitted, in order to prioritize other curriculum areas in this first year of implementation.

5 min 14. Let’s examine the Table of Contents (page i). Notice the incremental movement that is a distinctive feature of this curriculum. The instructional path echoes Module 1: counting in varied configurations, writing numerals, and composing and decomposing numbers.

Invite participants to consider the sequence of topics. Why aren’t the teen number concepts covered first, before counting to 100? (We return to teen numbers in Topic E, after counting to 100.)

Guide participants to realize:• In topic A, students need only the ability to count to 10, a skill from

Module 1. (Example: 10 and 4).• Composing and decomposing numbers, especially teen numbers, is a

highly complex skill.• Composition comes more easily to students than decomposition

(topic B). Recall that the concept of “more” is taught before “less” for the same reason. Addition is taught before subtraction. It is easier, both cognitively and developmentally, to “make” than to “break apart” or “take away.”

• In topic C students have to know that the “1” in 14 for example, represents 10 ones in order to decompose the number.

• Saying the number names in order is the least complex of skills. It requires memorization and extending a pattern (topic D). Knowing the structure of teen numbers supports students in gaining mastery of the counting sequence to 100, and builds early foundations in place value. For those reasons, working with numbers to 100 comes after substantial practice with teen numbers.

• We return to more complex work with teen numbers to finish the Module. The most complex work takes place in Topic E, where students represent teen numbers with equations, decompose to compare teen numbers, and reason about their representations.

• As in previous Modules, we finish with a fun, exploratory, culminating task in the final lesson. Students have the opportunity to demonstrate and celebrate the progress and achievements they have made in this Module.

• We encourage you to make it a truly celebratory event. Invite members of the school community, and allow students to “show off”

their accomplishments, similar to celebrations in other content areas: publishing parties, Science Fairs, etc.

Section: Grade K Module 5 Introduction Time: 57 minutes

In this section, you will be introduced to the Grade K Module 5 focus session.

Materials used include:• Grade K Module 5 PPT• Grade K Module 5 Facilitator Guide


5 min 15. To become familiar with Module 5:1) Read the narrative in the module overview (begins on page ii)2) Study the objective chart (pgs. vi and vii) in order to become familiar

with the Mathematics of this Module and the sequence of lessons.

6 min 16. Let’s take a look at Module 5 concepts in action.

4 min 17. Remind participants of need for anticipatory fluency. Counting the Say Ten Way started in fluency in Module 3, Lesson 1 so that students will now be fluent in counting to 20, and ready for the complex work with teen numbers in Module 5.

T: You’ve gotten so good at counting to ten, it’s time to start counting higher! Next is ten 1. Repeat please.

S: Ten 1.T: We can show it on our hands like this: ten (push out both hands, palms

out, as if doing a push-up exercise in the air, then pause with closed fists close to body), 1 (push out the right hand pinky finger). It’s your turn, ready?

S: Ten (push out both hands as if doing a push-up exercise in the air) and (closed fists, close to body), 1 (push out the left hand pinky finger).

T: Very good. Next is ten (push out both hands as if doing a push-up exercise in the air) and (closed fists, close to body), 2 (push out the right hand pinky and ring fingers). It’s your turn, ready?

S: Ten (push out both hands as if doing a push-up exercise in the air) and (closed fists, close to body), 2 (push out the left hand pinky and ring fingers).

4 min 18. Ten is such an important number that the first 9 days of this module focuses on students seeing teen numbers as 10 ones and some ones as opposed to 1 ten and some ones.

Bullet #1: Turn and talk about why this distinction is important.

The base-ten system is powerful because it allows students to bundle by 10 to create a new unit. In Kindergarten, we only work with one unit: ones. In G1-M2, students learn about making a new unit called a ten. As we explore Module 5, you will notice that we start to very precisely name the unit: 17 is 10 ones and 7 ones. In G1, 17 is 1 ten and 7 ones. Making 10 ones is a precursor to making a ten.

As adults we apply this concept of manipulating or combining units when thinking outside of base ten.

Examples:• I am 5’4”. I know that 5’4” (feet and inches) is also 60” and 4” (inches

only).• We have 70 minutes until break. I know 70 minutes (minutes only)

is also 1 hour 10 minutes (hours and minutes).• I want to take a 10 day vacation. I know that 10 days is also 1 week 3

days.

Each of these examples requires us to define a new unit number (12, 60, and 7).

Bullet #2: Understanding 10 as a unit is crucial in the base ten number system and foundational to future learning.

1) Solving addition and subtraction problems.2) Place Value3) Level 3 counting strategies: Decompose and addend and compose a

part with another addend (38 + 12 students think 12 is 10 and 2, 38 needs 2 to be 40 and I know 40 and 10 is 50).

4 min 19. 1. Call on a volunteer to count to 20 in another language if possible.2. In English the numbers eleven, twelve and thirteen don’t sound or

have the numbers one, two, or three in their names.

The numbers fourteen – nineteen, when spoken, we say the ones before the tens but when we write the number we write the tens before the ones.

10 min 20. Task:• Indicate the characters that represent the numbers 1, 2, 3 and 10 on

the chart (not necessary to pronounce the words in Chinese).• Ask participants to try and figure out how to write the numbers 11,

16 and 20. After wait time lower screen and reveal the answer.• Ask the participants to try again and write the number 21 in Chinese

characters.• Can you find the mistake in the last row? (36 is written as “three 6”

rather than 3 ten 6)

Reflection:• We expect students to understand teen numbers when many of our

conventions are arbitrary as explained on slide 12.• (Guide participants to realize that the pattern, along with their

knowledge of place value supported their understanding and ability to complete the task.)

Relate to Module:Refer to this quote in the Module Overview: “They ‘stand’ on the structure of the 10 ones and use what they know of numbers 1-9.” We just practiced MP. 7 “Look for and make use of structure.”• This was our inspiration for counting the “Say Ten” way. In some

countries this is called “Counting the Math Way.”• Page 5 of the K-5 NBT Progressions refers to this as the East Asian

way of counting.

6 min 21. Give participants time to read, discuss, and share.

0 min 22.

8 min 23. An example of Module 5 concepts in action.

3 min 24. • Students count all the objects in their bags relating the count to teen numbers which they say out loud. Identifying a group of 10 within teen numbers prepares student for Topic B where they use Hide Zero Cards, number bonds and write teen numbers. This lesson uses concrete materials to give the 1-digit in the tens place of teen numbers meaning as students move towards the abstract, the written numeral.

2 min 25. Here are some suggestions that will help with successful delivery.• Analyze the dialogue: anticipate misconceptions, scaffold into ideal

responses. Recall that the lesson is not a script.• Focus on the objective, remember that movement through the

concept is incremental, not “mile-wide, inch deep.” No need to cover everything in one lesson.

• It can be tempting to weave in extraneous information, and/or move ahead when you see students making progress.

• Examples of adding extraneous information: lesson includes the use of hide zero cards with teen numbers, teacher uses them to show numbers to 100, or brings out additional materials for modeling. “Let me show you how it looks on the Rekenrek!” Well-intentioned and enthusiastic teachers sometimes do this. It can derail a lesson, and leave struggling students confused.

• When teachers stay focused on these incremental objectives, they will find delivery to be more efficient, and see that there is sufficient time to reach all of components of the lesson within a given class period.

5 min 26. • In “A Story of Units” we advocate timeframe over taskframe, meaning that students should be encouraged to work hard for a designated period of time, rather than a designated task (i.e. a Problem Set in its entirety).

• This creates a natural form of differentiation, as some students will complete more problems in that allotted time than others.

• Since Problem Sets move from simple to complex this means that problems become increasingly challenging as students work.

• Model a parallel problem: Demonstrate an example (Print Lesson 16 problem set and show how to model a parallel problem).

• All directions and words should be read aloud to focus on the Math instead of reading proficiency.

Section: Topic A: Count 10 Ones and Some Ones Time: 26 minutes

In this section, you will focus on counting objects to ten and some ones using the Say Ten way.


• Sample Assessments


1 min 27. Topic A is very straightforward. You can see just by looking at the lesson objectives that we are going to continue to follow the concrete, pictorial, abstract sequence in Module 5.

3 min 28. • Start with a simple counting activity which bags have 10? Using an egg carton cut to have 10 spaces.

• Take bags of 10 and count out straw bundles of 10 to represent the bags that have 10 things in them.

• The Problem Set has children circle groups of 10. Getting them used to the idea of circling 10 before introducing teen numbers.

3 min 29. Again, we start with counting, but this time we are counting larger sets. Here children will start by putting objects in the egg carton, and then put any extra objects next to the carton. Introduce language, “I have 10 ones and ___ ones.”

Ask participants: What is happening here: composition or decomposition?

2 min 30. • The Application Problems are very fun and lighthearted ways to reinforce the idea that a teen number is 10 ones and some more ones.

• This lesson takes students to the next level of abstraction. Here, during the concept development they can’t move their objects to show 10 (like with the objects and egg cartons), but are asked to draw and circle 10 objects. This highlights embedded numbers.

• Here students will count in different configurations: lines, arrays, scattered, circular.

4 min 31. • The first part of the Concept Development has children working in partners, using linking cubes on their fingers to count the Say Ten way to 19. This is a great way to bring Counting the Math Way and Say Ten counting together.

T: (Place a cube on each of your 10 fingers) How many cubes do you see? (Ask for a helper)

T: (Place a cube on your helper’s right pinky finger.) Now how many cubes do you see?

S: Eleven! I see 10 and 1!T: You’re all correct! Eleven is 10 and 1! I’m going to teach you to count the

Say Ten way!T: (With a linking cube on each finger, raise your hands again.) How many

linking cubes is this?S: Ten!T: Every time Lucy adds another cube to her fingers we’ll Say Ten (show

your hands) and the number of ones you see on her fingers. Ready?S: (As helper adds cubes on her fingers from right to left in sequential order

up to 19.) Ten one, ten two, ten three, ten four, ten five, ten six, ten seven, ten eight, ten nine.

Then they count straws making a pile for each ten. The Problem Set requires significant set-up before leaving

students to work independently. Do the first problem together. (Demonstrate with counters and then dots.)

1 min 32. This is very similar to Lesson 4, but this time students work with 20 which allows them to make 2 groups of ten. This is a physical manifestation of the Say Ten way: 2 ten.

10 min 33. Show and discuss samples of assessments if available.

2 min 34. Materials needed:100 Rekenrek

Section: Topic B: Compose Numbers 11-20 from 10 and Some Ones; Represent and Write Teen Numbers

Time: 40 minutes

In this section, you will focus on advancing work with teen numbers by using manipulatives and working in reverse to gain

Materials used include:• Grade K Module 5 PPT

understanding at more abstract level. • Grade K Module 5 Facilitator Guide• Grade K Module 5 Lesson 6 CD


1 min 35. • In Topic B, students advance their work with teen numbers to a more abstract level by working with Hide Zero cards, Number Bonds, and working in reverse: from abstract to concrete, from abstract to pictorial.

5 min 36. • We have opted to call them Hide Zero cards, rather than Place Value cards because we are not using that language in the lessons, although it certainly lays the foundation for place value concepts. The goal is for students to regard the digit “1” in teen numbers as 10, rather than 1 ten.

• Thinking of the “zero” as still existing but being hidden, facilitates this conceptual understanding.

• Another reason is that place value cards are a commercially available product. We wanted to customize the cards used in this curriculum by providing the corresponding 5 group or ten frame on the back, giving students the ability to count all if necessary.

• Encourage students to count on from 10, but mastery of this skill is not expected.

• Allow participants to make and explore the hide zero cards.

5 min 37. • Model the RDW process as the Kindergarten version (say/draw/write).

• OK if students are approximating, that is, “pretend reading.” Important to develop the habit of and familiarity with procedure of RDW.

• Ask comprehension questions (i.e. How many boys? How many girls?).

• Focus is on counting all, rather than counting on, or addition, but if students realize this for themselves, and are able to do so accurately let’s not hinder them.

• Show actual student samples if available together with the next slide.

2 min 38. • Some samples are actual student work, some have been replicated here, but are based on student work.

• In the classroom, share student work, so that students can benefit from seeing their peers’ work, and may be inclined to try other types of drawings.

10 min 39. • Demonstrate the Concept Development

5 min 40. Show work samples that participants bring from their classrooms. Lead a discussion based on the samples.

2 min 41. • Guide participants to realize that the Hide Zero cards, in conjunction with the concrete and pictorial materials, develops conceptual understanding of the significance of the digit “1” in teen numbers.

• Reiterate that students are not asked to recognize the digit 1 in teen numbers as 1 ten (G1 standard), but rather as 10 ones, or simply “10” with the zero being hidden, as shown on the cards.

2 min 42. • Students extend their knowledge of number bonds to teen numbers.• Materials, representations, models, are familiar at this point. Call

attention to students’ growth. Recall their initial work with number bonds (within 10), and let them celebrate how far they’ve come.

• Notice the color change now at 10.

3 min 43. • This curriculum is built on the concretepictorialabstract progression of conceptual development but notice that in Lessons 8 and 9, students work from abstract to concrete and pictorial. Working in reverse can be a powerful experience for students.

• In these lessons, they start with the number. When using the Hide Zero cards, the zero is now hidden right from the start.

• They use their materials or drawings to model the number.• In partner work, they prove to their partner that they have modeled

the number accurately. This is where the 5 groups or ten frames on the back of the Hide Zero cards come into play. They can be used to verify, and provide a launching point for discussion.

1 min 44. • By working from abstract to pictorial, students show that they know the value of the digit “1” in the number 13 in this example.

1 min 45.

3 min 46. Call 3 participants up

T: (Show 7 dots.) How many do you see? (Give students time to count.)S: 7.T: How can you see 7 in two parts?S: (Coming up to the card.) 5 here and 2 here.T: Say the number sentence.S: 5and2makes7.T: Who sees 7 in two different parts?S: (Coming up to the card.) I see 3 here and 4 here.T: Say the number sentence.S: 3and4makes7.

Continue with other cards of seven.

Section: Topic C: Compose Numbers 11-20 from 10 and Some Ones; Represent and Write Teen Numbers

Time: 11 minutes

In this section, you will focus on understanding the teen number structure using number towers and stairs.



2 min 47. • Topic C Lessons build on the work of Module 1 when students learned about numbers 6-10 in relation to 5 using number stairs and finding embedded numbers in different counting configurations.

• Now, in Lessons 11 and 12 the teen number structure of 10 ones and some ones is reinforced as teen numbers are related to 10 using number towers (stairs). Number towers and stairs help students understand that each successive number name refers to a quantity that is one larger or one less (K.CC.4c)

• Topic C continues to mirror Module 1 in that students find the

embedded 10 in as many objects as 20 in linear, array, and circular configurations.

1 min 48. • Students make a rekenrek and relate the 20 beads to two sets of hands.

• This relates directly to grade 1 where they make a 10 using their magic counting sticks (see next slide).

4 min 49. This is the very first time students are introduced to this language of ten as a unit. Up until now, they have used 10 as a friendly number and see it as 10 individual ones. Now the top row of beads on the Rekenrek becomes not only 10 individual beads but 1 ten (push 10 across all at once.)Students go back to their work with their Hide Zero Cards and their Magic Counting Sticks, now rethinking their teen number as 1 ten and some more ones, as in 17 is the same as 1 ten and 7 ones.Let’s see how this understanding will help students solve addition and subtraction problems within 20.

NOTE to presenter: Will need 2 volunteers to be Partner A and Partner B as the presenter projects the hide zero cards as scripted.

T: Using your magic counting sticks, show me 10 ones.S: (Wiggle all 10 fingers.)T: Show me 1 ten. (Clasp 1 both hands.)S: (Clasp both hands.)T: (Project 14 with Hide Zero Cards.) With your partner show me 14 as a

ten and some ones.S: (Partner A clasps hands, Partner B shows 4 fingers.)T: How many tens are in 14?S: 1 ten.T: 14 is 1 ten and how many ones?S: 4 ones.

T: Let’s add 2. (Project 2 with the Hide Zero Card and write 14 + 2.) How will you do this? Will you add 2 to the ten or to the ones? (Split the Hide Zero Cards into 10 and 4)

S: To the ones.T: Add 2 more fingers.S: (Partner B adds 2 more fingers.)T: 4 and 2 is?S: 6.T: 10 and 6 is?S: 16.T: How many tens and ones make up 16?S: 1 ten 6 ones.

Repeat with 15 + 3.

Let’s subtract. With your partner, show me 13 as a ten and some ones. (Write 13 – 2.) Let’s take away 2. Can I take from the ones? (Yes.) Partner B, take 2 from 3. What do you have? (1.) Partner A and B, put your fingers together. What is 13 – 2? (11.)

With your partner show me 12 as a ten and some ones. Let’s take away 9. Can I take from the ones? (No.) Can I take from the ten? (Yes.) Partner A, unbundle your ten. (Show all fingers.)

Take away 9 all at once. (Show 1 finger.) What is 1 and 2? (3) So what is 12-9? (3)

Say the number sentence. (12 – 9 = 3.) Let’s try some more: 13 – 9, 15 – 8.

2 min 50. Discuss more than and less than phrases:• 16. 1 less is 15stating the pattern of 1 less (Extends the work of

GK-M1 to teen numbers.)• 15 is less than 16compare w/o quantifying (Relates to a

Kindergarten standard, but not the focus of this lesson.)• 15 is 1 less than 16comparing and quantifying (saying how much

more) (Goes beyond the standards and is linguistically complex for students at this age.)

2 min 51. • Lesson 13 reviews the notion that quantities arranged in one configuration can be changed to another configuration without changing the total but allowing a manipulation of the objects to make counting easier.

• Lesson 14 illustrates the need for finding the embedded 10 in teen numbers in the circular configuration. The circular configuration with larger numbers is challenging for young students. It also reinforces teen numbers as 10 ones and 4 ones.

Section: Topic D: Extend the Say Ten and Regular Count Sequence to 100

Time: 15 minutes

[minutes] In this section, you will focus on leading students beyond teen numbers to 100.



3 min 52. • Topic D leads students beyond teen numbers to 100 (K.CC.1) Students utilize their learning from Topics A-C with teen numbers 11-19 as they realize the number sequence is repeated over and over again within each decade as they explore counting to 100.

• Turn and talk about the sequence of objectives in Topic D.

2 min 53. • Thus far in Kindergarten the emphasis has been with numbers 1-20. Topic D extends this work to 100 and begins with counting on the decade. By counting the Say Ten and the regular way place value and rote counting by tens is reinforced.

• Lesson 15 is also a reminder that when we count up we should count down, which is a more challenging skill. (Demonstrate by having participants count down by fours starting at 40.)

1 min 54. • In Lesson 16 students count 9 beans and when they get to the Ten they can trade it for a 10-frame. This is a pre-cursor to the work they will be doing in first grade when they will think of 10 ones as 1 ten. It is also a foreshadowing of regrouping in addition and subtraction, also a G1 concept.

• Lesson 17 continues to develop rote counting across the 10. As the numbers get bigger and the counting sequences get longer crossing the 10 becomes a focus point as it is challenging for young children.

5 min 55. Do the problem set with participants:1. Show 50 dots using your hiding paper. Whisper count all the dots.

Say the last number in each row loudly and color the circle green.2. Show 60 dots using your hiding paper. Whisper count all the dots.

Put a blue box around the first dot in each row as you say the number loudly.

3. Show 70 dots using your hiding paper. Whisper count all the dots. Put a red triangle around the last dark dot as you say the number loudly.

By highlighting and saying loudly the first and the last dots students focus their count on crossing the 10. By highlighting the fifth dot students are seeing that they are saying “five” in the middle of each group of 10, foundational for rounding and estimation.

2 min 56. • Lesson 19 is optional because of the exploratory above standard nature of the lesson. Exposure to this type of work in Kindergarten will help students understand the work of Grade 1 and 2 (see next slide).

2 min 57. Like making a ten, taking from ten relies on the the knowledge of the bonds of 10, and it extends to multiples of ten.

A powerful means of guiding students towards understanding is to silently record a progression of problems like these, and allow students to detect the pattern on their own. Then challenge them to solve a problem that extends the pattern a little bit more. (CLICK to advance problems on the left side.)

Talk with a neighbor:How is there coherence between the Kindergarten lesson and the Grade 2 lesson?

Section: Topic E: Extend the Say Ten and Regular Count Sequence to 100

Time: 19 minutes

In this section, you will focus on using what students have learned about teen numbers to apply it to addition sentences, part-part whole relationships, and comparison of number.



1 min 58. Topic E focuses on using what students have learned about teen numbers to apply it to addition sentences, part-part whole relationships, and comparison of number.

2 min 59. • In Lesson 20 students demonstrate their understanding of teen number compositions and decompositions by working with number bonds and equations.

• Lesson 21 continues to have students represent teen number compositions and decompositions but now do it concretely with objects to demonstrate a depth of understanding. After substantial exposure to teen number concepts students interpret the meaning of the abstract equations and number bonds by modeling with concrete or pictorial materials. Complexity is added to this lesson by asking students to find a hidden part.

3 min 60. Let’s take a look at how this strategy is introduced to the students. Similar to introducing the Making Ten strategy in Topic A, the first 2 lessons in Topic B serve as preparatory lessons for the Take from Ten strategy.

Here is a word problem.Bailey Bunny has15 carrots. 10 are in a basket and 5 on a plate. She ate 9 carrots from the basket. How many carrots were left?

Here, the story problem explicitly asks the students to take away 9 from 10. (CLICK) When solving 15 – 9, students can see that 10 – 9 = 1 and 1 + 5 = 6. This allow students to begin using the take from ten strategy because the teen number is already separated into 2 smaller units for them, a unit of 10 and some ones and asks them to take 9 from 10 .

3 min 61. The next step in Grade 1 is to subtract 9 from a teen number without the context of a story where students are explicitly asked to take 9 from 12. Students should begin to decompose the teen number into 2 smaller units, a unit of 10 and some ones on their own and take 9 from Ten since they can’t take away 9 from 2.

Here, we show 12 – 9 at the pictorial level. (Click to advance animation to show the steps of 12- 9 pictorially)

3 min 62. • Lesson 22 has students decomposing two teen numbers into 10 ones and some ones to compare the numbers to each other. By doing this students see the embedded 10 in each of the teen numbers they are comparing. They are then guided to compare the ones that are left to decide which number is greater than or less than each other.

• This concept has future implications to Algebraic expressions. Here are two examples (write out on paper under a document camera):

10 + 7 ___ 9 + 1010 + 7 ___ 9 + 10 7 < 9

3x + 5 – 9 = 5 +12

3x + 5 – 9 = 5 + 12 3x – 9 = 12 +9 = +9 3x = 21 x = 7

2 min 63. • Lesson 23 and 24 has students synthesize all their learning about teen numbers and let’s them show their understanding of these numbers in a variety of ways.

• Being able to be flexible composing and decomposing teen numbers will facilitate students being able to manipulate these numbers to help them problem solve by creating easier problems in Grades 1 and 2 (see the next 2 slides).• Level 3 counting strategies (OAT progressions p. 6): Convert to

an Easier problem 38 + 12 (I know 12 is 10 and 2; 38 needs 2 to be 40; 40

and 10 is 50; 38 + 12 is 50)

2 min 64. Grade 1 Module 2 Topic B is devoted to introducing the Take from Ten strategy and provides opportunities for students to explore and practice this Level 3 strategy.

3 min 65. Grade 2 Topic A of Module 4, Sums and Differences to 100, students use and learn simplifying strategies.

They add and subtract multiples of 10, using number bonds to decompose and create equivalent but easier problems.

They learn arrow notation, which we call the arrow way. This strategy highlights place value, as students record the addition and subtraction of multiples of 10 and 100. It encourages students to use units the way they see best. Maybe they want to add tens first and then hundreds, or perhaps they prefer to start with hundreds.

Look at the various strategies a student might use to solve 26 + 30.

Section: Review Time: 13 minutes

In this section, you will review the key points of Grade K Module 5. Materials used include:• Grade K Module 5 PPT• Grade K Module 5 Facilitator Guide


0 min 66.

3 min 67. Recall that the Progressions Documents are the backbone of this curriculum, providing writers with knowledge about the mathematics, sequence of concepts, and models that shape these lessons. The Progressions, along with descriptive narratives provided with A Story of Units can be thought of as textbooks for Math teachers.

The Number and Operations in Base Ten, pages 1-10, Progressions Document will provide keen insight into the relationship between standards between grades K-2.

3 min 68. Take two minutes to turn and talk with others at your table. During this session, what information was particularly helpful and/or insightful? What new questions do you have?

Allow 2 minutes for participants to turn and talk. Bring the group to order and advance to the next slide.

2 min 69. Let’s review some key points of this session.

5 min 70.

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

● Grade K Module 5 PPT● Grade K Module 5 Facilitator Guide● Grade K Module 5 Module Overview● Grade K Module 4 Module Overview● Grade K Module 4 Lesson 6 CD● Sample Assessments

Additional Suggested Resources

● How to Implement A Story of Units● A Story of Units Year Long Curriculum Overview● A Story of Units CCLS Checklist● Operations and Algebraic Thinking Progression Document