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Module Focus: Grade 4 – Module 6 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 4 curriculum, A Story of Units. Key Points Decimals allow further application of fractions. Decimal and whole number units behave the same. In depth and engaging practice with fractions and decimal fractions strengthens number sense. Consider scaffolding to provide multiple entry points for students at all levels. Scaffolding Focused: Amplify Language
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Page 1: mc-14193-39844713.us-east-1.elb.amazonaws.commc-14193-39844713.us-east-1.elb.amazonaws.com/file/9…  · Web viewModule Focus: Grade 4 – Module 6: Grade 4 – Module 6

Module Focus: Grade 4 – Module 6 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 4 curriculum, A Story of Units.

Key Points● Decimals allow further application of fractions.● Decimal and whole number units behave the same.● In depth and engaging practice with fractions and decimal fractions strengthens number sense.● Consider scaffolding to provide multiple entry points for students at all levels.● 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?

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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 above.

Session Overview

Section Time Overview Prepared Resources Facilitator Preparation

Introduction 25 min Introduces Grade 4 Module 6• Grade 4 Module 6 PPT• Facilitator Guide

Review Grade 4 Module 6

Topic A: Exploration of Tenths

28 min

Explores the conceptual understanding of tenths as the decomposition of one 1 into 10 smaller units.

• Grade 4 Module 4 PPT• Facilitator Guide

Review Topic A

Topic B: Tenths and Hundredths

29 min

Explores decomposing 1 tenth into 10 hundredths and understanding the composition of a number with tenths and hundredths.

• Grade 4 Module 6 PPT• Facilitator Guide

Review Topic B

Topic C: Decimal Comparison

16 minExplores comparing decimals to hundredths using concrete contexts.

• Grade 4 Module 6 PPT• Facilitator Guide

Review Topic C

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Topic D: Addition with Tenths and Hundredths

21 minExplores adding fractions with denominators of 10 and 100.

• Grade 4 Module 6 PPT• Facilitator Guide

Review Topic D

Topic E: Money Amounts as Decimal Numbers

26 minExplores working with money amounts as decimals and applying fraction understanding to money.

• Grade 4 Module 6 PPT• Facilitator Guide

Review Topic E

Session Roadmap

Section: Introduction Time: 25 minutes

In this section, you will be introduced to the Grade 4 Module 6 focus session.

Materials used include:• Grade 4 Module 6 PPT• Grade 4 Module 6 Facilitator Guide• Grade 4 Module 6 End-of-Module Assessment

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

1 min 1. NOTE THAT THIS SESSION IS DESIGNED TO BE 145 MINUTES IN LENGTH.Welcome! In this Module Focus Session, we will examine Grade 4 – Module 6.

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

understanding across the module with a focus on the Concept Development within the lessons and how the Concept Development addresses each of the Focus Standards of Module 6

• 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.

2 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.

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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• Right angle and write angle• Second place for a race timed in seconds

Words with multiple meaning must be anticipated and then addressed, and

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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 G6-M5-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.

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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...”

1 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.

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1 min 8. We will begin by briefly viewing the Module Overview to understand the purpose of this module, and then we will take a look at the 4 Focus Standards within this module and how the concepts of decimals are developed in the Concept Development. Finally, we’ll take a look back at the Module, reflecting on all the parts as one cohesive whole.

Let’s get started with the Module Overview.

1 min 9. The sixth module in Grade 4 is Decimal Fractions. This module includes 16 lessons and is allotted 20 instructional days.

This module builds on understandings established in the previous module, Module 5 (Fraction Equivalence, Ordering, and Operations) of Grade 4. It picks up from the fraction understanding that students make in Module 5 as students extend their learning to express decimal fractions as decimals and to add decimal fractions. Students will also build the foundational knowledge necessary for success with decimals in Grade 5.

6 min 10. Take the next 5 minutes to briefly center yourself around the content of Module 6. Think about the learning students will use from Module 5 and previous modules. Think about any gaps that may need to be filled and how this work will prepare students for Grade 5.

Allow 5 minutes for participants to center themselves in this module.

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2 min 11. There are several new terms in this module that teachers should be aware of. Tenths and hundredths are terms that they heard during the fraction module, Module 5. Now we have a new understanding of these two terms in relation to where they lie in the place value chart.

(Click to advance the slide.)

Students have used expanded form in two different ways. One is to express the value of each place value as addends. When we call out “fraction expanded form” or “decimal expanded form”, we are referring to naming the value of each place as a multiplication sentence, seen here in the 2nd image.

(Click to advance images of expanded form.)

(Click to advance the slide.)

Finally, some of the most important terms occur in the first lesson. ALL numbers, ALL of them are decimal numbers. Until now, students referred to all the numbers they knew as “whole numbers”. “Whole numbers” are, in fact, decimal numbers as well.Decimal fractions are fractions with the denominators tenths, hundredths, thousandths, etc.

And, of course, the decimal point is pinnacle for understanding how to record a decimal number.

1 min 12. There are a few tools that are required by teachers in order to teach these lessons. The process for introducing tenths and hundredths require some of these tools, such as what you see listed.

At least one of each of these tools is important for teachers to have in order to introduce the two important and vital place values of tenths and hundredths. If, however, your school is able to offer more of these for each classroom, the experience will become more hands on.

Students will be measuring long strips of paper to the nearest tenth and weighing bags of rice to the nearest hundredth. Students will also observe

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amounts of water in beakers to the nearest tenth and hundredth.

Allow for ample time to search for these materials, prepare these materials, and plan how to implement these lessons. Consider using centers or rearranging a math block to allow teachers to share the materials amongst classrooms.

(Click to advance the slide.) The representations used in other modules and other grades to teach whole number understanding will be used again for decimal numbers as we are simply extending the place value chart two units to the right of the ones columns, and the models do not break down when we do so. This allows the students comfort and understanding of these new units.

5 min 13. (CLICK as speaking to advance through the 4 pages of the assessment.)

All 4 Focus Standards of this module will be taught in the 16 lessons and will be assessed here in the End-of-Module Assessment.

Looking at the assessment before beginning to plan or teach a module provides great insight into what skills students must be nearing mastery in. It allows you to see the models that will support the conceptual learnings which are introduced before abstract work is expected.

Keeping the end in mind allows teachers to plan backwards, knowing which areas of the standards and lessons are crucial. With the end goals in mind, teachers can then plan and go forward accordingly.

Classroom observers, such as administrators, can use the assessment as guidance for what kind of learning to expect to see in a classroom during this module.

Know that the Mid-Module Assessment can provide these same things but will only address the depth of the standards and content taught in the 1st half of the lessons. The Mid-Module assessment might provide better insight for the conceptual learning of a concept, instead of the culmination of a full study of a set of standards that the End-of Module assessment provides.

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Take about 3 minutes to complete Problem 6 of the End-of-Module Assessment. Don’t look at the sample student work yet. We will come back to the assessment at the end of the presentation to see what we have learned about decimals and what the standards are calling students to do.

1 min 14. Let’s discover how the concepts of this module are developed across the 4 Topics, keeping the 4 Focus Standards of this module at the forefront.

Section: Topic A: Exploration of Tenths Time: 28 minutes

In this section, you will focus on learning to develop the conceptual understanding of tenths as the decomposition of 1 one into ten smaller units.

Materials used include:• Grade 4 Module 6 PPT• Grade 4 Module 6 Facilitator Guide• Grade 4 Module 6 Selected Problems

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

1 min 15. Topic A includes 3 lessons that introduce concretely the idea that 1 one can be further decomposed. Until now, students had to think of a remaining number as a remainder, such as in division when ones could no further be subdivided. Students used metric measurement to introduce and to think about this as, for example, 1 kilogram can be decomposed into 10 smaller parts.

Because students need words to discuss their new learning, a majority of the New Terms are introduced in Lesson 1.

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Many of the representations used in Topic A are familiar (such as tape diagrams and number lines). We will decompose tape diagrams, number lines, and area models the same way we did with fractions, now just having a new method of recording, say 3 tenths. Instead of fraction form, we use decimal notation.

Other manipulatives are called for in order to introduce these new concepts concretely. Students will begin with weighing bags of rice on a digital scale and observing and decomposing the unit measurements found on meter sticks.

1 min 16. Read the standard, noting where it occurs, across the whole module. It is used in Topic E but is not a Focus Standard.

At the onset of Topic A, which covers tenths, and Topic B, which covers hundredths, the teacher is asked to use metric measurement to connect fraction understanding to decimal numbers. Students look at three different measurement models; a meter stick, a digital scale, and a liter container.

First, a meter stick is used to set a context. In looking at a meter stick, students will see that a meter stick can be divided into 10 parts. Let’s picture that. Doesn’t it visually appear in your mind as a tape diagram? Picture 30 centimeters on that meter stick. That’s 3 tenths if I drew a tape diagram to show 30 centimeters. I now have a context in which to write 3 tenths in unit language, as a fraction, and as a decimal. A digital scale is used to weigh bags of rice. A liter container is used to measure the capacity of water.

As with fractions, all focus is on decomposition. Just as we decompose 1 ten for 10 ones, we decompose 1 one for 10 tenths. This connection to the unit language of place value is vital, and the work is fundamental and foundational to any other decimal work for this module and subsequent grades.

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4 min 17. This lesson is the students’ first experience, in A Story of Units, with a decimal. Note that initial work with decimals is done concretely.

MODEL.1. Place 10 bags of rice, each weighing 1 tenth kilogram on a scale.2. Draw a tape diagram to represent 10 parts of 1 one. Label as fraction 1

tenth up to 10 tenths or 1.3. Draw a number line below, this time label decimals and introduce the

term as done on page 6.A.5.4. Remove the 10 bags, and then place only 1 bag. Identify the amount.

Record in unit language, fraction form, and decimal form. Repeat with 2 bags and 8 bags. Record what happens when the group of 2 bags and the group of 8 bags are placed on the scale together---- 0.2 + 0.8 = 1.0.

(CLICK). Here we see that those 10 – 1 tenth kilogram bags together represent a weight equal to 1 kilogram. The tape diagram models that pictorially, along with locating the fractions on the number line. Students can now represent a decimal fraction in decimal form.

Discuss activity with meter stick and cash register tape.

REFER TO LESSON 1 CONCEPT DEVELOPMENT for support on delivering this slide.

NOTE: During presentation, use of a digital scale with a kilograms reading. These are hard to find unless you search out a bakers or professional chef’s scale. Use of a spring scale with decimal readings is a good alternative.

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1 min 18. Students added one bag of rice at a time, working their way up to 10/10 or 1.0 and practiced writing each as a fraction and then in decimal form. Additionally, both a tape diagram and a number line were used to relate fractions to decimals.

1 min 19. After building to one, some bags were removed. Students stated the weight of the bags on the scale and off the scale. Together, the bags weigh 1 kg. Students expressed the sum of the bags as in fractional form and then in decimal form. Notice that we are not showing them how to add decimals, but rather we are expressing the addition of fractions in another way.

1 min 20. Discuss drawing a line 2 cm long. Extend the line 6 tenths cm. Record the total length as a fraction addition sentence and decimal addition sentence (as seen on slide).

Students are asked how many tenths are in 1 centimeter. (10 tenths) 1 area model represents 1 or 10 tenths, so shade 10 tenths to represent the 1 centimeter. Repeat for the 2nd centimeter. But with 6 tenths centimeter, only shade 6 tenths of the 3rd area model.

(CLICK.) Here are some sample images from Lesson 2 depicting what we just modeled together.

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3 min 21. Have participants represent 13 tenths using tenth number disks.

T: Talk with your partner. Is there any way we can use fewer disks to show this same value?

S: Bundle 10 tenths for 1 one.T: Do so. What disks do you have now?S: 1 one and 3 tenths.T: Express this number in decimal form. Show me your boards. (Snap.)S: (Show 1.3)T: Say this number. (Snap)S: 1 and 3 tenths.T: How many more to get to 2 ones? (Snap.)S: 7 tenths.

(CLICK.) Here is another example of 21 tenths bundled to show 2 ones 1 tenth.

4 min 22. Follow this script. Then CLICK to advance the slide.Repeat with 36.8 if participants need another example.

T: Hold up a place value disk with a value of 1 ten. We say the value of this disk is…?

S: 1 ten. Ten.T: (Draw or show 4 tens disks.) The total value of 4 of these is…?S: 4 tens. Forty.T: 4 tens written as a multiplication express is…?S: 4 × 1 ten. 4 × 10T: (Write the expression below the disks as pictures to the right.) 4 × 10

is…?S: 40. (Complete the number sentence.)T: (Draw or show 2 ones disks.) The total value of these 2 disks is…?S: 2 ones. Two.T: 2 ones written as a multiplication expression is…?S: 2 × 1. (Write the expression below the disks as pictures to the right.)

T: (4 × 10) + (2 × 1) is…?S: 42. (Complete the number sentence.)

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T: (Draw or show a tenth disk.) This place value disk says zero point one on it. We say the value of this disk is…?

S: 1 tenth.T: (Draw or show 6 one-tenth disks in five-group formation.) The total

value of 6 of these disks is…?S: 6 tenths.T: 6 tenths written as a multiplication expression is…?

S: 6 × 110 . (Write the expression below the disks as pictures to the right.)

T: Discuss the total value of the number represented by the disks with your partner.

S: Do what is in the parentheses first, then find the sum. 40 + 2 + 610 is 42

610

. 4 tens, 2 ones, 6 tenths. It’s like expanded form.

T: We have written 42 610 in expanded form, writing each term as a

multiplication expression. Just like with whole numbers, the expanded form allows us to see the place value unit for each digit.

T: (Point to (4 × 10) + (2 × 1) + (6 × 110) = 42

610 .) Talk with your partner.

How could you write this using decimal expanded form instead of fraction expanded form? Explain how you know.

S: (Work with partners, and write (4 × 10) + (2 × 1) + (6 × 0.1) = 42.6.) I know that 1 tenth can be written as zero point one and 42 and 6 tenths can be written as forty-two point six. We looked on our disks. We had 4 tens, 2 ones, and 6 disks that had 0.1 on them. We knew it was 42 +

0.6, so that helped us rewrite 42 610 as 42.6.

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1 min 23. Just as students located fractions on a number line in Grade 3, students use that knowledge here to plot decimal numbers on a number line, constantly decomposing the decimal number to consider the value of each unit as well as relating the decimal to its fraction counterpart.

8 min 24. Beginning the Module with tenths, students found that decimal fractions of tenths can be represented as decimal numbers. Students are gaining fluency to represent any number with tenths using decimal notation. They see that unit form and fraction form are equivalent to decimal form, and they see that expanded form can represent the value of each digit in a number.

(CLICK.) Now complete Problem #s 1-5 on the Problem Set.

Give participants 8 minutes to work.

3 min 25. Turn and talk to those around you about the difficulties that may come up for some students with the mathematics of this topic and talk about the types of scaffolds that may be effective.Give 2 minutes for discussion.

(CLICK to advance the Note for Multiple Means for Action and Expression.)

Here is an example of a UDL that is placed in Lesson 3 to remind the teacher about the pronunciation of the /th/ at the end of tenths. We can anticipate that this scaffold will be useful in the coming lessons, and applicable to hundredths as well.

Section: Topic B: Tenths and Hundredths Time: 29 minutes

In this section, you will focus on decomposing 1 tenth into 10 Materials used include:

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hundredths and understanding the composition of a number with tenths and hundredths.

• Grade 4 Module 6 PPT• Grade 4 Module 6 Facilitator Guide• Grade 4 Module 6 Selected Problems

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

1 min 26. Topic B introduces hundredths as the decomposition of 1 tenth into 10 hundredths as students relate 100 hundredths as being equivalent to 1 one. Beginning concretely by using a metric length model, students build their understanding of hundredths conceptually. Area models, tape diagrams, and number lines pictorially represent hundredths. Number disks again support the understanding of the value of each digit in a number and prepare students for the place value chart with decimals.

2 min 27. The term and notation for hundredths is introduced concretely by looking at a meter stick. Students know that 100 centimeters equals 1 meter. So 1 centimeter is 1/100 of a meter.

(Model.) This strip of paper, representing a tape diagram of a meter, is 1 meter long and is decomposed into 10 equal parts. 1 part is shaded, representing 1/10 of a meter. How many centimeters equal 1/10 meter? (10 centimeters.) How many hundredths of a meter equals 1/10 meter? (10/100 meter)

(Write 1/10 = 10/100 and 0.1 = 0.10.) Here is where students begin to represent tenths as hundredths.

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1 min 28. Read the standard, note where it occurs.

The last part of this standard will be covered during Topic D when students add decimal fractions. In Topic B, students add tenths and hundredths to show how decimal numbers are composed and to show the value of each unit.

(CLICK to highlight part of the standard.) This Topic really focuses on understanding that 24 hundredths is composed of 2 tenths and 4 hundredths. Since tenths and hundredths are unlike units, we decompose 2 tenths as 20 hundredths to make 24 hundredths.

(CLICK to advance the slide to show 2 visual models.) As always, we support the numerical work with visual models. Let’s take a look at some of the activities students will complete to understand this standard.

1 min 29. As seen here with a tape diagram, number line, and the various forms of recording, the models used with whole numbers and tenths apply to work with hundredths as well.

Note that by seeing 20 hundredths as 2 tenths, students can more efficiently shade a tape diagram or ‘hop’ on the number line instead of counting each hundredth.

3 min 30. (MODEL with 1 strip of meter paper with 2 tenths shaded.)

T: This strip of paper is 1 meter long. How many tenths are shaded?S: 2 tenths.T: So we say 2/10 meter is shaded. (Write) Use your tape diagram template

to represent this amount.Participants shade 2 tenths.T: (Write 2/10m + 5/100 m) Shade 5/100 meter more. What do we need to

do to shade that?S: Partition 1 tenth into 10 hundredths. (Shade 5 hundredths.)T: (Point to the 1st tenth.) How many hundredths are shaded here?

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S: 10 hundredths.T: (Point to the 2nd tenth). How many hundredths are shaded here?S: 10 hundredths.T: How many hundredths of a meter are shaded altogether? Explain to your

partner.

(CLICK.) Students are seeing that 1 tenth is equal to 10 hundredths. So to compose 25 hundredths, we think of it as 2 tenths + 5 hundredths which is also 20 hundredths + 5 hundredths.

This is similar to thinking of the number 25. 25 is ‘2 tens 5 ones’ or ‘20 ones + 5 ones’.

3 min 31. How does Lesson 4 allow for multiple entry points?

Allow participants to discuss for 2 minutes.

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).

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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.

(CLICK to advance the Note for Multiple Means for Action and Expression.)

3 min 32. Using area models, students show that 1 tenth is equal to 10 hundredths. They can write these as equivalent fraction and decimal statements.

(CLICK). Using what they know about equivalent fractions, students conjecture about finding equivalent tenths and hundredths (using prior learning of multiplying and dividing fractions).

Try it yourself. Use your area models to show that 3/10 is equal to 30/100. Write equivalent fraction and decimal statements, and show how those statements are, in fact, equal using multiplication and division.

Note that we are finding equivalent DECIMAL FRACTIONS. We are NOT finding equivalent decimals. We find the equivalent decimal fractions and then express the decimal fractions as decimal numbers. This is reflective of the standard 4.NF.6.

From here, students can now model hundredths using tape diagrams and area models.

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3 min 33. Show me 16 hundredths arranged in a 5 group formation.

(CLICK)

What is the value of each disk? (1 hundredth.)How many hundredths are there? (16 hundredths)Can we make a tenth? Do so with your partner. Tell your partner what you did. (10 hundredths can be traded for 1 tenth.)

(CLICK)

Draw a number bond to show 0.16 as tenths and hundredths.

(CLICK)

This number bond shows decimals and fractions. It is not critical if it is one form, another, or a combination. We want students to have fluidity and fluency between both forms.We want students to think about the most efficient way they can model hundredths. Just as with the tape diagram and area model, students didn’t have to decompose all of the tenths into hundredths. Same with place value disks, they can be bundled as tenths and hundredths.

1 min 34. Everything students have learned about mixed number fractions and their understanding of decimal fractions as decimal numbers prepares them to seamlessly transfer understanding to representing mixed number fractions as decimals. Again, this work is supported with pictorial models. To move back to the concrete, you could use 2 meter sticks or more than ten 1/10 kilogram bags of rice for students who need further conceptual support.

(Talk through the images on the slide.)

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2 min 35. Using your personal white board, write 3 ones 8 tenths as a decimal. (Write.) CLICK.

The ones and the tenths have a special place. CLICK. Label ones above the 3 and tenths above the 8. (Write.)

CLICK. Write 3 ones 8 hundredths as a decimal. (Write). Show your partner what you’ve written.

CLICK. Tell your partner why your answer is correct. (Talk.)

All 3 digits have a special place. Label them. (Write.) CLICK.

Write 3 ones 80 hundredths. (Write.) Label the units. Show your partner.

CLICK. Say this number. (Three and eighty hundredths) Express 80 hundredths as tenths. (8 tenths).

Explain to your partner why the first and last numbers that we wrote are equivalent and why their value is different than the value of the second number we wrote.(Participants discuss. Listen for good conversations to share out.)

Students will work just as you have to determine the importance of each place value unit and the value of each digit. Students will practice with other number sets as well to get a firm understanding of decimal notation.

A conversation around ‘zero’ may come up here or as a Debrief question. Remember zero can be the most important number in the base-10 system. Hide Zero cards may be an important tool to use in this conversation. Note that you can create decimal Hide Zero cards too. (Model Hide Zero cards, if available.)

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1 min 36. Students are asked to draw disks to represent 378.73. Here we have the place value disks. Students then write this number in unit form to help them in thinking about where to place each digit in a place value chart. Students then place the number on a place value chart that includes the name of each place, including tenths and hundredths.

T: The digit 3 is in which places? Say the largest place first.S: Hundreds and the hundredths.T: Say the value of the digit in the hundreds place.S: 3 hundreds.T: Say the value of the digit in the hundredths place.S: 3 hundredths.T: Their values sound so much alike. Discuss with your partner how to tell

them apart.S: (Participants discuss.)

CLICK

Next, just as students did with whole numbers, they write the value of each digit in expanded form. Instead of just adding the values of each place, we want to highlight the value of each unit and how many of each unit there are. Students will record this expanded ‘expanded form’ in decimal and fraction form.

1 min 37. Students may notice the pattern that develops and the symmetry that is occurring around the ones place in the place value chart. Note that it is NOT symmetric around the decimal point which is a common misconception. This conversation and graphic appears in the Debrief of Lesson 7.

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1 min 38. Just as students in lower grades learned how to rename 243 from hundreds, tens, and ones into just tens and ones, and then just ones, students also gain that fluency with decimal numbers, as now they can further decompose units across the decimal point. Of course, we start pictorially, using the area model so students can reason why 2.4 is the same as 24 tenths and 240 hundredths.

1 min 39. That work is moved most abstractly on the place value chart as students represent a decimal number as the chip method to further decompose, representing smaller units. This fluency will build across the lessons and will prepare students for their work with decimal operations in Grade 5.

5 min 40. To review, in Topic B, students work primarily with decimals between zero and one for at least part of a lesson and then extend to decimals greater than

1. Students can plot decimal numbers, record hundredths in expanded form, model with place value disks, and use the area model to represent decimal numbers. Templates, such as area models and number lines, are provided with many of the lessons.

Students are now gaining greater mastery of 2 of the Focus Standards (4.NF.5 and 4.NF.6) of this module. They are able to now represent fractions with the units tenths and hundredths in decimal form. They are also able to represent a decimal or fraction with tenths as an equivalent decimal or fraction of hundredths.

CLICK. Try Problems #s 6-11 on the Problem Set. (Give participants 5 minutes to complete.)

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Section: Topic C: Decimal Comparison Time: 16 min

In this section, you will focus on comparing decimals to hundredths using concrete contexts including metric measurements, comparing lengths, masses of objects, and the capacity of containers.

• Materials used include: Grade 4 Module 6 PPT• Grade 4 Module 6 Facilitator Guide• Grade 4 Module 6 Selected Problems

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

1 min 41. Topic C focuses on the comparison of decimal numbers up to hundredths. Students do this concretely with metric measurements, comparing lengths, masses of objects and the capacity of containers by recording the values on a place value chart. Using these concrete contexts, it allows students to place a context around what they are comparing, assisting in their justification and reasoning of the numbers. Students will also list a series of decimal numbers from greatest to least and from least to greatest.

1 min 42. Read the standard, note where it occurs.

(Click to advance the visual area model.)

7 tenths. 27 hundredths. 27 is greater than 7 so 27 hundredths is greater than 7 tenths.

Isn’t that what students sometime think? We want to help them see that models will verify our reasoning, and models precede numerical work so students can reach conclusions properly. Clearly a focus on the units is fundamental.

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2 min 43. Following the same practice of the first 2 topics, we begin decimal comparison with a concrete representation, weighing bags of rice, comparing beakers of water, and observing lengths on a meter stick, as shown here by these 2 tape diagrams.

Here, on my two meter sticks, I have ribbon (or colored duct tape) taped to the meter sticks in order to measure it. It is visually clear which is longer and which is shorter. This concrete model of the meter sticks and the pictorial model of the tape diagram will help to develop the conceptual foundation for comparing decimal numbers. Soon students will be expected to move abstractly.

This concrete level allows students to see that when there are zero ones, the number with more tenths is greater. The connection to writing the numbers in the place value chart moves students to the abstract level and allows students to reason about their answers.

Students record measurements in a place value chart and consider the whole decimal number in comparison to another decimal number.

Statements such as “____ is greater than ___” are made.

Students will also have other concrete experiences with weighing bags of rice and comparing the volume of liquid in 1 liter beakers and recording their measurements in a place value chart, organizing the materials from lightest to heaviest or from least to greatest, then making their comparison statements.

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1 min 44. Continuing with pictorial models to support the students’ understanding, area models and number lines represent given fractions and students compare fractions using the greater than, less than, or equal to symbols.

Eventually students are encouraged to make comparisons abstractly, reasoning with units.

6 min 45. In the last lesson of decimal comparison, students are faced with a set of cards with decimal numbers written in various forms that they must organize from least to greatest. You have a set of those cards that you cut this morning. Please organize them now.

Work with your partner to plot these points on a number line. You have the Lesson 11 number line template to do so. There are 3 number lines provided and 3 forms that the numbers are written in (unit form, decimal form, and fraction form). Consider using 1 line for decimals and 1 line for fractions. The 3rd line might be mixed forms. As you plot the points, think about equivalency.

(Give participants 4 minutes to work.)

Notice how this activity provides students a lot of communication around decimal number comparison and how they get a chance to reason and use their learning from the first 2 topics of this module, as well as to rely on their fraction knowledge.

Although mixed numbers were not used in this example, the Concept Development of the lesson provides other sets of numbers, including mixed numbers, for the students to compare and order.

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5 min 46. Students have now compared various decimal numbers, reasoning about their size. Students have used the familiar contexts of measurement to initiate these comparisons. In doing so, they have had conversations during Debriefs to discuss why it is not valid to compare weight to length (because the units are different). When making comparisons using the comparison symbols, students can ultimately justify their responses through pictures, numbers, or words.

CLICK.

Try Problem #s 14-15 on the Problem Set.(Give participants 4 minutes)

Section: Topic D: Addition with Tenths and Hundredths Time: 21 min

In this section, you will focus on adding two fractions with respective denominators of 10 and 100, thereby strengthening understanding of the relationship between decimal numbers and decimal fractions and extending understanding of fraction addition and finding equivalent fractions in order to add tenths and hundredths.

Materials used include:• Grade 4 Module 6 PPT• Grade 4 Module 6 Facilitator Guide• Grade 4 Module 6 Selected Problems

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

1 min 47. Although students in Grade 4 have a fluency of addition and subtraction of multi-digit whole numbers, not until Grade 5 do the standards allow students to add or subtract decimal numbers. Therefore, we strengthen students’ understanding of the relationship between decimal numbers and decimal fractions and extend their understanding of fraction addition and finding equivalent fractions in order to add tenths and hundredths. Students will decompose tenths into hundreds in order to add like units, hundredths to hundredths. Students will use similar strategies from fraction addition in Module 5 to add decimal fractions. The final number sentence will then be written in decimal form to, again, strengthen their understanding of the relationship between decimal fractions and decimal numbers. Students will

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also solve word problems, placing the addition into a context.

1 min 48. Read the standard, note where it occurs.

Now students will experience the full extent of this standard. One of the important focuses of this module is that students will not be adding or subtracting decimals using decimal notation. Students instead have an opportunity to strengthen their understanding of fraction addition in order to add decimal numbers. Students must make sure the decimal numbers are represented with like units, usually hundredths, and then add using unit or fraction form.

(Click to advance the slide to show 2 visual models.)

As always, we support the numerical work with visual models such as the area model and the place value chart.

1 min 49. (Each CLICK populates the next number sentence.)- 3 girls + 4 girls: like units so we can add.- 3 girls + 4 students: unlike units. We need to rename a unit. We don’t

know if the students are boys or girls, but we can call the girls students.

- 3 students + 4 students: Now we have like units and can add- 3 fifths + 4 fifths: Like units. We can add. We did this in Module 5.- 3 tenths + 4 tenths: Like units we can add. We also did this in Module 5.- 3 tenths + 4 hundreds: Unlike, but related units. There were 2 lessons

in Module 5 to introduce this concept, but now we will dive in deeper and make the connection to decimal fractions and decimal numbers.

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2 min 50. To add 3 tenths to 4 hundredths, students see that 3 tenths must be decomposed into 30 hundredths. They can do this mathematically by multiplying the numerator and the denominator by 10. They can also first, however, be supported visually.

CLICK. Here is the area model shaded for 3 tenths and the 4th tenth decomposed into 4 hundredths.

CLICK. The second area model shows how the student decomposed all tenths into hundredths to show 30 hundredths and 4 hundredths makes 34 hundredths.

CLICK. This place value chart is another way students can model the addition of tenths and hundredths. 3 tenths and 4 hundredths are at the top of the chart. 3 tenths are decomposed into 30 hundredths. Now there are 30 hundredths plus 4 existing hundredths which adds to 34 hundredths.

3 min 51. Students can always use models to support their work, but we are starting to move away from pictorial support, especially as students are gaining fluency with the relationship tenths have to hundredths.

Here, students see immediately they must rename tenths.

CLICK. They do so using multiplication.

CLICK. And they add together.

CLICK. Students are then encouraged to rename the sum as a decimal, really supporting the first standard taught in this module.

CLICK. Try one yourself.

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3 min 52. Let’s add. What must we do first? (Make like units.)

CLICK. Now that we have like units, I can add.

CLICK. I see that 117 hundredths is a fraction greater than 1. I can rename this as a mixed number by pulling out 1 or 100 hundredths.

CLICK. And I can write the answer as a mixed number fraction and decimal.

CLICK. Alternatively, I can add these two fractions using a method I learned in Module 5.

CLICK. Rename the tenths as hundredths.

CLICK. I can pull 50/100 from each fraction in order to make 1. Adding 10 hundredths and 7 hundredths in my head is easy.

CLICK. Then I can rename the sum as a decimal.

MODEL 9/10 + 64/100.

1 min 53. Students are then given a decimal number expression in which they must convert to a fraction number expression before solving. A slow sequence is given starting with adding 2 addends that are each less than one that have a sum less than one.

CLICK. Students then work with 2 addends less than one which have a sum greater than one. Students rename to find a mixed number.

CLICK. And finally, students work to add 2 mixed numbers.

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3 min 54. How does Lesson 14 with word problems allow for multiple entry points for UDLs?

Let participants talk for 2 minutes.

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.

(CLICK to advance the Note for Multiple Means for Representation and

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Engagement.)

6 min 55. Students now can both express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and use that technique to add two fractions. That is straight from the standard 4.NF.5. Students have also strengthened their ability to express decimals as fractions and fractions as decimals with denominators of 10 or 100. Although students are not directly adding decimal numbers in Grade 4, they are prepared to work with decimal operations in Grade 5 and extend their fraction addition to unlike units.

CLICK. Try Problems 14-17 on the Problem Set.

(Give participants 5 minutes)

Section: Topic E: Money Amount as Decimal Numbers Time: 26 min

In this section, you will focus on working with money amounts written as decimals, apply fraction understanding to money, and solve word problems.

Materials used include:• Grade 4 Module 6 PPT• Grade 4 Module 6 Facilitator Guide• Grade 4 Module 6 Selected Problems• Grade 4 Module 6 End-of-Module Assessment

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

1 min 56. Students come to Grade 4 with an understanding of the value of coins and of adding those coins together, writing their answer using a cent symbol. Because students are not introduced to the decimal until Grade 4, it is not necessary to teach the dollar sign and decimal to write 123 cents as dollar sign 1 point 23 ($1.23).

In this Topic, students will speak of coins being a fraction of a dollar, write the value of coins using a dollar sign and decimal, and solve word problems involving money.

Students will draw tape diagrams to model word problems and likely will use a number bond when adding. Remember, if money word problems are

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given, they must be solved in fraction form and converted back to a decimal.You can use money, fake or real, as a concrete entry point to this Topic. Images of money are given on the Problem Set and Homework.

1 min 57. Read the standard, note where it occurs.

The last two lessons of the Module use this standard to solve word problems involving money.

First, students relate their new decimal understanding to money, relating that 25 cents, or 1 quarter, is 25/100 of a dollar, or ¼ of a dollar.

Next, students solve word problems with money using the 4 operations. Since students cannot compute with decimals in decimal notation, students must consider using fraction form or unit form to solve. The lessons will provide student examples to model this work.

2 min 58. First students discuss the value of a coin. A penny is 1 cent. There are 100 pennies in a dollar so 1 penny is 1/100 of a dollar which is equal to $0.01. Students know how to record 1/100 as a decimal and the dollar sign is added. See how, if 2nd graders were writing dollars and cents using decimals, they wouldn’t have the foundational knowledge of decimals to understand their value?

CLICK. We practice with multiplies of a coin such as 7 pennies.

CLICK. Next, dimes.

CLICK. Lastly quarters. We choose not to utilize nickels as they are not in the base ten system supporting decimal work nor have we worked with the denominator of 20. We did choose quarters, however, because of its ease and familiarity. Think of geometry and quarter turns. The denominator of 4 is widely used in fraction work in Grades 3 and 4. Students have a sense of fluency with quarters. Challenge students with nickels, if appropriate. In fact, there is a Debrief question in Lesson 15 to remind you and let you know it wasn’t an oversight not to include them.

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CLICK. Next we ask students to find the value of 2 coins. 7 dimes 2 pennies.

CLICK. This is work from Grade 2. 72 cents.

CLICK. But, students can now tell you in a number sentence where 72 came from. It’s 7 copies of a dime and 2 copies of a penny.

CLICK. 72 cents is 72/100 of a dollar.

CLICK. And, students can record that value using a dollar sign and decimal.

10 min 59. Students can find the value of each addend written in fraction form and add the two fractions to solve. But, we find that adding in unit form is more efficient and connected to the way in which money is read. Also, students have yet to learn how to further divide fractions, hence we just use unit form so that all 4 operations with money are uniform.

CLICK. There are 2 solution samples here showing how the cents were decomposed to make another dollar.

Try Problem Set #18-20 now for about 4 minutes. Continue on to the word problems #21-22. We will review the word problems together.

(Give participants 5-8 minutes to complete the Problem Set.)

2 min 60. Use RDW process and solve together with participants. Click to advance the drawing, 2 solutions, and statement.

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2 min 61. Use RDW process and solve together with participants. Click to advance the drawing, 2 solutions, and statement.

1 min 62. Students have learned how to relate the value of coins to fractions of a dollar which, in turn, has allowed them to conceptually understand the meaning of the decimal when recording the value of money using a dollar sign and decimal point. Students can solve word problems involving money using the 4 operations but should solve using unit form.

CLICK.

Try Problem #s 23-28 on the Problem Set.(Give participants 10 minutes)

1 min 63. That is the end of our introduction to the Focus Standards addressed in Module 6 and the instructional sequence that the module follows.

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5 min 64. Now that we walked through the careful sequence and development for the conceptual understanding of decimals and their relationship to fractions, review the work you did prior on Problem 6. What have you learned since? What are some of your old habits that may have to fly out the window with the new CCSS?

Try your hand at some of the other 5 problems. Will students be familiar with the type of questioning on the assessment that is closely aligned to the standards?

How are you further prepared for implementation of this module and what further questions do you still have?

(ALTERNATIVE: If short on time, have participants reflect on these bullet points as they scan the student work sample of the End-of-Module Assessment.)

1 min 65. Read the key points for closing.

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

Video Reflect on a prompt Active learning Turn and talk

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Turnkey Materials Provided

Grade 4 Module 6 PPT Grade 4 Module 6 Facilitator Guide Grade 4 Module 6 End-of-Module Assessment Grade 4 Module 6 Selected Problems

Additional Suggested Resources● How to Implement A Story of Units● A Story of Units Year Long Curriculum Overview● A Story of Units CCLS Checklist