Project for Lesson Study

7/30/2019 Project for Lesson Study

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MC2

LIFT Research Lesson Template

Grade Level: 1st Date: Feb. 26, 2013

Instructor: Victoria/Mari # of Students:

Class Time: Class Type (check one):

Location: Regular SPED Bilingual/ESL OtherTombaugh 8:15

Dona Ana 12:30

Context: (Describe social/ cultural context of school)

I. Goals:

A. Overarching Goal: (What kind of people do you want your students tobe?)

"All students, meaning students with diverse learning needs, engage confidently in solving problems by self-selectingstrategies and tools to find solutions, and communicate their mathematics thinking and reasoning with each other."

B. Mathematics Process Goal: (What kind of mathematical thinkers do you want your students to be?)We want students to be critical thinkers, draw conclusions, persevere, speak math fluently, discuss their ideas and sharereasoning.

C. Math Content Goals: (Whatare your math goals for your students as a result of doing this unit?)CCSS.Math.Content.1.OA.3 Apply properties of operations as strategies to add and subtract.2Examples: If 8 + 3 = 11 is

known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can badded to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

D. Research Lesson Goal: (How does this research lesson fit with the other goals? What do you want to learn about your students from thisresearch lesson?)

How do students group two numbers to make ten?

How do students group 2 numbers to make ten in a three addend equation?

How do students learn and apply the associative property?

II. Description of math content learning goal: (1 to 2 sentences)

Students will work in groups to show how they add three numbers. They will explain which 2 numbers were added first and why.


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III. Description of the Research Lesson

Launch:

1. (15 min) Building a context for the lesson (Connecting to meaningful things or previous lesson):Role Play

Create the scenario of the confused teacher in which she needs a small group of seven students (actors). Shellrequest that the students get into a group of three. Students will group themselves. Count how many students are in

each of the 3 groups. (2-2-3; or 1-3-3)Then, she requests the students group themselves into 2 groups. Students get into two groups. Now we have a

group of 3 and a group of 4.

Now, the confused teacher realizes she only needs one group. How many are in one group? Review the process thatjust occurred. Write down the numbers?Model

Ask students to get in a circle on the carpet. Ask a student to be my partner. Model on the carpet how to play 3, 2, 1with the dice and the paper. Example, if three dice were rolled 3 + 5 + 2, students would record the three addends in

one column. Then, with those same three dice, theyd combine two dice dots to make a two addend equation, ex. 8 +2, and then combine to make one sum.

Essential Vocabula

Add

Plus

Equal

Total

Record

Easier Way

(Combine Lesson

2. Laying the framework for the learning experience (Introduce research lesson to students):Learning targets:

1. How can you communicate your ideas?

2. Can you show one way to add three numbers?

3. How can you group two numbers?


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Criteria for success:

The students can explain and/or name the strategy they used to group two of the three dice together to make two

addends, and then add the third number.

Possible Student Questions or Misconceptions Possible Teacher Questions/ Strategies/ ResponsesWhat do students need to know/be doing to

successfully engage in this part of the lesson?Observed Lesson Data

Model for the students possible questions we

might ask our partner to find out why he/she

pushed together the first 2 numbers.

How to add.

How to write the numbers on the recording

sheet.

Explore: Engaging students with concepts (Exploring, Investigating, Problem Solving):

Kids pair up in groups of two. Each pair receives three dice and recording sheet. Students take turns throwing dice and the other personrecords the three addends on each die in the 3 column, then two dice are pushed together (added together) to get a two addend equation

and recorded in the 2 column, finally all three dice are added together to get the sum. The roles are reversed and one person rolls the dic

and the other records.

After the students have played 2 or 3 times. Teacher will ask and chart some of the strategies the students are using to add the numbers.

Then she will ask them to play again, (a couple more times). Stop and ask for any other observations to add to the chart.

Next the teacher will roll 3 numbers and the whole class will record and decide how to add these specific numbers. Begin charting student

strategies of combining numbers. Which two numbers makes the most sense to combine first?

Students work in groups. Write down different ways to make the benchmark number and record it in their math journals.Roll dice (number cubes). Roll the dice. Use ten frames to show the numbers.

Student continue in pairs. They take turns recording the numbers thrown by the teacher, adding the first 2 numbers of their choice,recording it in the second column, and then writing the total sum of all the dice on the third column.

The student observing the student doing the sum, will ask, why did you choose those two numbers?

Or, students can discuss which 2 numbers to add first, and then asking if there is another way.

Roll 3 dice. Push two together. How do you group to make 2 addends?

Move from 3 dice to two ten frames.



Student might push 2 dice together because these

share the same color.

Students only way of adding is counting the

Which 2 numbers are you adding first? Why?

Is there another way to add the first 2 addends?

Students should be able to say which are the 2

numbers they added first, and give a reason

for choosing those 2 numbers.


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dots.

Sharing ideas/solutions (Whole group, small group, written):

As students work during the workshop the teacher will invite some of the students to share their strategies to finding the total sum.



Summarizing (Gathering Evidence How will you know students met the learning goal?):

Student will be able to verbalize how he/she added the 3 numbers.

The students will explain why they pushed together the first 2 dice.Teacher will use some of the samples of the students work to share with the rest of the class.

The charts can be used as an anchor chart, for future reference in the class.




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III. Description of the Research Lesson

Launch:

3. (15 min) Building a context for the lesson (Connecting to meaningful things or previous lesson):Role PlayCreate the scenario of the confused teacher in which she needs a small groups of seven students (actors).

TeacherShell request that the students get into a group of three. Students will group themselves. Count how manystudents are in each of the 3 groups. (2-2-3; or 1-3-3) Connect to the dice.

Then, she requests the students group themselves into 2 groups. Students get into two groups. Now we have agroup of 3 and a group of 4.

Now, the confused teacher realizes she only needs one group. How many are in one group? Review the process thatjust occurred. Write down the numbers?

Model

Ask students to get in a circle on the carpet. Ask a student to be my partner. Model on the carpet how to play 3, 2, 1

with the dice and the paper. Example, if three dice were rolled 3 + 5 + 2, students would record the three addends inone column. Then, with those same three dice, theyd combine two dice dots to make a two addend equation, ex. 8 +

2, and then combine to make one sum.

Throw 3 dice, ask how many dots? How do you know?

Essential Vocabula

Add

Plus

Equal

Total

Record

An easier way

Combine

4. Laying the framework for the learning experience (Introduce research lesson to students):Learning targets:

1. How do you add 3 numbers?

2. How do you slow down and share your thinking.


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Criteria for success:

We want you to share how you add 3 numbers.

Then, we want you to slow down and share how you added the 3 numbers.



Model for the students possible questions we

might ask our partner to find out why he/she

pushed together the first 2 numbers.

How to add.

How to write the numbers on the recording

sheet.

Explore: Engaging students with concepts (Exploring, Investigating, Problem Solving):

Kids pair up in groups of two. Each pair receives three dice and recording sheet. Students take turns throwing dice and the other personrecords the three addends on each die in the 3 column, then two dice are pushed together (added together) to get a two addend equation

and recorded in the 2 column, finally all three dice are added together to get the sum. The roles are reversed and one person rolls the dic

and the other records.

After the students have played 2 or 3 times. Teacher will ask and chart some of the strategies the students are using to add the numbers.

Then she will ask them to play again, (a couple more times). Stop and ask for any other observations to add to the chart.

Next the teacher will roll 3 numbers and the whole class will record and decide how to add these specific numbers. Begin charting student

strategies of combining numbers. Which two numbers makes the most sense to combine first?

Students work in groups. Write down different ways to make the benchmark number and record it in their math journals.Roll dice (number cubes). Roll the dice. Use ten frames to show the numbers.

Students work continue in pairs. They take turns recording the numbers thrown by the teacher, adding the first 2 numbers of their choice,recording it in the second column, and then writing the total sum of all the dice on the third column.

The student observing the student doing the sum, will ask, why did you choose those two numbers?

Or, students can discuss which 2 numbers to add first, and then asking if there is another way.

Roll 3 dice. Push two together. How do you group to make 2 addends?

Move from 3 dice to two ten frames.



Student might pushed together 2 dice together

because these share the same color.

Students only way of adding is counting the

Which 2 numbers are you adding first? Why?

Is there another way to add the first 2 addends?

Students should be able to say which are the 2

numbers they added first, and give a reason

for choosing those 2 numbers.


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dots.

Sharing ideas/solutions (Whole group, small group, written):

As students work during the workshop the teacher will invite some of the students to share their strategies to finding the total sum.



Summarizing (Gathering Evidence How will you know students met the learning goal?):

Student will be able to verbalize how he/she added the 3 numbers.

The students will explain why they pushed together the first 2 dice.Teacher will use some of the samples of the students work to share with the rest of the class.

The charts can be used as an anchor chart, for future reference in the class.




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Section 1: Introduction

When we first met as a team of K-1 teachers, we reflected on our students and what we felt were the most important skills and

concepts they needed to learn and acquire to become successful mathematicians as adults. Our overarching goal became that all of ourstudents, regardless of their learning needs, are to be able to engage confidently in solving problems by self-selecting strategies and to

to find solutions, and to communicate their mathematical thinking and reasoning with each other. With this goal in mind, we chose to

investigate two related focal points for our lesson study. First, how do students learn and apply the associative property? And second, h

do students group two numbers and add a third number, of a 3 addend equation?

The reason we chose this topic was due to the students low scores in the mid-year assessments for the CCSS-Math 1.OA.3,

both Kathryns and Annettes classrooms. This standard states:Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11

is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4,

the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative

property of addition.)

To help us prepare to teach the standard, we read Properties of Addition and Subtraction in Van de Walles book , Elementa

and Middle School Mathematics. More specifically, we read the first two parts that described the commutative and associative properti

for addition. Because both the CC standard and the text in the book described an example of associative property as finding thebenchmark number of 10, when adding three numbers in an equation, we thought that was the main purpose of teaching associative

property. After reading the standard more carefully, we realized that it was just one example of the kind of grouping the students migh

to find the sum of 3 addends.

The next step was to write learning targets that would include the math concept and our overarching goal for our students. Thetargets were posed as questions to guide the students work and how they would show and explain their thinking. The learning targets

were:

1. How can you communicate your ideas?

2. Can you show one way to add three numbers?


We followed with what we determined would be the Criteria for Success: The students can explain and/or name the strategy th

used to group two of the three dice together to make two addends, and then add the third number.

We decided to create an activity and a recording worksheet to help the students practice adding three numbers. We called the

activity 3-2-1, and proceeded to create the lesson plan to teach and help the students practice to learn the lessons objectives. The les

was introduced with a skit, that included a small group of students (7) being grouped into different sets of students. They were grouped

into three groups. The groups consisted of 3 students, 2 students, and a final group of 2 students. Then they were moved around to form

two groups, by combining the two groups of 2 students and keeping the other group of three students the same. And lastly, all the studewere brought together to form one group of 7. Through the skit we introduced the idea to the students that when given 3 numbers to ad

you can first combine 2 of the sets and then add the third number to create a whole group.

After the skit, the teacher modeled the activity, 3-2-1. This activity paired students and provided them with 3 dice and a

recording worksheet The objective of the activity was to have students practice throwing 3 dice, pushing together 2 dice of their choice

and then adding the third number to sum of the first combination of 2 dice. We used teacher observation of the conversation between th

students and the 3-2-1 recording worksheets showing the students work during the activity, to determine if the students had met the

learning goal.

Our hope was to help our students understand the mathematical concept of commutative and associative properties, and to be

able to communicate orally the process they used to solve the addition problem. We also wanted to learn what strategy they used to ad

the first 2 numbers. Was it adding doubles, counting on, or finding a bench mark number? We felt that the students mathematical

understanding and the procedure they used to find a solution was equally important, to understanding these two addition properties.The students in both classrooms are in the dual language program, using the Gomez and Gomez model, where math is always

taught in English. The students in the first grade are not dissuaded or discouraged to use their native language with each other. Kathryn

classroom demographics include 74% of her students as Socioeconomic Economic Status and Limited English Speaker. Annettes

classroom has 80% SES and 40% LES. As we planned the lesson, we felt that through the skit, the modeling of the activity, and the

paired grouping students would receive support both in language and cooperative learning.

Section 2 Mathematics Learning

We recognized that students understanding of the commutative property and their relational thinking impacted how easily the

were able solve a three addend equation using the associative property. In our preparations, we explored how we thought students

approached an equation with three addends. Students needed to have a firm understanding of the relationship between addendsthat th

addends in this type of equation are three parts of a whole. In order to successfully solve an equation, such as 6 + 4 + 4 = 14, students f


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need to select two addends to combine and then add the third. Students may begin adding two of the addends in any order that simplifie

or makes the equation efficient for them to solve. Students could use various strategies, such as doubles, making ten, fact families, etc.

combine two of the three numbers and then add the final to find the sum. The commutative property is a precursor to understanding the

associative property in that the addends can be reversed and yet the equation will remain true, for example 6 + 4 = 10 is the same as 4 += 10. For student to understand this concept, they need to understand that the addends are parts of a whole and the relationship therein.

Students also need to have a firm understanding of equivalency. When students move from three addends to an equation with two

addends, such as 2 + 3 + 3 = 2 + 6, the students need to understand that both sides of the equation are the same amount or that the who

has remained the same, but the parts or composition of the whole has changed.

Recording Sheet 1

We noted that the terminology we used and the structure of the recording sheet made a difference in the students understandi

of the steps in this process. In the first iteration of this lesson, approximately 30% had misconceptions that stemmed from relational

thinking. Out of this population, two common misconceptions occurred. Despite these misconceptions, the majority of the students solv

the three addend equation correctly, but these students were confused in terms of the role of the two addends in the solution.

Misconceptions 3 Addends 2 Addends Sum

Example 1 3 + 4 + 4 3 + 4 11

Example 2 3 + 4 + 4 3 + 4 7Example 3 3 + 4 + 4 34 + 4 11

In Example 1, students looked at the equation, not as parts of a whole, but as a solution to be solved from left to right by counting on. T

sum was not difficult to determine for them, but the students had a difficult time understanding the role of the two addend equation. Somany students just dropped the final addend. The recording sheet we used in the first lesson may have played a role in these

misconceptions in that it didnt support the conceptual understanding students needed to move from three addends to two and may hav

added to students misunderstanding in the use of numbers in the columns, rather than visuals. In Example 2, students once again dropp

one of the three addends and added the two addend equations to get the sum. Once again, the sum is correct for the two addends.

In Example 3, students used a similar strategy of counting on to solve the three addend equation and were fairly successful in finding th

correct sum, but did not understand how to regroup three addends into two. In our lesson study preparations, we had decided to use the

term push together two dice to indicate that students were to add two dice together when moving from three addends to two. We eve

physically pushed two dice together to show them how. Students picked up on the idea of pushing together, but not the concept behind

Therefore, students pushed two of the addends together to make a two digit number (example 3 + 4 + 4 = 34 + 4). Students did not see

34 as a two digit number, but just 3 and 4 pushed together. Therefore, the sum of the three addend equation remained 11 and not 38.

Students difficulties in shifting from three parts to two parts to one whole helped us in making decisions about how to change our seco

iteration of the lesson.Students misconceptions as well as our own growing understanding of the scaffolding students needed to be successful with the

associative property led us to make several critical, but small changes to our lesson approach. The first change we made was to the

recording sheet which allowed students to utilize an example of the concept underlying the associative property.

Recording Sheet 2


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In the second lesson, we also emphasized in our modeling how to move from three addends to two and lessened our focus on

sum. During the launch we utilized student modeling of the task by selecting student pairs that had added the three parts to make two. W

honed in on the strategies they used to scaffold the students conceptual understanding of the process. The student models set the stagethe more independent work during the exploration. We created a talking target focused on students naming the strategy they used inmaking the decision which two of the three addends to combine (see discussion below). We also changed the teacher terminology by

using both combine and push together interchangeably. These terms used in combination emphasized the process of how to move

from three addends to two.

The second group of students was successful in their use of multiple strategies to solve a three addend equation. They

demonstrated use of the associative property by freely selecting any two of the three addends together, such as 1 + 5 + 1= 5 + 2. Studen

selected to add the two 1s together despite their location in the equation. Students were not stuck in counting on from left to right as in

first group of students. After the exploration, student groups summarized their use of the associative property further demonstrating the

understandings.

As a team, we learned quite a bit about the mathematical content involved in the use of the associative property in first grade.

Although the Lesson Study team engaged in multiple conversations about the associative property, I do not think we fully understood

what students needed to know until after the first iteration of the lesson. In the Common Core Standard 1.OA.3, an example is used wh

students move from three addends to two by making ten. It took several discussions to recognize that students could use multiplestrategies, such as doubles or skip counting, to combine two of three addends. Despite these conversations, it wasnt until the actual

implementation of the lesson that we realized that students strategy preferences varied greatly and yet they were still demonstrating th

associative property. The majority of students actually preferred to group by using doubles. The other major learning that we, as teache

found was that students can derive the correct answer of a three addend equation without using the associative property, as demonstrate

in the first lesson study. Students approached the equation linearly rather than as an overall problem to be solved. They wanted to solve

left to right, one part at a time, rather than looking for and making use of the structure of the equation as in Math Practices 7. If the first

group of students had looked for efficient methods or structures of adding two of the three addends together, then students might have

grasped the associative property.

Section 3: Instructional Strategies

As we began designing our lesson we utilized the Math Accessibility Framework to plan and implement accessible math

instruction and support for our students. We considered the math by deciding which Common Core Standard we should focus on andthen decided on 1.OA.3 (apply properties of operations as strategies to add and subtract) since it is critical in order for students to build

that foundation of adding while developing various strategies, as they go on to the other grades. By comparing a variety of solution

strategies, students build their understanding of the relationship between addition and subtraction and by understanding the notion of tAssociative Property it builds flexibility for computation and estimating, which is a key element of number sense. Our lesson was

therefore structured to focus on specific learning goal and the students would have an opportunity to be part of the important mathemat

that they learned throughout the activity. Thus, by keeping the math at the forefront we thought about the Standard we were addressin

and asked ourselves these questions:

What is the math students are to know and be able to do?

What do we know about the math content and what do we need to know?

How is the activity designed so the students can access the math content?

We also considered the students by discussing their strengths and difficulties and had conversations about the fact that both the

classrooms are utilizing the Gomez and Gomez Bilingual Model, so it was crucial that we give our students more opportunities to learnefficient strategies of sharing their thinking and asking their Pair proper questions to clarify their mathematical thinking and collabor

on purposeful tasks. Kathryn and I, also emphasized that some of our students are ELLs and are at different levels of understanding


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academic and social language in English. Knowing this is crucial because creating a supportive classroom culture is respectful of learn

differences and allows students to feel comfortable in taking risks. Also, by doing the activity from our lesson, would the students rea

that you do not have to add left to right, but you can group addends and that you can reduce three addends to two by combining and it i

easier if you look for ways to make 10? These are some of the potential barriers we thought of when designing our lesson.In order to facilitate a lesson that would be a good match to our math goals and address our students strengths and needs, we utilized t

following Accessibility Strategies:

1. Helpedstudentsunderstandtasks(providedvisualandauditorydirections)2. Helpedstudentsaccessmathinvariedways(webuiltontheirpriormathknowledge;usedvisuals)3. Builtonstudentindependence(usedthinkalouds;modeledstrategies)4. Promotedunderstandingthroughdiscourse(studentsworkedinPairs)5. Createdasupportivelearningenvironment(activeparticipation,engagement,clarificationthroughthe1st

language(Spanish)

Algebraic thinking and doing the mathematics involves choosing, combining, and applying effective strategies for answering so rather

than ask the students what two dice they could push together to make it easier to add, we decided it would be more effective to use th

proper term of combining. Common Core utilizes the term, combining, as early as kindergarten when the students are learning the

concepts of composing and decomposing numbers from 11 to 19 into 10 ones.

When we began designing our learning targets for our lesson, we had decided on the following:1. How can you communicate your ideas?

2. Can you show one way to add 3 numbers?


The criteria for success in choosing these learning targets were for the students to be able to explain and/or name the strategy they usedgroup two of the three dice together to make two addends and then add the 3rd number.

Since the two classrooms that were involved in this lesson study (Annettes and Kathryns) are implementing the Gomez &

Gomez Dual Language Bilingual Model, in which they emphasize utilizing Bilingual Pairs (to support each others language and conte

learning), we also decided that our learning targets should reflect the notion of the two Pairs increasing their interaction but with the

teacher modeling how that interaction should sound like, since we did not do that in the first lesson. Common Core Standards require

students to think and respond at higher levels but many students simply have no idea of the processes used when learning new

information. What I and my lesson study colleagues realized after teaching the first lesson, is that there are multiple steps that go into

learning process and one way to break that down for our students was to model our thinking so that they would be able to do the same.

This is a sample of what Kathryn said to model that process: I want you to ask your partner- how did you add? Then she asked astudent to be her partner while she modeled the procedure of asking one another how they added the three numbers. We realized that

process was simple and assumed all our students would know how to talk through that process but without modeling our own thinkingprocess it is not that simple for all students. The whole purpose to model the strategy of sharing their thinking was to show our studen

how we are processing information in order to motivate them to higher levels of learning by making sure they actually understand wha

they are expected to do. In order to reflect our new insights after the first lesson, our Learning Targets were changed to the following:

1. How do you add three numbers?

2. Ask your partner, How did you add?

The Criteria for Success still called for the students to be able to add three numbers using strategies to make it easier, but now they sho

be able to share (explain) how they added the three numbers.

The biggest challenge, believe it or not, after the first lesson, was our Recording Sheet, in which the students wrote down their

numbers from rolling a dice three times. We realized the Sheet was not as clear to our students as it could have been; we decided to m

some minor changes and that we also needed to model the process of recording their numbers (see handout #1 and #2 to view the chan

we made to the Recording Sheet). With these changes, we knew our Launch portion of the lesson would last a little longer, but still wonot be over the recommended time of 15 minutes and would make the actual lesson clearer to the students.In order to engage the students, we used a couple of instructional strategies. The teacher, Mrs. Million, introduced herself and right awa

sparked the students interest by saying that her name has numbers in it, also teaches first grade and that she likes to have plays. She th

asked the students, Who likes to have plays? All the students raised their hands in delight because they all love plays. She then

continued by saying, I think for this lesson Im going to be a confused teacher but I need some students to help me. She rolled three

dice and got a total of 6 so she told the students she needed three groups of 6 students but then the teacher realized the lesson only need

two groups and the audience had to help the students figure out how to get into two groups. Then the teacher realized that she only

needed one group of students so again the audience helped them to regroup into only one group of six. The kids went from three adde

to two and then the sum-they were learning but in a fun, interactive way.

In the 1st lesson, the teacher emphasized that the students were all mathematicians and that mathematicians go back and check

their work. We believe, by stating this it allowed all of the students to feel comfortable taking risks and understand that the teacher is

facilitator not simply the person that knows everything. During the 1st lesson, the teacher also stopped at one point to say, Lets talk


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little bit about what youre doing because Im noticing different strategies that youre using. Can one of you share? Sharing various

strategies is a powerful tool because everyone solves problems differently and it provides an opportunity to look at multiple ways to so

problems. The teacher was utilizing the Accessibility Principle of gathering evidence of the effectiveness of strategies and let the

students reflect on the strategies they were using. Also, the teacher demonstrated the use of creating a learning environment wherestudents are actively engaged in problem solving, collaboration, and independent thinking. The teacher played an active role in their

construction of knowledge through her questioning strategies and guidance. For example, throughout the lesson, she asked the followi

Which numbers did you push? How much does that make? Can you record it on paper? Is there something we can write? How do you

know? What symbol can we write? Is there something to help you remember? What are you going to do next? The teachers talk, or

mathematical discourse, definitely plays an important role in students learning as evidenced during this Lesson Study.

For both lessons, the teachers put closure on the lesson by bringing all the students (whole-group) back to the front of the clasand summarized the learning that took place. For example, in the first lesson, the teacher mentioned that she realized the worksheet

(Recording Sheet) was a little confusing. To clarify the process of writing the three numbers they got from rolling the dice and adding

them together, she wrote on the recording sheet for her first role of three dice, 3, 1, 2. Then, on the second column when the students ar

supposed to combine two of the dice to get a two addend equation, but the student wrote 3 and 1. The students said that three and one i

four. Pointing to the two in the first column, the teacher then asked, What happened to this number- what was missing? A student

responded, If the 2 was there it would be right. The teacher responds, So we could write 4 + 2 = 6; yes we have to have all thenumbers to show the final answer. The teacher then said, What else is missing? A student responds, Putting the plus and the plus

On chart paper, the teacher then writes- ____+_____ and asks the students, I wonder if putting (drawing) the two dice together would

help you? What do you think? The teacher then drew two squares to signify the two dice on the paper. By discussing the recording

process of the game once again, the weakness of the Recording Sheet was identified through a meaningful discussion in which we

believe, made a big difference in their understanding of what should have been recorded on their sheet.

In the 2nd lesson, our new Learning Targets were written on chart paper for all to see, so the teacher put closure by asking the

students if they felt they were now able to add three numbers and if they asked their Pairs how they added during the activity. Rather taccepting just a yes answer she had several Pairs stand up and share their strategies and their thinking to the whole class. On chart

paper, see attached, she drew visuals to represent the dice and numbers 1 and 3 + 4 and two girls shared that they added one and three

and got 4 and that they also knew that 4 + 4 = 8. The teacher asked, Is doubles a good way to add two numbers together? Two othe

students shared that their three numbers were 6, 6, and 5. Then one said, I put 6+6 = 12 and put 5 more. The teacher asked, Why wthat easier? The students responded, In kinder I got confused but now I know the doubles. In fact, a few students said that they

grouped the numbers by ten, but the majority of the students used the strategy of doubles to add the three numbers. At the end of the

lesson, both teachers had students share their mathematical thinking, because all students bring strengths and experiences to mathemati

learning and this was an effective way to bring closure to the lesson.

Documents

Project for Lesson Study