my. web viewtitle of learning experience: adding doubles. nys standards/performance . indicators....

New York State Academy for Teaching and LearningFinal Learning Experience/Information Form

Contact InformationResiding Address (including street, city state, and zip-code) Malorie Cummings

7832 Catherine StDerby, NY 14047

Phone numbers Home Phone(716) 512 2245

Cell Phone(716) 521 4852

Email Address [email protected]

Title of learning Experience: Adding Doubles

NYS Standards/Performance Indicators

Common Core Standard: Mathematics

Domain: Operations & Algebraic Thinking (2.OA)

Cluster: Add and Subtract within 20

Standard 2: Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Peer Review Date: October 18th, 2012

Peer Review Focus Question: How can I improve my pre and post assessments, and my rubric?

Adding Doubles Cummings

School InformationGrade Level instructed Second Grade

Content Area addressed within LE Math

School District in which LE was implemented Cheektowaga

Specific School within District Maryvale Primary School

School Address (including street, city, state, and zip-code) 1 Nagel Drive, Cheektowaga, NY 122

Supporting Standard:

Common Core Standard: ELA

CCR Anchor: Foundational Skills –Read with sufficient accuracy and fluency to support comprehension.

Strand: Reading (RF)

Grade: 2

Standard 4a: Read grade-level text with purpose and understanding.

LEARNING CONTEXT

Purpose/Rational for Learning Experience:

The purpose of this lesson is to teach the students the concept of adding doubles. The students learn that a number sentence with two of the same addends is known as a doubles fact. The students grasp the concept of a doubles fact through SMART board technology. New vocabulary words such as addends, and doubles fact are also introduced. In addition, the students apply their knowledge of double facts by completing a math worksheet with a variety of question formats. Learning is enhanced through a doubles song and through real life application. As an introduction, an egg carton, a pair of die, dominoes, and even students themselves are used to demonstrate a doubles fact. Last, this lesson integrates both mathematics and ELA Common Core Standards.

Enduring understanding

- A doubles fact is a number sentence with the same addends.- The sum of a doubles fact can always be separated into two equal parts.

Essential Question(s):

- How do patterns help you solve problems?

Guided Question(s):

- What is a doubles fact?- How is a doubles fact different from other facts?- What is an addend?- Where do you see doubles in your everyday life?- What two numbers will always be the same in a doubles fact?


Congruency Table

Standard

2.OA.2

Student Task Learning Objectives(see page 9)

Student Work Assessment Tools

Add and subtract within 20.

Fluently add and subtract within 20 using mental strategies. By the end of Grade 2, know from memory all sums of two one-digit numbers.

(www.nysed.govcommon core

standards: mathematics pg.

18)

The students sing a doubles fact song through using their

rhythmic and mental skills.

Students will orally add

doubles facts up to 20 using a

doubles fact song

The students sing I Can Add

Doubles song with the lyrics and then once

more from memory.

The Students answer six (6) questions for their Doubles Pre-Assessment. This is worth four (4) points total. The students are required to answer four number sentence problems and then two (2) word problems.

The students will add three

doubles facts within twenty

then sort them in two vortexes: either doubles fact or non-doubles fact.

Students will add doubles facts within 20 to physically

separate them from non-double

facts on a SMART board

The students complete double facts on the SMART board. The first two double facts provide picture support. The last eight problems require students to find the missing addend and/ or sum

Students will write the missing addend or sum for each double

fact

Students will add or subtract a doubles fact

within 20 to find the missing part or

sum.

The students will complete pages 41 and 42 of the Envision Math Worksheet.

Supporting Standard

2.RF.4a

Students will read to solve double fact word problems

Students will complete page 42 on the Envision Math Worksheet. Page 42 requires

The Doubles Post-Assessment consists of thirteen questions. It is worth 16 points. This


http://www.nysed.gov/

Read with sufficient accuracy and fluency to support necessary comprehension.

(www.nysed.govcommon core standards ( ELA pg. 25).

the students to read the word problems, and then to write a word problem of their own.

assessment requires the students to draw the problem, solve for missing doubles, and to answer two multiple choice word problems.

Class Background

This Learning Experience focuses on a second grade classroom located at Maryvale Primary School in the town of Cheektowaga, NY. This lesson is taught in a general education classroom. All together there are 22 students in the classroom. There is one teacher in the classroom, besides myself. One student is diagnosed with ADHD and has an IEP. Another student is an ESL student who receives intervention for reading and language. In addition, there are two students who are pulled out for math intervention. Overall, there is a wide variety of learning levels in both areas of reading and mathematics in the classroom. Therefore, lessons have to be implemented effectively to achieve comprehension from the whole class for this lesson. Classroom rules and procedures, found in Appendix A and B, are always followed and creates a safe and effective learning environment. The floor plan in Appendix C illustrates the layout of the classroom this lesson is taught.

Overview of what students need to know/to be able to do in order to succeed.

Prior to Learning Experience:

- Students have background on how to add two single-digit numbers.- Students know a plus sign means to add.- Students should know the answer to an addition problem is known as the sum.- Students have the knowledge of some vocabulary words- Students know the rules and procedures of the classroom.- Students know the rules and procedures of the SMART board.- Students know how to write a number sentence

During and after the Implementation of the learning Experience

- Students have a better understanding of the words addends and doubles fact.- Students know how to write a doubles fact.- Students have a better understanding of the concept of a double.- Students are more aware of the adding doubles strategies.- Students become more fluent in reciting math facts. - Students gain a better understanding of the riddle, “when you add, you start with a part,

to join another part to find the sum or the whole”.


http://www.nysed.gov/

Key Subject Specific Vocabulary:

- double fact: a number sentence in which both addends are the exact same number.- addend: the number being added in a math fact.- part: another name for an addend - sum: the answer to and addition problem.

Assessment Plan

Tools

Diagnostic

Prior to this LE, students completed the doubles fact pre-assessment in mathematics. Students complete six questions by writing the missing double fact to complete both a horizontal math and a vertical math sentence. Students identify and write the sum of a doubles fact. The pre-assessment requires the students to read one word problem, to identify the doubles fact, then to write the doubles fact. Students also identify if a number sentence is a doubles fact or not; then explain why (Appendix E-I).

Formative

The students complete the EnVision math worksheet during guided and independent practice. Numbers one through 7 are replicated on the SMART board. The students take turns filling in the missing double and the sum. The EnVision worksheet is divided into two sections: the guided practice and the independent practice. The questions scaffold the students learning by first including pictures, then just by providing number sentences. An extension to the formative assessment is provided by number 17 where students are required to us algebraic skills to complete the doubles fact. The last set of questions includes word problems and a written response. This formative assessment scaffolds the students thinking and allows them to see the doubles facts in various formats (Appendix L).

Summative

The students complete one double-sided worksheet. The first side of the worksheet requires the students to fill in the missing double and the sum. There are six questions the students write their answers in. Then, there are four multiple choice questions consisting of two word problems and two number sentence problems. This side of the worksheet allows the students to practice what they have learned. On the other side of the worksheet, the students are required to show their thinking by drawing out the problem. Then the students write their doubles fact on the lines provided. This enrichment allows the students to exercise their algebra skills.

Doubles Rubric (Teacher Edition)


Category Exemplary4

Proficient3

Progressing2

Needs Improvement

1

Double Addition facts

The student completed the

problem by writing 3 correct

doubles fact



double facts



double fact

The student did not write a

double fact

Drawing

The student demonstrates the

concept of doubles by

drawing 6 of the correct double in

the space provided

The student demonstrates the concept of double by drawing 5 of

the correct doubles in the

space provided.

The student demonstrates the concept of double by drawing 4 of

the correct doubles in the

space provided.

The student draws less than four objects to

demonstrate the concept of a doubles fact.

Missing double and sum

The student writes 11-10 correct

addends and sums to show the

missing double

The student writes 8-9 correct addends and sums

to show the missing double

The student writes 6-7 correct

addends and sums to show the

missing double

The student writes 5 or less correct addends to show the missing double.

Correct number of multiple

choice

Out of 4 questions4=4 points3=3 points2=2 points1=1 point

0 = 0 points

Total: _____________ / 16

Comments:

Math Assessment Student Check- List:


Is your name on your paper?

Did you follow the directions?

Have you answered every question?

Do your answers make sense?

Is your handwriting neat?

Are you proud to hand this in?

Student Work

The pre-assessment is administered to all the second grade students prior to any explicit teaching on doubles facts. All 22 students are present for this assessment. The students are


allotted 10 minutes to take the pre-assessment. Due to the difference of academic levels, all students will work for the full 10 minutes to move on in order to allow time for everyone.

The post-assessment is administered the next day to all 22 students after instruction. Since there are more problems on the post-assessment, the students are allotted 15 minutes to complete it. All students completed the post-assessment within the 15 minute allotted time.

The following chart shows the scores of each student:

Participants Pre Assessment Score Post Assessment ScoreStudent # 1 3 3Student #2 1 2Student #3 4 4Student # 4 2 3Student # 5 2 4Student #6 4 4Student # 7 2 3Student # 8 2 4Student # 9 3 4Student # 10 4 4Student # 11 3 3Student # 12 4 4Student # 13 3 4Student # 14 3 4Student # 15 3 4Student # 16 3 3Student # 17 2 3Student # 18 4 4Student # 19 4 4Student # 20 2 3Student # 21 3 4Student # 22 2 4


Chart Data Overview

Attributes Pre Assessment Post Assessment DifferenceAverage 2.86 3.59 .73Median 3 4Mode 3 4Standard Deviation .8888 .59032

Pre Assessment Key

Level Score Number of StudentsDeveloping 2-1 8Proficient 3 8Distinguished 4 6

Post Assessment Key

Level Score Number of StudentsDeveloping 2-1 1Proficient 3 7Distinguished 4 14

The following graph shows pre and post information on the assessment:


Developing Proficient Distinguished0

2

4

6

8

10

12

14

16

Pre and Post Assessment Data

Pre-AssessmentPost-Assessment

Level of Performance

Num

ber o

f Stu

dent

s

Conclusion

From the graph, it is evident that students achieved the objective in the lesson in both the proficient and distinguished levels. The pre-assessment shows eight students were still developing, or progressing, double fact skills. The students were unable to identify why the given number sentence was not a doubles fact in addition to identifying the missing parts in the number sentence. However, the pos-assessment shows substantial growth. The students were able to identify the missing double, solve word problems requiring double facts, and show double facts by drawing out the two parts. Only one developing student remains while fourteen students reached the distinguished level. Yet, many students lost points due to incorrect drawings. Assistance is provided for two students who receive Response to Intervention instruction. Also, one student is English as a Second Language learner who needs one question blacked out on the post-assessment. Examples of student work can be found on Appendix (F,G,H and Q,R).

Procedure


Learning Objectives

1.0 Students will understand that the addends are the same in a doubles fact with 100% accuracy.1.1 Students will orally add doubles facts up to 20 using doubles fact song with 90%-

100% accuracy.1.2 Students will classify doubles facts from non-double facts on a SMART board

activity with 90% -100% accuracy.1.3 Students will add or subtract a doubles fact within 20 to find the missing part or

sum by complete the Envision Math Worksheet. 90% -100% accuracy.

Activate Prior Knowledge:

- The teacher reviews with the students what they know about doubles.- The teacher reviews what makes a doubles fact special or unique such as, the two

addends are the exact same.- The teacher administers the pre-assessment worksheet. The students are given about 10

minutes. There are only six questions on the pre-assessment but more time is given to those students who need it.

- There are not any multiple choice questions on the pre-assessment; therefore, the student who is an ESL learner does not need any text blacked out.

Anticipatory Set

- The teacher shows the students an egg carton, a domino piece and two die with the same number showing.

- The teacher then reviews with the students what they notice about the numbers display on each item.

- The teacher states the objective and that the purpose of the lesson is for the students to learn what makes a doubles fact a doubles fact, and how to solve double facts.

- The teacher opens up the modeled practice on the SMART board (Appendix K).- The teacher asks questions during the modeled practice and after to check for

understanding.- The teacher introduces the Double Fact Song (http://www.youtube.com/watch?

v=ljPKoNJH1Jg )

Modeling- The teacher rolls the die on the SMART board until the die shows a doubles fact.- The teacher clicks on the domino piece until the domino shows a doubles fact.- The students tell the teacher when he or she rolls two doubles on the die.


http://www.youtube.com/watch?v=ljPKoNJH1Jg


- Although the students would love to manipulate the die on the SMART board, the teacher moves on due to time constraints.

- The teacher thinks out loud to solve the doubles fact shown by the numbers rolled on the die.

- The teacher solves problems on the board that are horizontally formatted and vertically formatted.

- Once the teacher has modeled how to solve a doubles fact, the teacher pulls up student volunteers to write on the SMART board.

Guided Practice- In a whole group instruction, the teacher pulls up a SMART board activity that requires

the students to sort out number sentences.- The teacher calls on the students to come up and sort the doubles facts from the non-

doubles facts.- The teacher proceeds to the corresponding worksheet that each student has with his or her

clipboard.- The teacher calls on the students to come up to the SMART board to write down the

correct answer.- The teacher completes numbers1-7 with the students.- The teacher allows the students 20 minutes to complete number 9 -20 on their own.- The teacher posts up a riddle with doubles up on the board for the students to solve when

they are finished.

Independent Practice- The students complete numbers 9- 20 on their own with some assistance if needed. The

independent portion of the EnVision worksheet involves solving for the missing double fact and the sum.

- Connecting counting cubes are provided for the students for a concrete visual.- The independent practice also includes two algebra exercises where students apply their

knowledge of doubles.- The students then answer three word problems which require the use of double facts. In

addition, the students create their own double fact riddles by writing a story consisting of two or three sentences.

- Once the students are finished, they solve the riddle on the board.

Closure- As a whole group the students contribute the answers posted up on the board. The

students are asked to share what strategy they used to solve the riddle.- Then, the students take turns sharing their riddles. - The teacher verbally asks the students what is a double fact? What are examples of

double facts?

Technology Portion


The SMART board is used to project the interactive worksheet during the guided practice of the lesson. The students interact with the SMART board to sort, write and solve math problems.

The students also sing along with the Doubles song during the anticipatory set. The doubles song plays for 3 minutes. The tune is catchy and the linguistics is simple for the students repeat without having with words printed out in front of them. The song allows the students to repeat double facts with a rhythm from memory as required by the math common core (pg. 18).

Resources and Materials used for Instruction

Resources:

Envision Math worksheet (Pearson, 2012, pg. 39)

Doubles fact song (http://www.youtube.com/watch?v=ljPKoNJH1Jg )

Doubles fact song lyrics (Appendix D)

SMART board

Materials:

pencils egg carton

A pair of dice SMART Board activity

Pearson EnVisions Math Curriculum double dominoMODIFCATION TABLE

This learning experience has some modifications to meet the needs of every student in the classroom. Environmental, management along with instructional, materials and tasks were alter for some students due to the various learning styles in the classroom

Modification Type Specific Modification Rational Benefits

Environmental and Management

Preferential seating for student with ADHD

Students who enjoy chatting during the lesson are separated

Proximity to teacher allows for better

focus.

Students focus more on content rather than

on friends.

All students stay on task.

The students meet the intended

outcomes stated in the learning objectives

The teacher uses a Students compare Students see the



Instructional

sorting activity on the SMART board.

The worksheets contain word problems, math

sentences, and pictures and fill in the blanks.

between a doubles fact and a non-doubles fact.

Students can apply their skills in various

ways/strategies

difference between a doubles fact and a non doubles fact.

Students learn through multiple

intelligences.

Content/Material

The math problems are listed vertically and

horizontally

The lesson objectives are aligned to the NYS

Common Core.

Students see math sentences written in

two ways.

Students are receiving effective instruction.

The students are exposed to

different formats used on

assessments

Students learn material tested on the assessments.

TaskTime Lengthened or

shortened based on academic ability

Allows students to work at a pace that is comfortable for

them

Time Required

Planning:

Planning for this learning experience takes at least one hour. The teacher creates a variety of six problems for the pre-assessment. The guided and independent practice activities are provided by Pearson through the EnVision math program. However, the teacher creates the SMART board activity which correlates with EnVision math worksheet. The post-assessment is also provided by the Pearson through the EnVision math program. The teacher supplies the materials for the anticipatory set.

Implementation:

This lesson is based off a 45 minute mathematics period. Yet, this lesson may require more time for all students to share their riddles to the class.

Assessment (per student):


The scoring of the pre and post assessment takes 2 minutes to score for each student.

Schedule/Unit Plan:

The adding doubles lesson is introduced during the beginning of the year and should be taught within topic 2 of the EnVision math program. Second grade students review addition strategies at the beginning of the year. Thus, adding doubles is taught along with “making ten to add nine”, “adding multiple addends”, “adding near doubles” etc. The students build from this concrete level to higher levels of thinking when solving word problems in preceding topics. Memorizing double facts also helps the students improve their math facts. Therefore, learning various addition strategies is essential in the beginning of the year.

Reflection

This learning experience complements the addition strategies in topic 2 of the EnVision Math Program by Pearson. Each addition strategy throughout this unit allows students to scaffold their thinking to eventually apply the necessary skills to solve complicated word problems and equations. The goal of this lesson plan is to effectively deliver the content through engaging instruction so students are motivated and are continuously thinking about adding double facts for 45 minutes. After comparing pre-assessment and post-assessment data, it is clear most students met the objectives of this learning experience. According to the graph on page 8, several students are classified as developing before the lesson. The graph then shows zero students as developing after instruction for the post-assessment. Overall, most of the students have exemplified the skills they have learned through formal and informal assessments.

In order to get the students ready to learn, I incorporated visuals, technology and Gardner’s Multiple Intelligences within my lesson. The students remained engaged throughout the lesson since they were able to see a doubles fact in everyday objects such as an egg carton, two die, and a domino. The students were also able to see the pattern of a doubles fact through the use of connecting cubes.

Gardner’s Multiple Intelligences ensure all students’ learning styles are met. In this doubles lesson, the students learned through a linguistic style by singing the doubles song and by reading word problems. The students loved dancing and singing with their friends! In addition, the students were able to solve math problems by using numbers and operations. In this case, the students learned through logical experiences. The independent practice and post-assessment required the students to draw out their doubles fact. As a result, students who learn best through spatial applications were able to benefit from this part of the lesson.

Technology is becoming a vital part of student lives, and of the lives of professionals. As students grow into technology savvy individuals, they will be able to apply their knowledge and skills in different creative ways. In this lesson, the students interacted with the SMART board. I produced the SMART board activity to mirror the worksheet provided by the EnVision Math Program. However, the worksheet on the board was interactive. The students were able to come up to the SMART board to write in the missing addend, and to sort double facts from non-double facts. Last, the SMART board lesson had an audio piece which spoke to the students.


At the end of the lesson, two students mentioned how cool the SMART board was. Also, the students were singing the doubles song at the end of the day since the melody is catchy. I know the some materials were effective for instruction because the students would bring up the doubles lesson during other lessons throughout the week. This class now sings the doubles song during morning news in order to help them memorize their addition facts!

My learning experience was peer reviewed on October 18th, 2012. My peers were able to give me constructive feedback on all areas of my LE; especially on my focus question. My focus question was, “How can I improve my pre and post assessment, and my rubric”? In the future, I would use the suggestions to improve this lesson.

I would have the students come up to the SMART board to roll the dice and change the domino to a doubles fact themselves. In addition, the students could break off into teams to see who could sing the song with the double facts. Furthermore, to incorporate more literacy, a doubles fact story will enhance the learning process. Last, I would either use the students as examples of a doubles fact, or have them search around the room for a double of something. This would cover the bodily-kinesthetic learning style for those who, “learn by doing.”

I would personally like to thank my peers, and especially Jeff Arnold for this opportunity to share my learning experience. I greatly appreciate every warm and cool comment from my peer review group, and all of the input Jeff Arnold put into my learning experience midterm. I feel that I have truly grown from this experience and I look forward to continue to using this process to enhance my instruction.


Appendices


Appendices

A. Classroom Rules

B. Classroom Floor Plan

C. Classroom Procedures

D. Doubles’ Lyrics

E. Letter Home

F. Pre-Assessment

G. Pre-Assessment Teacher Exemplar

H. Pre-Assessment Rubric

I. Student Sample 1 (Pre-Assessment: Developing)

J. Student Sample 2 (Pre-Assessment: Proficient)

K. Student Sample 3 (Pre-Assessment: Distinguished)

L. SMART Board Activity

M. Guided & Independent Worksheet

N. Guided & Independent Worksheet Teacher Exemplar

O. Post-Assessment

P. Post-Assessment Rubric

Q. Post-Assessment Teacher Exemplar

R. Student Sample 1 (Post –Assessment: Developing)

S. Student Sample 2 (Post-Assessment: Proficient)

T. Student Sample 3(Post-Assessment: Distinguished)


Appendix A

Classroom Rules

1. Keep your hands, feet and materials to yourself.

2. Follow directions from the teacher the first time.

3. Raise your hand to be called on.

4. One friend speaks at a time.


Dear Parent or Guardian,

This week, we are starting our topic 2 from the EnVision Math program. This topic entails several addition strategies. Lesson 2 incorporates adding doubles. It is essential for students to learn how to recognize patterns to help solve problems. Furthermore, students are required to know from memory, the sum of two, single digit numbers from memory. Thus, we are looking forward to this doubles lesson.

Please encourage your son or daughter to find objects around the house that show doubles. In addition, I have attached the doubles song lyrics we will be singing every day during morning news. The consistency in school and at home will strengthen your child’s addition skills.

Thank you for your cooperation! If you have any questions, problems or concerns, please feel free to contact Mrs. House and myself at [email protected]

Sincerely,

Miss Cummings


mailto:[email protected]

Doubles Lyrics

Doubles, doubles I can add doubles.

It’s no trouble for me to add doubles.

One plus one equals two

Two plus two equals four

Four plus four equals eight

Eight plus eight equals sixteen

Nine plus nine equals eighteen

Ten plus ten equals twenty

Doubles, doubles I can add doubles.

It’s no trouble for me to add doubles.


Appendix B Room 31 Floor Plan


Student Desks Student Desks

Student Desks Student Desks

Teacher Desk Papers, Crafts

Guiding Reading

Math InterventionHomework hand in

Sink

Student Computers

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