New York State Academy for Teaching and Learning
Final Learning Experience/Information Form
Contact Information
Residing Address (including street, city state, and zip-code)
Phone numbers
Malorie Cummings
7832 Catherine St
Derby, NY 14047
Home Phone
(716) 512 2245
Email Address
Cell Phone
(716) 521 4852
[email protected]
School Information
Grade 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
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?
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
Student Task
2.OA.2
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.gov
common core
standards:
mathematics pg.
18)
Supporting
Standard
2.RF.4a
The students sing
a doubles fact
song through
using their
rhythmic and
mental skills.
Learning
Objectives
(see page 9)
Students will
orally add
doubles facts up
to 20 using a
doubles fact song
Student Work
Assessment Tools
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 PreAssessment. 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 nondoubles 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.
Students will
read to solve
double fact word
problems
Students will
complete page 42
on the Envision
Math Worksheet.
The Doubles PostAssessment consists of
thirteen questions. It is
Read with
sufficient
accuracy and
fluency to
support necessary
comprehension.
Page 42 requires
the students to
read the word
problems, and
then to write a
word problem of
their own.
worth 16 points. This
assessment requires the
students to draw the
problem, solve for
missing doubles, and
to answer two multiple
choice word problems.
(www.nysed.gov
common core
standards ( ELA
pg. 25).
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”.
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 preassessment 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 (2012) 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 (2012) 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
Double Addition
facts
Drawing
Missing double
and sum
Exemplary
4
The student
The student
completed the
completed the
problem by
problem by
writing 3 correct
writing 2 correct
doubles fact
double facts
The student
The student
demonstrates the
demonstrates the
concept of
concept of double
doubles by
by drawing 5 of
drawing 6 of the
the correct
correct double in
doubles in the
the space
space provided.
provided
The student writes
The student
11-10 correct
writes 8-9 correct
addends and sums addends and sums
to show the
to show the
missing double
missing double
Correct number
of multiple
choice
Total: _____________ / 16
Comments:
Proficient
3
Progressing
2
The student
completed the
problem by
writing 1 correct
double fact
The student
demonstrates the
concept of double
by drawing 4 of
the correct
doubles in the
space provided.
The student writes
6-7 correct
addends and sums
to show the
missing double
Out of 4 questions
4=4 points
3=3 points
2=2 points
1=1 point
0 = 0 points
Needs
Improvement
1
The student
did not write a
double fact
The student
draws less
than four
objects to
demonstrate
the concept of
a doubles fact.
The student
writes 5 or
less correct
addends to
show the
missing
double.
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
Student # 1
Student #2
Student #3
Student # 4
Student # 5
Student #6
Student # 7
Student # 8
Student # 9
Student # 10
Student # 11
Student # 12
Student # 13
Student # 14
Student # 15
Student # 16
Student # 17
Student # 18
Student # 19
Student # 20
Student # 21
Student # 22
Pre Assessment Score
3
1
4
2
2
4
2
2
3
4
3
4
3
3
3
3
2
4
4
2
3
2
Post Assessment Score
3
2
4
3
4
4
3
4
4
4
3
4
4
4
4
3
3
4
4
3
4
4
Chart Data Overview
Attributes
Average
Median
Mode
Standard Deviation
Pre Assessment
2.86
3
3
.8888
Post Assessment
3.59
4
4
.59032
Difference
.73
Pre Assessment Key
Level
Developing
Proficient
Distinguished
Score
2-1
3
4
Number of Students
8
8
6
Score
2-1
3
4
Number of Students
1
7
14
Post Assessment Key
Level
Developing
Proficient
Distinguished
The following graph shows pre and post information on the assessment:
Pre and Post Assessment Data
16
Number of Students
14
12
10
8
Pre-Assessment
6
Post-Assessment
4
2
0
Developing
Proficient
Distinguished
Level of Performance
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 (Pearson, 2012) 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.
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 nondoubles 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 (2012) 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 domino
MODIFCATION 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
Environmental and
Management
Specific Modification
Rational
Preferential seating for
student with ADHD
Proximity to teacher
allows for better
focus.
Students who enjoy
chatting during the
lesson are separated
Students focus more
on content rather than
Benefits
All students stay
on task.
The students meet
the intended
outcomes stated in
the learning
on friends.
Students compare
between a doubles
fact and a nondoubles fact.
objectives
Students see the
difference between
a doubles fact and
a non doubles fact.
The worksheets contain
word problems, math
sentences, and pictures
and fill in the blanks.
The math problems are
listed vertically and
horizontally
Students can apply
their skills in various
ways/strategies
Students learn
through multiple
intelligences.
Students see math
sentences written in
two ways.
The lesson objectives
are aligned to the NYS
Common Core.
Students are receiving
effective instruction.
The students are
exposed to
different formats
used on
assessments
Time
Lengthened or
shortened based on
academic ability
The teacher uses a
sorting activity on the
SMART board.
Instructional
Content/Material
Task
Students learn
material tested on
the assessments.
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.