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Elizabeth Sobieraj
DaemenCollege
EDU327 Teaching to the Standards
October 18, 2007
FINAL VERSION
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First Student Teaching PlacementGrade Level: 1 Subject(s): Math, Social Sciences, ELA
School District Name:Cheektowaga Sloan
School Name: Theodore Roosevelt Elementary
Title of Learning Experience: Vertical Dot Addition
Standard Area: MST-Math Science Technology
Standard: MST 3- Mathematics
Performance Indicator: 1.N.27 Use a variety of strategies to solve addition and subtraction problems with one- and two-digit numbers without regrouping.
Elementary /Beginning Level Intermediate Commencement
Alternate/Students with Disabilities
Peer Review Focus Question:
Does my learning experience follow the congruency table?
For updates on the NYSAcademy for Teaching and Learning visit:
www.nysalt.nysed.gov
Peer Review Date:
10/18 DaemenCollege Class: Teaching to the Standards
I. Learning ContextPurpose: To assess students’ ability to apply and communicate the basic addition skills and strategies to write and solve a vertical addition problem.
Goals:
Correctly write the numbers of the addition sentence from the dot cards.
Correctly place the numbers, + sign, and line representing the equals sign in the vertical addition format.
Communicate mathematically.
Become proficient with the skills of mathematics.
Enduring Understanding:
There is more than one way to write an addition sentence- both vertically and horizontally.
Pictures and/or dots are ways that will help us count numbers and add them together to form addition sentences and find their sums.
Essential Question:
Why is it important to be able to know how to write and solve both horizontal and vertical addition problems.
Guiding Questions:
Where does the + sign go in relation to the numbers (addends) in the vertical addition sentence?
Where does the line representing the equal sign go in relation to the numbers (addends) in the vertical addition sentence?
Does it matter if I switch the order of the numbers in the vertical addition sentences?
How do I read this vertical addition sentence?
The objectives to be achieved are as follows:
1.0 The learners will be able to write vertical addition sentences.
2.0 The learners will be able to find the sums of vertical addition sentences.
Grade Level and Ability: The students are instructed on a first grade level, which is where all students stand academically. There are 10 boys and 10 girls. While there are no students with an IEP in this class, there are 5 students receiving remedial mathematics classes.
Overview of What Students Need to Know and Be Able to Do:
In order for students to successfully complete the objectives of this learning experience, students need to:
Recognize and write a + sign
Recognize and write the line representing the equal sign in the correct places
Find the sums of an addition sentence
The Final Product of this Learning Experience Requires Students To:
Follow oral directions
Count the number of dots on the dot card and transfer that to the written number
Write numbers 1-10
Write vertical addition sentences
Find the sums of the vertical addition sentences (to 10)
Classroom Layout(See Attachment A)
To better assist the reader in understanding the layout of the classroom and where the learning takes place, a classroom layout can be found with the attachments at the end of the learning experience.
Classroom Rules/Classroom Management(See Attachment B)
Students are reminded of classroom rules before the beginning of the lesson. These rules can be found in the attachment section at the end of the learning experience.
Partnership & Material Procedures (See Attachment C)
If students finish early, they are given the opportunity to work in pairs using mini chalkboards, erasers, and chalk. The procedures for working in partnerships and for working with the above materials are located in the attachment section at the end of the learning experience.
Congruency Table
New YorkState Learning Standard: MST
Area: Mathematics
Content Standard: Standard 3-Mathematics
Content Strand: Number Sense and Operations
Band: Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Level: Elementary
Grade Level: 1
Performance Indicators/Core Guide Information / Instructional Task (What the standards mean in your own words) / Learning Objectives / Student Work / Assessment Tool
1.N.27 Use a variety of strategies to solveaddition and subtraction problems with one-and two-digit numbers without regrouping. / Students will create 2 vertical addition sentences, the addends (numbers being added) they are given on dot cards. After creating the vertical addition sentence, they will add the two numbers together to find the sums. / 1.0 The learners will be able to write vertical addition sentences.
2.0 The learners will be able to write sums of vertical addition sentences by adding the two addends in each problem. / Student work includes a piece of construction paper with two dot cards from which students construct vertical addition sentences and after find the sums. / Students work will be assessed using a three point rubric. The rubric measures the students ability to write the vertical addition sentence properly, make their numbers correctly, and find the correct sums.
Comments: ______
II. Assessment Plan(See Attachment D for rubric)
(See Attachment E for pretest)
(See Attachment H for student-friendly rubric)
Before the lesson begins, students will be given a pretest. This assessment is used to test prior knowledge of vertical addition of sums to ten. For students who may have had previous experience with vertical addition to ten, there is also a question where students can show any knowledge they have of double-digit vertical addition.
Throughout the learning experience, students are assessed both formally and informally. The formal assessment is the pretest as well as the written vertical addition sentences (2 per student) that are accompanied by dot cards. A teacher-made rubric was used to evaluate the formal assessment. Informal assessment takes place during the lesson in the form of questions and answers as well as when students write vertical addition sentences on their chalkboards to match the dot cards I held up.
The rubric that was used in scoring the written vertical addition sentences is located on the next page.
Vertical Addition Dot Card Rubric
3 / 2 / 1Format of Addition Sentence / Addition sentence is written vertically, and the + sign and line representing the equals sign are in the correct place. / Addition sentence is written vertically but either the + sign or the line representing the equals sign is in written incorrectly or in the wrong place. / Addition sentence is not written vertically and/or both the + sign and the line representing the equals sign are written incorrectly or in the wrong place.
The Sum / Both sums are correct. / 1 sum is correct and 1 sum is incorrect. / Both sums are incorrect.
Dots/Numbers / All dots are colored in (on dot cards) and the dot cards are lined up correctly with the number next to them. / 1 to 3 dots are missing color and/or 1 to 3 numbers do not match the number of dots next to them. / 4 or more dots are missing color and/or 4 numbers do not match the dots next to them.
Number Formation / All numbers are written correctly (there are no numbers that are reversed). / 1 to 3 numbers are written backwards. / 4 or more numbers are written backwards.
Comments: ______
Student Friendly Vertical Addition Dot Card Rubric
Name / / /Format of Addition Sentence / I wrote the vertical addition sentence the right way. / I wrote the + or line for the = sign in the wrong place. / I did not write the addition sentence vertically and/or I wrote the + and the line for the = in the wrong place.
The Sum / Both sums are right / 1 sum is right and 1 sum is wrong. / Both sums are wrong.
Dots/Numbers / All dots are colored and match the numbers I used in my addition sentence. / Some dots are missing colors and/or 1 to 3 numbers do not match the dots next to them. / 4 or more dots are missing color and/or 4 numbers do not match the dots next to them.
Number Formation / There are no numbers that are backwards. / 1 to 3 numbers are backwards. / 4 or more numbers are backwards.
Comments ______
**Because it is only the beginning of the school year, I will need to go over the rubric with them because otherwise they may have a difficult time with some words.
Scoring Rubric Explanation
The rubric above was designed specifically for the vertical dot addition assessment.
First, the rubric assesses the students’ ability to actually put the numbers correctly into a vertical addition sentence. Beyond this, the rubric also assesses the students on their ability to find sums correctly. Some students are still having a difficult time with the understanding of the one-to-one correspondence. Because of this, the students will also be evaluated on their ability to recognize that there is a specific number for the number of dots on the card. Finally, being in first grade several students reverse some numbers. They will be asked to make sure that all numbers are written correctly and to check to make sure they have not made any reversals.
Students are given one grade in Mathematics each week. The grades derived from the assessment will count towards the weekly math grade. These grades will then be used to calculate a student average in Mathematics for the first trimester. Each grade given in Mathematics is weighted equally.
Students are also given a rubric, however their version is student friendly. They are required to turn in the rubric with their assessment paper.
Common errors made by first grade students include…
1. leaving out the line representing the equals sign.
2. number reversals.
3. placing the plus sign directly under the first number.
Blank Assessment Tool
Please note that each student is given 2 different dot cards (each student’s assessment looks different although it still tests the same skill).
This blank assessment is located on the next page for the ease of making copies.
Name ______Date ______
Directions: Please use the dot cards provided to write two separate vertical addition sentences.
III. Student WorkStudent work is sorted into three different categories, based on a three point rubric (See Attachments). A score of a 9-12 indicates that a student has demonstrated a firm understanding of the material being taught. This level of competence is called the “distinguished” range. A score of a 5-8 indicates that the student is skilled at some of the steps needed to write a vertical addition sentence, but lacks the consistency required to be successful at this challenge most of the time. This level is called the “proficient” range. A score of a 1-4 indicates that the student is still struggling with vertical addition sentences and is called the “developing” range.
This learning experience was conducted with 20 students in grade 1. The teacher modeled writing a vertical addition sentence, asked the students to compare the vertical addition sentences with the horizontal addition sentences, then scaffolded the task of writing vertical addition sentences (from dot cards) on chalkboards. I was able to check students understanding when they showed me their chalkboards with the vertical addition sentences.
Upon scoring the student work, I found that 19 of the 20 students scored in the distinguished range and the other student scored in the developing range. The high success rate may be due to the familiarity between the developing and culminating activities. However, these scores do indicate that as a whole we can move on to the next topic.
Distribution of Student Scores
(x = one student)
Developing Proficient Distinguished
X
X
XX
XX
XX
XX
XX
XXX
XXXXX
12335678910111
IV. ProcedureTask One: Anticipatory Set Routine
1.Some of the students in the class act as manipulatives and find the sum of 3+4.
2. Discuss that there are two ways to write addition sentences and that they already know one.
3. Discuss that the second way is what they will learn and that they need to be able to do this so when they start adding double digits (and carry over) it will make it easier for them.
4. Students are given a pretest to see what students already know (See Attachment E).
5. Students write the horizontal addition sentence represented by the students standing up.
6. Model the same sentence, however this time write it vertically.
7. Engage the students in a discussion of the similarities and differences between the two types of addition sentences.
Task Two: Modeling
8. Hold up a very large dot card (See Attachment M for an example).
9. On the board, model the correct way students will use this dot card to write a vertical addition sentence.
Task Three: Guided Practice
10. Distribute small chalkboards, chalk, and erasers to each student.
11. Hold up one dot card and ask students to independently write the vertical addition sentences represented by this dot card and to find the sum.
12. Ask students to hold their chalkboard up so you can check their work once they have finished.
13. Give students feedback in the form of praise or what they need to do to fix a mistake.
14. Repeat steps 11-13 until the students demonstrate an understanding of writing vertical addition sentences and finding the sums.
15. Collect chalkboards, chalk, and erasers.
Task Four: Independent Practice
16. Have students take out their crayons, pencils, and glue.
17. Show the students the teacher exemplar of the assessment (See Attachment G).
18. Discuss the directions with students.
Steps:
a. Put their name at the top of the paper.
b. Glue the 2 dot cards on the left side of the construction paper vertically.
c. Write the vertical addition sentence that corresponds with each dot card.
d. Find the sum of each vertical addition sentence.
e. Color the dots.
f. Check all work.
g. Look over rubric to check own work
h. Turn in finished product.
19. Distribute 1 piece of construction paper and 2 dot cards to each student.
20. Students complete the assessment by writing vertical addition sentences represented by the dot cards.
Task Five: Closure
21. Students (as a class) will summarize the lesson by answering the following questions:
a. Why is it important to know how to write a vertical addition sentence?
b. Where does the plus sign go in a vertical addition sentence?
c. Where does the line go representing the equal sign in a vertical addition
sentence?
d. Is the sum the same or different if the addition sentence is set up vertically
instead of horizontally?
22. Have students clean their work area and collect all student work.
Task Six: Differentiated Instruction
23. Give students who have prior knowledge in the area (based on the pretest) bigger numbers to work with.
24. Students who finish early may work in partnerships to practice their vertical addition sentences further.
Steps:
a. One of the two students collect materials needed (chalkboard, chalk, eraser).
b. On the rug the two partners work together.
c. The first person writes a vertical addition sentence without the sum.
d. The second person finds and writes the sum.
e. Person one and person two change roles each turn.
-OR-
25. Students who finish early are also given the opportunity to use the computer and play vertical addition games that are located at the Harcourt website.
V. Materials Required for InstructionKey Reference Materials
Harcourt Math for Grade 1- Volume 1: Chapter 2, Lesson 4
Materials Used During Instruction
*Rolled Paper*Markers*Student Volunteers
*Dot Cards (large)*Small dot cards*Chalkboards
* Chalk & Erasers *Construction Paper*Pencils/Crayons
*Glue
Websites
VI. Instructional/Environmental ModificationsClassroom Set-Up
The classroom is set up in a way that benefits the most students. The desks allow students to be seated preferentially so that those who need more attention and proximity control are located in the front row, closest to the teacher. However, if other students require teacher attention (behaviorally or academically), the rows in which the desks are set up allow the ease of assisting them as well. (See Attachment A for classroom floor plan).
Modification Table
While the classroom setup is important in controlling the behavior and management of the class, it does not meet all needs. However, all the modifications that are used in this lesson are located in the following modification table. This modification table was designed to meet the needs of this first grade classroom and the students the lesson was designed for. Most, if not all, of the modifications can be used in other subject areas and in other classrooms.
Modification Table for Mathematics Lesson
Modification Type / Specific Modification / Rationale / BenefitsEnvironmental and Management / Overview of rules provided
Preferential seating
Students partnerships are selected by teacher / Established routine and expectations
Students are placed close to teacher and visuals as needed
Students can peer tutor one another / Students become responsible for their individual actions
Proximity control for teacher of students and less distraction for students
Students often learn by being reinforced in their own words (often similar to words of their peers)
Instructional / Students repeat directions/instructions / All students can actively participate in activity / Students will understand better if they can restate the directions in their own words
Content/Materials / Students may use a second manipulative / A second manipulative may be one they are more comfortable with or more familiar with / Recognize that there is more than 1 way of checking/finding an answer (dots) or other manipulative
Task / Time / Lengthened or shortened time based on academic abilities / Students can work at a pace that is comfortable for them
VII. Time Requirements
Preparation