Data Collection, Planning.

and Assessment: Analyzing Student

Growth for the Unit of Fractions

Victoria Cortese

Department of Education, Regent University

UED 496:Student Teaching ePortfolio

Dr. Flannagan

April 2024
Part 1

Summary of the Class

My data project analyzed my second placement which took place at Rena B. Wright

primary school. Rena B. Wright is a public, Title 1 school in Chesapeake. This project was

completed in a second grade inclusion classroom. There are sixteen students in the classroom,

nine of which are female and nine of which are male.

The Unit the project Analyzed

For my data project, I chose to assess the students in mathematics on SOL 2.4. This SOL

states, “the student will a) name and write fractions represented by a set, region, or length

model for halves, fourths, eighths, thirds, and sixths; b) represent fractional parts with models

and with symbols; and c) compare the unit fractions for halves, fourths, eighths, thirds, and

sixths, with models.”

The Pre -Assessment itself

The pre-assessment I used to measure my students' understanding of SOL 2.4 before

instruction was created by me using the SOL checkpoint. The assessment that I pulled questions

from was issued by the City of Chesapeake and called SOL Checkpoint - Fractions. As a school,

Rena B. Wright uses the 2.4 Checkpoint as a summative assessment after the unit is taught. The

pre-assessment was 10 questions long and was graded on a 10 point scale. I used my discretion

to take the questions from the checkpoint and change the fractions slightly. I also changed the

order of questions from the checkpoint. However, I made sure that every part of the SOL was

addressed. The pre-assessment had four questions that aligned with comparing the unit fractions
for halves, fourths, eighths, thirds, and sixths, with models. Two questions on the pre-assessment

were aligned to representing fractional parts with models and symbols. There were also four

questions aligned to naming and writing fractions represented by a set, region, or length model

for halves, fourths, eighths, thirds, and sixths.

Blank Copy of the Pre-Assessment

Student Name ________________________

SOL 2.4 Fractions Pre Assessment

1. Which shows two-thirds shaded?

2. Which model shows two fifths of the figure shaded?

3. Color 3/8 of the rectangle

4. What fraction of the dogs have spots?

O 1/4

O 2/3

O 3/4

O 4/5

5. What fraction of the cats have stripes?

O 3/5

O 3/4

O 5/6

O 2/5

6. Look at the fraction bars

Which number sentence is true for the shaded parts?

O 1/2 < 3/4

O 3/4 > 1/2

O 1/2 = 3/4

O 3/4 < 1/2

7. Which shows four fourths that equal one whole?

O

8. Consider the fraction shaded of the figure below.

Which of the following figures shows a fraction less than the fraction shown above?

O O

O O

9. Isabella drew a figure and shaded a fraction of the figure as shown.

Which figure shows a fraction more than the fraction Isabella shaded?
O
10. Consider the given figure

Which of the following shows a fraction less than the fraction shaded above?

O
Pre Assessment %
 out of 100%

Student 1 90%

Student 2 70%

Student 3 90%

Student 4 50%

Student 5 50%

Student 6 50%

Student 7 50%

Student 8 50%

Student 9 20%

Student 10 40%

Student 12 20%

Student 13 20%

Student 14 60%

Student 15 50%

Student 16 30%

Key

Red - low group (0% - 40%)

Yellow - middle group (50% - 60%)

Green - high group (70% - 100%)

Part 2 What the Data Showed

The second grade fractions unit was two weeks long. There were no school breaks that

interrupted or broke up this unit.

The data from the pre-assessment revealed that there were two different areas that needed tier

one instruction interventions. The first section that required this tier one instruction came from

question ten. Question ten asked the students to consider a model of a fraction that was given,

and then correctly select the model that represented a fraction less than the first fraction. As a

result of most students answering question ten incorrectly, I remediated and differentiated for

this skill.

Additionally, the data from the pre-assessment showed that most of the students got

question two incorrect. Question two asked the students to correctly identify the model that had

two-fifths shaded. Each model given was broken into five equal parts. In response, I also

differentiated and gave tier one instruction on the skill of identifying fractions based on given

models.

In accordance with the data from the pre-assessment, I chose to incorporate high yield

activities that helped students master the skills of comparing unit fractions with models,

representing fractional parts with models and symbols, and naming and writing fractions

represented by a set, region, or length model.

The Activities

Activity #1

Before the students could tackle the skill of comparing unit fractions, they had to first master

representing fractional parts with models and symbols. In order to reach this objective, I chose to

incorporate an activity I titled, “Partitioning shape mats.” This activity was done in small groups.

For this activity, each student was given a laminated sheet of paper with a circle, square, and

rectangle printed next to fraction boxes and lines to write the word form of the fraction. Each

student received one of those mats along with a dry erase marker. The students were given the

materials, and told to wait for the teacher to verbally give them a fraction. Once the teacher told

the students what the fraction was verbally, the students had to separate each shape into the

correct number of parts. This activity was differentiated for each group. The lower group were

given lower fractions to work with such as halves or thirds. The lower group did not have to

write the word form of the fraction. The middle group was given fractions like one-fourth and

one sixth. The high group was given harder fractions like one-sixth and one-eighth. The high

group was also required to write the fraction in word form.

 This is a real student example from my low group. After giving instructions, I verbally gave

the small group the fraction one-half. This student chose to write in the fraction word section

even though they were not required to. As you can see the student followed directions and did an

amazing job at dividing the shapes into equal parts and writing the unit fractions in each section.

This is a real student example from my high group. The student followed the directions well.

They correctly divided each shape and wrote the unit fractions. This student also correctly wrote

the word form without spelling help.

Activity #2

The purpose of the second activity was to help students master the skill of identifying

fractions of a set. To reach this objective, I chose to incorporate a task card activity. I had 12

different task cards with different problems. In addition to the question, each task card had a

visual model for the students to produce the fractions from. This activity was done in small
groups. To start, I informed the students that we were going to complete task cards. I told the

students that they would each get their own problem to solve on the whiteboard table with a dry

erase marker. Before giving each student their own task card, I modeled how to solve one of the

problems. I modeled the thought process behind identifying fractions of a set. I did this by

showing the students the visual representation on the task card. I read the question out loud and

then counted up the total number of objects. I reminded students that the total number of objects

is always my denominator. I then counted the number of objects that I was looking for. I

explained to the students that the selected number of objects is my numerator. Then, I gave each

student a different task card to complete on their own. I answered questions that the students had

and closely monitored student progress to check for understanding. In this activity, I

differentiated by giving the different groups different problems. My low group received easier

problems that had answers such as one-half and two-thirds, and one-third. My middle group

received cards with problems that had answers like one-fourth, three-fourths, and one-sixth. My

high group answered harder questions that had answers such as five-sixth, five-eights, six-

eighths, one-eighth.
This is a real student example from my low group. The set shown on the card has one green

button and one blue button. The student was able to correctly identify that the fraction of the set

was one-half.

This is a real student example from my high group. The task card asks the student to find the

fraction of the coins that are pennies. The student was able to correctly identify that there were

five pennies out of six total coins on the card.

Activity #3

The third activity that I incorporated into this unit was designed to help students meet the

objective of being able to compare fractions. The materials I used for this activity were fraction

bars, a dry erase marker, and a dry erase table. This task was completed in small groups. Each
student was given two fraction bars. Both fraction bars were divided into the same number of

pieces so the denominators were the same. The students were then instructed to write the fraction

for each fraction bar and compare them, writing a number sentence. My high students were given

more complex fraction bars than my lower students. For example, I gave one of my high students

the four-sixth and the five-sixth fraction bars to compare. One of my low students was given the

two-third and the one third bars to compare.

This real example of student work shows the growth that this activity yielded. When given the

two fraction bars, this student was able to correctly write the fractions and then compare them.

This real student example was from one of my lower students. They were able to correctly

identify that the fraction bars represented two-thirds and one-third. They were also able to

correctly state that two-thirds is greater than one third.

Activity #4

The fourth activity that I included in this unit helped the students further master the skill of

comparing fractions. The materials I used for this activity were pizza fractions, dry erase markers

and a dry erase table. This pizza fraction activity was chosen to specifically address a knowledge

gap. During a check for understanding, it came to my attention that the students struggled with

separating circles into equal parts. Many students wanted to separate circles in the same way that

they separated rectangles, making the spaces uneven. In doing this, the students had an

incomplete understanding of fractions representing multiple equal parts. I chose this activity

because it gives the students a visual representation of a very foundational skill within

understanding fractions. If my students couldn’t conceptualize the fact that fractions are made up

of equal parts then they can’t move forward in the unit and compare fractions in the way the SOL

assesses. As a result, I chose to address the knowledge gap using this pizza activity. This activity

was executed in small groups. At the table were multiple laminated paper pizzas cut into

different fractions. The instructions given to the students by the teachers were to create number

sentences based on the pizza slices given to them. For example, one student might receive a one-

fourth slice and a one-half slice. The student would then have to write (with their dry erase

marker) one-half is greater than one-fourth.

 Pictured above is a real student example of student work. The student who completed this

activity was in my high group. I gave this student in my high group a one-eighth and one-sixth

slice because they are smaller fractions, and therefore more difficult to work with. This student

was able to correctly write that one sixth is greater than one eighth.

The picture above shows real student work from my low group. I chose to give this student a

whole pizza and a one-third slice because it is visually easier to see that one-third is less than one

whole. The student was able to identify that the two fractions were one whole and one-third. The

student was then able to correctly write that one whole is greater than one-third.

Part 3
 For the post assessment, I gave the students the test that the city of Chesapeake created and

appointed. The pre and post assessment both align with SOL 2.4 which states, “the student will

a) name and write fractions represented by a set, region, or length model for halves, fourths,

eighths, thirds, and sixths; b) represent fractional parts with models and with symbols; and c)

compare the unit fractions for halves, fourths, eighths, thirds, and sixths, with models.” There

were three skills tied to this standard of learning. The skills are: name and write fractions

represented by a set, region, or length model for halves, fourths, thirds, sixths and eighths.

Represent fractional parts with models and with symbols. Compare the unit fractions for halves,

fourths, thirds, eights, and sixths.

Blank Copy of the Post Assessment

The Data

Pre Post
Assessment % Assessment %
out of 100% out of 100%

Student 1 90% 100%

Student 2 70% 90%

Student 3 90% 100%

Student 4 50% 80%

Student 5 50% 70%

Student 6 50% 90%

Student 7 50% 90%

Student 8 50% 90%

Student 9 20% 60%

Student 10 40% 70%

Student 12 20% 60%

Student 13 20% absent

Student 14 60% 80%

Student 15 50% 80%

Student 16 30% 40%

Key

Red - low group (0% - 40%)

Yellow - middle group (50% - 60%)

Green - high group (70% - 100%)

Discussion about the Data

The fraction unit is very important because identifying, naming, representing and comparing

fractions are skills that will follow students their entire lives. A second grade math class is not

the only time my students will need to understand fractions.

For my pre assessment, there were three students who passed. For my post assessment,

there were 11 students that passed. That means that my class went from a 0.1% pass rate to a

68% pass rate. I am very happy with the growth that I saw. Every student jumped at least 10%

and I had five students jump a whole 40%.

Student 16 started in my low group and ended in my low group. This student is currently in

the process of being tested to qualify for special education. As a result, their ability to learn is
greatly diminished because they don’t have access to the necessary resources for them to grow

academically.

Student 10 jumped from my low group to my high group. Even though this thirty percent

improvement wasn’t the largest amount of growth in the class, they were the only student who

went from my low group to my high group.

Student seven made a forty percent increase. This student is identified special education.

They go to the school's math club three times a week after school, where they receive further

remediation outside of the classroom.

In conclusion, every single one of my students made gains in this unit. However, I would

say that there is still room for remediation because there are still three students in my class who

failed and a few who were on the cusp of passing.

There were a few things in my project that I would change if I were to do it again. The

first thing I would do differently is use the same pre and post assessment. The only reason why I

did not use the same pre and post assessment is that I was urged by my cooperating teacher not

to. If I had used the same pre and post assessment, I would have been able to see growth question

by question in addition to growth as a whole. Another piece I would change in this project is

activity four. One of the reasons I would change this activity is that the students had a little

difficulty distinguishing the difference between what the one sixth slice looks like compared to

the one-eighth slice. This was a problem because it made it unnecessarily difficult for the

students to identify and write the fraction that the slice represented. All in all, most of my

students made significant growth through this unit, however there is always room for

improvement in the ways I can deliver instruction and create specific activities that increase

student learning.