The document discusses a report analyzing math performance at two elementary schools. It notes that students historically score low on fractions on standardized tests. The report identifies key areas of weakness: performing multi-step problems, lacking prior knowledge of concepts like multiplication facts, inability to check for reasonableness of answers, and underutilization of available resources. A goal is set to improve student mastery of adding fractions with unlike denominators through targeted instruction, practice, feedback and assessment. Pre- and post-tests will evaluate whether 75% of 5th graders can accurately add fractions with unlike denominators after instruction.

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Report 1
FRIT 7231
1. Introduction
1.1 What is your systemof interest?
Math is an area of weakness in both of our elementary schools. Each year students have GMAS (Georgia
Milestones) testing to determine if they are ready for the next academic year. 5th grade students must score a level two
or above in order to be promoted to the next grade level. Student scores affect the teacher’s growth scores and the
school’s CCRPI score.
1.2 What are the sub-systems?
Ability to Solve Multi-step problems - Students struggle when they have to put multiple steps together to form
an answer. For instance, students have to find a common denominator using the Least Common Multiple (LCM), get
equivalent fractions using multiplication facts, add, then simplify using the Greatest Common Factor (GCF). Students
who struggle with performing multi-step problems struggle with this process.

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Prior Knowledge - Students do not have the prior knowledge needed in order to complete all of the steps of the
problem. For instance, many do not know their multiplication facts fluently, and this causes problems when
performing the steps of adding fractions.
Reasonableness - Students do not know how to check to see if their answer is reasonable.
Resources Available - Students have a math book that they can take home each day. They also have a variety
of fraction manipulatives that they can each use in the classroom. They have several online programs to help build
content knowledge that they can access at school and at home such as Prodigy.com, Xtramath.com, and iReady.
1.3 What symptoms drew your attention to this systemof interest?
Students historically score low in Number and Operations with Fractions on the 5th grade GMAS. We noted
that current 5th grade students scored low in Numbers and Operations on the 4th grade GMAS. We anticipate that this
group will struggle with Fractions based on this information. We chose to do a needs analysis on adding fractions with
unlike denominators in hopes of finding a better way to teach this particular skill so that we can impact this particular
area of Numbers and Operations.

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2. Front-end Analysis
2.1 Are there performance gaps involved in this problem that justify a learning intervention?
Are there
performance gaps?
Yes. We determined that there is a performance gap. 18% of students are at the beginning learner stage at the
end of 5th grade. 46% are at the developing learner stage at the end of 5th grade. Only 36% of students are
proficient in math when they leave 5th grade.
Could they do it if
their life depended
on it?
No. Students are underperforming in this skill on GMAS as well as unit assessments.
What intervention is
needed?
Training -
1. Apply the steps of the process for adding fractions with unlike denominators. Students will receive
additional practice adding fractions with unlike denominators using iReady, a research based online
math program.
2. Know multiplication facts. Students will practice with www.multiplication.com and
www.xtramath.com .

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3. Apply the Least Common Multiple of two or more denominators to find a common denominator for
two unlike fractions.
4. Create equivalent fractions for two unlike fractions by using the common denominator.
5. Add the equivalent fractions.
6. Apply the Greatest Common Factors to simplify a fraction.
Coaching - Peer coaching may be utilized to provide guidance when the classroom teacher is working with
other students. Peer coaches will use a checklist to share with the teacher regarding the level of independence
achieved by the student who is being coached.
Feedback - The teacher will provide progress of formative assessments on skills.
Mentoring - None noted at this time.
Job Aids - For students who have an IEP, a multiplication chart or other specified accommodation will be
allowed as indicated in the IEP. Students will use fraction manipulatives during initial instruction and
practice with adding unlike fractions. Students will use a flow map for steps of the process during practice
activities.

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3. Needs Assessment
3.1 Optimals
3.1.1 What information and data would you collect?
We will use GMAS data to compare 5th grade achievement in the Numbers and Operations: Fractions area from
2017-18 to 2018-19. This will be lagging data as we will not be able to see the overall impact until the end of the year
or beginning of next school year.
3.1.2 How would you collect that information and data?
Sixty percent of students in 5th grade needed remediation in Numbers and Operations: Fractions according to
GMAS scores from 2017-2018. We will look at the same data for 2018-19 to see if our instructional plan had a
positive impact on learning therefore decreasing the achievement gap. We will use the information gathered from
GMAS data to guide our instruction and intensify the rigor needed in our lessons for the 2019-20 school year.
3.2 Actuals
3.2.1 What information and data would you collect?
We will administer a pretest and posttest to our students to determine their prior knowledge of adding fractions
with unlike denominators. We will gather information to determine if the students can get a common denominator,
equivalent fractions, add fractions, and simplify fractions.

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3.2.2 How would you collect that information and data?
We will collect this information by assessing the students with a pretest and post test using the testing site,
Illuminate. Illuminate tracks the standards that the students have mastered, and gives data where students have not met
the standard.
3.3 What are the discrepancies between the current (actual) and desired (optimal) state?
GMAS is given at the end of the school year. Since we are using GMAS data, we must use an assessment that mirrors
the GMAS questions. Illuminate is an assessment tool that provides questions similar in rigor to those on the GMAS. We
will use Illuminate for both our pre and post assessments so that we can have data that applies to our current student
proficiency levels.
3.4 What priorities can you assign to the identified discrepancies of goals?
We will ensure that our pre and posttests use valid and rigorous questions that mirror GMAS test items. These
assessments will give us current data for our students in order to adjust our instructional plan. This will allow us to meet the
needs of those students who are still not proficient with any of the identified skills.

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3.5 Prepare a learning goal statement.
3.5.1 Conduct a goals analysis for your problem.
Learning Goal Worksheet
Program: 5th Grade Math Instructors: Brannen and Popkin
Date: September 23, 2018
Learning Goal: Students will be able to add fractions with
unlike denominators.
MEASUREMENT
Class Evaluation…………..
Performance Test…………
On-the-Job Follow-Up…….
ROI Effect…………………
Learning Outcomes
Performance
(tasks to perform
goal)
Condition
(learning
environment)
Intellectual
Skills
Cognitive
Strategies
Verbal
Info
Motor
Skills
Attitude Criterion
(Restrictions, tools)
Find a common
denominator (use
the LCM)
Classroom or
small group
setting
x x A Multiplication Chart
and/or a fraction
equivalence chart will
be available for
students with IEP
modifications.

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Write equivalent
fractions with the
common
denominator
Classroom or
small group
setting
x x
Rewrite the
problem with
equivalent
fractions.
Classroom or
small group
setting
x x
Add equivalent
fractions
Classroom or
small group
setting
Simplify the
answer if needed
(using the GCF)
Classroom or
small group
setting
x x A Multiplication
Chart and/or a fraction
equivalence chart will
be available for
students with IEP
modifications.
Simplify the
answer converting
an improper
fraction to a mixed
number if needed
Classroom or
small group
setting
x x
3.5.2 Write out a goal statement in narrative form.
75% of our 5th grade students will be able to fluently add fractions with unlike denominators with 80%
accuracy by the end of the fractions unit based on our Illuminate post test data.

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4. Instructional Analysis
4.1 Goal Analysis
4.1.1 What is the domain classification and type of learning (or type and level of learned capability) for your
problem.
Adding fractions with unlike denominators is an intellectual skill. This skill requires students to complete
several steps with accuracy in order to get the correct answer. Students will need to use foundational knowledge of
multiplication, multiples, factors, and basic fractions that they have mastered in previous grades.
4.2 Subordinate Skills Analysis
4.2.1 Choose an appropriate analysis method and provide an example of a subordinate skills analysis associated
with the instruction that you will provide.
4.2.2 Show which skills are entry level skills.

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