differentiated assessment a capstone project submitted in...
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Differentiated Assessment
A Capstone Project Submitted in Partial Fulfillment
of the Requirements for the Degree
of Master of Arts in Teaching: Mathematics
Steven Schultz
Department of Mathematics and Computer Science
College of Arts and Sciences
Graduate School
Minot State University
Minot, North Dakota
Summer 2011
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This capstone project was submitted by
Steven Schultz
Graduate Committee:
Dr. Larry Chu, Chairperson
Mr. Timothy Morris
Dr. Patti Kurtz
Dean of Graduate School
Dr. Linda Cresap
Date of defense: June 17, 2011
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Abstract
Students come in all different shapes and sizes. Along with these students come
their varying degrees of knowledge and learning. I feel the best way to reach all of
these students is by teaching in a differentiated approach. The differentiated
approach is an approach that aids in elevating all levels of learning. In order to be
effective, a teacher must then test the students in the same manner. By creating
tests that measure multiple levels of learning, one can obtain a more accurate
measurement of their students' progress. The one-size fits all test does not elevate
all students and therefore should be modified to a differentiated approach.
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Acknowledgements
First and foremost I would express my thanks to my family, Renee and
Kale for allowing this to be possible. I am grateful for the Minot State University
staff for the hard work they put forth on behalf of their students. I also wish to
thank Tim Morris for his dedication in being my Capstone advisor as well as the
time and effort my committee has put forth through this process. A special thank
you goes to Laurie Geller and Larry Goodman for their help and friendship
through my undergraduate as well as my graduate studies.
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Table of Contents
Page
Abstract .................................................................................................................. iii
Acknowledgements ................................................................................................ iv
List of Figures ...................................................................................................... viii
Chapter One: Introduction .......................................................................................1
Statement of the Problem .............................................................................3
Statement of Purpose ...................................................................................4
Research Questions/Hypotheses ..................................................................4
Summary ......................................................................................................4
Chapter Two: Review of Literature .........................................................................6
Differentiation ..............................................................................................6
Low Level Learners .....................................................................................9
High Level Learners ..................................................................................11
Assessment in Differentiated Instruction ...................................................12
Summary ....................................................................................................14
Chapter Three: Research Design and Method .......................................................17
Setting ........................................................................................................17
Intervention/Innovation..............................................................................18
Design ........................................................................................................18
Description of Methods..............................................................................19
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Expected Results ........................................................................................22
Timeline for the Study ...............................................................................22
Summary ....................................................................................................23
Chapter Four: Data Analysis and Interpretation of Results ...................................24
Quiz 1 Results ............................................................................................24
Quiz 2 Results ............................................................................................26
Test 1 Results .............................................................................................27
Test 2 Results .............................................................................................28
Interpretation of Results .............................................................................29
Summary ....................................................................................................31
Chapter Five: Conclusions, Action Plan, Reflections, and Recommendations .....33
Conclusions ................................................................................................33
Action Plan.................................................................................................34
Reflections and Recommendations for Teachers .......................................35
Summary ....................................................................................................37
References ..............................................................................................................38
Appendices .............................................................................................................39
Appendix A: Institutional Review Board Approval Form .........................40
Appendix B: Principal Consent Form ........................................................41
Appendix C: Research Participant Consent Form .....................................43
Appendix D: Student Assent Form ............................................................46
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Appendix E: Quiz 1 ...................................................................................49
Appendix F: Quiz 2 ....................................................................................52
Appendix G: Test 1 ....................................................................................56
Appendix H: Test 2 ....................................................................................61
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List of Figures
Figure Page
1. Factors that Affect Learning ........................................................................8
2. Quiz 1 Results Comparing the Total Number of Problem Sets to the
Total Amount of Problem Sets not Attempted ..........................................25
3. Quiz 2 Results Comparing the Total Number of Problem Sets to the
Total Amount of Problem Sets not Attempted ..........................................26
4. Test 1 Results Comparing the Total Number of Problem Sets to the
Total Amount of Problem Sets not Attempted ..........................................27
5. Test 2 Results Comparing the Total Number of Problem Sets to the
Total Amount of Problem Sets not Attempted ..........................................28
Chapter One
Introduction
After I was hired for my first teaching position, I was very motivated to
create the best students. I was convinced that I could provide all the opportunities
for students to succeed. Success to me was that every student would earn an A. I
knew that I would have to work hard and provide multiple teaching strategies to
accomplish this project. This process would be very time consuming but well
worth it to show the world what I could do with a classroom full of kids. I was up
for the task.
It was day one in the fall of 2006. I had begun teaching my geometry class
remembering my goal: every student will earn an A. Geometry had always been
my favorite subject and I knew everything about it. The next two weeks were
going to show the world how Mr. Schultz took a group of ordinary students and
transformed them into extraordinary ones. I created lessons that were hands-on
and very engaging. I lectured in the traditional manner. I answered all questions
and provided tutor time to those who desired more help. Everything was going as
planned and finally the day of proof arrived. I handed out the first test and
anxiously waited to gather the results. I could not wait to post the scores and show
everybody that they had all earned an A on the test. The results were in and to my
surprise, students earned A’s, B’s, C’s, D’s and worst of all some F’s. How could
this be? I began to evaluate my testing.
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The problem surfaced quickly! Many students were leaving problems
blank. In some cases, the problems that they left untouched were worth enough
points to drop a letter grade. Why were they leaving problems blank? I often
pondered this common occasion while trying to create better assessments.
Assessment in every one of its forms is the greatest measurement tool that
is used in education. Everything that a student does within his educational life is
assessed. I began to evaluate my assessments after the dreadful first test I gave.
Through the years, I have made modifications to my assessments which have
made them better tools. While I have been seeing improvement, it has not been
significant enough for my satisfaction. I had often wondered if it was the structure
of my test that was causing the blank problems to occur. Still in search of better
assessment structure, I got an idea from an assessment I took while in college.
The test I took was in a pre-calculus graduate school course. The
instructor presented the test, and its structure was quite different than I had
previously seen. For some areas of the test, she had made multiple problems
testing the same concept. The problems were worth different point values, and she
allowed us to choose the problem we wanted to do. Since each problem was
worth a different amount of points, I quickly realized that they were much
different in their degrees of difficulty but still tested the same concept. There were
questions where the only problem I knew how to do was the easiest, lowest point
value, and did not have a guess on how to do the more difficult problems. I began
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to reflect on the tests my students had done where they left problems blank. Did
they know how to conceptually do the problems? If a similar problem of less
difficulty was available would they have been able to do it?
As I began to research this style of testing, I realized that if I changed my
test structure to the one I had experienced, I would provide a better assessment
tool. I felt that if I pursued this project I would reduce the amount of blank
problems which would create a significant improvement in my test scores. If I
spent the time to develop this style of testing and differentiate the assessment to
all learners, it would save a lot of time and energy on my part and in turn raise the
scores of my students. And in turn, I could teach to all students, not just the
middle.
Statement of the Problem
Assessments are tools to measure progress. Within the learning
environment, there are many forms of assessment. Within my classroom, the
focus of assessment is the use of quizzes and formative and summative tests.
Often these tests and quizzes are good forms of measurement of learning;
however, most tests have limited levels of problems. If the problem on the test is
too difficult, then students may leave the problem blank. Usually when students
leave a problem blank, they are saying they have not progressed that far or have
not learned the concepts taught.
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Statement of Purpose
I created assessments that are differentiated, meaning that they test
multiple levels of learning. By doing so, I hoped to accelerate all levels of
learning. My purpose for this project was to teach to all students. If I desired to
teach to all levels of students, I must test them in the same manner. As a result, I
felt that the amount of blank (skipped) problems would decrease dramatically, and
students would show that they had learned the material.
Research Questions/Hypotheses
Would changing the structure of a test to a differentiated format increase
test scores and would it decrease the amount of skipped problems?
Summary
All students deserve the opportunity to learn and to be taught at their level.
Many teachers teach to the middle which slows the learning of the higher level
students and is too fast for the lower level students. By teaching in a differentiated
approach, you aim your teaching strategies to all levels of learners. I believe that
the differentiated approach is very good for all learners, but how are we
evaluating these students? Are these students still evaluated in the traditional
manner with a middle to high level problem testing a concept? Since I teach in a
differentiated approach, testing in the traditional manner created a conflict with
the way the students were taught. By having problems varying in degree testing
the same concept, students were able to choose their level allowing the higher
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level students to do more difficult problems, and the lower level were still
challenged at their level, resulting in fewer skipped problems.
Chapter Two
Review of Literature
Assessment is the greatest tool used to evaluate students. Teachers have
many different styles of presenting information to their students. Most teachers
adjust their teaching strategies to meet the needs of their students. However, are
all students learning at the same pace? Are they capable of doing what they are
taught? Are the students being evaluated in the same manner? The dynamics of a
classroom determine how a teacher needs to present their lessons so all levels of
learners can learn. In the classroom, a teacher may find low level learners, middle
level learners and high level learners in the same class being taught the same
material. A teacher may find that he or she needed to incorporate many different
styles and teaching strategies to meet the needs of the lower level learners, higher
level learners and everyone in between. The problem that arises is the fact that
most teachers evaluate these students with the same middle level assessment tool.
I will explain how to differentiate and apply assessment strategies to meet the
needs of all students.
Differentiation
According to Tomlinson (1999), differentiation is a process of doing
“whatever it takes to ensure that struggling and advanced learners, students with
varied cultural heritages, and children with different background experiences all
grow as much as they possible can each day, each week, and throughout the year”
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(p. 2). The challenges arise due to the wide variety of students within a classroom.
Differentiation is the process of teaching to all students. One must modify their
teaching strategies to meet these needs.
Teachers must believe that all students can learn and be successful in order
for differentiation to work. When teachers believe that their students can become
successful, they can then create the environment to do so. By creating an
environment for learning, teachers can help all students learn. “For students to
succeed, they need to believe that they can learn and that what they are learning is
useful, relevant, and meaningful for them” (Gregory & Chapman, 2002, p. 1).
Differentiation starts all students with success stimulating their minds to believe
that they can and will learn.
Differentiation starts with knowing the learners. Teachers must begin
evaluating their students immediately. Teachers must keep in mind that there is an
order in differentiating. One must first “always remember the purpose of
instruction” (Norlund, 2003, p. 4). Concepts and content can then be adjusted to
the students’ needs. Many teachers spend their summers planning lessons that
focus on standards and their curriculum. Unfortunately, when they get their new
students in the fall, their program doesn’t fit the needs of their students (Gregory
& Chapman, 2002). The one size fits all classroom no longer exists. Many
different learning styles exist, resulting in no single teaching style being able to
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accommodate all students. Figure 1 shows how different learning is affected by
various factors throughout the day (Gregory & Chapman, 2002).
Figure 1. Learning Styles: Learning is Affected by Such Factors as Time of Day
and Environment. Adapted from Differentiated Instructional Strategies by Gayle
Gregory & Carolyn Chapman, 2002.
Differentiation comes in many different styles and forms. It continuously
changes as a teacher’s students change year to year. Since differentiation is such a
broad topic, I have chosen to discuss the teaching strategies for low level learners
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and high functioning gifted learners. Many of these students are found within the
same classroom, and both levels of learners need to learn and grow.
Low Level Learners
Low level learners are often left behind when a teacher teaches in the
traditional style. This level of learning is often described as the slow learners.
These students usually have low IQs in the range of seventy five to eighty five.
These students can usually keep at a steady rate when dealing with memorization
but often have difficulties with abstract concepts. Slow learners are often labeled
as lazy and unmotivated (Norlund, 2003). “Students who are slow learners
frequently see school as a punishment, but classroom strategies enable teachers to
tap into these students’ strengths to enable them to succeed” (Shaw, 2010, p.12).
Shaw lists characteristics of slow learners as shown:
Slow learners
Have low intelligence but do not qualify for special education.
Perform at much higher levels when the material or concept taught
is presented in a concrete manner.
Have difficulty understanding and explaining the skills,
knowledge, and strategies presented.
Have difficulty managing their time as well as accomplishing long-
term goals.
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Achieve more when given an ample amount of time to complete a
task.
Usually have a lack of motivation when it comes to learning.
Show drops in self esteem.
Are at a high risk of not completing high school. (Shaw, 2010)
Most slow learners have never enjoyed success within the classroom.
School is difficult and most slow learners see school as a hardship with little to no
reward. In the differentiated classroom, all students have a better opportunity to
succeed. It is very important to provide successful opportunities for these slow
learners. Mathematics, especially Algebra and above, pose great difficulties to
these learners. In order for slow learners to be effective and succeed, a teacher
needs to take abstract concepts and make them concrete (Norlund, 2003).
Slow learners tend to learn in a more concrete form. This type of learner
works and learns best with hands on activities. A teacher needs to provide
manipulatives and plenty of practice. “A general rule of thumb when working
with students who are slow learners is to slow the pace of instruction, vary
instruction as little as possible on a single task, and provide plenty of practice”
(Norlund, 2003, p. 46). These students will perform more efficiently using the
“see it, touch it, do it approach” (Shaw, 2010, p. 14). Slow learners respond well
in learning environments where experimentation and discovery learning are used.
When these students can have hands-on activities, they learn more information
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resulting in more retention of the concepts taught. Assessment in this style can
prove to be very successful to this type of learner. Slow learners learn in a much
different approach than high level learners.
High Level Learners
High level learners are often categorized as the gifted learner. “As a group,
gifted learners tend to comprehend complex ideas quickly, learn more rapidly and
go into greater depth than their peers” (Manning, Stanford, & Reeves, 2010, p.
146). The gifted learner desires more information. They often are not challenged
and school becomes too easy. As with slow learners, gifted learners are in
desperate need of modifications to allow them to learn at their ability. When
teaching a concept, one may just teach the concept and then give practice to
establish learning. It is a common misconception that high level learners need
more problems to increase learning. Most students will hide their gift if the result
is more problems of the same style. The gifted student should be provided with
various real world applications as well as more complex problems. These
problems should require higher order thinking skills on problems that are open-
ended (Rotigel & Fello, 2004).
Students who are gifted desire to be challenged. They wish for challenges
that enhance concepts and cause them to think. Enrichment activities often
enhance and motivate these high level thinkers. The problem arises when these
gifted learners are in the regular classroom. Often the regular classroom is
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insufficient in meeting the needs of these high achievers. It is up to the classroom
teacher to provide enrichment through differentiating instruction for the needs of
all students (Rotigel & Fello, 2004). Assessing all the students within the
classroom is more than a just a test; it is a tool to evaluate your students and your
teaching techniques to meet the needs of all learners.
Assessment in Differentiated Instruction
Assessment is sometimes described as an evaluation of learning.
“Assessment and evaluation both describe a process of collecting and interpreting
evidence for some purpose” (Harlen, 2007, p. 12). In a differentiated classroom,
assessment occurs quite regularly. Teachers need to offer students the opportunity
to be evaluated. Students need and desire continual feedback to gauge their own
learning. Without feedback, one cannot improve. The problem with testing is that
most often it is done at the end of a unit instead of during. The teacher then has a
difficult task of trying to correct or change a student’s mistakes. Differentiated
instruction uses a variety of tests. Pretests, testing while learning and then a post
test is the common order of assessing students within a differentiated classroom
(Gregory & Chapman, 2002).
Pre testing occurs at the beginning of a unit. It is recommended that you
administer a pretest two weeks before starting a new unit. Some characteristics of
pretests should be followed to provide a good tool in developing instructional
strategies. Teachers should develop a test in which no one can earn a 100% or a
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0%. Questions should challenge each student and spark interest. The test should
include the simple problems but continue on through the most complex. To
engage all learners, both hands on and abstract problems should be included. The
problems should also be scattered throughout the test so the students do not feel
that the easy ones are first and increase in difficulty throughout the test. The use
of pretest results should gauge instructional practices to aid all students (Chapman
& King, 2005).
Testing while learning involves a series of quizzes that check for
understanding and also are used to evaluate one’s teaching practice. This type of
testing is called formative testing. “The name formative is used because they are
designed to inform instructional practice” (Wright, 2008, p. 167). Frequent use of
formative assessments makes it possible for teachers to modify and improve the
teaching process as it occurs. Formative assessments also provide proper pacing.
According to Robert Wright (2008), there are four parts of the learning cycle:
instruction, formative assessments, feedback for teacher and student, and
modification due to the results of the formative assessments. These four ideas are
great tools for the teacher during the time of learning. The results of formative
assessments inform the teachers where the students still may be struggling
allowing the teacher to make the necessary modifications before the post tests are
given.
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Post tests are important because these tests show reportable progress and
are usually included in a student’s final grade. These post tests are called
summative assessments. Summative assessments come at the end of a unit. These
tests act as a summary for the unit and are “critically necessary for reporting
progress to the parents and for recording student success” (Wright, 2008, p. 165).
The main focus of summative assessments is to measure what has been taught.
The test content should address the goals and objectives that were in place at the
time of the pre-assessment and measures the progress made toward achieving
them (Wright, 2008). These post tests should be created with the same focus that a
teacher has taught. If the teacher taught in a hands-on manner, then the concept
should also be available to do hands on during assessment. It is important in a
summative assessment to measure what has been taught and to mimic the style in
which they were taught. By creating summative tests in this manner, measurement
of learning is more valuable and accurate (Chapman & King, 2005).
Summary
As can be seen, differentiated instruction is necessary in meeting the needs
of all students. Too often teachers teach to the middle, leaving many students
behind. Whether a slow learner or a gifted learner, all students need to be
successful. Engaging activities will provide retention. Each learner desires more
information, and many different teaching styles need to be implemented in order
for this style to be successful.
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Among the most important, all students need to be held responsible for
their achievement. The use of assessment is the key to a teacher's understanding
of student growth. Assessment is not just a test; it is a tool used to evaluate all of
our students. It is clear now that one test will not assess all learners. It is important
that what a teacher uses for an assessment should provide the opportunity for all
students to succeed. If teaching in a differentiated approach, the one size fits all
test is not appropriate and will not be a success to all. Testing should provide slow
learners the opportunity to succeed by testing the concept with concrete problems.
The higher level learners should be tested on the same concept but with more in
depth complex problems showing real world applications.
All of the above mentioned test strategies can be accomplished if one
changes the format. By making a few modifications in the assessments, a teacher
can give more opportunities for the students to show that they have retained
knowledge about the concepts being taught. By making better quizzes and tests,
the teacher is providing more accurate measurements of learning. The quizzes can
be more formative which would show the areas where students are struggling
because the students were given many different ways to show what they have
learned.
In chapter 3, the format of the above mentioned assessment strategy will
be explained. According to the research, the one size fits all approach does not
give an accurate measure of learning, and adding multiple problem sets creates
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more opportunities for a student to show they have learned a concept. Better yet,
this style of testing also shows the degree of difficulty of a concept the student has
learned.
Chapter Three
Research Design and Method
The focus of this project was to create better assessment tools providing
more accurate data indicating student learning. I changed my quiz and test
structure based on research and design strategies mentioned in chapter 2. The test
structure gave more choices and opportunities for students to show that they had
learned the material. This chapter will explain the direction and focus of the test
modifications I incorporated.
Setting
At the time of the study, I taught in a high school located in a midwestern
state. The population of the high school was about 1400 students in grades 10-12.
This high school is one of two public high schools in this city. The city also has
two private high schools. My normal routine consisted of seeing over 100
students each day. My classroom sizes averaged 21 - 24 students. I conducted this
project in my two geometry classes. These classes are of size 20 and 24 students
consisting of mostly sophomores. The combined enrollment of the two classes
consisted of forty sophomores, three juniors and one senior. Due to the fact that
the changes occurred in the test structure, there were minimal circumstances that
would affect the study. I started the process of differentiated testing by explaining
the new structure of the tests to the students. I also gave them short quizzes based
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on the new structure. By the time the chapter assessment occurred, each student
had several opportunities to adjust to the future test structure.
Intervention/Innovation
My purpose of this project was to obtain a better measurement of what
concepts were retained throughout the extent of a chapter. I modified my test
structure to see if I could prevent students from skipping problems, leaving them
blank, and receiving no credit.
Design
My project mainly focused on data collection. I only changed the way that
I assessed my students. According to the research, one should be assessed in the
same manner as they are taught. If that is so, I needed to change my test structure
to get a full understanding of what was being retained. I taught in a differentiated
approach and often had to change the degree of difficulty in problems to adapt my
teaching to the levels of students being instructed. What I have found is students
who skip problems on tests know how to do a similar problem evaluating the
same concept. I had often asked myself the question, am I evaluating problems, or
was I interested in the overall concept? The obvious answer was to grade
concepts.
I started my project at the beginning of the second semester (early
January) of 2011 after approval from Minot State University's Institutional
Review Board found in Appendix A. I received approval from my principal using
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the form in Appendix B. I had the students turn in their parental consent forms
and student assent forms, found in Appendix C and D, before giving them their
first quiz. I started collecting my data as soon as the first quiz was completed.
Because these were formative quizzes, I used the data to modify or make
corrections to the format. I made any necessary changes to my teaching strategies
also. The greatest tool for data collection was taken from the unit test. I collected
data from the quizzes, but I focused a lot of attention on the process of teaching
the students the format and leaving the unit test as the final measurement.
I chose to evaluate my project through the collection of data because it
involves the measurement of learning. I collected data based on the number of
problems left blank on quizzes and tests as well as calculating test results to see if
averages had also increased. I compared these results to the previous tests taken
this school year. My research and design plan involved the collection of data, so I
chose the quantitative approach.
Description of Methods
Differentiated testing is testing a variety of levels of difficulty within the
same concept. It would be similar to giving problems out of the A, B and C levels
of difficulty from the book. The tests consisted of questions in this format: 1a,
worth 4 points, may just test to see if they know basic knowledge of the concept
taught. 1b, worth 5 points, would challenge the concept with a greater degree of
difficulty. And finally, 1c, worth 6 points, would show mastery of the concept
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with a more difficult problem. The students chose which problem out of the set
that they would do. I also allowed the students to do all the problems in the set, if
time allowed, and graded the problems that earned the student the most points.
This idea encouraged the students to challenge themselves and do the higher level
problems knowing they had the security of completing the lower level problem
first. At the top of each test, I had the percentages for the problem sets on the test.
Using the example above, if a student chose to do 1a, he or she would earn four
out of six points. While the student did not earn the maximum amount of points
available for this problem set, by not leaving it blank, they did earn some points
which is better than zero. The idea of this format was to prevent the possibility of
not earning points if you know the basic concept and should reduce the amount of
skipped problems on the exam. A perfect score on the test would be no mistakes
on the upper (c) level problems.
I started by giving out a quiz. I had instructed all of the students on how
the format had changed. I began with very basic quizzes that were formative and
brief. I continued to give these quizzes and built upon them by adding more
problem sets.
Data was collected using the results of both formative quizzes and
summative tests which are found in Appendix E through Appendix H. The
formative quizzes were given during the instruction of new concepts within the
unit. There were two quizzes and one summative test for unit 1 and only 1
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summative test for unit 2 due to its small size. The study consisted of two units
using the before mentioned format.
The results of these quizzes and tests were used as follows: 1) the amount
of problems left blank were tallied and compared to previous quizzes and tests,
and 2) the average scores were computed and compared to the previous scores.
These two data collections were used to see if a differentiated testing structure
would decrease the amount of skipped problems and increase test scores. The
quizzes were formative by design while the unit/chapter tests were summative.
The data collected was analyzed and compared to recent tests as well as
the previous year’s class averages. I tallied the amount of problems left blank and
showed a comparison of that quiz or test and the previous ones taken throughout
the year. I always wanted to research ways of writing good assessments. In my
research, I found ways to make my data more accurate. I believed that this
intervention would be a great success. The students had multiple choices of
varying degree of difficulty problems and had the agency to choose the problem
best suited for their knowledge level. The result expected was a minimum of
skipped problems resulting in more earned points, resulting in higher averages.
Better yet, the results were expected to produce a more accurate form of
measurement on the retention of conceptual knowledge displayed in the unit.
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Expected Results
I believed that this intervention would be a great success. A test that
incorporated multiple problems per concept would provide more opportunities for
students to show what they had learned. I wanted to research ways of writing
good assessments. In my research, I had found ways to make my students' testing
scores more accurate. I felt that the change in my measurement tool would prove
to show less skipped problems resulting in higher averages and more precise data.
As with any intervention, the possibility of difficulty was present. The
changes to the tests could have caused some confusion. The students had many
more problems to choose from than on my previous tests. The format of the test
had them choose which problems they desired to do. This idea could have caused
the students to over analyze each group of problems resulting in wasting time. I
taught the students about the new format and presented them with many examples
of the procedure. I started the intervention by giving mini quizzes and built up to
the unit test.
Timeline for the Study
I chose to start this project at the beginning of the third quarter which
began the second week of January. I collected data soon after and continued to
collect for eight weeks. The students were given two quizzes and a chapter test in
the first unit, and a chapter test in the second unit due to its shortness in length.
Forty four students were actively involved yielding plenty of data.
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Summary
Students within the same classroom have many different learning styles.
In order to teach all of the students, a teacher must change their style of
instruction. The method I have found successful is differentiating your instruction
methods. While differentiating you are creating opportunities for all students to
learn. The problem that arises is most teachers use the same assessments for their
classes which usually test the middle to high levels. By differentiating
assessments, such as tests and quizzes, a teacher will obtain a better measurement
of learning, because the students are presented multiple problems testing the same
concept giving the students a better opportunity to succeed.
Chapter Four
Data Analysis and Interpretation of Results
This study was conducted with forty sophomores, three juniors and one
senior. The main purpose of the study was to expose students to a differentiated
style of testing. If the students are taught in a differentiated manner, the idea of
teaching to different levels should carry over to assessing them as well. For this
study I chose to evaluate quizzes and tests. The students were tested in a
differentiated manner by the use of two quizzes and two tests which covered the
space of eight weeks and covered two units of geometry. The students were taught
and exposed to the differentiated style of testing prior to the first quiz being given.
My focus question to be analyzed was, "Would changing the structure of a test to
a differentiated style increase test scores and decrease the amount of skipped
problems?” In this chapter, a detailed explanation of the results will be presented.
The quizzes and tests were given in the following order: quiz 1, quiz 2 and test 1
were for unit 1, and test 2 for unit 2. Unit 2 was a shorter unit than unit 1 and
there was no need for a quiz before test 2.
Quiz 1 Results
The students were given quiz 1, found in Appendix E, as their first
differentiated assessment. The quiz format was explained to the students, and they
were given instruction on how it was going to be graded. I informed them
whichever problem they completed in the set that generated the most points was
25
the problem I would count toward their quiz score. The results for quiz 1 are
given in Figure 2 below as compared to the two parts of the research question. I
tallied the amount of skipped problems as well as the total amount of problem
sets. The study was conducted in two geometry classes with a combined total of
44 students.
Figure 2. Quiz 1 results comparing the total amount of problem sets to the total number of
problem sets not attempted. The total number of problem sets was computed by taking the total
amount of students multiplied by the total amount of problem sets on the quiz. So, 44 students
times 3 problems sets per quiz gave a total of 132 total problem sets.
The average score on quiz 1 for the participating students was 83.04%.
The data given in Figure 2 shows the amount of total problem sets which was
computed by taking the total amount of participating students and multiplying by
the number of problem sets per quiz. For quiz 1, there were three problem sets per
26
quiz multiplied by forty-four students resulting in 132 total problem sets. No
students skipped any of the problem sets on Quiz 1.
Quiz 2 Results
The students were given Quiz 2, found in Appendix F, as their second
differentiated assessment. Again the format of the quiz was explained to the
students and they were reminded of the protocol they followed in Quiz 1. The
results are shown in Figure 3 using the same format as Figure 2.
Figure 3. Quiz 2 results comparing the total amount of problem sets to the total number of
problem sets not attempted. The total number of problem sets was computed by taking the total
amount of students multiplied by the total amount of problem sets on the quiz. Quiz 2 had 5
problem sets.
Looking at Figure 3, no students skipped any of the problem sets. There
was an increase in the amount of problem sets because there were 5 problem sets
on quiz 2 and only 3 problem sets on quiz 1. The total amount of problem sets
27
was computed by multiplying the amount of problem sets on the quiz by the
number of participating students. The students were given the same amount of
time as quiz 1. The averege score of the participating students was 84.1%.
Test 1 Results
Test 1, found in Appendix G, tested the contents of unit one. The results
are given in Figure 4 using the same format as Figure 2; however, the scale is
given in log scale to show the data in each bar of the graph. The students were
given fifty minutes to complete the test.
Figure 4. Test 1 results comparing the total amount of problem sets to the total number of problem
sets not attempted. The total number of problem sets was computed by taking the total amount of
students multiplied by the total amount of problem sets on the test. There were 12 problem sets for
Test 1.
The students were given test 1 as their third differentiated assessment.
Because the students had completed quiz 1 and quiz 2, they understood the test
format and few directions were needed. As shown in Figure 4, two total problem
28
sets were skipped on this assessment; however, they were both on the same test.
Only one of the 44 students had skipped a problem set. The test average was an
82.3%.
Test 2 Results
Test 2, found in Appendix H, tested the contents of unit two. The results
are given in Figure 5 using the same format as Figure 2. The students were given
fifty minutes to complete the test.
Figure 5. Test 2 results comparing the total amount of problem sets to the total number of problem
sets not attempted. The total number of problem sets was computed by taking the total amount of
students multiplied by the total amount of problem sets on the test. There were 15 problem sets on
Test 2.
Test 2 had an increased amount of problems, yet they were given the same
amount of time to complete it. No students skipped any problem sets. The average
score on test 2 was 89.7%.
29
The four assessments used the differentiated method to test the knowledge
presented in these units. The lectures were given in a differentiated style and the
practice problems were given with varying degrees of difficulty. When explaining
the assignment to the students, I told them which degree each problem had. I told
them what the A, B and C level problems were on the assignment and what
degree each could represent on a test. The results of the two quizzes and two tests
showed that only two assessment problems were skipped in the two units.
Interpretation of Results
The first part of my research question was, would changing the style of my
tests increase test scores. The scores and averages of the tests did increase;
however, the biggest change seemed to be in the lower grades, the F-C range. As
compared to the last two unit tests, there were fewer students who failed or earned
D's. The increase in the scores by the students who originally earned a D or F, had
more effect on the class averages increasing than the students who usually earn
A's and B's. No significant changes occurred with the scores earned by the
students who normally earn A's. The A students remained A students and the
averages of the A students had a slight increase, but I feel the rigor was increased
because this format allowed me to put more difficult problems in each set to
challenge them.
As for individual test scores, very few students failed any of the quizzes or
tests. The F students, the ones that usually skip a lot of problems, had increased
30
their scores and some even increased two letter grades. The study was given
during the third quarter and no student failed quarter three. I also believe that the
participating average could have increased more if some outliers were removed.
By removing the outliers on test 1, which was the removal of the bottom 4 scores,
the average would have increased from 82.3% to 85.7%. One student on test 2 did
every problem of every set and turned in the test in ten minutes. The student
informed me that he or she was having a bad day and didn’t care. That student did
poorly on test 2 which really hurt the average which was 89.7% and would have
been 93.1% without that student's score. I decided to remove the outliers only
after speaking to the individual mentioned above.
I believe this style of testing increases the rigor of your tests. Because
these tests were differentiated, they were not created to test the middle level
students. The upper level students had a chance to do upper level difficulty
problems to earn their A, so they had to work that much harder. Also testing in
this manner allowed the quizzes to be formative and pinpointed the amount of
material students had mastered. If the student was only capable of doing the
lowest level problems, I could work with them so they could gain more
knowledge and confidence to be able to successfully complete more rigorous
problems.
The second part of my research question was, would changing the style of
my tests cause more student participation on the problems resulting in fewer
31
skipped problems. My focus was to decrease the amount of skipped problems
because when students skip problems, you have no data to evaluate what they
have learned or what they still need to learn to accomplish the goals set for the
unit. Before this study was done, these students had many assessments where
some students had skipped at least one problem during the first semester. I hoped
that this style of testing would change this problem.
To my surprise, only two total problems were skipped during the entire
study, and those two problems were skipped by the same individual. I did not
coach these students on what I was looking for as part of the study, so students
did not know that I was specifically counting skipped problems. At the end of the
study I explained what I was collecting while evaluating the tests and the student,
who had skipped the problems, told me they would have attempted the problems
had they known what I was doing. I was glad that the results were not skewed by
the students knowing that. I expected the amount of skipped problems would
decrease, but these results surpassed my expectations due to the fact there were
seven total skipped problems on the two quizzes given before starting this project.
Summary
As I began to compute the results of my project, I had some time to think
and reflect about the changes that were made in the way I taught and tested during
this time. What came to mind is the students were not necessarily doing more, but
they were giving me much more usable knowledge than I had before in my
32
teaching career. The formative quizzes really helped me change the way the
students were getting the information but also gave me information on what
concepts students were retaining. Due to the fact that almost all students did not
skip any problems, I knew what the students retained and what they needed to
continue to do to become better at the goals set in the units. The participation
averages were good and all around the students liked this style of testing. At the
end of my study I had asked the question "What do you think of the testing style
that I used this quarter?" The question was free response, but the answer most
agreed upon was being able to relax during the test. The students did not get as
frustrated about not mastering the difficult problems because they had a fall back
plan in still earning points by doing the easier problems in the problem set. The
students stated they liked the freedom in choosing how they earned their points
and knowing the possible points they could earn on each problem. Over all, the
students liked this style of testing. The only question left is, is it worth the time in
correcting and creating this style of tests in my future years of teaching? Chapter
five will explain all the pros and cons of this project and explain the future of my
classroom based on this project.
Chapter Five
Conclusions, Action Plan, Reflections, and Recommendations
Conclusions
The purpose of my research was to give all students an opportunity to
succeed. The students were taught in a differentiated format and were tested using
the same concept. My main intention was to focus on testing in a manner that
showed what a student retained during a specific unit. I wanted an accurate
measurement of student knowledge. I realized that my students were not all on the
same level of learning, so I based my testing on different levels of difficulty. By
creating problems with varying degrees of difficulty, I could see what level each
student could achieve. The results were outstanding.
I had two main focuses during this study. The first was decreasing the
amount of skipped problems, or those not attempted. During the study, only two
assessment problems were skipped in the entire eight week period. Due to these
results being so good, I was able to assess all the students and know what level
they were achieving. When the students do not skip problems, I gain a better
measurement of their learning level because the students have attempted to
successfully complete the problem. My quizzes became accurate formative
assessments resulting in the ability to tailor my lessons to pinpoint the areas for
improvement. I could then assign problems based on each student’s need rather
than assigning the same style problems to every student.
34
Secondly, I desired to raise the scores of my students. I felt that if the
students attempted more problems, they would earn more points. This idea was
also accomplished. With the varying levels of problems per set, the students were
attempting the problems that they felt comfortable doing. Each level of student
had gained percentage points in their test averages but that is not the most distinct
improvement. I had usually created tests at the middle level, but now I had three
tiers of problems. The upper level students were completing more difficult
problems than before which may not have increased their percentages much, but
their knowledge had much more growth. In order to earn an A on the test, the
students had to complete the upper level problems, which they did. At the same
time, the lower level learners were completing problems rather than skipping
them, therefore these students now were earning points on problems rather than
earning no points for leaving the problems blank. The result for these learners was
again an increase in test scores.
Action Plan
I plan to continue to create tiered assessments with the intention of
focusing on formative assessments. The formative assessment component created
many opportunities to modify my lesson plans and allowed me to pinpoint the
areas of focus. I will modify the tests a bit by focusing more on creating problem
sets for the bigger concepts rather than all concepts. At times, I struggled to find
different levels of problems within a set due to the nature of the concept and
35
would have one problem for that type rather than trying to create three. I will
continue to put the point values for each problem on the tests so the student can
see what each problem is worth as well as the number of points that can be earned
by attempting the problem.
My project also opened my eyes to having mini-quizzes, a short quiz to
gauge student learning. By making those quizzes differentiated, they became
formative and set the tone for the next lesson. I was amazed and extremely
satisfied with the results and will continue to use formative differentiated
assessments.
Reflections and Recommendations for Teachers
While working through this project, a few items come to mind. I was
astonished that this concept actually worked so well. I expected that it would
work, but not to the degree that it did. The students claimed that they were more
relaxed taking the tests and quizzes due to the options they had in completing the
problems. Due to the formative nature, this project also helped me become a
better teacher, because my lessons were now focused on student need. However,
with all the success, there does come some frustrations.
The main frustration is time. Time is very precious and well spent and
needed in this project. I created tests and quizzes with three problems per set. At
times I had fifteen to eighteen problem sets resulting in 45 or more problems per
test per student. I had informed the students to do any if not all of the problems
36
and I would grade the problem in the set that earned them the most points. These
tests then took a long time to grade especially when I had 50 students in my class.
The result is a lot of problems to grade which makes the turnaround time on the
test longer, or I spent more time after school correcting the test to get them back
sooner. This issue has channeled my thoughts to focusing on formative quizzes.
They are quicker to grade and aid in lesson planning. This frustration does subside
when you get the results for your students. To see scores go up while the rigor
also goes up is an awesome feeling as a teacher. I felt during this project I had
increased the rigor while making my students more comfortable when testing.
To a person reading this paper, I would give the advice to start small.
Make differentiated mini-quizzes and modify your lessons based on the results.
This modification happens in a couple of ways. The first is you see where the
students are struggling and then you can modify your lessons based on fixing the
struggles. The other is when the students show that they get it and understand the
concept. This formative review allows you to move on as a teacher rather than
teaching what has already been mastered, preventing boredom and lack of
motivation among students.
Surprisingly, the research says that this works. I was stunned that so many
researchers have studied and presented ideas for differentiated testing. By
researching and reviewing what other instructors have accomplished and tried, I
was able to form a plan for my style of teaching. Among the most memorable
37
items of research, I noticed several different authors say there is no such thing as a
one-size fits all test. This project helped me realize that there is no use in
reinventing the wheel, and I can use the ideas that have already been proven
successful.
Summary
The pros definitely outweigh the cons when it comes to this project. By
differentiating your teaching and testing, students can become more
knowledgeable about the concepts and the retention of the learned concept is
better. The students are more comfortable taking the tests because of the options,
as well as, the point values per problem are given in the sets.
Although time is an issue, students are learning. The rigor is increased and
students are able to prove what they are capable of doing. I teach to elevate my
students and show them what they are capable of doing. I enjoy showing my A
students that there is no ceiling to their learning as well as convincing my low
level students that they are not failures and are good at math. By differentiating
my assessments, I am able to provide an opportunity for all students to elevate
their learning. By completing this project I am now confident that the “one size
fits all test” has found its end in my classroom.
38
References
Chapman, C., & King, R. (2005). Differentiated assessment strategies. Thousand
Oaks, CA: Corwin Press.
Gregory, G. H., & Chapman, C. (2002). Differentiated instructional strategies.
Thousand Oaks, CA: Corwin Press.
Harlen, W. (2007). Assessment of learning. Los Angeles, CA: Sage Publications.
Manning, S., Stanford, B., & Reeves, S. (2010). Valuing the advanced learner:
Differentiating up. Clearing House: A Journal of Educational Strategies,
Issues and Ideas, 83(4), 145-149.
Norlund, M. (2003). Differentiated instruction. Lanham, MD: Scarecrow Press.
Rotigel, J., & Fello, S. (2004). Mathematically gifted students: How can we meet
their needs? Gifted Child Today, 27(4), 46-51.
Shaw, S. R. (2010). Rescuing students from the slow learner trap. Principal
Leadership, 12-16.
Tomlinson, C. A. (1999). The differentiated classroom: Responding to the needs
of all learners. Alexandria, VA: Association for Supervision and
Curriculum Development.
Wright, R. J. (2008). Educational assessment. Los Angeles, CA: Sage
Publications.
Appendices
40
Appendix A
Institutional Review Board Approval
41
Appendix B
Principal Consent Form
I. Research Background (to be completed by researcher)
Title of the Study: Differentiated Testing
Name of Researcher: Steven Schultz Phone: (701) 527-2932
Street address: 6605 71st Ave. NE City: Bismarck, North Dakota
Zip: 58503
E-mail: [email protected]
II. Description of Research Proposal
Researcher is to provide the principal with a copy of the executive summary and
the time requirement form.
III. Agreement (to be completed by principal)
I, ___________________________, principal of ____________________school,
understand
the study and what it requires of the staff, students, and/or parents in my
school,
that the privacy and confidentiality of any staff or student will be protected,
that I have the right to allow or reject this research study to take place at my
school,
that I have the right to terminate the research study at any time,
that I have the right to review all consent forms and research documents at
any time during the study until project is completed and defended.
42
I grant permission to the researcher to conduct the above named research in
my school as described in the proposal.
I DO NOT grant permission to the researcher to conduct the above named
research in my school as described in the proposal.
I understand that data should be released only by the departments that own
them. My staff and I shall not release data to the researcher without
approval from the IRB.
Signature of Principal:_______________________________________
Ken Erickson, Principal, Bismarck High School
43
Appendix C
Differentiated Testing
Research Participant Consent Form
Purpose of the Research
I am currently working toward earning my Masters of Arts of Teaching:
Mathematics degree through Minot State University. To earn my degree, I am
conducting an action research project for approximately eight weeks starting in
January 2011, at the beginning of the second semester to determine if changing
my test format will increase the overall grades produced on tests and quizzes.
Specific Procedures
In my two geometry classes, I plan on changing the format of the tests to give
more opportunities for students to show what conceptual knowledge they have
retained within a specific amount of time. The format will consist of having
multiple problems to choose from out of a problem set. The problems will range
in point values depending on their level of difficulty.
Duration of Participation
Your student will participate in an eight week collection of test and quiz data.
Benefits to the Individual
Students often tell the teacher that the problem they were tested with gave them
difficulties, but they could do problems that resembled it in their homework. I
plan on giving them multiple problems to choose from resulting in a better
likelihood that they will know how to compute one of the problems in the set.
Also the opportunity to choose should decrease the amount of problems left blank
on the tests.
Alternatives to Participation/Withdrawal from Study
If you decide to not allow your child to participate, he/she will still do all of the
tests. Their scores will be omitted from the data set I collect. Your child’s
participation in this study is voluntary, and choosing not to participate in this
study will not affect his/her grade in any way. If you decide to allow the
participation of your child in this study, you may withdraw at any time during the
44
study by contacting me at 701-323-4800 or email me at
Confidentiality
All data will be treated confidentially by the researcher. Names of participants
and their data sets will be kept in a locked file cabinet in the researcher’s office
and will be destroyed once the paper has been defended and approved. The
researcher agrees to maintain strict confidentiality which means your student’s
name will not be discussed or divulged with anyone outside of this research
project. The researcher will also make sure confidential information will not be
discussed in an area that can be overheard that would allow an unauthorized
person to associate or identify the student with such information.
Offer to Answer Questions
If you have any questions or concerns during the study, feel free to contact me at
701-323-4800 or email me at [email protected]. If you have
questions about the right of research subjects, contact the Chairperson of the MSU
Institutional Review Board (IRB), Brent Askvig at 701-858-3052 or
Thank you for your consideration.
45
Consent Statement
You are voluntarily making a decision whether or not to participate in this study.
The only data collected will be the scores of the student with no attached name.
Check yes if you approve followed by your signature. You will be given a copy of
this consent form to keep in your possession.
Yes, I approve. No, I do not approve.
__________________________________________
Participant (Please Print Student’s Name above)
___________________________________________Date________________
Signature of Parent or Guardian
___________________________________________Date__________________
Signature of Researcher
46
Appendix D
Differentiated Testing
Student Assent form
Purpose of the Research
I am currently working toward earning my Masters of Arts of Teaching:
Mathematics degree through Minot State University. To earn my degree, I am
conducting an action research project for approximately eight weeks starting in
January 2011, at the beginning of the second semester to determine if changing
my test format will increase the overall grades produced on tests and quizzes.
Specific Procedures
You are currently in one of my two geometry classes. I plan on changing the
format of the tests to give more opportunities for you to show what conceptual
knowledge you have retained within a specific amount of time. The format will
consist of having multiple problems to choose from out of a problem set. The
problems will range in point values depending on their level of difficulty.
Duration of Participation
As a student, you will participate in an eight week collection of test and quiz data.
I will be collecting your scores on the tests and quizzes as well as tallying the
amount of problems left blank.
Benefits to the Individual
Students often tell the teacher that the problem they were tested with gave them
difficulties, but they could do problems that resembled it in their homework. I
plan on giving you a test with multiple problems to choose from resulting in a
better likelihood that you will know how to compute one of the problems in the
set. Also the opportunity to choose should decrease the amount of problems you
skip on the tests because you forgot how to do it.
Alternatives to Participation/Withdrawal from Study
If you decide not to participate, you will still do all of the tests. Your scores will
not be included in the data set. Your participation in this study is voluntary, and
choosing not to participate in this study will not have a negative affect on your
47
grade in any way. If you decide to participate in this study, you may withdraw at
any time during the study by contacting me.
Confidentiality
All data will be treated confidentially by the researcher. Names of participants
and their data sets will be kept in a locked file cabinet in the researcher’s office
and will be destroyed once the paper has been defended and approved. The
researcher agrees to maintain strict confidentiality which means your name will
not be discussed or divulged with anyone outside of this research project. The
researcher will also make sure confidential information will not be discussed in an
area that can be overheard that would allow an unauthorized person to associate
or identify the student with such information.
Offer to Answer Questions
If you have any questions or concerns during the study, feel free to contact me at
701-323-4800 or email me at [email protected]. If you have
questions about the right of research subjects, contact the Chairperson of the MSU
Institutional Review Board (IRB), Brent Askvig at 701-858-3052 or
Thank you for your consideration.
48
Consent Statement
You are voluntarily making a decision whether or not to participate in this study.
The only data collected will be the scores of the tests with no attached name.
Check yes if you approve followed by your signature.
Yes, I approve. No, I do not approve.
__________________________________________
Participant (Please Print Your Name above)
___________________________________________Date________________
Signature of Participant
___________________________________________Date__________________
Signature of Researcher
49
x
13
12
x
4
2
Appendix E
Quiz 1
Geometry Quiz Name__________________
Pythagorean Theorem
Note: if you only do the A level problems you will earn at best a 70%. B level =
85% C level = 100%. If you have time to do all problems, I will grade the
problems that earn you the most points.
Find the unknown side length. Simplify answers that are radicals.
3pts 1A)
3.5pts B)
4pts C) Use the directions above and then: Tell whether the side lengths
form a Pythagorean triple.
15
10
x
50
3 pts 2A) What is the length of the hypotenuse of a right triangle with leg
lengths of 5 inches and 12 inches?
A. 11 inches B. 13 inches C. 15 inches D. 17
inches
3.5pts B) A computer screen is approximately 10.75 in. high and 13.25 in. wide.
A computer screen is advertised by giving the approximate length of the
diagonal of its screen. How should this computer screen be advertised?
4pts C) As part of your exercise routine, you jog around the neighborhood
block which is shaped like a right triangle. Your street, the hypotenuse of
the triangle, is 850 feet long. If the total distance around your block is 2000
feet, what are the lengths of the other two streets that enclose your block?
51
3pts 3A) Find the perimeter of the following diagram.
4pts B) Find the area and perimeter of the following.
5pts C) A farmer is planning on cultivating a triangular plot of land as shown in
the diagram. The plot has an area of 12,600 square feet. Find the perimeter.
52
Appendix F
Quiz 2
Geometry Name_________________________
Quiz Right Triangles
Note: if you only do the A level problems you will earn at best a 70%. B level =
85% C level = 100%. If you have time to do all problems, I will grade the
problems that earn you the most points.
Solve for the indicated variable.
3pts 1A)
3.5pts B)
53
4pts C)
Solve the special right triangle for problem sets 2 & 3.
3pts 2A) 3.5pts 2B)
4pts 2C)
3pts 3A) 3.5pts 3B)
54
4pts 3C)
3pts 4A) Solve for the measure of angle A. Round to the nearest tenth.
4pts 4B) Solve the right triangle. Round to the nearest tenth.
55
4.5pts 4C) Solve the right triangle. Round to the nearest tenth.
2pts. 5) Describe a real world application in which being able to solve right
triangles would/could be necessary.
56
Appendix G
Unit 1 Test
Test Name________________________
Geometry
Chapter 7
45 total points available. If you only do the A problems, max score =72%,
B problems max score = 84.5%, C problems max score = 100%. Remember that
you can mix and match. You may do all of the problems (time permitting) and I
will grade the problem(s) that earns you the most points! GOOD LUCK!
3pts 1A) Find the value of x.
For 1B and 1C, find the value of x and write your answer in simplest radical form.
4pts 1B) 4.5pts 1C)
x 13
4
57
2pts 2A) Decide if the following lengths of segments can form a right triangle.
10, 12, 14
2.5pts 2B) State whether the triangle with the given sides is right, obtuse or
acute.
13, 12, 18
3pts 2C) Determine whether the lengths of the line segments can form a
triangle. If so, label the triangle as right, acute or obtuse.
14, 48, 50
2pts 3A) Complete the proportion. 3pts 3B) Find the exact
value of x. FG
DF =
4pts 3C) In the following right triangle, find the length of the altitude to the
hypotenuse.
58
For problem sets 4 and 5, find the value of the variables.
2pts 4A) 3pts 4B)
3.5pts 4C)
2.5pts 5A) 3pts 5B)
3.5pts 5C)
59
Do each of the following problems because there is no significant level of
difficulty in this section. Round answers to the nearest tenth. Either you know it
or you don’t! GOOD LUCK!
6. 7.
8. 9.
Find the approximate measure of angle P in the following 2 problems. Do both of
these problems!
10. 11.
60
Solve the right triangle and round answers to the nearest tenth.
4pts 13A) 4.5pts 13B)
5pts 13C)
61
Appendix H
Unit 2 Test
Test
Name______________________
Geometry
Chapter 8
45 total points available. If you only do the A problems and the required, max
score =75.5%,
B problems and the required, max score = 86.5%, C problems and the required,
max score = 100%. Remember that you can mix and match. You may do all of
the problems (time permitting) and I will grade the problem that earns you the
most points! GOOD LUCK!
In the following, find the sum of the interior angles of the given polygons. Do all
problems 1 – 4 in this section.
1. Heptagon 2. Octagon 3. 24-gon 4. 80-gon
Find the value of x. Choose your problem(s) in this section.
3pts 5A) 3.5pts 5B) 4pts 5C)
62
Find the value of x. note: there are only 2 levels of difficulty on this problem set.
3pts 6A) 4pts 6B)
Find the value of each variable in the following set of parallelograms.
2 pts 7A) 2.5pts 7B)
3pts 7C) The measure of one interior angle of a parallelogram is 42 degrees
more than twice the measure of another angle. Find the measure of each
angle.
63
Find the indicated measure in parallelogram HIJK. DO ALL OF PROBLEMS 8 -
13!
8. HI = 9. KH =
10. GH = 11. HJ =
12. m KIH = 13. m JIH =
2pts 14A) Classify the parallelogram.
64
4pts 14B) Classify the special quadrilateral and then find the values of x and
y.
4.5pts 14C) Classify the special quadrilateral and then find the values of x and
y.
65
2pts 15A) Find the measure of angle B, C and D.
2.5 pts 15B) Find the measure of angle J and K.
3pts 15C) Find the measure of angle E and T.
66
2 pts 16A) Find the length of the midsegment.
3pts 16B) Find the length of line segment MN.
3.5 pts 16C) Find the value of x.