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Teacher Work SampleFall 2009
Algebra II
Pre-Professional Experience
Professional Development School
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Table of Contents
General Section
Introduction…………………………………………………… 3-4
Philosophy of Education……………………………………… 5-7
Teacher Work Sample
Section I: Contextual Factors…………………………………. 8-12
Section II: Learning Goals……………………………………. 13-14
Section III: Assessment Plan…………………………………. 15-20
Section IV: Design for Instruction…………………………… 21-34
Section V: Instructional Decision-Making…………………… 35-37
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Introduction
Junior Field is meant for a student to teach at a school one day a week. But I thought,
what am I really going to get out of this experience by only teaching a class one day a week. So
I had the idea of teaching a whole unit for ten days straight. This way I would be able to
experience what my Senior Field was going to be like and I would also have real information and
data to use for my Teacher Work Sample. I believe that teaching for ten days straight prepared
me for my Senior Field, where I feel teaching once a week would just have been an extension of
Sophomore Field.
Doing a Teacher Work Sample also gave me a purpose and a goal for my Junior Field. I
was required to plan my own unit, teach my own unit, and analyze its outcomes. I made
connections with the students and learned how each student learned, how they worked, and the
progress they made throughout this unit. This TWS provides credible evidence of my ability to
provide learning for all students. The Teacher Work Sample also encompasses my short, but
privileged and honored, experience as an Algebra II teacher at Rahway High School. I am very
grateful for this opportunity because of the people I had the chance to work with. My Clinical
Instructor and Cooperating Teacher were so unbelievably helpful and without them, I would not
have the knowledge or experience I need in order to begin my Senior Field.
The unit that I taught was exponential growth, decay, and compound interest. This unit
was the focus of my Teacher Work Sample. By organizing a set of learning goals, an assessment
plan, and design for instruction I was able to evaluate the students’ comprehension of each
element of my unit plan and reflect on my success as a teacher. This unit includes the College of
Education learning outcomes by integrating knowledge of subject matter, understanding student
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learning, accommodating diverse learning, and the ability to manage a classroom. With the
completion of this Teacher Work Sample, I have acquired the essential skills needed to begin my
teaching career.
With this opportunity, I realized how much impact a teacher has on a student’s life. I am
glad to know that I have made an impact, but more importantly, the students made an impact on
my life and the beginning of my teaching career. I feel that without this experience I would not
have had the opportunity to understand the real meaning of teaching.
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Philosophy of Education
The truth is that up until now I never wanted to be a teacher. It was my parents who
pushed me to be a teacher; they told me that as a teacher I will have good benefits and the best
benefit of all is that I will have my summers off. They also told me that a major advantage of
being a teacher is when I decide to have a family of my own, I will be able to raise my children
instead of having a daycare raise them for me. I was young, naïve, and indecisive, so a teacher is
what I was going to be.
Growing up, I was a competitive gymnast. My dream as a little girl was obviously to go
to the Olympics, along with every other little girl in America, but more importantly I wanted to
be a gymnastics coach. My parents told me that a coach was not a real career, but I figured out
that if I became a teacher I could also coach high school gymnastics. This is when becoming a
teacher started to appeal to me, but not for the right reasons just yet.
The philosopher, David Perkins once stated “The metaphor (coaching) with sports is
meant quite seriously...the coach stands back, observes the performance, and provides guidance.
The coach applauds strengths, identifies weaknesses, points up principles, offers guiding and
often inspiring imagery, and decides what kind of practice to emphasize.” I have been a
gymnastics team coach at a club gym for the past four years; this is actually where I realized the
real reason I should become a teacher. For each girl that I coach I make goals for the upcoming
season and daily practice assignments. But the main goal for every girl is to qualify for the state
championship. Recently I have realized how much this relates to writing teacher lesson plans
even though I do not write my gymnastics lesson plans down on paper.
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My favorite part of coaching gymnastics is watching a child learn a new skill or receive a
good score in a competition. When I realized this, I realized that teaching is exactly what I am
made for. When a student is able to grasp a new mathematics concept or receives a good grade
on a big test, the amount of excitement that a student has is the main reason I want to become a
teacher. In gymnastics, when a child does not understand the concept of a skill you must change
the language you are using, figure out a different way to explain it, or demonstrate it so the child
can visualize and comprehend it. The same goes for teaching, when a child does not understand
a mathematics concept, you must change the math jargon that you are using, try to explain it to
them in an alternate way, or use some visuals in order for the student to grasp it.
Building a relationship with each one of my gymnasts is very important to me. I know
how they learn, how they work, and their family background. This will also carry over when I
teach. I will take into account Gardner’s Multiple Intelligences of how each student learns
differently. I will also be aware of how they work and their family background; do they work
the best in groups or individually, do they have a good work ethic or a bad one, and how much
support they are getting at home.
I also love learning, and as a teacher I know I will still get to be a student. I will learn
from my experiences, I will learn from my colleagues, and most importantly I will learn from my
students. I will also continue to learn so I am able to teach my students math in a modern way
instead of an ancient one. I want to get my students excited about learning and excited about
mathematics so I will always be looking for new and improved ways to teach.
I believe in writing lesson plans that coincide with the New Jersey Core Curriculum
Content Standards, which also motivate students to want to learn mathematics by showing them
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how it relates to the real world. I do not want students to learn math just because they are going
to be tested on it, but because they like it and want to learn. If there are students who are having
trouble, I will do everything possible in order for them to grasp the concept. I will make it a
point to develop a relationship with each and every one of my students. But my main goal is for
my students to view math as fun.
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I: Contextual Factors
Community, District, and School Factors
Rahway is a 4.1 square mile city that is located in the southern part of Union County,
New Jersey. The city is fifteen miles southwest of Manhattan and five miles west of Staten
Island so it is considered to be a part of the New York Metropolitan area. Rahway is bordered to
the Northwest by Clark, to the Northeast by Linden, and to the South by Woodbridge.
According to the United States Census Bureau, the city of Rahway has a population of
28,189 people. Of the 28,189 people residing in Rahway, 60.2% are Caucasian, 27.1% are
African American, 13.9% are Hispanic, 3.6% are Asian, .2% are American Indian or Alaskan
native, and .1% are Native Hawaiian or Pacific Islander.
Of Rahway’s population of 28,189t, there are 10,381 household units and 2.63 persons
per household. The United States Census Bureau reports that the median household income is
$50,729 and the per capita income is $22,481. The census also approximates that 7.1% of the
population is living below poverty; including 9.3% of those under age 18 and 8.2% of those are
age 65 or over.
The number of students enrolled in Rahway High School in the 2006-2007 school year
was 1184. As of 2007, Rahway High School had a graduation rate of 87.5%, which is a decrease
of .8% from the previous year. There was also a 3% dropout rate in the 2006-2007 school year,
which is a decrease of .7% from the previous year. The 12.5% of seniors who did not graduate
was primarily due to the fact of the inability to score proficiently on the High School Proficiency
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Assessment test. This includes 42.3% of students who did not score proficient on the
mathematics section of the HSPA.
Classroom Factors
The length of Rahway’s HS school day is eight hours and seven minutes with six hours
and ten minutes of instructional time. In New Jersey, the average school day is six hours and
fifty minutes with five hours and fifty three minutes of instructional time. The average class size
of Rahway High School is fifteen students compared to 20.8 students for the New Jersey
average.
Technology is unquestionably present in Rahway High School. There are 136 computers
connected to the internet. Of these 136 computers, 75 are in classrooms, 12 are in the library,
and 49 are in the computer labs. The student to computer ratio is 8.7. Every classroom contains
an internet connected computer which is convenient for teachers to take attendance and to
compute grades using the online grading system called Power School. Each classroom is also
equipped with a television, which is used for the morning announcements, and an overhead
projector. All mathematics teachers are also given a class set of graphing calculators which are
handed out and collected each period.
Student Characteristics
Although Rahway High School is a very diverse community, for 76.1% of students,
English is their first language. This is followed by Spanish being the first language for 19.5% of
students and 4.4% whose first language is not English or Spanish. Also, 3% of students are
Limited English Proficient and 17% of students are classified for Individualized Education
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Program. On the other hand, 22.1% of Rahway’s juniors and seniors are placed in Advanced
Placement classrooms. There are a total of 212 students in Advanced Placement classrooms,
nine of which are taking AP Calculus.
In the 2006-2007 school year, 262 students at Rahway High School were tested on the
Mathematics portion of the HSPA test. Of those 262 students, 12.2% tested advanced, 48.1%
tested proficient, and 39.7% tested partial. In the state of New Jersey, 23.2% tested advanced,
50.2% tested proficient, and 26.6% tested partial. Rahway High School had 13.1% more
students that tested partial on the HSPA than the New Jersey average. Of the 262 Rahway
students that took the mathematics portion of the HSPA test, 104 of them tested partial.
Rahway High School has 78% of their student population that take the Scholastic
Assessment Test. The average score from 2006-2007 was a 440 which is ten points above the
50th percentile, but sixty points below the state average.
Instructional Implications
When planning my instructional design and assessment I will keep in mind the fact that
Rahway is so diverse. I will teach as a motivator and not as a dictator. I will also allow for
students to help each other and/or group work daily. Students are able to relate to each other
more than I can relate to them. Students will be able to get the message across in a way that I am
not able to but will also assist me in teaching because of the numerous language and cultural
barriers. I will also be able to see if students fully understand the concept when they put it into
their own words when explaining it to a classmate.
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My lesson will include some technology but will mostly rely on student interaction and
visuals. The students will have access to graphing calculators but I will not permit the students
to use them daily. There are too many students that rely on calculators for elementary
mathematics. I will allow the use of calculators when graphing and for higher levels of
mathematics. I will use an overhead projector daily for my lecture, class notes, and sometimes
for visuals. I will use visuals as often as possible in order to meet the different styles of learning
that students may have and to assist in furthering the understanding of the lesson.
I will also take into account the fact that such a large percentage of students are testing
below proficient on the High School Proficiency Assessment test and the average score on the
Scholastic Assessment Test is only at the 50th percentile. I believe that students’ scores on these
tests reflect their liking of mathematics. Most students, no matter what school they attend, say
they hate math. When a student hates a subject they are not going to want to put any effort into
learning new material, and coming in for extra help is absolutely out of the question. I strongly
believe that this is why students do not score well on these tests. It is not that they are incapable
of learning new mathematics concepts, it is that they just hate math. If teachers were to make
math more fun and show students exactly how math relates to the real world, instead of teaching
directly from the textbook and teaching only for these tests, students may actually enjoy and
want to learn in their mathematics classes.
I will do my best at trying to relate everything possible to the real world. Obviously not
all mathematics concepts can directly relate, but in the end most of them do. In my lessons, I
will not only teach from the textbook, but I will find outside sources to help me assist the
students in learning. I will also construct a project for students to do in groups that they will
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have to use mathematics concepts and equations in real life situations. I believe this will
motivate students to want to learn and actually like math by showing them how they will have to
use it in their own lives’ one day.
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II: Unit Learning Goals
Learning Goals for Exponential Growth, Decay, and Functions
1. SWBAT calculate the multiplier for exponential growth and decay.
2. SWBAT construct and evaluate exponential expressions to model growth and decay situations.
3. SWBAT predict and distinguish an exponential function as representing exponential growth or
exponential decay.
4. SWBAT calculate the growth of investments under various conditions.
Alignment with NJCCCS
Learning Goal 1: NJCCCS: 4.1.B, 4.2.D, 4.3.A
Learning Goal 2: NJCCCS: 4.2.D, 4.3.B, 4.5.A, 4.5.B, 4.5.C, 4.5E
Learning Goal 3: NJCCCS: 4.2.B, 4.2.C, 4.3.A, 4.3.B, 4.4.A, 4.4B, 4.5.B, 4.5.C, 4.5.D
Learning Goal 4: NJCCCS: 4.1.B, 4.2.D, 4.4A, 4.5.A, 4.5.D, 4.5.B, 4.5.E
Types and Levels of Learning Goals
The four learning goals for the exponential growth, decay, and functions unit focus on the
higher levels of Bloom’s Taxonomy. Mathematics requires the three highest levels of Bloom’s
Taxonomy which are Analysis, Synthesis, and Evaluation. But the three lower levels,
knowledge, comprehension, and application, are also a necessity. In mathematics, to be able to
define, identify, and write (terms found in the lower levels) concepts is just not enough. One
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must be able to calculate, construct, and predict (terms found in the higher levels) in order to
fully understand mathematics concepts.
Appropriateness of Learning Goals
Mathematics is like building blocks. Every time a teacher starts a new unit or section,
they do not ever start from the bottom; they build on top of already learned concepts. This unit
will be completely new and unique to the students. Even though it will be like nothing they have
ever seen before, it does not mean they do not already have skills that will assist them.
Each goal will be assessed by the student’s comprehension and performance on Do
Now’s, class work, homework, quizzes, and a unit project. Before beginning the unit, I will pre-
assess the students by giving them a small quiz that will review concepts that they should already
know and need to have in order to dive into this unit. This review quiz will assist me in planning
my lessons for this unit to the student’s ability and knowledge.
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III: Assessment Plan
Overview of Assessment Plan
The assessment plan for the Exponential Growth, Decay, and Functions Unit includes a
variety of methods to assess its objectives. For each of the four learning goals, there is pre-
assessment, formative assessment, and post assessment. Pre-assessments include a pre-
assessment quiz and daily Do Now’s. Formative assessments include class work and homework.
Post assessments include two quizzes and a two-day project. Students with various learning
styles, English Language Learners, as well as others who have special needs will also be
successful throughout this unit due to teacher modifications, cooperative learning groups, and
visual aids.
Description of Pre-Assessment
The pre-assessment for this unit will be given in the form of a ten question quiz. The
students will be informed that this quiz will not count against them but they will receive extra
credit points for correct answers which will be added to their post assessment quiz #2. This
incentive will be given so the results of the pre-assessment quiz will be as valid as possible.
Each question on the quiz is directed toward a specific learning goal.
Learning Goal 1: SWBAT calculate the multiplier for exponential growth and decay.
The first four questions on the pre-assessment quiz are aligned with the first learning
goal. In order to calculate the multiplier for exponential growth or decay, one must change a
percent into a decimal and add or subtract this number from one hundred depending on if the
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question is about growth or decay. The first four questions on the quiz ask the students to write
the percent as a decimal.
Learning Goal 2: SWBAT construct and evaluate exponential expressions to model growth and
decay situations.
The next two questions on the pre-assessment quiz are aligned with the second learning
goal. In order to construct and evaluate exponential expressions to model growth and decay
situations, one must extract information from a word problem, set up an exponential expression,
and evaluate an exponential expression. These two questions on the quiz ask the students to
evaluate exponential expressions.
Learning Goal 3: SWBAT predict and distinguish an exponential function as representing
exponential growth or exponential decay.
The following two questions on the pre-assessment quiz are aligned with the third
learning goal. In order to predict and distinguish an exponential function as representing
exponential growth or exponential decay, one must read and understand that an exponential
growth graph is increasing and an exponential decay graph is decreasing. These two questions
on the quiz ask the students to determine if the graph is increasing or decreasing.
Learning Goal 4: SWBAT calculate the growth of investments under various conditions.
The last two questions on the pre-assessment quiz are aligned with the third learning
goal. In order to calculate the growth of the investments under various conditions, one must
calculate an expression for different values of a variable. These two questions on the quiz ask
the students to evaluate expressions for two different values.
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Description of Formative Assessment
Formative assessments for this unit will include daily Do Now assignments, in-class
assignments, and independent homework assignments which assess all four learning goals.
Do Now assignments will be given daily for the students to complete within the first five
minutes of the class period. These Do Now assignments do one of two things, either review the
lesson from the previous day or introduce a new topic for that particular day. Do Nows check
for understanding of the concepts learned from the previous day or they check for the
background knowledge that is necessary in order for the new concept to be taught.
In-class assignments will also be given daily. The in-class assignments include
worksheets and problems on the overhead. In-class worksheets enable students to practice the
concepts recently learned with the support of the teacher and other students. Students are
welcome to work together and assist each other with any questions and confusion they may have.
Problems that the teacher writes on the overhead projector check for understanding throughout a
daily lesson. This will allow the teacher to see if the students comprehend what was taught up
until that point and therefore will permit the teacher to move on to the next part of the lesson.
Independent homework assignments will be given daily with the exception of Fridays.
Homework assignments allow students to further their understanding of the topic independently
and also provide additional practice. Homework assignments are mostly problems from the book
but occasionally can be worksheets. These assignments let students check for their own
comprehension of the topic. It also gives them an opportunity to see what their weakness is and
where the confusion is occurring so they will be able to ask questions following day.
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Description of Post Assessment
Post Assessments for this unit will include a group project and two quizzes which assess
all four learning goals.
The group project assesses all four learning goals. Students will work and complete the
project the day before the unit quiz. This project will allow the teacher to check for the students’
comprehension of the whole unit. This project also lets students review for the quiz they will be
taking the following day.
Students will take two quizzes during this unit. One will be given about half-way
through the unit and the other will be given at the conclusion of the unit. The first quiz will
assess the first two learning goals. The mastery of these learning goals will be required to move
ahead in this unit. The second quiz will assess all four of the learning goals. This quiz will be a
unit quiz. Each question on both quizzes will be directed toward a specific learning goal.
Learning Goal 1: SWBAT calculate the multiplier for exponential growth and decay.
The first three questions on quiz one are aligned with the first learning goal. The first
four questions on quiz two are aligned with the first learning goal. These questions ask the
students to find the multiplier for each rate of exponential growth or decay.
Learning Goal 2: SWBAT construct and evaluate exponential expressions to model growth and
decay situations.
The last seven questions on quiz one are aligned with the second learning goal. These
questions ask the students to evaluate the expressions give x, y, and z and write the exponential
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expression and predict the population of bacteria for a time period. The next three questions on
quiz two are aligned with the second learning goal. These questions ask the students to
determine whether each table represents linear, quadratic, or exponential function.
Learning Goal 3: SWBAT predict and distinguish an exponential function as representing
exponential growth or exponential decay.
The following four questions on quiz two are aligned with the third learning goal. These
questions ask the students to tell whether each function represents exponential growth or decay
and write the exponential expression and predict the population of bacteria for a time period.
Learning Goal 4: SWBAT calculate the growth of investments under various conditions.
The last two questions on quiz two are aligned with the fourth learning goal. These
questions ask the students to find the final amount for each investment.
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Assessment Overview
Learning Goal 1
SWBAT calculate the multiplier for
exponential growth and decay.
Pre-Assessment
Pre-Assessment Quiz: problems 1-4
FormativeAssessment
Class work: 3/27, 3/30
Homework: 3/30, 3/31, 4/8
Post Assessment
Quiz #1: problems 1-3
Quiz #2: problems 1-4
In-class Project
Learning Goal 2
SWBAT construct and evaluate exponential
expressions to model growth and decay
situations.
Pre-Assessment
Pre-Assessment Quiz: problems 5-6
FormativeAssessment
Class work: 3/27, 3/30, 3/31
Homework: 3/30, 3/31, 4/8
Post Assessment
Quiz #1: problems 4-10
Quiz #2: problem 10-11
In-class Project
Learning Goal 3
SWBAT predict and distinguish an
exponential function as representing
exponential growth or exponential decay.
Pre-Assessment
Pre-Assessment Quiz: problems 7-8
FormativeAssessment
Class work: 4/1, 4/2, 4/3
Homework: 4/1, 4/2, 4/8
Post Assessment
Quiz #2: problems 8-9
In-class Project
Learning Goal 4
SWBAT calculate the growth of investments
under various conditions.
Pre-Assessment
Pre-Assessment Quiz #9-10
FormativeAssessment
Class work: 4/3, 4/6, 4/7, 4/8
Homework: 4/6, 4/7, 4/8
Post Assessment
Quiz #2: problem12-13
In-class Project
V: Design for Instruction
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Results of Pre-Assessment
The pre-assessment for all four learning goals was a ten question quiz. According to the
amount of questions answered correctly students earned extra credit points, which will be added
to their final quiz. For every correct answer, students earned half of a point. Students were able
to earn up to a total of five extra credit points. These results reflect one class which includes
twenty-one students.
Overall, the students scored well on the pre-assessment quiz. All of the students were
able to answer more than half correct. Correct answers ranged from six out of ten to nine out of
ten. Four students answered six out of ten questions correct and earned three extra credit points.
Seven students answered seven out of ten questions correct and earned three and a half extra
credits points. Four students answered eight out of ten questions correct and earned four extra
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credit points. Six students answered nine out of ten questions correct and earned four and a half
extra credit points. In the end, the pre-assessment quiz was beneficial to all of the students.
The students did very well on the questions pertaining to learning goals one, two, and
three. For learning goal one, 71% of the students answered all of the questions correctly. For
learning goal two, 67% of students answered all of the questions correctly. For learning goal
three, 76% of students answered all of the questions correctly. The students have good
background knowledge for these three learning goals. Students will be able to learn and catch on
easily with the lessons related to these three learning goals.
On the other hand, 67% of students answered all of the questions wrong that are relevant
to learning goal four. The students seemed to have a tough time with the skill for this learning
goal. Due to the lack of their background knowledge and confusion for this learning goal, time
and practice for this skill have been implemented into to first lesson plan.
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Questions one through four on the pre-assessment quiz assessed the first learning goal:
SWBAT calculate the multiplier for exponential growth and decay. The students are very
knowledgeable in this area because fifteen out of twenty-one students answered all four of the
questions correctly. Five students answered three out of the four questions correctly. One
student answered two out of the four questions correctly. The results for the pre-assessment of
the first learning goal conclude that majority of the students understand how to write a percent as
a decimal. This skill will be helpful when students are calculating the multiplier for exponential
growth and decay.
Questions five and six on the pre-assessment quiz assessed the second learning goal:
SWBAT construct and evaluate exponential expressions to model growth and decay situations.
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The students are pretty familiar with this area because fourteen out of twenty-one students
answered both questions correctly. Seven students answered one out of the two questions
correctly. The results for the pre-assessment of the second learning goal conclude that majority
of the students understand how to evaluate exponential expressions. This skill will be helpful
when students are constructing and evaluating exponential expressions to model growth and
decay.
Questions seven and eight on the pre-assessment quiz assessed the third learning goal:
SWBAT predict and distinguish an exponential function as representing exponential growth or
exponential decay. The students seem very educated in this area because sixteen out of twenty-
one students answered both questions correctly. Two students answered one out of the two
questions correctly. Three students answered neither of the questions correctly. The results for
the pre-assessment of the third learning goal conclude that majority of the students, with the
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exception of a few, understand how to determine if the graph is increasing or decreasing. This
skill will be helpful when students are predicting and distinguishing an exponential expression as
representing exponential growth or exponential decay.
Questions nine and ten on the pre-assessment quiz assessed the fourth learning goal:
SWBAT calculate the growth of investments under various conditions. The students appear to
be not very experienced in this area because no one answered both questions correctly. Thirteen
students answered one out of the two questions correctly. Eight students answered neither of the
questions correctly. The results for the pre-assessment of the fourth learning goal conclude that
the students have minimal understanding of how to evaluate exponential expressions for
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numerous values. This skill will be needed when students calculate the growth of investments
under various conditions. Due to the results of the pre-assessment for this learning goal and the
necessity of this skill in this unit, extra time and practice of evaluating exponential expressions
will be set aside.
Unit Overview
Day One: 3/27 Day Two: 3/30
Objective: Learning Goals 1 & 2; SWBAT:
Calculate the multiplier for exponential growth.
Construct and evaluate exponential expressions to model growth situations.
Objective: Learning Goals 1 & 2; SWBAT:
Calculate the multiplier for exponential decay.
Construct and evaluate exponential expressions to model decay situations.
Do Now:
Write the percent as a decimal.
Write the decimal as a percent.
Do Now:
Find the multiplier of exponential growth. Pg. 358 #15,16
Activity:
Modeling bacterial growth example
Evaluate exponential expression: 6.1 pg. 959 #13, 14, 16, 17
Modeling Human Population Growth: Pg. 356 Example 1
Students: Find the multiplier of growth: Pg. 358 #5,6
Students: Human Population Growth: Pg. 356 Try This
Closure: Human Population Growth: Pg. 358 #13
Activity:
Human Population Growth Refresher: Pg. 359 #47
Physical Science Light Decay: Pg. 362 #50
Modeling Biological Decay: Pg. 357 Example 2
Students: Find the multiplier of decay: Pg. 358 #7,8
Students: Biological Decay: Pg. 357 Try This
Closure: Biological Decay: Pg. 358 #14
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Homework:
None……Have a good weekend!
Homework:
Find the multiplier for each rate of exponential growth or decay. Pg. 358 #17-23
Evaluate each expression. Pg. 358 #24-35 even
Growth and Decay Word Problems. Pg. 359 #48-49
Day Three: 3/31 Day Four: 4/1
Objective: Learning Goals 1& 2; SWBAT:
Construct and evaluate exponential expressions to model growth and decay situations.
Define and analyze the parts of an exponential equation that models growth and decay situations.
Objective: Learning Goal 3; SWBAT:
Predict an exponential function as representing exponential growth or exponential decay.
Differentiate between exponential growth and exponential decay functions.
Do Now:
You are hanging out with 1 friend. After each hour, the amount of friends you are hanging out with doubles. How many friends are you hanging out with after the first hour? After the second? After the sixth?
Do Now:
Rounding numbers.
Activity:
Students: Think, Pair, Share: pg. 358 #1-4
Population of Bacteria: Pg. 359 #36
Homework Questions?
Closure: Growth and Decay Worksheet
Activity:
Quiz
Graphing Sets of Functions: Growth and Decay
Closure: Determine Y Intercepts
Homework:
Finish worksheet for homework.
Homework:
Determine whether each function represents exponential growth and
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STUDY FOR QUIZ! decay. Pg. 367 #16-24
Match each function with its graph. Pg. 367 #25-28
Day Five: 4/2 Day Six: 4/3
Objective: Learning Goal 3; SWBAT:
Identify exponential function as representing exponential growth or exponential decay.
Distinguish graphs of exponential function as representing exponential growth or exponential decay.
Objective: Learning Goal 4; SWBAT:
Describe the transformations from one function to another of equations and graphs.
Calculate the growth of investments when interest is compounded only once a year.
Do Now:
Make a table for each of the three graphs. Write the values of x for each graph, if y = -2, -1, 0, 1, 2.
Do Now:
Describe the transformation made from the graph of the blue function to the graph of the red function.
Activity:
Linear, Quadratic, and Exponential Graphs and Forms of Equations
Students: Identifying Functions: Pg. 367 #10-15
Transformations: Vertically and Horizontally
Closure: Students graph transformations
Activity:
Transformations: Vertically, Horizontally, Stretched, and Compressed:
Students: Describe Transformations: Pg. 368 #38-43
Students: Graph Transformations
Compound Interest Investment Example
Students: Use Compound Interest Formula: Pg. 959 #16-17
Closure: Car Loan Problem
Homework:
Finish graphs Identify each function as linear,
quadratic, or exponential.
Homework:
None……Have a good weekend!
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Pg. 959 6.2 #1-6
Day Seven: 4/6 Day Eight: 4/7
Objective: Learning Goal 4; SWBAT:
Evaluate the growth of investments when interest in compounded numerous times a year.
Calculate the growth of investments under various conditions.
Objective: Learning Goals 4; SWBAT:
Analyze the financing of a car loan.
Choose and defend the better car payment deal.
Do Now:
What does annual mean? What does semi-annual mean? How many quarters are in a year? How many months are in a year? How many days are in a year?
Do Now:
Evaluate expressions using the compound interest formula.
You want to buy a car that costs $20,000 and you have $5,000 for a down payment. Your loan has a 7% interest for 4 years.
Activity:
Compound Interest n=1 Refresher: 2 Cases
Students: Compound Interest n=1 Refresher: 2 Cases Group work
Compound Interest: Annually, Semiannually, Quarterly, Monthly, Daily
Closure: Compound Interest Worksheet
Activity:
Financing a Car Loan Worksheet: groups of 2
Closure: A Car Dealer Offers Two Deals Worksheet
Homework:
Finish Compound Interest Worksheet
Homework:
Finish A Car Dealer Offers Two Deals Worksheet
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Day Nine: 4/8 Day Ten: 4/9
Objective: Learning Goals 1,2,3,4; SWBAT:
Prepare and finance a car loan payment.
Predict the worth a car is worth when it is paid off.
Compare and graph the depreciation of a car and a car’s final cost.
Objective: Learning Goal 1,2,3,4; SWBAT:
Find the multiplier for rates of exponential growth or decay.
Determine whether tables represent linear, quadratic, or exponential function.
Tell whether functions represent growth or decay.
Write the exponential expression and predict the population of bacteria for certain time periods.
Find the final amount of investments.
Do Now:
The car you want to buy costs $20,000. A car depreciates 20% immediately after it is driven off the lot. How much is the car worth when you drive it off the lot?
A car depreciates 10% per year starting with the 1st year. You’re able to pay your car off in 4 years. You’re able to pay your car off in 4 years. What is your car worth once you have completely paid it off? (Hint: The value of your car has decayed.)
If you borrow $1,000 at 9% interest and you can afford to pay about $100 a month to the bank. How many years will it take you to pay it off?
Do Now:
Any Questions? (10 minutes)
Activity:
GROUP PROJECT
Activity:
QUIZ on Sections 6.1 and 6.2
Homework: Homework:
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Quiz Practice Worksheet
None…..Spring Break!
Description of Activities
Activity 1:
Think, Pair, Share is an activity where students are asked four questions. They begin
thinking about and writing their answers down. Then students pair up and share their answers
with each other. Lastly the students and teacher discuss the four questions. The questions that
the students are given are critical and challenging. They do not ask what the answer to a
problem is, the questions ask why and how is that the answer to the problem. Most students can
answer the problems given for class work or homework but are not able to explain how or why
they got their answer. The most important part of mathematics is to be able to be able to explain
the process in which you came to the answer and this activity addresses that.
Activity 2:
Financing a Car Loan is an activity that shows students how buying a car works.
Students are given a table of six different ways to finance the same car. The table gives the cost
of the car, the down payment on the car, the annual interest rate on the loan, and the length of the
car payment for six different options. Students are to fill out the table for all options by
calculating the amount financed in a loan, the monthly car payment, the total cost of the car
payments, the final cost of the car, and the financing charges of the loan. The students are then
asked questions that compare the six different options of financing the same car. Then the
students are asked what the determining factors in choosing one payment plan over another are.
This activity is a preview for the group project.
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Activity 3:
The group project is the biggest activity in this unit. The students will work in groups of
two or three to finance two cars and then compare them. They will choose two cars. One car
will be on the cheaper side and the other car will be on the more expensive side. The teacher
will then reveal the costs of the two cars, the amount that students have for a down payment, the
amount they have for a monthly payment, and the interest rate for a loan. The students will
calculate how many years it will take to pay off each car, the final cost of each car, and the
amount paid in financing charges.
The teacher will then inform students the amount that a car is worth depreciates as soon
as it is driven off of the lot and that is also depreciates every year. The students are then asked to
calculate how much the car will be worth when it is finally paid off. Lastly, students will make
two bar graphs; one for each car. The bar graphs will compare how much each car is worth to
the total amount paid at the end of every year. The students are then asked which car they would
choose based on how much the car is worth when it is paid off and how much in total is paid in
financing charges.
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Technology
The use of an overhead projector will be daily. The students are able to read and copy
the notes and questions better because the projector enables the enlargement of what is written
on the transparencies. The overhead projector also allows the teacher to face the students while
writing and explaining opposed to the blackboard where the teacher has their back to the
students. Eye contact and the ability to see everything that is going on is very important when
teaching students.
The use of graphing calculators will also be daily. Students will not only use these
scientific calculators to solve equations, but also to graph equations. Students will use graphing
calculators to assist them in their Do Nows, Class work, Group Project, and Quizzes. The
knowledge of how to use a graphing calculator is very powerful today in the 21st century.
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Section V: Instructional Decision-Making
In a perfect world, a teacher’s lesson plans would be carried out flawlessly. The teacher
would be able to include everything necessary in a lesson, students would grasp all material, and
no modifications would be required. But this is not a perfect world; lesson plans are not carried
out flawlessly and modifications are required. There is no such thing as perfection; everyone and
everything has room for improvement. Making modifications to a lesson plan does not mean a
lesson or concept was taught incorrectly, but modifications are made in order for students to be
able to develop and progress further with the task at hand.
A perfect example of this was a modification that I made due to students confusion with
rounding. The day prior to quiz number one, I had the students complete a word problem
worksheet as practice for the quiz. This assignment was to be handed in for a grade. As I was
correcting these worksheets, I realized that most students’ troubles were not with writing the
equation or even evaluating it, but with rounding their answers. I had assumed by Algebra II,
students were able to round. This unfortunately was not the case. Very few students
remembered the rounding rules and this was a problem because the quiz required students to
round their answers.
As a result of the students’ confusion with rounding, the day of the quiz I added a
rounding Do Now. The Do Now consisted of six numbers with different rounding instructions.
This provided students with more practice and also allowed for students to clear up any
confusion or questions they may have had. It came as a shock to me as I was going over the
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answers to the Do Now, how many students actually had trouble with rounding. As I explained
each answer, a light bulb seemed to switch on with the students that were having difficulties.
This modification had positive results. Not to say that every student was able to round all
answers correctly on the quiz. But I did notice a big improvement from the previous day’s class
work. Majority of the students rounded correctly but there were still a select few that did not.
With these students, most of the misunderstanding seemed to be with reading directions correctly
not with actually rounding. I believe the students found this modification to be very helpful, as
did I.
Another modification that I made was a small addition to clear up some uncertainty with
the in-class project. This basis of the in-class project was to have students make the connection
of the newly learned concept of compound interest with something they could relate to,
something like buying a car. This project required students, in groups, to pick two cars of their
choice. Then, estimate the amount of time it would take to pay off each car with a loan, the final
cost of each car, and the total amount paid in financing charges given a set down payment,
monthly payment, and interest rate. The students then had to calculate the worth of each car
when it was paid off in full given a set depreciation rate. Lastly, the students had to compare the
amount of time it would take them to pay off the car, the amount paid in financing charges, and
the worth of each car when it was finally paid off to decide which car would be the better choice.
This project was not a walk in the park for the students.
I had two Do Now questions planned that would assist the students in calculating the
worth of their cars. But there was a lot of confusion with the first part of the project, determining
the amount of time it would take to pay off each car with a loan. This required students to guess
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a number of years and check to see if the monthly payment was about the same as the set amount
I had given them. I taught one class like this and then I decided a modification had to be made in
order to clear up some of the misunderstanding.
For the following three classes I added a third Do Now question. With this question, I
walked students through the process of guessing and checking the amount of years it would take
to pay off a small loan. This Do Now question aided students in comprehending the necessary
steps needed in calculating the first part of the project. Questions still arose, but that was to be
expected. Even though this modification took a little more class time to carry out than I would
have liked, but the students seemed to be more independent and on track with the group project.
Once again, this was another successful modification.
Both of the modifications made, I could not have previously planned. As a new teacher, I
was not able to project all of the issues that the students could have possibly run in to. But I was
able to make changes where necessary in order to assist the students in furthering their
understanding of certain concepts. I believe that being able to realize where modifications need
to be made is a big part of becoming a better teacher.
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VI: Analysis of Student Learning
