ACP PORTFOLIO
By
Alexandra Shott
Bruce Caraway
Adjunct Certification Program
November 27, 2015
TABLE OF CONTENTS
I. Syllabus snapshot
II. Student Preparation Strategy
III. BOPPS Lesson Plan
IV. Test Questions
V. Rubic
VI. Showcase Presentation
VII.Reflective Essay
1
Math 1314 College Algebra
Instructor contact information
Instructor: Alexandra Shott Office Phone: Cell 832-721-7420, no text
Office: 13.303 Office Hours: MW 3:30-5
E-mail: [email protected]
(or hours of availability)
Welcome to
Course Title: College Algebra Course Subject: Math 1314
Required Material:
College Algebra; Enhanced w/ Graphing Utilities, 6th ed. by Sullivan and
Sullivan
ISBN # 9780321199911
Graphing Calculator
Instructor guidelines and policies
Attendance: ATTENDANCE POLICY:
Attendance to all classes is expected. Instructors are required to keep accurate records of attendance.
Statistics show that students who maintain good attendance perform much better in the course; therefore,
attendance is critical. If you cannot attend class regularly, you should notify the registrar that you would
like to drop the course. Do not assume you will automatically be dropped for non-attendance. Students
who do not formally withdraw will receive an “F” in the course. Communication with me is critical!
Assignments: You may either use My Math lab (you need to purchase a session with the
electronic book instead of the hard copy book) or home work from the book
Make-up Exams: No make-ups or late submissions are allowed except by advance arrangement with
me. Major exams are scheduled in advance to ensure that you will be able to attend exam day. If you
know you will miss an exam please let me know and I can make arrangements for you to take it in the
assessment center. No make-ups or late submissions are allowed except by advance arrangement with
me. Major exams are scheduled in advance to ensure that you will be able to attend exam day.
Therefore, NO Make-up Exams will be given!! If you know you will miss an exam please let me know
and I can make arrangements for you to take it in the assessment center.
Cell phones: Cell phones need to be turned off or on vibrate. If you have an emergency
phone call please go into the hall quietly and take it in the hall. You may use you cell phone in
my class for snap shots of the screens and as a calculator only with my permission.
Tentative Instructional Outline: Chapters 2, 3, 4, 5, 6, 8.2
Week Activities and Assignment Objectives and Details
1-8/29 Syllabus/ Ch. 2.1 Intercepts; Symmetry Holiday No School
2-9/5 Ch. 2.2 Lines
3-9/12 Ch. 2.3 Circles
Labor Day
Ch. 8.2 Matricies
Ch. 3.1 Functions
Ch. 3.2 The Graph of a Function
Week Activities and Assignment Objectives and Details
Ch. 3.3 Properties of Functions No School
4-9/19 Test Chapters 2, 8
4-9/26 Ch. 3.4 Library of Functions; Piecewise-defined
Functions
Ch. 3.5 Graphing Techniques: Transformations
Ch. 4.1 Linear Functions and Their Properties
5-10/3 Ch. 4.3 Quadratic Functions and Their Properties
Ch. 4.4 Building Quadratic Models
Ch. 4.5 Inequalities Involving Quadratic Functions
6-10/10 Test Chapter 3
7-10/17
Ch. 5.1 Polynomial Functions and Models
8-10/24 Ch. 5.2 Real Zeros of a Polynomial Function
9-10/31 Ch. 5.3 Complex Zeros: Fundamental Theorem of
10-10/31 Algebra
Test Chapter 4
Ch. 5.4 Properties of Rational Functions
Ch. 5.5 The Graph of a Rational Function
Ch. 5.6 Polynomial and Rational Inequalities
Ch. 6.1 Composite Functions
Ch. 6.2 Inverse Functions
Ch. 6.3 Exponential Functions
11-11/7 Test Chapter 5
12-11/14 Ch. 6.4 Logarithmic Functions
Ch. 6.5 Properties of Logarithms
Ch. 6.6 Logarithmic and Exponential Equations
13-11/21 Ch6.7 growth and decay
Ch6.8 money problems
14-11/28
15-12/5 Thanksgiving
Test Chapter 6
16-12/12 Final Exam Review
Final Exam
Complete BOPPPS College Algebra Lesson
COURSE: Math 1314 College Algebra
Lesson Title: Graphing Piece Wise or Greatest Integer Functions.
Bridge: A quick review of graphing quadratics. Reminder that all translations in graphing functions are the same.
BLOOM QUESTION (ANALYSIS): How so you know the difference between and left/right shift and the up/down shift in translating a graph?
Pass out instructions for graphing copied from power point.
End with: Today we will be practicing graphing Piecewise or Greatest Integer Functions (show the slide with the learning objectives stated)
5 minutes
Course Student Learning Outcome:
By the end of this lesson, students will be able to:
Apply graphing techniques.
Learning Objectives: By the end of this lesson, students will be able to
1. Demonstrate and apply knowledge of properties of functions, including domain and range, operations, compositions, inverses, and piecewise defined
functions. (Comprehension)
2. Recognize, graph and apply polynomial, rational, radical, exponential, logarithmic, and absolute value functions and solve related equations
(applications)
Pre-Assessment:
The student will review graphing of a quadratic, by actually graphing one and finding it domain, range, x and y intercepts.
5 minutes
Participatory Learning:
Time Instructor Activities Learner Activities Lesson Materials
Slide ppt. on graphing
10 min Define and relate uses of piecewise functions Go over the definition and uses of a piece wise/greatest integer Functions
function Use TI-84 emulator, student
hand out
BLOOM QUESTION (EVALUATION):
Slides
20 min Demonstrate function with a TI-84 calculator Demonstrate graphing of Piecewise/greatest integer functions
simulator on the computer on TI-84 emulator for students
BLOOM QUESTION (EVALUATION):
25 min Assist students/answer questions Have student 1st work on the stamp problem by their selves,
then work on the cell phone problem with a neighbor
BLOOM QUESTION (COMPREHENSION)
15 min Review results BLOOM QUESTION (SYNTHESIS): Blank graphic organizer
Go over the result with students and answer their questions,
then have them fill out a graphic organizer on the steps to
graphing.
Post-assessment: NEW TECHNOLOGY show student Khan Acadeny video on graphing greatest integer functions 5 min
Summary: fill out a graphic organizer on the steps to graphing 5 min.
See Attached PPT
A) Demonstrate and apply knowledge of properties of functions, including domain and range,
operations, compositions, inverses, and piecewise defined functions.
B) Recognize, graph and apply polynomial, rational, radical, exponential, logarithmic, and absolute
value functions and solve related equations.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values
of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points
to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts
and turning points.
(g) Use the graph to find the domain of f. and the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.
1) f(x) = (x + 3)(x - 1)^2
Bloom’s synthesis
2) Zeros: 2, multiplicity 2; -2, multiplicity 2; degree 4
A) f(x) = x4 + 8x2 + 16 B) f(x) = x4 - 4x3 + 8x2 - 8x + 16
C) f(x) = x4 + 4x3 - 8x2 + 8x – 16 D) f(x) = x4 - 8x2 + 16
Bloom’s application
Determine the slope and y-intercept of the function.
3) h(x) = -11x + 5
Bloom’s Comprehension
Solve the problem.
4) Conservationists tagged 140 black-nosed rabbits in a national forest in 2009. In 2011, they tagged
280 black-nosed rabbits in the same range. If the rabbit population follows the exponential law,
how many rabbits will be in the range 5 years from 2009?
A) 369 rabbits B) 792 rabbits C) 1584 rabbits D) 185 rabbits
Bloom’s analysis
Name: __________________________________________ Date: ______________________ Class: _______
Five-Step Cycle
Title: ______________________________________
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Graphing : Graphing polynomials
Teacher Name: Mrs. Shott
Student Name: ________________________________________
CATEGORY 4 3 2 1
Type of Graph Graph fits the data Graph is adequate Graph distorts the Graph seriously
Chosen well and makes it and does not distort data somewhat and distorts the data
easy to interpret. the data, but interpretation of the making interpretation
interpretation of the data is somewhat almost impossible.
data is somewhat difficult.
difficult.
Labeling of X The X axis has a The X axis has a The X axis has a The X axis is not
axis label. labeled.
clear, neat label that clear label that
describes the units describes the units
used for the used for the
independent variable independent
(e.g, days, months, variable.
participants\' names).
Labeling of Y The Y axis has a The Y axis has a The Y axis has a The Y axis is not
axis clear, neat label that clear label that label. labeled.
describes the units describes the units
and the dependent and the dependent
variable (e.g, % of variable (e.g, % of
dogfood eaten; dogfood eaten;
degree of degree of
satisfaction). satisfaction).
Accuracy of Plot All points are plotted All points are plotted All points are plotted Points are not plotted
correctly and are correctly. correctly OR extra
correctly and are easy to see. points were included.
easy to see. A ruler
is used to neatly
connect the points or
make the bars, if not
using a
computerized
graphing program.
Data Table Data in the table is Data in the table is Data in the table is Data in the table is
well organized,
accurate, and easy organized, accurate, accurate and easy to not accurate and/or
to read.
and easy to read. read. cannot be read.
Date Created: Nov 09, 2015 08:50 am (CST)
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ACP Showca
Name: Alexand
Discplin
Date: Novem
ase Portfolio
dra Shott
e: Math
mber 23,2015
Table of Contents
• Student Preparation Strategy
• BOPPPS lesson-be sure to highlight
• CAT
• Questions
• Technology
• Reflection
t the following:
Describe student prepa
• A quick review of graphing quadra
• BLOOM QUESTION (ANALYSIS): Ho
between and left/right shift and th
graph?
• Pass out instructions for graphing c
them to get out their calculators
aration strategy
atics
ow so you know the difference
he up/down shift in translating a
copied from power point ans ask
BOPPPS – BRIDGE
• Apply graphing techniques to piece
functions.
e wise and greatest integer
BOPPPS – OBJECTIVES
• 1. Demonstrate and apply knowled
including domain and range, opera
piecewise defined functions. (Com
• 2. Recognize, graph and apply poly
exponential, logarithmic, and abso
related equations (applications)
dge of properties of functions,
ations, compositions, inverses, and
mprehension)
ynomial, rational, radical,
olute value functions and solve
BOPPPS- PRE-ASSESSME
• The student will review graphing o
f(x)=x^2+2x+1
• finding it domain, range, x and y in
ENT
of a quadratic, by actually graphing
ntercepts.
BOPPPS- PARTICIPATOR
• Students need to be able to graph
• Did they get the answer?
• CAT using a graphic organizer to or
the calculator
• NEW TECHNOLOGY show student
greatest integer functions
RY LESSON
all functions
rganize their notes on graphing on
Khan Academy video on graphing
BOPPPS- POST-ASSESSM
• How will you know if objectives ha
• The students will be able to graph
integer function
MENT
ave been met?
h a real world piece wise or greatest
BOPPPS- SUMMARY
• Students will be able to apply grap
functions to get real world answers
phing techniques to all types of
rs
Personal Reflection on M
• I enjoyed the experience, but it wa
believe.
My ACP Experience
as more work than I was lead to
Piecewise Functions
2007 MS Mathematics Framework
• Algebra: e. Write, graph, and analyze
linear and nonlinear functions (such as
quadratic, greatest integer)
Why Piecewise Functions?
• What factors are important when
determining the price of a phone call?
• How do you distinguish the price of a five
minute call versus a five and one-half
minute call?
• How do phone companies use functions to
determine your local phone bill?
“Step functions” are a type of piecewise functions.
y x
The ceiling function (or least integer function)
will round any number up to the nearest integer.
4.7 5 4.7 4
“Step functions” are sometimes used to describe real-life
situations.
y x
The greatest integer function (or floor function) will
round any number down to the nearest integer.
4.7 4 4.7 5
Greatest Integer/Floor Function:
y greatest integer x
y x, y x, y §x¨
The TI-84 command for the floor function is int (x).
Graphing the greatest integer function:
The calculator “connects the The open and closed circles do
dots” like a staircase instead not show, but you can just see
of just the steps. the steps.
Greatest Integer Function
• [3.7] = 3
• [15.25] = 15
• [4] = 4
• [4.999] = 4
• [0.14] = 0
• [-1.5] = -2
Graphs of the floor & ceiling functions
y x
y x
How Much Is That Phone Call?
Phone companies will determine the price of a call by rounding the length of the
call to a certain time period (either one minute or six seconds). For instance, a
local weekday call on Long D’s Basic Residential plan will cost $0.25 each minute.
Suppose that Long D’s also charges a $0.15 connection fee for each call.
f(x) is the cost of placing a phone call that lasts x minutes
Examples minutes cost
0<x<1 40¢
f (1 minute, 44 seconds) 65¢
f (3 minutes, 2 seconds) 115¢ 1<x<2 65¢
f (4 minutes, 58 seconds) 140¢ 2<x<3 90¢
f (7 minute, 30 seconds) 215¢ 3<x<4 115¢
4<x<5 140¢
5<x<6 165¢
Long D’s Basic Residential Plan
Postage Stamp Function
f(x) is the cost of mailing a letter that weighs x ounces
Examples Weight cost
0<x<1 32¢
f (.78) 32¢ 1<x<2 55¢
f (2.11) 78¢ 2<x<3 78¢
f (5.01) 147¢ 3<x<4 101¢
4<x<5 124¢
5<x<6 147¢
Postage Stamp Function
How Much Has It Rained?
Alexandra Shott
Lonestar’s University Park
November 27, 2015
I enjoyed the Adjunct Certification Program course material and I also enjoyed meeting my
fellow adjuncts. I was happy that the adjuncts came from a wide variety of educational fields. I
enjoyed the discussions we had both before class and during class. The variety of solutions to
similar problems is always helpful.
I found that the varied backgrounds of our group increased the value of the program. It
allowed me to see my students in different curriculum. I found similar student apathy no
matter what the course, similarities in student involvement across the curriculum, and other
behaviors exhibited by students no matter what the course. For example all of us who teach in
person classes had problems with tardies and attendance and each of us had a different
solution that worked for us. I am planning on starting each of my winter mini-mester classes
with a short quiz over the previous day’s lesson. This should cure the tardy problem and the
apathy about homework in my Trig class.
During the course we looked at a variety of ways to introduce technology into our classes, CAT.
Not all of the CAT’s were appropriate for a STEM subject like mathematics. Writing journals,
short essays and other forms of writing what the student has learned are not always adaptable
to the math classroom. However, concept maps, surveying background knowledge and group
assignments can be easily introduced into the math classroom. Yes, all students have to write,
but math students have to learn the process to solve the problem. Concepts maps are a good
way for them to write down the learning process to use for homework.
I have my students use a concept map when I am instructing them on how to graph on a
calculator. I found a circular concept map that allows the student to list the steps as I go over
them in class. Many of my younger students do not need anything more than a quick refresher
on the graphing calculator, but many of my more mature students did not use calculators in
high school and they need step by step instruction. When I do start graphing and matrices I
always allow time in class for my students to practice both individually and with a partner. This
allows the mature student to get help not only form me but from their fellow students. Not
only do we do a practice problem as a group, but then I give them an individual problem to
work in class so they gain confidence.
As I stated at the beginning of the essay I enjoyed the class and meeting my fellow adjuncts
from different fields. Over the course we discussed Boppps, Rubics, CAT, millennials, difficult
students, snap shot syllabi, and motivation of students. It was informative to get the ideas and
opinions of my fellow adjuncts on these topics. I got many ideas especially for the snap shot
syllabus, rubics, and motivating students. The snap shot syllabus should stop some of my
students from losing it or never looking at it. I had always felt that rubics were so hard to come
up with in math, but now that I know how many math rubics are on the internet and how easy
they are to use I plan to incorporate some in to my class room. Using rubics when we are doing
group work on the graphing calculator will increase the student involvement and therefore
make it a more effective learning tool.
While I enjoyed the discussions in the ACP program I would like to see some more course
specific professional development opportunities. As a math professor professional
development that targets CAT, Technology, lesson plans and student motivation in the math
classroom would me most helpful. This is especially turn for the adjunct teaching
developmental and lower level math courses like College Algebra. This is the area where there
is the most student apathy and the largest groups of brand new adjuncts. All new adjuncts
(those who have not taught before) need the ACP course. I have taught for Lonestar for the last
10 years and the ACP was a nice refresher on lesson plans and motivation, but I really
benefitted the most form the CAT and technology part of our lessons.