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: ______________________________________

www.studenthandouts.com

© Student Handouts, Inc.

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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

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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.