graphing logarithmic functions using transformations
DESCRIPTION
Graphing Logarithmic Functions Using Transformations. Presenter: Anthony Mussari School Name:S t. Joseph's Collegiate Institute District Name: Buffalo City Schools Guiding Teacher: Mr. Thomas Quagliana Time Frame: Two Days (Lecture and Assessment). - PowerPoint PPT PresentationTRANSCRIPT
Graphing Logarithmic Functions Using Transformations
Presenter: Anthony MussariSchool Name: St. Joseph's Collegiate InstituteDistrict Name: Buffalo City SchoolsGuiding Teacher: Mr. Thomas QuaglianaTime Frame:Two Days (Lecture and Assessment)
Grade level: Tenth and Eleventh (Boys Only)Course Name: Algebra II & Trigonometry HonorsStudent Total: Sixty-FiveGeneral Ability: Accelerated / Advanced Placement
The Standard…
Standard: F-BF.3. Identify the effect on the graph of replacing f(x) by f(x) + k, k•f(x), f(k•x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
Mathematics NYS Common Core
The Standard…
Standard: F-BF.3. (Continued)Experiment and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Mathematics NYS Common Core
The Learner Will Be Able To… Identify the effect on the graph of f(x) for specific values of k by replacing f(x) with
f(x) + kk• f(x)f(k•x)f(x + k)
In addition find the value/s of k given the graph of f(x).
Essential Question???
What will happen to the graphs of yi = f(x) when composed with a constant ki ?
Handout WRKSHT
Guiding Questions???
What are the characteristics of the parent functionyi = f(x)?
How does one read a graph?
When is it appropriate to use transformations?
Graphing with transformations can generate images on a host of parent functions.
Different images provide unique inferences.
Enduring Understanding!!!
Illustrate to the learner, by way of guided notes and interactive lecture, of how to Identify the effect on the graphs of f(x) by replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k.
The Procedure!!!
Note Packet
A take-home assignment will require the student to find and state the equation of a logarithmic function by identifying the effect on the graph by replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k.
The Procedure!!!
Take-Home WRKSHT
The Logarithmic Rubric and Quiz # 3.8 will be used to formally asses and quantify each of the students’ understanding.
The Procedure!!!
Rubric and Quiz
Student work, Developing.
Student work, Proficient.
Student work, Distinguished.
Student work, The Data.ClassificationsPre-Instruction
Number of students
Percentage of students
Distinguished 0 00.00 %Proficient 3 04.60%
Developing 62 95.40 %
ClassificationsPost-Instruction
Number of students
Percentage of students
Distinguished 43 66.15 %Proficient 13 20.00 %
Developing 9 13.85 %
Developing
Proficient
Distinguished
0 10 20 30 40 50 60 70
Post
Number of Students
Cla
ssifi
catio
ns
Pre
Modification Table.Modification
TypeSpecific
ModificationRationale for Modification
Benefits of Modification
Instructional Guided Notes
Students produce
complete and accurate lecture
notes.
GN increase students’ active
engagement with course
content.
Students who take accurate notes and study them laterconsistently receive higher test scores than students who only listen to the lecture and read the text*.
* Heward, William L., Improving The Effectiveness Of Your Lectures. Retrieved from http://ada.osu.edu/resources/fastfacts/Guided-Notes-Fact-Sheet.pdf (08 May 2012).
Reflection Table.
Peer Review Suggestion
Topic of Suggestion
Rationale for Suggestion
Evidence found in the Learning
Experience
How do you plan on eventually
integrating the graphing
calculators into the students’
learning?
Technology Integration
The NYS Common Core addresses the use of a calculator or technology to demonstrate the
effects of a transformation.
Anticipatory Set:
Thank You!!!To my peer reviewers,
Christopher, Shelly, Jessica, Mary, Karissa, Meghan, Sarah, and Dr. Arnold,
You all provided may useful comments, both warm and cold, for which I would like to formally thank you for.
This Presentation Has Been Brought To You By….
Anthony J. Mussari
To contact via:
Post: E-Mail: Phone:
Anthony J. Mussari [email protected] 716.380.6313c/o Daemen College4380 Main Street Amherst, NY 14226
Fin