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 amussari@daemen.edu 716.380.6313c/o Daemen College4380 Main Street Amherst, NY 14226

Fin