NEW YORK STATE ACADEMY FOR TEACHING AND LEARNING
Learning Experience
Informational Form-Final: 01 May 2012
Name:
Location:
E-Mail:
Anthony J. Mussari
Buffalo, New York
amussari@daemen.edu
Current Teaching Position:
Grade Level:
Name of School:
Cooperating Teacher:
School District:
School Address:
School Phone:
Title of Learning Experience:
Grade Level:
Common Core Learning Standard:
Domain/Level:
Student Teacher
Tenth and Eleventh (All Boys)
St. Joseph's Collegiate Institute
Thomas Quagiliana
Independent College-Prep
845 Kenmore Ave
Buffalo, NY 14223
716.874.4024
Graphing Logarithmic Functions with Transformations.
Ten and Eleven (Mixed Grade Level)
Mathematics
Functions. Building Functions. (F.BF.3)
Standard F-BF.3.Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for
specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases 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.
Peer Review Focus Question:
Besides graphing how can students demonstrate clear conceptual
understandings of the effects on graphs due to transformations?
Learning Context
Purpose and Rational
The ability to translate a given equation into an image expedites the process of finding a solution to a
given problem. Moreover, when learners see a graphic image and receive some key facts about the
graph, with an understanding of transformations, one is able to derive the equation for the image. This
process of translation and transformation is a necessity in the informational age. Overall, graphs allow a
learner to solve mathematical equations, physical problems, as well as make logical inferences with an
image. Lastly, graphing is an essential part on the New York State Algebra II and Trigonometry Regents
Exam, to prevent disservice to the learner as well as to insure proper preparation for the exam graphing
with transformations ought to be addressed.
Enduring Understanding:
 Graphing with transformations can generate images on a host of parent functions.
 Graphs allow data to be represented visually and opportunities to find and compare
trends, to make logical inferences.
Essential Question:
 What will happen to the graphs of 𝑦𝑖 = 𝑓(𝑥) when a constant 𝑘𝑖 is introduced?
Guiding Questions:




What are the characteristics the parent function 𝑦𝑖 = 𝑓(𝑥)?
How does one read a graph?
Where does the constant 𝑘𝑖 translate the image?
When is it appropriate to use transformations?
Anthony J. Mussari
01 May 2012
pg. 2
Congruency Table
Course Name and Grade Level
Domain/Level
Algebra II Trig. Grades 10 and 11
F.BF.3
NYS Common Core Learning
Standards
Mathematics (Page 59).
Standard: F-BF.3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and
negative); find the value of k given the graphs. Experiment with cases 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.
Instructional Task
Using lecture, modeling, and examples,
found within the Guided Note Packet,
state the definition of logarithm, and the
three unique parts of a logarithmic
equation. Moreover, detail how to
represent a function f(x) in both
logarithmic and exponential forms
Using lecture, modeling, and examples,
found within the guided notes illustrate
the effects, on the graph of
𝒇(𝒙 + 𝒌𝟏 ) + 𝒌𝟐 = 𝐥𝐨𝐠 𝒃 (𝒙 + 𝒌𝟏 ) + 𝒌𝟐
For the specific values 𝒌𝟏 = 𝟎,
and 𝒌𝟐 = 𝟎.
(Introduce this function as the
Parent Function)
Using the In Class Worksheet illustrate
the effects, on the graph of f(x) by
replacing f(x) with f(x) + k, k∙f(x),
f(k∙x), and f(x + k) for specific values
of k such that 𝒌𝒊 ≠ 𝟎.
Assign the Take-Home Worksheet for
homework.
Assign Logarithmic Quiz # 3.8
Anthony J. Mussari
Learning
Objective
The learner will be able
to define the three unique
parts of a logarithmic
equation
In Addition, The learner
will be able to solve
problems by using
function notation and
changed forms.
The learner will be able
to list the characteristics
of the Parent Function
when f(x) is replaced
with the composition of
f(x) + k and f(x + k) for
specific values 𝒌𝟏 = 𝟎,
and 𝒌𝟐 = 𝟎.
With aid the learner will
be able to identify the
effects on graphs of f(x)
by replacing f(x) with
f(x) + k, k∙f(x), f(k∙x),
and f(x + k) for specific
values of k.
Independently, at home,
the learner will be able to
identify the effects on
graphs of f(x) by
replacing f(x) with f(x)
+ k, k∙f(x), f(k∙x), and f(x
+ k) for specific values
of k.
Independently, in class,
the learner will be asked
to identify the effects on
graphs of f(x) by
replacing f(x) with f(x)
+ k, k∙f(x), f(k∙x), and f(x
+ k) for specific values
of k, without Aid.
01 May 2012
Student Work
Specific guided
examples, found within
the guided notes, of
how to solve problems
by using function
notation and how to
evaluate logarithmic
equations in changed
form.
A graph of
𝒇(𝒙) = 𝐥𝐨𝐠 𝒃 𝒙 is
sketched in the guided
note packet with the
given specific values of
ki
A list is then made
asserting the six main
characteristics of the
effects of specific
values of ki using
𝒇(𝒙) = 𝐥𝐨𝐠 𝒃 𝒙.
Assessment Tool
Since the learners are expected
to copy, store, and maintain the
guided notes, the rational
assessment to implement is to
collect each of the learners note
books at the end of each quarter
and give a grade for
completion. The Learner’s
notebooks must list and
identify the effects on graph
of f(x)=lo by replacing f(x)
with f(x) + k, k∙f(x), f(k∙x), and
f(x + k) for specific values of
k. (both positive and negative);
and how to find the value of k
given the graphs. In addition, how
to experiment with cases and
illustrate an explanation of the
effects on the graph using
technology.
Assist, if need be, the
learners in the
completion of the
In Class Worksheet
Complete the
Take-Home Worksheet
The Take-Home Worksheet is
collected the following class
and given a grade of either
Complete/Satisfactory
Complete/Unsatisfactory
Incomplete/Satisfactory
Incomplete/Unsatisfactory
Complete the
Logarithmic Quiz # 3.8
The Logarithmic Rubric will
be used to assess the students
ability to identify the effects
on graphs of f(x) by replacing
f(x) with f(x) + k, k∙f(x), f(k∙x),
and f(x + k) for specific values
of k.
pg. 3
Class Background
This learning experience is designed to address two class periods of Algebra II and Trigonometry honors
students, of mixed grade levels (tenth and eleventh) at Saint Joseph's Collegiate Institute, in Buffalo
New York. The three sections of students, totaling sixty-five learners, share the same set of classroom
rules. There are no students with special needs and therefore no need for modifications environment, or
instruction type. Moreover, this Learning Experience is developed with modifications in place which,
are specifically identified, rationalized, and supported in the Modification Table (pg.17), to insure every
learner is successful.
Overview of Prior, Current, and Post Knowledge
Prior to Implementation:
 The effects on a familiar graph of 𝑓(𝑥) by replacing 𝑓(𝑥) with:𝑓(𝑥) + 𝑘,𝑘𝑓(𝑥), 𝑓(𝑘𝑥),
and 𝑓(𝑥 + 𝑘) for specific values of 𝑘.
 How to identify the parent function given 𝑦𝑖 = 𝑓(𝑥).
 How to graph a function given 𝑦𝑖 = 𝑓(𝑥) using a table of values.
During Implementation:
 The characteristics of the logarithmic function 𝑦𝑖 = 𝑓(𝑥) = log 𝑏 𝑥.
 How to construct a table of values.
 How to graph a function.
After Implementation:
 The effects on 𝑦𝑖 = 𝑓(𝑥) = log 𝑏 𝑥 when replacing 𝑓(𝑥) with:𝑓(𝑥) + 𝑘,𝑘𝑓(𝑥), 𝑓(𝑘𝑥),
and 𝑓(𝑥 + 𝑘) for specific values of 𝑘.
 How to construct a transformations table of values.
 How to graph the function 𝑦𝑖 = 𝑓(𝑥) = log 𝑏 𝑥 after all transformations have been
completed.
Anthony J. Mussari
01 May 2012
pg. 4
Vocabulary
Function
A rule or relationship that assigns to each number 𝑥 in the function's domain a
unique number 𝑓(𝑥).
Graph
A visual model of a mathematical relationship.
Image
The resulting point or set of points under a given transformation; in any function
𝑓 , the image of 𝑥 is the functional value 𝑓(𝑥)corresponding to .
Domain
The input value of a function, or independent variable.
Range
The output value of a function, or dependent variable.
Notation
Symbol
Definition
𝒇(𝒙)
The value of the function when evaluated at 𝑥.
The mathematical notation for a constant it can
be either positive or negative.* ).
Less-than
Greater-than
Implies, Then
𝒌
<
>
⟶
*N.B. c is not used as it stands for either
Circumference, C, or in the Theory of General
Relativity, c, is used for the speed of light in
Einstein’s world famous equation, E=mc2.
Anthony J. Mussari
01 May 2012
pg. 5
Assessment Plan
Diagnostic:
As this is the first time the logarithmic functions are introduced the diagnostic assessment is informal
where general questions about the logarithmic function* are asked by the instructor and orally responded
to by the learners. An oral diagnostic takes place to mitigate the influence over poor grades, and
prevents setting the learners up for failure.
* The questions for the oral diagnostic, (answers provided in the procedure section).




Has anybody heard of a Logarithmic Function before?
Does anybody remember what the Exponential Function looks like?
Which line do you reflect a function over to find its inverse image?
If an Exponential Function is the inverse to the Logarithmic Function what should the
image of a Logarithmic Function look like?
Formative:
The students will actively participate during the lecture by responding to individual issues** when
asked. Moreover, the learner completes the guided note packet during the lecture. Please note the
learner's completed notebooks are collected at the end of the quarter and receive a grade. The questions
to be utilized during the guided not lecture are:
**The questions for the formative diagnostic, (answers provided in the procedure section).













What is the difference between a logarithm and an exponent?
What is the difference between Exponential and Logarithmic form?
How does one find the inverse of a function algebraically?
What base do common logarithms have?
What base do natural logarithms have?
Why do we change from Logarithmic form into Exponential form when graphing
Logarithmic Functions?
What is the difference between a function of “x” and a function of “y”?
If the base of a Logarithm is greater than one, does the function increase or decrease?
If the base of a Logarithm is greater than zero but is also less than one, does the function
increase or decrease?
What point is a characteristic or featured in a Logarithmic Function?
What is the domain of a Logarithmic Function?
What is the Range of a Logarithmic Function?
Does a Logarithmic Function have an Asymptote?
Anthony J. Mussari
01 May 2012
pg. 6
Summative:
The students are given a homework assignment, which specifically addresses the topic of
graphing logarithmic functions with transformations. The assignment is collected at the
beginning of the next class after the opportunity for questions and corrections. The assignment is
given either a complete (reasonable effort, both questions answered) or incomplete (less-than
reasonable effort, only one or no questions answered) grade. After the home work is turned in
issue the formal assessment (Quiz # 3.8 ) allow for tem minutes to pass(fifteen minutes max.),
collect and grad against The Logarithmic Rubric.
Rubric Alignment
Standard: F-BF.3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific
values of k (both positive and negative); find the value of k given the graphs. Experiment with cases 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.
Distinction
Level
Description
Alignment to Indicator
Distinguished
Or
Point Level (4)
A correct graph is
drawn and all
calculations are
correct
The leaner finds (Solves) and identifies (Sketches) all of
the effects on the graph by replacing f(x) with 𝒌𝟏 f(x+𝒌𝟐 )
+ 𝒌𝟑 ,for specific values of 𝒌𝒊 (both positive and negative;,
by producing the correct equation for the image of a given
function under the effects of 𝒌𝒊 .
Proficient
Or
Point Level (3)
A graphing error is
made or one
mathematical error
The leaner finds (Solves), all the effects on the values of
the graph by replacing f(x) with 𝒌𝟏 f(x+𝒌𝟐 ) + 𝒌𝟑 , for
specific values of 𝒌𝒊 (both positive and negative); but is
unable to identify (Sketch) any of the effects of 𝒌𝒊 on the
image of 𝒇(𝒙) = 𝒌𝟏 f(x+𝒌𝟐 ) + 𝒌𝟑 .
Developing +
Or
Point Level (2)
More than one
mathematical error is
made
The leaner finds (Solves) some of the effects on the values
of the graph by replacing f(x) with 𝒌𝟏 f(x+𝒌𝟐 ) + 𝒌𝟑
for specific values of 𝒌𝒊 (both positive and negative); and
is unable identify (Sketch) any of the effects of 𝒌𝒊 on the
image of 𝒇(𝒙) = 𝒌𝟏 f(x+𝒌𝟐 ) + 𝒌𝟑 .
Developing
Or
Point Level (1)
Completely incorrect,
irrelevant, incoherent,
or a correct response
with obviously
incorrect procedure
The leaner is unable to find (Solve) any of the effects on
the values of the graph by replacing f(x) with
𝒌𝟏 f(x+𝒌𝟐 ) + 𝒌𝟑 , for specific values of 𝒌𝒊 (both positive
and negative); and is unable identify (Sketch) any of the
effects of 𝒌𝒊 on the image of 𝒇(𝒙) = 𝒌𝟏 f(x+𝒌𝟐 ) + 𝒌𝟑 .
Anthony J. Mussari
01 May 2012
pg. 7
The Logarithmic Rubric:
Name:________________________________________
Value
4
3
2
1
Specific Criteria
A correct graph is drawn and all calculations are correct
A graphing error is made or one mathematical error
More than one mathematical error is made
Completely incorrect, irrelevant, incoherent, or a correct response with obviously
incorrect procedure
The grade is calculated by dividing the value earned by four. The Quotient is then multiplied by 100 to
establish the learners received percentage. No rounding is necessary.
Total Earned:_______
Grade:_____________
Comments:
Homework counts for forty percent of the learner's overall quarter grade. Therefore, it is to the learner's
benefit to establish a proficient or distinguished grade for all the homework.
Anthony J. Mussari
01 May 2012
pg. 8
Student Work
Classifications and Distribution
Classifications:
 Distinguished Classification requires the learner to earn a rubric score of four.
 Proficient Classification requires the learner to earn a rubric score of three.
 Developing Classification requires the learner to earn a rubric score of one or two.
Distributions
Pre Assessment:
Classifications
Number of students
Percentage of students
Distinguished
Proficient
Developing
0
3
62
00.00 %
04.60%
95.40 %
Classifications
Number of students
Percentage of students
Distinguished
Proficient
Developing
43
13
9
66.15 %
20.00 %
13.85 %
Post Assessment:
Classifications
Graphic Representation of the Pre and Post assessment Data:
Distinguished
Proficient
Post
Pre
Developing
0
20
40
60
80
Number of Students
Anthony J. Mussari
01 May 2012
pg. 9
Conclusion
Pre –Assessment Data
(𝑥𝑟 )
Post-Assessment
Data (𝑥𝑠 )
Descriptive Statistics
𝑁𝑢𝑙𝑙 (𝐻0 ) 𝑎𝑛𝑑 Alternative(𝐻𝑎 )
Hypotheses:
𝑥𝑟 ≈ 1.6308
̅̅̅
𝑥̅𝑠 ≈ 3.4923
{
𝑠𝑟 ≈ 0.5747
𝑛𝑟 = 65
𝐻0 : ̅̅̅
𝑥𝑟 = 𝑥̅𝑠
𝐻𝑎 : 𝑥𝑟 ≠ 𝑥𝑠
(𝑖𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 𝑖𝑠 𝑖𝑛𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒)
(𝑖𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 𝑖𝑠 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒)
𝑠𝑠 ≈ 0.8125
Using A Two Tail Testy, With a Level of
Significance 𝛼=0.01
or with 99% certainty we find our critical
region bound by
→ 𝑍𝛼 = ±2.575
𝑛𝑠 = 65
((𝑥
̅̅̅𝑟 − 𝑥̅𝑠 ) − (𝜇𝑟 − 𝜇𝑠 ))
𝑍𝑥̅ =
𝑠
𝑠
√ 1𝑟 + 𝑛𝑠
𝑠
∗
*In this Calculation we must assume that (𝜇𝑟 − 𝜇𝑠 ) = 0 because of the null hypotheses,𝑥
̅̅̅𝑟 = 𝑥̅𝑠 .
𝑍𝑥̅ =
((1.6308 − 3.4923) − (0))
√0.5747 + 0.8125
1
65
≈ −3.1904
Results:
Since 𝑍𝑥̅ < 𝑍𝛼 there is significant evidence to reject
the null hypotheses and conclude, instruction is
effective.
Using the graphic representation compiled from the raw data one finds that instruction appears to
be effective. In addition when viewing the collected data one sees about 86% of the learners
demonstrated their understanding at either a distinguished or proficient level, this also alludes to
the same conclusion, as the graphic data, or that instruction appears to be effective.
However, the learners still at the developing level require further direct instruction to mitigate
the magnitude of conceptual misunderstanding. Help is urged and available for the learner to
seek either before or after school based on whichever is more convenient for the learner and / or
their guardian to arrange.
Anthony J. Mussari
01 May 2012
pg. 10
Procedure
Curricular Placement
This year we have covered the transformations on lines, parabolas, exponential functions, and now we
are moving to logarithmic functions
Logarithmic and Exponential Functions Unit Time Line
Section
1
2
3
4
Topic
Exponents,
rational and
negative
Radical
Equations
and
Equations
with
Exponents
Exponential
Functions
Class Time
Required
2.5 Days
2.0 Days
3.0 Days
5
6
Logarithmic
Rules
Applications
of
Exponential
Functions
1.0 Day
2.5 Days
Logarithmic
Functions
Section for
Learning
Experience
2.0 Days
Diagnostic Assessment:
The questions and answers for the oral diagnostic,
 Has anybody heard of a Logarithmic Function before?
 Does anybody remember what the Exponential Function looks like?
 See 𝑦 = 𝑏 𝑥 on graph below.
 Which line do you reflect a function over to find its inverse image?
 The line 𝑦 = 𝑥.
 If an Exponential Function is
the inverse to the Logarithmic
Function what should the image
of a Logarithmic Function look
like?
 See 𝑦 = log 𝑏 𝑥 on graph
at right.
20
15
𝑦 = 𝑏𝑥
𝑦=𝑥
10
5
𝑦 = log 𝑏 𝑥
0
-10
-5
0
5
10
15
-5
-10
Anthony J. Mussari
01 May 2012
pg. 11
20
Anticipatory Set:
Using a graphing calculator graph and identify the change on 𝑦 = 𝑥 2 under the given transformation. for
𝑦 = 𝑥2
Graphing Key
𝑦1 = 𝑥 2 + 2 (shift up two units)
𝑦2 = 𝑥 2 − 2
𝑦3 = (𝑥 + 2)2 (shift to the left two units)
1
(shift down two units)
𝑦4 = (𝑥 − 2)2
(shift to the right two units)
5
𝑦5 = 2 𝑥 2 (closer to x-axis)
Anthony J. Mussari
𝑦 = 𝑦𝑖
𝑦6 = 2 𝑥 2 (closer to y-axis)
01 May 2012
pg. 12
Input:
The input for the lesson will be a lecture on logarithmic functions and the effects of transformations on
logarithmic graphs.
 What is the difference between a logarithm and an exponent?
 A logarithm is an exponent
 What is the difference between Exponential and Logarithmic form?
 ⏟
𝑥 = 𝑏𝑦
𝑎𝑛𝑑 ⏟
𝑦 = log 𝑏 𝑥
Exponential
Logarithmic
 How does one find the inverse of a function algebraically?
 Switch the x and y in a given equation and then solve it for y.
 What base do common logarithms have?
 Common logs have a base of 10.
 What base do natural logarithms have?
 Natural logs have a base of e.
 Why do we change from Logarithmic form into Exponential form when graphing
Logarithmic Functions?
 It is more efficient to represent x as a function of y, and then let the values for y
vary.
 What is the difference between a function of “x” and a function of “y”?
 With a function of “x” one lets the x values vary. With a function of “y” one lets
the y values vary.
 If the base of a Logarithm is greater than one, does the function increase or decrease?
 Logarithms with a base greater than one increase.
 If the base of a Logarithm is greater than zero but is also less than one, does the function
increase or decrease?
 Logarithms with a base greater than zero but less than one decrease.
 What point is a characteristic or featured in a Logarithmic Function?
 The point (1,0)
 What is the domain of a Logarithmic Function?
 { x | x ∈ (0,∞) }
 What is the Range of a Logarithmic Function?
 { y = f(x) |y ∈ (-∞, ∞) } or all real numbers, or ℝ.
 Does a Logarithmic Function have an Asymptote?
 Yes, the parent function will never cross the line x = 0, or the y-axis.
Anthony J. Mussari
01 May 2012
pg. 13
Model:
Since the input for the lesson is a lecture on logarithmic functions and the effects of transformations on
logarithmic graphs the Guided note packet issued at the beginning of the unit will be utilized for the
modeling the conceptual aspects of the lesson, through interrogatives and examples.
 Example 1, to write 2 = log 5 25 in exponential form.
 Remember that 𝑦 = log 𝑏 𝑥 → 𝑏 𝑦 = 𝑥. So given example 1
2 = log 5 25
{52 = 25}
→
1
 Example 2, to write 92 = 3 in logarithmic form.
 Remember that 𝑏 𝑦 = 𝑥 → 𝑦 = log 𝑏 𝑥. So given example 2
1
92 = 3
 Example 3, to Solve log12 𝑥 = 2 for 𝑥.
 Remember that 𝑦 = log 𝑏 𝑥
1
{ = log 9 3}
2
→
𝑏 𝑦 = 𝑥. So we can rewrite 3 as
→
log12 𝑥 = 2
→
122 = 𝑥
→ { 𝑥 = 144}
1
 Example 4, to Solve 2 = log 𝑥 16 for 𝑥.
 Remember that 𝑦 = log 𝑏 𝑥
𝑏 𝑦 = 𝑥. So we can rewrite 4 as
→
1
= log 𝑥 16
2
𝑥 2 = 16
1 2
(𝑥 2 ) = (16)2
→
 Example 5, to evaluate log √3 9.
 Remember that 𝑦 = log 𝑏 𝑥
𝑦
→
{𝑥 = 256}
𝑏 𝑦 = 𝑥. First we rewrite 5 as
→
𝑦 = log √3 9
→
1
→
→
3 2 = 32
𝑦
√3 = 9
𝑦
→
=2
2
→
{ 𝑦 = 4}
Lastly Graph the three examples at the end of the logarithmic function section in the guided note packet.
Be sure to allude to the fact that one must first change the given function from logarithmic form to
exponential form, then pick an arbitrary set of values for y and not x then solve the new function of “y”
for x. In general the set A = {-3, -2, -1, 0, 1, 2, 3} is sufficient for the values of y. After the values for y
have been determined, substitute them in to the function of y and then solve each equation for the
corresponding value of x. After all the values for y have been substituted in make a table of values and
plot the points. (See page 2 of appendix A6.).
Anthony J. Mussari
01 May 2012
pg. 14
Guided Practice:
A note sheet, with two examples, is issued to the learners at the end of the lecture. This worksheet
provides an opportunity for the learners further their own conceptual understanding of how to graph
logarithmic functions using transformations by following along and completing the given task at hand
with support and guidance. (Please note a detailed key for the note sheet is provided in appendix A9.).
Independent Practice:
A worksheet with two examples is assigned for homework. Remember the assignment is given either a
complete (reasonable effort, both questions answered) or incomplete (less-than reasonable effort, only
one or no questions answered) grade. (See appendix A10. for a completed worksheet).
Closure:
An informal discussion about the geometric translations due to algebraic transformations. Also a
handout will be given which states the effects of transformations.
Formative Assessment:
The learner is given a ten minute quiz, Quiz #3.8 approximately on the day the homework is corrected
and collected.
Anthony J. Mussari
01 May 2012
pg. 15
Resources
Materials:





Guided note packet
Guided practice work sheet
Home worksheet
Transformations closure sheet
Quiz 3.8
Supplies:




Pen or pencil
Straight edge
Guided not packet in notebook
Worksheets
Technology:
 Calculators
Anthony J. Mussari
01 May 2012
pg. 16
Time Required:
Planning:
For this learning experience planning takes three to five hours and includes all the time needed
for copying and organizing the guided note packets, the in class and take home assignments, the
in class and take home assignments’ keys, as well as the key for the quiz. The total time for the
copying takes about two hours. As for the remaining one to three hours, ample time ought to be
given by the instructor to internalize the diagnostic and formative assessments, and to establish
self-proficiency with the material covered in the lesson.
Implementation:
This learning experience requires the learners to participate in a lecture, complete a guided
practice assignment, receive and complete an independent practice worksheet, and finally take a
quiz the following day. To accomplish the task of implementation, two class periods (or about
ninety minutes) is allotted to complete the learning experience.
Assessment:
As stated earlier the assessment takes about ten minutes of class time for the students to complete
(allow for fifteen minutes as an absolute maximum if need be). The grading time for the
Homework and Quiz ought to be about three to five minutes per student.
Anthony J. Mussari
01 May 2012
pg. 17
Reflection
This learning experience is executed during the exponential and logarithmic functions unit and addresses
the effects of transformations for logarithmic functions. Moreover, to accomplish proficiency in the
experience, one must first learn how to change form, for logarithmic to exponential form, and the
algebras for both logarithmic and exponential functions. I feel this task is accomplished if the learner
participates in the lecture and follows along in their notes. However, since not all of the students are
classified as distinguished, further refinement of this lesson ought to be considered. To bolster the
struggling students’ conceptual understanding extracurricular help is made available. In addition, the
developing students are urged to seek help during their lunch period by me, the department chair, and
the assistant principal.
This learning experience was peer reviewed at Daemen College, on 20 Mar 2012. The reviewers,
Christopher, Shelly, Jessica, Mary, Karissa, Meghan, Sarah, and Dr. Arnold, provided may useful
comments, both warm and cool, that I would like to formally acknowledge. The comments provided
enough support to insure this learning experience is of a fine grain and high quality. Thank you all so
much for your insight, time, and thought.
Anthony J. Mussari
01 May 2012
pg. 18
Appendices
A1.
Guided Note Packet (blank)
A2.
Take-Home Worksheet (blank)
A3.
Logarithmic Rubric
A4.
Classroom Rules
A5.
Floor Plan
A6.
Guided Note Packet (complete)
A7.
In-Class Worksheet (blank)
A8.
Closure Handout
A9.
In-Class Worksheet (complete)
A10.
Take-Home Worksheet (complete)
A11.
Peer-Review Comments
Anthony J. Mussari
01 May 2012
pg. 19