Technology Based Module CIP Using Mobile Apps

FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 1
Cognitive Information Processing
Function Families
Martha Townsend
Georgia Southern University

Cognitive Information Processing
Function Families
Instructional Goals
CIP Goals
(Driscoll, 2005,
p. 71-110)
Methods of Instruction
Technology-Based Student Activities
Gain and keep the
attention of
students.
The students will start each day of class by watching an
entertainingSlideRocket Presentation on function families via their
iPads or iPhones. This presentation includes a meaningful
storywith color, audio, and animation.
The teacher will keep students focused on learning usingTeacher's
Assistant Pro which allows teachers to keep track of student
actions, behaviors, and achievements in the classroom. The
teacher will view each student’scomputer screen on the teacher
computer and monitor their activities. The teacherwill interact
with students through the management software to keep them
engaged and on-task.
The students will use applets to explore and experiment with
functions. These provide interactive entertainment.
Incorporate relevant
prior learning.
The students will complete a warm-up activity each day. The
questions on the warm-up will cover the previous lesson on the
characteristics of function.
The teacher will analyze student responses and use ClickerSchool
Virtual Clicker to communicate feedback to the students.
Highlight and stress
important
information.
As students watch the presentation they will fill in anote-taking
guide with a section labeled “Cues”. In this box they should type
in key ideas.
The teacher will use the teacher computer and overhead projector
to display key words and important facts.
Present lesson in an
organized manner.
The lesson, which is presented in story format, will followa logical
sequence as it introduces new concepts and skills.
Once students have mastered the characteristics of manipulating
the example graph, they will recognize the parent graphs and
slowly begin to apply those same properties.
Studentswill take each of the parent graphs and shift them up or
down in accordance to their equation. Next students will advance
to the more complex concept of reflecting a function over the x-
axis. Finally,the studentswill combine the steps for vertically
manipulating a function.
(continued)

Instructional Goals (continued)
Show students how
to chunk related
information.
The graphic organizers and note-taking guideswill allow students
togroupthe concepts into categories with manageable steps.
The activities and lesson will teach students inductive reasoning as
theyconstruct or evaluate general propositions about functions.
These are derived from specific examples.
Provide activities
for students which
allow them to
elaborate on new
information.
The students will perform activities that will allow them to
connect the graphing of more complex functions to what they
already know about the behaviorsof basic functions.
The students will perform activities that will allow them to
connect the graphing of functions to each other.
The students will look for similarities and differences between the
functions,their algebraic equations, and their graphs.
Show students how
to use coding when
memorizing
concepts and facts.
The students will learn what the graph of each function looks like
by relating it to an animal that is similar in appearance.
The students will learn the names of the functions by giving the
corresponding animals a name that starts with the same letter.
The students will learn how to algebraically manipulate the graph
of a function by relating the aspects of their equations to the
behaviors of the animal.
Provide students
the opportunity for
repetition of
learning.
The students will receive the information and practice on applying
the behaviors of functions several times in various ways.
The students will collaborate with peers and ask questions or help
explain the material.
The students will complete homework activities that reinforce the
material that was learned that day.
Provide activities
for automaticity of
fundamental
concepts and skills.
The students will continue to review graphing skills and the basic
properties of functions through practice worksheets and the test
review.
The students will use ClickerSchool Virtual Clickersubmit answer
towarm-up activities on the basic concepts involved with functions
and receive immediate feedback.
The students will access applets on the Internet that will allow
them to practice manipulating the graphs of functions in the
coordinate plane.
Prior Relevant Learning Focus
Essential Questions Key Definitions
What are the characteristics
of a function and how can
you implement and apply
these characteristics to
arrange and illustrate the
function in multiple ways?
• Coordinate plane
• Relation
• Ordered pair
• Independent variable
• Dependent variable
• x-coordinate
• y-coordinate
• x|y chart
• Abscissa
• Ordinate
• Input
• Output
• Table
• Function
• Graph
• Domain
• Range
• Vertical
line test

Learning Focus for Function Family Lesson
Essential Questions
Key Definitions
(Should be stressed and highlighted)
What are the properties of the parent graphs
of linear, quadratic, cubic, absolute value,
and square root functions and how can you
implement and apply these properties to
identify, compare, and illustrate the
functions?
• Maximum
• Minimum
• Absolute Value
• Parent Graph
• Zero
• Linear
• Quadratic
• Parabola
• Radical
• Infinity
• Cubic
How can you recognize ifthe parent graphs
and equations of linear, quadratic, cubic,
absolute value, and square root
functionshave been vertically affected?
How can you distinguish among, implement,
and demonstrate vertical transformations of
linear, quadratic, cubic, absolute value, and
square root functions?
• Coefficient
• Reflection
• Solution
• Increasing
• Shrink
• Decreasing
• Average rate of
change
• Slope
• End behavior
• Stretch
• Shift
Prior Relevant Learning Objectives
Students
should
have already:
At the beginning of this lesson
students should be able to:
Comprehended
and interpreted
the
characteristics
of relations and
functions.
• Develop and illustrate a relation in multiple ways without the use of
Quick Graphbut by using tables, x|y charts, listing of ordered pairs, or
graphs in the coordinate plane.
• Identify and arrange the domain and range of a relation by looking at a
table, x/y chart, a listing of ordered pairs, or graph.
• Deduce and classify a relation as being a function by looking at a
table, x/y chart, or a listing of ordered pairs.
• Perform and apply the vertical line test to determine if a graph is a
function.
• Calculate to develop x|y charts of functions from their equations and
illustrate these functions in the coordinate plane.
• Demonstrate graphs of functions using Quick Graph.

Learning Objectives
Related to Cognitive Information Process
Students completing
this lesson will:
Students that successfully complete
this lesson will be able to:
Understand, recognize,
evaluate, and analyzethe
properties of the parent graph
equations of linear,
quadratic, cubic, absolute
value, and square root
functions.
• Identify, define, describe, and label the parent graph
equations and organize, classify, and summarize this
information.
• Determine if an equation is one of the parent graph
equations.
• Differentiate between and compare the equations of
parent graph functions.
• Develop and produce theparent graph equations from
memory.
• Recall and recognize the characteristic of the equations
of parent graphs.
Understand, recognize,
evaluate, and analyze the
characteristics of the parent
graphs of linear, quadratic,
cubic, absolute value, and
square root functions.
• Identify, define, describe, and labelthe graphs of
functionsthat are linear, quadratic, cubic, absolute value
orsquare root and organize, classify, and summarize this
information.
• Determine if a graph is one of the parent graphs.
• Differentiate between and compare the parent graphs.
• Develop and produce illustrations ofthe parent
graphsfrom memory.
• Recall and recognize the characteristics of parent graphs.
Synthesize, interpret,
evaluate, and apply the
vertical transformations of
linear, quadratic, cubic,
absolute value, and square
root function equations.
• Identify, define, describe, and label the vertical shift,
vertical stretch, vertical shrink, and vertical reflection of
linear, quadratic, cubic, absolute value, and square root
function equations and organize, classify, and summarize
this information.
• Determine if an equation is a parent graph equation that
has been vertically transformed.
• Recall and recognize the vertical transformations that can
be applied to parent graph equations.
• Differentiate between and compare the different vertical
transformations of parent graph equations.
• Compare and contrast parent graph equations to
equations that have been vertically transformed.
• Develop and produce equations of linear, quadratic,
cubic, absolute value, and square root functions by
combining, implementing, and executing the rules of
transforming graphs.
• Explain the different transformations that can be applied
to a parent graph equation.
(continued)

Learning objectives (continued)
Synthesize, interpret,
evaluate, and apply the
vertical transformations of
the graphs of linear,
quadratic, cubic, absolute
value, and square root
functions.
• Identify, define, describe, and label the vertical shift,
vertical stretch, vertical shrink, and vertical reflection of
linear, quadratic, cubic, absolute value, and square root
graphs and organize, classify, and summarize this
information.
• Determine if a graph is simply a parent graph that has
been vertically transformed.
• Recall and recognize the vertical transformations that can
be applied to parent graphs.
• Differentiate between and compare different graphs of
functions that have been vertical transformed.
• Compare and contrast parent graphs to graphs that have
been vertically transformed.
• Develop and produce illustrations of the graphs of linear,
quadratic, cubic, absolute value, and square root
functions by combining, implementing, and executing
the rules of transforming graphs.
• Explain the different transformations that can be applied
to a parent graph equation.

Standards
(Common Core Georgia Performance Standards)
(CCGPS)
Students will analyze functions using different representations.
https://www.georgiastandards.org/Common-
Core/Common%20Core%20Frameworks/CCGPS_Math_9-12_Accel-GeometryB-
AdvAlgebra_Standards.pdf
MCC9‐12.F.IF.7
Characteristics of functions
Students will graph functions expressed symbolically and show key features of the graph.
They will do this by hand in simple cases and using technology for more complicated cases.
MCC9‐12.F.IF.7a MCC9‐12.F.IF.7b MCC9‐12.F.IF.7c
Students will graph linear
and quadratic functions.
Students will graph square
root and absolute value
functions.
Students will graph cubic
functions.
Lesson Management
Day Lesson Activities Homework
1-3
• Warm-up with immediate feedback from
ClickerSchool Virtual Clicker
• Transition of Buzz Presentation
• Graphic organizer
• Note-taking guide
• Practice worksheet
• Applet activity
• Post on discussion board
• Review lesson presentation
• Review notes
• Homework practice sheet
4
• Review activity with immediate feedback
from ClickerSchool Virtual Clicker
• Applet activity for review
• Post on discussion board
• Extra activity if time
• Review all presentations
• Review all notes
• Review all graphic organizers
5
• Final assessment with immediate
feedback from ClickerSchool Virtual
Clicker
Audience
The audience for this lesson is an Accelerated CCGPS Analytic Geometry B / Advanced
Algebra Mathematics class. There are 24 students, 16 female and 8 males. This class is taught
on a block schedule and meets 1.5 hours every day. The class has been together since the
beginning of the second semester of the school year (approximately 14 weeks), and they are
comfortable working collaboratively. They are already familiar with Google Groups, Google
Drive, and Quick Graph. They have a Google account. They have already set up a folder that
is shared with the teacher which is used for submitting their completed assignments.

Learning Environment
Student Activities Using
Technology-Based
Instruction
(Samples of some of the
activities are attached.)
• Warm-ups
• Note-taking guides
• Graphic organizers
• Student practice activities
• Additional-time activity
• Manipulative activity
• Online discussions
• Multiple-choice assessment
Function Families Lesson
Setting Offers:
(Samples of some of the
presentation slides are
attached.)
• Student access to individual computer
• Common starting point for all students
• Incorporation of prior learning
• Technology-based instruction
• All material accessible through Google Drive
• All material turned in electronically
• Audio and video for delivery of content
• Differentiated sources (if students do not an iPad or an
iPhone for their own personal use, the school will issue
them an iPad for classroom use.)
o ClickerSchool Virtual Clickeractivities
o Teacher's Assistant Pro
o Google Groups
o Quick Graph
o Google Drive
o Internet research
o Applets
• Repetition of learning through a variety of practice
• The use of imagery to retain new information
• Communication with peers
• Additional activity for those that finish early
• Appropriate alignment of learning activities with objectives
and assessment
Assessments
Students will be assessed on their attention to the lesson, their ability to complete their note-
taking guides, charts, and graphic organizers, practice worksheets, and their collaboration
with their peers and teacher (see rubric). They will receive separate grades on their warm-ups
and homework assignments based on correctness. Students will take a multiple choice
assessment and submit their answers using Google Forms and ClickerSchool Virtual Clicker.
Thesefinal assessments cover all objectives on the lesson.

Justification for a Technology-Based Module
Students will have a complete online experience
Technology Class Set-up and Activities
Google Drive:
Shared
Documents
• The teacher will share a Google document with the class that will have the
instructions and requirements for completing the lesson. It will contain all
web-links used in the lesson.
Google Drive:
Shared
Folders
• The teacher will share a lesson folderwiththe class. Itwill includethe
following documents: objectives, rubrics, charts, graphic organizers, practice
worksheets, and note-taking guides. These will be read-only documents, but
students will make copies of them so that they can edit their own version.
• The students should already have a “turn-in folder” set up that is shared
withthe teacher. To turn in anassignment, the student will add the completed
material to the turn-in folder and it will be available to the teacher.
Google
Groups
• Students will respondtoothers ideas.
• Students will provide new resources and ideas related to functions.
• Students will elaborate on the material.
• Students will offer help to other students.
• Students will post responses to teacher questions.
Google Drive:
Google Forms
• Students will submit answers to multiple choice assessments
SlideRocket
Presentation
Software
• Students will observe a lesson presentation
Internet • Students will perform research required for an “additional time” activity
On-line
Mathematical
Applets
• Students will explore characteristics of functions.
o Multi-Function Data Flyer:
http://www.shodor.org/interactivate/activities/
o Slider Graph:
o http://math.hws.edu/javamath/basic_applets/SliderGraph.html
ClickerSchool
Virtual
Clicker
• Teachers and students will use this interactive response system app using
their iPads or iPhones to submit responses to warm-ups and assessments.
Teacher's
Assistant Pro
• The teacher will keep track of student actions, behaviors, and achievements
in the classroom using this iPhone or iPad app.
Quick Graph:
Your
Scientific
Graphing
Calculator
• The student will use this app to graph functions. These results will then be
emailed to the teacher.

Assessment of Lesson Rubric
Justification of CIP
CIP
Activity
Limited
1
Developing
2
Proficient
3
Exemplary
4
CLASSROOM
ATTENTION
Focuses attention
on all aspects of
the lesson.
Focusing attention
allows for the
processingof
important
information while
ignoring
impertinent
information.
Cannot focus
attention
♦ Does not
evaluate
material when
prompted
by teacher
♦ Cannot
maintain a
focus of
attention
despite
cognitive
efforts which
may cause
some level of
anxiety
Requires
redirection
♦ Evaluates
material only
when prompted
by teacher
♦ Requires
considerable
degree of
cognitive effort
to focus
attention
Requires
minimal
redirection
♦ Recognizes
teacher
cues to
evaluate
material
♦ Requires little
cognitive
demand for
successful
completion
Maintains strong
focus and
attention on all
components of
the lesson
♦ Systematically
evaluates
material
without needing
the cues from the
teacher
♦ Demands self-
monitoring or
self-regulation of
own level of
attention
PRACTICE
WORKSHEETS
Makes connections
among
mathematical
ideas and concepts
and procedures.
When students can
make connections
among multiple
representations
they can develop
meaning and solve
problems.
♦ Has no
connection of
the concepts or
meaning to the
facts, rules,
formulas, or
definitions
being learned
♦ Partially
identifies
similarities and
differences
between
concepts but
only by saying
they are
opposites
♦ Cannot solve
problems using
procedures
♦ Has no
connection of
the concepts or
meaning to the
procedure being
used
♦ Identifies
some
similarities and
differences
between
concepts
♦ Struggles with
general
procedures and
solving
problems
♦ Has some
ability to make
connections
between
concepts or
meaning to the
procedure being
used
♦ Identifies
specific
similarities and
differences
between
concepts
and makes
generalizations
♦ Follows
general
procedures but
requires a lot of
thought
♦ Experiments
with new
information and
procedures
and uses them in
different ways
♦ Identifies
specific
similarities and
differences
between
concepts and can
make
generalizations
and
identify
behaviors
♦ Follows
general
procedures and
can do so with
ease
(continued)

Functions Families Lesson Rubric (continued)
PRACTICE
WORKSHEETS
Synthesizes or
brings together
information.
When students
can retrieve
learned concepts,
rules, formulas,
processes, or
definitions it helps
them to gain
meaning and
understanding of
new information
for final
interpretation.
Cannot synthesize
information
♦ Misunderstands
the material
Synthesizes a
majority of
the
information
incorrectly
♦ Focuses on
generating
correct
responsesrath
er
thanestablishi
ng
mathematical
understanding
Synthesizes the
information
somewhat
precisely
♦ Understands
the material,
though there
may be a few
minor errors
Provides a
highly
imaginative and
individualized
synthesis of the
information
♦ Understands
all concepts in
the material
GRAPHIC
ORGANIZERS
AND
CHARTS
Organizes and
charts so that
data and ideasare
correctly
categorizedand
represented
When students
represent
information in
multiple ways it is
easier for them to
encode and store
information.
Cannot organize
information
♦ Creates
graphic
organizers and
charts that are not
complete and do
not correctly
represent the
material
♦ Displays no
sense of
organizationand
categorization
Requires
assistance to
select an
appropriate
organizational
strategy
♦ Requires
assistance to
create graphic
organizers
and charts that
accurately or
clearly
represent the
material
♦ Attempts to
showorganizat
ion and
categorization
but struggles
Completes
organizers
withminor
problems with
organization
♦ Creates
organizers and
charts that
accurately
represent
the concepts
and
understanding
of the topic
♦ Displays a
relatively good
sense of
organization
and
categorization
Independently
selects an
appropriate
organizational
strategy
♦ Creates
organizers and
charts that
accurately depict
the concepts and
understanding of
the topic but can
also do it in
different ways
♦ Creates highly
organized and
effective
organizers and
charts
(continued)

Function Families Lesson Rubric (continued)
GRAPHIC
ORGANIZERS
AND
CHARTS
Effectively
interprets
When students
analyze the
usefulness of
information and
reflect to develop
personal meaning
and knowledge.
♦ Grossly
misinterprets the
information
♦ Makes little or
no attempt to
determine what
information is
necessary to
complete given
task
♦ Makes some
significant
errors in
interpreting
the
information
♦ Cannot
determine
effectively
what
information is
needed to
complete a
given task
♦ Understands
and gives
interpretation of
most of the
information
♦ Makes some
errors in
determining
what
information is
needed for a
given task
♦ Interprets all of
the information
in accurate and
highly intuitive
ways
♦ Accurately
determines what
information is
reliable and
relevant to
complete a given
task
NOTE-TAKING
GUIDES:
SUMMARY
Summarizes
information
When students
process new
information it is
easier for concepts
and ideas to be
stored into their
memory.
♦Retells findings
♦ Does not put the
material in own
words
♦ Does not have
key ideas nor
accurate phrases
♦ Does not setup
the material with
original examples
♦Summarizes
information
♦ Puts some
of the material
in own words
♦ Has few key
ideas and
accurate
phrases
♦ Sets up
material but
without
examples
♦Creates
Relationships;
draws
conclusions
♦ Rephrases
most all of the
material
♦ Has most key
ideas and
accurate phrases
♦ Sets up
material and has
some original
examples
♦Applies
learning to
new, different
situations
♦ Condenses and
rephrases all of
the material
♦ Has all key
ideas and
accurate phrases
♦ Sets up
material with
original
examples
NOTE-TAKING
GUIDES: CUES
Identifies and
labels key ideas,
asks questions
that connect these
ideas.
When students
focus on key ideas
they determine the
importance of new
information.
♦ Does not
accurately seek
out needed
information
♦ Fails to use the
most critical
questioning
techniques
connecting
information
♦ Makes little
or to assess
beneficial
information
♦ Fails to ask
significant
questions for
connecting
information
♦ Accurately
assesses the
lesson to
identify
beneficial
information
♦ Uses
appropriate
questioning
techniques to
connect
information
♦ Insightfully
determines
beneficial
information and
effectively seeks
it out
♦ Effectively
uses a variety of
questioning
techniques to
connect
information
resources
(continued)

Function Families Lesson Rubric (continued)
NOTE-TAKING
GUIDES: NOTES
Labels and
categorizes notes
When students
adapt and
reorganize
information it is
easier for them to
process new facts.
Sorts data
♦ Lists
information
inaccurately,
includes
unimportant
information,
and leaves out
important
details
Orders and
ranks data
♦ Processes the
information
incompletely or
includes many
errors
Classifies
information
♦ Processes the
information
completely with
few errors
Classifies
information and
makes
comparisons
♦ Accurately and
insightfully
processes
information
POSTS
Communicates
When students
collaborate with
other students and
teachers, it creates
situations where
they can repeat,
elaborate, explain,
and self-question.
Ignores any
form of
communication
from teacher
and other
students
♦ Does not
offer any
feedback
♦ Does not
acknowledge
ideas and
comments
♦ Explains
information
related to the
concepts but
only with
assistance
Responds
briefly to
teacher and
other students
comments and
ideas
♦ Pays little
attention to the
details of others
ideas and
comments
♦ Offers very
little feedback
with no
discussion
♦ Explains
the
information
fromthe
concepts but it
may not
be clear or
related
to the
procedures
Explains and
gives reasons
for agreement
and/or
disagreement
of comments
and ideas of
teacher and
other students
♦ Critiques or
supports ideas
and comments
♦ Asks simple
questions
♦ Explains the
information
related to the
concepts
in a clear way
that is
easily
understood
Actively seeks
out ideas and
comments of
teacher and other
students
♦ Asks questions
to clarify ideas
and comments
and suggests
possibilities
♦ Suggests
support of ideas
and comments
♦ Explains
the information
related to the
concepts
and draws
conclusions from
it
which are
understandable
to
another

Justification of Cognitive Information Processing
(Processing, storage, and retrieval of knowledge in the mind)
(Driscoll, 2005, p. 71-110)
CIP
Process
Technology-Based
Teaching Strategies
Student Strategies
Selective
attention
Actively
focusing on
certain
important
stimuli while
excluding
others
♦ Signaling students:The teacher sends messages
through ClickerSchool Virtual Clickerclassroom
management software alerting students that are
off-task.
♦ Moving around:The teacher periodically walks
around the computer lab.
♦ Utilizing a variety of materials: The lesson
requires students to access several different types
of technology:
• Google Groups
• Quick Graph
• Computers
• Social networking
• Google Drive
• Internet research
• Applets
♦ Capturing student interest: The presentation
contains animation and audio which is captivating
to the students. The animals that represent the
functions are meaningful, colorful, and attractive.
♦ Highlighting stimulus features: The note-
taking guide has students defineand highlight the
key words and definitions.
♦ Giving material meaning: The lesson
presentation makes the material meaningful to the
students by relating the functions to animals.
♦ Keeping the classroomin order: The lesson
mandates that students work independently on the
computer. The collaboration with peers is totally
online via Google Groups. This setting helps to
keep the classroom free of noise and distractions.
♦ Encouraging the reduction of student
impulsiveness: Teachers reassure students that
they have the time necessary to complete the
lesson because it is broken down into five days.
♦ Assigning learning objectives: The lesson
provides teachers with a new set of learning
objectives that they assign to the material and then
share with students.
♦ Adhering to cues
from the teacher
which alerts
attention to lesson
activities
♦ Recognizing the
features of the
presentation that
signalimportant
information
♦ Recognizing the
complexity of new
information and
devoting a greater
amount of attention
tolearningit
(continued)

Justification of Cognitive Information Processing (continued)
Automaticity
Devoting little
attention to a
task because
the basic skills
that are
involved in
completing it
are habitual
♦ Questioning students about material: The
teacher asks students individual questions on the
basics of functions through ClickerSchool Virtual
Clickerand Google Groups.
♦ Providingstudents with practice of basic
skills: Teachers assign warm-up practice exercises
on the basic concepts related to the lesson.
♦ Encouraging students to practice extensively:
Teachers encourage students to complete
worksheets and provide homework that continues
this practice.
♦ Overlearning the
material by
constantly studying
♦ Continuing to
practice even though
the problemsare
correct
♦ Reworking
problems presented
in the lesson
♦ Completing
homework practice
assignments
Pattern
recognition
and perception
Recognizing
familiar
patterns as
examples of
concepts and
principles
already stored
in memory
♦ Providing opportunities for linking
information: The lesson requires students to
compareand match behaviors and characteristics of
the new functionsto the corresponding behaviors
and characteristics of the simple functions that
were previouslystored in memory.
♦ Requiring thatstudentsgenerate unique
examples and non-examples: This lesson
supports feature analysis meaning that it shows an
example of a function then requires the students to
generate a counter-example. Students use their
note-taking guides to develop original and
alternate examples. They use a graphic organizer
to create and fill-in their own non-examples.
This activity helps students understand what is
meaningful and critical when analyzing a function.
♦ Offering extensive practice:The lesson offers
anextensive amount ofpracticeon the graphing of
functions usinga variety of techniques.This
ensures that students overcome any past
experiences or prior learning that might interfere
with their ability to process this new knowledge.
♦ Overcoming predetermined perceptions:
Teachers monitor students’achievements and give
immediate feedbackClickerSchool Virtual Clicker
so that they do not judge students based on
preconceived notions.
♦ Focusing on the
material in the
review warm-ups
and linkingit to
information about
the new functions
♦ Paying close
attention to the
examples in the
presentation in an
effort to create
original counter-
examples
♦ Taking advantage
of the extensive
practice so that any
past learning
experiences will not
interfere with
linking previously
learned material to
new information
(continued)

♦ Offering opportunities for guided
discovery:The lesson usescharts and graphic
organizers to help students identifythe relevant and
irrelevant characteristics of parent functions and
their related vertical transformations.
♦ Presenting situations to analyze conditional
situations:The lesson presents students with
relatedsets of concepts and procedures dealing
with functions and their transformations. It then
provides them with worksheets where they analyze
graphs to determine if certain transformations have
been applied to them (if/then).
Chunking
1. Increasing
working
memory
capacity
through
creating larger
bits or taking
small bits of
information
and chunking
them together
♦ Breaking down the material: The lesson is
broken down into understandable and manageable
parts per day to counteract the limitations of short-
term memory. Students learn the characteristics of
functions bit by bit over the course of five days.
♦ Organizing learning tasks: This lesson
organizes the learning tasks according to
complexity. First of all students recognize
important information and respond to this
information by filling in a note-taking guide. Next
they follow procedures and apply definitions as
they complete their graphic organizers and charts.
Finally they form concepts and apply rules as they
solve the problems on their practice worksheets.
♦ Promoting inductive reasoning:The lesson
provides students with examples of parent graphs
and the charts have students derive and discuss
theirgeneral characteristics (inductive reasoning).
♦ Following the
guidelines of the
note-taking guide
and filling it in
appropriately
♦ Taking the
complex information
from the lesson
presentation and
breaking it down
into manageable
parts
♦ Completing the
tasks of the lessons
in the appropriate
order: note-taking,
charts and
organizers, then
practice worksheets
(continued)

Rehearsal
Repeating
information in
an effort to
maintain itso it
can be applied
♦Providing students with charts and graphic
organizers:This lesson has a variety of charts and
graphic organizers that categorizes the same
information about functions in several different
ways.
♦ Providing opportunities for student
practice:The teacher arranges for a variety of
practice opportunities. The goal is to help the
learner generalize the concepts, principles, and
skillsrelated to function families so that they can
be applied to different problem situations.
♦ Promptingdiscussions:The lesson provides for
discussion posts where students have the
opportunity to explain or to help clarify the
problems that others are having. This interaction
creates situations for students to repeat learned
information which will helps them to maintain it.
♦Asking students redundant questions:Because
of the use ofTeacher's Assistant Pro
classroom management software, teachers have
the domain to periodically ask students questions
throughout the course of the lesson. This allows
students to reiterate the material and express their
knowledge.
♦ Filling in several
charts and graphic
organizers to
continually work
with the information
♦ Completing a
variety of practice
problems after each
lesson presentation
♦ Completing
homework practice
assignments
♦ Completing a
review assignment
♦ Helping others by
asking and
answering questions
♦ Answering
teacher- asked
questions about
lesson content
(continued)

(continued)
Encoding
Relating
incoming
information to
concepts and
ideas already in
memory so that
the material is
more
memorable
♦ Organizing instruction:The teacher provides
students with graphic organizers that help them
group related information into categories and lists.
Using these aids, students name and define the
function, reference it to a category, and define its
specific attributes.
♦ Mediating: The lesson uses the story about Buzz
and the way he behaves to teach vertical
transformations of the graphs of functions and how
they relate to specific equations. This way of
presenting the material makes the steps and
procedures involved in transforming graphs more
meaningful and easier to remember.
♦ Incorporating mnemonics: The lesson relates
the names of the functions to the namesof the
animals representing the functions by starting the
names with the same letter.
♦ Incorporating imagery:The lesson provides
students with the means to remember what the
graph of each function looks like by connecting it
to an animal that is similar in appearance.Students
also use imagery tricks to help remember how
each animal behaves under certain circumstances
and relates this back to its corresponding function.
♦ Providing mental scaffolding:The lesson uses
charts and graphic organizers to provide students
the opportunity to link new material about function
families with relevant prior knowledge about basic
functions
♦ Providing a frame of reference: The lesson
acknowledgesparent graphs as being a frame of
reference. Characteristics and behaviors of these
graphs are learned first. Then students apply
complex techniques, including procedures and
visualizations,to these graphsto create the more
complex structures.
♦ Using graphic
organizers to help
work practice
problems
♦ Encoding
information in more
than one way by
using mnemonic
devices, acronyms,
and imagery
♦ Elaborating on
new information by
providing unique
examples of each
type of graph on
note-taking guides
♦ Self-questioning
♦ Making
information
meaningful by
relating it to
personal life (This
activity is prompted
by discussions on
the discussion
board.)
♦ Using note-taking
guides to take notes
using unique words
and phrasing
♦ Using note-taking
guides to summarize
information
♦ Imposing
subjective
organization
♦ Posting inferential
questions on
discussion board
♦ Including prompts
in notes while filling
in the note-taking
guide

Retrieval
Bringing back
previously
learned
material
♦ Offering opportunities of recall: This lesson
makes recall easier by offering studenta multitude
of practice exercises that present questions in a
variety of ways.
• Cued recall: The students complete practice
exercises with the aid of graphic organizers
which provide cuesthat help students
remember the desired information.
♦ Offering opportunities for recognition:
• Yes/no type of recognition: On sections that
require students to interpret the vertical
reflection of a graph, students must
determine if graph is in the normal position
or flipped over the x-axis.
• Forced choice recognition: On warm-ups,
reviews, and the assessments, this lesson
requires that students only recognize which
answer is correct by presenting them with
multiple-choice questions. They must only
make a decision or judgment.
♦ Offering opportunities for encoding
specificity: The lesson is entirely technology-
based with many multiple choice practice
exercises. All assessments are multiple choice and
technology-based; therefore, cues that are used by
students to facilitate encoding will also serve as
the best retrieval cues at test time.
♦ Offering opportunities to counteract
interference: The lesson provides a lot of
practice on previously learned material through the
warm-up activities; therefore, retroactive
interference (interference from newly learned
material) is not of concern to the student.
♦ Offering opportunities to counteract
proactive interference: The lesson has students
signal key ideas and definitions which counteract
proactive interference (interference from
previously learned material); therefore, it is not of
concern to the student.
♦ Accessing the
lesson at home for
further study
♦ Reviewing the
presentation as
needed to ensure that
the important
concepts will be
remembered
♦ Practicing all
material using the
graphic organizer for
guidance
♦ Using the note-
taking guide to study
and complete
practice exercises
♦ Being a state-
dependent learners
by not taking a drug
that might cause
drowsiness during
learning

Justification of Alignment
CIP
Learning
Objective
Instructional Strategy Types of Assessment
Retrieve
Students will be
able to:
• recall
• duplicate
• memorize
• recognize
• relate
• reproduce
• matches
• identifies
• selects
• indicate
• choose
The Web-based instruction presentation
will:
• Explain how learners will be expected to
recall the information
• Draw attention to key features of the
material
• Provide a meaningful context for
effective encoding of information
• Provide memorization tricks
• Provide cues for effective recall and
generalization of information
Formative Assessments
Questions are convergent
• Multiple-choice warm-ups
• Homework assignments
• Practice worksheets
• Teacher questioning
Summative Assessments
Exam items of the form:
reproduce, identify, or select
Items are convergent with limited
answers.
• Multiple-choice objective test
Understand
Students will be
able to:
• classify
• summarize
• compare
• explain
• restate
• paraphrase
• define
• label
• list
• name
• order
• describe
• discuss
• generalizes
• assemble
• organize
• collaborate
• communicate
• individualize
Google Groups will:
• Provide an environment for question-
and-answer sessions
• Provide an environment where students
can review material with others
can teach others
The Web-based instruction presentation
will:
• Present a variety of observable,concrete
examples related directly to the
information
• Encourage learners to recall previously
learned information
• Give examples that illustrate concepts or
rules
• Relate the information to preexisting
knowledge
• Present cues to the organization of
concepts
• Break down the process of performing
or applying rules into steps
• Present all terms clearly using the
fewest number of words to convey the
meaning
• Class discussions
• Graphic organizers
• Charts
• Note-taking guides
• Teacher questioning
• Posts
Summative Assessment
Items are convergent
Exam items of the form:, label,
list, describe, define,explain, or
summarize
(continued)

Justification of Alignment (continued)
• Define categories
• Group related terms or units
• Present the material into manageable
parts
• Present information so that it can be
made into chunks
• Present a variety examples
• Present rule applications and highlight
the distinctive features of examples,
definitions, and procedures.
• Encourage the development of graphic
organizers and charts
• Encourage the writing of well-
developed notes
• Provide activities for summary and
closure
Apply
Students will be
able to:
• execute
• implement
• engage
• execute
• practice
• demonstrate
• employ
• solve
• use
• chart
• compute
• discover
• establish
• inform
• participate
• predict
• provide
• relate
• transfer
• utilize
Lesson format will:
• Schedule occasions for practice and
spaced review
• Encourage the recall of relevant rules
and concepts
• Provide practice in multiple contexts
• Provide guided practice with immediate
feedbackClickerSchool Virtual Clicker
• Present a variety of practice that allow
the students to practice applying the
rules or identifying/describing concepts
• Encourage guidance throughout early
stages of practice using graphic
organizers
• Provide learners with opportunities to
engage with concepts and rules using
applets
• Encourage the use of mental practice
• Arrange repeated practice
• Require students to demonstrate
problem-solving
• Require studentsto demonstrate
application of rules, methods, or
procedures
Questions may be convergent or
divergent.
• Warm-ups
• Problem worksheets
• Homework sheets
Exam items of the form: apply,
use, solve, demonstrate, employ
(continued)

Analyze
Students will be
able to:
• differentiate
• determine
• consider
• investigate
• analyze
• calculate
• compare
• contrast
• differentiate
• distinguish
• examine
• experiment
• question
• categorize
Google Groups will:
• Provide an environment for students to
respond to others ideas
can elaborate on material
can analyzeon material
Lesson format will:
• Activities that require the analysis of
important information
• Activities that determine how
procedures involved in the material
work together
• Activities that require analyzing a final
outcome to see how it was produced
• Activities for students to analyze
content using computer applets
divergent.
• Posts
• Practice Worksheets
Summative Assessment
Exam items of the form: analyze,
compare, distinguish, examine,
test
Evaluate
Students will be
able to:
• assess
• rate
• criticize
• rank
• decide
• assess
• calculate
• decide
• argue
• defend
• conclude
• justify
Google Groups will:
• Provide an environment for students to
self-question
critique the comments of others
discuss the appropriateness of
procedures
Lesson format will:
• Provide activities for evaluating material
to determine if it fulfills given purpose
• Provide activities to demonstrate
processes for evaluating material
• Provide activities torate and rank
material
divergent
• Posts
• Charts
Exam items of the form: evaluate,
argue, assess, defend, judge,
predict, rate, support
Create
Students will be
able to:
• develop
illustrate
• produce
• construct
• discover
• establish
Google Groups will:
can provide new resources and ideas
• Provide information feedback as to the
creativity or originality of comments
Lesson format will:
• Provide activities for generating and
constructingnew outcomesbased on
rules and procedures
Small group discussions
divergent
• Posts
(continued)

• formulate
• generate
• initiate
• originate
• perform
• give
examples
• sketch
• show
• express
• Encourage learners to identify and select
their own examples and non-examples
of concepts and rule applications if
possible.
divergent
Exam items of the form: develop,
plan, prepare, propose, construct,
design, formulate, create,
assemble

Figure A
Sample Slidefrom SlideRocketPresentation
MEET BUZZ
Buzz is a freshman in High School and lives with
his parents. The street that he lives on is the y-
axis.
f(x) = Buzz
Buzz is at his parents'
home when his stinger
is on the origin. We call
this the “origin point”.

Figure B
Sample Slide from SlideRocketPresentation: Vertical Shift
BUZZ VISITING FRIENDS
Vertical Shift
Buzz likes to visit his friends on the street:
(y-axis).
Buzz visits Bill
when he moves
his origin point 5
blocks up.
f(x) = Buzz + 5
Buzz visits Nancy
when he moves his
origin point 7
blocks down (-7).
f(x) = Buzz – 7

Figure C
Sample Slide from SlideRocketPresentation: Vertical Reflection
SLEEPING BUZZ
Vertical Reflection
When Buzz sleeps, he sleeps upside (vertically flips
over his origin point). When we refer to Buzz in
this position, we write
f(x) = -Buzz.
The negative sign in front of his name indicates
that he is in the sleeping
position. If there is
not a sign at all
or a positive sign is in
frontthis means that
he is in the awake
position.
This is Buzz asleep
at his parent's
house.

Figure D
Sample Slide from SlideRocketPresentation: Vertical Shrink
YOUNG BUZZ
Vertical Shrink
When Buzz was young he was short and fat. When
we refer to Buzz at this age, we put a number
between 0 and 1 in front of Buzz. The smaller the
number the fatter Buzz gets.
f(x) = (¼)Buzz.
This is a young Buzz
at his parents’ house.

Figure E
Sample Slide from SlideRocketPresentation: Vertical Stretch and Shift
YOUNG BUZZ
Vertical Stretch and Shift
When Buzz gets old he will be tall and thin. When
we refer to Buzz at this age, we put a number
greater than 1 in front of Buzz. The larger the
number the taller and thinner Buzz gets.
f(x) = (5)Buzz + 3.
This is an older Buzz
at a friend’s house that
lives 3 blocks up.

Figure F
Sample Slide from SlideRocketPresentation Introducing “Linus”
Introduction of Function Animals
Animal Name: “Linus”
Function Name: Linear Function
Graph Name: Line
Math Symbol: x
Animal Symbol: see below

Figure G
Sample Slide from SlideRocketPresentation Introducing “Abby”
Animal Name: “Abby”
Function Name: Absolute Value Function
Graph Name: Absolute Value
Math Symbol: |x|

Figure H
Sample Slide from SlideRocketPresentation Introducing “Curt”
Animal Name: “Curt”
Function Name: Cubic
Graph Name: Cubic
Math Symbol: x3

Figure I
Sample Slide from SlideRocketPresentation Introducing “Squirm”
Animal Name: “Squirm”
Function Name: Square Root Function
Graph Name: Radical
Math Symbol:

Figure J
Sample Slide from SlideRocketPresentation Introducing “Rachel”
Animal Name: “Rachel”
Function Name: Rational Function
Graph Name: Rational
Math Symbol:
2
4
-3

Figure K
Sample Slide from SlideRocketPresentation Introducing “Quinton”
Animal Name: “Quinton”
Function Name: Quadratic Function
Graph Name: Parabola
Math Symbol: x2
Animal Symbol: (see below)

Figure L
Screen Shot of Appletsfor Manipulation of Functions
Multi-Function Data
Slide Graph

Figure M
Sample Warm-up Quizon the Basic Behaviors of Functions

Figure N
Note-taking Guide
Name: Class: Date: Lesson Topic:
Learning Objectives:
CUES
(After
class)
• Key ideas
• Questions that connect ideas
• Diagrams and charts
• Prompts for studying
PRESENTATION
NOTES
(During class)
• Short and concise phrases
• Symbols and abbreviations
• Labels and categories
• Lists and tables
• Spaced out facts
SUMMARY
(After Class)
• In own words
• Original examples
• Most important key ideas
• Accurate phrases for quick reference

FigureO
Sample Chart
Fill in the
organizer
according to the
information you
viewed during the
presentation.
Animal
Name
Animal
Symbol
Math
Symbol
Function
Name
Name of
Graph

Figure P
Sample Chart
According to the
condition of Buzz
below, fill in the cells
using the directions at
the top of each
column. Follow the
example done for you.
Description of
How Buzz
changed
Mathematical
Operation
That Create This
Change
Mathematical
Name of the
Change That Took
Place
Asleep and younger
Upside down
and fatter
Negative
number
between 0 and 1
multiplied by
Buzz
Vertical
reflection and
vertical shrink
Awake at his parents
Visiting a friend and
awake
Younger at his parents
house and asleep
Older at his friend’s
house and awake
Younger at his
friend’s house
Older and awake at
his parents’ house
Asleep at his friends
house and younger

Figure Q
Sample Graphic Organizer
Definition Facts/Characteristics
Examples
Non-Examples
Examples
Non-Examples
Examples
Non-Examples
Linear
Function
Quadratic
Function
Cubic
Function

FigureR
Sample Practice Worksheet on Writing Equations
Look at each graph
below and fill in
each cell according
to the heading at
the top of each
column. An
example is given.
Animal Name
Awake
or
asleep
Age of
Animal
Math
Symbol
Possible
Equation
Quadratic + 6 X2
f(x) =
6x2

FigureS
Look at each graph
below and fill in each
cell according to the
heading at the top of
each column. An
example is given.
Function
Notation
=
Awake
Or
Asleep
(+ or
-)
Possible
Age
Function
Symbol
+
-
or
“nothing”
Vertical
Position
f(x)= + 5 x2 - 6

FigureT
Look at each graph
below and fill in each
cell according to the
heading at the top of
each column. An
example is given.
Awake +
Asleep -
Age of
Animal
Math
Symbol
Up +
Down –
# of
units
Possible
Equation
- 7 √x - 5
f(x) = -7√x -
5

Figure U
Sample Practice Worksheet Drawing Graphs
Place a box around each of the 4
parts of the equations below.
Name the animal in the blank
provided. Fill in the chart
according to the directions at
the top of each column.
Box 1 Box 2 Box 3 Box 4
Sketch of
Possible
Graph
(in 1,2,3,4 order)
Draw
Graph
Awake or
Asleep
Draw
Animal
At Age
Draw
Parent
Graph
How
many
Units
Up or
Down?
3rd 2nd 1st 4th
(example)
animal: Quinton .
Down
7
y = - (1
/4) x3
+ 2
animal_________
y = -5x + 2
animal_________
y = (1
/3) √x - 5
animal_________

FigureV
Sample Review Activity on Shifting Parent Graphs
Graph
Awake or
asleep
Possible Age of
Animal
Shape of
the graph
Shift up or down
1.
A. +
B. -
2.
A. 1
/2
B. 2
C. 1
3.
A. x D. x3
B. |x| E. √x
C. x2
F. 1
/x
4.
A. + 3
B. - 2
C. no shift
5.
A. +
B. -
6.
A. 1
/2
B. 2
C. 1
7.
A. x D. x3
B. |x| E. √x
C. x2
F. 1
/x
8.
A. + 3
B. - 2
C. no shift
9.
A. +
B. -
10.
A. 1
/2
B. 2
C. 1
11.
A. x D. x3
B. |x| E. √x
C. x2
F. 1
/x
12.
A. + 3
B. - 2
C. no shift
13.
A. +
B. -
14.
A. 1
/2
B. 2
C. 1
15.
A. x D. x3
B. |x| E. √x
C. x2
F. 1
/x
16.
A. + 3
B. - 2
C. no shift
17.
A. +
B. -
18.
A. 1
/2
B. 2
C. 1
19.
A. x D. x3
B. |x| E. √x
C. x2
F. 1
/x
20.
A. + 3
B. - 2
C. no shift
21.
A. +
B. -
22.
A. 1
/2
B. 2
C. 1
23.
A. x D. x3
B. |x| E. √x
C. x2
F. 1
/x
24.
A. + 3
B. - 2
C. no shift
25.
A. +
B. -
26.
A. 1
/2
B. 2
C. 1
27.
A. x D. x3
B. |x| E. √x
C. x2
F. 1
/x
28.
A. + 3
B. - 2
C. no shift

FigureW
Activity on Linear Regression Which Serves as an Additional Activity
“Extra Time” Activity
Basics of Linear Regression
Page 1
If you complete all components of the lesson on Function Families, use the extra
time to complete this activity.
1. Before you perform any Internet research, estimate the ages of each
of the famous people above. Fill in the appropriate column in the chart
(x-value).
2. Using the Internet, research each of the famous people and record
their ages in the appropriate column in the chart (y-value).
How well were you able to estimate the ages of these famous
people?
3. To help answer this question, first of all make a scatterplot
usingtheestimate of their age as the x-value and the actual age asy-
value. Use the graph paper attached. Be sure to give it a title, use
appropriate increments on the axes, and label each axis.
4. If you estimated the age correctly, what istrue about this point?
5. Sketchagraphofthe line of estimates that were 100% accurate.
6. What is the equation of this line?
7. What does it mean if a point on your scatterplot is above this line?
(continued)

Figure W (continued)
Page 2
8. In general, did you overestimate or underestimate the ages of your
famous people?
9. How can you tell this from your scatter plot?
10. Plot the points on Quick Graph.
11. Have Quick Graph calculate linear regression and draw this line. What is
the equation of this line?
12. Sketch this line on your graph paper.
13. Write a paragraph that discusses the slopes of your lines and the
characteristics of your data. What conclusions can you draw?
(continued)

Figure W (continued)
Page 3
Famous Person
Estimated Age
x-value
Actual Age
y-value
Bill Clinton
Tom Cruise
Hillary Duff
Miley Cirus
Carrie Underwood
Abraham Lincoln(age at death)
Babe Ruth(age at death)
“The Rock”
George Washington
Tim Allen
Oprah Winfrey
Cleopatra(age at death)
Barney
Einstein(age at death)

FigureX
SampleAssessment Questions
(continued)

FigureX(continued)
Sample Assessment Questions

References
Driscoll, M.P. (2005). Psychology of learning for instruction (3rd ed.). Boston: Allyn and Bacon

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