1.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 1
Cognitive Information Processing
Function Families
Martha Townsend
Georgia Southern University
2.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 2
Cognitive Information Processing
Function Families
Instructional Goals
Goals
(Driscoll, 2005,
p. 71110)
Methods of Instruction
TechnologyBased Student Activities
Gain and keep the
attention of
students.
The students will start each day of class by watching an
entertainingSlide Rocket Presentation on function families with
color, audio, and animation.
The teacher will periodically walk around the laband redirect
students that are offtask.
The teacher will keep students focused on learning using SMART
Sync™ classroom management software. 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.
Incorporate relevant
prior learning.
The students will complete a warmup activity each day via Smart
Notebook Software clickers. The questions on the warmup will
cover the previous lessons on the characteristics of a function.
The teacher will analyze student responses and use SMART
Sync™ to communicate feedback to the students.
Highlight and stress
important
information.
The teacher will provide notetaking guides to accompany each
day’s lesson.Students will receive a hard copy as well as a
computer copy using Google Documents. They should fill these
in as they watch the presentation.
The teacher will use the teacher computer and overhead projector
to display key words and important definitions.
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 be slowly introduced to the algebraic
parent graphs.
Studentswill then take each of the parent graphs and shift them up
or down. Next students will move to the more complex concept of
reflecting a function over the xaxis. Finally,the lessonwill show
students how to combine the steps for vertically manipulating a
function.
3.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 3
Show students how
to chunk related
information.
The graphic organizers and notetaking guideswill allow students
togroupthe concepts into categories and manageable steps.
The activities will teach students inductive reasoning as theywill
construct or evaluate general propositions about functions that 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 functions to what they already know about
the behaviors of positive and negative numbers.
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
different functions andtheir algebraic equations.
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
animals that are connected to each graph a name that starts with the
same letter.
The students will learn how to graphically manipulate the graph of
a function by relating the aspects of their equations to the behavior
of the animal.
Provide students
the opportunity for
repetition of
learning.
The students will receive the information and practice on 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 throughout the course of the lesson through
warmup activities and the test review.
The students will use the Senteofreeresponse system to access
drill and practice on the basic concepts involved with functions.
The students will access a SMARTNotebook file that will allow
them to practice manipulating the graphs of functions in the
coordinate plane.
4.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 4
Prior Relevant Learning Objectives
Students
should
have already:
At the beginning of this lesson
students should be able to:
Learned about
the
characteristics
of relations and
functions.
• Represent a relation in multiple ways without the use of a calculator
using tables, xy charts, listing of ordered pairs, or graphs in the
coordinate plane.
• Identify domain and range of a relation by looking at a table, x/y chart,
a listing of ordered pairs, or graph.
• Determine if a relation is a function by looking at a table, x/y chart, or
a listing of ordered pairs.
• Apply the vertical line test to determine if a graph is a function.
• Create xy charts of functions from their equations and graph these
functions in the coordinate plane.
• Graph functions using a TI83 Plus graphing calculator.
Learning Objectives for Function Family Lesson
Students completing
this lesson will:
Students that successfully complete
this lesson will be able to:
Learn about the properties of
the parent graph equations of
linear, quadratic, cubic,
absolute value, and radical
functions.
• Identify the parent graph equations of linear, quadratic,
cubic, absolute value, and radical functions.
• Match the parent graph equations of linear, quadratic,
cubic, absolute value, and radical functions with their
appropriate algebraic name.
• Determine if an equation is linear, quadratic, cubic,
absolute value or radical by looking at an equation.
Learn about the
characteristics of the parent
graph of linear, quadratic,
cubic, absolute value, and
radical functions.
• Match the parent graphsof linear, quadratic, cubic,
absolute value, and radical functions with their
appropriate name.
• Identify if a function is linear, quadratic, cubic, absolute
value or radical by looking at the graph.
• Sketch the parent graph of a linear, quadratic, cubic,
absolute value, and radical function by looking at an
equation.
Learn about vertical
transformations of linear,
quadratic, cubic, absolute
value, and radical functions.
• Identify the vertical shift, vertical stretch, and vertical
reflection of linear, quadratic, cubic, absolute value, and
radical functions by looking at an equation.
• Sketch the graph of linear, quadratic, cubic, absolute
value, and radical functions by looking at an equation
and applying the appropriate transformations.
• Match an equation of linear, quadratic, cubic, absolute
value, and radical functions with a picture of a graph.
5.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 5
Prior Relevant Learning Focus
Essential Questions Key Definitions
What are the characteristics of a
function and how can you use those
characteristics to represent the
function in multiple ways?
• Coordinate plane
• Relation
• Function
• Independent variable
• Dependent variable
• xcoordinate
• ycoordinate
• xy chart
• Input
• Output
• Table
• Ordered pair
• Graph
• Domain
• Range
• Vertical line test
Learning Focus for Function Family Lesson
Essential Questions
Key Definitions
(Should be stressed and highlighted)
What are the characteristics of the
parent graphs of linear, quadratic,
cubic, absolute value, and radical
functions?
• Linear
• Absolute Value
• Cubic
• Quadratic
• Parabola
• Radical
• Infinity
• Zero
• Parent Graph
• Maximum
• Minimum
How arethe parent graphs of linear,
quadratic, cubic, absolute value, and
radical functionsvertically affected
when their parent graph equations are
added to and/or multiplied by a
number.
• Coefficient
• Reflection
• Solution
• Increasing
• Decreasing
• Stretch
• Shrink
• Shift End behavior
• Average rate of
change
• Slope
6.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 6
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_912_AccelGeometryB
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.
Audience
The audience for this lesson is anAccelerated CCGPS Analytic Geometry B / Advanced
Algebra Mathematics class. There are 24 students, 16 female and 8 males. 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 already familiar with SMART
Notebook software, Senteo freeresponse system, Google Drive, and TI83 Plus graphing
calculators.
7.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 7
Learning Environment
Student Activities Using
TechnologyBased
Instruction
(Samples of some of the
activities are attached.)
• Warmups on previously learned material
• Notetaking guides
• Graphic organizers
• Student practice activities
• Famous People Graphing Activity (“Additional Time
Activity”)
• Final assessment via Senteo Clickers
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
• Technologybased instruction
• Audio and video for delivery of content
• Differentiated sources
o Senteo freeresponse system activities
o SMART Notebook software
o Social networking
o TI83 Plus graphing calculators
o Google drive
o Internet research
• Repetition of learning through a variety of practice
• The use of imagery to retain new information
• Communication with peers (Google Groups)
• Additional activity for those that finish early
• Appropriate alignment of learning activities with objectives
and assessment
Assessment
Students will be assessed on their attention to the lesson, their ability to fill in their notetaking
guides and graphic organizers, and their collaboration with their peers and teacher (see rubric).
They will receive separate grades on their warmups, practice worksheets, and homework
assignments based on correctness. Students will take a multiple choice assessment using the
Senteo clickers that covers all objectives on the lesson.
8.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 8
Lesson Management
Day Lesson Activities Homework
1
• Warmup Day 1
• Transition of Buzz Presentation Day 1
• Graphic organizer
• Notetaking guide
• Practice worksheet
• Review Presentation from
website
• Review notes
• Homework practice sheet
2
• Warmup Day 2
• Transition of Buzz Presentation Day 2
• Graphic organizer
• Notetaking guide
• Practice worksheet
• Applet activity
• Review Presentation from
website
• Review notes
• Homework practice sheet
3
• Warmup Day 3
• Transition of Buzz Presentation Day 3
• Graphic organizer
• Notetaking guide
• Practice worksheet
• Applet activity
• Review Presentation from
website
• Review notes
• Homework practice sheet
4
• Review activity
• Peer collaboration review game
• Review all presentations
• Review all notes
• Review all graphic organizers
5
• Final assessment with immediate
feedback
Engage
• Students will participate in a lesson that has them watch a presentation with animation and
audio.
• Students will be engaged by using SMART Notebook software to practice manipulation
of functions.
Explore
• Students will explore characteristics of functions by using SMART Notebook software to
practice vertical manipulation of functions.
• Students will explore characteristics of functions by using TI83 Plus graphing calculators
to practice vertical manipulation of functions.
Explain
• Students will complete graphic organizers and notetaking guides using their own words.
• They will complete practice worksheets and an assessment which will display their
knowledge of function transformation.
• Students will offer help to other students via the Google Group Discussion Board.
9.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 9
Elaborate
• Students will use the Google Group Discussion Board to post new resources and/or ideas
related to functions.
• Students will elaborate on the material by posting discussions related to new information
about functions.
• Students will post wellwritten responses with evidence supporting their position/opinion
on the topic.
10.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 10
Function Families Lesson Rubric
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
selfregulation of
own level of
attention
PRACTICE
WORKSHEETS
Makes connections
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
♦ Student can
partially
identify
Some
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
♦ Student can
identify
specific
similarities and
differences
between
concepts
generalizations
♦ Struggles with
general
procedures and
solving
problems
♦ Has some
ability to make
connections
between
concepts or
meaning to the
procedure being
used.
♦ Student can
identify
specific
similarities and
differences
between
concepts
and make
generalizations
♦ Follows
general
procedures but
has to put a lot
of thought into
it
♦ 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
11.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 11
PRACTICE
WORKSHEETS
Synthesizes or
brings together
information
When students can
retrieve learned
concepts, rules,
formulas, or
definitions it helps
them to gain
meaning and
understanding of
new information.
Cannot
synthesize
information
♦ Makes little
or no attempt
to determine
what
information is
necessary to
complete given
task
♦
Misunderstand
s the material
Synthesizes a
majority of the
information
incorrectly
♦ Cannot
determine
effectively what
information is
needed to
complete a
given task
♦ Focuses on
generating
correct
responsesrather
thanestablishing
mathematical
understanding
Synthesizes the
information
somewhat
precisely
♦. Makes some
errors in
determining
what
information is
needed for a
given task
♦ Understands
the material,
though there
may be a few
minor errors
can explain the
event
Provides a
highly
imaginative and
individualized
synthesis of the
information
♦ Accurately
determines what
information is
reliable and
relevant to
complete a given
task
♦ Understands
all concepts in
the material can
explain the
answer
GRAPHIC
ORGANIZERS
Organizes data
and ideas
When students
represent
information in
multiple ways, such
as visual diagrams,
manipulatives,
symbols, and
problem situations,
it is easier for them
to encode and store
information.
Cannot
organize
information
♦ Creates
graphic
organizers that
are not
complete and
do not
correctly
represent the
material
♦ Displays no
sense of
organization
Requires
assistance to
select an
appropriate
organizational
strategy
♦ Requires
assistance to
create graphic
organizers that
are
accurate or
clear
♦ Attempts to
showorganizati
on but struggles
Completes
organizers
withminor
problems with
organization
♦ Creates
organizers that
accurately
represent
the concepts
and
understanding
of the topic
♦ Displays a
relatively good
sense of
organization
Independently
selects an
appropriate
organizational
strategy
♦ Creates
organizers that
accurately depict
the concepts and
understanding of
the topic but can
also do it in
different ways
♦ Creates highly
organized and
effective
organizers
12.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 12
NOTETAKING
GUIDES
Identifies,
highlights, and
labels key
information and
ideas
When students
focus their
attention on
certain key issues
in the lesson,they
gain assistance
indetermining the
importance of new
information.
♦ Does not
accurately seek
out needed
information
♦ Fails to use
the most
important
techniques for
gathering
information
♦ Makes little or
to assess
beneficial
information
♦ Fails to use
some significant
techniques for
gathering
information
♦ Accurately
assesses the
lesson to
identify
beneficial
information
♦ Uses
appropriate
techniques to
gather
information
♦ Insightfully
determines the
types of
information that
would be
beneficial and
effectively seeks
out that
information.
♦ Effectively
uses a variety of
information
gathering
techniques and
information
resources
NOTETAKING
GUIDES
Labels and
categorizes notes
When students
adaptand
reorganize
information for a
specific task, it is
easier for them to
process new
information.
Sorts data
The processing
of the
information is
not complete
or there are
many errors
Orders and
ranks
data
There are some
errors, such as
listing
unimportant
information and
missing
important
details or
simply having
incorrect
information.
Classifies
information
.
♦Analyzes
information in
detail
Classifies
information and
makes
comparisons
♦ Accurately and
insightfully
processes
information
NOTETAKING
GUIDES
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
setup the
material with
original
examples
Summarizes
information
♦ Puts some of
the material in
own words
♦ Sets up
material but
without
examples
Creates
relationships
and
draws
conclusions
from
information
♦ Puts almost
all of the
material in own
words
♦ Sets up
material and has
some original
examples
Independently
applies
learning to
new and
different
situations
♦ Condenses the
material and puts
it all in own
words.
♦ Sets up
material with
original
examples
13.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 13
POSTS
Effectively
interprets
When students
overlearn basic
skills by
performing
extensive practice
it ensures that they
can recall these
concepts with little
thought or
attention.
♦ Grossly
misinterprets
the information
♦ Explains
information on
a
graph, table, or
chart but only
with assistance
♦ Makes some
significant
errors in
interpreting the
information
♦ Explains
the
information on
a
graph, table or
chart, but it may
not
be clear or
related
to the
requirements
♦ Understands
and gives
interpretation of
most of the
information
♦ Explains the
information
related to the
concepts
in a clear way
that is
easily
understood
♦ Interprets all of
the information
in accurate and
highly intuitive
ways
♦ Explains
the information
related to the
concepts
and draws
conclusions from
it
which are
understandable
to
another
POSTS
Communication
When students
collaborate with
other students and
teachers, it creates
situations where
they can elaborate
and selfquestion.
It also provides
opportunities for
them to make the
information
personal and more
meaningful.
Ignores any
form of
communication
from teacher
and other
students
♦ Does not
offer any
feedback
♦ Does not
acknowledge
ideas and
comments
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 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
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
14.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 14
Justification of Cognitive Information Processing
(Processing, storage, and retrieval of knowledge in the mind)
(Driscoll, 2005, p. 71110)
CIP
Process
Teaching Strategies
Student Strategies
and
Responsibilities
Selective
attention
Actively
focusing on
certain
important
stimuli while
excluding
others
♦ Signaling:The teacher sends messages through
SMART Sync™ classroom management software
alerting those that are offtask.
♦ Moving:The teacher periodically walks around
the computer lab.
♦ Utilizing variety of materials: The lesson
requires students to access several different types
of technology:
• SMART Notebook software
• Senteo freeresponse system
• TI83 Plus graphing calculators
• Computers
• Social networking
• Google drive
• Internet research
♦ Capturing interest: The lesson 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 teacher
displays the key words and definitions on the
overhead.
♦ Giving meaning: The lesson presentation makes
the material meaningful to the students by relating
the functions to animals.
♦ Keeping order: The lesson mandates that the
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 reduction of impulsiveness:
Teachers ensure students that they have the time
necessary to complete the lesson because it is
broken down into five days.
♦ Students adhere to
cues from the
teacher which alerts
them to focus and
pay attention while
watching the lesson
presentation, taking
notes, and working
through the practice
worksheets.
♦ Students recognize
the features of the
presentation that
signalimportant
information.
♦ Students recognize
the complexity of
new information and
devote a greater
amount of attention
tolearningit.
15.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 15
Automaticity
Devoting little
attention to a
task because
the basic skills
that are
involved in
completing it
are habitual
♦ Questioning: The teacher asks students
individual questions on the basics of functions
through SMART Sync™ and Senteo freeresponse
system.
♦ Offering practice of basic skills: Teachers
assign warmup practice exercises on the basic
concepts related to the lesson.
♦ Assigning objectives: Teachers share the
learning objectives with students.
♦ Encouraging extensive practice: Teachers
encourage students to complete worksheets and
provide homework that continues this practice.
♦ Students overlearn
the material by
constantly studying.
♦ Studentscontinue
to practice even
though they may be
getting the
problemscorrect.
♦ Students rework
problems presented
in the lesson to see if
they can continue to
get a correct answer.
♦ Students complete
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
compare or match behaviors and characteristics of
the new graphs to the corresponding behaviors and
characteristics of the functions that are already
stored in memory.
♦ Providing examples and nonexamples: This
lesson supports feature analysis meaning that it
shows an example of a function then makes
students generate a differing or counterexamples.
This 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 through
the Senteo freeresponse system and give
immediate feedback so that they do not judge
students based on preconceived notions.
♦ Students focus on
the material in the
review warmups so
that they can link
previously learned
information about
graphs to the new
graphs.
♦ Students pay close
attention to the
examples in the
presentation so that
they can create their
own counter
examples.
♦ Students take
advantage of the
extensive practice so
that any past
learning experiences
will not interfere
with their ability to
link new
information.
Chunking
Increasing
working
memory
capacity
through
creating larger
bits
♦ Breaking down the material: The lesson is
broken down into understandable and manageable
parts to counteract the limitations of shortterm
memory. Students learn the characteristics of
functions bit by bit over the course of five days.
♦ Organizing learning tasks: The lesson is
highly organized so that students can easily chunk
the information on their own.
♦ Students follow
the guidelines of the
notetaking guide.
♦ Students take the
complex information
from the lesson
presentation and
break it down into
manageable parts.
16.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 16
Rehearsal
Repeating
information in
an effort to
maintain it
♦ Providing practice.The teacher arranges for a
variety of practice opportunities. The goal is to
help the learner generalize the concept, principle,
or skill to be learned so that it can be applied to
different problem situations.
♦ Students complete
a variety of practice
problems after each
lesson presentation.
♦ Students complete
homework practice
assignments.
♦ Students complete
a review assignment
the day before the
test.
Encoding
Relating
incoming
information to
concepts and
ideas already in
memory so that
the new
material is
more
memorable
♦ Organizing instruction:The teacher provides
students with a graphic organizer handout that
helps them to process the information from the
lesson. They name and define the concept to be
learned, reference it to a larger category and define
specific attributes. Scheme  an organization of
concepts, principles, rules, etc. that define a
perspective and presents specific action patterns to
follow.
♦ Mediating: The lesson uses the story about
Buzz to teach the properties of specific graphs of
functions and how they relate to their
accompanying equation.
♦ 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 relating it to
an animal that is similar in appearance. personal
experience (information in stories and analogies)
♦ Providing mental scaffolding:The lesson
provides students with the opportunity to link new
material with what is relevant prior knowledge.
♦ Offering guided discovery:The lesson uses
elaboration and multiple contexts to help students
identify relevant and irrelevant characteristics of
the parent graphs.
♦ Showing methods of elaboration:The lessons
provide students with examples and nonexamples
and have them create their own.
♦ Promoting reasoning techniques:Inductive
(example/experience > definition) and deductive
(definition > examples)
♦ Presenting propositioning techniques:The
lesson gives students interrelatedgroups of
concepts and relationships such as when they learn
♦ Students use their
graphic organizer to
help them work
practice problems.
♦ Students encode
information in more
than one way by
using mnemonic
devices, acronyms,
and imagery.
♦ Students elaborate
on new information
by providing their
own examples of
each type of graph
within their notes.
♦ Students make
information personal
and meaningful by
relating it to their
own life. This
activity is prompted
by discussions on
the discussion board.
♦ Students use the
notetaking guide to
take notes in their
own words.
♦ Students use the
notetaking guides to
summarize the
information.
♦ Students impose
their own subjective
organization
♦ Students post
inferential questions
♦ Students include
17.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 17
the properties of graphs. It has students fill in and
analyze if/then statements.
♦ Teaching scripting:The lessondevelops general
information about a series of stepsinvolved in
graphing functions and has students apply these
steps to attain either a picture of a graph or an
algebraic equation.
♦ Providing a frame of reference: The lesson
offers complex organizational techniques
including concepts and visualizations that provide
a reference point from whichgraphs and graph
manipulations are analyzed.
♦ Delivering programming: This lesson provides
a set of rules that define what students shoulddo
when the equations of parent functions have been
added on to or multiplied by a number.
♦ Focusing on reality: The parent graphs offer a
basic way of perceiving, thinking, valuing, and
doing something associated with the realworld.
♦ Modeling:The parent graphs or algebraic
equations of function describecharacteristicsof the
more elaborate graphs.
♦ Helping learners become "self
regulated":Teachers assist students in selecting
and using appropriate learning strategies such as
summarizing and questioning by providing note
taking guides and structured guidance on the
discussion board.
study questions in
their notes as they
fill in the notetaking
guide.
Retrieval
Bringing back
previously
learned
material
♦ Offering opportunities of recall: This lesson
asks students to generate graphs by hand and has
them use these graphs to answer questions on the
practice exercises and test. This lesson offers lots
of practice in a variety of ways which makes recall
easier.
• In free recall situations, learners must
retrieve previously stored information
with no cues or hints to help them
remember. The practice worksheets offer
free recall.
• Cued recall tasks are those in which a
hint or cue is provided to help learners
remember the desired information.
Students use their graphic organizers to
assist with this type activity.
♦ Offering opportunities for recognition: This
lesson requires that students must only recognize
which answer is correct by utilizing multiple
choice questions on warmups and the assessment.
Students must make a decision or judgment.
♦ Because the lesson
presentation is
online, students have
the opportunity to
access it at home.
♦ Students review
the presentation as
needed to ensure that
they will remember
the important
concepts.
♦ Students learn the
material on the
computer using the
SMART Notebook
software to help
them manipulate
parent graphs. They
then take the test and
complete all
activities at the
18.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 18
Yes/no recognition: Determine if the relation is a
function.
Forced choice recognition: Multiple choice
assessments.
♦ Offering opportunities for encoding
specificity: The lesson is entirely technology
based and all assessments are technologybased.
Whatever cues 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 lots of practice
on previously learned material through the warm
up activities, so retroactive interference
(interference from newly learned material) is
counteracted.
Offering opportunities to counteract proactive
interference: The lesson has teachers signal key
ideas and definitions which counteract proactive
interference or when previous learned material
interferes with what students are trying to learn
now.
computer with the
notebook page and
graphic organizer at
their disposal.
♦ Students use the
notetaking guide
and elaborately take
notes in own words.
♦ Students are state
dependent learners.
They do not take a
drug that might
cause drowsiness
during learning.
19.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 19
Sample Slide A
Slidefrom SlideRocketfrom Function Families Presentation
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”.
20.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 20
Sample Slide B
Slide from SlideRocketPresenting Vertical Shift from Function Families Presentation
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
21.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 21
Sample Slide C
Slide from SlideRocketPresenting Vertical Reflection from Function Families Presentation
BUZZ SLEEPING
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
front means that he is
in the awake position.
This is Buzz asleep
at his parent's
house.
22.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 22
Sample Slide
Slide from SlideRocketIntroducing “Linus” from Function Families Presentation
Introduction of Function Animals
Animal Name: “Linus”
Function Name: Linear Function
Graph Name: Line
Math Symbol: x
Animal Symbol: see below
23.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 23
Sample Slide
Slide from SlideRocketIntroducing “Abby” from Function Families Presentation
Introduction of Function Animals
Animal Name: “Abby”
Function Name: Absolute Value Function
Graph Name: Absolute Value
Math Symbol: x
Animal Symbol: see below
24.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 24
Sample Slide
Slide from SlideRocketIntroducing “Curt” from Function Families Presentation
Introduction of Function Animals
Animal Name: “Curt”
Function Name: Cubic
Graph Name: Cubic
Math Symbol: x3
Animal Symbol: see below
25.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 25
Sample Slide
Slide from SlideRocketIntroducing “Squirm” from Function Families Presentation
Introduction of Function Animals
Animal Name: “Squirm”
Function Name: Square Root Function
Graph Name: Radical
Math Symbol:
Animal Symbol: see below
26.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 26
Sample Slide
Slide from SlideRocketIntroducing “Rachel” from Function Families Presentation
Introduction of Function Animals
Animal Name: “Rachel”
Function Name: Rational Function
Graph Name: Rational
Math Symbol:
Animal Symbol: see below
2
4
3
27.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 27
Sample Slide
Slide from SlideRocketIntroducing “Quinton” from Function Families Presentation
Introduction of Function Animals
Animal Name: “Quinton”
Function Name: Quadratic Function
Graph Name: Parabola
Math Symbol: x2
Animal Symbol: (see below)
28.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 28
Sample Warmup QuizA
Warmup QuizusingSMART Notebook on the Basic Behaviors of Functions
29.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 29
Sample Notetaking Guide A
Notetaking Guide for the Behavior of Basic Parent Graphs
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
• Lists and tables
• Space out facts
SUMMARY
(After Class)
• In own words
• Original examples
• Most important key ideas
• Accurate phrases for quick reference
30.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 30
Sample Graphic OrganizerA
Organizeron Google Documents Categorizing Connections Between Functions Animals and
Algebraic Functions
Fill in the
organizer
according to the
information you
viewed during the
presentation.
Animal
Name
Animal
Symbol
Math
Symbol
Function
Name
Name of
Graph
31.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 31
Sample Graphic OrganizerA
Organizer on Google Documents Categorizing Relationships Between Behaviors of Functions
Animals and Behaviors of Algebraic Functions
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
32.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 32
Sample Practice WorksheetA
Practice Worksheet on Google Documents Relating the Graph of a Function to an Appropriate
OneStep Equation Using Cues from the Function Animals
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
33.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 33
Sample Practice WorksheetB
Practice Worksheet on Google Documents Relating the Graph of a Function to an Appropriate
Equation Using Cues from the Function Animals
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
Quadratic + 6 X2
f(x) = 6x2
34.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 34
f(x) = + 5 x2
 6
Sample Worksheet C
35.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 35
Practice Worksheet on Google Documents Relating the Graph of a Function to an Appropriate
Equation Using Cues from the Function Animals
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
36.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 36
Sample Practice WorksheetD
Practice Worksheet on Google Documents Relating the Equation of a Function to an
Appropriate Graph Using Cues from the Function Animals
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_________
37.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 37
Sample Assessment Review or Extra Practice Activity A
Review Activity on Shifting Parent Graphs Completed with Cues from Behaviors of Function
Animals
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
38.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 38
Sample Additional Activity B, p. 1
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
(xvalue).
2. Using the Internet, research each of the famous people and record
their ages in the appropriate column in the chart (yvalue).
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 xvalue 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?
39.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 39
Sample Additional Activity B, p. 2
Activity on Linear Regression Which Serves as an Additional Activity
“Extra Time” Activity
Basics of Linear Regression
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 your TI83 Plus graphing calculator.
11. Have the calculator 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?
40.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 40
Sample Additional Activity B, p. 3
Activity on Linear Regression Which Serves as an Additional Activity
“Extra Time” Activity
Basics of Linear Regression
Page 3
Famous Person
Estimated Age
xvalue
Actual Age
yvalue
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)
41.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 41
Sample Assessment Questions A, p. 1
Sample Assessment Questions for Functions Families Copied from SMART Notebook to be
Used with Senteo FreeResponse System
42.
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 42
Sample AssessmentA, p. 2
Sample Assessment Questions for Functions Families Copied from SMART Notebook to be
Used with Senteo FreeResponse System
Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.
Be the first to comment