Technology based module cip martha townsend

FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 1

Cognitive Information Processing

Function Families

Martha Townsend

Georgia Southern University


Cognitive Information ProcessingFunction Families

Instructional Goals

Goals(Driscoll, 2005,

p. 71-110)

Methods of InstructionTechnology-Based Student Activities

Gain and keep the attention of students.

The students will start each day of class by watching an entertaining Slide Rocket Presentation on function families with color, audio, and animation.

The teacher will periodically walk around the lab and redirect students that are off-task.

The teacher will keep students focused on learning using SMART Sync™ classroom management software. The teacher will view each student’s computer screen on the teacher computer and monitor their activities. The teacher will interact with students through the management software to keep them engaged and on-task.

Incorporate relevant prior learning.

The students will complete a warm-up activity each day via Smart Notebook Software clickers. The questions on the warm-up 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 note-taking 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 follow a 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.

Students will 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 x-axis. Finally, the lesson will show students how to combine the steps for vertically manipulating a function.


Show students how to chunk related information.

The graphic organizers and note-taking guides will allow students to group the concepts into categories and manageable steps.

The activities will teach students inductive reasoning as they will 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 and their 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 warm-up activities and the test review.

The students will use the Senteo free-response system to access drill and practice on the basic concepts involved with functions.

The students will access a SMART Notebook file that will allow them to practice manipulating the graphs of functions in the coordinate plane.


Prior Relevant Learning Objectives

Students should

have already:

At the beginning of this lessonstudents 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, x|y 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 x|y charts of functions from their equations and graph these

functions in the coordinate plane.• Graph functions using a TI-83 Plus graphing calculator.

Learning Objectives for Function Family Lesson

Students completingthis lesson will:

Students that successfully completethis 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 graphs of 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.


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• x-coordinate• y-coordinate• x|y chart

• Input• Output• Table• Ordered pair• Graph• Domain• Range• Vertical line test

Learning Focus for Function Family Lesson

Essential QuestionsKey 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 are the parent graphs of linear, quadratic, cubic, absolute value, and radical functions vertically 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


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.7Characteristics 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 an Accelerated 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 free-response system, Google Drive, and TI-83 Plus graphing calculators.




Learning Environment

Student Activities UsingTechnology-Based

Instruction(Samples of some of the activities are attached.)

• Warm-ups on previously learned material• Note-taking 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• Technology-based instruction• Audio and video for delivery of content• Differentiated sources

o Senteo free-response system activitieso SMART Notebook softwareo Social networkingo TI-83 Plus graphing calculatorso Google driveo 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 note-taking guides and graphic organizers, and their collaboration with their peers and teacher (see rubric). They will receive separate grades on their warm-ups, 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.


Lesson Management

Day Lesson Activities Homework

1

• Warm-up Day 1• Transition of Buzz Presentation Day 1• Graphic organizer• Note-taking guide• Practice worksheet

• Review Presentation from website

• Review notes• Homework practice sheet

2

• Warm-up Day 2• Transition of Buzz Presentation Day 2• Graphic organizer• Note-taking guide• Practice worksheet• Applet activity



3

• Warm-up Day 3• Transition of Buzz Presentation Day 3• Graphic organizer• Note-taking guide• Practice worksheet• Applet activity



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 TI-83 Plus graphing calculators to practice vertical manipulation of functions.

Explain

• Students will complete graphic organizers and note-taking 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.


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 well-written responses with evidence supporting their position/opinion on the topic.


Function Families Lesson Rubric

Limited1

Developing2

Proficient3

Exemplary4

CLASSROOM ATTENTION

Focuses attention on all aspects of the lesson

Focusing attention allows for the processing of important information while ignoring impertinent information.

Cannot focus attention

♦ Does not evaluate material when promptedby teacher♦ Cannot maintain a focus of attention despite cognitive efforts which may cause some level of anxiety

Requires redirection

♦ Evaluates material only when promptedby teacher♦ Requires considerable degree of cognitive effort to focus attention

Requires minimal redirection

♦ Recognizes teachercues toevaluate material♦ Requires little cognitive demand for successful completion

Maintains strong focus and attention on all components of the lesson

♦ Systematicallyevaluates materialwithout needing the cues from the teacher♦ Demands self-monitoring or self-regulation 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 identifySome similarities anddifferences 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 identifyspecific similarities anddifferences betweenconceptsgeneralizations♦ Struggles with general procedures and solving problems

♦ Has some ability to make connections between concepts or meaning to the procedure being used.♦ Student can identifyspecific similarities anddifferences betweenconceptsand makegeneralizations♦ Follows general procedures but has to put a lot of thought into it

♦ Experimentswith new information and proceduresand uses them indifferent ways♦ Identifiesspecific similarities anddifferences betweenconcepts and can makegeneralizations,andidentify behaviors♦ Follows general procedures and can do so with ease


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♦ Misunderstands 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 responses rather than establishing 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 theanswer

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

♦ Createsgraphic 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 areaccurate or clear♦ Attempts to show organization but struggles

Completes organizers with minor problems with organization

♦ Creates organizers thataccurately representthe concepts andunderstanding of the topic

♦ Displays a relatively good sense of organization

Independently selects an appropriate organizational strategy

♦ Creates organizers thataccurately depictthe concepts andunderstanding of the topic but can also do it indifferent ways♦ Creates highly organized and effective organizers

NOTE-TAKING GUIDES

Identifies, highlights, and labels key information and ideas

♦ Does not accurately seek out needed information♦ Fails to use the most important techniques for gathering

♦ 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

♦ Insightfully determines the types of information that would be beneficial and effectively seeks out that information.


When students focus their attention on certain key issues in the lesson, they gain assistance in determining the importance of new information.

information gather information

♦ Effectively uses a variety of information-gathering techniques and information resources

NOTE-TAKING GUIDES

Labels and categorizes notes

When students adapt and 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 ranksdataThere are some errors, such as listing unimportant information and missing important details or simply having incorrect information.

Classifies information

.♦Analyzes information in detail

Classifiesinformation andmakes comparisons

♦ Accurately and insightfully processes information

NOTE-TAKING 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

Summarizesinformation

♦ Puts some of the material in own words♦ Sets up material but without examples

Createsrelationships anddrawsconclusionsfrominformation

♦ Puts almost all of the material in own words♦ Sets up material and has some original examples

Independentlyapplieslearning tonew anddifferent situations

♦ Condenses the material and puts it all in own words.♦ Sets up material with original examples


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♦ Explainsinformation on agraph, table, orchart but only with assistance

♦ Makes some significant errors in interpreting the information♦ Explainstheinformation on agraph, table orchart, but it may notbe clear or relatedto the requirements

♦ Understands and gives interpretation of most of the information♦ Explains theinformation related to the conceptsin a clear waythat iseasily understood

♦ Interprets all of the information in accurate and highly intuitive ways♦ Explainsthe informationrelated to the conceptsand drawsconclusions from itwhich areunderstandable toanother

POSTS

Communication

When students collaborate with other students and teachers, it creates situations where they can elaborate and self-question. 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/ordisagreementof 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


Justification of Cognitive Information Processing(Processing, storage, and retrieval of knowledge in the mind)

(Driscoll, 2005, p. 71-110)

CIPProcess

Teaching StrategiesStudent 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 off-task.♦ 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 free-response system• TI-83 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 signal important information.♦ Students recognize the complexity of new information and devote a greater amount of attention to learning it.

Automaticity

Devoting little attention to a task because

♦ Questioning: The teacher asks students individual questions on the basics of functions through SMART Sync™ and Senteo free-response system.♦ Offering practice of basic skills: Teachers

♦ Students overlearn the material by constantly studying.♦ Students continue to practice even


the basic skills that are involved in completing it are habitual

assign warm-up 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.

though they may be getting the problems correct.♦ 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 non-examples: This lesson supports feature analysis meaning that it shows an example of a function then makes students generate a differing or counter-examples. This helps students understand what is meaningful and critical when analyzing a function.♦ Offering extensive practice: The lesson offers an extensive amount of practice on the graphing of functions using a 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 free-response system and give immediate feedback so that they do not judge students based on preconceived notions.

♦ Students focus on the material in the review warm-ups 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 short-term 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 note-taking guide.♦ Students take the complex information from the lesson presentation and break it down into manageable parts.

Rehearsal

Repeating informatio

♦ 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

♦ Students complete a variety of practice problems after each lesson presentation.


n in an effort to maintain it

different problem situations. ♦ 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 names of 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 non-examples and have them create their own.♦ Promoting reasoning techniques: Inductive (example/experience --> definition) and deductive (definition --> examples)♦ Presenting propositioning techniques: The lesson gives students interrelated groups of concepts and relationships such as when they learn the properties of graphs. It has students fill in and analyze if/then statements.♦ Teaching scripting: The lesson develops general information about a series of steps

♦ 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 note-taking guide to take notes in their own words.♦ Students use the note-taking guides to summarize the information.♦ Students impose their own subjective organization♦ Students post inferential questions♦ Students include study questions in their notes as they fill in the note-taking guide.


involved 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 which graphs and graph manipulations are analyzed.♦ Delivering programming: This lesson provides a set of rules that define what students should do 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 real-world.♦ Modeling: The parent graphs or algebraic equations of function describe characteristics of 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.

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 warm-ups and the assessment. Students must make a decision or judgment.

Yes/no recognition: Determine if the relation is a function.Forced choice recognition: Multiple choice assessments.

♦ 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 computer with the notebook page and graphic organizer at their disposal.


♦ Offering opportunities for encoding specificity: The lesson is entirely technology-based and all assessments are technology-based. 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.

♦ Students use the note-taking 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.


Sample Slide A

Slide from SlideRocket from 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”.


Sample Slide B

Slide from SlideRocket Presenting Vertical Shift from Function Families Presentation

BUZZ VISITING FRIENDSVertical 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


Sample Slide C

Slide from SlideRocket Presenting Vertical Reflection from Function Families Presentation

BUZZ SLEEPINGVertical 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.


Sample Slide

Slide from SlideRocket Introducing “Linus” from Function Families Presentation

Introduction of Function Animals

Animal Name: “Linus” Function Name: Linear FunctionGraph Name: LineMath Symbol: xAnimal Symbol: see below


Sample Slide

Slide from SlideRocket Introducing “Abby” from Function Families Presentation


Animal Name: “Abby” Function Name: Absolute Value FunctionGraph Name: Absolute ValueMath Symbol: |x|Animal Symbol: see below


Sample Slide

Slide from SlideRocket Introducing “Curt” from Function Families Presentation


Animal Name: “Curt” Function Name: CubicGraph Name: CubicMath Symbol: x3

Animal Symbol: see below


Sample Slide

Slide from SlideRocket Introducing “Squirm” from Function Families Presentation


Animal Name: “Squirm” Function Name: Square Root FunctionGraph Name: RadicalMath Symbol: √ xAnimal Symbol: see below


Sample Slide

Slide from SlideRocket Introducing “Rachel” from Function Families Presentation


Animal Name: “Rachel” Function Name: Rational FunctionGraph Name: Rational

Math Symbol:1x

Animal Symbol: see below

2

4

-3


Sample Slide

Slide from SlideRocket Introducing “Quinton” from Function Families Presentation


Animal Name: “Quinton” Function Name: Quadratic FunctionGraph Name: ParabolaMath Symbol: x2

Animal Symbol: (see below)


Sample Warm-up Quiz A

Warm-up Quiz using SMART Notebook on the Basic Behaviors of Functions


Sample Note-taking Guide A

Note-taking 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


Sample Graphic Organizer A

Organizer on 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

AnimalSymbol

Math Symbol

Function Name

Name of Graph


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 youngerUpside

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

Sample Graphic Organizer A

Organizer on Google Documents Categorizing Relationships Between Behaviors of Functions Animals and Behaviors of Algebraic Functions


Sample Practice Worksheet A

Practice Worksheet on Google Documents Relating the Graph of a Function to an Appropriate One-Step 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 NameAwake

or asleep

Age of Animal

MathSymbol

PossibleEquation

Quadratic + 6 X2 f(x) =

6x2

Sample Practice Worksheet B


Practice Worksheet on Google Documents Relating the Graph of a Function to an Appropriate Equation Using Cues from the Function Animals


Function

Notation=

AwakeOr

Asleep

(+ or -)

Possible

Age

Function

Symbol

+-

or“nothi

ng”

Vertical

Position

f(x)

= + 5 x2 - 6

Sample Worksheet C



Awake + Asleep -

Age of Animal

MathSymbol

Up +Down –

# of units

PossibleEquation

- 7 √x - 5 f(x) = -7√x - 5

Practice Worksheet on Google Documents Relating the Graph of a Function to an Appropriate Equation 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 ofPossibleGraph

(in 1,2,3,4 order)

Draw Graph

Awake or Asleep

Draw AnimalAt Age

DrawParentGraph

How manyUnits Up or

Down?

3rd 2nd 1st 4th

(example)

animal: Quinton .

Down 7

y = - (1/4) x3 + 2

animal_________

y = -5 x + 2

animal_________

y = (1/3) √x - 5

animal_________

Sample Practice Worksheet D

Practice Worksheet on Google Documents Relating the Equation of a Function to an Appropriate Graph Using Cues from the Function Animals


Sample Assessment Review or Extra Practice Activity A

Review Activity on Shifting Parent Graphs Completed with Cues from Behaviors of Function Animals

GraphAwake or

asleepPossible Age of

AnimalShape ofthe 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

Sample Additional Activity B, p. 1


Activity on Linear Regression Which Serves as an Additional Activity

“Extra Time” ActivityBasics 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 using the estimate of their age as the x-value and the actual age as y-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 is true about this point?

5. Sketch a graph of the 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?



“Extra Time” Activity


Basics of Linear RegressionPage 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 TI-83 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?




“Extra Time” ActivityBasics of Linear Regression

Page 3

Famous PersonEstimated Age

x-valueActual 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)

Sample Assessment Questions A, p. 1


Sample Assessment Questions for Functions Families Copied from SMART Notebook to be Used with Senteo Free-Response System


Sample Assessment A, p. 2

Sample Assessment Questions for Functions Families Copied from SMART Notebook to be Used with Senteo Free-Response System

Technology based module cip martha townsend

Technology

Transcript of Technology based module cip martha townsend