Technology Lesson Plan Assignment: Quadratice Functions

Quadratic FunctionsQuadratic Functions

Technology Infused Lesson Plan:Technology Infused Lesson Plan:

By Dan ArtBy Dan Art


• Grade Level:Grade Level: 9 9thth grade regular class grade regular class• Subject Area:Subject Area: Integrated Algebra Integrated Algebra• Topics AddressedTopics Addressed: Quadratic Functions: Quadratic Functions• Tools used: Tools used:

– SMART Notebook SoftwareSMART Notebook Software– TI-Smartview SoftwareTI-Smartview Software– Online Graphing Calculator– TI-83 Plus Graphing Calculators (Class set)TI-83 Plus Graphing Calculators (Class set)– Online Resources such as RegentsPrep.orgOnline Resources such as RegentsPrep.org

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

Description of UnitDescription of Unit

• Purpose: Purpose: – Students will have the opportunity learn about Students will have the opportunity learn about

Quadratic Functions from both the algebraic & Quadratic Functions from both the algebraic & graphing standpointsgraphing standpoints

* Most of the technology used in this unit with be used during * Most of the technology used in this unit with be used during the graphing half of the unitthe graphing half of the unit

– Students will be able to make connections between Students will be able to make connections between functions algebraically and graphically functions algebraically and graphically

– Students will integrate the use of technology into their Students will integrate the use of technology into their understanding of mathematical conceptsunderstanding of mathematical concepts


• Prior Knowledge: Prior Knowledge: – Students have just finished their unit on Factoring Students have just finished their unit on Factoring

using the three main methods (GCF, DOTS, & By using the three main methods (GCF, DOTS, & By Grouping), so they should be primed and ready to Grouping), so they should be primed and ready to solve quadratic equations algebraicallysolve quadratic equations algebraically

– Students have used all of the necessary technologies Students have used all of the necessary technologies in a previous unit on Linear Functions in a previous unit on Linear Functions

• Students should have a basic understanding of how to use:Students should have a basic understanding of how to use:– TI-83 Plus Graphing CalculatorsTI-83 Plus Graphing Calculators– The InternetThe Internet


• Task:Task:– Students will learn to solve Quadratic functions Students will learn to solve Quadratic functions

algebraically algebraically – Students will learn to graph each function in class by Students will learn to graph each function in class by

hand and on their TI-83 Plus Graphing Calculatorhand and on their TI-83 Plus Graphing Calculator– For homework those students without a graphing For homework those students without a graphing

calculator at home will be able to use a very helpful calculator at home will be able to use a very helpful online graphing calculator, which contains all of the necessary tools they will need

– Students will be shown tricks to solve Quadratic Students will be shown tricks to solve Quadratic functions quicker and easier using technologyfunctions quicker and easier using technology

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

ProceduresProcedures• Day 1: Day 1:

– Students will learn how to solve Quadratic Students will learn how to solve Quadratic equations EQUAL to zero algebraically.equations EQUAL to zero algebraically.

•Define: Quadratic EquationsDefine: Quadratic Equations

•Factor equations that are already Factor equations that are already set equal to zeroset equal to zero

•Check solutionsCheck solutions

xx22 – 3x – 28 = 0 – 3x – 28 = 0

(x-7)(x+4) = 0(x-7)(x+4) = 0

x-7=0 x+4=0x-7=0 x+4=0

+7 +7 -4 -4+7 +7 -4 -4

x=7 x=-4x=7 x=-4

{7,-4}{7,-4}

axax22 + bx + c = 0 + bx + c = 0


– Students will learn how to solve Quadratic Students will learn how to solve Quadratic equations NOT equal to zero algebraically.equations NOT equal to zero algebraically.

xx22 – 7x = 28 – 7x = 28

-28 -28-28 -28

xx22 – 3x – 28 = 0 – 3x – 28 = 0

(x-7)(x+4) = 0(x-7)(x+4) = 0

x-7=0 x+4=0x-7=0 x+4=0

+7 +7 -4 -4+7 +7 -4 -4

x=7 x=-4x=7 x=-4

{7,-4}{7,-4}

•Set equations not already equal Set equations not already equal to zero, equal to zeroto zero, equal to zero

•Once equal to zero, factor and Once equal to zero, factor and solve the same way as previous solve the same way as previous lessonlesson

•Check solutionsCheck solutions


– Students will learn how to solve problems that Students will learn how to solve problems that lead to quadratic equations algebraically.lead to quadratic equations algebraically.

•Set up a quadratic equation from a word problemSet up a quadratic equation from a word problem

•Solve and check the solution(s) from the equationSolve and check the solution(s) from the equation

•Determine the appropriate root (solution) to use from the word Determine the appropriate root (solution) to use from the word problemproblem


– Students will learn about Quadratic Functions Students will learn about Quadratic Functions (Parabolas) graphically(Parabolas) graphically

•Identify the equation of a Identify the equation of a Parabola (quadratic equation)Parabola (quadratic equation)

•Graph a parabola given it’s Graph a parabola given it’s domaindomain

•Identify the coordinates of the Identify the coordinates of the turning point & if it’s a min. or turning point & if it’s a min. or max.max.

•Identify if the parabola opens Identify if the parabola opens upward or downward from the upward or downward from the equation equation

y = axy = ax22 + bx + c + bx + c

ProceduresProcedures• Day 4 (continued): Day 4 (continued):


•Teacher: SMART Notebook Software & TI-Smart View SoftwareTeacher: SMART Notebook Software & TI-Smart View Software

•Students: TI-83 Plus Graphing Calculators (Class set)Students: TI-83 Plus Graphing Calculators (Class set)

•Teacher demonstrates the simplicity of graphing up at the board Teacher demonstrates the simplicity of graphing up at the board using the SMART Notebook Software (contains great visuals in using the SMART Notebook Software (contains great visuals in gallery)gallery)

•While students use their TI-83 Plus Graphing Calculators, the While students use their TI-83 Plus Graphing Calculators, the teacher uses TI-Smart View Software to model in the front of the teacher uses TI-Smart View Software to model in the front of the roomroom



•After exposing students to parabolas in the previous lesson and After exposing students to parabolas in the previous lesson and mentioning the connections between parabolas and quadratic mentioning the connections between parabolas and quadratic equations, the TI-83 Plus Graphing Calculators become much equations, the TI-83 Plus Graphing Calculators become much more involved in this lessonmore involved in this lesson

•Using the Graphing Calculator, we will go over the connections Using the Graphing Calculator, we will go over the connections between the Y= screen, table, and graphbetween the Y= screen, table, and graph

ProceduresProcedures• Day 5 (continued): Day 5 (continued):


•Students become comfortable with their graphing calculators, Students become comfortable with their graphing calculators, come up to the Intelliboard and demonstrate using the TI-come up to the Intelliboard and demonstrate using the TI-SmartView, then the SMART Notebook Software.SmartView, then the SMART Notebook Software.•HW – students who don’t own a graphing calculator at home will HW – students who don’t own a graphing calculator at home will use a great free Online Graphing Calculatoruse a great free Online Graphing Calculator

•No student will miss out on the opportunity to use technologyNo student will miss out on the opportunity to use technology•If they don’t have Internet at their home, than the school’s If they don’t have Internet at their home, than the school’s library has Internet, or they can stay after school with me and library has Internet, or they can stay after school with me and use the graphing calculators for their HWuse the graphing calculators for their HW•This is a resource found by one of my students, I always This is a resource found by one of my students, I always encourage my students to look for useful technologiesencourage my students to look for useful technologies


– Students will learn the effects of changing the Students will learn the effects of changing the coefficient or constant of a quadratic equation coefficient or constant of a quadratic equation has on the parabola has on the parabola

•Discovery lessons like this are much easier when using Discovery lessons like this are much easier when using technologies like these. As a teacher you are able to visually technologies like these. As a teacher you are able to visually display more examples up at the board.display more examples up at the board.•Because all of the students have graphing calculators, they are Because all of the students have graphing calculators, they are able to go through so many more examples and see what happens able to go through so many more examples and see what happens when you change different parts of the quadratic equations.when you change different parts of the quadratic equations.•What happens to the graph, table, and equation (always making What happens to the graph, table, and equation (always making the connections)the connections)•The teacher is able to step back from the spotlight and let their The teacher is able to step back from the spotlight and let their students discover and teach each other, the teacher circulates students discover and teach each other, the teacher circulates lending a helping handlending a helping hand

ProceduresProcedures• Day 7: Presentation DayDay 7: Presentation Day

– Students will present their Graphing Quadratic Students will present their Graphing Quadratic Functions Group Presentations Functions Group Presentations • Students have the opportunity to present (in small groups) on any topic Students have the opportunity to present (in small groups) on any topic covered in the Graphing Portion of this Quadratics unitcovered in the Graphing Portion of this Quadratics unit•Students are given a rubric to help them understand the teacher’s Students are given a rubric to help them understand the teacher’s expectationsexpectations•Working on these presentations and observing their classmates’ Working on these presentations and observing their classmates’ presentations will help prepare them for the unit testpresentations will help prepare them for the unit test

• Day 8: Unit TestDay 8: Unit Test-- Students will take a full period unit test on -- Students will take a full period unit test on


ResourcesResources

• Textbook:Textbook: – Gantert, Ann X. (2007). AMSCO’s Integrated Algebra 1. New York, Gantert, Ann X. (2007). AMSCO’s Integrated Algebra 1. New York,

NY: AMSCO School Publications, Inc.NY: AMSCO School Publications, Inc.

• Software:Software: – SMART Notebook Software & TI-SmartView SMART Notebook Software & TI-SmartView

• Web Resources:Web Resources: – Online Graphing Calculator -Online Graphing Calculator - http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.htmlhttp://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

• OtherOther: : – TI-83 Plus Graphing Calculators, lined & graph paper, rulers, pencilsTI-83 Plus Graphing Calculators, lined & graph paper, rulers, pencils

Teacher PreparationTeacher Preparation• Technology is a great asset, but the best teacher knows never to Technology is a great asset, but the best teacher knows never to

depend on it, because you never know when it will “decide” not to depend on it, because you never know when it will “decide” not to workwork

• The teacher of course must feel comfortable with all technologies The teacher of course must feel comfortable with all technologies being used in order for it to add to the lesson, technology can get in being used in order for it to add to the lesson, technology can get in the way if not used properlythe way if not used properly

• For this lesson specifically: For this lesson specifically: – Make sure your Firewall does not block the Online Graphing Calculator Make sure your Firewall does not block the Online Graphing Calculator

so that you can demonstrate it to the class the right way (instead of just so that you can demonstrate it to the class the right way (instead of just giving them the URL)giving them the URL)

– It might be a good idea to have TI-SmartView open prior to the lesson, It might be a good idea to have TI-SmartView open prior to the lesson, so that you don’t have to wait for the program to openso that you don’t have to wait for the program to open

– At the beginning of the year or at least unit, find out which of your At the beginning of the year or at least unit, find out which of your students has a graphing calculator at home and which of your students students has a graphing calculator at home and which of your students doesn’t have the Internet at home doesn’t have the Internet at home

Student Centered Learning ActivitiesStudent Centered Learning Activities

• Much of the graphing portion of the unit is student-Much of the graphing portion of the unit is student-centeredcentered

• Students are to work in pairs or small groups and Students are to work in pairs or small groups and together discover the many different connections and together discover the many different connections and make predictionsmake predictions

• Each student has their own calculator, this makes it very Each student has their own calculator, this makes it very easy for smooth transitions from lecture, to pair/group easy for smooth transitions from lecture, to pair/group work, to student centered learningwork, to student centered learning

• So often in Math it is the top students in the class So often in Math it is the top students in the class discovering new ideas, but this unit like other graphing discovering new ideas, but this unit like other graphing units I have found allow all of the students a chance to units I have found allow all of the students a chance to discover (so many discoveries, some easier for visual discover (so many discoveries, some easier for visual learners, others for auditory, and other for kinesthetic learners, others for auditory, and other for kinesthetic learners)learners)

EvaluationEvaluation

• Quadratic Functions Unit TestQuadratic Functions Unit Test

• Graphing Quadratic Functions Group Graphing Quadratic Functions Group Presentation RubricPresentation Rubric

Evaluation Evaluation (continued)(continued)

CRITERIA TO BE CRITERIA TO BE EVALUATEDEVALUATED

44 33 22 11

Duration of Duration of PresentationPresentation

Length of Length of presentation was 5-presentation was 5-10 minutes10 minutes

Length of Length of presentation was presentation was below 3-5 minutesbelow 3-5 minutes

Length of Length of presentation was 1-3 presentation was 1-3 minutesminutes

Presentation was Presentation was less than 1 minuteless than 1 minute

Integration of Integration of TechnologyTechnology

Technology Technology effectively enhanced effectively enhanced presentationpresentation

Technology helped Technology helped presentationpresentation

Technology was Technology was IneffectiveIneffective

Lack of TechnologyLack of Technology

Point of View - Point of View - PurposePurpose

Establishes a Establishes a purpose early on and purpose early on and maintains a clear maintains a clear focus throughout. focus throughout. The audience knows The audience knows from the beginning from the beginning exactly what they will exactly what they will learn. learn.

Establishes a Establishes a purpose early on and purpose early on and maintains focus for maintains focus for most of the most of the presentation. presentation.

There are a few There are a few lapses in focus, but lapses in focus, but the purpose is fairly the purpose is fairly clear. clear.

It is difficult to figure It is difficult to figure out the purpose of out the purpose of the presentation. the presentation.

Understanding of Understanding of MaterialMaterial

Advanced Advanced understanding of understanding of mathematical mathematical concepts concepts

Adequate Adequate understanding of understanding of mathematical mathematical conceptsconcepts

Moderate Moderate understanding of understanding of mathematical mathematical conceptsconcepts

Inadequate Inadequate understanding of understanding of mathematical mathematical conceptsconcepts

Graphing Quadratic Functions Presentation RubricGraphing Quadratic Functions Presentation Rubric

Higher Order ThinkingHigher Order Thinking• KnowledgeKnowledge

– Students will learn many definitions in this unit (quadratic equation, parabola, Students will learn many definitions in this unit (quadratic equation, parabola, turning point, root, etc)turning point, root, etc)

• ComprehensionComprehension– Students will be able to describe and discuss what a parabola will look like based Students will be able to describe and discuss what a parabola will look like based

on the provided information (quadratic equation or table of values)on the provided information (quadratic equation or table of values)• ApplicationApplication

– Students will be able to properly graph a parabola based on the provided Students will be able to properly graph a parabola based on the provided informationinformation

• AnalysisAnalysis– Students will be able to compare and contrast the difference between changing a Students will be able to compare and contrast the difference between changing a

coefficient vs. changing a constant has on the parabola coefficient vs. changing a constant has on the parabola • SynthesisSynthesis

– Students will be able to formulate a quadratic equation when given the table of Students will be able to formulate a quadratic equation when given the table of values or graph or the parabolavalues or graph or the parabola

• EvaluationEvaluation– Students will be able to predict what effect a change to a coefficient or constant Students will be able to predict what effect a change to a coefficient or constant

of a quadratic equation has on a parabolaof a quadratic equation has on a parabola

New York StandardsNew York Standards

• Algebra StrandAlgebra Strand– A.A.8A.A.8 Analyze and solve verbal problems that involve Analyze and solve verbal problems that involve

quadratic equationsquadratic equations – A.A.11A.A.11 Solve a system of one linear and one quadratic Solve a system of one linear and one quadratic

equation in two variables, where only factoring is equation in two variables, where only factoring is required required

Note: The quadratic equation should represent a parabola and the solution(s) Note: The quadratic equation should represent a parabola and the solution(s) should be integers.should be integers.

– A.A.26A.A.26 Solve algebraic proportions in one variable which result Solve algebraic proportions in one variable which result in linear or quadratic equationsin linear or quadratic equations

– A.A.27A.A.27 Understand and apply the multiplication property of zero to Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients solve quadratic equations with integral coefficients

and and integral rootsintegral roots– A.A.28A.A.28 Understand the difference and connection between roots of a Understand the difference and connection between roots of a

quadratic equation and factors of a quadratic quadratic equation and factors of a quadratic expressionexpression

– A.A.41A.A.41 Determine the vertex and axis of symmetry of a parabola, Determine the vertex and axis of symmetry of a parabola, given its equation (See A.G.10 )given its equation (See A.G.10 )

New York Standards New York Standards (continued)(continued)

• Geometry StrandGeometry Strand– A.G.4A.G.4 Identify and graph linear, quadratic (parabolic), Identify and graph linear, quadratic (parabolic),

absolute value, and exponential functions absolute value, and exponential functions – A.G.8A.G.8 Find the roots of a parabolic function graphically Note: Find the roots of a parabolic function graphically Note:

Only quadratic equations with integral solutions.Only quadratic equations with integral solutions.– A.G.10A.G.10 Determine the vertex and axis of symmetry of a Determine the vertex and axis of symmetry of a

parabola, given its graph (See A.A.41) Note: parabola, given its graph (See A.A.41) Note: The The vertex will have an ordered pair of integers and vertex will have an ordered pair of integers and the the axis of symmetry will have an integral value.axis of symmetry will have an integral value.

ISTE StandardsISTE Standards• Basic operations and conceptsBasic operations and concepts

– Students demonstrate a sound understanding of the nature and Students demonstrate a sound understanding of the nature and operation of technology systems. operation of technology systems.

– Students are proficient in the use of technology.Students are proficient in the use of technology.

• Social, ethical, and human issuesSocial, ethical, and human issues– Students understand the ethical, cultural, and societal issues related to technology. Students understand the ethical, cultural, and societal issues related to technology.

– Students understand the ethical, cultural, and societal issues related to technology.Students understand the ethical, cultural, and societal issues related to technology. – Students develop positive attitudes toward technology uses that support lifelong Students develop positive attitudes toward technology uses that support lifelong

learning, collaboration, personal pursuits, and productivity.learning, collaboration, personal pursuits, and productivity.

ISTE Standards ISTE Standards (continued)(continued)

• Technology productivity toolsTechnology productivity tools– Students use technology tools to enhance learning, increase Students use technology tools to enhance learning, increase

productivity, and promote creativity. productivity, and promote creativity. – Students use productivity tools to collaborate in constructing Students use productivity tools to collaborate in constructing

technology-enhanced models, prepare publications, and technology-enhanced models, prepare publications, and produce other creative works. produce other creative works.

• Technology problem-solving and decision-Technology problem-solving and decision-making toolsmaking tools – Students use technology resources for solving problems and Students use technology resources for solving problems and

making informed decisions. making informed decisions.