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Technology Lesson Plan Assignment: Quadratice Functions
 

Technology Lesson Plan Assignment: Quadratice Functions

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    Technology Lesson Plan Assignment: Quadratice Functions Technology Lesson Plan Assignment: Quadratice Functions Presentation Transcript

    • Quadratic Functions By Dan Art Technology Infused Lesson Plan:
    • Quadratic Functions
      • Grade Level: 9 th grade regular class
      • Subject Area: Integrated Algebra
      • Topics Addressed : Quadratic Functions
      • Tools used:
        • SMART Notebook Software
        • TI-Smartview Software
        • Online Graphing Calculator
        • TI-83 Plus Graphing Calculators (Class set)
        • Online Resources such as RegentsPrep.org
    • Description of Unit
      • Purpose:
        • Students will have the opportunity learn about Quadratic Functions from both the algebraic & graphing standpoints
          • * Most of the technology used in this unit with be used during the graphing half of the unit
        • Students will be able to make connections between functions algebraically and graphically
        • Students will integrate the use of technology into their understanding of mathematical concepts
    • Description of Unit
      • Prior Knowledge:
        • Students have just finished their unit on Factoring using the three main methods (GCF, DOTS, & By Grouping), so they should be primed and ready to solve quadratic equations algebraically
        • Students have used all of the necessary technologies in a previous unit on Linear Functions
          • Students should have a basic understanding of how to use:
            • TI-83 Plus Graphing Calculators
            • The Internet
    • Description of Unit
      • Task:
        • Students will learn to solve Quadratic functions algebraically
        • Students will learn to graph each function in class by hand and on their TI-83 Plus Graphing Calculator
        • For homework those students without a graphing 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 functions quicker and easier using technology
    • Procedures
      • Day 1:
        • Students will learn how to solve Quadratic equations EQUAL to zero algebraically.
      • Define: Quadratic Equations
      • Factor equations that are already set equal to zero
      • Check solutions
      ax 2 + bx + c = 0 x 2 – 3x – 28 = 0 (x-7)(x+4) = 0 x-7=0 x+4=0 +7 +7 -4 -4 x=7 x=-4 {7,-4}
    • Procedures
      • Day 2:
        • Students will learn how to solve Quadratic equations NOT equal to zero algebraically.
      x 2 – 7x = 28 -28 -28 x 2 – 3x – 28 = 0 (x-7)(x+4) = 0 x-7=0 x+4=0 +7 +7 -4 -4 x=7 x=-4 {7,-4}
      • Set equations not already equal to zero, equal to zero
      • Once equal to zero, factor and solve the same way as previous lesson
      • Check solutions
    • Procedures
      • Day 3:
        • Students will learn how to solve problems that lead to quadratic equations algebraically.
      • Set up a quadratic equation from a word problem
      • Solve and check the solution(s) from the equation
      • Determine the appropriate root (solution) to use from the word problem
    • Procedures
      • Day 4:
        • Students will learn about Quadratic Functions (Parabolas) graphically
      • Identify the equation of a Parabola (quadratic equation)
      • Graph a parabola given it’s domain
      • Identify the coordinates of the turning point & if it’s a min. or max.
      • Identify if the parabola opens upward or downward from the equation
      y = ax 2 + bx + c
    • Procedures
      • Day 4 (continued):
        • Students will learn about Quadratic Functions (Parabolas) graphically
      • Teacher: SMART Notebook Software & TI-Smart View Software
      • Students: TI-83 Plus Graphing Calculators (Class set)
        • Teacher demonstrates the simplicity of graphing up at the board using the SMART Notebook Software (contains great visuals in gallery)
        • While students use their TI-83 Plus Graphing Calculators, the teacher uses TI-Smart View Software to model in the front of the room
    • Procedures
      • Day 5:
        • Students will learn about Quadratic Functions (Parabolas) graphically
      • After exposing students to parabolas in the previous lesson and mentioning the connections between parabolas and quadratic equations, the TI-83 Plus Graphing Calculators become much more involved in this lesson
      • Using the Graphing Calculator, we will go over the connections between the Y= screen, table, and graph
    • Procedures
      • Day 5 (continued):
        • Students will learn about Quadratic Functions (Parabolas) graphically
      • Students become comfortable with their graphing calculators, come up to the Intelliboard and demonstrate using the TI-SmartView, then the SMART Notebook Software.
      • HW – students who don’t own a graphing calculator at home will use a great free Online Graphing Calculator
        • No student will miss out on the opportunity to use technology
        • 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 use the graphing calculators for their HW
        • This is a resource found by one of my students, I always encourage my students to look for useful technologies
    • Procedures
      • Day 6:
        • Students will learn the effects of changing the coefficient or constant of a quadratic equation has on the parabola
      • Discovery lessons like this are much easier when using technologies like these. As a teacher you are able to visually display more examples up at the board.
      • Because all of the students have graphing calculators, they are able to go through so many more examples and see what happens when you change different parts of the quadratic equations.
      • What happens to the graph, table, and equation (always making the connections)
      • The teacher is able to step back from the spotlight and let their students discover and teach each other, the teacher circulates lending a helping hand
    • Procedures
      • Day 7: Presentation Day
        • Students will present their Graphing Quadratic Functions Group Presentations
      • Students have the opportunity to present (in small groups) on any topic covered in the Graphing Portion of this Quadratics unit
      • Students are given a rubric to help them understand the teacher’s expectations
      • Working on these presentations and observing their classmates’ presentations will help prepare them for the unit test
      • Day 8: Unit Test
        • -- Students will take a full period unit test on Quadratic Functions
    • Resources
      • Textbook:
        • Gantert, Ann X. (2007). AMSCO’s Integrated Algebra 1. New York, NY: AMSCO School Publications, Inc.
      • Software:
        • SMART Notebook Software & TI-SmartView
      • Web Resources:
        • Online Graphing Calculator - http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
      • Other :
        • TI-83 Plus Graphing Calculators, lined & graph paper, rulers, pencils
    • Teacher Preparation
      • 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 work
      • 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 the way if not used properly
      • For this lesson specifically:
        • 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 giving them the URL)
        • 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 open
        • 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 doesn’t have the Internet at home
    • Student Centered Learning Activities
      • Much of the graphing portion of the unit is student-centered
      • Students are to work in pairs or small groups and together discover the many different connections and make predictions
      • Each student has their own calculator, this makes it very easy for smooth transitions from lecture, to pair/group work, to student centered learning
      • So often in Math it is the top students in the class discovering new ideas, but this unit like other graphing units I have found allow all of the students a chance to discover (so many discoveries, some easier for visual learners, others for auditory, and other for kinesthetic learners)
    • Evaluation
      • Quadratic Functions Unit Test
      • Graphing Quadratic Functions Group Presentation Rubric
    • Evaluation (continued) Graphing Quadratic Functions Presentation Rubric Inadequate understanding of mathematical concepts Moderate understanding of mathematical concepts Adequate understanding of mathematical concepts Advanced understanding of mathematical concepts Understanding of Material It is difficult to figure out the purpose of the presentation. There are a few lapses in focus, but the purpose is fairly clear. Establishes a purpose early on and maintains focus for most of the presentation. Establishes a purpose early on and maintains a clear focus throughout. The audience knows from the beginning exactly what they will learn. Point of View - Purpose Lack of Technology Technology was Ineffective Technology helped presentation Technology effectively enhanced presentation Integration of Technology Presentation was less than 1 minute Length of presentation was 1-3 minutes Length of presentation was below 3-5 minutes Length of presentation was 5-10 minutes Duration of Presentation 1 2 3 4 CRITERIA TO BE EVALUATED
    • Higher Order Thinking
      • Knowledge
        • Students will learn many definitions in this unit (quadratic equation, parabola, turning point, root, etc)
      • Comprehension
        • 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)
      • Application
        • Students will be able to properly graph a parabola based on the provided information
      • Analysis
        • Students will be able to compare and contrast the difference between changing a coefficient vs. changing a constant has on the parabola
      • Synthesis
        • Students will be able to formulate a quadratic equation when given the table of values or graph or the parabola
      • Evaluation
        • Students will be able to predict what effect a change to a coefficient or constant of a quadratic equation has on a parabola
    • New York Standards
      • Algebra Strand
        • A.A.8 Analyze and solve verbal problems that involve quadratic equations
        • A.A.11 Solve a system of one linear and one quadratic equation in two variables, where only factoring is required 
              • Note: The quadratic equation should represent a parabola and the solution(s) should be integers.
        • A.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equations
        • A.A.27 Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots
        • A.A.28 Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression
        • A.A.41 Determine the vertex and axis of symmetry of a parabola, given its equation  (See A.G.10 )
    • New York Standards (continued)
      • Geometry Strand
        • A.G.4 Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions
        • A.G.8 Find the roots of a parabolic function graphically  Note: Only quadratic equations with integral solutions.
        • A.G.10 Determine the vertex and axis of symmetry of a parabola, given its graph (See A.A.41)  Note: The vertex will have an ordered pair of integers and the axis of symmetry will have an integral value.
    • ISTE Standards
      • Basic operations and concepts
        • Students demonstrate a sound understanding of the nature and operation of technology systems.
        • Students are proficient in the use of technology.
      • Social, 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 develop positive attitudes toward technology uses that support lifelong learning, collaboration, personal pursuits, and productivity.
    • ISTE Standards (continued)
      • Technology productivity tools
        • Students use technology tools to enhance learning, increase productivity, and promote creativity.
        • Students use productivity tools to collaborate in constructing technology-enhanced models, prepare publications, and produce other creative works.
      • Technology problem-solving and decision-making tools
        • Students use technology resources for solving problems and making informed decisions.