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UNIVERSITY OF MAINE AT FARMINGTONCOLLEGE OF EDUCATION, HEALTH AND REHABILITATION
LESSON PLAN FORMATEDU 361 Secondary/Middle Math Methods
Teacher’s Name: Mrs. Hardy and Ms. Trefethen Lesson #: 1Grade Level: 8th Grade Numbers of Days: 1Topic: Quadratic equations and reallife application of parabolaRoom Arrangement: Long rows of tables to accommodate four students per row facing the front ofroom
PART I
Objectives:Students will understand that the graph of a quadratic equation changes when the coefficients of theequation changes.Students will know the definition of quadratic equation, its graph, and realworld application.Students will be able to recognize the reallife application of the graph of quadratic equations.Product: GeoGebra
Common Core State Standards (CCSS) Alignment (List Content Area, Grade Level, Domain(s), Standard(s), and Cluster(s))Content Area: AlgebraGrade Level: 9th GradeDomain: Reasoning with equations and inequalitiesCluster: Solve equations and inequalities in one variableStandards:4. Solve quadratic equations in one variable.
Which CCSS Mathematical Practice(s) will be addressed (list the number and the description):CCSS.Math.Practice.MP4 Model with mathematics.Mathematically proficient students can apply the mathematics they know to solve problems arising ineveryday life, society, and the workplace. In early grades, this might be as simple as writing an addition
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equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan aschool event or analyze a problem in the community. By high school, a student might use geometry tosolve a design problem or use a function to describe how one quantity of interest depends on another.Mathematically proficient students who can apply what they know are comfortable making assumptionsand approximations to simplify a complicated situation, realizing that these may need revision later. Theyare able to identify important quantities in a practical situation and map their relationships using suchtools as diagrams, twoway tables, graphs, flowcharts and formulas. They can analyze thoserelationships mathematically to draw conclusions. They routinely interpret their mathematical results inthe context of the situation and reflect on whether the results make sense, possibly improving the modelif it has not served its purpose.
Rationale: (for both the CCSS standards and the practice(s))In this lesson, we will focus on the definition and graph of quadratic equations. We will also introducethe realworld application of the graphs of quadratic equations. Students will be able to compare andcontrast quadratic equations and linear equations using Venn Diagram. Students will be able to imagineand analyze possible reallife applications of the graph of quadratic equations. Students willdemonstrate their understanding of the relationship between the coefficients and the graph of quadraticequation through reallife application.
Assessments
Pre AssessmentHook activityAttribute gameWe will play an Attribute game as a whole class to assess students’ understanding on linear equationsand quadratic equations. See Teaching and Learning SequenceConceptAttainmentHook/PreAssessmentAttribute Game
Formative (Assessment for Learning)Section I – checking for understanding during instructionThinkpairshare:Students will brain storm possible application of the graph of quadratic equations by themselves first.Then they will have a discussion with a partner regarding their brainstorm. Each pair of students sharetheir thoughts with the rest of the class.Section II – timely feedback for product (self, peer, teacher)SelfStudents will selfassess their GeoGebra based on the tutorial which will be given to them whenthey start.PeerStudents will get in groups of four, trade their products with a partner, and get peer feedback.TeacherTeachers will answer any questions the students might have.
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Summative (Assessment of Learning): (Description of Product)GeoGebraStudents will use GeoGebra to manipulate the graph of quadratic equation in order to playa level of “Angry Birds.” Each level of the game is set up differently, so the students can manipulate thegraph in GeoGebra and analyze the relationship between the graph and the coefficient.
IntegrationTechnology and SAMR LevelGeoGebra will be used at the Modification level, because students will be able to manipulate graphs inGeoGebra to witness and analyze the change and relationship between the coefficients and the graphs ofquadratic equations. Without GeoGebra, students won’t be able to witness the change of coefficientsand graphs instantly.
Other Content Areas:EnglishStudents will verbally express their understanding on linear equations, and the possible reallifeapplication of the graphs of quadratic equations.
Instructional Model
Concept Attainment
Rationale:By using concept attainment instructional model, the students will be able to experiment, observe, findpatterns, make hypothesis and eventually reach the concepts. Throughout this process, they will engagein group and class discussions, using examples and non examples to fully understand the definitions andrelationships among equations, functions, linear equations, inequalities, and quadratic equations. Thestudents will be able to retain their new understanding better than if I used the traditional directinstruction model.
GroupingsSection I Graphic Organizer & Cooperative Learning used during instructionStudents will use the Coefficient and Parabola graphic organizer to record their own observation whileplaying the Angry Birds game using Geogebra. Then students can share their learning with peers fromtheir groups
Section II – Groups and Roles for ProductStudents will work on their own Geogebra and Angry Birds game. Then they can share their learningwith a partner.
Differentiated Instruction
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Motivational Strategy (Tell which Posamentier and Krulik motivational strategy will be used andcredit them. Describe how you are using it and why.) NOTE: Use a variety across the unit.
Use of Recreational Mathematics
We will play the “Attribute” game as a whole class, which utilizes the students’ knowledge in a VennDiagram of linear equations and quadratic equations, their analyzing and problem solving skills. SeeTeaching and Learning SequenceConcept Attainment Hook/PreAssessment AttributeGame
Krulik, K. & Posamentier, A. (2012). The Art of Motivating Students for Mathematics Instruction.Part of The Practical Guide Series. McGraw Hill: New York, NY. ISBN: 9780078024474
Multiple Intelligences StrategiesLogical: Utilizing Venn Diagram to organize their reasoning and thoughts will help and strengthenstudents’ logical skills.Verbal: Partner work, group and class discussion will allow students to verbalize their thoughts andopinions.Visual: Venn Diagram, graphs, and Angry Birds game will help students visualize the quadraticequations and their graphs.Intrapersonal: Students will get chance to work on their own, to logically derive the rules of theAttribute game, to brainstorm the reallife application of the graphs of quadratic equations, and to reflecton their learning.Interpersonal: Students will have opportunities to work with a partner, a group of peers and as wholeclass.Kinesthetic: Students are invited to form a halfcircle around the whiteboard while we play theAttribute game.Naturalist: Students can use examples from the nature while they brainstorm the possible reallifeapplications of graphs of quadratic equations.
Modifications/AccommodationsFrom IEP’s ( Individual Education Plan), 504’s, ELLIDEP (English Language LearningInstructional Delivery Education Plan) I will review student’s IEP, 504 or ELLIDEP and makeappropriate modifications and accommodations.
Plan for students who are missing prerequisite skill(s):● Functions and equations● Linear equations● Venn Diagram
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● GeogebraWe will assess and review students’ understanding of linear equations, functions and equations while weplay an Attribute game. We will use Venn Diagram as the game board. Students will utilize Geogebrato analyze the relationship of coefficients and the graph of quadratic equations.
We will have other resource, such as websites and materials, posted on our Weebly.
Plan for accommodating absent students:We will have all materials, including the Attribute game and answer key, web links with supportingmaterials, link to GeoGebra project, and link to Padlet exit ticket, posted on our Weebly.
Extensions (tiering, gifted students, the students who already know it, etc…)There will be extra materials on the Weebly for students to explore the topic of quadratic equations andparabolas
Materials, Resources and TechnologyList all the items you need for the lesson, including handouts.
LaptopsGeogebra software on the laptopsAttributes written on colored card stockWeebly AlgebraQ.E.
Source for Lesson Plan and ResearchList all URLs and describe.http://www.mathsisfun.com/algebra/quadraticequationgraph.htmlExplore the quadratic equations:Manipulative quadratic equation and its graph.http://www.mathsisfun.com/algebra/quadraticequationrealworld.htmlReal world examples ofquadratic equations: set an equations for each real world example, solve it, and use common sense tocheck the answer.http://www.mathsisfun.com/geometry/parabola.htmlParabola: information and terminology onparabola in and its applicationhttp://www.purplemath.com/modules/grphquad2.htmGraphing Quadratic Functions: The LeadingCoefficient / The Vertex.PART II: Note: The purpose of Part II is to take everything from Part I and make it come alivewith details in such a way that you can easily teach from it but also a substitute unfamiliar withyour content area could carry out the lesson.
Teaching and Learning Sequence (4045mins)
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The tables and chairs will be arranged into long rows to accommodate four students per row facing thefront of room.
Concept AttainmentHook/PreAssessmentAttribute Game● Grouping of students (2 minutes)
When students arrive, each of them will draw a slip of paper. Students will be dividedinto groups of four based on the colors of their paper. There will be one mathematicalexpression, terminology, or graph, written on each slip of paper.
● Open (5 minutes)1) Briefly display objects.We will have a list which contains all the attributes displayed on the projector for all the studentsto see.2) State student’s task: to discover our rule of grouping all the attributes.
● Body (10 minutes)3) Present examples and counterexamples of the concept or rule.Students will take turns to hand in their slips of paper to the teachers. The teachers willput slips of paper in their rightful place within the Venn Diagram.4) Allow students to test their hypothesized rules by (a) citing their own examplesand nonexamples and/or (b) talking with peers.Each student can take a guess on the rules by which we place all the attributes into theVenn Diagram. They will be reminded that their hypothesized rules have to conform all the datapresented. The teachers may present more examples or counterexamples to help studentsderive the rules if it’s necessary.
● Close (10 minutes)5) Allow the rule to be stated for the class.Students should be able to derive the rule of one set in the Venn Diagram being “linearequations,” maybe even the rule for the universal set being “Algebra.” The teachers will revealthat the rule for the other set is “quadratic equations.”6) Allow for observations of the content and process of the lesson.
○ State the focus of this lesson:Quadratic equations,Their graphs,Reallife applications of the graphs.
○ We will focus on the set of quadratic equations and further explain anyterminologies or definitions presented in the set.
7) Invite further explorationStudents will do ThinkPairShare to explore the possible reallife applications of the graph ofquadratic equations.
● Geogebra and one reallife application of the graphs of quadratic equations (15
6
minutes)○ Tutorial
The teachers will ask students’ previous experience with GeoGebra and offer quicktutorial if it’s needed.
○ Angry Birds and quadratic equationsStudents will play three levels of Angry Birds. They will manipulate the graphs of
quadratic equation to ensure that the bird can knock the pigs off. While manipulating the graph,they will take notes, using Coefficient and Parabola graphic organizer, on the shape of the graphin relation to the value of the coefficients a, b, and c. Students can compare their observationswithin their group.
● Exit ticketPadlet (3 minutes)Students will use Padlet, which will be linked to our Weebly, as an exit ticket to reflect ontheir experience during this lesson.
Content Notes
Quadratic equations:(extracted from Quadratic Equations http://www.mathsisfun.com/algebra/quadraticequation.html )
An example of a Quadratic Equation:
The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x2).
It is also called an "Equation of Degree 2" (because of the "2" on the x)
The Standard Form of a Quadratic Equation looks like this:
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● a, b and c are known values. a can't be 0.● "x" is the variable or unknown (you don't know it yet).
Here are some more examples:
In this one a=2, b=5 and c=3
This one is a little more tricky:
● Where is a? In fact a=1, as we don't usually write"1x2"
● b = 3● And where is c? Well, c=0, so is not shown.
Oops! This one is not a quadratic equation, because it ismissing x2 (in other words a=0, and that means it can't be
quadratic)
Hidden Quadratic Equations!
So the "Standard Form" of a Quadratic Equation isax2 + bx + c = 0
But sometimes a quadratic equation doesn't look like that! For example:
In disguise → In Standard Form a, b and c
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x2 = 3x 1 Move all terms to lefthand side
x2 3x + 1 = 0 a=1, b=3, c=1
2(w2 2w) = 5 Expand (undo thebrackets),and move 5 toleft
2w2 4w 5 = 0 a=2, b=4, c=5
z(z1) = 3 Expand, and move 3to left
z2 z 3 = 0 a=1, b=1, c=3
5 + 1/x 1/x2 = 0 Multiply by x2 5x2 + x 1 = 0 a=5, b=1, c=1
HandoutsList the items that need to be printed out for the lesson and attach a cameraready copy.
List of attributes for the Attribute game as slips of paperCoefficient and Parabola graphic organizer
Maine Standards for Initial Teacher Certification and RationaleWrite the standard number, the description of the standard, and rationale statementpertaining to this lesson.
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List of Attributes for the Attribute Game y = mx + b --slope-intercept form
variables
coefficients
x-intercepts
y-intercepts
y – y1 = m(x – x1) --point-slope form
constants
slope
y = 2x2 – 5x + 7
y = t(t-4) + 2
Ax + By + C = 0 --general form (A and B cannot both be 0)
3√x – 57 = 24
7xy2+ 2y
3= 11
parabola
y = ax2 + bx + c (a ≠ 0) --standard form
y = -3(x – 5)2
– 9
y – 6 = x2
y = x2
y = a(x – h)2 + k -vertex form, vertex (h, k)
vertex
roots
Citation:
Graph of quadratic equation is retrieved from:
http://www.mathsisfun.com/algebra/quadratic-equation.html
Graph of linear equation is retrieved from:
http://www.mathsisfun.com/definitions/linear-equation.html
Set A: Quadratic Equations
parabola,
vertex,
y = ax2 + bx + c (a ≠ 0) --standard form
y = a(x – h)2 + k --vertex form, vertex (h,k)
y = 2x2 – 5x + 7
y = t(t-4) + 2,
y = -3(x-5)2-9
y - 6 = x2
y = x2
Set B: Linear Equations
slope
y = mx + b --slope-intercept form
y – y1 = m(x – x1) --point-slope form
Ax + By + C = 0 (A and B cannot both be 0)
--general form
variables,
coefficients,
root(s),
x-intercepts,
y-intercepts,
constants,
3√x – 57 = 24,
7xy2+ 2y
3= 11
Universal Set: Algebra
Created by Meng Hardy 11/24/13
Attribute Game
Citation:
Graph of quadratic equation is retrieved from:
http://www.mathsisfun.com/algebra/quadratic-equation.html
Graph of linear equation is retrieved from:
http://www.mathsisfun.com/definitions/linear-equation.html
Coefficients and Parabola Name: _____________ Date: 11/26/2013
What happens to the parabola when the coefficients of quadratic equations change?
y = ax2 + bx + c
When
(certain coefficient is…)
Then
(the graph of the function is…)
Evidence
(Sketch what you observed)
a = 0 y is a line,
or y is an linear function
a > 0
a < 0
|a| >1
|a| <1
Created by Mrs. Hardy, 11/25/13