L5+Thiry,+Simone


 * **__ Teacher’s Name __**** : ** Ms. Thiry **__Lesson #:__ 5 __Facet:__** Apply
 * __ Grade Level __**** : 9-12 ** **__Numbers of Days:__ 3**
 * __ Topic: __** Algebraic Equations

// Common Core State Standards //
 * __ PART I: __**
 * __ Objectives __**
 * Student will understand that ** different methods should be used to solve quadratic equations in one variable, depending on the initial form of the equation.
 * Student will know ** factoring, completing the square, approaches to solving quadratic equations,
 * Student will be able to do ** solve quadratic equations by completing the square and factoring.
 * Product: ** Prezi
 * __ Maine Learning Results (MLR) or Common Core State Standards (CCSS) Alignment __**

// Content Area: Algebra //

// Grade Level: High School //

// Domain: Reasoning with Equations and Inequalities //

// Standards: 1. Understand solving equations as a process of reasoning and explain the reasoning. //

// 2. Solve equations and inequalities in one variable // The teacher will check periodically for understanding by asking students to rate their understanding on a scale of 1-5. Students will write one method they feel confident with and one method that is still confusing on an exit ticket. Students will learn from a variety of sources, and will have opportunity to correct their methods after learning from their peers. The teacher will circulate the room during the group work period to address misconceptions and monitor the students’ work. Each group will self-assess their presentations using the checklist before they submit the final product. Students will create a digital presentation that shows how to solve a given quadratic equation in 2 ways. In addition to solving the equation, the presentation must explain why we have multiple ways of solving equations, and which one was best fitted to solving this equation. Students will use a cluster organizer to organize the different methods for solving quadratics clustered around the definition of a quadratic equation. Students will become experts in one of the techniques and then explain it to their peers in the jigsaw method. Students will send one student from each predetermined table group to a different section for the jigsaw. After explaining to their table groups, students will form their own groups for the Prezi, provided there is one expert from each area per group.
 * Rationale: ** The CCSS Standard ‘Solve equations and inequalities in one variable’ encompasses the ability to solve quadratic equations, including the processes of factoring and completing the square. This lesson explicitly covers those processes.
 * __ Assessments __**
 * __ Formative (Assessment for Learning) __**
 * Section I – checking for understanding during instruction **
 * Section II – timely feedback for products (self, peer, teacher) **
 * __ Summative (Assessment of Learning): __**
 * __ Integration __**
 * Technology: ** Students will work with their group to create a Prezi presentation that shows different methods for solving quadratic equations.
 * Content Areas: ** English: Students will use verbal skills to compose their one-minute papers and to teach their classmates.
 * __ Groupings __**
 * Section I - Graphic Organizer & Cooperative Learning used during instruction **
 * Section II – Groups and Roles for Product **


 * __ Differentiated Instruction __**
 * __ MI Strategies __**
 * Verbal: ** Students will verbally explain their Prezi presentation and explain how they solved equations.

** Visual: ** Students will use the visual components of a Prezi to display several methods for solving quadratic equations. Students will visualize the equation breaking into 2 parts as a result of factoring.

** Logical: ** Students will use a series of steps to determine which method they should use to solve a quadratic.

** Interpersonal: ** Students will work together in jigsaws and presentation groups to master the material.

** Intrapersonal: ** Students will use the exit ticket to check-in with their own understanding, and will work individually to become an expert with one of the methods.

**Musical:** An example given during instruction will relate the different methods to different fingerings to produce the same note when playing certain instruments.
 * __ Modifications/Accommodations __**
 * // From IEP’s ( Individual Education Plan), 504’s, ELLIDEP (English Language Learning Instructional Delivery Education Plan) //**// I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations. //


 * Plan for accommodating absent students: S ** tudents should email me the morning they know they will not be in school if possible. They will then check in with me upon their return to school for make-up assignments.
 * __ Extensions __**
 * Type II technology: ** Students will use Prezi to create a digital presentation of different ways to solve quadratic equations.


 * Gifted Students: ** Students will be given the opportunity to consider what the graphs of quadratic equations look like and predict what would happen if we introduced a second variable.

// List all the items you need for the lesson. // Fire Extinguisher labels. Laptops (at least one for every 4 students) Cluster Organizers Whiteboard/Whiteboard markers Distribution Worksheets Homework Worksheets Jigsaw Outlines Game Board Printouts Dice // List all URL and describe. // Completing the Square: [] Completing the Square Interactive Presentation: [] Factoring Quadratics : [] [] Factoring a Difference of Squares: [] [] Prezi tutorial: [] Algebra Connect Game: [] “I have, Who has?” Matching Game: []
 * __ Materials, Resources and Technology __**
 * __ Source for Lesson Plan and Research __**
 * __ PART II: __**

// Total Class time (320 min): Students will work with their table groups for the first two days of class. Students will count of by 3’s to determine groups for the Factoring Game, and those will become their groups for the Prezi project. // // Day 1: // // Hook: Fire Extinguishers (5 min) // // Review Worksheet: Distribution (15 min) // // Boardwork: Factoring (25 min) // // Team-Pair-Solo: Factoring (30 min) // // Exit Cards (5 min) //
 * __ Teaching and Learning Sequence __**** (Describe the teaching and learning process using all of the information from part I of the lesson plan) **// Take all the components and synthesize into a script of what you are doing as the teacher and what the learners are doing throughout the lesson. Need to use all the WHERETO’s. (3-5 pages) //

// Day 2: // // Review Homework (20 min) // // “I have, Who has?” Matching Game (25 min) // // Algebra Connect Factoring Game (35 min) //

// Day 3: // // Review Homework (10 min) // // Jigsaw (30 min) // // Report Back (35 min) // // One – Minute Paper (5 min) //

// Day 4: // // Review Jigsaw (15 min) // // Graphic Organizer – Check in (10 min) // // Break into Glogster Groups (5 min) // // Work on Glogster (45 min) // // Checklist Check-in (5 min) // // Revise Glogster (10 min) // Students will understand that different methods should be used to solve quadratic equations in one variable, depending on the initial form of the equation. We need to know how to determine what methods to use in the face of different problems. Fire extinguisher example: Students will come into class and examine the fire-extinguisher labels on their tables. When should you use this fire extinguisher? There are different fire extinguishers for different types of fires; there are different methods for solving different quadratic equations. Also, like there is one type of fire extinguisher that can be used in most situations, we usually use factoring to solve quadratics. Students will be able to solve quadratic equations using multiple methods. **Where, What, Why, Hook, Tailors : Visual, Logical**

Students will know quadratic equations, radicals, difference of squares, completing the square and factoring. We will begin with a review of distribution. Students will work on a Distribution Worksheet where they will first distribute with numbers, then distribute a single number into a statement with a variable, and finally to distributing a binomial into another binomial. The last examples (binomial to binomial) will become the class’s first examples of how to factor during the boardwork section. The teacher will then provide other examples for students to puzzle out as a class. Students will use the Team- Pair-Solo model to work on factoring in their groups. At the end of class the students will complete an exit card telling where they are with the material, and explaining what part of the subject is still confusing. On the second day, after a review of the homework (students will write which problems they had difficulties with on the board, and each team will be assigned a problem to complete and then present), we will use the “I have, Who has?” matching game. We will play two or three rounds of this game depending on time allowances and then continue to the Algebra Connect Factoring Game. On the third day of class, we will spend a few minutes going over the homework and then continue to learn the different methods for solving quadratics. An example given during instruction will relate the different methods to different fingerings to produce the same note when playing certain instruments. Students will use the cluster organizer to organize the different methods for solving quadratics clustered around the definition of a quadratic equation. Students will become experts in one of the techniques, and then come back to explain it to their group. Students will use a one-minute-paper to compare the differences between completing the square, difference of squares, factoring by grouping and regular factoring. Students will use a series of steps to determine which method they should use to solve a quadratic. **Equip, Explore, Refine Tailors : Visual, Verbal, Logical, Interpersonal, Musical** Students will learn from a variety of sources, and will have opportunity to correct their methods after learning from their peers. Students will work with their group to create a Prezi presentation that shows different methods for solving quadratic equations. Students will verbally explain their Prezi presentation and explain how they solved equations. Students will use the visual components of a Prezi to display several methods for solving quadratic equations. Students will visualize the equation breaking into 2 parts as a result of factoring. Students will take their best examples of solving equations in the different methods and put them in the Prezi**. Experience, Revise, Rethink, Tailors : Logical, Verbal, Intrapersonal, Visual**

The teacher will check periodically for understanding by asking students to rate their understanding on a scale of 1-5. Students will write one method they feel confident with and one method that is still confusing on an exit ticket**.** **The teacher will evaluate the Prezi projects based on the same rubric that students used to evaluate their product. The different methods of solving quadratics by factoring will be used to help introduce students to quadratic equations and to the quadratic formula in the next lesson. Evaluate, Tailors: Verbal, Logical**

Students will know….. // Develop detailed content notes so a substitute or a colleague can teach your lesson. (2-3 pages) //
 * __ Content Notes __**

__ Definitions: __

Quadratic Equation: A quadratic equation is a polynomial of the second degree. This means any equation where the highest power for the variable is 2. (for example x-squared).

Radical: A radical is a root sign. We know how some square roots already. Radicals are the mathematical signs that signify square roots.

Factoring: Factoring is breaking a number or algebraic expression down into parts. We have some experience factoring numbers, but we can also factor quadratics.

Difference of Squares: Any quadratic in the form x2 – y2 where y2 is a perfect square integer, can be factored into the form (x + y)(x – y). It is called a difference of squares because it is a perfect square subtracted from a perfect square (which is the same as the difference between the two).

Completing the Square: Completing the square is the process by which you take an imperfect quadratic equation and solve it by bringing the constant (c) to the other side, and then add the number necessary to turn the variable side into a perfect square (in the form (x + y)2 where y is some number). You can then solve the equation by taking the square root of the constant side (remember that when you take the square root you have to include both positive and negative roots) and solving for the variable.

Factor by Grouping: We factor by grouping by pulling one term out of two different parts of an equation, leaving behind a common factor (e.g. x(x + 2) – 3(x + 2) becomes (x – 3)(x + 2)).

__ Example Problems: __

Distribution Problem Answers:

x2 + 5x + 6 = 0 x times x = x2, 3 times 2 = 6. Check: 3x + 2x = 5x (x + 3)(x + 2) = 0 When you multiply two numbers together and get 0, you know that at least one of them has to equal zero. Therefore, either x + 3 = 0 or x + 2 = 0 So x = -3 or x = 2

b + 4b – 5 = 0 b times b = b2, -1 times 5 = -5. Check: 5b + -b = 4b There are only two sets of factors for -5, -1 and 5 or 1 and -5. But only -1 and 5 add up to 4, so that is what we should choose. (b – 1) (b + 5 ) = 0 b = 1 or b = -5

x2 - 6x – 7 = 0 There are only two sets of factors for -7, and only 1 and -7 add up to -6, so we should pick those to get: (x – 7) (x + 1) = 0 x = 7 or x = -1

(a2 + 2a – 24) = 0 There are a lot of factors of -24. We factor -24, but only -4 and 6 add up to 2. Therefore we can factor into (x + 6) (x – 4) = 0 x = -6 or x = 4

Team-Pair-Solo Problems:


 * 1) x2 + 10x + 16 = 0

(x + 2) (x + 8) = 0

x = -2 or -8


 * 1) x2 – 26 + 48 = 0

(x – 2) (x – 24) = 0

x = 2 or x = 24


 * 1) m2 – 7m + 12 = 0

(m – 4) (m – 3) =0

m = 4 or m = 3


 * 1) v2 – v – 56 = 0

(v – 8) (v + 7) = 0

v = 8 or v = -7


 * 1) x2 + 5 – 36 = 0

(x – 4) (x + 9) = 0

x = 4 or x = -9


 * 1) p2 – 3 – 40 = 0

(p – 8) (p + 5) = 0

p = 8 or p = -5

Jigsaw: Difference of Squares: Students will fill out the worksheet. Factor by Grouping: Will work with me first. Completing the Square: Will work online first using this completing the square activity. []

Factor by Grouping Example: x2 – 3x + 5x – 15 = 0

x(x – 3) + 5(x – 3) = 0

(x + 5) (x – 3) = 0

x = -5 or x = 3

We see that this equation is the same as x2 + 2x – 15 = 0, which is easily factorable. However, this is one way to factor, and will be useful later, and can be easier depending on which form the equation is in. This will show up again later on when we talk about polynomials of degrees greater than two.

Difference of Squares Example:

Use the formula for difference of squares: (x2 – a2) = (x – a) (x + a)

x2 - 9 = 0

(x – 3) (x + 3) = 0

x = 3 or -3

Completing the Square Example:

x2 + 4x – 5 = 0 First move the constant (non-variable term) to the other side. x2 + 4x = 5 Then divide the coefficient of the second term by 2 (4/2 = 2). Square that number (22 = 4). Add the square to each side of the equation. x2 + 4x + 4 = 5 + 4 Factor the perfect square. (x + 2)2 = 9 Solve for the variable x + 2 = 3 or x + 2 = -3 (Remember to take both the positive and negative roots of the constant side.) So, x = -5 or x = 1 // List the items that need to be printed out for the lesson. // Cluster Graphic Organizer Checklist Worksheets Algebra Connect Factoring Trinomials Gameboard Matching Activity
 * __ Handouts __**


 * __ Maine Standards for Initial Teacher Certification and Rationale __**


 * // Standard 3 – Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development. //**


 * //__ Learning Styles __//**


 * // Clipboard: //** Clipboard students will be able to see the connections between factoring and the other methods for solving quadratics and will benefit from the explicit instructions for each activity.


 * // Microscope: //** Microscope students will develop an understanding of why different methods of solving quadratics work, and why understanding different methods is important and applicable to real life.


 * // Puppy: //** Puppy students will benefit from the groupwork portions of the lesson, as well as the periodic check-ins which will help promote comfort and confidence with the material.


 * // Beach Ball: //** Beach Ball students will benefit from learning from a variety of different sources, online videos, peers and the teacher while having the opportunity to spread ideas out onto a cluster diagram.


 * // Rationale: //****// This lesson plan includes components that cater to all four learning styles, which will maximize student engagement in the activities. By tailoring the lesson to several learning types, I am not only allowing students to thrive by utilizing their strengths, but also exposing them to a wide range of other areas to help them develop new ways of thinking. //**


 * // Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory. //**


 * // Content Knowledge: //** Students will create a digital presentation that shows how to solve a given quadratic equation in 3 ways.

// Common Core State Standards //
 * // MLR or CCSS: //**

// Content Area: Algebra //

// Grade Level: High School //

// Domain: Reasoning with Equations and Inequalities //

// Standards: 1. Understand solving equations as a process of reasoning and explain the reasoning. //

// 2. Solve equations and inequalities in one variable //


 * // Facet: //** Students will create a digital presentation that shows how to solve a given quadratic equation in 3 ways. Students will solve equations, which is an application of the new knowledge.


 * // Rationale: //****// This lesson was planned with the goal of addressing the Common Core standard. Students demonstrated their understanding of the standard in a Prezi presentation in which they solved specific example equations. //**


 * // Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs. //**


 * // MI Strategies: //** Verbal: Students will verbally explain their Prezi presentation and explain how they solved equations.

Visual: Students will use the visual components of a Prezi to display several methods for solving quadratic equations. Students will visualize the equation breaking into 2 parts as a result of factoring.

Logical: Students will use a series of steps to determine which method they should use to solve a quadratic.

Interpersonal: Students will work together in jigsaws and presentation groups to master the material.

Intrapersonal: Students will use the exit ticket to check-in with their own understanding, and will work individually to become an expert with one of the methods.

Musical: An example given during instruction will relate the different methods to different fingerings to produce the same note when playing certain instruments.


 * // Type II Technology: //** Prezi – Digital Presentation


 * // Rationale: //****// This lesson addresses seven of Howard Gardner’s Multiple Intelligences to cater to a variety of different learners. Students with all proclivities can benefit from a deeper understanding of the content based on the opportunities given in the lesson. The use of Prezi presentation software allows students to visually link their solutions to the problems while they explore the similarities, differences and benefits of using multiple methods to solve equations. //**


 * // Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner. //**


 * // Formative: //** The teacher will check periodically for understanding by asking students to rate their understanding on a scale of 1-5. Students will write one method they feel confident with and one method that is still confusing on an exit ticket. Students will use a one-minute-paper to compare the differences between completing the square, difference of squares, and factoring. Students will learn from a variety of sources, and will have opportunity to correct their methods after learning from their peers. Groups will self-assess their digital posters before submitting the final product.


 * // Summative: //** Students will work with their group to create a Prezi presentation that shows different methods for solving quadratic equations.

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 * // Rationale: //****// This lesson includes a variety of formative assessments to check for understanding and address misconceptions throughout the learning process. It also includes a polished summative assessment that accurately demonstrates student knowledge that has been revised and refined through formative assessment feedback. //** || [[image:http://www.wikispaces.com/_/4k0z606x/i/c.gif width="1" height="600"]] ||  ||
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