L4+Douglass,Brianna+Elizabeth


 * UNIVERSITY OF MAINE AT FARMINGTON**
 * COLLEGE OF EDUCATION, HEALTH AND REHABILITATION**
 * LESSON PLAN FORMAT**


 * __Teacher’s Name__****:** Ms. Douglass **__Date of Lesson__:** 10/08/10
 * __Grade Level__****:** 11  **__Topic__:** Algebra - Application


 * __Objectives__**
 * Student will understand that** through manipulation, equations can be solved.
 * Student will know** quadratic equation, quadratic formula, max/min, the connection between the graph and the answers found in factoring.
 * Student will be able to do** use factoring in quadratics, where factoring is appropriate.

// Maine Learning Results: Mathematics - D. Algebra // //Equations and Inequalities// //Grades 9 - Diploma// //2 - Students solve families of equations and inequalities.//
 * __Maine Learning Results Alignment__**
 * Rationale:** Students will be able to factor, when appropriate, in order to solve equations.


 * __Assessment__**

During the lesson students will have many opportunities to explore and experience answering questions by using their factoring skills. Formative assessments will be used to assess student’s progress with the material. These will include various practice problems worked on individually and with partners or teams. To begin students will use the step-by-step graphic organizer to record information about the factoring process, examples and tips. This graphic organizer is set up in a fashion so to allow students to jot down a short description of what they did and then record an example. Students will be allowed to continue to add to the step-by-step chart throughout the lesson. They may write down examples that we go over in class, add hints for themselves and work with peers to compare charts. During class students will work together as a team on factoring problems then with partners. After this, students will work on factoring problems individually during class and hand in what they accomplished. I will encourage students to complete the problems like a quiz and refrain from asking me any questions since the class will use these practice problems in the next day’s activities. The next day students will be split into partners and given two of the worksheets from the previous days class. It will have been photocopied without the name of the person who completed it in order to try and keep this activity anonymous. As a team students will work to grade these "quizzes" by marking the ones that are wrong and marking the mistake. Afterward we will go over the problems as a class discussing common mistakes and ways to avoid them. During these activities students will receive feedback from their peers and myself. Students will be encouraged to ask questions and be part of the discussion based portion of the lesson.
 * Formative (Assessment for Learning)**

At the end of the lesson students will work partners to create a web using a program called webspiration around the idea factoring. They should include all scenarios that we have covered including quadratics with 1 as a leading coefficient, something other than 1 leading coefficient, having to factor out a common factor first and 1 that can't be factored. They should include at least one problem for each scenario that they struggled with either when working on teams and with partners or on the self-quiz. Within the web students should complete these problems correctly and describe how to complete it. Their web should describe these processes step-by-step (just like on the graphic organizer) and include examples that show how to solve using factoring.
 * Summative (Assessment of Learning)**


 * __Integration__**
 * Technology: ** At the end of the lesson students will be asked to create a web using a program called webspiration around the idea factoring. They should include all scenarios that we have covered including quadratics with 1 as a leading coefficient, something other than 1 leading coefficient, and having to factor out a common factor first. Their web should describe these processes step-by-step (just like on the graphic organizer) and include examples that show how to solve using factoring. They should also include one example that shows a polynomial that can't be factored and describe why.


 * Other Content Area:**
 * Art:** Students will be able to show their creativity on their web at the end of the lesson. They will be able to be as artistic as they want but must still include the appropriate information.

During class students will participate in the team-pair-solo activity where they will first work together as a team on factoring problems then with partners. After this, students will work on factoring problems individually during class and hand in what they accomplished. I will encourage students to complete the problems like a quiz and refrain from asking me any questions since the class will use these practice problems in the next days activities. The next day students will be split into partners and given two of the worksheets from the previous days class. It will have been photocopied without the name of the person who completed it in order to try and keep this activity anonymous. As a team students will work to grade these "quizzes" by marking the ones that are wrong and marking the mistake. Afterward we will go over the problems as a class discussing common mistakes and ways to avoid them. During these activities students will receive feedback from their peers and myself. Students will be encouraged to ask questions and be part of the discussion based portion of the lesson.
 * __Groupings__**


 * __Differentiated Instruction__**

**Strategies:**
 * Visual: ** students will be able to use the graphic organizer in order to record the process of factoring.
 * Intrapersonal:** Students will be able to work by themselves during the team pair solo activity.
 * Interpersonal:** Students will get the opportunity to work with others during the team pair solo activity.
 * Musical:** Students will be able to listen to a song about factoring.
 * Verbal:** Students will be able to talk out problems with their groups or partner.
 * Logical:** Students can solve problems in a logical process following their graphic organizer.

**Modifications/Accommodations** ( //I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.//) Absent: If a student is absent during this lesson than he/she needs to talk to me before if the absent is known in order to get assignments and notes. If the absence is not planned (sickness, emergency, etc) then the student should talk to another student in class and get any assignments. If the student can't complete the work because they need a worksheet or they have clarifying questions then they need to e-mail me to set up a meeting time or drop by my room before the next class.

**Extensions**
 * Technology: ** At the end of the lesson students will be asked to create a web using a program called webspiration around the idea factoring. They should include all scenarios that we have covered including quadratics with 1 as a leading coefficient, something other than 1 leading coefficient, and having to factor out a common factor first. Their web should describe these processes step-by-step (just like on the graphic organizer) and include examples that show how to solve using factoring. They should also include one example that shows a polynomial that can't be factored and describe why.


 * __Materials, Resources and Technology__**


 * laptops
 * paper
 * textbooks
 * Web checklist and Webspiration Tutorial
 * factoring worksheets
 * Whiteboard
 * markers
 * calculators


 * __Source for Lesson Plan and Research__**

[] - A site describing the simplest factoring examples. [] - A site describing how to factor harder examples. [] - the webspiration site.


 * __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.//**
 * //Rationale://** The beach ball learner will enjoy the creativity involved with creating the web at the end of the lesson. As long as all the information is in there these students can get as creative and self-expressive as they want. They will also enjoy not having a routine for everyday, doing new things is important. Clipboard learners will benefit from the rubric created for the web so that they can be detailed and efficient. They will also enjoy using the graphic organizer so that the process of factoring will be written down step-by-step including examples in an organized fashion. Being able to discuss within class both as a group and also in partners or groups will help the microscope learners. They will be able to analyze what the answers found in factoring really mean when graphing. Puppy learners want a comfortable and encouraging atmosphere and so therefore I will allow students to work with who they want at various times during class but I will also have students work in groups chosen randomly so that they are able to become more comfortable with each other. As the teacher I will also not allow students to put each other down but we will also have fun so that for puppies we can create a comfortable environment.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * //Rationale://** The beach ball learner will enjoy the creativity involved with creating the web at the end of the lesson. As long as all the information is in there these students can get as creative and self-expressive as they want. They will also enjoy not having a routine for everyday, doing new things is important. Clipboard learners will benefit from the rubric created for the web so that they can be detailed and efficient. They will also enjoy using the graphic organizer so that the process of factoring will be written down step-by-step including examples in an organized fashion. Being able to discuss within class both as a group and also in partners or groups will help the microscope learners. They will be able to analyze what the answers found in factoring really mean when graphing. Puppy learners want a comfortable and encouraging atmosphere and so therefore I will allow students to work with who they want at various times during class but I will also have students work in groups chosen randomly so that they are able to become more comfortable with each other. As the teacher I will also not allow students to put each other down but we will also have fun so that for puppies we can create a comfortable environment.


 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**
 * //Rationale://**
 * Visual: ** students will be able to use the graphic organizer in order to record the process of factoring.
 * Intrapersonal:** Students will be able to work by themselves during the team pair solo activity.
 * Interpersonal:** Students will get the opportunity to work with others during the team pair solo activity.
 * Musical:** Students will be able to listen to a song about factoring.
 * Bodily/kinesthetic:** Students will be able to actively play out the act of factoring.
 * Logical:** Students can solve problems in a logical process following their graphic organizer.


 * Technology:** At the end of the lesson students will be asked to create a web using a program called webspiration around the idea factoring. They should include all scenarios that we have covered including quadratics with 1 as a leading coefficient, something other than 1 leading coefficient, and having to factor out a common factor first. Their web should describe these processes step-by-step (just like on the graphic organizer) and include examples that show how to solve using factoring. They should also include one example that shows a polynomial that can't be factored and describe why.

Formative: During the lesson students will have many opportunities to explore and experience answering questions by using their factoring skills. Formative assessments will be used to assess students progress with the material. These will included various practice problems worked on individually and with partners or teams.To begin students will use the step-by-step graphic organizer to record information about the factoring process, examples and tips. This graphic organizer is set up in a fashion so to allow students to jot down a short description of what they did and then record an example. Students will be allowed to continue to add to the step-by-step chart throughout the lesson. They may write down examples that we go over in class, add hints for themselves and work with peers to compare charts. During class students will work together as a team on factoring problems then with partners. After this, students will work on factoring problems individually during class and hand in what they accomplished. I will encourage students to complete the problems like a quiz and refrain from asking me any questions since the class will use these practice problems in the next days activities. The next day students will be split into partners and given two of the worksheets from the previous days class. It will have been photocopied without the name of the person who completed it in order to try and keep this activity anonymous. As a team students will work to grade these "quizzes" by marking the ones that are wrong and marking the mistake. Afterward we will go over the problems as a class discussing common mistakes and ways to avoid them. During these activities students will receive feedback from their peers and myself. Students will be encouraged to ask questions and be part of the discussion based portion of the lesson.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * //Rationale://**

Summative: At the end of the lesson students will work with partners to create a web using a program called webspiration around the idea factoring. They should include all scenarios that we have covered including quadratics with 1 as a leading coefficient, something other than 1 leading coefficient, having to factor out a common factor first and 1 that can't be factored. They should include at least one problem for each scenario that they struggled with either when working on teams and with partners or on the self quiz. Within the web students should complete these problems correctly and describe how to complete it. Their web should describe these process step-by-step (just like on the graphic organizer) and include examples that show how to solve using factoring.

Students will arrive and immediately sit down at their previously assigned seats. Tables and or desks will be arranged in groupings of four in order to make transition in the cooperative learning activity (team-pair-solo) smoother.
 * __Teaching and Learning Sequence__****:**

Day 1: - Students will watch a video about[| factoring]. 5 minutes - Instruction will be given about factoring with a leading coefficient other than 1, having to find a common factor first and techniques to solving by factoring. 30 minutes - Students will work in teams to practice factoring. 15 minutes - Students will work with partners to practice factoring. 15 minutes - Students will work individually to take a "quiz" on factoring. 15 minutes

Day 2: - Students will get together with their partners from last class and two of their peers quizzes will be given to them in order to grade. 15 minutes - As a class we go over every one of the problems on the quiz and have a discussion about common mistakes. Students will be encouraged to ask questions to clarify factoring. 40 minutes - The webspiration checklist will be handed out and students will have the rest of class to work on it. 25 minutes

Day 3: - Webs are due.

Students will understand that through manipulation, equations can be solved this is an important skill because problems involving factoring and quadratics can be found in many careers and everyday situations, such as finding maximum profit. I will hook my students by having them listen to a factoring song on this [|video]. The MLR is //students solve families of equations and inequalities.//
 * Where, Why, What, Hook Tailors: Musical**

During this lesson students will know quadratic equation, quadratic formula, max/min, the connection between the graph and the answers found in factoring (see content notes). I will provide this information through individual, group, formative and summative assessment, discussion and traditional instructional time. For groupings students will participate in the team-pair-solo activity where they will first work together as a team on factoring problems then with partners. During these activities students will be encouraged to act out, draw or discuss problems with their partner(s). After this, students will work on factoring problems individually during class and hand in what they accomplished. I will encourage students to complete the problems like a quiz and refrain from asking me any questions since the class will use these practice problems in the next days activities. The next day students will be split into partners and given two of the worksheets from the previous days class. It will have been photocopied without the name of the person who completed it in order to try and keep this activity anonymous. As a team students will work to grade these "quizzes" by marking the ones that are wrong and marking the mistake. Afterward we will go over the problems as a class discussing common mistakes and ways to avoid them. During these activities students will receive feedback from their peers and myself. Students will be encouraged to ask questions and be part of the discussion based portion of the lesson. For the summative assessment students will complete a web on the computer using the program webspiration. This web will be completed individually and will need to demonstrate they understand factoring by describing the process and including examples of different scenarios.
 * Equip, Explore, Experience** **Tailors: Interpersonal, Intrapersonal, Verbal**

During the lesson students will have many opportunities to explore and experience answering questions by using their factoring skills. Formative assessments will be used to assess students progress with the material. These will included various practice problems worked on individually and with partners or teams.To begin students will use the step-by-step graphic organizer to record information about the factoring process, examples and tips. This graphic organizer is set up in a fashion so to allow students to jot down a short description of what they did and then record an example. Students will be allowed to continue to add to the step-by-step chart throughout the lesson. They may write down examples that we go over in class, add hints for themselves and work with peers to compare charts. During class students will work together as a team on factoring problems then with partners. After this, students will work on factoring problems individually during class and hand in what they accomplished. I will encourage students to complete the problems like a quiz and refrain from asking me any questions since the class will use these practice problems in the next days activities. The next day students will be split into partners and given two of the worksheets from the previous days class. It will have been photocopied without the name of the person who completed it in order to try and keep this activity anonymous. As a team students will work to grade these "quizzes" by marking the ones that are wrong and marking the mistake. Afterward we will go over the problems as a class discussing common mistakes and ways to avoid them. During these activities students will receive feedback from their peers and myself. Students will be encouraged to ask questions and be part of the discussion based portion of the lesson. At the end of the lesson students will work partners to create a web using a program called webspiration around the idea factoring. They should include all scenarios that we have covered including quadratics with 1 as a leading coefficient, something other than 1 leading coefficient, having to factor out a common factor first and 1 that can't be factored. They should include at least one problem for each scenario that they struggled with either when working on teams and with partners or on the self quiz. Within the web students should complete these problems correctly and describe how to complete it. Their web should describe these process step-by-step (just like on the graphic organizer) and include examples that show how to solve using factoring.
 * Explore, Experience, Rethink, Refine** **Tailors: Visual, Logical,** **Interpersonal, Intrapersonal, Verbal**

I will be providing feedback to the students during the team-pair-solo activity and also when students work in pairs to correct their peer's quizzes. Peer feedback will be given also during the team-pair-solo activity where students will work collaboratively to answer questions. Students will be able to correct themselves during this activity on both their practice problems and on their graphic organizer. Students will be able to self assess themselves during these activities as well along with correcting the quizzes at the end of the class. All homework is practice with factoring just like we have been doing in class and the next lesson involves evaluating a problem and determining the most efficient way of solving that problem. Factoring is a technique that is used to solve polynomials and so this will be used in the next lesson.
 * Evaluate Tailors: Visual, Logical, Interpersonal, Verbal**

Factoring polynomials with 1 as the leading coefficient - see content notes from lesson 3
 * __Content Notes__**

Factoring polynomials with a leading coefficient other than 1 1. 2x2 + 6x + 4 (2x + )(x + ) start with the leading coefficient. Here the only factors of 2 are 2 and 1. (2x + 2)(x + 2) the factors of 4 are 4, 1 but when multiplying those with 2 and 1 will not give us the middle number 6. So it has to be 2, 2. When you multiply 2x2 = 4 and 2x1= 4 and add up the answers it gives us the middle number.

2. 6x2 - 2x - 4 (3x )(2x ) here we have a minus so we have to somehow combine the products of the factors of 6 and 4 in a subtraction problem to get the middle number -2. (3x + 2)(2x - 2) Here we have -6 + 4 = -2

3. 4x3 - 8x2 - 60x 4x (x2 - 2x - 15) first, factor out the GCF 4x2. 4x (x - 5)(x + 3) Then factor the polynomial.

Factoring isn't appropriate 1. x2 + x - 1 You can't factor this because the factors of 1 can't be subtracted in a way to equal 1.

2. x2 + 3x + 1 You can't factor this because the factors of 1 can't be added together to get 3.

3. x2 - 3x + 10 You can't factor this because the factors of 10 can't be subtracted in a way to equal 3.

Web Checklist Quiz Factor worksheet Step-by-Step graphic organizer
 * __Handouts__**