L6+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:** 10/12/10 **Grade Level:** 11 **Topic:** Algebra - self-knowledge

**__ Objectives __** ** Student will understand that ** solving equations can be related to real world situations. **Student will know** x, y axis, slope, quadratics, factoring, x, y intercepts**,** quadratic formula, completing the square. **Student will be able to** recognize what styles of problem solving they are strong and weak at.

**__ Maine Learning Results Alignment __** // Maine Learning Results: Mathematics - D. Algebra // //Equations and Inequalities// //Grades 9 - Diploma// //2 - Students solve families of equations and inequalities.// **Rationale:** Students will be able to self-assess their abilities to solve problems different ways.

**__ Assessment __** ** Formative (Assessment for Learning) ** During the lesson students will have many opportunities to explore and experience using problem solving techniques to solve problems. 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 web graphic organizer to record information about the different ways to solve a problem. This graphic organizer is set up in a fashion so to allow students to jot down a short description of how to use that technique and then record an example. Students will be allowed to continue to add to their web 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 participate in a Jigsaw activity where students will be asked to partner up with either the first or second person they were matched with during the hook activity. They will then become experts on one of the problem solving techniques we have discussed. The experts will then be dispersed and will help their peers in completing the worksheet. 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.

**Summative (Assessment of Learning)** At the end of the lesson students post a blog entry explaining their strengths and weaknesses pertaining to problem solving. Throughout the unit students should have been blogging about the techniques we have discussed and whether or not they feel they understand it fully or are weak at it. Students will make goals throughout the unit as well in order to better the techniques they are weak at. They will also ask an adult in their lives whether they feel they are good or not at math and if they feel they use it in everyday life. At the end of this lesson students should sum up what they have been saying throughout the unit explaining their strengths and weaknesses, whether they feel they have improved in any of them and things they can do in order to help themselves. Although this has to be in a blog students are welcome to create a prezi or glogster and link it to the blog. This entry though should be substantial at explaining their own personal strengths and weaknesses. Students will be given a checklist when assigned this assignment and then during this lesson they will have to grade themselves using the checklist.

**__ Integration __** ** Technology: ** At the end of the lesson students post a blog entry explaining their strengths and weaknesses pertaining to problem solving. Throughout the unit students should have been blogging about the techniques we have discussed and whether or not they feel they understand it fully or are weak at it. At the end of this lesson students should sum up what they have been saying throughout the unit explaining their strengths and weaknesses, whether they feel they have improved in any of them and things they can do in order to help themselves. Although this has to be in a blog students are welcome to create a prezi or glogster and link it to the blog. This entry though should be substantial at explaining their own personal strengths and weaknesses.

**Other Content Area:** **English -** Students will be writing out a blog entry about their strengths and weaknesses.

**__ Groupings __** During class students will participate in a Jigsaw activity where students will be asked to partner up with either the first or second person they were matched with during the hook activity. They will then become experts on one of the problem solving techniques we have discussed. The experts will then be dispersed and will help their peers in completing the worksheet. 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.

**__ Differentiated Instruction __** ** Strategies ** **Visual:** Drawings and pictures can be drawn to find a solution to a problem. **Logical:** Riddles, logic problems and word problems will be given to practice problem solving. **Interpersonal:** Group work and activities will be given during class. **Intrapersonal:** The option of working alone will be given on in class assignments. **Verbal:** Students are free to talk out problems with others. **Bodily/knesthetic:** Students are able to act out a problem to get a better idea of how to solve it.

**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 post a blog entry explaining their strengths and weaknesses pertaining to problem solving. Throughout the unit students should have been blogging about the techniques we have discussed and whether or not they feel they understand it fully or are weak at it. At the end of this lesson students should sum up what they have been saying throughout the unit explaining their strengths and weaknesses, whether they feel they have improved in any of them and things they can do in order to help themselves. Although this has to be in a blog students are welcome to create a prezi or glogster and link it to the blog. This entry though should be substantial at explaining their own personal strengths and weaknesses.

**__ Materials, Resources and Technology __**
 * laptops
 * paper
 * textbooks
 * worksheet
 * Whiteboard
 * markers
 * calculators

**__ Source for Lesson Plan and Research __** [] - this site gives a good explanation of problem solving techniques. [] - this site provides many logic problems

**__ 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 blog 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. Clipboard learners will benefit from the checklist created for the blog so that they can be detailed and efficient. They will also enjoy using the graphic organizer so that the techniques for all the problem solving techniques can be combined in an organized chart. Being able to discuss within class both as a class or in groups will help the microscope learners. 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:** During this lesson students will look once again at all the problem solving techniques we have discussed during this unit, substitution, elimination, quadratic formula, factoring, completing the square (see previous content notes). We will also discuss general techniques such as discussing or talking out a problem, drawing a picture or acting out the problem. Students will know x, y axis, slope, quadratics, factoring, x, y intercepts**,** quadratic formula, completing the square. Students will be able to use all these problem solving techniques and be able to self-assess which ones they are strong and weak at. Being able to recognize strength and weakness is an important skill. And so at the end of the lesson students will create a blog entry that sums up their strengths and weaknesses throughout the whole unit.

**//Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//** **Rationale:** **Visual:** Drawings and pictures can be drawn to find a solution to a problem. **Logical:** Riddles, logic problems and word problems will be given to practice problem solving. **Interpersonal:** Group work and activities will be given during class. **Intrapersonal:** The option of working alone will be given on in class assignments. **Verbal:** Students are free to talk out problems with others. **Bodily/knesthetic:** Students are able to act out a problem to get a better idea of how to solve it.

**Technology:** At the end of the lesson students post a blog entry explaining their strengths and weaknesses pertaining to problem solving. Throughout the unit students should have been blogging about the techniques we have discussed and whether or not they feel they understand it fully or are weak at it. At the end of this lesson students should sum up what they have been saying throughout the unit explaining their strengths and weaknesses, whether they feel they have improved in any of them and things they can do in order to help themselves. Although this has to be in a blog students are welcome to create a prezi or glogster and link it to the blog. This entry though should be substantial at explaining their own personal strengths and weaknesses.

**//Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//** **Rationale:** Formative: During the lesson students will have many opportunities to explore and experience using problem solving techniques to solve problems. 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 web graphic organizer to record information about the different ways to solve a problem. This graphic organizer is set up in a fashion so to allow students to jot down a short description of how to use that technique and then record an example. Students will be allowed to continue to add to their web 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 participate in a Jigsaw activity where students will be asked to partner up with either the first or second person they were matched with during the hook activity. They will then become experts on one of the problem solving techniques we have discussed. The experts will then be dispersed and will help their peers in completing the worksheet. 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. Summative: At the end of the lesson students post a blog entry explaining their strengths and weaknesses pertaining to problem solving. Throughout the unit students should have been blogging about the techniques we have discussed and whether or not they feel they understand it fully or are weak at it. Students will make goals throughout the unit as well in order to better the techniques they are weak at. They will also ask an adult in their lives whether they feel they are good or not at math and if they feel they use it in everyday life. At the end of this lesson students should sum up what they have been saying throughout the unit explaining their strengths and weaknesses, whether they feel they have improved in any of them and things they can do in order to help themselves. Although this has to be in a blog students are welcome to create a prezi or glogster and link it to the blog. This entry though should be substantial at explaining their own personal strengths and weaknesses. Students will be given a checklist when assigned this assignment and then during this lesson they will have to grade themselves using the checklist.

**__ Teaching and Learning Sequence __** 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 (partners) smoother.

Day 1: - Students will write down on a note-card a strength and weakness then they will be mixed up and distributed so that a students must find the note-card's owner. 5 minutes - Students will brainstorm as a class about general problem solving techniques they use and also about specific ones we've discussed in class (substitution, elimination, quadratic formula, factoring, completing the square) they will record these on their word web. 25 minutes - Students will be given a work sheet 5 math problems that use 5 different techniques we've learned. This is where students will get together with their partner from the hook activity and become experts on one technique, they will then help their peers in a Jigsaw activity. 25 minutes - The last blog entry assignment will be explained. 5 minutes - Students will be able to work on their blog, logic problems or riddles for the rest of the class. 20 minutes Day 2: - Students will be able to share their blogs if they want with the rest of the class. 15 minutes - We will discuss any weaknesses that students have. 30 minutes - The WebQuest will be introduced and the rest of class will be given to students to start the project. 35 minutes

Students will understand that solving equations can be related to real world situations. Problem solving this is an important skill because problems are found in everyday life and knowing how to handle them is important. I will hook my students by write down on a note-card a strength and weakness then they will be mixed up and distributed so that a students must find the note-card's owner. The MLR is //students solve families of equations and inequalities.// **Where, Why, What, Hook Tailors: Interpersonal**

During this lesson students will know x, y axis, slope, quadratics, factoring, x, y intercepts**,** quadratic formula, completing the square (see content previous content notes) and other problem solving techniques. I will provide this information through individual, group, formative and summative assessment, discussion and traditional instructional time. For groupings each student must find the partner that they were matched with during the note card activity. Then these partners will teach and help their peers with becoming stronger in this particular problem solving technique we have learned. 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 post a blog entry explaining their strengths and weaknesses pertaining to problem solving. Throughout the unit students should have been blogging about the techniques we have discussed and whether or not they feel they understand it fully or are weak at it. At the end of this lesson students should sum up what they have been saying throughout the unit explaining their strengths and weaknesses, whether they feel they have improved in any of them and things they can do in order to help themselves. Although this has to be in a blog students are welcome to create a prezi or glogster and link it to the blog. This entry though should be substantial at explaining their own personal strengths and weaknesses. **Equip, Explore, Experience** **Tailors: Interpersonal, Logical, Visual, Verbal, Bodily, Intrapersonal**

During the lesson students will have many opportunities to explore and experience using problem solving techniques to solve problems. 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 web graphic organizer to record information about the different ways to solve a problem. This graphic organizer is set up in a fashion so to allow students to jot down a short description of how to use that technique and then record an example. Students will be allowed to continue to add to their web 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 participate in a Jigsaw activity where students will be asked to partner up with either the first or second person they were matched with during the hook activity. They will then become experts on one of the problem solving techniques we have discussed. The experts will then be dispersed and will help their peers in completing the worksheet. 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 post a blog entry explaining their strengths and weaknesses pertaining to problem solving. Throughout the unit students should have been blogging about the techniques we have discussed and whether or not they feel they understand it fully or are weak at it. At the end of the lesson students post a blog entry explaining their strengths and weaknesses pertaining to problem solving. Throughout the unit students should have been blogging about the techniques we have discussed and whether or not they feel they understand it fully or are weak at it. Students will make goals throughout the unit as well in order to better the techniques they are weak at. They will also ask an adult in their lives whether they feel they are good or not at math and if they feel they use it in everyday life. At the end of this lesson students should sum up what they have been saying throughout the unit explaining their strengths and weaknesses, whether they feel they have improved in any of them and things they can do in order to help themselves. Although this has to be in a blog students are welcome to create a prezi or glogster and link it to the blog. This entry though should be substantial at explaining their own personal strengths and weaknesses. Students will be given a checklist when assigned this assignment and then during this lesson they will have to grade themselves using the checklist.
 * Equip, Explore, Experience, Revise, Refine ** **Tailors:** **Interpersonal, Logical, Visual, Verbal, Bodily, Intrapersonal**

During this lesson students will receive feedback from both me and their peers through the cooperative learning activity (partners). Students will be able to ask me questions about their blog at the end of the class during free time as well as self-assess themselves using the checklist given to them. The only homework given is to work on their blog for the next class. **Evaluate Tailors: Interpersonal**

**Content Notes** Completing the Square:





Factoring: 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. Quadratic Formula:

Elimination: 1. -x – y = 8 __x – 3y = 8__ - 4y = 16 y = - 4 then put -4 back in for y in one of the equations to find x. -x + 4 = 8 x = - 4 2. -2x – 2y = 6 multiply this equation by 5 so that when adding the two together the x’s are eliminated. 10x + 10y = -30 -10x – 10y = 30 __10x + 10y = -30__ 0x + 0y = 0 infinite number of answers 3. 12x – 13y = 2 -6x + 6.5y = -2 multiple the equation by 2. 12x – 13y = 2 __-12x + 13y = -4__ 0 = -2 no solution because 0 does not equal -2. Substitution: 1. y = 4x – 9 y = x – 3 replace y in one of these equations with what y equals in the other equation. 4x – 9 = x – 3 3x = 6 x = 2 then replace x in one of the equations with 2. y = 2 – 3 y = -1

**Handouts** Worksheet Riddles/Logic problems Blog Checklist