L1+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__:** 10/4/10
 * __Grade Level__****:** 11 **__Topic__:** Algebra - Empathy


 * __Objectives__**
 * Student will understand that** solving equations can be related to the real world situations.
 * Student will know** how to recognize inequalities and linear equations, use and manipulate exponents and know how to solve and graph families of inequalities and equations.
 * Student will be able to do** consider how equations and inequalities are used in real world situations.

//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 use equations and inequalities to solve real world problems.


 * __Assessment__**

The first day of class students will take a pre-assessment because it is the first day of the unit I need to know what students already know about inequalities and equations. This will be in the form of a quiz but it will not be graded it simply is information for me. Another formative assessment students will use is the cluster/word web to record thoughts or word problems that use equations/inequalities in real world settings. Students will first jot down ideas or specific examples of how and where any type of equation or inequality are used in situations outside the classroom. They will then be split into teams of four to discuss their web of thoughts and ideas. Students may take examples and ideas from their peers, that they may not have included in their own web brainstorm, and add them to it. While this is going on each team will receive a piece of paper that has eight problems on it. Each team will work together to answer these word problems involving inequalities and linear equations. Then after each team has agreed on an answer each team member must choose two problems to present. They must give the answer but also explain how their team arrived at that answer. During this exercise students will work together and get feedback from their peers. After the activity each student must turn in a piece of paper with work and the answer to each question, this will be checked and given back to the students for more feedback.
 * Formative (Assessment for Learning)**

Students will interview an adult that uses equations/ inequalities in their everyday life. The interview should be recorded on garage band and an approved script must be written before hand that lays out what questions will be asked during the interview. The interview must include at least 8 questions that have to do with the equations or inequalities and how they use them. It should also include a real example of how the adult uses a specific equation or inequality. The podcast should be detailed and understandable because it will be presented to the rest of the class.
 * Summative (Assessment of Learning)**


 * __Integration__**
 * Technology:** Students will record an interview with an adult and ask them about how they use equations and inequalities in real world situations. This will be recorded using GarageBand and students will be required to add music or jingles to enhance their podcast.


 * Other Content Areas:**


 * English: ** Before students actually complete the interview they must turn in a paper that includes the questions they plan to ask about equations and inequalities.


 * __Groupings__**

Students will use the cluster/word web to record thoughts or word problems that use equations/inequalities in real world settings. Students will first jot down ideas or specific examples of how and where any type of equation or inequality are used in situations outside the classroom. They will then be split into teams of four to discuss their web of thoughts and ideas. Students may take examples and ideas from their peers, that they may not have included in their own web brainstorm, and add them to it. After each person gets a chance to refine his or her web a sheet with eight word problems will be handed out. Each team will work together to answer these word problems involving inequalities and linear equations. Then after each team has agreed on an answer each person in the group will pick two problems to explain and give the answer to. Each students will pass in a piece of paper after this activity with their work and answers on it for feedback.


 * __Differentiated Instruction__**

**Strategies:** **Logical:** Calculators will be used to graph, solve problems and check answers about inequalities and equations. **Verbal:** Students will be able to listen to the guest speaker talk about how inequalities and equations are used in his or her life. **Visual:** A graphic organizer will be used to organize thoughts about how equations and inequalities are used in real world problems. **Intrapersonal:** Students will get the chance to work by themselves on problems involving inequalities and equations. **Interpersonal:** Students will be able to work in groups and partners throughout the lesson to discuss and work on problems involving inequalities and other equations. **Naturatlist:** Word problems will be given about nature where students have to demonstrate their knowledge of inequalities and equations.

**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:** Students will record an interview with an adult and ask them about how they use equations and inequalities in real world situations. This will be recorded using GarageBand and students will be required to add music or jingles to enhance their podcast.


 * __Materials, Resources and Technology__**


 * Student's laptops
 * My laptop
 * Textbook
 * graphic organizers (cluster/word web)
 * word problem worksheets
 * inequality practice sheet
 * equations practice worksheets
 * systems of equations and inequalities worksheets
 * White board
 * Garage Band tutorial


 * __Source for Lesson Plan and Research__**

[|Inequalities] - This website gives extensive information about solving and graphing inequalities.

algebra 2.pages- This document has great information, including worksheets for absolute value inequalities.

[|Algebra II] - This website gives extensive worksheets for Algebra II.

[|Inequalities] - This website gives extensive information about solving and graphing inequalities.

[|One-Step Linear Equations] - This resource explains how to solve one-step linear equations.

[|Multiple Step Equations]- This resource gives examples and explains how to solve multiple step equations.

[|Systems of Equations -]This resource explains how to solve and graph systems of equations.

[|Systems of Inequalities]- This resource gives information on how to solve and graph systems of inequalities.


 * __Maine Standards for Initial Teacher Certification and Rationale__**

The puppy learners will be provided the opportunity to listen to explanations as well as talk out problems and solutions in supportive groupings during cooperative learning. Puppy learners will also be able to be imaginative when completing their Garage Band interview both with who they interview and how they use technology to aid their presentation.
 * //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://** Students will be learning how inequalities and equations apply to the real world. The clipboard leaner will flourish with use of a graphic organizer that allows them to see explanations of how equations are used in real life and brainstorming all their ideas onto paper in an organized fashion. These learners will also benefit from visually seeing how equations relate to the real world through the guest speaker. Much of what math really is, is learning problem solving techniques and so therefore the microscope learner will be able to analyze problems and solve them. The microscope learner will also like have discussions during the group activities in order to uncover material. I will encourage students practice problems for homework but this will not be graded and so the beach ball learners will enjoy the extensions and spontaneity. Those students that are beach ball learners will have the option to choose how they solve a problem whether it be algebraically, acting it out or drawing a picture in order to understand better the use of inequalities and equations in the real world.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * //Rationale://** During the empathy lesson students will learn about inequalities and equations involving multiple steps in order to solve (see content notes). They will graph families of equations and inequalities and work on word problems that relate to real life situations. Students will create a cluster/word web that brainstorms thoughts and examples where inequalities and equations are used in the real world. They will then be able to group together and compare webs, students will learn about their peers and also themselves during this activity. Students will be given choices during parts of the unit and will also be encouraged to problem solve using pictures, talking it out or acting it out. At the end of the lesson students will create a podcast interview that connects equations and inequalities to an adult that they know personally.

**Logical:** Calculators will be used to graph, solve problems and check answers about inequalities and equations. **Verbal:** Students will be able to listen to the guest speaker talk about how inequalities and equations are used in his or her life. **Visual:** A graphic organizer will be used to organize thoughts about how equations and inequalities are used in real world problems. **Intrapersonal:** Students will get the chance to work by themselves on problems involving inequalities and equations. **Interpersonal:** Students will be able to work in groups and partners throughout the lesson to discuss and work on problems involving inequalities and other equations. **Naturatlist:** Word problems will be given about nature where students have to demonstrate their knowledge of inequalities and equations.
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**
 * //Rationale://**


 * Technology:** Students will record an interview with an adult and ask them about how they use equations and inequalities in real world situations. This will be recorded using GarageBand and students will be required to add music or jingles to enhance their podcast.


 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * //Rationale://**
 * Formative:** The first day of class students will take a pre-assessment because it is the first day of the unit I need to know what students already know about inequalities and equations. This will be in the form of a quiz but it will not be graded it simply is information for me. Another formative assessment students will use is the cluster/word web to record thoughts or word problems that use equations/inequalities in real world settings. Students will first jot down ideas or specific examples of how and where any type of equation or inequality are used in situations outside the classroom. They will then be split into teams of four to discuss their web of thoughts and ideas. Students may take examples and ideas from their peers, that they may not have included in their own web brainstorm, and add them to it. While this is going on each team will receive a piece of paper that has eight problems on it. Each team will work together to answer these word problems involving inequalities and linear equations. Then after each team has agreed on an answer each team member must choose two problems to present. They must give the answer but also explain how their team arrived at that answer. During this exercise students will work together and get feedback from their peers. After the activity each student must turn in a piece of paper with work and the answer to each question, this will be checked and given back to the students for more feedback.
 * Summative:** At the end of the lesson students will interview an adult that uses equations/ inequalities in their everyday life. The interview should be recorded on garage band and an approved script must be written before hand that lays out what questions will be asked during the interview. The interview must include at least 8 questions that have to do with the equations or inequalities and how they use them. It should also include a real example of how the adult uses a specific equation or inequality. The podcast should be detailed and understandable because it will be presented to the rest of the class.

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 (numbered heads together) smoother.
 * __Teaching and Learning Sequence__****:**

Day 1: - The guest speaker (custodian, lunch lady, secretary, etc) will be in the classroom when the students arrive. He or she will then quickly explain to the students how they use equations and/or inequalities in their everyday life. It could be that the lunch lady has to use equations in order to determine the amount of food to cook or the custodian determining the amount of floor polisher to order. 5 minutes - The pre-assessment quiz of the student's skills will be given along with a short MI test. 15 minutes - Students will then listen to an overview of solving multiple step equations and families of equations for a variable. Students are encouraged to ask clarifying questions if something is not explained well. 30 minutes - Students will then use the graphic organizer cluster/word web to write down ideas, thoughts and examples of how inequalities and equations are used in real world applications. 5 minutes - They will then compare their cluster/word web with their team members adding new ideas and discuss their thoughts and ideas with each other. 5 minutes - Students will then be asked to complete practice problems on solving inequalities and equations individually. When a student finishes his or her paper will be checked for wrong answers, they will then have a chance to correct these mistakes during class or for homework. 15 minutes - At the end of class students will receive the interview project and rubric. Students will be encouraged to work on finding their adult whom they want to interview and start writing out questions they hope to ask that person. 5 minutes

Day 2: - Instruction about how to solve families of equations and inequalities will be given. 25 minutes - Students will then split up into their table groups a sheet of paper will be passed out with word problems involving linear inequalities and equations. Each team member must pick two problems they want to report how their team came up with the answer. During this activity students will be encouraged to act out the problems or draw pictures for themselves in order to better understand it. 30 minutes - Instruction will be provided about how to use GarageBand. 10 minutes - The rest of the class is free work time. Where the students can choose to work on homework problems or their interview. Between this and next class students must have recorded their interview. 15 minutes

Day 3: - Each student will receive a card at the beginning of class with either a family of equations or the answers to two variables. They will then have to find the partner that makes their family of equations true. 5 minutes - Students will then move into their groups, that were decided in the last activity and work together to graph and solve families of equations. Feedback from me will be given to each team. 20 minutes - More instruction about solving and graphing inequalities and equations will be given and any questions or misconceptions will be addressed. 20 minutes - Students will work on their interview, editing, adding music and jingles and making it perfect to present the next class. If students finish than they are free to start their practice problems that were assigned for homework. 35 minutes

During this lesson students will understand that solving equations can be related to the real world situations. Equations and inequalities are important and being able to solve and graph them can be useful in real life situations where numbers are involved. The MLR that this lesson is focusing on is //students solve families of equations and inequalities.// In order to grab the interest of my students I will bring in a special guest from the school (lunch lady, custodian, secretary, etc) and how them explain quickly how they use equations and or inequalities in their every day life.
 * Where, Why, What Tailors: visual, verbal**

Students will know how to recognize inequalities and linear equations, use and manipulate exponents and know how to solve and graph families of inequalities and equations (see content notes). This will be taught through a combination of formative and summative assessment. A pre-assessment will be used to determine what students already know and what they don't. Individual work will include creating an interview using GarageBand, working on practice problems and creating a word web. A more traditional approach will be taken during parts of the lesson where student will listen to me describe how to solve and graph inequalities and equations but during this students will be greatly encouraged to ask clarify questions about the topic. Many group activities will also be incorporated into this lesson. Students will be split into teams of four to discuss their web of thoughts and ideas and also to solve problems. Each team member will pick two problems to present to the class. During this exercise students will work together and get feedback from their peers. After the activity each student must turn in a piece of paper with work and the answer to each question, this will be checked and given back to the students for more feedback. I will be checking understanding during the group activities, individual work and based on the papers turned in.
 * Equip, Experience, Explore Tailors: verbal, visual, interpersonal, intrapersonal**

Students will be able to explore the information about inequalities and equations by using the cluster/word web where they brainstorm about how equations are used in real world situations. They will then experience the information by participating in a team activity where they work together to solve word problems which will range in topics. Team groupings will be predetermined by how they are seated. During this activity each group will work together to complete each problem then each student will pick two problems they would like to present to the class. I will be assessing progress during this and also reviewing refined papers turned in afterwords with their teams answers and work. Students will also work on inequality and equation problems individually which they will pass in for feedback. Students will be asked to think about the differences between inequalities and linear graphs. Students will have the opportunity to change answers on their paper after presenting during the group activity and any worksheet or practice problems may be revised after receiving feedback from me or peers.
 * Explore, Experience Tailors: verbal, visual, logical, interpersonal, intrapersonal, naturalist**

Students will be able to self-assess their progress during the group activity where they will have the opportunity to think about how they personally like to solve a problem. Students will be given the optional to complete problems by drawing, talking or acting it out. Also during the group activity students will be provided with plenty of feedback from both me and the class. After which they can assess how well they are doing solving or graphing a problem. During the group activities I will be able to provide feedback on the spot but when any practice problems or homework are turned in they will be handed back the next class. The recorded interview will be graded using a rubric that will be provided to all students when the assignment is assigned. This is so students can self-asses themselves while completing the project. The topic of inequalities and equations will be covered in depth with many examples of solving and graphing. A mixture of individual and group work will be used in order to provide feedback in class instead of the next day which will happen with passed in homework assignments. All in class work will be about solving word problems or graphing inequalities and equations will connect directly to the homework problems that will provide extra practice in the same content.
 * Evaluate Tailors: interpersonal, intrapersonal, logic, visual, verbal**

Students will know how to recognize inequalities and linear equations, use and manipulate exponents and know what the domain is and how to find it. Domain: The domain of a function is the set of all possible input values (usually x), which allows the function to work. 1. What is the domain of 4x -2 = y Any number can be put into x so the domain is all real numbers. 2. What is the domain of 1/(x – 3) = y The domain is all real numbers except 3 because that would mean the denominator is 0. Multi-Step linear Equations: 1. 4x – 2 = 14 4x = 16 added 2 to each side. x = 4 divided each side by 4. Inequalities: 1. 2p – 4p £ -2 -2p £ -2 p ≥ 1 when dividing by a negative you must flip the inequality sign 2. x + 6 ≥ 11 or x + 3 ≤ -2 if it is an “or” solve each one separately. x ≥ 5 or x ≤ -5 3. -6 ≤ -2n ≤ 2 when it is an “and” separate them and solve. -6 ≤ -2n -2n ≤ 2 3 ≥ n n ≥ -1 and combine your answers in an “and” -1 ≤ n ≤ 3
 * __Content Notes__**

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 For graphing examples see the answer sheet to the handouts provided .
 * __Handouts__**

Systems of Inequalities-1.pdf- Systems of Inequalities handout (see attached) Systems of Equations Word Problems-3.pdf- Systems of Equations Word Problem Handout (see attached) Solving Inequalities-1.pdf- Solving Inequalities Handout (see attached) Graphing Linear Inequalities.pdf- Graphing Linear Inequalities Handout (see attached) Compound Inequalities.pdf- Compound Inequalities Handout (see attached)