L2+Stoutamyer,+Mykayla

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

Teacher’s Name:** Ms. Mykayla Stoutamyer **Date of Lesson:** Lesson 2 (Application)
 * Grade Level:** Grade 9 **Topic:** Equations and Inequalities (Solving linear equations algebraically)

__**Objectives**__
Student will understand that the equations have many ways for being solved. Student will know how to solve ax+b=k algebraically. Student will be able to solve systems of linear equations and inequalities in 2 unknowns and interpret their graphs.

__**Maine Learning Results Alignment**__
a. Solve systems of linear equations and inequalities in two unknowns and interpret their graphs.
 * Maine Learning Results: Mathematics-D. Algebra**
 * Equations and Inequalities**
 * Grades 9-Diploma**
 * 2. Students solve families of equations and inequalities.**


 * Rationale:** Students will learn how to solve linear equations algebraically and then check their answers with the graph or table on the calculator.

__**Assessment**__
Solving linear equations algebraically can be difficult. To help ease this difficulty off of my students I plan on having them use a [|step-by-step chart] to show every process of solving the equations. With this technique I will hopefully be able to easily pin-point my students errors and be able to correct them smoothly and swiftly. I do not plan to have my students use this process forever, just long enough till they feel comfortable with the procedure and I believe that they are ready to do it without it. As an assessment, this chart will be able to help me see where my students are in relation to accuracy in solving equations. Another formative assessment that I would like to use is an in class discussion over practice problems. I would like my students to do practice problems in class and then ask students to demonstrate how they went about solving it, either on the board or verbally, whichever they prefer. With this I hope to see that students understand the process and are not simply going through the motions. This will also enable me to catch problems early in commonly thought areas. Also, at the end of class I would like to give my students an exit card. On this exit card will be a few practice problems that they must solve before leaving the room. With these problems, I hope to see how far my class has come to understanding how to solve equations. I will also see if there is an issue I have to recover in class the next day or if there is something I don't have to recover because everyone understands it already. I also feel that homework practice problems is an effective way to judge students' understanding. I want to use homework problems as extra practice for the concept and not a grade.
 * Formative (Assessment for Learning)**

I will be asking students to add to their wiki study guides. I feel as though this will be an accurate assessment of their learning over the first two lessons and it will also show me if they can connect the two lessons and use them together to solve problems. I will still be assessing the study guide with a checklist, but I think that I am going to use two separate checklists; one for lesson 1 and one for lesson 2. This way students won't be over whelmed in either situation. I would also like to give the students a quiz over both lesson 1 and 2. I feel as though this is the most accurate way to see if students can solve equations in a variety of ways. I can grade the quiz and get an idea of who still does not get it or who is in complete understanding.
 * Summative (Assessment of Learning)**

__**Integration**__
Technology: Students will be finishing their study guides on the wiki. They will still have to use a variety of medias and resources just like in lesson 1.

English: The students will be doing a lot of reading and writing when it comes to solving equations. I am going to want them at first to write out exactly what they did and to read different examples of how to solve equations. All of this requires English.

__Groupings__
In this lesson, I feel the most effective cooperative group is pairs. Students will be put into pairs to try and solve a more difficult equation using the [|step-by-step chart]. This will give students a chance to use one another and solve an equation that they may or may not have been able to do on their own. "Two heads are better than one." Partners will be random. Either before class starts or while they are doing practice problems I will hand out equations on slips of paper. Each equation the students will have to solve and then they will have to find the other person in the room who has the same answer as them. This pairing will use their newly acquired skills and will also get them socializing with their peers. In these groups students will be equals. They will communicate with each other and use the chart to solve the problem together. I will be walking around the room and making sure that everyone is participating in the solving process and not one person doing all the work. Pairs will then elect one person to report what they did to solve the problem. The other student will be able to add additional information after the first is done talking. I will assess the group work by observing their work time. I will make comments of those groups who seem to be working well together to solve a problem and noting those groups where one person does all the work. This will just be recorded as participation.

__**Differentiated Instruction**__
__Verbal__: Students discussing with each other how to solve the problem. I explain to them how to solve the problem. __Logic__: Students will solve equations algebraically. __Musical__: I will play classical music in the background while students work independently. __Visual__: Students will use the graphic organizer to solve equations at first. __Interpersonal__: Students will be working in pairs to solve an equation. __Intrapersonal__: Students working on solving problems alone (**Tailor**).
 * Strategies**

//I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.//
 * Modifications/Accommodations**

Absent Students: Students who are absent from this lesson will have to set up a meeting time with me to get a mini lecture. I feel this is the best way to learn how to do this material. In this meeting students will do some of the in class problems that their peers completed using the [|step-by-step chart]. Students will have to set up this meeting over e-mail before returning to school, so as soon as they return to school a meeting can take place. The student will then have to get the homework problems done, just like the rest of the class, as well as their study guide. If a student knows that he or she is going to be absent ahead of time, I would still like to meet with the student and give the mini lecture and also give them some additional resources to consult while they are absent to complete the necessary assignments. Students are responsible to talk to me.

Every student will finish his or her wiki study guide following the appropriate checklists. Again, using this technology will allow them to bring in outside resources that will help them understand the material better. Pictures, videos, songs, and other resources are necessary to use and must be relevant to the material. Also, all students will have to take a quiz over lessons 1 and 2. Although this does not use a technology, students will have to take it to show me their understanding of solving linear equations in a variety of ways.
 * Extensions**

__**Materials, Resources and Technology**__

 * slips with equations on them for grouping
 * answers to the slips
 * [|step-by-step charts]
 * laptop, laptop cart, or desktop access
 * student's partial study guides
 * graphing calculators
 * chalkboard, whiteboard, or smartboard
 * practice problems handout
 * answers to practice problems
 * second checklist for study guide
 * textbook
 * homework problems
 * answers to homework problems
 * quiz review problems
 * quiz
 * quiz answers key

__Source for Lesson Plan and Research__
These first three sites are like lessons on how to solve those types of equations. It breaks the process down step by step. [|Solving one step linear equations] [|Solving multi-step linear equations] [|Solving equations with parentheses]

[|Place to check answers] - This is a great tool for students on coolmath.com if they do not abuse it. Students can check their answers by typing them into the site.

Practical Mathematics Sixth Edition. Palmer, Jarvis, Mrachek, Bibb. Copyright 1977 - This book is an older introduction to algebra and has some nice examples and explanations.

__**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:** Beach ball learners in my class will still be pleased with their choices during the study guide. This study guide will enable my students to pick and choose and be creative in creating something that they will be able to learn the information from. Clipboards will still be happy with the study guide assignment as well because they will still be able to organize the information I have given to them in the best way for them to learn the material. Also, clipboards will enjoy the quiz setup because everything will be organized with specific directions with what I want them to do on each problem. The study guide is another appeal to the microscopes as well as the in class discussion. We will be discussing solving more than one way and microscopes will be able to analyze their work. They will also be able to check their work to make sure that they fully understand what is going on. Just like in lesson 1, in lesson 2 I plan on making my classroom a supportive and safe place to ask questions and get clarification on problems. Puppies will be able to get help during class while they are doing problems and be able to ask questions on how I arrived at that answer so that the misunderstandings are cleared up before mistakes are made.


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

Rationale:** In this lesson, students are going to apply the knowledge that they learned in lesson 1 and use it to check their solutions to problems. I will be teaching my students how to solve linear equations algebraically and then they will be able to check their solutions using a graphing calculator and the techniques that they learned in lesson 1. Students will then add this new algebraic knowledge to their wiki study guide and find additional resources that help them to learn the material. After making the study guide, students will take a quiz over the material and show me that they can solve linear equations in more than one way. This uses all the knowledge that they have learned in lessons 1 and 2 and applies it to problems where they are asked to solve using one technique or another.


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

Rationale:** __Verbal__: Students discussing with each other how to solve the problem. I explain to them how to solve the problem. __Logic__: Students will solve equations algebraically. __Musical__: I will play classical music in the background while students work independently. __Visual__: Students will use the graphic organizer to solve equations at first. __Interpersonal__: Students will be working in pairs to solve an equation. __Intrapersonal__: Students working on solving problems alone

Students will be using the same Type II technology that they used in lesson 1; the wikispace. Students will add to their wiki study guides the information that they learned in this lesson about how to solve linear equations algebraically. Students will still have a checklist of aspects that they must incorporate in their study guides. They will still use songs, videos, and pictures to enhance their wiki and to add some sort of reminder of how to do something. Students will have to continue to be creative.


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

Rationale:** Students will be taught the steps of the solving linear equations algebraically by using a [|step-by-step chart]. Hopefully by using this chart I will be able to pin point students' errors and correct them before they continue to make them and get stuck in that habit. This chart will also give me an idea of what the students do or do not understand because I will be able to see their process done out with every problem. Throughout the entire class we will be having discussions about how to solve a particular problem and talking about how we can check our own work to see if we are right. Through this discussion I can see who is on the same page and who might still need some more explanations or examples. I would also like to use an exit card. These exit cards will be able to show me how much the students have gained during my class because they will have to solve two or three problems before exiting the room. I will review these problems and see where the trouble areas are. I will also assign the students homework that will not be graded on correctness but on what they have gotten done. These homework assignments will enable me to also see where students are struggling with a concept. If I know where the trouble is, I can quickly remedy it before it continues and hinders further performances.

I want students to add onto their study guides from lesson 1 and use a new checklist to do so. This study guide will show me that they have connected the two lessons and will also show me that they understand what is going on. I will use a checklist to assess these study guides. I would also like to quiz the students on both lesson 1 and lesson 2. I feel this is the most accurate way to see if students can solve equations through a variety of techniques. This quiz will be assessed by an answer key that I have made up ahead of time.

__Teaching and Learning Sequence__
I feel like setting the desks up in twos is the more effective way to teach this lesson. I feel those twos should be placed in rows, however. A lot of this lesson will be conducted in a lecture form with independent and pair work throughout the class. The rows of twos will enable every student to be able to see the board clearly for the lecture, but also enable an easy setup for pair work.

Day 1: Day 2: Day 3: Students will fully understand the many different ways that they can solve a linear equation. They will see where these applications come into play in the real world, finding the answer to a budget or to find out how much spending money they have. The lesson will also be focused around getting the students able to pass the MLR "//**Students solve families of similar equations and inequalities**//." The hook I want to use on my students is to show them how to figure out their spending money for the week. **(Where, What, Why, Hook, Tailor: Logical, Verbal, Visual, Interpersonal, Intrapersonal, Musical).**
 * Students will enter class, receive a slip of paper with an equation on it, and get settled for class (3-5 minutes).
 * Students will be handed multiple [|step-by-step charts] and be taught how to use them to solve linear equations algebraically and then they will solve some in class examples (music with be playing lightly in the background) (20-25 minutes).
 * Students will solve their equation on their slip of paper and then find a peer who has found the same answer. They will then go to a pair of desks and get ready for the next instructions (5-8 minutes).
 * I will put a more difficult example on the board for the pairs to solve using the [|step-by-step charts]. Students will collaborate and find the best way for solving the problem (10-12 minutes).
 * Students will say what their answers were and we will discuss how they went about solving the problem (3-5 minutes).
 * Students will be given more examples to do in class and be given the time to ask questions that they feel have not been addressed (10-15 minutes).
 * I will give students the second checklist for the study guide and give them their homework problems (1-2 minutes).
 * Students will complete an exit card before leaving class (5-8 minutes).
 * Students will enter class, get homework questions ready, and get settled for class (3-5 minutes).
 * Students will ask any necessary questions over the homework and then pass it in (10-12 minutes).
 * Students will be given more examples to do while I review the homework (15-20 minutes).
 * Students will be able to work on their study guides and ask any questions that they have (20-25 minutes).
 * Students will hopefully be given back their homework and be able to ask questions (5-10 minutes).
 * Students can continue working on study guides, ask more questions, or work on practice problems (remainder of class).
 * Students will enter class and have any last minute questions ready to go (3-5 minutes).
 * Students will be given the opportunity to ask any questions that they may still have about the lesson (5-10 minutes).
 * I will do a mini review over what is going to be covered on the quiz (10-15 minutes).
 * Students can ask any last minutes clarifying questions (5-10 minutes).
 * Student will take the quiz (20-30 minutes).
 * Any remaining time I will play some sort of math game with the students.

Students will know how to solve y=ax+b algebraically and then use knowledge gained in lesson 1 to check their work. I plan on teaching the students how to do solve these by using a [|step-by-step chart]. By showing them step-by-step on how to solve these equations, I hope to implant a process into their heads that they will be able to recall without the chart. I plan on having the students solve practice problems in class individually and in pairs so that they can learn the process. I will give ample opportunities to have them ask me questions about areas they are having difficulty with so that I can correct the misunderstandings early. Understanding during classroom examples will be obtained through the questions that students ask and the class discussions about how they solved particular problems. Like in lesson 1, if two different answers are found, we as a class will solve the problem, step-by-step and find the error. See content notes below. **(Equip, Explore, Rethink, Tailors: Logical, Verbal, Visual, Interpersonal, Intrapersonal).**

I have always found that when trying to solve a difficult math problem, the most effective way to get the right answer is to use a friend. In this lesson, students will pair up with a peer and solve a complicated linear equation using the [|step-by-step chart]. This partner work will hopefully iron out some misconceptions that students might have been having with solving linear equations on their own. Since these pairs will be decided randomly through the use of matching, students will not be able to choose a friend to work with and not help solve the problem. The only role that a student in a pair might receive is the reporter. Other than that I want students to be equals in the problem solving process and both record their work. The reporter will simply tell the class the answer that they found. Getting students to solve a difficult problems makes them really use the knowledge gained in lesson 1 so they will check their work and hopefully discover their own mistakes if they do not arrive at the same answer. Through this application of prior knowledge to newly acquired knowledge, students will be grateful to know a way to check their solutions so that they can get the correct answer on a quiz or test. I will constantly be wandering around the room, listening to student discussions and answering any questions that may pop up. Evidence of my students' learning will come when they have completed the study guide they started in lesson 1 after adding the lesson 2 knowledge and after they have taken the quiz. Both of these assessments will enable me to see what they understand and what they may still have questions or misunderstandings over. Since the study guide will be reviewed before the quiz, students will be able to see the comments I have made and be able to ask more questions if necessary. Homework, exit cards, and in class examples will provide my students with an avenue for practicing their skills and reviewing what they know and don't know. Since these problems are not graded, students will be able to learn from their mistakes and not be penalized for them. The [|step-by-step chart] will be a clear way for students to see exactly where they keep making their mistakes and they will be able to fix them before the quiz. **(Explore, Experience, Rethink, Revise, Refine, Tailors: Interpersonal, Intrapersonal, Logical, Verbal, Visual).**

Students will use the [|step-by-step charts] to self assess their process of solving linear equations. By using this chart, students will be able to pinpoint where they repeatedly make a mistake and be able to focus on correcting that area. Students will also use the checklists provided to them for the study guide. To make sure they include everything, students will have to complete the checklist themselves and see what they have included or forgotten. In class examples will be solved during the class so students can see their mistakes. Homework will be reviewed and given back as soon the same class and I will be providing feedback throughout the entire class. Any questions that students have will be answered almost immediately and given the proper explanation needed to ensure that the misunderstanding is cleared up. This lesson ties directly to the homework that I will be assigning and since students will have to solve everyday problems with equations they will have to know how to do this process. **(Evaluate, Tailors: Interpersonal, Intrapersonal, Logical, Verbal).**

[|One step linear equations] are those equations that you only have to do one thing in order to solve them. Examples are x+3=9 or 3x=9. To solve these equations you have to do the opposite of the operation being done to x. However, you have to do this operation to both sides. So for x+3=9, the opposite of the operation +3 is -3. When you do this to both sides you get x+3-3=9-3. Since x+3-3 is the same as saying x+0, we have x=9-3. 9-3 is 6 so the answer is x=6. You can check your solution by inputting 6 for x. This gives you 6+3=9 which is true. [|Multi-step linear equations] are like the name implies; they are equations that require more than one step in order to solve. Examples of these are 3x-3=9 and (x/2)+7=11. These can sometimes confuse students because they want to use the order of operations to solve. However, this is not the case. To solve these equations you have to solve the operation you would do last in the order of operations and work your way backwards. Once you isolate which operation you are starting with, you do the same thing you would do for one step linear equations; do the opposite of the operation and make sure you do this to both sides. In the example 3x-3=9, the last operation you would do in the order of operations is the -3, so when solving this equation it is the first thing you do. The opposite operation of -3 is +3 so you have to add 3 to both sides. This leaves you with the equation 3x=12. Now you are left with one operation multiplying by 3. The opposite of multiplication is division, so you have to divide each side by 3. This leaves you with x=12/3 so x=4. Again to check your solution substitute 4 for x. You'll get 3(4)-3=9, 13-3=9 which checks out. Other multi-step equations deal with x being on both sides of the equation like 4x-3=-2x+9. To solve these we first must get the x's on the same side of the equation. You do this just like you would do with numbers. If you have a -2x, you +2x. Once you do this you get 6x-3=9. This type of problem looks just like the one above and is solved the same way. [|Equations with parentheses] only have one extra step and this is applying the distributive property first before solving for x. An example is 3(x+2)=12. To apply the distributive property you have to multiply 3 by everything inside the parentheses. This means you need to multiply 3 by x to get 3x AND you have to multiply 3 by +2 which gives you +6. Now you have the equation 3x+6=12. This is solved just like the multi-step equations above.
 * Content Notes**

Examples: 12x+9=15 (Answer: 1/2) 3x+4=10 (Answer: 2) (3x-2)/2=8 (Answer: 6) More to come when I have time to find some decent ones.

Second checklist for study guide Homework problems Equation slips Practice problems [|Step-by-step charts] Quizzes
 * Handouts**