# Accommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego

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1 Accommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego Courtney O Donovan Class: Algebra 1 Day #: 6-7 Grade: 8th Number of Students: 25 Date: May 12-13, 2011 Goal: Students will learn how to solve systems of equations using elimination by adding and subtracting. Objectives: Students will solve systems of equations using elimination by addition and subtraction. Students will collaborate with each other as they work through problems using algebra tiles and examples. Standards: 8.EE b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. NCTM Standards: The NCTM Standard being addressed in this lesson is problem solving and representation. Students will be completing an activity in which they will use algebra squares to represent linear equations. This way, students can begin to see how to use elimination to solve systems of equations. They can see how the variables are eliminated by either adding or subtracting the equations. Problem solving will be emphasized so that students know they can use whatever method they would like to solve the systems. The NCTM Standard of representation is also being addressed. Students are using algebra squares to represent the equations and their solutions to solve the system of linear equations. Materials: Elmo Paper 14 bags of Algebra Tiles 1 Bag of Algebra Tiles with the symbol that the tile represents written on the tile 25 Algebra Tile Activity worksheets 25 worksheets for homework LiveScribe Pen Warm-Up: Solve this system using substitution and check your answers using the graph to find the point of intersection: 2y +x = - 4

4 I will go over to Diego s group and ask his group if they have any questions. I will just go through what is required again so he understands. If will ask him if he needs any more help and then proceed to have his group work on the activity I will walk around the class checking in with students progress and answering any questions they might have. Then we will come back as a class and discuss problems. I will ask the groups to share their results on the board and explain to the class what they did. Diego will be allowed extra time to complete the activity, approximately 5 to 10 minutes more. Closure: I will tell students that tomorrow we will review how to formally solve systems of linear equations using elimination by addition and subtraction. I will ask them to hand in their worksheets for class credit.

5 Warm-Up: (5-10 min) Discuss the activity that we did the previous day. Transition: Now please take out a piece of paper and a pencil to take notes with and we will begin to discuss what it means to solve systems of equations by elimination by adding and subtracting. Procedure (25 min): 1. Using the Elmo, I will write notes on a piece of loose leaf paper, and the class will take notes on what I write down and what we discuss as a class involving the method of elimination. I will begin by asking the students what was the definition of elimination that we discussed yesterday. We will write down the definition. During the notes section of section I will use a LiveScribe Pen, which is an assistive technology. This would allow me to record the notes and then post them on the class website for Diego and other students to review later. I will also be highlighting important words and steps, such as the word elimination and adding and subtracting and the steps. 2. We will then what it means to eliminate by adding and subtracting as it pertains to systems of equations. I will stress that we are getting rid of a variable and that is where elimination comes into play. This may confuse them at first so I am prepared to address any questions they may have. 3. Then I will explain when we eliminate by addition and when we eliminate by subtraction. Here I will use the mathematical process notes as described in the article by Sally Hunt. These notes are set up in a way where there is a table that contains the examples and on the side an explanation for what is means and why. This helps to outline the process so that Diego can better understand how to use the process to solve the problems. They will be set up their notes like this in their notebooks: Problem Process -6x + 3y = 4 6x + 2y = 6 Describe what we did. Write directions for solving systems of linear equations by elimination. We add the two equations if the coefficients of one variable are opposite of each other (i.e. -6x and 6x, the coefficients are -6 and 6 respectively so they are opposite of each other so we add the equations because then -6x+6x =0 and we eliminate the x variable) Ex. -6x + 3y = 4 6x + 2y = 6 We add these equations because the coefficients attached to the x are -6 and 6. Since -6 and 6 are opposite integers. We subtract two equations if the coefficients of one variable are the same (i.e. 6x and 6x both have coefficients of 6, so we subtract the equations because 6-6=0 and that eliminates the x-variable) Ex. 6x + 3y = 4 6x + 2y = 6 We subtract these equations because looking at the x-variable the coefficients attached are 6 and 6. Since these are the same integers in order to eliminate

7 one and explain why we choose x. I will then ask if the coefficients on the x-values are opposites. Then I will show them they are not because the coefficient on both x-variables are 1 and if we used addition we would still have the x-variable and we would not have eliminated any variable. Since the signs on the coefficients are the same, we subtract the equations. 8. In order to subtract the equation, I will show them that they must do the following: I will explain that they are not only subtracting the x-values but they must subtract all the terms in the bottom equation from all the terms in the top equation. To make this clearer for students, I will show them that they can distribute the negative sign to all the terms in the bottom equation to get: So now they just subtract and get the following answer: y = 1 9. (10 min) I will then tell them that they will use substitution again to find the x-value now that they have the y-value. I will ask them to choose from the original equations which one they would like to use. I will emphasize that they need to choose from the original equations in order to get the correct solution. So as a class we will work out the rest of the problem. Walk over to Diego and make sure that he is writing his notes down and that he is working on the material. Ask him how he feels about the new material and if I need to make any clarifications. 10. Now that we have solved a couple of systems as a class, I will have the students work on some in partners. Students will be partnered with the same peers they were the day before. This way Diego will be partnered with the same peer who he is comfortable working with. He will also be allowed 10 extra minutes to work on them. Diego will also be given a worksheet with the Word Problem Process Notes and the word problems will be written to be more coherent for him to address his reading level. They will be put on the Elmo. They will be word problems. This way they can begin to use the method on their own. The problems will be the following: 1. Six Flags was chosen for a senior trip. The senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Ever van had the same number of students in it as did the buses. Find the number of students in each van and in each bus. 2. Sharon and Paul are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and bags of daffodil bulbs, Sharon sold 10 bags of windflower bulbs and 12 bags of daffodil bulbs for a total of \$380. Paul sold 6 bags of windflower bulbs and 8 bags

8 of daffodil bulbs for a total of \$244. What is the cost each of one bag of windflower bulbs and one bag of daffodil bulbs? After giving them about 10 minutes to work, during which I will be walking around observing student work and answering questions, I will have a pair come to the board and show their work and explain what they did to the class. I will then ask if everyone came up with the same answer and if there are any questions, I will address them then. For the word problems, I will have the following sheet for Diego to work on as he solves them. They are Word Problem Process Notes. He will have used these process notes when he solved word problems that required him to solve systems of equations by substitution. So this will be familiar to him. They are found after the lesson. I also decreased the reading in the word problem and left the vital information needed to solve the problem. He will turn this in at the end of class. If I notice that Diego is doing the correct work, I will ask him if he would like to present the problem to the class. If not, then he can continue working or listen. Closing: (5 min) I will close by reviewing this new method of solving systems by elimination. I will ask them what are the steps involved by solving systems of equations. I will also discuss how there are multiple ways of solving these systems of equations and the way they choose to solve them is up to them. Students will turn in their work on the examples for class participation for the day. Extension: If time allows, I will allow students to begin their homework for that night which will be a worksheet with the systems of equations that they will need to solve by elimination by adding and subtracting. There will also be a part in which students can choose which method, of the methods they have learned thus far, to solve them. Assessment: I will be assessing students throughout the lesson. I will be walking around when they are working on the algebra tiles to begin to see what the students are coming up with. The worksheets that they turn in will be checked for class participation but I will go through the worksheets and see if students understand the concept. I will also be observing and assessing their work on the examples in class they turned in. The final assessment will be a homework sheet that students will complete and turn in for a grade. This will be able to help me in determining where students stand on solving systems of equations by elimination. It will help me decide whether or not to take more time to go over this concept or to see if they understand enough to move on to solving systems of equations by multiplying

9 Name Date Fun with Algebra Tiles Directions: Solve the following systems of equations using the algebra tiles. Explain what how you solved the system. a. 3x - y = 5 x + y =3 b. x + 4y = 10 x + 2y = 6

10 Name Date Fun with Algebra Tiles (Accommodated) Directions: Use algebra tiles to solve the problems. Write the steps you took to solve the problems. a. 3x - y = 5 x + y =3 Steps: b. x + 4y = 10 x + 2y = 6 Steps:

11 This will be on a foldable so that students can open it up to the right page to find the steps. Solving Systems of Equations Graphing Substitution Elimination Matrices Steps: Steps: Steps: Steps:

12

13 Name DIEGO Date Word Problem Process Notes Number 3: There are 8 vans and 8 buses with 240 students. There are 4 vans and 1 bus with 54 students. Question: How many students can the van hold and the bus hold? Write the question. List clue words and facts. Identify the variable(s). Make a drawing. Choose a strategy. Solve the problem. Use elimination. Write your answer in a complete sentence. Check your answer.

14 Number 4: Sharon sold 10 bags of sunflowers and 12 bags of daffodils for a total of \$380. Paul sold 6 bags of sunflowers and 8 bags of daffodils for a total of \$244. Question: What is the cost each of one bag of sunflowers and one bag of daffodils? Write the question. List clue words and facts. Identify the variable(s). Make a drawing. Choose a strategy. Solve the problem. Use elimination. Write your answer in a complete sentence. Check your answer.

15 Name Date Solving Systems of Equations by Elimination Solve the systems of equations using elimination. 1. x+ 2y = x - y = 30 -x +y = 5-3x + 7y = x + 6y = x - 9y = x + 6y = 26 4x + 3y = -9 Solve the systems of equations using any method you have learned so far. 5. x + 2y = x + 12y = - 6-2x+y =- 4 2x + 5y = 0 Solve the following word problem: Two small jugs and one large jug can hold 8 cups of Kool-aid. One large jug minus one small jug holds 2 cups of Kool-aid. How many cups of Kool-aid can each jug hold?

16

17 Name_DIEGO Date Solving Systems of Equations by Elimination (Accommodated Homework) Solve the systems of equations using substitution. You can use your graphic organizer. 1. x + 2y = x - y = 30 -x + y = 5 2x + y = - 4 Solve the systems of linear equations using elimination. You can use your graphic organizer. 3. 5x + 6y = x - 9y = x + 6y = 26 4x + 3y = -9

18 Solve the following word problem by filling out the Word Problem Process Notes: - Suppose Ken has 25 coins in nickels and dimes only and has a total of \$1.65. How many of each coin does he have? - There are 25 nickels and dimes. - The total amount of money in nickels and dimes is \$ How many nickels and dimes does Ken have? Write the question. List clue words and facts. Identify the variable(s). Make a drawing. Choose a strategy. Solve the problem. Use elimination. Write your answer in a complete sentence. Check your answer.

19 Co-Teaching This Lesson If I were to co-teach this lesson, I would use the Alternative Teaching style. This would most benefit my students because I could teach to the larger portion of the class while my coteacher taught to a smaller group comprised of students who may need extra help. I would put Diego in this smaller group. He would have the directions of the activity read to him again and he would be able to have more one-on-one time with the co-teacher. I would teach the activity and the notes section to this larger portion and then have the co-teacher do the same with the other group. During the activity, we would both walk around the classroom observing how the class is getting along with the activity. This will give me a chance to work with the students in the smaller groups and determine if they understand the material and if there needs to be any more clarifications. I think that it is important that both teachers interact with all the students so that if one misses an important fact or needs help making students understand, the other can step in and give further explanations. I think that all the co-teaching styles are beneficial to student s learning. I do not think that any teaching style is better than the other and there are definitely times during a class that one style may work better than another. In the case of this lesson, I used the alternative teaching style as way to reach those students who may still be struggling with the material and need more assistance. They get more individual attention by working with the coteacher. I could also set up to co-teaching the opposite way such that I teach to the smaller group and the co-teacher teaches to the larger portion of the class. I think that it is important that one teacher does not always teach to the smaller group, which may have students who need extra help or that has students who are excelling, and the other teacher teaches to everyone else. Each teacher should be interacting with all the students for those same reasons

20 that I stated above when both teachers are walking around the classroom. It is important that both teachers build relationships with all the students, so that students feel comfortable seeking help from both teachers and that they are valued by both.

21 Reflection This assignment has made me more aware of the ways in which I can accommodate my lessons for students with disabilities. For this assignment, I chose to accommodate my lesson for Diego. The lesson I chose to make the accommodations was already written for a class comprised of unmotivated students. In order to make the lesson more engaging for students, I created an activity using algebra tiles. I used this activity to help make abstract algebraic ideas more concrete for them by providing them with these manipulatives so they could work hands on with the algebra. The lesson was on solving systems of linear equations by elimination. Although this activity may be more engaging for the unmotivated students, it may cause difficulty for Diego who learns better orally rather than with visuals. To accommodate the activity for Diego, I first split the groups up into pairs. By working in pairs, students need to work together to solve the problems using the tiles and share the ideas about how to go about this. I would pair Diego with someone he is comfortable working with because he has a fear of looking stupid in front of his classmates. I would also ask him to show his work in front of the class, if I knew that it was correct and he felt comfortable in doing so. This would increase his confidence in his work and may lessen any frustration he might feel. I will make sure that I repeat directions to his pair to ensure that he understood what he is supposed to do. I will again explain how to use the algebra tiles and I will be writing the process for solving the systems with the tiles on the Elmo so students, especially Diego may reference them throughout the activity. Diego does well in memorizing processes so this will be of use to him. I will ask him if he needs any more clarification and make sure to praise him for being on task and working hard. I think it is important to provide this moral to

22 support to Diego and to all students as a way to make sure that they feel that they are valued members of the classroom as well as help with classroom management. Finally, I will give Diego algebra tiles that are labeled so that he can see how the tiles represent each symbol in the system. This will help with his difficulty with visuals. By giving him this extra support, he will not be focused on what square represents what symbol but rather it will aid him in setting up the equations and then to solve them. It will be more focused on the mathematical content rather than the ability to use algebra tiles. Other accommodations I made for Diego was to use the LiveScribe pen. This pen automatically records the lesson as I write which I can then load up on the classroom website. This is where students, especially Diego, can go and review the material that we went over in class. Diego could make sure that the notes he toke in class matches up with the ones on the website and fill in any gaps he may have or clarify any concepts he was having difficulty with. This is especially helpful since Diego learns best orally. In addition to using the LiveScribe pen, I also used two different process notes, mathematical process notes during the notes portion of class and the world problem process notes that will be used while the class is working on their own problems and that Diego may use on his homework. These notes help organize students and match examples to the more abstract concepts. Because Diego does well at memorizing formulas and processes, these notes will help match up the processes he needs to know to specific examples and give a reason for doing them. In order to address Diego s reading level, I limited the amount of information in the word problems and also wrote them in bullet form so that Diego will be able to look at each bullet and see what the problem is asking him to do. The bullets will be able to organize the information. I think this will help Diego focus more on the math rather than the reading

23 involved. I also addressed some vocabulary by changing certain words. They were minor vocabulary words but they could still distract Diego and cause some frustration. They were windflower bulbs and daffodil bulbs which I just changed to sunflowers and daffodils. With regards to assessment, Diego will turn in his Fun with Algebra Tiles Worksheet and his Word Problem Process Notes at the end of each day s class, just like the rest of the class turns in their in-class assignment sheets. The Word Problem Process Notes were an accommodation to the in-class problems. Diego was given the same word problem but it was broken up using bullet points so that it was not too much reading. The homework which Diego will turn in also was accommodated. I explicitly told him what method to use to solve the equations because he has difficulty choosing the appropriate mathematical method. The word problem is also different because Diego does well with monetary problems. So I changed his word problem to one about money that would peak his interest and show off his strength but still assess whether or not he can take a word problem and solve it using the elimination method from class. Although I did make many accommodations to the lesson, there are a couple of aspects during the lesson that remained unchanged. I kept the part of the lesson where I went over the answers to the quiz. I think that this is important in order for students to see where their mistakes are. By giving the answers orally in addition to visually writing them on the board, Diego can correct any mistakes he made and see why he made them. I also did not change the warm-up for day two because it was a discussion on the algebra tiles activity from the day before. This discussion will help Diego to recall what we learned the day before which we will go in depth this day.

24 These accommodations are necessary for Diego to succeed in the class. It is important, as a teacher that I differentiate my lessons appropriately and plan prior to the lesson how I am going to support my students to help them gain a deeper understanding of the mathematical content. I believe that these accommodations address the areas of concerns with regards to Diego s ability to learn.

25 The General Educator s Role in Special Education SPED 405B - Carty Fall 2011 Accommodations assignment RUBRIC Name: Courtney O Donovan Signature: Criteria Points Comments Brainstorming checklist attached and clearly addresses these things for the lesson provided: Input (what the teacher does/instruction) Output (what the student does / produces) Student Behavior Testing / Evaluation Note: There may be crossover between categories Lesson Plan makes it very clear where accommodations were made compared to the original. (fonts, underlined, bold, color, headings, etc ) Accommodations are present for: a reading component of some kind at least one handout a student product (something that the student will produce) preferably, some sort of student-centered or guided activity an assessment of student learning that targets your lesson objective(s) Accommodations are valid and meet the needs of the student chosen. There are no components of the lesson that were not addressed and remain a hindrance to learning for the student chosen. Reading component clearly labeled as original and accommodated and text is at a lower level./ more accessible Description of a way to co-teach this lesson includes: *Model(s) of co-teaching you would use of those discussed in class and why it/they would work for this lesson. *The responsibilities of each teacher during the lesson (where will they be? How will students be grouped? What will each teacher be doing instructionally during the class period?) Reflection includes: *A clear, succinct explanation and rationale for the changes and accommodations made to my lesson and how they match the needs of my selected student. *An explanation of where the lesson did not need to be changed or accommodated since it already was planned in such a way that it met the needs of the student chosen. *Overall reflection on the process / assignment. /15 /5 /30 /10 /10 TOTAL /70

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