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= = Understanding By Design Systems of Equations Lesson (Steve Tobar) Which is the best method to solve a system of equations? A linear equation in two variables can represent relationships between quantities Some real-world situations can be translated into a system of equations The solution of a system of equations is the ordered pair that satisfies both equations. |||| How do you set up a system of equations to solve a real life problem? How do you solve a system of equations? || Which is the best method to solve a system of equations? What are the advantages and disadvantages of the two methods used to solve a system of equations? How can variables and equations be used to represent the relationship between quantities? How to solve real life situations by using systems of equations? || Students will know… |||||| Skills Students will be able to… || They will also know how to solve a system of equations by using the best possible method.
 * Title of Lesson |||| Solving Systems of Equations || Grade Level |||| 11th ||
 * Curriculum Area |||| Algebra II || Time Frame |||| One week long ||
 * Developed By |||||||||| Steve Tobar ||
 * Identify Desired Results (Stage 1) ||
 * Content Standards ||
 * Students will learn how to solve a system of equations by using three different methods: graphing, substitution, and elimination. They will learn how to set up systems of equations to solve problems in the real world and they will be able to choose the best method depending on the system of the equations. ||
 * Understandings |||||| Essential Question(s) ||
 * Overarching Understanding |||| Overarching || Topical ||
 * To solve systems of equations by using the graphing method, the substitution or the linear combination methods.
 * Knowledge
 * They will know how to represent a word problem with a system of equations.

|||||| Solve a system of equations by using the graphing, the substitution and the linear combination methods To understand the advantages, and disadvantages of these methods. Read and interpret a real-world situation and develop a system of equations that accurately reflects the situation

|| Band A charges $600. Band B charges $350 plus $1.25 per ticket sold. Determine the number of tickets for which the cost of the two bands would be equal. A caterer charges a fixed cost for preparing dinner and an additional cost per person served. 100 students will cost $750 and 150 students will cost $1050. Find the caterer’s fixed cost and the cost per person. Assume that 200 students will attend. Write a report listing which band you will choose and the ticket price you will need to charge to break even. Repeat assuming 300 students. || How was it creating this lesson?
 * Assessment Evidence (Stage 2) ||
 * Performance Task Description ||
 * Have students plan a dinner with a Band. The ticket price should be as low as possible to encourage attendance.
 * Other Evidence ||
 * Have students design their own word problem by applying it to a real life situation of their own. They can work in groups of two or three. They must also solve the word problem and present their answers to the class. ||
 * Learning Plan (Stage 3) ||
 * Where are your students headed? Where have they been? How will you make sure the students know where they are going? |||||||| Students have learned to solve systems of equations by using the graphing method. However the graphing method has many disadvantages and therefore better methods are needed. Although, the substitution and the linear combination methods have a few disadvantages, these methods for solving systems of equations are superior methods than the graphing method. ||
 * How will you hook students at the beginning of the unit? |||||||| For a warm up activity, when introduction the substitution method, have students solve a system of equations with fractions by using the graphing method. Students will try to understand they need a better method for solving this system of equations. ||
 * What events will help students experience and explore the big idea and questions in the unit? How will you equip them with needed skills and knowledge? |||||||| Go over the substitution and linear combination methods, students will then be asked to solve more systems of equations by using both methods. Have students work with a partner, and have them present their answers to the class. ||
 * How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work? |||||||| The goal now is for them to discover which method is better to be used when given a system of equations. Each method has its own advantages and disadvantages. ||
 * How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit? |||||||| Have students work with a partner. Have them discuss their answers and the process. Also, have them write their answers on the board and present their answer to the class. ||
 * How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit? |||||||| Have a discussion of how to pick the best method to solve a system of equation. Go over more examples by having them explain which would be the best method and why. ||
 * How will you organize and sequence the learning activities to optimize the engagement and achievement of ALL students? |||||||| During the week, I would have the warm up activities, go over the warm up and the homework, introduce the lesson by going over the word problem and doing extra examples. Then have students work with a partner on some problems. I would then have the students write the answers on the board and present their answers to the class. ||

It was a little challenging at first. My problem was I wasn’t sure where to start. After a little while, the lesson started to build itself with the various goals and activities. What I like about this format is that I really had to think about the lesson and to come up with a good performance task so I decided to do some research over the internet.

What difficulties did you encounter?

I guess coming up with the overarching and the topical essential questions was a little difficult to me. I haven’t taught Algebra II in a while now and in fact, this is my second year teaching this subject, so getting the “big picture” and how the lesson would fit in the overall scheme of concepts was a little challenging. I had to open an algebra II book and look at all the chapters and sections in order to see the big picture and how this lesson would fit in it.

Did you like the format?

The Word format was a little confusing. I made a few changes and I also did some research on the internet to see some sample lessons in Algebra II. This helped a lot. I think the second time I use this format will be a lot better and faster for me. I have to say, I actually use this lesson during one of my classes and the vice-principal, who happened to stop by my room that day to do an informal observation was very pleased and interested to know where I had learned about this new and exciting format. He also gave me an article with a list of more essential questions for practice.

What are additional questions you now have?

On the last part of the lesson, the Learning Plan, the questions seemed a little confusing. I tried to answer these questions in my own way in order to finish the lesson. I would definitely like to see more sample lessons that use this similar format to help more.

Comments from Lisa Sarinelli: Considering I am a third grade teacher, and did not so well in Algebra I, it took me a few minutes to really understand the complete unit. I thought your performance task idea of having the students schedule a dinner/dance was fabulous. It was a great real world connection. As 11th grades, the students will be planning proms over the next two years and could use this lesson to help them find affordable caterers and bands. Is there away you could connect this task to your learning plan? Also, I am a little confused on how your students will be assessed on the their task. It says they will write a report listing which band they will choose and the ticket price they will need to charge to break even. Will the students have to write a specific type of report? Perhaps, they could write up a phone call to the band and caterer they picked or did not pick and explain why. Or, could they present their choice of band and caterer pick to the school board (the class) and explain/convince them why they are the best hire? Finally, I think the students would enjoy the task! I know how difficult it can be picking bands and caterers... I'm planning trying to plan a wedding!  From Omar Minaya I think that your plans are great. Your plans are very clear and very word friendly. Also the performance task you chose is very applicable to everyday situations. I am also a math teacher. As a matter of a fact I teach geometry and I think your graphing ideas are great. I am not sure whether these students are creating one project for the whole class or one each. If it is one for the whole class it seems many will not be able to do too much work. Assigning groups of 4 to 5 students and allowing them to chose how big or small (within certain range) they want the concert be would probably help get more interesting results.