L4+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 4 (Empathize)
 * Grade Level:** Grade 9 **Topic:** Equations and Inequalities

__**Objectives**__
Student will understand that quadratic equations have different methods for solving. Student will know how to factor and will know the quadratic formula. Student will be able to relate techniques for solving linear equations to those techniques used for quadratic equations.

__**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 continue learning how to solve quadratic equations, but will learn a new technique in doing so.

__**Assessment**__
Students will again use a [|step-by-step chart] to initially learn how to use the quadratic formula. Since many mistakes can be made by using this formula, the chart will enable students to pin-point their mistakes and correct them effectively. The charts will also allow me to see commonalities in students' mistakes so that I can help my students through the difficult part. Students will work through practice problems that we have completed in the previous lesson to see if they arrive at the same answer. This will show the students that both methods are acceptable for arriving at an answer. Students will also solve problems that are not easily solved with factoring. These problems will assist them in completing their blogs.
 * Formative (Assessment for Learning)**

Students will complete a blog about the different techniques for solving quadratics. They will write about which technique they like better and why and also about which system they will use more frequently and why. These blogs will not be assessed by a rubric, but more so assessed as being completed and covering the material needed for that blog. I think students will be given a checklist so they can view the requirements.
 * Summative (Assessment of Learning)**

__**Integration**__
Technology: Students will be using a free online blogging site to write a blog about the techniques for solving quadratic equations.

English: Students are going to be writing so they will have to know and use their English skills of sentences and correct grammar.

__Groupings__
Students are going to do [|think-pair-shares] during this lesson. This will allow my students to think individually about the question "Why can't you solve every quadratic equation by factoring?" Then they will be partnered up by who they are sitting next to in that class time. Since the desks will be put into pairs, it will make it easier. One person in the pair will be the nominated spokesperson and when time is up, the spokesperson will report to the class on their answers to the questions. I will assess my students participation in their pairs by walking around the room and making sure both people are talking and that they are on task. These [|think-pair-shares] will give the students some ideas for their blogs as well as get them thinking about how they are going to solve a quadratic equation that cannot be factored.

__**Differentiated Instruction**__
__Musical__: The video of the boys singing the quadratic equation will appeal to the musical learners. __Logical__: Students will solve a variety of quadratic equations using different techniques. __Verbal__: I will explain the different techniques that one can use to solve quadratic equations and I'll walk them through the steps of how to solve them, __Visual__: The step by step graphic organizer will appeal to my visual learners. __Intrapersonal__: The students will blog about their favorite solving method and will also solve problems on their own. __Interpersonal__: Students will do the think-pair-share about why someone cannot always factor to solve quadratic equations.
 * Strategies**

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

If a student is absent from this lesson, they are going to have to contact me by email so that we can set up a time to get the notes. I feel this lesson needs to be explained by myself to the student and the meeting will enable this is happen. When I meet with the student, we will talk about the question "Why can't you solve every quadratic equation by factoring?" and then I will show him or her how solve more complicated quadratics by using the quadratic formula. The absent student will be given the practice problems, homework assignment, and the blog assignment before leaving the meeting.

Every student will write a blog about which technique they like better to solve quadratics and which system they are going to use more frequently and why. This Type II technology of blogs will enable students to use video clips, pictures, and/or songs to express their ideas and back up their thoughts.
 * Extensions**

__**Materials, Resources and Technology**__

 * video clip of [|boys singing quadratic formula]
 * [|step-by-step charts]
 * blog directions
 * blog checklist
 * practice problems
 * homework problems
 * textbook
 * chalkboard, whiteboard, or smartboard
 * practice problem answer key
 * homework problem answer key

__Source for Lesson Plan and Research__
[|Boys singing quadratic formula] - This video will help some of my students with remembering the quadratic formula because it is put to a beat. [|Quadratic formula] - This site is a simple explanation on using the quadratic formula to solve quadratic equations. [|Quadratic equation solver] - This solver will help students in correcting their answers and to see where they have made a mistake. [|Algebra skills] - This site has a lesson on almost every aspect of quadratic equations that may students may need assistance with. [|Quadratic equations] - This site is a simplistic explanation for solving quadratics. It also includes a quiz to test your knowledge. [|Explanation of quadratic formula] [|Solving by factoring]- This purple math site provides explanations and examples for using a factored quadratic to solve quadratic equations. [|How to factor]

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 balls will enjoy having an initial choice in how they want to solve quadratic equations. I am hoping, however, that with certain problems they will see that one technique is more efficient than another. But they do have the choice. Beach balls also have their own choice on what they want to reflect upon in their blog. Microscopes will love the class discussion about how they think they should solve quadratic equations based on their knowledge of linear equations. They will also like the discussion about why we cannot always use factoring to solve these quadratics. Microscopes will be able to use their deeper thinking skills and really dive into quadratics. My clipboards will enjoy the lecture type setting of presenting how to correctly solve quadratic equations. Since both techniques have a sequential way of using them, clipboards will feel very comfortable using these procedures. Like every other lesson, mistakes are not going to be made out like negatives. Instead they are going to be used as learning points and ways to avoid them in the future. Puppies will love the safe environment of knowing that mistakes are not a big deal and that they can ask questions to fix them in the long run.


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

Rationale:** Students will be seeing which technique they like better and why, but also considering which technique they would use most often use and why. This reflective process enables them to empathize with the other side so that they can choose more clearly. They also get to see why the quadratic formula was made and maybe appreciate it more even though it is slightly complicated to remember. Students will be learning how to solve more equations than the simple linear ones and they will be able to add this knowledge to their repertoire.


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

Rationale:** __Musical__: The video of the boys singing the quadratic equation will appeal to the musical learners. __Logical__: Students will solve a variety of quadratic equations using different techniques. __Verbal__: I will explain the different techniques that one can use to solve quadratic equations and I'll walk them through the steps of how to solve them, __Visual__: The step by step graphic organizer will appeal to my visual learners. __Intrapersonal__: The students will blog about their favorite solving method and will also solve problems on their own. __Interpersonal__: Students will do the think-pair-share about why someone cannot always factor to solve quadratic equations.

Students will be using the Type II technology of blogs in this lesson. These blogs are Type II because they are using the internet which contains pictures, songs, and videos that they can use to back up their ideas and views.


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

Rationale:** I will use a variety of informal assessments to check for understanding from my students. One of which is the [|step-by-step charts] that my students will be using to solve quadratic equations by factoring and with the quadratic formula. The students and I will be able to pin-point where mistakes are happening and I can address the problem quickly. The [|think-pair-share] will also be used as an informal assessment. Students will be paired up after thinking about the question "Why can't you always use factoring when solving quadratic equations?" This will then turn into a class discussion about this question. Another class discussion that will be used as an informal assessment is that of how students think they can solve these quadratic equations. This discussion will allow me to see where the students mind tracks are and ways in which I can help them see the correct way. I will also use practice problems to gauge how much they understand and how much more work needs to be done.

The formal assessment that I will use is the blog. Students will have to blog about which solving technique that they like better and why and also which one they will use more frequently and why. I will assess these using a checklist since I cannot grade opinion. I just want to make sure everything is covered and appropriate.

__Teaching and Learning Sequence__
I think that my classroom should be arranged in pairs which are facing the front of the room. This will allow students to easily get into pairs for the [|think-pair-share] as well as see the board and be able to take notes about solving quadratic equations. I think the pairs will also enable students to discuss with someone that they are comfortable with since most students sit next to someone they know.

Day 1: Day 2: Student will understand that quadratic equations have different methods for solving. In this lesson students will be learning two different ways in which to solve quadratic equations and they will also be comparing these two techniques and debating which one they prefer and why. They will be shown examples of where they can use quadratic equations in the real world by seeing how fast the computer will take to smash to the ground. Every student will be able to meet the MLR of solving "//**families of equations and inequalities**//." Since they are solving equations, they are clearly meeting the standard. **(Where, Why, What, Hook, Tailors: Logical, Verbal, Visual, Interpersonal, Intrapersonal, Musical).**
 * Students will enter class, be seated, and get ready for class to begin (3-5 minutes).
 * I will do a quick review over what they have learned about in the last lesson (3-5 minutes).
 * Students and I will have a discussion about ways in which they think they can solve quadratic equations. During this discussion I will prove or disprove why their answers are wrong (15-20 minutes).
 * I will show the students how they can solve quadratic equations by factoring and give them some practice problems to do (15-20 minutes).
 * I will give the students a problem that is difficult to solve with factoring and see what kinds of suggestions that they have for solving these types of quadratic equations. I will also let them know that next class is when we will actually learn the way to solve these problems (10-15 minutes).
 * I will assign the homework problems on factoring and let the students get started. This time will also be allotted to asking me questions and doing class examples that they still have not grasped (15 minutes).
 * Students will enter class, get seated, and get their homework out (3-5 minutes).
 * We will go over any questions on the homework (5-10 minutes).
 * I will do a review over what they thought about solving the difficult quadratic equation. We will have a mini discussion again on how they think they can solve it (10-15 minutes).
 * I will introduce the quadratic formula by playing the video of the boys singing and then we will do some practice problems using the quadratic formula. The practice problems will be ones that we have already solved using factoring (10-15 minutes).
 * Students will think individually about why they can't always use factoring to solve equations (3-5 minutes).
 * Students will get with the person sitting next to them and talk about the same question (5-10 minutes).
 * We will have a class discussion about the same topic (5-10 minutes).
 * I will hand out the blog directions (3-5 minutes).
 * I will assign the homework problems (3-5 minutes).
 * Any extra time will be allotted to asking me questions.

I plan on lecturing and giving the students notes after they try to figure it out on their own. After this lecture students will know how to factor and will know the quadratic formula. Since no one learns well with a plain, old lecture, I am going to incorporate a [|video of boys singing], individual reflection, pair discussions, class discussions, and practice problems in order to teach my students the techniques for solving quadratic equations. Throughout all of the discussions I will correct misunderstandings and show them the proper way to solve quadratics. I will also use practice problems to see what my students understand about the two solving techniques. SEE CONTENT NOTES. **(Equip, Explore, Rethink, Tailors: Musical, Interpersonal, Intrapersonal, Logical, Visual, Verbal).**

Students will be using higher order thinking by trying to use their prior knowledge to figure out how to solve quadratic equations on their own. By having a class discussion, we will try to figure it out with my guidance. Students will also reflect and discuss why they think the quadratic formula is used and factoring is not the only technique. Student will be able to relate techniques for solving linear equations to those techniques used for quadratic equations. Since the discussion about solving the quadratics is comparing linear techniques with those they think they would use to solve quadratic equations it fits perfectly. I will simply keep the conversation going and ask questions that will hopefully prompt my students to arrive at the correct answer. I will group my students in pairs by where they choose to sit in the classroom for that lesson. One person will be chosen as a reporter and report what the pairs talked about revolving around the question. My students will show learning by the discussions, the [|step-by-step charts], the practice problems, and then at the very end, by their blogs. All of these assessments will give me an idea of where my students are understanding the material and the problem areas that I have to address. Students will get ample opportunities to revise their practice problems and work through their mistakes so that they fully understand the problem. This technique will help them so they can pin-point the issue and avoid it while completing the homework. **(Explore, Experience, Rethink, Revise, Refine, Tailors: Logical, Visual, Verbal, Interpersonal, Intrapersonal).**

Students will self-asses by filling out the checklist before turning in their blog. This will make sure that they have included everything that I have asked for. Also students will self-assess by writing the blog. They will have to think about which technique they like better and also which one they would use more frequently and why. These questions get the students thinking about themselves and why they like one way better than another. I will provide feedback for my students through the discussions when they say something that isn't correct, I will show them why and then help them arrive at the correct answer. I will also be constantly answering questions and clarifying common problems with the examples so that everyone is on the same page and understanding the material. This lesson connects to what they will be doing in the next two lessons with solving everyday situations with equations and they will need to know how to solve quadratic equations to do this effectively. **(Evaluate, Tailors: Logical, Intrapersonal, Interpersonal, Verbal).**

I will be using a combination of the following resources to teach my students how to factor simpler quadratic equations and also what the quadratic formula is and how to use it properly. These resources will also be a place my students can reference for a different examples or explanations. In [|order to factor], you are going to have to find numbers to fill in for the spaces (x+/- _)(x+/- __). For example x2+5x+6=0 can be factored down into (x+2)(x+3). In order to factor this you need to find factors of 6 that can be added up to equal a positive 5. Those factors are 3 and 4. The operation in front of the constant (the addition in front of the 6) tells us that the signs of the factors are the same and the operation in from of the 5x tells us the signs of the factors are positive like the addition sign. If the sign in front of the constant is a negative or subtraction it tells us the factors are of opposite signs. One is negative and one is positive. Once you know the factors and the signs of the factors, you simply plug them into the equation (x+/- _)(x+/-__ ). Factoring can only be done for more simple quadratic equations. If they are not simple enough to factor, you have to use the quadratic formula. The quadratic formula is this:. In order to find the roots and solve complicated quadratics you simply have to fill in the corresponding a, b, and c values and solve. To find those values you have to look at the general quadratic formula (ax2+bx+c=y) and find the corresponding numbers that match the a, b, and c values. For example, 5x2+6x+8=0, the a value is 5, the b value is 6 and the c value is 8. Fill those numbers into the equation and solve. I am not going to solve it out because it gets really messy on a computer. There is one thing to remember though when solving with the quadratic formula, the quadratic must be set equal to 0.
 * Content Notes**

Resources: [|Boys singing quadratic formula] - This video will help some of my students with remembering the quadratic formula because it is put to a beat. [|Quadratic formula] - This site is a simple explanation on using the quadratic formula to solve quadratic equations. [|Quadratic equation solver] - This solver will help students in correcting their answers and to see where they have made a mistake. [|Algebra skills] - This site has a lesson on almost every aspect of quadratic equations that may students may need assistance with. [|Quadratic equations] - This site is a simplistic explanation for solving quadratics. It also includes a quiz to test your knowledge. [|Explanation of quadratic formula] [|Solving by factoring]- This purple math site provides explanations and examples for using a factored quadratic to solve quadratic equations. [|How to factor]

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.


 * Handouts**
 * [|step-by-step charts]
 * homework problems
 * practice problems
 * blog directions
 * blog checklist