L6+Dube,+Brittany

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

Teacher’s Name:** Ms. Dube **Lesson:** Lesson 6 - Explanation
 * Grade Level:** 9th and 10th **Topic:** Linear Equations and Inequalities

__**Objectives**__

 * Student will understand that factoring is useful when working with linear equations.**
 * Student will know the quadratic formula, what linear equations are, and how to factor linear equations using the quadratic formula.**
 * Student will be able to demonstrate the quadratic formula in factoring.**

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


 * Rationale:** Students will learn to apply the quadratic formula when factoring equations.

__**Assessment**__
Students will be assessed in many different formats throughout this lesson. Students will first answer the “question of the day.” This will check for comprehension on the material that was covered in the lesson before. Students will also fill out a graphic organizer that will indicate their comfort level on the material. This graphic organizer will be collected, given feedback, and returned at the beginning of the next class. At the end of the lesson, a non-graded quiz will be administered to give an indication to both the teacher and students as to the progress that is coming along in the classroom. Upon completion of the lesson, students will be asked to write an entry in their blog to describe how they feel they are progressing in the class.
 * Formative (Assessment for Learning)**

With technology becoming more and more popular and time becoming more and more scarce, why not bring the lesson along with you where you go? Podcasts are becoming a very popular tool in the classroom. Students will work in pairs to create their very own podcast to explain what the quadratic equation is and how it is used to factor. The trick to this project is to relay information that is very visual in a way that it can be understood by just hearing it. By doing this, each student can learn all they ever wanted to know about the quadratic equation while doing something like working out at the gym! **Product: Garage Band.** Students will be graded on this project by the use of a checklist.
 * Summative (Assessment of Learning)**

__**Integration**__
__Technology:__ Students will be given the opportunity to use Garage Band and GeoGebra. Both of these programs are technology that is used in the classroom to promote further learning. Garage Band is a Type II technology because it utilizes technology and does the job that no other technology in the classroom can do.

__Music:__ The “hook” was a rap of the quadratic equation. Students will be using garage band to create sound files that target the idea of the quadratic formula. __English:__ Students will use language while creating and recording the script for the project. __Art:__ Students will need to be creative about the way that they present their material so to keep the audience engaged.

__Groupings__
Students will have filled out their “Mathematical Partner Sheet” prior to this lesson. Upon arrival to class, there will be a problem on the board that incorporates the ideas that have been talked about recently in class. Students will need to solve this problem that is on the board. The numerical answer that results from this equation will indicate what number partner is chosen from the chart. Once these partnerships have been established, partners will sit together at a cluster of desks with another group. Students will participate in the “Think-Pair-Share” activity to solve the graphic organizer that was given. Students will work on this with their partner and the other students who are present at the cluster. Students will also get the opportunity to discuss the topic as a class. Students will also refer to their peers for feedback when discussing the problems on the quiz. This gives students the ideas and learning that allow for more complex learning to occur.

__**Differentiated Instruction**__

 * Strategies**
 * **Verbal -** In a group setting, students will discuss the answers they found for the quiz questions.
 * **Logical -** Students will be required to use the quiz equations and graph them using [|GeoGebra].
 * **Kinesthetic -** In a group, students will need to create an interpretive dance that explains the quadratic equation and how it is used.
 * **Visual -** Students will use the "[|Goal-Reasons Web]" to visually map out the steps for factoring an equation using the quadratic formula.
 * **Intrapersonal -** Students will have time after reviewing the quiz to evaluate themselves on how they feel they are progressing with the material. Each student will be expected to write a blog of this reflection.
 * **Interpersonal -** Students will work in groups and as a class to discuss the process of factoring the equations on the quiz.
 * **Musical -** The musical rap presented at the beginning of the lesson will provide the students with a way to remember the quadratic formula in a different format.

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

In the event that a student is absent for this lesson, I ask that the student contact me as soon as possible to plan a meeting to go over the material. I will introduce them to the Garage Band project and expectations. He or she will be paired up with a partner to go over the graphic organizer. All of the information about the class, activities, and assignments will be available on the class Wiki. This will allow for the student to be able to access the information from any computer.

Students are going to create a Garage Band product at the end of this lesson. Garage band is a Type II technology because it is used as a supplementary aide to work through the task process. Garage band contains some resources and functions that provide a more interactive level of technology as opposed to a textbook. Students will be given the opportunity to raise the bar during the Garage Band project by being presented with additional scenarios and guidelines for the project. Students will use this Type II technology to create different ways that people could utilize the different ideas that someone can learn about the quadratic equation. If students need to tier down the project, a vocabulary list to follow while making the project will be provided.
 * Extensions**

__**Materials, Resources and Technology**__
Materials:
 * Mathematical Partner Sheet
 * "Hook"
 * Non-Graded Quiz
 * Graphic Organizer
 * Chalk
 * Chalkboard
 * Graphing Calculator
 * Graph Paper
 * Paper
 * Pencil
 * Computer
 * Internet
 * Text Book
 * Garage Band

Resources:

[|Quadratic Formula Tutoring] [|Solving the Quadratic Formula] [|Interactive Self-Evaluation] [|Garage Band Tutorial] [|"Hook"] [|GeoGebra]

Technology:
 * "Hook" Video
 * Blog
 * Graphing Calculator
 * Computer
 * Internet
 * Internet Links
 * Garage Band

__Source for Lesson Plan and Research__
Links for this lesson plan:
 * [|Quadratic Formula Tutoring] - Students can use this site as a reference on how to solve problems using the quadratic formula. The process and different examples are shown so that students have a break down of how to solve these equations.
 * [|Solving the Quadratic Formula] - Students can use this site as an overview on solving problems while using the quadratic formula. This site shows the formula, explanation, graphing techniques, and practice problems.
 * [|Interactive Self-Evaluation] - Students can use this site as a tool to solidify their knowledge of using the quadratic formula. Practice problems allow students to input their answers and receive instant feedback on the correct answer.
 * [|Garage Band Tutorial]- Students who are unfamiliar with the program Garage Band can view this tutorial to have a better understanding of how to use the program.
 * [|GeoGebra] - Students can use this online graphing program to create visuals of the different problems and equations presented during the lesson of quadratic formula use.
 * [|"Hook"] - This is a rap that was created by students about the quadratic formula and how to use it. This will allow students another resource to solidify the material using a different intelligence.

Pre-Designed Lesson Plans:


 * [|Web-based lesson] - This lesson plan breaks down the ideas of the quadratic formula for teaching. This lesson shows different teaching concepts, assessment ideas, and practice problems for students.
 * [|Quadratics and the Graphing Calculator] - This lesson targets the idea of using the quadratic formula with the graphing calculator. Students can utilize the technology available by programming the calculators to solve equations using the quadratic formula.
 * [|Properties of the Quadratic Formula] - Students will learn all the basic ideas that are needed to solve and utilize the quadratic formula. This lesson teaches the basics of identifying the main components that are needed to solve quadratic formula problems.

__**Maine Standards for Initial Teacher Certification and Rationale**__
Rationale:** Throughout this lesson, the different learning styles are all targeted at different points. “Beach ball” students will benefit from the variety of different activities that are present throughout the instruction of the lesson. There are many different applications that are used to teach and enforce the material. These students will benefit from the different viewpoints that each activity will bring. “Clipboard” students benefit from the structure that proves to be consistent throughout the unit. These students will also appreciate the organization of the graphic organizers. These organizers take the material that is learned and place it into an organized visual. “Microscope” students will appreciate the detail that is placed in the break down of the concepts of the lesson. While using the graphic organizer, students are able to break down the different components of the quadratic formula and how it works. “Puppy” students will benefit from the positive learning environment that is created in this classroom. Students are encouraged to be positive with one another and encourage each other along their journey of learning. If students do not feel safe or comfortable, they will be encouraged to come talk to the teacher or write on a private blog that will be checked by the teacher.
 * //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:** During this lesson, students will learn the components of the quadratic formula that make it work and process numbers the way it does. In breaking down the process, students will see the way that the equation is constructed and the different components that make it what it is. While breaking down the different parts of the equation, students will understand what each part functions as and how all these parts work as a whole to give an output. Students will hopefully recognize how this equation relates to linear equations and inequalities that were previously learned. Through the graphing process, students will gain a better visual as to how the different components work together to create the picture.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** Students will get the opportunity to experience this lesson through many different intelligences. Students will verbally talk through the different parts and ideas regarding the quadratic formula in partners, groups, and as a class. By talking through these ideas, students are gaining a deeper knowledge of the material. This is because they not only have to understand it, but they have to have a deep enough understanding that they can explain their reasoning to others. As part of the learning process, students will use graphic organizers and the program GeoGebra to create visuals for the material of the lesson. These visuals also serve as a logical organization of the material. These organizers help to break down the concepts into more simplistic or step-by-step concepts. To get the body involved in the lesson, students will need to create an interpretive dance to represent the graphs that they are seeing when they graph the quadratic equations that they have been working with. This provides a deeper connection for each student because it is relating the mathematics to his or her own body. In processing both the graphic organizer and graphs, students are creating a visual representation for the lesson that they are learning. These tools can serve as reference tools to look back on for a quick reminder as to what the lesson was about. Students get the chance to have music connected to their mathematical learning process. The rap presented at the beginning of the lesson serves as the “hook” in engaging students to want to learn more about the material. This rap will provide students with another resource to recall the information of this lesson. Intrapersonal students will get the chance to reflect upon their learning and the material. Students will be given the opportunity to refine their work during class discussions of the material. Students will also be asked to blog about their learning experiences thus far in the learning process. For those social students, there are going to be discussions. Students reach a higher level of comprehension when they need to describe the different concepts of a topic to another person. Students can also benefit from hearing the different concepts of the lesson from a student that they can possibly relate to. Students will be using a couple different Type II technologies to enhance their learning throughout this lesson. Students will be responsible for creating a learning podcast on the lesson using Garage Band as the assessment piece for this lesson. This is a Type II technology because students are being asked to take the learned material and transfer it to another format There are no other resources in the classroom that can function in quite this way.
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//

Rationale:** Students will be assessed in many different ways throughout this lesson. Students will first answer the “question of the day.” This will check for previous comprehension on the material that was covered in the lesson before. Students will also fill out a graphic organizer that will indicate their comfort level on the material. This graphic organizer will be collected, given feedback, and returned at the beginning of the next class. At the end of the lesson, a non-graded quiz will be administered to give an indication to both the teacher and students as to the progress that is coming along in the classroom. After the lesson, students will be asked to write and entry in their blog to describe how they feel they are progressing in the class. Students will work in pairs to create their very own podcast to explain what the quadratic equation is and how it is used to factor. The trick to this project is to relay information that is very visual in a way that it can be understood by just hearing it. In doing this, each student can learn all they ever wanted to know about the quadratic equation while doing something like working out at the gym! Students will be graded on this project by the use of a checklist to ensure all the required material was covered correctly.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//

__Teaching and Learning Sequence__
For this lesson, the desks will be arranged in clusters of four desks. There will be two pairs of two students at each of these clusters. Students will have filled out their “Mathematical Partner Sheet” prior to this lesson. Upon arrival to class, there will be a problem on the board that incorporates the ideas that have been talked about recently in class. Students will need to solve this problem that is on the board. The numerical answer that results from this equation will indicate what number partner is chosen from the chart. Once these partnerships have been established, partners will sit together at a cluster of desks with another group. Day 1: Students will solve the[| problem] on the board and find their partner. (5 minutes) Students will complete the “Question of the Day.” (10 minutes) New concepts of the [|lesson] will be presented. (20 minutes) Students will be presented with the graphic organizer. Students will need to work on this organizer individually. (5 minutes) As part of the [|“Think-Pair-Share”]activity, students will then work with their partner. (5 minutes) The class will discuss the ideas that were covered by the [|graphic organizer]. (10 minutes) Students will take a [|non-graded quiz] and graph the equations using [|GeoGebra]. (20 minutes) The [|Garage Band] project will be discussed and introduced. (5 minutes) With any remaining time, students will act out their graphs using their body. (any remaining time)

Through this lesson, students will understand that factoring is useful when working with linear equations. Students will gain a deeper understanding as to how these equations and graphs help to relate to things in real-world situations. Students will explore how the graphs represent different studies in nature and business examples. The Maine Learning Result that this lesson focuses on is "students solve families of equations and inequalities." To “hook” the students, a rap will be presented that explains the ideas and workings of the quadratic formula in a creative way. Students will be able to walk away from this lesson with another memorable way to remember the concepts that are covered by this equation.
 * Where, Why, What, Hoo**k, **Tailors: Visual, Verbal, Logical, Interpersonal, Bodily, Musical**

Students will know the quadratic formula, what linear equations are, and how to factor linear equations using the quadratic formula. This material will be covered in numerous ways so that each student’s intelligence is taught to. Musical students will be targeted with the music in the “hook.” Visual, verbal, logical, intrapersonal, and interpersonal students will all benefit from different components of the “Think-Pair-Share” activity. Each student requires different settings to learn. That is why there are many opportunities throughout this lesson for each student to find the way that helps him or her to thrive best to retain the material. Students will be assessed in many different ways throughout this lesson. Students will first answer the “question of the day.” This will check for previous comprehension on the material that was covered in the lesson before. Students will also fill out a graphic organizer that will indicate their comfort level on the material. This graphic organizer will be collected, given feedback, and returned at the beginning of the next class. At the end of the lesson, a non-graded quiz will be administered to give an indication to both the teacher and students as to the progress that is coming along in the classroom. At the end of the lesson, students will be asked to write and entry in their blog to describe how they feel they are progressing in the class.Since podcasts are becoming a very popular tool in the classroom, students will work in pairs to create their very own podcast to explain what the quadratic equation is and how it is used to factor. The trick to this project is to relay information that is very visual in a way that it can be understood by just hearing it. By doing this, each student can learn all they ever wanted to know about the quadratic equation while doing something like working out at the gym! Students will be graded on this project by the use of a checklist to ensure all the required material was covered correctly. Judging by the level of understanding and comprehension throughout these different forms of assessment will prove the level of the students’ learning and comprehension.
 * Equip, Explore, Rethink,** **Tailors: Verbal, Visual, Interpersonal, Intrapersonal, Logical (see content notes)**

Students will participate in discussions that will increase their level of learning. Students reach a higher level of comprehension when they need to describe the different concepts of a topic to another person. Students can also benefit from hearing the different concepts of the lesson from a student that they can possibly relate to. After this lesson, students will be able to demonstrate the quadratic formula in factoring. This lesson builds off of the previous lessons. The knowledge that was gained in the past lessons prove to show up to be built upon in the present lesson. Upon arrival to class, there will be a problem on the board that incorporates the ideas that have been talked about recently in class. Students will need to solve this problem that is on the board. The numerical answer that results from this equation will indicate what number partner is chosen from the chart. Once these partnerships have been established, partners will sit together at a cluster of desks with another group. Each student will assume the role of the listening partner, talking partner, and contributor to the class discussion. There are many different ways that students can contribute to this lesson to demonstrate mastery and help other students to further their learning. Students will be able to show their evidence of learning by the different activities and products that are created. In class, their participation in the discussions, activities, graphic organizers, and the non-graded quiz are all ways that the teacher and students can check where each student stands in learning the material. Each student will also be working with a partner to create a podcast on Garage Band. This allows students to demonstrate their ability to relay the information to another person solely by verbal means. This will demonstrate learning because the student must use only one form of communication to demonstrate the information. Students will also be blogging to track their progress of learning and reflect upon their own standings in the class. During class, students will be able to make edits to their graphic organizer and non-graded quiz during discussions and conversations with other students. This allows the students to learn from each other and have self-discovery moments of learning. This form of learning will prove to be more beneficial in the end.
 * Explore, Experience, Rethink, Revise, Refine,** **Tailors: Visual, Verbal, Logical, Intrapersonal, Interpersonal**

Students will be given a couple different chances to self-assess. During class, students will complete the graphic organizer. As students conference with other students and participate in class discussions, students will be able to edit their papers. This allows the student to assess where he or she stands with the comprehension of the material. Students will also be asked to blog about their experience and learning in class. The blogs are a running journal of each student’s own ideas on their learning in class. Students will be given feedback in a couple different formats during the class. During the class discussion, students will be given immediate feedback based on the direction that the discussion is progressing toward. Students will also receive feedback from peers while working on the cooperative learning activity. At the beginning of the following class, students will receive their graphic organizer back with the teacher’s feedback. This allows students to judge where they stand and still have time to address any trouble areas. Students will build upon all of this material later on in the progression of the course and in higher math courses. This information is a base to many other mathematical ideas.
 * Evaluate,** **Tailors: Visual, Verbal, Logical, Intrapersonal, Interpersonal**


 * Content Notes**
 * [|Quadratic Formula Tutoring] - Students can use this site as a reference on how to solve problems using the quadratic formula. The process and different examples are shown so that students have a break down of how to solve these equations.
 * [|Solving the Quadratic Formula] - Students can use this site as an overview on solving problems while using the quadratic formula. This site shows the formula, explanation, graphing techniques, and practice problems.
 * [|Interactive Self-Evaluation] - Students can use this site as a tool to solidify their knowledge of using the quadratic formula. Practice problems allow students to input their answers and receive instant feedback on the correct answer.
 * [|Garage Band Tutorial]- Students who are unfamiliar with the program Garage Band can view this tutorial to have a better understanding of how to use the program.
 * [|GeoGebra] - Students can use this online graphing program to create visuals of the different problems and equations presented during the lesson of quadratic formula use.
 * [|"Hook"] - This is a rap that was created by students about the quadratic formula and how to use it. This will allow students another resource to solidify the material using a different intelligence.
 * [|Web-based lesson] - This lesson plan breaks down the ideas of the quadratic formula for teaching. This lesson shows different teaching concepts, assessment ideas, and practice problems for students.
 * [|Quadratics and the Graphing Calculator] - This lesson targets the idea of using the quadratic formula with the graphing calculator. Students can utilize the technology available by programming the calculators to solve equations using the quadratic formula.
 * [|Properties of the Quadratic Formula] - Students will learn all the basic ideas that are needed to solve and utilize the quadratic formula. This lesson teaches the basics of identifying the main components that are needed to solve quadratic formula problems.

Question of the Day "Goal-Reasons Web" Graphic Organizer Non-graded Quiz Garage Band Assessment Checklist
 * Handouts**