L5+Bowden,+Scott

**COLLEGE OF EDUCATION, HEALTH AND REHABILITATION **  **LESSON PLAN FORMAT ** 
 * UNIVERSITY OF MAINE AT FARMINGTON **
 * Teacher’s Name: ** Mr. Bowden **Lesson:** Self-Knowledge
 * Grade Level:** 9 **Topic:** Systems of Linear Equation

**__Objectives__**
 * Student will understand that ** algebraic equations of one degree are represented as lines.
 * Student will know** system of equations.
 * Student will be able to** realize the solution to a system is an ordered pair.

**__Maine Learning Results Alignment __** Maine Learning Results – Mathematics D. Algebra Equations and Inequalities Grades 9-Diploma 2. Students solve families of equations and inequalities


 * Rationale:** This lesson covers methods to solving systems of linear equations. This information will allow students to solve families of linear equations that have two variables.

**__Assessment__** The students begin working on their final project research and mathematics. When the research and proper mathematics are done the first time, the students will hand it in to the teacher for feedback before continuing on their project. Homework will be handed in to the teacher so that lessons can be modified to match the process and content gaps of students. This homework assignment will be unscored and students will have the opportunity to view the answers before handing in the piece. The students will have an rake graphic organizer that they can use to gather the presented material in a divided fashion of method and steps. Students will not hand these in, but will be able to call upon it later as study material. At the end of the lesson, the teacher will review valuable information that should be included. Students will write journal or blog entries that are reflective of their thoughts on the lesson. The teacher will check them at the end of the lesson to modify the lesson structure for future classes.  In this lesson, the teacher will begin discussing the final project for the unit. Students will have the tools necessary after this lesson to plan the mathematics for their final presentation. The students will have to do research and for the end of the lesson, provide the teacher with their completed mathematics for evaluation. These will be worth the same as a quiz, not a separate benchmark. Additionally, the students will take a low-stakes quiz relating to the material covered in the lesson. The final outcome from this piece will be the performance task. Students will be given ample time to complete the task, but introduced to it here.
 * Formative (Assessment for Learning) **
 * Summative (Assessment of Learning)**

**__Integration__** <span style="font-family: "Times New Roman","serif";">Technology: The students will begin working on their WebQuest and final project. It will be the beginning of a longer term project.

English: Students must be able to explain and analyze their researched information.

Economics: Students will be researching an economic crisis and analyzing it.

 <span style="font-family: "Times New Roman","serif";">Students will decide which two states out of the given ones they would like to research for the final project. They will also indicate whether they would rather work in pairs or a group of three. The teacher will match students up based upon those choices and divide students up into pairs or groups of three. Students will divide up the project and the mathematics and research between the members of the group and will define roles such as broadcaster, cameraman, field man, etc. Students will keep these groups through this lesson and in the presentation.
 * __<span style="font-family: "Times New Roman","serif";">Groupings __**<span style="font-family: "Times New Roman","serif";">

**__Differentiated Instruction__**
 * <span style="font-family: "Times New Roman","serif";">Strategies **<span style="font-family: "Times New Roman","serif";">


 * Interpersonal** - Students work in groups to begin work on performance task.
 * Intrapersonal** - Students consider answers to problems in class for themselves and form their own ideas.
 * Visual** - Students continue to graph lines.
 * Logical** - Students complete relevant computation.
 * Verbal** - Students discuss the material in class.
 * Musical** - Illustrate intersections of lines as chords of instruments.


 * Modifications/Accommodations**

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

Absent Students: The teacher will provide office hours for the students' use. It is up to the student to either contact a classmate to review the material or to contact the teacher before the next period. If the absence is for an extended period, the teacher can assign or obtain a tutor for the student. The assignments and the notes for the class will be available on the teacher/class wikispace page. If students have internet access, they can use a video conference software such as skype to be a virtual participant if they are willing or able to do so. Additionally, students who are absent during this lesson will need to contact the teacher immediately or beforehand so they can be divided into the proper group and have time to catch up on research.

In this lesson, students will have the opportunity to compare three states for their gas prices. This comparison won't be shown in the final project, they will do the two states they were assigned, but will have the chance to compare to a third and get some additional credit or homework points for completed work outside of the project.
 * Extensions**

 <span style="font-family: "Times New Roman","serif";"> <span style="font-family: "Times New Roman","serif";">Teacher computer Projector/TV Screen for the computer Graphing Calculators for students who don't already have them. Stuff to write on the whiteboard/chalkboard with Graphic Organizers - Rake. Lesson 5 Quiz Textbook and teacher notes Graph Paper for student work on graphing Some kind of food Rubrics from their roof model Student models to bring home if they choose
 * __<span style="font-family: "Times New Roman","serif";">Materials, Resources and Technology __**<span style="font-family: "Times New Roman","serif";">

 <span style="font-family: "Times New Roman","serif";">How to solve a system by substitution: [] How to solve a system by elimination: [] How to solve a system graphically: [] A list of tutorials about iMovie from Apple: [] A list of tutorials about Windows Movie Maker from Microsoft: [] Mr. B's first movie: [] A comprehensive look at solving systems: [] A rake Graphic Organizer: [] <span style="font-family: "Times New Roman","serif";">The Gas Crisis WebQuest: [] **__<span style="font-family: "Times New Roman","serif";">Maine Standards for Initial Teacher Certification and Rationale __**<span style="font-family: "Times New Roman","serif";"> Rationale:** Clipboard: Students will have structure in their project and in instruction. They will have a set of instructions and protocol that they can refer to while they're working. Beach Ball: Students will have the option of what states or regions they would like to discuss on their project. They will also have the opportunity to research an additional state and compare that to the ones they are doing already. Microscope: Students will use this project to become more familiar to the material by using it in an analytical way. They will have the chance to put the material into a different context and examine it from such. Puppy: Students will have the support from teacher and classmates to make comments and give answers without being looked down upon. Students will feel comfortable in their environment.
 * __<span style="font-family: "Times New Roman","serif";">Source for Lesson Plan and Research __**<span style="font-family: "Times New Roman","serif";">
 * //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:** This lesson was based around the fact that students will understand that algebraic equations of one degree can be represented as lines. This was discussed when students were researching gas prices and using their linear trends to make assumptions. This lesson acts as a way for students to solve families of equations and inequalities when they isolate variables prior to graphing equations as discussed in the Maine Learning Result for this lesson. Students learn concepts relating to lines, equations of lines, parallel and perpendicular lines, independent and dependent variables, and forms of linear equations. When the lesson is complete, students will be able to realize the solution to a system is an ordered pair.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** The following strategies will be used in this lesson.
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//


 * Interpersonal** - Students work in groups to begin work on performance task.
 * Intrapersonal** - Students consider answers to problems in class for themselves and form their own ideas.
 * Visual** - Students continue to graph lines.
 * Logical** - Students complete relevant computation.
 * Verbal** - Students discuss the material in class.
 * Musical** - Illustrate intersections of lines as chords of instruments.

Technology: The students will begin working on their WebQuest and final project. It will be the beginning of a longer term project.

Rationale:** Students will have the opportunity to assess their own learning while they do it. The students begin working on their final project research and mathematics. When the research and proper mathematics are done the first time, the students will hand it in to the teacher for feedback before continuing on their project. Homework will be handed in to the teacher so that lessons can be modified to match the process and content gaps of students. This homework assignment will be unscored and students will have the opportunity to view the answers before handing in the piece. The students will have an rake graphic organizer that they can use to gather the presented material in a divided fashion of method and steps. Students will not hand these in, but will be able to call upon it later as study material. At the end of the lesson, the teacher will review valuable information that should be included. Students will write journal or blog entries that are reflective of their thoughts on the lesson. The teacher will check them at the end of the lesson to modify the lesson structure for future classes. In addition to the teacher being able to assess their progress. In this lesson, the teacher will begin discussing the final project for the unit. Students will have the tools necessary after this lesson to plan the mathematics for their final presentation. The students will have to do research and for the end of the lesson, provide the teacher with their completed mathematics for evaluation. These will be worth the same as a quiz, not a separate benchmark. Additionally, the students will take a low-stakes quiz relating to the material covered in the lesson. The final outcome from this piece will be the performance task. Students will be given ample time to complete the task, but introduced to it here. **__<span style="font-family: "Times New Roman","serif";">Teaching and Learning Sequence __**<span style="font-family: "Times New Roman","serif";"> The room will be set up with desks in table groups of 4 like lesson 3.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//

Agenda:

Day 1. Students take their seats (5 minutes) Teacher hands back scored roof rubric and students can gather their models to bring home (10 minutes) Discussion: More Musical Math! Intersecting Music = chords! (5 minutes) Instruction: How to solve a system graphically. (10 minutes) Students do practice problems independently or in groups (5 minutes) Instruction: How to solve a system by Substitution and Elimination (15 minutes) Students work on practice problems. (10 minutes) iMovie introduction! Presentation: Mr. Bowden's 1st ever movie production! (5 minutes) Students are divided into groups for their performance task. (10 minutes) Teacher assigns homework. Students have remaining time for homework (5 minutes)

Day 2. Students take their seats with their P.T. Group (5 minutes) Performance Task Land! Students begin working on their WebQuest: Spending time gathering information and research, composing the mathematics for the project. The teacher will be available to provide support. (60 minutes) Students hand in completed work at the end of the period for the teacher to give feedback on. (5 minutes) Explanation: Keep thinking about the WebQuest! We will come back to it in a few classes! This was just to put it out there and get you started on it! (10 minutes)

Students will understand that algebraic equations of one degree can be represented as lines. **//Students understand how to solve families of equations and inequalities.//** This material is useful across the disciplines like economics. At the beginning of the lesson, the teacher will talk briefly about music relating to math again. Since musical notes intersect, what comes out of it? With music, it's a chord, with lines, it's an ordered pair. **Where, What, Why, Hook, Tailor: Musical, Intrapersonal**

Students will know about systems of equations. During instruction, the teacher will pose questions to the students at the end of each subtopic giving them time to try problems within that subtopic before moving on to the next subtopic. Different kinds of learning will be targeted here, the material will be visible on the board, discussed mathematically, and spoken about. The teacher will reference the rake graphic organizer by discussing different methods of solving linear equations: [|Graphically], by [|algebraic substitution], and by [|elimination]. One side will have the vocabulary/term for the method, the other will have the steps that match the method. The teacher will assess understanding of the material using the quiz at the end of the lesson, the homework assignment to be handed out, and the mathematics and research for the movie. This lesson revolves around introducing the systems of equations and how to solve them. **Equip, Explore, Tailor: Visual, Verbal, Intrapersonal, Logical**

The students will begin by starting the mathematics for the WebQuest in their groups and handing it in. The teacher will give feedback on them and the students will rework the mathematics before moving forward with the WebQuest. The rake map will be used for students to put system methods on one side and methods on the other. The teacher will go over what material would be good to be on it. This will not be collected, but can be used as a study guide for homework or any quizzes. In addition, at the end of the lesson, students will take a low stakes quiz over the material from the lesson to be scored. Students will decide which two states out of the given ones they would like to research for the final project. They will also indicate whether they would rather work in pairs or a group of three. The teacher will match students up based upon those choices and divide students up into pairs or groups of three. Students will divide up the project and the mathematics and research between the members of the group and will define roles such as broadcaster, cameraman, field man, etc. Students will keep these groups through this lesson and in the presentation. At the end of the lesson, students will be able to realize that the solution to a linear system is an ordered pair. **Experience, Revise, Refine, Rethink, Tailor: Logical, Interpersonal**, **Visual**, **Verbal**

At the end of instruction for the lesson, students will complete a limited number of homework assignments from the textbook for the course. The answers for these problems will be located in the back of the textbook. Students will also do blogs or journal entries reflecting on their experience with the lesson, what they liked and thought worked, in addition to what they didn't like and how they think the teacher can make modifications. These will be checked and commented on by the teacher nightly, if they are blogs. If they are paper journals, they will be collected daily and the teacher will read them and comment on them. If homework comes from the book, the teacher will be responsible to assign problems that have answers in the back of the textbook. The mathematics for the WebQuest will be scored on accuracy of research and mathematical accuracy. It will count as a quiz grade. This will connect to future lessons because the information may be called upon. The project will have students reflect upon this information in a lens that they might not have considered otherwise. It may also connect to students who are interested in acting, journalism, or script writing. Students will use this material on future assessments. **Evaluate, Tailor: Verbal, Logical, Intrapersonal**


 * __Content Notes__**

Solving a system:

[|Graphically]:

Look at the graphs of the two equations. Where they physically intersect is their solution. This would say that the solution to a system of equations is the same as an intersection of two lines.

[|Substitution]:

Given y = 2x + 3 and y = 5x - 3, both equations are solved for y, so they can be set equal to say 2x + 3 = 5x - 3 since they have exactly one intersection point. So, x = 2. Substitute 2 in for x in either of the equations to get y = 7. Additionally, given the equations y = 2x + 3 and 5x - y = 3, one equation is solved for y so we can substitute 2x + 3 in for y in the other equation to give 5x - (2x + 3) = 3. So, 5x - 2x -3 = 3, so 3x = 6, so x = 2. Now we substitute 2 in for x in the y = 2x + 3 equation to give y = 7. The solution is (2,7)

[|Elimination]:

Given 2x - 5y = 1 and 4x + 3y = 15. To solve this, we must eliminate either x or y by adding one equation to the other. Since x is more logical because 4 is the GCF of 2 and 4, we'll multiply the first equation by -2 to give the 2 equations -4x + 10y = -2 and 4x + 3y = 15. Adding them together gives 0x + 13y = 13. Dividing by 13 gives y = 1. Substitute the value of y into one of the equations to give 2x - 5(1) = 1. So 2x - 5 = 1 --> 2x = 6, so x = 3. The solution is (3,1)

Movie Broadcasting

This tutorial for [|iMovie] and [|movie maker] will assist in doing the final project of the WebQuest.

Lesson 5 Quiz Graphic Organizer Lesson 5 Worksheet
 * __Handouts__**