L5+Cobleigh,+Justin


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


 * Teacher’s Name:** Mr. Cobleigh **Date of Lesson:** Perspective
 * Grade Level:** 8 **Topic:** Parallel and Perpendicular Lines

__**Objectives**__

 * Student will understand that** graphs can be drawn from equations and vice versa.
 * Student will know** what perpendicular and parallel lines look like on graphs and also create their equations.
 * Student will be able to** compare parallel and perpendicular linear equations to the graphs of others.

__**Maine Learning Results Alignment**__
Maine Learning Results: Mathematics - D. Algebra Functions and Relations Grade 8 Students understand and use basic properties of linear relationships using y = mx + b.


 * Rationale:** This lesson will introduce students to the concepts of parallel and perpendicular lines.

__**Assessment**__

 * Formative (Assessment for Learning)**

Students will work on continuing a flow chart that will connect all of the lessons together. If students need another copy of this flow chart, there are some available to either re-organize their thoughts or that the entire unit does not fit on to one chart. Students will also use a sequence chart to keep their thought process clear about how they would find a line that was perpendicular to a given equation. Students will work in groups of four on a jigsaw activity that is aimed at having students try out learning material on their own and then being able to repeat it to their classmates. During time when students are allowed to start in on their homework or are trying examples that were done as a class, the teacher will be walking around to answer any questions that may arise as well as spotting common errors people may make and attempting to help guide them in the right direction. Some questions that could be asked during the lecture are, but are not limited to: How do you tell if a set of lines are parallel? How do you tell if a set of lines are perpendicular? How do you find the equation of a parallel / perpendicular line? Students are given time at the end of class to write a journal entry reflecting on the lesson that was just presented to them. Students are encouraged to talk about what they liked, what they did not like, what they had trouble understanding, what are some lingering questions they have, etc... Students are not limited to these for responses. They are to be a starting point to help guide students in the right direction. If there is a common question amongst students that was not brought up during class time, it would be fit in to the next day's class in order to clear up the issue of understanding.


 * Summative (Assessment of Learning)**

For this project, students are given pairs of equations and they have to determine if they are parallel, perpendicular, or neither. Students are to first to sketch out by hand the equations to see what conclusion they can get from that. Once the pairs of equations have been sketched and you have determined that they are parallel, perpendicular, or neither, students will use GeoGebra to plot and draw their graphs. From here, they can use the built in functions of the program to see if their assumptions are correct. Each student will be selected to present an individual problem with their outcome for it. The work for all of the other problems is to be written down, neatly, and then passed in. (20 points)

__**Integration**__

 * Technology:** Students will be using GeoGebra in their final projects for this lesson.


 * Geography** could be brought into the lesson with having students create a road map that consisted of parallel roads and perpendicular roads.

__Groupings__
The first activity students will be participating in is the jigsaw activity. In this activity, students will be split up into groups of four using the count off method, where students are numbered 1-4 and then all of the same number get together. Group size could vary depending on the amount of students in class on that given day. One pair of students within the group will work with a set of equations and determine if they are perpendicular or parallel. The other pair of students will be doing the same with a different set of equations. Once the pairs have come to a result, they will share with the other pair and then report out to the class what they did to solve their problems. Students will also be participating in a three-corners activity where a set of equations will be read out to the class and students will group together on whether they believe the set of equations were parallel, perpendicular, or neither. Groups for the final project will be determined through a random draw from a hat. These group sizes will vary depending on the amount of students present.

__**Differentiated Instruction**__

 * Strategies**
 * Verbal:** Discussion during a lecture can be done for those who can express their methods through words.
 * Logical:** Working on example problems during lecture will apply to those who need to see the process of finding parallel and perpendicular lines done out.
 * Visual:** Mini-whiteboards can be used to work out problems and then students can get feedback on their process by seeing what other students may have done to get a result.
 * Kinesthetic:** Three corners game - students move to whichever side of the room corresponds to the relationship of two lines.
 * Naturalist:** Weather depending, the three corners activity could be taken outdoors asking students to gather in different areas outside to represent each of the three line relationship choices.
 * Interpersonal:** Students can work in groups or pairs on sample problems to bounce ideas off of each other in coming to their solutions.
 * Intrapersonal:** Students work independently on problems to broaden their understanding.

I will review student's IEP, 504 or ELLIDEP and make appropriate modifications and accommodations. __Absent:__ If a student is absent from class, it will be expected that they check the class wikispace to get the content notes as well as the homework assignment and attempt the work. Students should come to class with possible questions if they have misunderstandings. If this is unable to be done, and students are in school the next day, the student needs to see me to get caught up.
 * Modifications/Accommodations**


 * Extensions**

Students will use GeoGebra in their final projects for this lesson to show if their pair of equations are perpendicular, parallel, or neither.

__**Materials, Resources and Technology**__

 * Markers
 * Textbook
 * Sample Problems Handout
 * Flow Chart Organizer
 * Sequence Chart Organizer
 * Journals
 * Laptops (Students and Teacher)
 * LCD Projector

__Source for Lesson Plan and Research__

 * [] - Purple Math's explanation of parallel and perpendicular lines.
 * [] - Tutorial from West Texas A&M University on finding parallel and perpendicular lines.
 * [] - Lesson on parallel and perpendicular lines from a homeschooling website. This would be a great site for parents to reference.
 * [] - Video Tutorial on comparing sets of equations.

__**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:** Beachball - During the three-corners activity, students will be allowed to go the corner of the room that they have decided is the correct answer to the question at hand. Granted that there is a correct answer, students should go to the one they think is correct. It is their choice. They should not gravitate towards one answer just because all of the other students in the class went to that one particular answer. Clipboard - Visuals are going to be a big part of this lesson. Graphic representations of parallel and perpendicular lines will help students have an idea of what a set of parallel or perpendicular equations looks like. Also, they would be able to see just how each piece of the equation affects the resulting graph. Microscope - When working in the jigsaw and three-corners activities, students will be discussing with their group members and with other members of the class as to how they came to their answers as well as where errors may have occurred. Students are encouraged to talk with their classmates about how they think lines or equations are parallel or perpendicular and why a set of lines or equations would not be either. Puppy - Students will be encouraged to listen to their group members in their collaboration as well as help figure out where misunderstandings may occur. Students want to be aware that some of their peers may not be as open to discussing problems with others because they do not want to be wrong. I want to encourage students to be open to discussion with their peers and to be able to bounce ideas off of each other.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * Rationale:** Students will know what perpendicular and parallel lines look like on graphs and also create their equations (reference content notes at the end of this lesson). //**Students understand and use basic properties of linear relationships using y = mx + b.**// The facet that I used for this lesson was perspective in that I hope //students will be able to compare parallel and perpendicular linear equations to the graphs of others.// I chose this facet because I want students to be able to look at a set of lines on a graph or to look at a set of equations and see how they compare to each other. I want students to be able to look at lines and tell if they are parallel or perpendicular so that they have a way to compare the two if they are ever asked to. Also, I want students to be able to see how the equations are affected and how they relate when lines are parallel or perpendicular.


 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**
 * Rationale:** Using the multiple intelligences:


 * Verbal:** Discussion during a lecture can be done for those who can express their methods through words.
 * Logical:** Working on example problems during lecture will apply to those who need to see the process of finding parallel and perpendicular lines done out.
 * Visual:** Mini-whiteboards can be used to work out problems and then students can get feedback on their process by seeing what other students may have done to get a result.
 * Kinesthetic:** Three corners game - students move to whichever side of the room corresponds to the relationship of two lines.
 * Naturalist:** Weather depending, the three corners activity could be taken outdoors asking students to gather in different areas outside to represent each of the three line relationship choices.
 * Interpersonal:** Students can work in groups or pairs on sample problems to bounce ideas off of each other in coming to their solutions.
 * Intrapersonal:** Students work independently on problems to broaden their understanding.

Type II Product: GeoGebra


 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * Rationale:** Assessing student learning is very important and this is how I am going to do so:


 * Formative (Assessment for Learning):** Students will work on continuing a flow chart that will connect all of the lessons together. If students need another copy of this flow chart, there are some available to either re-organize their thoughts or that the entire unit does not fit on to one chart. Students will also use a sequence chart to keep their thought process clear about how they would find a line that was perpendicular to a given equation. Students will work in groups of four on a jigsaw activity that is aimed at having students try out learning material on their own and then being able to repeat it to their classmates. During time when students are allowed to start in on their homework or are trying examples that were done as a class, the teacher will be walking around to answer any questions that may arise as well as spotting common errors people may make and attempting to help guide them in the right direction. Some questions that could be asked during the lecture are, but are not limited to: How do you tell if a set of lines are parallel? How do you tell if a set of lines are perpendicular? How do you find the equation of a parallel / perpendicular line? Students are given time at the end of class to write a journal entry reflecting on the lesson that was just presented to them. Students are encouraged to talk about what they liked, what they did not like, what they had trouble understanding, what are some lingering questions they have, etc... Students are not limited to these for responses. They are to be a starting point to help guide students in the right direction. If there is a common question amongst students that was not brought up during class time, it would be fit in to the next day's class in order to clear up the issue of understanding. At the beginning of the first class period, students will have to take a quiz over lessons 3 and 4 to see if they have retained what they learned and are able to apply it.


 * Summative (Assessment of Learning):** For this project, students are given pairs of equations and they have to determine if they are parallel, perpendicular, or neither. Students are to first to sketch out by hand the equations to see what conclusion they can get from that. Once the pairs of equations have been sketched and you have determined that they are parallel, perpendicular, or neither, students will use GeoGebra to plot and draw their graphs. From here, they can use the built in functions of the program to see if their assumptions are correct. Each student will be selected to present an individual problem with their outcome for it. The work for all of the other problems is to be written down, neatly, and then passed in. (20 points)

__Teaching and Learning Sequence__
Student's desks will be arranged in groups to facilitate the jigsaw activity as well as the GeoGebra project. Desks will also want to be away from walls as much as possible for the Three-Corners activity. I will be teaching from a central point at the front of the classroom.

Outline of Agenda Day 1 (80 Minutes) Day 2 (80 Minutes) Day 3 (80 Minutes)
 * Students will have a quick question and answer session on the material covered in lessons 3 and 4 before taking a quiz. (10 minutes)
 * Students will take a quiz covering lessons 3 and 4. Once students have finished, they are to hand in their quiz and work quietly on any other work they have for my class or for another class until all of the other students have completed the quiz. (20 minutes)
 * Challenge Hook. Students will be challenged to see if they can create the graphs of parallel or perpendicular lines. Also, students should see if they are able to create the equations for the lines. (10 minutes)
 * Students will be introduced to the concepts of parallel and perpendicular lines. The definitions of parallel and perpendicular will be introduced, students will work on creating graphs of parallel and perpendicular lines, as well as compare the equations of these sets of lines. Students will be given some time to work individually on sample problems. The teacher will be walking around the room answering questions as well as helping students wherever they have misconceptions. Once students have shown that they have completed the test problems, they will be given their homework to start in on. (30 minutes)
 * The students should respond in their journals reflecting on the material that was just presented. Students should mention any questions they have that were not mentioned in class so that they can be included in the review session at the start of the next class period. (10 minutes)
 * Student's quizzes will be returned to them and students will have the chance to ask questions about them. If there were any common errors made by several students, they would be gone over as a class to help clear it up. (10 minutes)
 * To review the material introduced in the previous day's lesson, students will participate in a Three-Corners activity. A set of equations will be placed on the board and students will have to move to the area of the room that has been designated with a sign stating if the equations are parallel, perpendicular or neither. Before moving to a new set of equations, the real answers should be discussed and how they actually are correct. //Weather depending, this activity could be moved outdoors using different areas outside as the meeting places for the different relationships between the equations.// (20 minutes)
 * Once returning to the classroom, if outside, the class will participate in a Jigsaw activity that will get students working together to come to correct answers. Students will be put into groups of 4, or appropriate size depending on the amount of students in class, and broken up into pairs from there. Each pair of students will be given a set of equations that they will need to graph and determine if they are parallel, perpendicular, or neither. Once both pairs have come to answers with their equations, the pairs of students will discuss with the others what they did to get their answer and discuss any difficulties that may have existed. (20 minutes)
 * Students will be introduced to GeoGebra, the application that they will be using for their final assessment for this lesson. Students will be downloading the application to their laptops and the teacher will go through some of the various functions that the program can do. There will be a brief overview of the final project and the pairs/groups of students for this project will be randomly assigned. They will also be given their sets of equations to start the hand-written part of the assignment which is to create the graphs of the equations and determine if they are parallel, perpendicular, or neither. They also need to have any work that they did to determine the relationship of the lines written down as all work will be collected and is part of the grade for the assessment. For those who want to have a good start on their projects, the hand-written part should be done for homework to have more time to work with GeoGebra in the next class period. Students will also be given a copy of the checklist that will be used for grading so that they are aware of what is required. (30 minutes)
 * Students should get straight to work using GeoGebra to compare their equations and to see if the answers of their hand-written work is actually what should have been the result. Students should create a short powerpoint showing their work and any images taken from GeoGebra of their graphs. These will be presented to the class. All written work should be gather together to be handed in at the time of the group's presentation. (30 minutes)
 * Student presentations of their graphs and GeoGebra images. Students should explain their mathematical processes used as well as what they came to as an answer. These presentations should be no longer than 5 minutes each. (30 minutes)
 * After student presentations are complete, groups will fill out an evaluation form about the project itself and how well they felt their group worked together. These should be turned in before the class period is over. Groups will also get to look at their grades, as the teacher will be filling out the checklist as the presentation is given, and a copy for each student will be made available during the next class period. A sneak peek at the next lesson will also be given to the students to have something to look forward to. The hint to the final project of the unit could also be introduced. (20 minutes)

Students will understand that graphs can be drawn from equations and vice versa. When looking at a road map, the roads intersect and run parallel to others just as lines can. //**Students understand and use basic properties of linear relationships using y = mx + b**//. Before the students are shown what the equations of parallel or perpendicular lines look like, students will be challenged to see if they can create them for themselves. This will require that students have a prior knowledge of what parallel and perpendicular mean, but if they do not know, that is OK. That is part of the lesson to come. This challenge is just to get students thinking and help them to get into the mood of mathematics!
 * Where, Why, What, Hook Tailors: Verbal, Visual, Logical, Interpersonal, Intrapersonal**

Students will know what perpendicular and parallel lines look like on graphs and also create their equations. //See Content Notes//. Students will be expanding on their flow chart organizer for the unit by adding the ideas of parallel and perpendicular lines in that it can be connected back to prior lesson material, slope as an example. Students can also use a sequence chart that will walk through what they all did to find the equations of parallel or perpendicular lines. For instruction, students will be taking notes on what the equations of parallel and perpendicular lines look like as well as what their graphs look like. During the lecture, students will be asked questions such as, but not limited to: How do you tell if a set of lines are parallel? How do you tell if a set of lines are perpendicular? How do you find the equation of a parallel / perpendicular line? Students will also be given time after the lecture has finished to work on some sample problems that involve them trying to find out what the relationship is between two equations. The teacher will be available around the room to answer any questions as well as to help students on a certain piece of the material. Students will also be given a worksheet towards the end of class which will require them to take the knowledge that was just presented to them in the lesson and apply it to the problems. Students will also be responding in their journals, at the end of class, to anything about the lesson that they want to talk about. This journal is for the purpose of the teacher to get an understanding of where students are with the material and to see if there were any questions that were left unanswered at the end of class. Students would be encouraged to write these questions down for the teacher to see so that they can be addressed at the beginning of the next class during the review session.
 * Equip, Explore, Rethink, Revise, Refine Tailors: Verbal, Visual, Logical, Interpersonal, Intrapersonal**

Students will be able to compare parallel and perpendicular linear equations to the graphs of others. For group activities, students will be participating in a three-corners activity. In this activity, which can be done either indoors or outdoors, depending on the weather at the time, a set of equations will be written on the board and students will have to move to an area of the room or outdoor area to the relationship they feel the equations have, either parallel, perpendicular or neither. Once students have gone to their areas, one or more students will need to justify why they feel that they are in the correct area. Once the correct answer has been determined, a new set of equations will be introduced and students will repeat the above process until all of the pre-arranged sets of equations have been discussed. Students will also participate in a jigsaw activity. This activity will get students working together to come to correct answers. Students will be put into groups of 4, or appropriate size depending on the amount of students in class, and broken up into pairs from there. Each pair of students will be given a set of equations that they will need to graph and determine if they are parallel, perpendicular, or neither. Once both pairs have come to answers with their equations, the pairs of students will discuss with the others what they did to get their answer and discuss any difficulties that may have existed. For the final project in this lesson, students will be working with GeoGebra. The exact lesson is discussed at the beginning of this packet in the Formative Assessment section.
 * Organize, Experience, Explore Tailors: Verbal, Visual, Logical, Kinesthetic, Naturalist, Interpersonal, Intrapersonal**

For self-assessment, students will be given a copy of the checklist used to grade the GeoGebra presentations beforehand so that they are sure that all of the necessary pieces were included. Students will be given their grades when all of the presentations are over because the teacher will be grading while the actual presentation is being conducted. I want students to know as soon as possible what they got for a grade because I want them to know how they did. However, this grade may be subject to change since only one of the sets of equations the groups were given are to be presented. Once I have had a chance to look over the papers of work that they were to pass in with the other problems, I can adjust the grades accordingly, looking at the work all of them did outside of class on coming to their solutions. Looking at the work of students will also give me a chance to see where they are at with the material that was covered in the lesson and to give me an idea as to if some students may need a recap of a certain concept or if the lesson presented itself as too easy. Also after all of the presentations have finished, all of the groups will be given a reflection sheet to complete. The purpose of these sheets is to get feedback from students about what worked and what didn't in the process of completing this project, as well as how they felt they worked as a team during the project process. I want students to be able to realize what worked in their group, and what may not have worked that way the next time a group project is assigned, students will be able to take prior knowledge of what things worked and apply them to the new situation. Student's input is also valued in that it could shed light on some pieces of the lesson that worked out really well or to some piece that did not work out quite as well. If I was to do this project again in the future, I would want to know what the student's perspective was on it, so that I know if it would work well in future classes.
 * Evaluate Tailors: Verbal, Visual, Logical, Interpersonal, Intrapersonal**


 * Content Notes**

Student will know what perpendicular and parallel lines look like on graphs and also create their equations.

__//Definitions//__ Parallel Lines: Equations in which the slope is the same but the y-intercept is different. Perpendicular Lines: Equations in which the slopes are negated reciprocals and can have different y-intercepts.

__//Example Problems//__
 * **In - Class Examples** || **Individual or in Pairs Afterwards** ||
 * Given a set of lines, determine if they are parallel or perpendicular.

1) y = 2x + 5, y = 2x + 3

Parallel because of same slope but different y-intercept

2) y = 3x - 6, y = -1/3x - 3

Perpendicular because of negated, reciprocal slope

3) y = 2x - 5, y = x + 2

Neither because no properties were satisfied. || Given a set of lines, determine if they are parallel or perpendicular.

1) y = 4x - 4, y = -1/4x + 6

Perpendicular because of negated, reciprocal slope

2) y = 3x + 1, y = 3x - 9

Parallel because of same slope but different y-intercept

3) y = 1/3x - 4, y = -1/3x - 4

Neither because no properties were satisfied. ||
 * Given 2 points, create a graph to determine if the lines are parallel or perpendicular.

1) Points (0,0), (4,4) & Points (1,0) , (5,4)

a) Plot the points on a graph.



b) Connect the two corresponding points to create the lines.



c) By looking at the resulting lines, we can tell that these points created two parallel lines.

2) Points (0,0), (4,4) & Points (2,0) , (-1,3)

a)

b)

c) Perpendicular || Given 2 points, create a graph to determine if the lines are parallel or perpendicular.

1) Points (3,2), (-1,4) & Points (0,0) , (-3,2)

a + b)



c) Neither since the lines will cross but not at a 90deg angle.

2) Points (1,4), (2,6) & Points (5,0) , (6,2)

a + b)



c) Parallel since the lines have the same slope and will never cross each other.

3) Points (3,4), (5,2) & Points (2,1) , (6,5)

a + b)



c) Since the lines cross at a 90deg angle, the lines are perpendicular. ||

__//**After students have completed the individual problems and have shown them to the teacher, they will be given the homework to start in on before class ends**//__


 * Handouts**
 * Flow Chart
 * Sequence Chart
 * Quiz over Lessons 3 & 4: Slope, Velocity and Point-Slope Form
 * Homework Problems Sheet
 * Sets of Equations for Jigsaw & Three Corners Activity
 * Sets of Equations for GeoGebra Project
 * GeoGebra Project Checklist
 * GeoGebra Project Reflection Sheet