L4+Cobleigh,+Justin


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


 * Teacher’s Name:** Mr. Cobleigh **Date of Lesson:** Empathy
 * Grade Level:** 8 **Topic:** Linear Equations in Point / Slope Form

__**Objectives**__

 * Student will understand that** a linear relationship takes the form of y = mx + b.
 * Student will know** that linear relationships can be written in more than one form.
 * Student will be able to** be open to different ways to write linear equations**.**

__**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 point / slope form of writing linear equations.

__**Assessment**__

 * Formative (Assessment for Learning)**

Students will continue to expand on their unit flow charts to see how slope-intercept format can be connected back to slope-intercept from and standard form. Students will also use a Step-by-Step chart that will allow them to organize their mathematical process. Students will participate in a numbered heads activity. This is an activity where a group of 4 or 5 students are given an equation and they work together to solve it. The teacher then calls out a number and the person in the group that has been designated as that number shares out to the class what the group got for their answer. Students will also have the opportunity to ask questions during the lecture portion of class to clarify anything that is unclear at the current time. Also during the lecture, students could be asked questions consisting of, but not limited to: What is standard form? What is slope-intercept form? What is point-slope form? When would you want to use each form of a linear equation? How would we convert one form to another? Students would also be given work time towards the end of class to either work individually or with their peers around them on some sample problems. Students will have the opportunity to ask the teacher also if there are any pieces of linear equations that needs clarification. The final 10 minutes of class will be designated for students to write a quick journal response about something they liked about class, the material, etc... For students who are not comfortable asking questions during class, this would be a good way for them to ask and get an answer.


 * Summative (Assessment of Learning)**

Students will learn that there are a few different ways in which linear equations can be written. To show these different ways, students working in pairs will create a wikispace that explains the different ways of writing these equations and which situations they would be used in. Some items that students need to include are: (1) and overview of what linear equations are, (2) When would we want to use standard form and what are advantages/disadvantages of it, (3) 1-2 examples of graphs being solved for their equations in either form. All work associated with the examples can be on a word document that is attached to the wiki. I also encourage students to explore the wiki and see if there are any widgets that would be appropriate to use in this assignment. The way that the information is organized on the wikispace is entirely up to the students as long as the required pieces are included. (30 points)

__**Integration**__

 * Technology:** Students will create a wikispace at the end of this lesson to recap what they have learned.


 * English** will be used in this lesson. Students will be expected to have a wiki that is completely free of grammatical and spelling errors.

__Groupings__
Students will participate in a numbered heads activity. This is an activity where a group of 4 or 5 students are given an equation and they work together to solve it. The teacher then calls out a number and the person in the group that has been designated as that number shares out to the class what the group got for their answer. Groups will be selected through students being numbered 1-4, and they will have to create a group that has one of each number contained within it. At the end of class, students will also be allowed to work with students around them on sample problems that should be finished for homework if they are not in class.

__**Differentiated Instruction**__

 * Strategies**
 * Verbal:** Students can discuss with their classmates about the different ways of writing linear equations.
 * Logical:** Students can work on converting linear equations into different forms.
 * Visual:** Writing out equations and showing how pieces can be attributed to graphs and then converted to another form of equation.
 * Musical:** Students can create a pneumonic device used to remember which pieces go to each of the equations.
 * Interpersonal:** Sample problems can be worked on in pairs or with groups to see where some misconceptions may be.
 * Intrapersonal:** Students can work individually on sample problems to check their understanding of linear equations.

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 create a wikispace as the final project in this lesson to show the pros and cons of each form of writing linear equations.

__**Materials, Resources and Technology**__

 * Markers
 * Textbook
 * Sample Problems Handout
 * Flow Chart Organizer
 * Step-by-Step Organizer
 * Journals
 * Laptops (Student and Teacher)
 * LCD Projector

__Source for Lesson Plan and Research__

 * [] - Point-Slope Form and how to solve for it.
 * [] - What is point-slope form?
 * [] - Adjust slope and point to see resulting graphed line.
 * [] - Explanation of Point-Slope Form

__**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 - This lesson introduces students to a different way of solving a linear equation. Beach balls like to have choices and introducing the point-slope form will allow them to select with equation will work best for them and hopefully be able to solve any linear equation that may come their way. Clipboard - Visual direction is a big part of math. When it comes to converting linear equations from one form to another, drawing out a graph can be helpful in finding a point or finding the slope of the line. Having the picture of a graph will allow students to see what exactly they are writing down. Microscope - The hook for this lesson is intended to start discussion. I want to pose the question of who thinks point-slope and slope-intercept forms can both represent the same line. The intent is to get a multitude of answers and engage my students in a discussion of whether or not they believe they can both represent the same line. Puppy - Going along with the discussion, I want to have all students feel comfortable in being involved. It should be like a brainstorming session where all ideas are accepted, whether they are right or wrong, and help students work their way through solving the linear equations for the missing pieces.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * Rationale:** Students will know that linear relationships can be written in more than one form (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 empathy in that I hope //students will be able to be open to different ways to write linear equations//. I chose this facet because it emphasizes the need to be flexible and realize that there may be multiple ways to reach a solution. Not all questions are going to have one, solid answer. It will become important as a teacher to realize that students will tend to prefer one way of solving over another and that is OK. It is all about students using the resources they have to come to an answer. If they find that point-slope form may not work for a particular question, they may switch over to slope-intercept form to reach their answer. Both methods would be acceptable.


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


 * Verbal:** Students can discuss with their classmates about the different ways of writing linear equations.
 * Logical:** Students can work on converting linear equations into different forms.
 * Visual:** Writing out equations and showing how pieces can be attributed to graphs and then converted to another form of equation.
 * Musical:** Students can create a pneumonic device used to remember which pieces go to each of the equations.
 * Interpersonal:** Sample problems can be worked on in pairs or with groups to see where some misconceptions may be.
 * Intrapersonal:** Students can work individually on sample problems to check their understanding of linear equations.

Type II Product - Wikispace


 * //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 continue to expand on their unit flow charts to see how slope-intercept format can be connected back to slope-intercept from and standard form. Students will also use a Step-by-Step chart that will allow them to organize their mathematical process. Students will participate in a numbered heads activity. This is an activity where a group of 4 or 5 students are given an equation and they work together to solve it. The teacher then calls out a number and the person in the group that has been designated as that number shares out to the class what the group got for their answer. Students will also have the opportunity to ask questions during the lecture portion of class to clarify anything that is unclear at the current time. Also during the lecture, students could be asked questions consisting of, but not limited to: What is standard form? What is slope-intercept form? What is point-slope form? When would you want to use each form of a linear equation? How would we convert one form to another? Students would also be given work time towards the end of class to either work individually or with their peers around them on some sample problems. Students will have the opportunity to ask the teacher also if there are any pieces of linear equations that needs clarification. The final 10 minutes of class will be designated for students to write a quick journal response about something they liked about class, the material, etc... For students who are not comfortable asking questions during class, this would be a good way for them to ask and get an answer.


 * Summative (Assessment of Learning):** Students will learn that there are a few different ways in which linear equations can be written. To show these different ways, students working in pairs will create a wikispace that explains the different ways of writing these equations and which situations they would be used in. Some items that students need to include are: (1) and overview of what linear equations are, (2) When would we want to use standard form and what are advantages/disadvantages of it, (3) 1-2 examples of graphs being solved for their equations in either form. All work associated with the examples can be on a word document that is attached to the wiki. I also encourage students to explore the wiki and see if there are any widgets that would be appropriate to use in this assignment. The way that the information is organized on the wikispace is entirely up to the students as long as the required pieces are included. (30 points)

__Teaching and Learning Sequence__
Student's desks will be arranged in groups of 4 to accommodate the Numbered Heads Activity. I will be teaching from a central vantage point at the front of the classroom.

Outline of Agenda Day 1 (80 Minutes) Day 2 (80 Minutes) Day 3 (80 Minutes)
 * Students will be given a short period of time to ask any questions lingering about previous lessons. (5 minutes)
 * The teacher will hook students in to the lesson by asking them, "Do you think linear equations can be written in a different form?" Follow up with the video of the different forms of linear equations at [] (5 minutes)
 * Students will be introduced to the point-slope form or writing linear equations and will work through a few sample problems as a class. Students may also be asked to complete one or two on their own before the class moves on. During the time students are working on individual problems, the teacher will be walking around the classroom making themselves available to answer any questions from students. (30 minutes)
 * Numbered Head Activity - Students will participate in a numbered heads activity. This is an activity where a group of 4 or 5 students are given an equation and they work together to solve it. The teacher then calls out a number and the person in the group that has been designated as that number shares out to the class what the group got for their answer. Groups will be selected through students being numbered 1-4, and they will have to create a group that has one of each number contained within it. (20 minutes)
 * Students will be given the final portion of class to write out their journal entry reflecting on the lesson and writing any questions they may have. After the journal entry is written, students are to start on their homework problems. They are allowed to work with the students around them or individually. (20 minutes)
 * Students will be given time to ask questions about the homework or point-slope form in general. (20 minutes)
 * The teacher will handout the checklist and requirement of the wikispace project. I will also give students a tutorial on creating a wiki and how to edit and add pages. (30 minutes)
 * Students will choose their partners and get started on creating their wiki. They will have the remainder of the class to work on creating the wiki and designing how they want their wiki to look. For homework, students will have to create sample problems that they will use on their wikispace to show which formula would be appropriate in a given situation. (30 minutes)
 * Students will have the first part of class to put together their wikispaces. It should be expected that all students should need to do is upload their math work onto the wiki. (20 minutes)
 * Each pair of students will take turns presenting their wiki to the class. Students who are not presenting at a given time will have a copy of the checklist used for grading to see if they feel that all required pieces of the wiki were present. Students should try to limit their presentations to under 5 minutes. (50 minutes)
 * Students will take the final portion of class finishing up any checklist that were not completed during presentations. Students should also respond in their journals about what they enjoyed or noticed. The journal entry should be completed for homework if time in class runs out. (10 minutes)

Students will understand that a linear relationship takes the form of y = mx + b. Students will be hooked with a provocative question: Who thinks that y = mx + b and y = m(x - x1) + y1 are the same equation? The question will be followed up by a video of the different types of linear equations []. //**Students understand and use basic properties of linear relationships using y = mx + b**//. Students will have a few minutes in which discussion can happen on whether or not the above mentioned equations stand for the same thing. This will get them into the mind of thinking about linear equations. Before showing students how to solve for point-slope form, a review will be done over the concept of slope-intercept form as well as a review on graphing linear equations. Once lecture begins and they have seen an example or two, they will see that both slope-intercept and point-slope forms can represent the same equation.
 * Where, Why, What, Hook Tailors: Verbal, Visual, Logical, Intrapersonal, Interpersonal**

Students will know that linear relationships can be written in more than one form. //See Content Notes//. Students will continue to use their flow chart organizer to expand their knowledge of how the entire unit will fit together. Students will be able to keep a list of the different ways linear equations can be written so they have some options of which they can use in a given situation. Students will also use a Step-by-Step chart to help keep them organized in solving for a given piece of the point-slope formula. It can also help in seeing how equations can be given in one form and then transformed into the other. Students will be questioned during lecture with questions such as: What is point-slope form? What is m? What is x1 or y1? Can you show how these equations relate? How do you take an equation in slope-intercept form and put it into point-slope? These questions will help students to understand the main concepts of the lesson. Students will have some time where they will be working on sample problems. They will be allow to work either individually or in groups and have the chance to ask questions to both their classmates and the teacher. The teacher should be floating around the room at this time to help students one-on-one when they become stuck and to also correct them if it's clear that they are making a mistake. Students will also be asked to respond to the lesson in their journal if there were any questions that they did not want to bring up in class. This will allow the teacher to see where students are and to help reiterate a topic if necessary.
 * Equip, Explore, Rethink, Revise, Refine Tailors: Verbal, Visual, Logical, Intrapersonal, Interpersonal, Kinesthetic**

Students will be able to be open to different ways to write linear equations. During class, students will participate in a numbered heads activity. This is an activity where a group of 4 or 5 students are given an equation and they work together to solve it. The teacher then calls out a number and the person in the group that has been designated as that number shares out to the class what the group got for their answer. Groups will be selected through students being numbered 1-4, and they will have to create a group that has one of each number contained within it. At the end of class, students will also be allowed to work with students around them on sample problems that should be finished for homework if they are not in class. Once students feel comfortable that they can distinguish the difference between different ways of writing linear equations, students will work in pairs and create a wikispace in which they will discuss the different ways of writing linear equations. Students will also be asked to give an example of converting between point-slope and slope-intercept forms. They will need to discuss the differences between the equations, which situations would best fit the use of each of the equations and provide an example of each equation being used. These wikispaces will be shared with the class and each student must talk when presenting; it should not be just one person talking.
 * Organize, Experience, Explore Tailors: Verbal, Visual, Interpersonal, Intrapersonal**

The wikis that are created by students will be graded using a checklist. This will contain all of the pieces that the wikispace needs to include on it. A few things, but not limited to just these, would be what each equation is, what the pieces of the equation mean, etc... While students are presenting, the audience members will all have a blank copy of the checklist to fill out anonymously and will be turned over to the groups after presenting. This is a way for students to give honest feedback without having it known that you said something critical of the presenters. It is important to emphasize the positive pieces and how to expand on those rather than to point out the negative pieces. It is a good morale booster to see what you did well. Before the final project for the lesson, students will be working on sample problems to get used to point-slope form. While students are working on this, the teacher is to be floating around the room to help those students who require assistance or to reiterate a topic if a certain question is coming up multiple times.
 * Evaluate Tailors: Verbal, Visual, Interpersonal, Intrapersonal, Logical**


 * Content Notes**

Students will know that linear relationships can be written in more than one form.

__//Definitions//__ Point-Slope Form: y - y1 = m (x - x1), where //m// is slope and //(x1,y1)// is a point on the graph.

__//Example Problems//__


 * **In-Class Examples** || **Individual or in Pairs Afterwards** ||
 * Given slope and a point, Solve for point-slope form.

1) Slope = 3, Point (2,5) => Slope = m, Point (x1,y1)

y - 5 = 3 (x - 2)

2) Slope = 5, Point (-4,-3)

y + 3 = 5 (x + 4) || Given slope and a point, Solve for point-slope form.

1) Slope = 2, Point (4,4)

y - 4 = 2 (x - 4)

2) Slope = -6, Point (2,-4)

y + 4 = -6 (x - 2) ||
 * Given 2 points, Solve for point-slope form.

1) Points (3,4), (5,8)

Need to find slope of the line: __8-4__ = �485

y + 8 = (3/2)(x + 5)
|| Given 2 points, Solve for point-slope form.

1) Points (5,6), (7,8)

__8-6__ = �497

y + 2 = (4/5)(x + 3)
||
 * Given slope and y-intercept, Solve for point-slope form.

1) Slope = 4, Y-int = 3

Since the y-int is when x = 0, we have the point that exists on the graph as (0,3)

y - 3 = 4 (x - 0)

2) Slope = -5, Y-int = -2

y + 2 = -5 (x - 0) || Given slope and y-intercept, Solve for point-slope form.

1) Slope = 3, Y-int = 5

y - 5 = 3 (x - 0)

2) Slope = 7, Y-int = -10

y + 10 = 7 (x - 0) || __//**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**
 * Step-by-Step Chart
 * Flow Chart
 * Sample Problems
 * Wikispace Checklist