L2+Cobleigh,+Justin


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


 * Teacher’s Name:** Mr. Cobleigh **Date of Lesson:** Interpret
 * Grade Level:** 8 **Topic:** Graphing Linear Equations

__**Objectives**__

 * Student will understand that** graphs can be drawn from equations and vice versa.
 * Student will know** how each piece of an equation translates over to a graph.
 * Student will be able to** illustrate a graph from an equation and vice versa**.**

__**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 is going to introduce students to graphing linear equations.

__**Assessment**__

 * Formative (Assessment for Learning)**

Students will work with a flow chart organizer to put together the concept taught in lesson one, which explained what linear equation are, and see how that lesson applied to learning how to graph linear equations. Students will also participate in a Round Robin style activity. Students will randomly be split up into groups of an equal size in which groups will be given an equation to graph. The group will work together to do so and then share out to see the answers. If there are differing answers, it can be discussed what may have gone wrong. Students will also be posed questions during instruction such as: Is the slope positive or negative? Is it a horizontal line? Is it a vertical line? What would those two cases mean? Students would also be given the opportunity to work together with their peers or individually on taking some linear equations and graphing them and also taking a graph and being able to create the equation. Sample problems would be assigned for homework for students to practice with. Before a certain class period ends, students will be asked to respond to the day's lesson in a journal entry. There is free range to talk about the lesson as long as it does not stray off task. The main purpose of this journal is to give the teacher an idea of where the students are and where questions are to help students better understand.


 * Summative (Assessment of Learning)**

Students, working individually, will be given a list of varying equations in which they will need to graph. Before using the graphing application on NLVM, students must first draw out by hand what they think would be the outcome of the graphs. Once they have had the opportunity to draw out the graphs by hand, students can use the graphing application on NLVM to compare their graphs to those shown through the internet tool. You will want to then draw the graphs that were gotten online onto your handwritten ones for comparison. If there were some graphs that did not come out the same, why do you think that happened? Did you misread your equation? Did a negative sign get lost? Those are some sample questions that could be answered. This is an individual project and one equation will be given to each student to present their results in front of the class. (20 points)

__**Integration**__

 * Technology:** The graphing application on the [|National Library of Virtual Manipulatives] will be used in the final project.


 * Art** could be incorporated into this lesson. Drawing is used in creating graphs of the given equations.

__Groupings__
Students will participate in a Round Robin style activity. Groups will be selected at random and will be of equal size. Students will be given an equation that needs to be graphed or be given a graph that needs its equation written and, working as a team, come up with what the answer is. The solutions will be shared out to the class to see if students can come to a consensus. If there is a difference in some answers, it can be discussed as to where the group may have gone wrong in their thought processes.

__**Differentiated Instruction**__

 * Strategies:**
 * Verbal:** Students are involved in lecture and discussion on graphing.
 * Logical:** Students work on example problems of converting equations to graphs and vice versa.
 * Visual:** Using mini-whiteboards, students can write out their attempts to converting to graphs and compare with other students.
 * Kinesthetic:** The class can use a life-size grid and use the students as points on the line.
 * Naturalist:** The life-size grid mentioned in above can be moved to an outdoor setting.
 * Interpersonal:** Students can work in pairs or as groups on creating graphs.
 * Intrapersonal:** Students work individually to convert equations to graphs.

I will review student's IEP, 504 or ELLIDEP and make appropriate modifications and accomodations. __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 the grapher application on the National Library of Virtual Manipulatives website to create the graphs of given linear equations.

__**Materials, Resources and Technology**__

 * Markers
 * Textbook
 * Sample Problem Handouts
 * Mini-Whiteboards
 * Flow Chart Organizer
 * Laptops (Students & Teacher)
 * LCD Projector
 * Sidewalk Chalk
 * Journal

__Source for Lesson Plan and Research__

 * [] - Flow Chart Organizer used in class.
 * [] - Graphing Application on NLVM used for the final product.
 * [] - Purple Math Step-by-Step on creating a graph from an equation.
 * [] - Graphing Tutorial and sample problems follow.

__**Maine Standards for Initial Teacher Certification and Rationale**__

 * //Standard 3 - Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development.//**
 * Rationale:** Beach Ball - There are a couple of different resources that are used in this lesson from the mini-whiteboards to moving the lesson of graphing off of the whiteboard and to the outdoors and to a life-size chalk grid. Clipboard - There will be a sequence to the process taken in creating graphs. At first, students will be taught how to create a table of points before moving to the coordinate grid. Microscope - Discussions would be held in the Round Robin activity to get the groups working together and coming to an answer to creating the graph that they all, as a group, can agree on. Puppy - I would hope that students are being honest and truthful on their checklists that are being completed during student presentations. I do not want to see all put downs as comments, I would like to see ways in which things could be improved. Focus on the positive and not the negative.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * Rationale:** Students will know how each piece of an equation translates over to a graph and vice versa (reference content notes at the end of the lesson). **//Students understand and use basic properties of linear relationships using y = mx + b//**. The facet that I used for understanding in this lesson was interpret in that I hope //students will be able to illustrate a graph from an equation and vice versa//. I chose this facet because I want students to be able to see what each piece of the linear equation actually does to the picture displayed on the graph. Graphing is a big piece in high up mathematics classes and learning now by doing the basic pieces now, students will have a foundation for their later classes.


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


 * Verbal:** Students are involved in lecture and discussion on graphing.
 * Logical:** Students work on example problems of converting equations to graphs and vice versa.
 * Visual:** Using mini-whiteboards, students can write out their attempts to converting to graphs and compare with other students.
 * Kinesthetic:** The class can use a life-size grid and use the students as points on the line.
 * Naturalist:** The life-size grid mentioned in above can be moved to an outdoor setting.
 * Interpersonal:** Students can work in pairs or as groups on creating graphs.
 * Intrapersonal:** Students work individually to convert equations to graphs.

Type II Product - Use of the Graphing Application on the National Library of Virtual Manipulatives


 * //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 with a flow chart organizer to put together the concept taught in lesson one, which explained what linear equation are, and see how that lesson applied to learning how to graph linear equations. Students will also participate in a Round Robin style activity. Students will randomly be split up into groups of an equal size in which groups will be given an equation to graph. The group will work together to do so and then share out to see the answers. If there are differing answers, it can be discussed what may have gone wrong. Students will also be posed questions during instruction such as: Is the slope positive or negative? Is it a horizontal line? Is it a vertical line? What would those two cases mean? Students would also be given the opportunity to work together with their peers or individually on taking some linear equations and graphing them and also taking a graph and being able to create the equation. Sample problems would be assigned for homework for students to practice with.


 * Summative (Assessment of Learning):** Students, working individually, will be given a list of varying equations in which they will need to graph. Before using the graphing application on NLVM, students must first draw out by hand what they think would be the outcome of the graphs. Once they have had the opportunity to draw out the graphs by hand, students can use the graphing application on NLVM to compare their graphs to those shown through the internet tool. You will want to then draw the graphs that were gotten online onto your handwritten ones for comparison. If there were some graphs that did not come out the same, why do you think that happened? Did you misread your equation? Did a negative sign get lost? Those are some sample questions that could be answered. This is an individual project and one equation will be given to each student to present their results in front of the class. (20 points)

__Teaching and Learning Sequence__
Students desks will be arranged in groups to accommodate the Round Robin activity and I will be instructing from the front of the classroom.

Outline of Agenda Day 1 (80 Minutes) Day 2 (80 Minutes)
 * Class will be started with a video of the example activity that we will be doing later in the lesson. (5 minutes)
 * Students will be introduced to graphing linear equations. The teacher will be at the whiteboard / SMARTboard working through example problems (//See Content Notes//) and walking students through the first couple of graphs. The process would start with creating a table of points that are on the graph and then translating the points over to the coordinate grid. In addition to students taking notes, they are more than welcome to ask questions wherever they are needed to help clarify any point of the lesson. (30 minutes)
 * Round Robin Activity - Students will be randomly placed into equally sized groups and each group is given a mini-whiteboard with a marker. A linear equation or graph of a linear equation is placed on the board and the groups would be required to find the option that was not put on the board. The group has to work together to come to an answer that they all can agree on. One person from the group will report out and hold up the whiteboard to the class to see the groups answer. If the team gets it right, they gain a point and at the end, the team with the most points will win a prize, to be determined at a later date. If there is an incorrect answer displayed, as a class, we could come up with how that problem came out wrong and see what we could do to fix it. //Weather depending, this activity could be switched with the outdoor activity that is scheduled for tomorrow.// (35 minutes)
 * These last few minutes will be used as a wrap-up time to get all materials put away and allow students to respond to the lesson in their journals. While they are doing so, the teacher is to hand out the worksheet of example problems that students are to do for homework. (10 minutes)
 * The first few minutes of class will be used to go over any questions that students may have had over the homework assignment. (10 minutes)
 * Outdoor Graph Activity - The class will move outdoors to a life-size coordinate grid drawn out on the ground. Students will use the mini-whiteboards to create a table of points for a given linear equation and students will then become the points on the life-size graph and create the line. //Weather depending, this activity could be switched with the Round Robin activity that was scheduled for the previous day.// (30 minutes)
 * Students will be introduced to the graphing application on the National Library of Virtual Manipulatives. The teacher will put in an example linear equation and show how the program will draw the graph. Students will then choose an equation from a sheet of linear equations and create the graph first by hand and then on the graphing application. Students should show all of their work because it will be presented to the class on the whiteboard. (20 minutes)
 * Students will present their linear equations and their graphs to the class and how they got to their answer. Other students not presenting will have copies of the checklist used to grade to see if they felt all parts of the presentation were met or not. (20 minutes)

Students will understand that graphs can be drawn from equations and vice versa. Hills and valleys can be drawn as graphs and their sides can be attributed to a specific linear equation. //**Students understand and use basic properties of linear relationships using y = mx + b**//. Students will be hooked by watching a video [] of an activity that we, as a class, can participate in at a later date. For pre-assessment, students will participate in a quick review session of the previous lesson on linear equations to make sure that students understand what linear equations are and what they look like in order to translate them over to a graph. Students will be at their desks for this and I will be from a central teaching point at the front of the room.
 * Where, Why, What, Hook Tailors: Visual, Verbal, Kinesthetic, Naturalist**

Students will know how each piece of an equation translates over to a graph and vice versa. //See Content Notes//. Students will use the flow chart organizer that was passed out during the previous lesson to build on the idea of linear equations and to see how the graphing of linear equations goes along with writing them out. They will be able to put the two pieces together and use them in future lessons. Students will also respond to questions such as: What is the x-axis? What is the y-axis? How do you create points? How do you set up a table? Students will be allowed work time towards the end of class to work on sample problems of graphing lines. They will be allowed to work independently or quietly with their peers. During this time, the teacher will be floating around the room being available to answer any questions that arise. Students will also participate in an outdoors activity of a life-size graph where students are the points on a line. At the end of the first day, student's will be responding to the day's lesson in their journals reflecting back on what they learned or misunderstood. This is a way for the teacher to gauge where students are and to also review topics if it seems necessary.
 * Equip, Explore, Rethink, Revise, Refine Tailors: Logical, Visual, Verbal, Kinesthetic, Naturalist, Interpersonal, Intrapersonal**

Students will be able to illustrate a graph from an equation and vice versa. Using a Round Robin style activity, students will be randomly placed into groups of equal size and each group will be given a mini-whiteboard and marker. An equation will be placed on the main whiteboard in which the groups need to create the graph for. A graph could also be placed on the board and the students need to create the linear equation. Once all groups have come to an answer, we go around the room looking at the answers and seeing which ones are correct. If there are any that appear incorrect, as a class, we'll try to determine where the error occurred and think of ways to help avoiding that error. Once students have gotten a handle on graphing equations by hand, they will be given a sheet of equations in which they need to create graphs of. After that is done, using the graphing application on the National Library of Virtual Manipulatives, students will enter the equation to see the resulting graph. They will be able to compare what they came up with to the actual graph and also see where they may have made errors. Students will present one of the equations, and their process of getting to the graph, to the class.
 * Organize, Experience, Explore Tailors: Logical, Visual, Verbal, Intrapersonal, Interpersonal**

Each student will be given a checklist for each presentation so that they can tell if they saw all parts of the presentation mentioned. These would all be anonymous and the presenting students would get these back in the next class. I would also have the same checklist which would be counted towards the grade. Students would get these back as soon as possible to see how they did and see if there is anything that they should change for future presentations. When students are given sample problems to work on in class, I will be floating around to help any student that needs the help. If there is a problem that appears to be happening for several students, I would take the time to re-explain that part to the class in order to have my students have a better understanding of the topic of graphing linear equations.
 * Evaluate Tailors: Interpersonal, Intrapersonal, Visual, Verbal**


 * Content Notes**

Students will know how each piece of an equation translates over to a graph.

__//Definitions//__ x-axis - horizontal line of the graph of possible x-values when y = 0 y-axis - vertical line of the graph of all possible y-values when x = 0 (x,y) - any point on the graph with a specific x and y coordinate

__//Examples - Tables and Graphs//__

(1) y = x

(a) Create a table of possible points. Choose the x-values that you want and to find the y-values, substitute the x-values into the original equation. (b) Plot the points onto your coordinate plane
 * **X** || **Y** ||
 * -2 || -2 ||
 * -1 || -1 ||
 * 0 || 0 ||
 * 1 || 1 ||
 * 2 || 2 ||



(c) Connect the points with a line and that is the graph of the line y = x



(2) y = -x

(a)
 * **X** || **Y** ||
 * -2 || 2 ||
 * -1 || 1 ||
 * 0 || 0 ||
 * 1 || -1 ||
 * 2 || -2 ||

(b+c)

What do you notice about changing the coefficient from positive in the first example to the negative in the second?

(3) y = 2x & y = (1/2)x

(a)
 * = **X** ||= **y = 2x** ||= **y = (1/2)x** ||
 * = -2 ||= -4 ||= -1 ||
 * = -1 ||= -2 ||= -(1/2) ||
 * = 0 ||= 0 ||= 0 ||
 * = 1 ||= 2 ||= (1/2) ||
 * = 2 ||= 4 ||= 1 ||

(b+c)

What do you notice about the coefficients when they are whole numbers or rational numbers?

(4) y = x + 1 & y = x - 1

(a)
 * = **X** ||= **y = x + 1** ||= **y = x - 1** ||
 * = -2 ||= -1 ||= -3 ||
 * = -1 ||= 0 ||= -2 ||
 * = 0 ||= 1 ||= -1 ||
 * = 1 ||= 2 ||= 0 ||
 * = 2 ||= 3 ||= 1 ||

(b+c)

What do you notice happens to the graph when there are numbers added and subtracted to the equation?

Equations for students to graph individually: (1) y = 2x + 3 (2) y = (1/3)x - 5 (3) y = 3x + 7 (4) y = (1/2)x - 2


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


 * Handouts**
 * Flow Chart
 * Sample Problems
 * +/-/x/÷ Sheet
 * Sheet of Equations for Final Product
 * Checklist to Evaluate Presentation