L3+Cobleigh,+Justin


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


 * Teacher’s Name:** Mr. Cobleigh **Date of Lesson:** Explanation
 * Grade Level:** 8 **Topic:** Rate of Change (Slope) and Velocity

__**Objectives**__

 * Student will understand that** linear relationships are characterized by a constant rate of change.
 * Student will know** how to calculate rate of change, also known as slope, and velocity.
 * Student will be able to** demonstrate how to find a constant rate of change (slope) and velocity**.**

__**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 slope and velocity.

__**Assessment**__

 * Formative (Assessment for Learning)**

Students will expand on the Flow Chart organizer they were given in the first class to connect slope and velocity to linear equations and their graphs. They will also use a Step-by-Step organizer to show the steps that are necessary for finding slope and velocity. Students will also work in Think-Pair-Share groups and report out to the class. The teams pairs of students will be chosen through the +/-/x/÷ sheet that should be previously filled out. The pairs of students will be given a couple of equations in which they will need to find the slope of. They will first work individually to see what they come up with for an answer. Next, students will work with their partner to see if the answers were the same, and if they were not, they would work together to see where an error had occurred. Once this process has ended, groups of students will take their turns demonstrating to the class their equations and how they came to their answers. During the class lecture, students will be periodically questioned with some questions being: What is m? Is it positive or negative? Which formula did you use? What does a vertical line mean? What does a horizontal line mean? What does a positively sloped graph look like? What does a negatively sloped graph look like? What happens to the lines when slopes change but y-intercepts stay constant? Outside of the Think-Pair-Share activity, students would work either individually or in groups on example problems solving for slope and velocity. Students will also be asked to respond in a journal entry to the opening day of the lesson. What material did they understand? Are there any lingering questions? Those are some questions that they could answer but they are certainly not limited to them.


 * Summative (Assessment of Learning)**

After learning about how to calculate slope and velocity, students will work in groups of 3-4 students in creating an interactive SMARTboard presentation on how to calculate for slope and velocity. Each team will be given a list of equations and graphs in which they must solve for the two components. The presentation must show their answers and how they came to them. It is up to the group how many of their problems they choose to present to the class, with a minimum of one per group member. All other problems can be handed in on paper neatly, and with all of the appropriate work. I would like these presentations to be more than a PowerPoint where students are just reading off of the screen. There should be creativity put into the presentation so that you can keep the audience's attention. (50 points)

__**Integration**__

 * Technology:** SMARTboards will be used for student's final presentations on slope and velocity.


 * Science** would be pertinent in this lesson as slope and velocity would be used in physics applications.

__Groupings__
Students will work in Think-Pair-Share groups and report out to the class. The teams pairs of students will be chosen through the +/-/x/÷ sheet that should be previously filled out. The pairs of students will be given a couple of equations in which they will need to find the slope of. They will first work individually to see what they come up with for an answer. Next, students will work with their partner to see if the answers were the same, and if they were not, they would work together to see where an error had occurred. Once this process has ended, groups of students will take their turns demonstrating to the class their equations and how they came to their answers. They will also be allowed to work on sample problems and homework problems with their peers to collaborate in solving for slope and velocity.

__**Differentiated Instruction**__

 * Strategies**
 * Verbal:** Students can be involved in lecture and discussion to answer any unclear concepts of slope and velocity.
 * Logical:** Students can work on example problems to see if they can use the slope and velocity formulas effectively.
 * Visual:** Pictures and diagrams can be drawn on the board during instruction to go along with word problems.
 * Kinesthetic:** Students can create a life-size grid and take the slope of specific lines.
 * Musical:** Students can create a pneumonic device to remember the pieces of the slope and velocity formulas.
 * Naturalist:** The student life-size grid can be moved outdoors.
 * Interpersonal:** Students can work in pair or groups to solve problems for slope and velocity.
 * Intrapersonal:** Students can work individually to solve problems and review their thought processes in coming to an answer.

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 an interactive SMARTboard presentation to show their processes in solving for slope and velocity.

__**Materials, Resources and Technology**__

 * Markers
 * Textbook
 * Sample Problems Handout
 * Flow Chart Organizer
 * Laptops (Student and Teacher)
 * LCD Projector
 * SMARTboard
 * Journal

__Source for Lesson Plan and Research__

 * [] - How to find slope and y-intercepts to create graphs.
 * [] - Sample Slope Problems
 * [] - Solve Ax + By = C for y and be able to calculate the slope.
 * [] - Solving for Velocity
 * [] - Explanation of Velocity and how to find it.

__**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 - Students will be given free range on what they choose to add to their SMARTboard presentations as long as it includes the math requirements that are stated on the checklist that will be used for grading. Clipboard - When it comes to finding slope, there is a specific process that needs to be followed in order to find the value. If there is one number out of place, it can change the answer to a problem significantly. Microscope - Students will be focusing on detail in their solving processes for slope and velocity. All of their work has to be shown in order to receive full credit so they have to include every little detail. Leaving one part out, and getting an incorrect answer could go hand-in-hand in that the problem could have been with the missing piece. Puppy - Students will be allowed to choose their groups of 3 for this project. It will allow for students to work with those people in the class with which they feel more comfortable. I would not want them to have to work with someone who they do not get along with at all.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * Rationale:** Students will know how to calculate rate of change, also know as slope, and velocity (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 in this lesson was explanation in that I hope //students will be able to demonstrate how to find a constant rate of change (slope) and velocity//. I chose this facet because I want students to be able to explain what they did to reach their answer. I want them to get used to the idea of showing all of their work that was done to reach their goal. Math work can get confusing and writing out all of the steps that were taken will make it easier to pinpoint where any errors may have occurred.


 * //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 be involved in lecture and discussion to answer any unclear concepts of slope and velocity.
 * Logical:** Students can work on example problems to see if they can use the slope and velocity formulas effectively.
 * Visual:** Pictures and diagrams can be drawn on the board during instruction to go along with word problems.
 * Kinesthetic:** Students can create a life-size grid and take the slope of specific lines.
 * Musical:** Students can create a pneumonic device to remember the pieces of the slope and velocity formulas.
 * Naturalist:** The student life-size grid can be moved outdoors.
 * Interpersonal:** Students can work in pair or groups to solve problems for slope and velocity.
 * Intrapersonal:** Students can work individually to solve problems and review their thought processes in coming to an answer.

Type II Product - SMARTboard Presentation


 * //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 expand on the Flow Chart organizer they were given in the first class to connect slope and velocity to linear equations and their graphs. Students will also work in Think-Pair-Share groups and report out to the class. The teams pairs of students will be chosen through the +/-/x/÷ sheet that should be previously filled out. The pairs of students will be given a couple of equations in which they will need to find the slope of. They will first work individually to see what they come up with for an answer. Next, students will work with their partner to see if the answers were the same, and if they were not, they would work together to see where an error had occurred. Once this process has ended, groups of students will take their turns demonstrating to the class their equations and how they came to their answers. During the class lecture, students will be periodically questioned with some questions being: What is m? Is it positive or negative? Which formula did you use? What does a vertical line mean? What does a horizontal line mean? What does a positively sloped graph look like? What does a negatively sloped graph look like? What happens to the lines when slopes change but y-intercepts stay constant? Outside of the Think-Pair-Share activity, students would work either individually or in groups on example problems solving for slope and velocity. Students will also be asked to respond in a journal entry to the opening day of the lesson. What material did they understand? Are there any lingering questions? Those are some questions that they could answer but they are certainly not limited to them.


 * Summative (Assessment of Learning):** After learning about how to calculate slope and velocity, students will work in groups of 3-4 students in creating an interactive SMARTboard presentation on how to calculate for slope and velocity. Each team will be given a list of equations and graphs in which they must solve for the two components. The presentation must show their answers and how they came to them. It is up to the group how many of their problems they choose to present to the class, with a minimum of one per group member. All other problems can be handed in on paper neatly, and with all of the appropriate work. I would like these presentations to be more than a PowerPoint where students are just reading off of the screen. There should be creativity put into the presentation so that you can keep the audience's attention. (50 points)

__Teaching and Learning Sequence__
Student's desks will be arranged in a U-form and I will be instructing from the opening 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 session in which they are allowed to ask any lingering questions about linear equations, such as what it's pieces are or how to graph them. (10 minutes)
 * Students will take a quiz over creating linear equations and how to graph them. Once they have finished the quiz, it is to be passed in and they are to work quietly on other homework, either for my class or any other until others have finished. (20 minutes)
 * Students will be shown a car traveling down a hill. They will be asked if they know how fast the position is changing to see if some may already know, and for those who do not, they are about to find out. (5 minutes).
 * Students will be introduced to slope and velocity and how to solve for both of them. //See Content Notes//. They will be introduced to the slope formula(s) and also the formula for finding velocity. The teacher will walk students through a few example problems. (30 minutes)
 * Students will start in on sample problems and any that are not completed in class are to be completed for homework. Students will also respond to the material covered in a journal entry. They are encouraged to reflect on what they got out of the lesson and to mention any questions they have still after the lesson has finished. They are certainly not limited to these as responses. (15 minutes)
 * Students will be allowed to ask questions about the previous night's homework and go over any problems that they had difficulty with. (15 minutes)
 * The teacher will introduce to students the SMARTboard presentation project and go over the requirements. Students will also be given a copy of the checklist to ensure that they include all of the required pieces. If available, the teacher will provide a quick example of a presentation. (15 minutes)
 * Students will have the remainder of the class to work on their presentations with their groups. By the end of the class, students should have all of their work on the problems completed and have a general idea of what their presentation will look like. For homework, groups will plan on what their presentations will consist of and have ideas ready to go. If students wish to start in on their presentation before the class period is over, they are more than welcome to. (50 minutes).
 * Students get straight to work on their SMARTboard presentations. It should be final touches being put on their project before presentation time. (40 minutes)
 * SMARTboard presentations. Students not presenting are to be filling out the checklists with their feedback sandwiches to be given to the presenters next class. (30 minutes)
 * Wrap up of the SMARTboard presentations and collect all checklists. There will be a quick mentioning of the topic to be covered in the next lesson. (10 minutes)

Students will understand that linear relationships are characterized by a constant rate of change. When we drive a car, our speed (velocity) is always changing either when we push on the accelerator or are going down a hill. //**Students understand and use basic properties of linear relationships using y = mx + b.**// A demonstration of a car going downhill will be used and it will be traveling at a constant rate of change and velocity. For pre-assessment, students will review the concepts of linear equations and how to graph them. They will finally be figuring out what exactly the //m// means in the equation. During lecture, students will be at their desks and I will be teaching from a central vantage point. During the Think-Pair-Share activity, students will be allowed to move around the room to work.
 * Where, Why, What, Hook Tailors: Visual, Verbal, Logical, Interpersonal, Intrapersonal**

Students will know how to calculate rate of change, also know as slope, and velocity. //See Content Notes//. Continuing with the flow chart organizer, students will be able to connect slope and velocity to the previous concepts of linear equations and graphs. They will be able to see how the //m// works in y = mx + b and how it affects the lines on the graph. They will also keep track of the steps taken to solve for slope and velocity in a Step-by-Step organizer. Students will be periodically questioned with some questions such as: What is m? Is it positive or negative? Which formula did you use? What does a vertical line mean? What does a horizontal line mean? What does a positively sloped graph look like? What does a negatively sloped graph look like? What happens to the lines when slopes change but y-intercepts stay constant? Students will be allowed some time to work on a few sample problems, either individually or with a partner, and to ask questions if they do not understand a part of solving for slope or velocity. During the work time, the teacher will be floating around the room to check up on student's progress and to make themselves available to help where necessary. Students will also respond in a journal entry to any questions they may have lingering or to how they reacted to the material that was presented in the lesson.
 * Equip, Explore, Rethink, Revise, Refine Tailors: Visual, Verbal, Logical, Interpersonal, Intrapersonal**

Students will be able to demonstrate how to find a constant rate of change (slope) and velocity. Students will also work in Think-Pair-Share groups and report out to the class. The teams pairs of students will be chosen through the +/-/x/÷ sheet that should be previously filled out. The pairs of students will be given a couple of equations in which they will need to find the slope of. They will first work individually to see what they come up with for an answer. Next, students will work with their partner to see if the answers were the same, and if they were not, they would work together to see where an error had occurred. Once this process has ended, groups of students will take their turns demonstrating to the class their equations and how they came to their answers. Once students have become comfortable with finding the slope of a line and velocity, in groups of three, students will be given a coordinate points in which they will need to create a graph of, and also find the equation of the line. They also need to find the velocity that someone would be traveling to reach the bottom in a designated amount of time. Students will put all of their work onto an interactive SMARTboard presentation to be presented to the entire class. Only one equation will be presented however there will be one set of coordinate points per group member.
 * Organize, Experience, Explore Tailors: Verbal, Visual, Musical, Intrapersonal**

Students will be graded using a checklist so ensure that they included each part of the require math work. Students not participating in the presentation will all be given a copy of the checklist to anonymously fill out during the presentation to provide feedback to the team. Students will be asked to write on the back of their checklists a feedback sandwich, which consists of a positive aspect of the presentation, a statement about what could have used some improvement and finally a compliment about the presentation as a whole.* The teacher will also be filling out the checklist and the feedback sandwich to provide feedback to the team. These checklist would be returned to the presenting students as quickly as possible. As students are working on sample problems in class, I will be floating around the classroom or at my desk available to provide assistance to any student who requires it. Also, if there seems to be a recurring question, I would take the time to do an example or two on the board of a specific type of problem to ensure that it is made clearer for my students.
 * Evaluate Tailors: Interpersonal, Intrapersonal, Visual, Verbal, Musical (If music is included in presentations)**


 * Content Notes**

Students will know how to calculate rate of change, also know as slope, and velocity.

__//Definitions//__ Slope Formula: m = (Y2-Y1)/(X2-X1), where //m// is slope and the points (X1,Y1) & (X2,Y2) are used. The slope formula can also be remembered as rise / run. VelocityFormula: v = d/t, where //v// is velocity, //d// is distance, and //t// is time.

__//__Example Problems__//__


 * //Slope://**
 * **In - Class Examples** || **Individual or in Pairs Afterwards** ||
 * Given 2 Points, solve for slope using the standard formula.

1) Points (2,4), (6,8) => (X1,Y1) , (X2,Y2)

m = (8-4) / (6-2)

m = 4 / 2

m = 2

2) Points (1,1), (7,9)

m = (9-1) / (7-1)

m = 8 / 6

m = 4 / 3 || Given 2 Points, solve for slope using the standard formula.

1) Points (4,5), (16,10)

m = (10-5) / (16-4)

m = 5 / 12

2) Points (10,12), (5,6)

m = (6-12) / (5-10)

m = -6 / -5

m = 6 / 5 ||
 * Looking at the graph, use rise over run to find the slope.

1)

__Rise__ = __1__ = 1 Run 1

2)

__Rise__ = __2__ Run 3

3)

__Rise__ = __1__ Run -2 || Looking at the graph, use rise over run to find the slope.

1)

__Rise__ = __2__ = 2 Run 1

2)

__Rise__ = __1__ Run 5

3)

__Rise__ = __-3__ Run 2 ||
 * Given distance and time, solve for the velocity.

1) Distance = 100ft, Time = 10sec

v = 100ft / 10sec

v = 10ft/sec

2) Distance = 35yds, Time = 7sec

v = 35yds / 7sec

v = 5yd/sec || Given distance and time, solve for the velocity.

1) Distance = 50mi, Time = 25min

v = 50mi / 25min

v = 2mi/min

2) Distance = 600km, Time = 4hr

v = 600km / 4hr

v = 15km/hr ||
 * Given a velocity and either distance or time, solve for the missing piece.

1) Velocity = 15ft/sec, Time = 10sec

15ft/sec = d / 10sec (10sec) (10sec) 150ft = d

2) Velocity = 25mi/hr, Distance = 50mi

25mi/hr = 50mi / t (50mi) (50mi) 1250hr = t || Given a velocity and either distance or time, solve for the missing piece.

1) Velocity = 100yd/min, Time = 5min

100yd/min = d / 5min (5min) (5min) 500yd = d

2) Velocity = 2500ft/sec, Distance = 10000ft

2500ft/sec = 10000ft / t (10000ft) (10000ft) 25000000sec = t || __//**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
 * Step-by-Step Organizer
 * Sample Problems
 * +/-/x/÷ Sheet
 * SMARTboard Presentation Checklist
 * Sheet of Equations for SMARTboard Presentation
 * Quiz over Lessons 1 & 2: Creating Linear Equations and Graphing

~ Feedback Sandwich idea taken from a rubric created by Dr. Theresa Overall.