L6+Cobleigh,+Justin


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


 * Teacher’s Name:** Mr. Cobleigh **Date of Lesson:** Apply
 * Grade Level:** 8 **Topic:** Distance and Midpoint Formulas

__**Objectives**__

 * Student will understand that** linear relationships are characterized by a constant rate of change.
 * Student will know** how to solve for the distance and midpoint between two given points on a line.
 * Student will be able to** solve for the distance and midpoint between two given points**.**

__**Maine Learning Results Alignment**__
Maine Learing 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 distance and midpoint formulas.

__**Assessment**__

 * Formative (Assessment for Learning)**

Students will use the flow chart that has been used for the entire unit to connect the distance and midpoint formulas to the big picture of linear relationships. Students will also be using a step-by-step chart to document the steps that are taken to solve for the distance and midpoints. For cooperative learning in this lesson, students will participate in a three-minute review. In these groups, which students will be allow to chose, they are to discuss how they would find distance and midpoint and ask questions to their classmates, to possibly get them working together to solve any issues that have arisen. Students will also have time where they are working on example problems from the lecture and also some time to be working on the homework assignment. During this time, the teacher will be around the room checking in on student's progress as well as answering any questions that may come up. If there appears to be a common error that is occurring amongst the students, the time will be taken, either in this class or the next, to recap that certain part of the lesson to ensure that students know what exactly it is that they are supposed to be doing at the certain step. During the lecture, students could be asked questions such as, but are not limited to: What is distance? What is midpoint? How do you find distance/midpoint? What would happen if you are given points, but the coordinates are not specified? Students will participate in Math Baseball, which is explained in more detail in the Day 1 section of the agenda outline in the Teaching and Learning Sequence. Students will also be responding in a journal entry as to what their thoughts were on the lesson. Students are encourage to talk about, but are not limited to, what they liked / disliked about the lesson or are there any lingering questions that did not get answered that you would like the answer to. These could be addressed in the beginning of the next class period during the homework review session.


 * Summative (Assessment of Learning)**

For this Comic Life project, students, working in pairs, are to create a comic that explains the concepts of distance and midpoint. Each pair of students will be given a set of points and through a digital story, they must figure out the distance and the midpoint. Also, distance is a topic that can easily be related to a real life situation, such as traveling from one place to the next. In addition to your digital story of solving for distance and midpoint, students need to pick two cities, find out what the distance is between the two, and find how long it would take them to get there given a specific speed of travel. (30 points)

__**Integration**__

 * Technology:** Students will be using Comic Life as their final projects for this lesson.


 * Geography** could be brought into this lesson with students having to take maps and calculate the distance between two cities.

__Groupings__
Students will be participating in a three-minute review during this class. What will happen is that students will be allowed to chose their own groups, of no more than three people, and will discuss the homework problems that had been assigned. The goal of this exercise is to see what students did to get to their answers, and if there are some different answers for the same equation, the students can work it out amongst themselves to see where the error(s) may have occurred and can work out the correct answer. This activity will be used as part of the homework review time at the start of class so that hopefully some of the conversation during this review will spark some questions that may need to be answered when we come together as a class. Students will also be participating in a Math Baseball activity in which the teams would be decided upon based on a random splitting of the class into 2 teams. Students will also be allowed to work together on homework at the end of the first class day to help each other get to an answer if someone is struggling.

__**Differentiated Instruction**__

 * Strategies**
 * Verbal:** Students can have conversations with others or during lecture to see how the calculation process works.
 * Logical:** Example problems can be provided for students to figure out solutions of distance and midpoint for.
 * Visual:** Pictures of the lines and the specified points could be done to give a visual representation of what a problem is looking for.
 * Kinesthetic:** Students could take points on a life-size graph grid and calculate the distance between each other.
 * Musical:** Students could create a pneumonic device that could help them to remember the distance and midpoint formulas.
 * Naturalist:** The life-size grid mentioned in the kinesthetic section could be moved outdoors.
 * Interpersonal:** Groups or pairs of students can work out practice distance and midpoint problems.
 * Intrapersonal:** Individual students can work on example problems of solving for distance and midpoint.

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 and 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 Comic Life as their final project for this lesson.

__**Materials, Resources and Technology**__

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

__Source for Lesson Plan and Research__

 * [] - Introduction to the Distance Formula
 * [] - Interactive tool for finding distance.
 * [] - Introduction to the Midpoint Formula
 * [] - Explanation and examples of using the midpoint formula

__**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 - When students work in the three-minute review, they will be allowed to choose who they want to work with. Also, during the Comic Life final project, students are required to include a digital story and include certain explanations. Other than these two things, the students will have entire autonomy in creation of the comics. Clipboard - For the final project, the grading process is going to be done with a rubric. This rubric will be provided to the students beforehand so that they know what is expected of them in their comics. The use of the step-by-step organizer will help to keep students organized on how to find the distance and midpoints of a set of points. Microscope - Students will be discussing with their peers during the three-minute review that will be used as a starter to the homework review session at the start of the second class period. Students are also encouraged to participate in class lecture if there are any questions that arise as well as if they want to help in solving a problem. Puppy - The main goal of the three-minute review is to get students working together and bouncing ideas off of each other. I want students to be able to support each other and help them when one is struggling. Everyone should feel comfortable going to others in their times of need.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * Rationale:** Students will know how to solve for the distance and midpoint between two given points on a line (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 apply in that I hope //students will be able to solve for the distance and midpoint between two given points//. I chose this facet because I want students to be able to apply what they have learned about linear equations before and apply them to using the distance and midpoint formulas. I want students to be able to realize that these formulas are ones that people may use all the time when they want to find out what the most direct route to a destination is. Since the shortest route between places is always a straight line, the formula could be applied to those situations to find out what the distance would be. The points that are used could be the latitude and longitude coordinates of the cities.


 * //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 have conversations with others or during lecture to see how the calculation process works.
 * Logical:** Example problems can be provided for students to figure out solutions of distance and midpoint for.
 * Visual:** Pictures of the lines and the specified points could be done to give a visual representation of what a problem is looking for.
 * Kinesthetic:** Students could take points on a life-size graph grid and calculate the distance between each other.
 * Musical:** Students could create a pneumonic device that could help them to remember the distance and midpoint formulas.
 * Naturalist:** The life-size grid mentioned in the kinesthetic section could be moved outdoors.
 * Interpersonal:** Groups or pairs of students can work out practice distance and midpoint problems.
 * Intrapersonal:** Individual students can work on example problems of solving for distance and midpoint.

Type II Product: Comic Life


 * //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 use the flow chart that has been used for the entire unit to connect the distance and midpoint formulas to the big picture of linear relationships. Students will also be using a step-by-step chart to document the steps that are taken to solve for the distance and midpoints. For cooperative learning in this lesson, students will participate in a three-minute review. In these groups, which students will be allow to chose, they are to discuss how they would find distance and midpoint and ask questions to their classmates, to possibly get them working together to solve any issues that have arisen. Students will also have time where they are working on example problems from the lecture and also some time to be working on the homework assignment. During this time, the teacher will be around the room checking in on student's progress as well as answering any questions that may come up. If there appears to be a common error that is occurring amongst the students, the time will be taken, either in this class or the next, to recap that certain part of the lesson to ensure that students know what exactly it is that they are supposed to be doing at the certain step. During the lecture, students could be asked questions such as, but are not limited to: What is distance? What is midpoint? How do you find distance/midpoint? What would happen if you are given points, but the coordinates are not specified? Students will also be responding in a journal entry as to what their thoughts were on the lesson. Students are encourage to talk about, but are not limited to, what they liked / disliked about the lesson or are there any lingering questions that did not get answered that you would like the answer to. These could be addressed in the beginning of the next class period during the homework review session.


 * Summative (Assessment of Learning):** For this Comic Life project, students, working in pairs, are to create a comic that explains the concepts of distance and midpoint. Each pair of students will be given a set of points and through a digital story, they must figure out the distance and the midpoint. Also, distance is a topic that can easily be related to a real life situation, such as traveling from one place to the next. In addition to your digital story of solving for distance and midpoint, students need to pick two cities, find out what the distance is between the two, and find how long it would take them to get there given a specific speed of travel. (30 points)

__Teaching and Learning Sequence__
Students desks will be in groups of 3 to accommodate the three-minute review session to be used in the second class period. 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 where they may ask questions pertaining to any of the lessons that are on linear relationships. (5 minutes)
 * Question Hook: Who knows how people calculate the distance between two places on a map and discuss thoughts. (5 minutes)
 * Students will be introduced to the distance and midpoint formulas. There will be generic formulas presented as well as how to solve for the answers. During this time, students will be working together as a class as well as in pairs / individually in order to practice their skills of these formulas. The teacher will be available during individual work time to answer any questions that students may come across. After students have completed their assigned practice problems, they are to be shown to the teacher and the homework for next class will be handed out (25 minutes)
 * Students will be playing MATH BASEBALL!* The class will be split up into two teams and there will be a baseball diamond on the board. Teams will take turns being up to bat and pitching. One team will pitch out an equation and the teacher will decide on whether it would be worth a single, double, triple or homerun. If the batting team is able to get it correct, they would get the appropriate amount of points based on the amount given, i.e. single, double, etc... The batting team would also have a specific batting order so all students have a chance to participate. When students are at bat, they are not allowed to receive help from their team members however team member are allowed to talk to each other when not batting. If a team gets the answer wrong, that would count as an out and the game would progress. Each team would get the customary 3-outs per inning and the game would be 3-innings long. The team with the highest score at the end would be the winner. (25 minutes)
 * Students will be given this last piece of class to respond to the material covered in this lesson in their journals. Students are encouraged to write any questions that may not have been touched on in class so that they can talked about in the start of the next class period. (20 minutes)
 * Students will participate in a three-minute review in which groups of 4, or the size that is appropriate with the amount of students in class, and from there will split into pairs. One pair will discuss the distance part of the homework and the other pair will discuss the midpoint portion. The two pairs will then come together and review with the other pairs on their respective sections. This is in hopes of getting students more comfortable in collaborating with each other. (10 minutes)
 * Students will now be introduced to their projects for this lesson. They will be creating a comic through Comic Life. Students will need to download the software to their computers if it has not been already. The teacher will lead a tutorial session on some of the basic features of the software and then students will have the chance to experiment with the software with their peers. Students will also be introduced to the idea of a digital story. This is the use of technology to tell a story of someone doing any life situation, in this case, it would be solving for distance or midpoint. (30 minutes)
 * The students will be placed into their pairs, which they will be allowed to choose for themselves, and start talking about what they want to have be carried out in their story. They will have to choose whether they want to talk about distance or midpoint; it is not necessary for them to mention both. Students will need to create some sort of storyboard or outline of what they would like to have done in their comic. This needs to be completed before this class period is over. Time will be allowed at the beginning of next class for work time but these will also need to be complete for presentation in the next class. Students will also have copies of the rubric that will be used for evaluating the projects and presentations. (40 minutes)
 * Students are to get straight to work on their comics and digital story. This session should be mostly taking a few final pictures as well as putting the finishing touches on their text. Students should be prepared to present these comics to the class. (30 minutes)
 * The pairs of students will take their turns presenting their comics to class. These presentations should take the classroom through their story as if we were all really there. The presenters should stay in character to do so. If at all possible, getting the class' involvement in the presentations would be an added touch but is not required. (40 minutes)
 * Students are to fill out the reflection sheet on the project process and presentation. The completion of this sheet will be what allows the student to be done for the day. (10 minutes)

Students will understand that linear relationships are characterized by a constant rate of change. Distance and midpoints can be associated with travel in trying to find how much time it could take to travel a certain distance. //**Students understand and use basic properties of linear relationships using y = mx + b**//. Before students are introduced to what the distance and midpoint formulas are, students will be asked how they think distance is actually calculated. The main goal of that question is to get students thinking about how distance actually is calculated as well as how could math be connected to the real world. It is all too common that math is questioned as to where you are going to want to use the distance formula. If someone wanted to find the distance between two cities, the latitude and longitude readings could be used as the points that can be placed into the distance formula.
 * Where, Why, What, Hook Tailors: Visual, Verbal, Logical, Interpersonal, Intrapersonal**

Students will know how to solve for the distance and midpoint between two given points on a line. //See Content Notes//. Students will finalize their flow charts that were provided at the beginning of the unit and connect all of the lessons to linear relationships. The main idea of the flow chart was just that, to show students that several different pieces of math can be connected back to one big, overarching idea. This is a common characteristic of math and getting students used to the idea now will get them to the point of asking themselves, "How will this piece of math be used in future lessons or how has it been used to make past lessons easier?" Students will also be given a step-by-step organizer to keep the steps of solving for the distance and/or midpoint of a line straight. The smallest of errors can make an entire problem go in a completely opposite direction. If someone has a question about where to go next in their process, this organizer could be referenced and then the student could possibly answer their question(s) for themselves. During the lecture portion of class, students could be asked questions such as, but not limited to: What is distance? What is midpoint? How do you find distance/midpoint? What would happen if you are given points, but the coordinates are not specified? Students will also be allowed to work with others around them to bounce questions off of, or to work out entire problems. I want all of my students to feel comfortable in asking questions of those around them without having to feel as though they would be made fun of. At the end of the first class period, students will be asked to reflect on the lesson in a journal entry. Students are encouraged to write down their thoughts on the lesson as well as any questions that they may have had that were not answered in that class period. These questions could be discussed at the start of the next class period. Students are not limited to the above mentioned prompts for their writings but they can be used as a starting point to branch off of.
 * Equip, Explore, Rethink, Revise, Refine Tailors: Verbal, Visual, Logical, Interpersonal, Intrapersonal**

Students will be able to solve for the distance and midpoint between two given points. One activity that students will be participating in is a game of Math Baseball. The class will be split up into two teams and there will be a baseball diamond on the board. Teams will take turns being up to bat and pitching. One team will pitch out an equation and the teacher will decide on whether it would be worth a single, double, triple or homerun. If the batting team is able to get it correct, they would get the appropriate amount of points based on the amount given, i.e. single, double, etc... The batting team would also have a specific batting order so all students have a chance to participate. When students are at bat, they are not allowed to receive help from their team members however team member are allowed to talk to each other when not batting. If a team gets the answer wrong, that would count as an out and the game would progress. Each team would get the customary 3-outs per inning and the game would be 3-innings long. The team with the highest score at the end would be the winner. Students will also participate in a three-minute review session at the start of the second class period. During this activity, Students will be split into groups of 4, or the size that is appropriate with the amount of students in class, and from there will split into pairs. One pair will discuss the distance part of the homework and the other pair will discuss the midpoint portion. The two pairs will then come together and review with the other pairs on their respective sections. This is in hopes of getting students more comfortable in collaborating with each other. The final project of this lesson will have students working in pairs to create a digital story through the use of Comic Life. For a more detailed description, please look at the formative assessment section at the beginning of this packet.
 * Organize, Explore, Experience Tailors: Verbal, Visual, Logical, Kinesthetic, Interpersonal, Intrapersonal**

Students are going to have their comics and presentations evaluated through a rubric that will be provided beforehand to all students. They should use the guidelines set down by the rubric to create their projects so that they know what is expected of them. Students will also be given a reflection sheet to fill out after all of the presentations are complete. The main goal of this sheet is to get feedback from the students as to how they think the project went. This is also time for students to tell me how they felt they worked with their partner. I want to know if working with partners was a good idea of if this project was better suited for individuals or bigger sized groups. I would also like to know if the combination of digital story and Comic Life was a good idea of it the two ideas should be split up into two different projects. Through all of the oral presentations that students have given over the course of this unit, there was the underlying lesson of public speaking. I want students to feel more comfortable speaking out to a bigger size group because there are going to be instances where that is necessary. When being interviewed for a job, it may require a presentation to a group of people, and having the experience of presenting to a group of people you know may make that easier to do later on. This is just another way of creating a real-life application of school. The rubrics containing final grades for the project will be returned to students on the next class day. It is important to give students feedback on how they did on their projects as well as show where they could use some improvement if they were to ever do another Comic Life presentation in the future. Later on in their schooling career, students could be asked to create a presentation of their choosing for any class. This project provides another avenue that students could take that is away from the typical PowerPoint or lecture directly to a group of people.
 * Evaluate Tailors: Verbal, Visual, Logical, Interpersonal, Intrapersonal**


 * Content Notes**

Students will know how to solve for the distance and midpoint between two given points on a line.

__//Definitions//__ Distance Formula: sqrt ((X2-X1)^2 + (Y2-Y1)^2), where points (X1,Y1), (X2,Y2) are used. Midpoint Formula: ((X1+X2)/2, (Y1+Y2)/2), where points (X1,Y1) , (X2,Y2) are used.

__//Example Problems//__
 * **In - Class Examples** || **Individual or in Pairs Afterwards** ||
 * Given two points, Solve for the distance.

1) Points (0,0), (3,4) => (x1,y1) , (x2,y2)

d = sqrt ((3-0)^2 + (4-0)^2)

d = sqrt (3^2 + 4^2)

d = sqrt (9 + 16)

d = sqrt (25)

d = 5

2) Points (2,3), (4,5)

d = sqrt ((4-2)^2 + (5-3)^2)

d = sqrt (2^2 + 2^2)

d = sqrt (4 + 4)

d = sqrt (8) || Given two points, Solve for the distance.

1) Points (1,1), (6,13)

d = sqrt ((6-1)^2 + (13 - 1)^2)

d = sqrt (5^2 + 12^2)

d = sqrt (25 + 144)

d = sqrt (169)

d = 13

2) Points (2,4), (6,5)

d = sqrt ((6-2)^2 + (5-4)^2)

d = sqrt (4^2 + 1^2)

d = sqrt (16 + 1)

d = sqrt (17) ||
 * Given a graph with two points marked, Solve for the distance.

1) Determine the coordinates of the given points.

(-4,-3), (4,3)

Solve for the distance as done above.

d = sqrt ((4-(-4))^2 + (3-(-3))^2)

d = sqrt (8^2 + 9^2)

d = sqrt (64 + 81)

d = sqrt (145)

2)

(-8,-6), (10,1)

d = sqrt ((10-(-8))^2 + (1-(-6))^2)

d = sqrt (18^2 + 7^2)

d = sqrt (324 + 49)

d = sqrt (373) || Given a graph with two points marked, Solve for the distance.

1)

(-3,-3), (5,5)

d = sqrt ((5-(-3))^2 + (5-(-3))^2)

d = sqrt (8^2 + 8^2)

d = sqrt (64 + 64)

d = sqrt (128)

2)

(-6,-1), (12,2)

d = sqrt (12-(-6))^2 + (2-(-1))^2)

d = sqrt (18^2 + 3^2)

d = sqrt (324 + 9)

d = sqrt (333) ||
 * Given two points, Solve for the midpoint.

1) Points (0,0), (3,4) => (x1,y1) , (x2,y2)

midpoint = ((0+3)/2, (0+4)/2)

midpoint = (3/2, 2)

2) Points (2,3), (4,5)

midpoint = ((2+4)/2, (3+5)/2)

midpoint = (3, 4) || Given two points, Solve for the distance.

1) Points (1,1), (6,13)

midpoint = ((1+6)/2, (1+13)/2)

midpoint = (7/2, 7)

2) Points (2,4), (6,5)

midpoint = ((2+6)/2, (4+5)/2)

midpoint = (4, 9/2) ||
 * Given a graph with two points marked, Solve for the midpoint.

1) Determine the coordinates of the given points.

(-4,-3), (4,3)

Solve for the midpoint as done above.

midpoint = ((-4+4)/2, (-3+3)/2)

midpoint = (0, 0)

2)

(-8,-6), (10,1)

midpoint = ((-8+10)/2, (-6+1)/2

midpoint = (1, -5/2) || Given a graph with two points marked, Solve for the midpoint.

1)

(-3,-3), (5,5)

midpoint = ((-3+5)/2, (-3+5)/2)

midpoint = (1, 1)

2)

(-6,-1), (12,2)

midpoint = ((-6+12)/2, (-1+2)/2)

midpoint = (3, 1/2) || __//**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 Organizer
 * Step-by-Step Organizer
 * Sample Homework Problems
 * Comic Life Project Rubric
 * Comic Life Presentation Rubric
 * Project Reflection Sheet

~ Math Baseball Idea from []