L1+Doran,+Christopher


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


 * Teacher’s Name:** Mr. Doran
 * Date of Lesson:** Interpret
 * Grade Level:** 10th
 * Topic:** Identifying Graphs

__**Objectives**__

 * Student will understand that** there are multiple types of graphs, functions, and techniques used to identify them
 * Student will know** formulas such as the distance formula, midpoint, and slope formula.
 * Student will be able to** find a correct set of functions to create a shape within a given area.

__**Maine Learning Results Alignment**__
Maine Learning Results: Mathematics - D. Algebra Functions and Relations (4) Grades: 9-Diploma Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques


 * Rationale:** Students are meeting this understanding by being able to graph different types of quadratic functions, as well as being able to write a quadratic function based on a graph.

__**Assessment**__

 * Formative (Assessment for Learning)**

Students will complete homework assignments dealing with graphs and functions. These assignments will be reviewed by the teacher to see what the students know and understand, fixing any errors that were made. Also, at the beginning of class there will be an opportunity to go over any questions that the students may have based on the homework. During class practice problems will be used for students to understand how to use the material they've learned today. A graphic organizer outlining different key concepts will be helpful for students to learn the correct mathematical terms. Cooperative work will also be used for students to learn the math skills needed. A quiz on graphs and functions will be the major way to check for students' understanding.


 * Summative (Assessment of Learning)**

In a team of 3, students will find a correct set of functions that will create a shape with a given area using GeoGebra. You will be given one function (each group will have a different function and area range) and be asked to find two more functions that will give the correct area range. A separate sheet of paper should be handed in so that I can check the process and work involved in arriving to the solution. Grading will be done by using a checklist. //**(25 points)**//

__**Integration**__

 * Technology**: Students will use GeoGebra software to graph linear functions.


 * Art**: Students will sketch multiple types of graphs of functions.

__Groupings__
Students will then get in groups of 3 and work towards finding a correct set of equations to end up with a certain area closed off by the graphs. Students will hold up a number of fingers (1-5) and will find two other people who's total number of fingers held up adds to an odd number.

__**Differentiated Instruction**__

 * Strategies:**


 * Linguistic:** Students can partake in class discussion on multiple types of functions.
 * Logical:** Use of mathematical concepts and practice problems for students to work on.
 * Visual:** White board used to display graphs of algebraic functions.
 * Kinesthetic:** Three corners game-students will move to a certain side of the room depending on what type of graph (quadratic, rational, irrational) they think an algebraic function said iso.
 * Interpersonal:** Cooperative learning activity based on identifying graphs.
 * Intrapersonal:** Work on practice problems on graphing alone for an allotted amount time.


 * Modifications/Accommodations**

I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.


 * Absent:** If a student is absent, it will be the student's responsibility to get any work that was missed that day and make a plan with me on how to get caught up. If the student is unable to attend school, yet is well enough to participate, the use of Skype will be possible to get the information. Students will need to email me beforehand to let me know that they will be skyping in so I can plan accordingly.

Students will utilize type II technology by using GeoGebra software to find a set of three or more functions that create a certain area enclosed by the curves.
 * Extensions:**

__**Materials, Resources and Technology**__
Students will need:
 * a notebook
 * pencil
 * ruler
 * graphing calculator
 * textbook
 * 3 ring binder
 * laptop

I will need:
 * white board markers
 * laptop
 * graphing calculator
 * Venn Diagram handout
 * pen/pencil
 * Rubric for project
 * Quiz

__Source for Lesson Plan and Research__
[| http://www.eduplace.com/graphicorganizer/] A Venn Diagram for the students [|www.youtube.com/watch?v=ct27eWhMreo] Youtube video on graphing functions [] Graphing Linear Functions [] Graphing Quadratic Functions

__**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 - In finding the remaining two lines in their Geogebra project, students will have one free choice of any type of line they wish to graph as long as they obtain the desired area range. Clipboard - During class lectures, a general overview of what I'm looking for on the project will be given, and a rubric will be handed out so students have a reference to what needs to be done. Microscope - In their groups students will work together to solve a set of equations that give them their given area range. Puppy - Students will have the opportunity to ask questions whenever they need extra assistance. No question is a dumb question.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**


 * Rationale:** Students will need to know formulas such as the distance formula, midpoint formula, and slope formula. (Reference content notes at the end of the lesson//) **Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques**//. The facet that I chose for understanding in this lesson was interpret in hopes that //students will be able to find a correct set of functions to create a shape within a given area.// I chose this facet because I want students to be able to understand how to manipulate not only lines, but also other types of functions as well.


 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**


 * Rationale:** Using the different multiple intelligences:


 * Linguistic:** Students can partake in class discussion on multiple types of functions.
 * Logical:** Use of mathematical concepts and practice problems for students to work on.
 * Visual:** White board used to display graphs of algebraic functions, youtube video in hook.
 * Kinesthetic:** Three corners game-students will move to a certain side of the room depending on what type of graph (quadratic, rational, irrational) they think it is.
 * Interpersonal:** Cooperative learning activity based on identifying graphs.
 * Intrapersonal:** Work on practice problems alone for an allotted amount time.

Type II Product: Geogebra


 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * Rationale:** This is how I plan on assessing student learning:


 * Formative (Assessment for Learning)**

Students will complete homework assignments dealing with graphs and functions. These assignments will be reviewed by the teacher to see what the students know and understand, fixing any errors that were made. Also, at the beginning of class there will be an opportunity to go over any questions that the students may have based on the homework. During class practice problems will be used for students to understand how to use the material they've learned today. A graphic organizer outlining different key concepts will be helpful for students to learn the correct mathematical terms. Cooperative work will also be used for students to learn the math skills needed. A quiz on graphs and functions will be the major way to check for students' understanding.


 * Summative (Assessment of Learning)**

In a team of 3, students will find a correct set of functions that will create a shape with a given area using GeoGebra. You will be given one function (each group will have a different function and area) and be asked to find two more functions that will give the correct area. A separate sheet of paper should be handed in so that I can check the process and work involved in arriving to the solution. Grading will be done by using a checklist. //**(25 points)**//

__Teaching and Learning Sequence__
Students will come into the classroom and take their seats in their assigned seats; the desks will be placed in a parabola shape (or multiple parabolas) opening up to the front of the room.

Agenda:

Day 1: (80 minutes)
 * Objectives: At the beginning of class, explain what the students will learn and how they will show me that they've learned it. Go over the syllabus. (15 minutes)
 * Video hook: Students will watch a brief video on how to graph a certain function. (5 minutes)
 * Pre-assessment: Students will take a brief quiz to see what they already know/don't know regarding how to identify graphs and functions. (5 minutes)
 * Hand out graphic organizers and start listing off different ways which functions and graphs can be recognized (15 minutes)
 * Write different sets of functions on the board and have their graphs up as well and as a class, match up the functions with their graphs. (30 minutes)
 * Separate students into their groups and give them homework problems to complete. I will be available for assistance if they need it. (10 minutes)

Day 2: (80 minutes)
 * Go over any questions from the homework assigned last class and do any problems students had trouble with. (10 minutes)
 * Students will take a short matching quiz on identifying functions with their graphs. No calculators will be allowed for this quiz. (10 minutes)
 * Introduction and explanation of Geogebra software. (30 minutes)
 * Introduction to the Geogebra project. (10 minutes)
 * Students will get into their groups from the previous class and receive their area range and their given function. The rest of class time will be devoted to working on the project. (20 minutes)

Day 3: (80 minutes)
 * Hand back quizzes and go over any questions that the students may have on the quiz or the homework assigned last class. (10 minutes)
 * Students will finish up their projects, doing any last minute calculations needed before presentations. (25 minutes)
 * Students present their final products with their calculations. (25 minutes)
 * Students will self assess their work with their group by reflecting on what they learned (15 minutes)
 * Brief summary of what is to come in the next lesson (5 minutes)


 * __//Paragraph 1//__**

Students will understand that there are multiple types of graphs, functions, and techniques used to identify them//.// There are multiple types of different functions and uses for them every day in businesses. //Students understand and interpret the characteristics of functions using graphs, tables, and algebra techniques.// Hook students with a sample lesson video to spark interest in graphing functions - [|www.youtube.com/watch?v=ct27eWhMreo]**.** Once the video is done, students will take a preassessment quiz to see what students already know about identifying and graphing functions. **Where, Why, What, Hook, Tailors: Visual, Verbal, Logical**


 * __//Paragraph 2//__**

Students will need to know formulas such as the distance formula, midpoint, and slope formula. Students will use a Venn Diagram to determine important concepts used to identify graphs, functions, and which are used for both. I will draw a Venn Diagram on the board and list off what the students come up with for different techniques and strategies on identifying graphs. Students will respond to the question "how to recognize the different types of functions based on the graphs shown and vice-versa" **Equip, Explore, Rethink, Tailors: Intrapersonal, Interpersonal, Verbal, Logical, Visual**


 * __//Paragraph 3//__**

Students will be able to find a correct set of functions to create a shape within a given area. Students will get in groups of 3 and work towards finding a correct set of equations to end up with a certain area closed off by the graphs. Students will hold up a number of fingers (1-5) and will find two other people who's total number of fingers held up adds to an odd number. Students will work on practice problems in class with their group and at home by themselves, or with their group if they desire, to practice their skills and will take a quiz the following day after they have cleaned up their skills. (Introduce GeoGebra here, have students get familiar with the software) **Organize, Experience, Refine, Revise, Tailors: Interpersonal, Intrapersonal, Verbal, Kinesthetic, Logical**


 * __//Paragraph 4//__**

Students will self assess their group work with a peer-evaluation sheet. They will evaluate how much each member of the group contributed to the overall product, and how well the group communicated with each other. They will also reflect on the project about what they liked and didn't like, what they would do differently next time, and what changes could be made to make the project better for future students. With providing timely feedback, when the students are working on homework problems or on their project, I will make myself available to students if they have questions. I will also walk around the room and ask the students to show me a homework problem they've completed so I can correct any mistakes or praise them for their good work. Their quizzes will be graded quickly and given back to them the next class period. I will allow any questions the students may have regarding the quizzes that they took and go over any problems they want to from the homework and quiz. This lesson ties into the next one because they will use the techniques learned in this lesson to correctly identify quadratic graphs.
 * Evaluate, Tailors: Interpersonal, Intrapersonal, Verbal, Visual**


 * Content Notes**

Students will need to know formulas such as the distance formula, midpoint formula, and slope formula.

In class I will graph functions such as, but not limited to:


 * y = 2x - 4
 * y = -x/2 + 2
 * y = -4x - 6
 * x = y + 3

These functions and more will be used to have students correctly match them with their graphs by using the techniques discussed earlier in class. Homework problems will be assigned from the textbook.


 * Handouts**


 * Checklist/Rubric
 * Graphic Organizer
 * Practice Problem Worksheet
 * Syllabus
 * Self assessment sheet