L3+Doran,+Christopher


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


 * Teacher’s Name:** Mr. Doran
 * Date of Lesson:** Explain
 * Grade Level:** 10th
 * Topic:** Using concepts with graphs

__**Objectives**__

 * Student will understand that** concepts such as rate of change, increasing/decreasing over intervals, and intercepts are used to identify graphs.
 * Student will know** the definition of: function, limit, rate of change, x-intercept, y-intercept, asymptote, and vector.
 * Student will be able to** demonstrate the concepts involved in identifying graphs.

__**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:** This lesson is a follow up on the last lesson and will have students use their previous knowledge to draw graphs based on functions given to them.

__**Assessment**__
Students will complete homework problems and practice problems to practice using these concepts in and out of class. These assignments will be brought up the next class period to see what the students know and what they still don't understand. At the beginning of the next class there will be a time where students can ask any questions they had regarding the material taught to them. The Cluster/Word Web graphic organizer that was used in the previous lesson will be revisited and reviewed for students to relearn what they already know and reteach some misconceptions they may have had about a few terms. Half of the students will be given a function and the other half will be given a graph of a function. They will then get up and move around the room trying to find their match (the person with the graph is looking for the person with the matching equation, and the person with the equation is looking for the person with the matching graph). They will collaborate together and share how they were able to identify that they were partners and what clues they looked for when searching for each other.
 * Formative (Assessment for Learning)**

In teams of two students will give a presentation on a given function using the National Library of Virtual Manipulatives' graphing tool (navigation and explanation will be done in class). In this presentation, you will each need to explain the process of identifying the type of function you have. Make sure to use key terms including: rate of change, increasing, decreasing, asymptote, and limit. Grading will be done using a checklist. //**(30 points)**//
 * Summative (Assessment of Learning)**

__**Integration**__

 * Technology:** Students will use their laptops and go to the National Library of Virtual Manipulatives' website and use the grapher tool there to display a graph while explaining the different parts of it.


 * Art:** Students will be drawing graphs of given functions individually and with a partner during this lesson.

__Groupings__
Half of the students will be given a function equation and the other half will be given a graph of a function. They will then proceed to get up and move around the room trying to find their match (the person with the graph is looking for the person with the matching equation, and the person with the equation is looking for the person with the matching graph).

__**Differentiated Instruction**__

 * Strategies**


 * Linguistic:** The use of word problems on identifying quadratic graphs from the textbook or created by the teacher will engage these learners.
 * Logical:** A sequence of steps to identify quadratic graphs will be given to the class to target these learners.
 * Visual:** Quadratic graphs drawn on the board will help make these graphs easier to see, thus aiding these types of learners.
 * Musical:** A catchy short song might be used to list off these different concepts of identifying quadratic graphs.
 * Interpersonal:** The use of group work or a class discussion on graphing quadratic functions will engage these learners.
 * Intrapersonal:** Individual work on practice problems will help these learners identify quadratic graphs.
 * Kinesthetic:** Students will be up and moving around the room trying to find their matching graph/equation that another classmate has.


 * 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.


 * Extensions**

Students will use the National Library of Virtual Manipulatives' grapher tool on their website to display a graph of a function and discuss the key parts of the graph to the rest of the class.

__**Materials, Resources and Technology**__
Students will need:
 * Pencil
 * Notebook
 * Textbook
 * Graphing Calculator
 * Laptop
 * 3 Ring Binder

I will need:
 * White board markers
 * Laptop
 * Graphing Calculator
 * Cluster/Word Web handout
 * Pen/Pencil
 * Quiz
 * Projector

__Source for Lesson Plan and Research__
[] -- Examples of different quadratic functions and worked out example problems [] -- How to graph quadratic functions [] -- Matching activity dealing with 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 - Students will be up and moving around trying to find their partner by matching a graph to an equation or an equation to a graph. Microscope - While going around the room searching for the one graph/equation that is a match, students will need to analyze each graph and equation to determine if their graph/equation is a match. Clipboard - Students will make a list of what they're looking for with their equation or graph and will check with other people based on their criteria until they have their match. Puppy - Through this activity, students will be working with each other and helping each other out in trying to find their matching partner. This requires every student to be cooperative with each other.


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


 * Rationale:** Students will need to know the definition of: function, x-intercept, y-intercept, asymptote, and limit. (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 I chose for this lesson is explain, hoping that at the end of it, //students will be able to demonstrate the concepts involved in identifying graphs//. I chose this facet because I want students to be able to tell me exactly why a certain graph behaves the way it does or how they know that a certain quadratic has a unique shape.


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


 * Rationale:**


 * Rationale:** Using the different Multiple Intelligences:


 * Linguistic:** Use of word problems dealing with quadratic functions/graphs from the textbook or created by the teacher could be used
 * Logical:** Creating a list of sequential steps would help these learners understand the steps in identifying graphs.
 * Visual:** The white board will be used to display different graphs and students will be asked to associate these graphs with functions
 * Interpersonal:** The cooperative learning activity would provide enough time for these students to engage in the material.
 * Kinesthetic:** I could have students arrange themselves into different curves using their bodies as different points along a graph
 * Naturalist:** The activity used for Kinesthetic learners could be moved outside to provide a better environment for this activity.
 * Kinesthetic:** Students will be up and moving around the room trying to find their matching graph/equation that another classmate has.

Type II product: 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:** This is how I plan to assess student learning:

Students will complete homework problems and practice problems to practice using these concepts in and out of class. These assignments will be brought up the next class period to see what the students know and what they still don't understand. At the beginning of the next class there will be a time where students can ask any questions they had regarding the material taught to them. The Cluster/Word Web graphic organizer that was used in the previous lesson will be revisited and reviewed for students to relearn what they already know and reteach some misconceptions they may have had about a few terms. Half of the students will be given a function and the other half will be given a graph of a function. They will then get up and move around the room trying to find their match (the person with the graph is looking for the person with the matching equation, and the person with the equation is looking for the person with the matching graph). They will collaborate together and share how they were able to identify that they were partners and what clues they looked for when searching for each other.
 * Formative (Assessment for Learning)**

In teams of two students will give a presentation on a given function using the National Library of Virtual Manipulatives' graphing tool (navigation and explanation will be done in class). In this presentation, you will each need to explain the process of identifying the type of function you have. Make sure to use key terms including: rate of change, increasing, decreasing, asymptote, and limit. Grading will be done using a checklist. //**(30 points)**//
 * Summative (Assessment of Learning)**

__Teaching and Learning Sequence__
Students will come into the classroom and take their seats at their desks which have been arranged into a parabola.

Agenda:

Day 1: (80 minutes)


 * Do a warm-up exercise at the beginning of class where I graph a function on the board and ask students to tell me what the function might closely resemble (10 minutes)
 * Explain to students how to graph a quadratic function and how to recognize a quadratic function based off of a graph (20 minutes)
 * Have students work on a few example problems by themselves. I will go around the room and answer any questions and provide feedback for when they are done (15 minutes).
 * Give half the students an equation and the other half of the students a graph. Students will then go around the room in an activity to find their matching graph (20 minutes).
 * With their last matching partner, I will briefly explain the group project that they will be doing, then assign a few homework problems which they can work on (15 minutes)

Day 2: (80 minutes)


 * I will begin class by going over the homework, seeing if there are any questions students may have, and also do a quick review session. (15 minutes)
 * Students will then take a quiz on graphing quadratic functions and writing quadratic equations. (15 minutes).
 * Introduction to the National Library of Virtual Manipulatives and tutorial session (15 minutes).
 * Students will get together with their partner and work on their project for the rest of the class (35 minutes).

Day 3: (80 minutes)


 * Review the quiz at the beginning of class, going over any concerns students may have (10 minutes)
 * Students will meet up with their partner at the beginning of class and make any adjustments to their project if needed (10 minutes)
 * Presentations of group projects (40 minutes)
 * Student reflections on the project and briefly explain the next section (20 minutes).

Students will understand that concepts such as rate of change, increasing/decreasing over intervals, and intercepts are used to identify graphs. Graphs are used in businesses everyday to show company income. It is also a great method for practicing problem solving. //Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.// At the beginning of class, a graph of a function will be on the board and students will be asked to figure out which function is displayed. I will then explain how to graph quadratic functions and write quadratic functions by looking at a graph. **Where, What, Why, Hook, Tailors: Verbal, Interpersonal, Intrapersonal, Logical, Visual**

Students will need to know the definition of: function, x-intercept, y-intercept, asymptote, limit, and vector. Students will use the cluster/word web from the last lesson to review these terms and add in the one new term. Students will respond to the question: "Why do different algebraic techniques affect the function and its graph?" By doing so they will have to take into account each of the concepts they've learned and use them to figure out what changed the original graph, as well as identify graphs based on their equations. **Equip, Explore, Rethink, Tailors: Logical, Visual, Interpersonal, Intrapersonal**

Students will be able to demonstrate the concepts involved in identifying graphs. In pairs, students will work to graph quadratic functions and write quadratic functions when they're given a graph of a function. Half of the students will be given a function equation and the other half will be given a graph of a function. They will then proceed to get up and move around the room trying to find their match (the person with the graph is looking for the person with the matching equation, and the person with the equation is looking for the person with the matching graph). Students will take a quiz on how to graph quadratic functions and how to write quadratic equations when given a graph. The follow class day I will go over the quiz with the students and answer any questions regarding it. Students will get together with their partner as I demonstrate and explain how to use the grapher tool on the National Library of Virtual Manipulatives' website. **Organize, Experience, Refine, Revise, Tailors: Intrapersonal, Verbal, Logical, Kinesthetic, Interpersonal**

Students will self assess their work by correcting their own homework problems and continue attempting more and more example problems. I will be able to provide feedback on students' progress by going around the room and checking their example/homework problems, correcting any mistakes that they're making along the way. The quiz that they took will be graded quickly and handed back the next class period At the beginning of each class I will allow for students to ask questions regarding the homework or quiz. In the next lesson, students will be looking at multiple types of graphs all in one section and they will need to be able to discern the difference between two quadratic functions. **Evaluate, Tailors: Verbal, Logical, Intrapersonal, Interpersonal**


 * Content Notes**

Students will need to know the definition of: function, x-intercept, y-intercept, asymptote, vector, and limit.

Function: A function is an equation that when you input one value (usually for X) your output consists of one possible value. In a graph, a function will pass the vertical line test, where if you draw a straight vertical line, the line only hits one value for all x-values on the graph.

x-intercept: The x-intercept is defined as what x value(s) will give an answer of 0. In a graph, it will be the place(s) where the function crosses the x-axis.

y-intercept: The y-intercept is defined as what y value you’ll get when you plug 0 in for x. In a graph, it will be the place(s) where the function crosses the y-axis.

Asymptote: An asymptote is an invisible line that a function will approach, but never touch. There are vertical and horizontal asymptotes.

Limit: A limit is what value your function approaches when you plug in a certain x-value. This isn’t necessarily what y-value you get because some limits are infinity.

Vector: A vector is a geometric entity characterized by a magnitude and a direction


 * Handouts**


 * Graphic Organizer