L3+Douglass,Brianna+Elizabeth


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


 * __Teacher’s Name__****:** Ms. Douglass **__Date of Lesson__:** 10/6/10
 * __Grade Level__****:** 11  **__Topic__:** Algebra - interpretation


 * __Objectives__**
 * Student will understand that** problems can be solved and represented in different mediums (symbols, tables, graphs).
 * Student will know** the x/y intercept, connections between a graph and it's equation, domain, max/min.
 * Student will be able to do** make sense of graphs in order to solve problems.

// Maine Learning Results: Mathematics - D. Algebra // //Equations and Inequalities// //Grades 9 - Diploma// //2 - Students solve families of equations and inequalities.//
 * __Maine Learning Results Alignment__**
 * Rationale:** Students will use graphs of many different equations in order to solve problems.


 * __Assessment__**

During the lesson students will have many opportunities to explore and experience answering questions by using their graphing skills. Formative assessments will be used to assess students progress with the material. These will included various practice problems worked on individually and with partners or teams.To begin students will use the tree chart to record information about each type of graph including points of interest and formulas if applicable. The tree chart has many branches coming out of the trunk so that students will be able to use one tree chart per type of graph where they can record specific details about each type of graph (absolute value, inequality, linear, quadratic), points of interest, how to find them and any formulas. The tree chart can be used during instructional time, group or individual work so that students can record examples as well. Students will continue to add to their tree charts as they continue to work on problems, have discussion with other students when in groups or listening to instruction. After this, students will participate in a three minute review where I will stop and ask students to get into groups and discuss what has been said, work on a problem and ask clarifying questions in only three minutes. Students will also be able to work with a partner or individually on practice problems during class. During these activities students will receive feedback from their peers and myself. I will be roaming the room during these activities, answering any questions. Students will also be working on GeoGebra graphing and explaining the points of interest and what they represent. They will be creating a small portfolio about graphing that include their tree charts, these Geogebra graphs and any homework and practice problems so that I can assess myself and the students progress, this will not be graded.
 * Formative (Assessment for Learning)**

At the end of the lesson teams of students will be creating a wiki where they will answer questions using their graphing skills. They will receive their questions and must show/explain how they got the answer using graphing. A graph for each must be included and an explanation of how they were able to solve the problem. Students are encouraged to get creative with creating their wiki but it must be neat and easily readable and include the appropriate information. It will be scored using a checklist that will be passed out when they are given the assignment.
 * Summative (Assessment of Learning)**


 * __Integration__**
 * Technology:** During class students will be able to use GeoGebra to graph equations and solve practice problems about the graph. At the end of the lesson students will also have the opportunity to work with a partner to create a wiki. They will be given problems that they must answer using their knowledge about graphing. For each one they must explain and show how they solved the problem using the graph. Many of the problems will be about points of interest so it is necessary that their graphs include any intercepts and the appropriate max and mins.


 * Other Content Areas:** Science: Students will continue to work with quadratics and understand more how they connect to science. Many of their word problems will include physics problems that they must solve using the graph of the equation.

Students will participate in a three minute review where I will stop and ask students to get into groups and discuss what has been said, work on a problem and ask clarifying questions in only three minutes. Students will also be able to work with a partner or individually on practice problems during class. During these activities students will receive feedback from their peers and myself. I will be roaming the room during these activities, answering any questions. At the end of the lesson teams of students will be creating a wiki where they will answer questions using their graphing skills. They will receive their questions and must show/explain how they got the answer using graphing. A graph for each must be included and an explanation of how they were able to solve the problem. Students are encouraged to get creative with creating their wiki but it must be neat and easily readable and include the appropriate information. It will be scored using a rubric that will be passed out when they are given the assignment.
 * __Groupings__**


 * __Differentiated Instruction__**

**Strategies:**
 * Visual: ** Students will visualize the problem in a graph.
 * Interpersonal:** Students will be able to work in groups on graphing, answering and asking questions.
 * Intrapersonal:** Students will be able to work alone on their GeoGebra graphs.
 * Bodily/kinesthetic:** Students will be able to work out the problem physically.
 * Logical:** Will be able to answer graphing questions using logical problem solving.
 * Naturalist:** Students will get a chance to solve graphing problems related to nature.

**Modifications/Accommodations** ( //I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.//) Absent: If a student is absent during this lesson than he/she needs to talk to me before if the absent is known in order to get assignments and notes. If the absence is not planned (sickness, emergency, etc) then the student should talk to another student in class and get any assignments. If the student can't complete the work because they need a worksheet or they have clarifying questions then they need to e-mail me to set up a meeting time or drop by my room before the next class.

**Extensions**
 * Technology: ** During class students will be able to use GeoGebra to graph equations and solve practice problems about the graph. At the end of the lesson students will also have the opportunity to work with a partner to create a wiki. They will be given problems that they must answer using their knowledge about graphing. For each one they must explain and show how they solved the problem using the graph. Many of the problems will be about points of interest so it is necessary that their graphs include any intercepts and the appropriate max and mins.


 * __Materials, Resources and Technology__**


 * Laptops
 * graph paper
 * textbooks
 * Wiki Checklist and Tutorial
 * Max/Min worksheet
 * factoring worksheet
 * Whiteboard
 * markers
 * calculators
 * GeoGebra software

[] - a site explaining how to factor [] - a site explaining the quadratic formula [] - a site describing the max/min
 * __Source for Lesson Plan and Research__**


 * __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://** The beach ball learner will enjoy the creativity involved with creating the wiki at the end of the lesson. As long as all the information is in there these students can get as creative and self-expressive as they want. They will so enjoy not having a routine for everyday, doing new things is important. Clipboard learners will benefit from the rubric created for the wiki so that they can be detailed and efficient. They will also enjoy using the graphic organizer so that all their thoughts, ideas and examples can be written done in an organized fashion. Being able to discuss within class both as a group and also in partners or groups will help the microscope learners. They will be able to analyze what the the points of interest really mean on a graph. Puppy learners want a comfortable and encouraging atmosphere and so therefore I will allow students to work with who they want at various times during class but I will also have students work in groups chosen randomly so that they are able to become more comfortable with each other. As the teacher I will also not allow students to put each other down but we will also have fun so that for puppies we can create a comfortable environment.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * //Rationale://** During this lesson students will continue to better their graphing skills and be able to interpret the meaning of graphs in order to answer questions. Students will be able to graph different types of equations (see content notes from lesson 2) and understand what the x and y intercepts, slope and max/min (see content notes). Students will also continue to understand quadratics and will learn the formula to find the max or min of the bell shape. There will be many word problems given and in order to solve these they need to understand what the domain, intercepts, and slope are and how to find it. At the end of the lesson students will have to, working with a partner, answer questions using their graphing skills and on a wiki show the graph and explain how they came up with their answer.


 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**
 * //Rationale://**
 * Visual: ** Students will visualize the problem in a graph.
 * Interpersonal:** Students will be able to work in groups on graphing, answering and asking questions.
 * Intrapersonal:** Students will be able to work alone on their GeoGebra graphs.
 * Bodily/kinesthetic:** Students will be able to work out the problem physically.
 * Logical:** Will be able to answer graphing questions using logical problem solving.
 * Naturalist:** Students will get a chance to solve graphing problems related to nature.


 * Technology:** During class students will be able to use GeoGebra to graph equations and solve practice problems about the graph. At the end of the lesson students will also have the opportunity to work with a partner to create a wiki. They will be given problems that they must answer using their knowledge about graphing. For each one they must explain and show how they solved the problem using the graph. Many of the problems will be about points of interest so it is necessary that their graphs include any intercepts and the appropriate max and mins.

Formative: During the lesson students will have many opportunities to explore and experience answering questions by using their graphing skills. Formative assessments will be used to assess students progress with the material. These will included various practice problems worked on individually and with partners or teams.To begin students will use the tree chart to record information about each type of graph including points of interest and formulas if applicable. The tree chart has many branches coming out of the trunk so that students will be able to use one tree chart per type of graph where they can record specific details about each type of graph (absolute value, inequality, linear, quadratic), points of interest, how to find them and any formulas. The tree chart can be used during instructional time, group or individual work so that students can record examples as well. Students will continue to add to their tree charts as they continue to work on problems, have discussion with other students when in groups or listening to instruction. After this, students will participate in a three minute review where I will stop and ask students to get into groups and discuss what has been said, work on a problem and ask clarifying questions in only three minutes. Students will also be able to work with a partner or individually on practice problems during class. During these activities students will receive feedback from their peers and myself. I will be roaming the room during these activities, answering any questions. Students will also be working on GeoGebra graphing and explaining the points of interest and what they represent. They will be creating a small portfolio about graphing that include their tree charts, these Geogebra graphs and any homework and practice problems so that I can assess myself and the students progress, this will not be graded.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * //Rationale://**

Summative: At the end of the lesson teams of students will be creating a wiki where they will answer questions using their graphing skills. They will receive their questions and must show/explain how they got the answer using graphing. A graph for each must be included and an explanation of how they were able to solve the problem. Students are encouraged to get creative with creating their wiki but it must be neat and easily readable and include the appropriate information. It will be scored using a checklist that will be passed out when they are given the assignment.

Students will arrive in class and sit down anywhere they would like. Tables or desks will be in twos arranged facing the board so that students will already be in pairs for the hook activity and three minute review.
 * __Teaching and Learning Sequence__****:**

Day 1: - Each partner group will receive a note card with either a graph or equation on it. They must find the corresponding note card to their own. This group is the group that the students will complete their wiki with at the end of the lesson. 5 minutes - The wiki checklist and tutorial will be given as well as an introduction to the portfolio. 15 minutes - The tree chart graphic organizer will be passed out so students will be able to use it. 5 minutes - More information will be provided about quadratic graphs. The quadratic formula will be explained. 20 minutes - Three minute review activity. 3 minutes - How to find the max and min of a quadratic graph will be explained. 15 minutes - Another 3 minute activity. 3 minutes - Students will be able to start on their homework practice problems till the end of class. 14 minutes

Day 2: - Homework review will be given so that students will be able to ask any questions they have over quadratics and max/min.15 minutes - Students will work with their three minutes review partners to complete a couple word problems. They will be able to use GeoGebra in order to graph the equations if needed. 20 minutes - An introduction to factoring will be given. 15 minutes - 3 minutes review. 3 minutes - Students will be able to work individually or with a partner on completing factoring problems and then we will go over them as a class. 27 minutes

Day 3 - As a class we will work on solving word problems by graphing. 30 minutes - students will turn in their portfolios. 5 minutes - The rest of the class will be given to students to work on their wiki's. 45 minutes

Students will understand that problems can be solved and represented in different mediums (symbols, tables, graphs) because being able to make sense of graphs is an important skill for many careers (accountant, scientist, etc). I will hook my students by giving each pair of students a note card, this card has either a graph or equation on it they must find the card that corresponds with their own. The MLR is //students solve families of equations and inequalities.//
 * Where, Why, What, Hook Tailors: Visual, Interpersonal**

During this lesson students will know the x/y intercept, connections between a graph and it's equation, domain, max/min, quadratic formula and how to factor (see content notes). I will provide this information through individual, group, formative and summative assessment, discussion and traditional instructional time. Group work will include students participating with a partner to discuss and review information about what has just been said during the three minute review activity. Through this activity students will receive feedback from their peers and also me because I will be roaming around answering any questions and at the end will ask if any groups have a question. Students will also get a chance to work within teams to create a wiki at the end of the lesson to demonstrate that they can answer a question by graphing. They will have to understand what the intercepts, slope, domain and max/min mean in the context of a word problem in order to create a wiki answering questions using graphing. Traditional instruction will be mixed in on order to give students enough information to complete group and individual work. Discussion with the whole class will also be included in instruction to have students participate in their own learning. The summative project will be completed online on a Wiki, this allows students to create a web page interlinked to other pages.
 * Equip, Explore, Experience Tailors: Logical, Interpersonal, Intrapersonal**

During the lesson students will have many opportunities to explore and experience answering questions by using their graphing skills. Formative assessments will be used to assess students progress with the material. These will included various practice problems worked on individually and with partners or teams.To begin students will use the tree chart to record information about each type of graph including points of interest and formulas if applicable. The tree chart has many branches coming out of the trunk so that students will be able to use one tree chart per type of graph where they can record specific details about each type of graph (absolute value, inequality, linear, quadratic), points of interest, how to find them and any formulas. The tree chart can be used during instructional time, group or individual work so that students can record examples as well. Students will continue to add to their tree charts as they continue to work on problems, have discussion with other students when in groups or listening to instruction. After this, students will participate in a three minute review where I will stop and ask students to get into groups and discuss what has been said, work on a problem and ask clarifying questions in only three minutes. Students will also be able to work with a partner or individually on practice problems during class. During these activities students will receive feedback from their peers and myself. I will be roaming the room during these activities, answering any questions. Students will also be working on GeoGebra graphing and explaining the points of interest and what they represent. They will be creating a small portfolio about graphing that include their tree charts, these Geogebra graphs and any homework and practice problems so that I can assess myself and the students progress, this will not be graded. At the end of the lesson teams of students will be creating a wiki where they will answer questions using their graphing skills, this will be the summative assessment. They will receive their questions and must show/explain how they got the answer using graphing. A graph for each must be included and an explanation of how they were able to solve the problem. Students are encouraged to get creative with creating their wiki but it must be neat and easily readable and include the appropriate information. It will be scored using a checklist that will be passed out when they are given the assignment.
 * Explore, Experience, Rethink, Refine Tailors: Naturalist, Bodily, Logical, Interpersonal, Intrapersona, Visual**

I will be able to give feedback during class when students do practice problems and during the 3 minute review where I can answer any clarifying questions. Students will be able to discuss with their partners the information and so will also receive feedback from their peers during the 3 minute review and working on practice problems**.** I will be looking at the students portfolio and giving it back to them during the third day so that I can assess the classes mastery level of the content. Here I can clarify any common mistakes if need be. Students will also be able to self-assess themselves by using the rubric passed out the first day on the team wiki project. Students can self-assess themselves as well during the 3 minute review where they can compare tree charts and review what each person has written down. Homework assignments will be the exact things we've been working on in class. Students will get to practice finding max and mins and also factoring and using the quadratic formula. Later on during the third day we will do examples of solving word problems using graphing so that they have more experience before completing their homework of creating a wiki.
 * Evaluate Tailors: Intrapersonal, Interpersonal, Logical**

For slope, x/y intercepts and domain see content notes from lesson 2.
 * __Content Notes__**

Quadratic: is a polynomial that looks like ax2 + bx + c, where abc are all constants.

Quadratic formula:



the quadratic formula finds the x coordinate of the x-intercepts.

Factoring 1. x2 + 7x + 6 (x + 6)(x + 1) In order to make sure you factored right multiply this and make sure it equals what you started with. Here the 2 x intercepts will be -6 and -1.

2. x2 + 6x + 8 (x + 4)(x + 2) Using the factors of 8 (1,8 and 2,4) combine them somehow (using only addition because there's no subtraction in our original equation).

3. x2 - 7x + 10 (x - 2)(x - 5)

Finding the max or min: formula: x = -b/2a this is only the x coordinate. In order to find the y coordinate you must substitute what you find for x back into the original equation.

Wiki Checklist Tree Chart Factoring Worksheet
 * __Handouts__**