L2+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 - Perspective


 * __ Objectives __**
 * Student will understand that ** problems can be solved and represented in different mediums (symbols, tables, graphs).
 * Student will know ** relationships between graphs and answers found algebraically, recognize quadratic graphs, x/y intercepts, slope.
 * Student will be able to do ** analyze a graph and determine if it's linear, quadratic, inequality or absolute value.

// Maine Learning Results: Mathematics - D. Algebra // //Equations and Inequalities// //Grades 9 - Diploma// //2 - Students solve families of equations and inequalities.// **Rationale:** Students will be able to recognize different graphs involving many equations and inequalities.
 * __ Maine Learning Results Alignment __**


 * __ Assessment __**

During the lesson students will have many opportunities to explore and experience graphs and equations. 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 idea wheel to record information about each type of graph. The wheel is split into quarters and students will be able to use each piece to record any specific details about each type of graph (absolute value, inequality, linear, quadratic) during instructional time, group or individual work. Students will continue to add to the wheel as they continue to work on problems, have discussion with other students when in groups or listening to instruction. After this students receive their idea wheel, the next activity is the think-pair-share. Students will be asked to think about a problem by themselves first then discuss it with a partner and then share their team's answer and discussion with the whole class. This is will be done with many problems through the lesson so that students first get to try the problem by themselves and then they can discuss their answers or thoughts with a partner and finally with the remainder of the class. While students are trying to solve the question given they will be encouraged to draw pictures, talk out a problem physically demonstrate the question or whatever technique they need to utilize in order to produce an answer and have a thoughtful discussion with their partner. During this activity students will receive feedback from their peers and myself when presenting their answers to the class. Also any homework or practice problems will be turned in, not to be graded, but to assessment myself as a teacher and also the progress of my students.
 * Formative (Assessment for Learning) **

Students will be separated in groups of five to create a poster online using Glogster. Each team will be given five different graphs that they must as a team determine whether each graph is linear, quadratic, inequality or absolute value. They must then explain how they determined each, write an equation and provide important information (slope, max/min, x/y intercepts, etc). The glogster must be neat, creative and organized and include the appropriate information. Students will be evaluated by using a rubric that will be provided to them at the start of the assignment.
 * Summative (Assessment of Learning) **

Students will be separated in groups of five to create a poster online using Glogster. Each team will be given five different graphs that they must as a team determine whether each graph is linear, quadratic, inequality or absolute value. They must then explain how they determined each, write an equation and provide important information (slope, max/min, x/y intercepts, etc). The glogster must be neat, creative and organized and include the appropriate information. GeoGebra will be used so that students can graph equations and explore the differences between graphs using a computer software program.
 * __ Integration __**
 * Technology: **


 * Other Content Areas:**
 * Science: ** For many students math is something that is not connected to the real world, especially quadratics are hard for students to connect to. Because of this I will connect quadratics to projectile motion in physics.

Students will be split into groups during the think-pair-share activity within this lesson. They will first work and think about a problem by themselves and then they will be grouped into pairs so that they can take part in a discussion about ideas for solving the problem or what the answer is. After students have been given ample time to have a thoughtful discussion each partner team will be asked to tell the rest of the class how they solved the problem or possible solutions to go about finding the answer. We will then have a discussion as a class about different graphs and ideas about which is which. Here students will get feedback from their fellow peers and also me when they present or when I clarify a question during the partner discussion. Students will also get to work in groupings during the Glogster project where they will work together to recognize graphs, explain why the graph is a certain type and provide important information.
 * __Groupings__**


 * __Differentiated Instruction__**


 * Visual: ** Students will be able to use a graphic organizer to visualize the important parts of a graph.
 * Verbal:** Students will able to talk about graphs, equations and other mediums during the think-pair-share.
 * Interpersonal:** During the think-pair-share students will be able to discuss a problem with their partner.
 * Logical:** Students will use problem solving techniques to find an unknown value.
 * Bodily:** Students will be to physically demonstrate the look of a graph.
 * Intrapersonal:** During the "think" part of the think-pair-share students will individually think about a problem before discussing it with their partner.

**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: ** Students will be separated in groups of five to create a poster online using Glogster. Each team will be given five different graphs that they must as a team determine whether each graph is linear, quadratic, inequality or absolute value. They must then explain how they determined each, write an equation and provide important information (slope, max/min, x/y intercepts, etc). The glogster must be neat, creative and organized and include the appropriate information. GeoGebra will be used so that students can graph equations and explore the differences between graphs using a computer software program.


 * __Materials, Resources and Technology__**


 * Laptops
 * Graph Paper
 * Textbooks
 * Glogster Rubric and Tutorial
 * Absolute Value Worksheet
 * Graphing Absolute Value Worksheet
 * Introduction to Quadratics Worksheet
 * Whiteboard
 * projector
 * markers
 * calculators
 * GeoGebra software


 * __Source for Lesson Plan and Research__**

[] - a great site explaining how to graph systems of linear inequalities.

[] - a site explaining slope and y-intercept in word problems.

[] - a site explaining solving absolute-value equations

[] - a site explaining how to graph quadratics.


 * __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://** For those students who are clipboard learners examples, the graphic organizer, pictures and graphs are all very useful**.** Examples of certain techniques and graphs will be given to show students how to complete a problem. These examples can be recorded on their idea wheel graphic organizer so that information about each graph along with examples of graphs can be seen visually at any time in an organized, structured fashion. Microscope learners will enjoy the discussion-based instruction during this lesson along with the think-pair-share activity where they can analyze problems with their partner along with present their ideas to the class. During the lesson students are able to ask questions along with discuss problems as a whole if a problem has been poised. For students who learn better in a beach ball way they will be provided the opportunity to act out the problem, draw, graph or solve algebraically during the partner or group discussion and projects. All students will be encouraged to do homework and participate in class work but beach ball learners will enjoy extensions on homework since this will not be graded. The puppy learner will benefit from a comfortable atmosphere in class along with encouragement during class activities. These learners will also enjoy being able to work in a group for the final project, a glogster, where they can also demonstrate their creativity.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * //Rationale://** During the lesson students will continue to improve their graphing skills and be able to think about equations from a different perspective. Students will be able to recognize different graphs (linear, absolute value inequality, absolute value and quadratic) and also a refresher on finding x and y intercepts, slope and domain will be provided (see content notes). Students will have to find the equation of the absolute value and inequality graphs and be able to graph the equation. An intro to simple quadratic equations will be given how to recognize the equation and graph and given the equation determining the look of the graph. At the end of the lesson students will create a glogster describing and determining types of graphs. They will work in teams to create the glogster and present it to the class.


 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**
 * //Rationale://**
 * Visual: ** Students will be able to use a graphic organizer to visualize the important parts of a graph.
 * Verbal:** Students will able to talk about graphs, equations and other mediums during the think-pair-share.
 * Interpersonal:** During the think-pair-share students will be able to discuss a problem with their partner.
 * Logical:** Students will use problem solving techniques to find an unknown value.
 * Bodily:** Students will be to physically demonstrate the look of a graph.
 * Intrapersonal:** During the "think" part of the think-pair-share students will individually think about a problem before discussing it with their partner.


 * Technology:** Students will be separated in groups of five to create a poster online using Glogster. Each team will be given five different graphs that they must as a team determine whether each graph is linear, quadratic, inequality or absolute value. They must then explain how they determined each, write an equation and provide important information (slope, max/min, x/y intercepts, etc). The glogster must be neat, creative and organized and include the appropriate information. GeoGebra will be used so that students can graph equations and explore the differences between graphs using a computer software program.

For summative assessment students will be separated in groups of five to create a poster online using Glogster. Each team will be given five different graphs that they must as a team determine whether each graph is linear, quadratic, inequality or absolute value. They must then explain how they determined each, write an equation and provide important information (slope, max/min, x/y intercepts, etc). The glogster must be neat, creative and organized and include the appropriate information. Students will be evaluated by using a rubric that will be provided to them at the start of the assignment.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * //Rationale://** During the lesson students will have many opportunities to explore and experience graphs and equations. 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 idea wheel to record information about each type of graph. The wheel is split into quarters and students will be able to use each piece to record any specific details about each type of graph (absolute value, inequality, linear, quadratic) during instructional time, group or individual work. Students will continue to add to the wheel as they continue to work on problems, have discussion with other students when in groups or listening to instruction. After this students receive their idea wheel, the next activity is the think-pair-share. Students will be asked to think about a problem by themselves first then discuss it with a partner and then share their team's answer and discussion with the whole class. This is will be done with many problems through the lesson so that students first get to try the problem by themselves and then they can discuss their answers or thoughts with a partner and finally with the remainder of the class. While students are trying to solve the question given they will be encouraged to draw pictures, talk out a problem physically demonstrate the question or whatever technique they need to utilize in order to produce an answer and have a thoughtful discussion with their partner. During this activity students will receive feedback from their peers and myself when presenting their answers to the class. Also any homework or practice problems will be turned in, not to be graded, but to assessment myself as a teacher and also the progress of my students.

Students will arrive and sit anywhere they would like. Tables or desks will be arranged in a U-shape facing the board so that more discussion based instruction and exploration of the material can be done. This will also be easy for students to get into partners to work on the think-pair-share activity.
 * __Teaching and Learning Sequence__****:**

Day 1: - Students will watch the [|mathmaticous] video to get their attention. 5 minutes - Students will listen to instruction and review about linear and inequality graphs. Students will be encouraged to ask questions and participate in a discussion about graphing equations. Students will be introduced to absolute value and quadratic graphs. At the beginning of this students will be given the idea wheel handout so that they can record information about different graphs during the instruction and discussion. 30 minutes - Students will be given a problem to work on by themselves. They will then discuss the problem with the person sitting to their right. After students have worked and discussed the problem each partner group will be asked to present their answer, thoughts and or ideas about the problem given. This think-pair-share activity will be down with multiple problems. 30 minutes - Students will be given the rubric for the glogster project as well as an introduction to using glogster and some of the capabilities. Students will also be divided into teams during this time. 15 minutes

Day 2: - Students will get a chance to do practice problems on graphing using GeoGebra by themselves at the beginning of class. 15 minutes - More instruction will be given on graphing families of equations, absolute value inequalities, how to recognize quadratics and absolute value graphs. 30 minutes - Time will be given for groups to work on their glogster project in class. Students may work together to identify graphs or become familiar with glogster. I will also be available for clarification and help with graphing and equations and also using glogster. 35 minutes

Day 3: - Glogster Presentations

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 watching a quick video called Mathmaticous that is a kid singing about math to the rhythm of Fergie's Fergalicious song. The MLR is //students solve families of equations and inequalities.//
 * Where, Why, What, Hook Tailors: Musical/Verbal**

During this lesson students will know the relationships between graphs and answers found algebraically, recognize quadratic graphs, x/y intercepts, slope (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 talk about and answer questions about graphs during the think-pair-share activity. They will first ponder or work on a graphing problem by themselves and then discuss their thoughts with a partner (the person sitting to their right). After enough time is given for each group to discuss the problem students will present their thoughts and ideas to the class. Through this activity students will receive feedback from their peers and also me about graphing. During this activity students work by themselves, with a partner and as a class. Students will also get a chance to work within teams to create a glogster at the end of the lesson to demonstrate that they can recognize types of graphs, explain why a graph is which and include important information about each. 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 using a program called Glogster. This allows students to create online posters that include images, text and also music.
 * Equip, Explore, Experience Tailors: Visual, Intrapersonal, Interpersonal, Verbal, Bodily, Logical**

During the lesson students will have many opportunities to explore and experience graphs and equations. 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 idea wheel to record information about each type of graph. The wheel is split into quarters and students will be able to use each piece to record any specific details about each type of graph (absolute value, inequality, linear, quadratic) during instructional time, group or individual work. Students will continue to add to the wheel as they continue to work on problems, have discussion with other students when in groups or listening to instruction. After this students receive their idea wheel, the next activity is the think-pair-share. Students will be asked to think about a problem by themselves first then discuss it with a partner and then share their team's answer and discussion with the whole class. This is will be done with many problems through the lesson so that students first get to try the problem by themselves and then they can discuss their answers or thoughts with a partner and finally with the remainder of the class. While students are trying to solve the question given they will be encouraged to draw pictures, talk out a problem physically demonstrate the question or whatever technique they need to utilize in order to produce an answer and have a thoughtful discussion with their partner. During this activity students will receive feedback from their peers and myself when presenting their answers to the class so that they can continue to add and correct their idea wheel. GeoGebra software program will be used so that students can graph equations on the computer and receive feedback from me. Also any homework or practice problems will be turned in, not to be graded, but to assessment myself as a teacher and also the progress of my students. For summative assessment students will be separated in groups of five to create a poster online using Glogster. Each team will be given five different graphs that they must as a team determine whether each graph is linear, quadratic, inequality or absolute value. They must then explain how they determined each, write an equation and provide important information (slope, max/min, x/y intercepts, etc). The glogster must be neat, creative and organized and include the appropriate information. Students will be evaluated by using a rubric that will be provided to them at the start of the assignment.
 * Explore, Experience, Rethink, Refine Tailors: Logical, Intrapersonal, Interpersonal, Verbal, Visual, Bodily**

I will be able to give feedback during class when doing the think-pair-share activity as well as the GeoGebra activity. This is so that students will be able to correct their mistakes during class and add or correct their idea wheel so that they can clarify questions before starting the Glogster team project. Students will also be able to self-assess themselves when participating in the think-pair-share and discussing problems with their partner students can also add thoughts and ideas to their idea wheel. The rubric for the glogster will be given to each team member at the start of the project so that students can assess whether or not they have all the necessary information or not. Feedback for this project and any homework assignment will be given back the next day and any common mistakes will be corrected. These homework assignments will cover the same thing that students are doing in class recognizing different graphs (especially quadratics) and graphing families of equations such as absolute value and inequalities.
 * Evaluate Tailors: Intrapersonal, Interpersonal, Logical, Visual, Verbal**

Students will know relationships between graphs and answers found algebraically, recognize quadratic graphs, x/y intercepts, slope. The x-intercept is where the function crosses the x-axis. Finding the x-intercept (put 0 in for y) 1. 25x2 + 4y2 = 9 25x2 + 4(0) = 9 x2 = 9/25 x = ± 3/5 Take the square root of both sides in order to undo the x2. But because -22 and 22 are both 4 it must be plus or minus. The y-intercept is where the function crosses the y-axis. 1. 25x2 + 4y2 = 9 25(0) + 4y2 = 9 4y2 = 9 y2 = 9/4 y = ± 3/2 Slope is the change of y over the change of x and it determines the steepness of the line and whether the line is increasing or decreasing. In order to find the slope of a line you need to have 2 points of the line. 1. (3, 4) and (-2, 1) __ D __ __y__ __4 – 1__ __3__ so the slope is 3/5. D x 3 + 2 5
 * __Content Notes__**

2. 3x + 6 = y In an equation like this one where it is in the form mx + b =y the slope is the “m” so here it would be 3. Graphs: This is an example of a linear graph where the slope is negative because the line is decreasing.

This is an example of a quadratic graph (y=x2) it creates what is called a parabola.

This is an example of a absolute value graph.

See attached
 * __Handouts__**