L1+Sullivan,+Joseph

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

** LESSON PLAN FORMAT **


 * __ Teacher’s Name __**** : ** Mr. Sullivan **__Lesson__ __#:__** 1 **__Facet__:** Interpretation
 * __ Grade Level __**** : ** High School **__Numbers of Days:__** 2
 * __ Topic: __** Graphing systems of equations


 * __ PART I: __**

Students will understand that equations and inequalities can be solved graphically. Students will know the basics to setting up equations Students will be able to translate inequalities or equations from statements to graphs Product: Online graphing application
 * __ Objectives __**

Common Core State Standards Content Area: Algebra Grade Level: High School Domain: Reasoning with Equations and Inequalities Cluster: Represent and solve equations and inequalities graphically Standard: 10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could also be a line). And 11, 12. Rationale: Students will learn to recognize components of systems of equations within word problems and be able to graphically model the data, leading to the ability to reason with the information.
 * __ Maine Learning Results (MLR) or Common Core State Standards (CCSS) Alignment __**


 * __ Assessments __**
 * __ Pre-Assessment: (Lesson 1 only) __** ​MI Survey for students to identify which of the intelligences are most prominent in their skill set, and which learning styles best suit their needs. Also, it will set the stage for students to stay engaged within the lesson as they recognize components affiliated with their learning style embedded in the lesson. KWL: Students will create a chart that outlines what they know about graphing equations and inequalities, as well as what they hope to learn from the unit.

One Last Question- assessment for before students leave, with additional space provided for students to express what is determined to be "understood," as well as what they would like to learn from the unit. Responses will not be graded, but will be analyzed and given feedback on.
 * __ Formative (Assessment for Learning) __**
 * Section I – checking for understanding during instruction **

There will be a rubric handed out for students to self-assess their graphing products, and then the teacher will review the products and provide written feedback.
 * Section II – timely feedback for products (self, peer, teacher) **

Online Graphing Application: Create and model an example system of equations (25 points)
 * __ Summative (Assessment of Learning): __**


 * __ Integration __**
 * Technology: ** The online graphing application is an computer simulator that models information students input.
 * Content Areas: ** Art, by creating a graph students must employ an artistic understanding to predict how the graph will look.

An idea rake graphic organizer will be used by groups to identify important components necessary to solve a system of equations.
 * __ Groupings __**
 * Section I - Graphic Organizer & Cooperative Learning used during instruction **

Students will work in small groups to create their products, as determined by their in-class groups. Groups will be determined after the MI survey, and will consist of 4 students with different learning styles.
 * Section II – Groups and Roles for Product **

determining goals, finding important variables, and setting up graphs.
 * __ Differentiated Instruction __**
 * __ MI Strategies __**
 * Verbal/Linguistic:**Discussion and small group work will allow students to verbally work through the processes of
 * Logical/Mathematical:** The step-by-step approach demonstrated by the teacher on the board will appeal to logically-inclined students
 * Visual/spacial:** Utilizing a graphic organizer will help visual students track the progress of their strategy.
 * Bodily/kinesthetic:** As a demonstration, students will use their bodies to create human graph models which will illustrate graphing in a kinesthetic manner.
 * Musical/rhythmic:** Music can be incorporated into the background during group work.
 * Interpersonal:** Students will be allowed to collaborate in groups to create their theories on possible solution methods, and there will be group OTR's during the second day's example walk-through.
 * Intrapersonal:** The pre-assessment at the beginning of the lesson will encourage students to assess their preexisting knowledge, and the "One Last Question" exit ticket will enable students to reflect on which parts of the material they are comfortable with, and which parts they would like more clarification on.
 * Naturalist:** The scenario of the sample word problem will be presented as a florist contemplating which flowers to buy.


 * __ Modifications/Accommodations __**
 * // From IEP’s ( Individual Education Plan), 504’s, ELLIDEP (English Language Learning Instructional Delivery Education Plan) //**// I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations. //

Students will come see the teacher and have a short discussion on what they missed in class. Students will receive a photocopy of one groups graphic organizer, as well as the teacher's example that was used on the board. The assessment will be assigned and will be expected to be completed under standard absence guidelines.
 * Plan for accommodating absent students: **

The online graphing application is an computer simulator that models information that students input.
 * __ Extensions __**
 * Type II technology: **​
 * Gifted Students: ** Students seeking a more difficult challenge can determine how the max of a profit scheme would change given a new set of variables, and can assist other students having difficulty.


 * __ Materials, Resources and Technology __**
 * Laptops
 * Idea rake graphic organizer
 * Whiteboard/smartboard/chalkboard
 * Projector


 * __ Source for Lesson Plan and Research __**
 * Idea Rake- http://www.eduplace.com/graphicorganizer/pdf/idearake.pdf - Graphic organizer used to help students identify important components when graphing.
 * Fooplot- http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDB9XQ-- - Online graphing application used for student products.
 * One Last Question-http://www.stemresources.com/static/tools/Assessments/Formative/OneLastQuestion/index.html - Formative Assessment designed to assess student thought processes through the graphing process.
 * System of Equations Question- http://www.sosmath.com/soe/SE/SE.html- Question to be used aschecking for understanding question.
 * MI Survey- http://www.bgfl.org/custom/resources_ftp/client_ftp/ks3/ict/multiple_int/questions/results.cfm- Hook and MI survey from Birmingham Grid for Learning.
 * Florist Question - http://answers.yahoo.com/question/index?qid=20101203131413AASY1ZA- Hook Tie-In Question and class example.


 * __ PART II: __**

// AGENDA: // // DAY 1) // // MI Survey. (30 Mins) // // Group Rearrangement. (5 Mins) // // Pre-Assessment: KWL. (10 Mins) // // Pass out graphic organizers and introduce systems of equations, having students formulate ideas on how to solve the question. (15 Mins) // // Address questions and walk through the correct method of dealing with systems of equations. (15 Mins) //
 * __ Teaching and Learning Sequence __**** (Describe the teaching and learning process using all of the information from part I of the lesson plan) **// Take all the components and synthesize into a script of what you are doing as the teacher and what the learners are doing throughout the lesson. Need to use all the WHERETO’s. (3-5 pages) //

// DAY 2) // // Have students return to groups from the prior day and hand back graphic organizers with feedback on them. (10 Mins) // // Discuss class-wide misconceptions. (10 Mins) // // Pass out new graphic organizers to each student and instruct students to write corrected understandings on the new organizers. (10 Mins) // // Introduce online graphing application, FooPlot, and demonstrate a walk through problem. (15 Mins) // // Assign example problems to groups by having them pick from a hat. (5 Mins) // // Have students work amongst their groups to model the given equation using FooPlot. (20 Mins) // // Hand out exit ticket "One Last Question." (10 Mins) // Tables will be arranged into small clusters of 4's. Students will understand that equations and inequalities can be solved graphically. //Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could also be a line).//It is important to be able to model information using a graph. Students will begin the class using laptops, taking the MI survey provided at http://www.bgfl.org/custom/resources_ftp/client_ftp/ks3/ict/multiple_int/questions/results.cfm. Results will be recorded by students and reported to the teacher before students are split into groups of four based on differing intelligence inclinations. The KWL will be administered, having students respond to the question on the board. An Idea rake will be passed out to each group, and students will attempt to formulate an idea on how to help the gardener on a budget. Connect the example question to MI theory and throughout the class have students identify the components of the lesson that addresses their specific intelligence profile. Students will work in their table groups to develop an idea on how to solve the sample maximization problem, using the graphic organizer to decide which components of the problem are most important to be considered when approaching such a problem. Students will know how to identify important conceptual areas that will provide the framework to reason with equations or inequalities. (See Content Notes) Students will use an idea rake graphic organizer along with peer discussions to formulate and eventually understand the important components to solving a systems problem. While students cooperate, the teacher will walk through the example step-by-step on the board, as determined by class progress. As an element of these explanations, the teacher will have students participate in human graph modeling. As work continues in groups, the teacher will float around the classroom and assist groups having trouble finding important parts. Once all groups have completed their idea rakes, the teacher will run through the full process of identifying, solving, and graphing the system of equations. Students will be able to translate inequalities or equations from statements to graphs. Groups will receive their graphic organizers from the previous day with teacher feedback written, and each student will be provided another copy of the graphic organizer. Students will review comments made by the teacher and correct misconceptions in original reasoning, and each write their new understandings of important components and approach on the new graphic organizer. The teacher will then demonstrate how an online graphing application can be used to model the system of equations, and walk students through the process of accessing the webpage and interacting with the interface. Following this, the students will work amongst their groups to model a system of equations picked out of a hat using FooPlot. Music will be played in the background. To check for understanding, a "One Last Question" exit ticket will be used to assess what students understand about the unit so far, and the teacher will provide feedback. Students will self-assess using peer review within their groups. The teacher will provide timely feedback to students by responding orally to common misconceptions, and using written feedback to address specific students concerns. This connects to the next lesson and future assignments because it gives students the ability to identify important facets of solving equations graphically.
 * Where, Why, What, Hook, Tailors: Interpersonal, Naturalist, Logical**
 * Equip, Explore, Rethink, Revise, Tailors: Interpersonal, Linguistic, Spatial, Kinesthetic**
 * Explore, Experience, Revise, Refine, Tailors:** **Spatial, Linguistic, Logical, Intrapersonal, Musical**
 * Evaluate, Tailors: Intrapersonal**

Students will know how to identify important conceptual areas that will provide the framework to reason with equations or inequalities. First, they will take an MI survey, which will act as a hook, conversation point, and also help the teacher understand a little more about the class. Instruct students to take the surveys on the computer and have students turn them in by drawing/writing/presenting the results in a hard copy format that can be referred to later in the year. While students are busy taking their inventory, float around the classroom and check for anybody having difficulty understanding or with technical issues. Following completion of the survey, students will be come to the front of the class and will split into groups of four, determined by their different intelligences. The teacher will write the sample question on the board while groups become acclimated to their new orientations, and students will receive a KWL about how to approach the question. Once these are collected, each group will receive an Idea Rake, and the teacher will direct students to work within their groups on where to look and how to set up a system of equations problem. Once all groups reach certain milestones in the process, there will be a short break and the teacher will have groups present their findings, writing a step-by-step guide as the lesson progresses. At each stage groups will be able to correct their organizer. When applicable, students will represent graphs that model information in the problem. At the end of the class the teacher will field questions from students and quickly run through the entire process again. At the beginning of day two, students will return to their groups and review their feedback from the teacher. New idea rakes will be passed out to each student, and the teacher will address any common misconceptions students have. Following this, students will take 10 minutes to rewrite important components and steps on their graphic organizers for personal use. The class will then shift gears and take out their laptops, and the teacher will introduce www.fooplot.com, showing students how to interact with the interface and use the application to model a system of equations. Groups will work on their products together, and music will be played in the background. Once all the products have been completed, students will be provided "One Last Question," which will ask for an overview on how to approach a system of equations problem, as well as which parts are easy and which need more clarifying.
 * __ Content Notes __**

The MI survey takes place online and provides feedback in a graphic view. Students will be asked to represent this to the teacher and can do so in any way they would like, whether by bar graph, web, graphic, writing, or by the original image.

Example Question: A florist needs to prepare for Mother's Day. He needs to order flowers that will maximize his profit. Roses: The florist’s cost is $20 per dozen; the profit over the cost is $20 per dozen. Tulips: The florist’s cost is $5 per dozen; the profit over the cost is $8 per dozen. The florist can order no more than 60 dozen flowers. A minimum of 20 dozen tulips must be ordered. The florist cannot order more than $450 worth of roses and tulips.

FooPlot is very straightforward, but does not identify points of intersection between lines or shade. Students can either print out their products and manually write in points, or take a screen shot and use an image editing application to illustrate the points.

"One Last Question" will be The air-mail rate for letters to Europe is 45 cents per half-ounce and to Africa as 65 cents per half-ounce. If Shirley paid $18.55 to send 35 half-ounce letters abroad, how many did she send to Africa? Idea Rake One Last Question Assessment **Clipboard**: Students will use their idea rakes to organize their thoughts on solving systems of equations, and the teacher will demonstrate a step-by-step approach on the board. The question at the end will give students closure on what they understand about the topic, and there will be a clear procedure copied down on students' individual graphic organizers. //** Puppy: **//​Music will encourage a comfortable learning environment, and group work will promote an encouraging atmosphere with supportive members. Also, no groups will feel left out because the teacher will have a running example on the board for reference.
 * __ Handouts __**
 * __ Maine Standards for Initial Teacher Certification and Rationale __**
 * // Standard 1 – Learner Development. The teacher understands how learners grow and develop, recognizing that patterns of learning and development vary individually within and across the cognitive, linguistic, social, emotional, and physical areas, and designs and implements developmentally appropriate and challenging learning experiences.//**
 * //__ Learning __ Styles: //**
 * // Microscope: //**Students will attempt to determine the important components and progression on their own, and help each other discover the true components and formulas. Class discussions will help students learn from common misconceptions, and students will analyze concepts when graphing and plotting points of intersection.
 * Beach Ball: **Students will use graphic organizers and computers to complete the lesson, students will be required to adapt to different seating patterns as determined by their groups, students will choose which method they would like to use in presenting their MI results to the teacher, and the example question extends to real life.
 * Rationale: ** This lesson demonstrates competency in Standard 1 because it addresses the learning needs outlined for all learners, and gives all types of participants the ability to succeed.
 * Standard 6 - Assessment. The teacher understands and uses multiple methods of assessment to engage learners in their on growth, to monitor learner progress, and to guide the teacher's and learner's decision making.**


 * Formative: **
 * Assessment for Learning: ** One Last Question
 * Pre-Test: ** KWL, MI Survey


 * Summative: ** Online Graphing Application


 * Facet: **Interpretation
 * Rationale: **A variety of formative assessments and a summative assessment allow for students to illustrate their knowledge of the content in a multitude of ways, which encourages meaningful learning instead of memorization.
 * Standard 7 - Planning Instruction. The teacher plans instruction that supports every student in meeting rigorous learning goals by drawing upon knowledge of content areas, curriculum, cross -disciplinary skills, and pedagogy, as well as knowledge of learners and the community context.**

Common Core State Standards
 * MLR or CCSS: **

Content Area: Algebra

Grade Level: High School

Domain: Reasoning with Equations and Inequalities

Cluster: Represent and solve equations and inequalities graphically

Standard: 10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could also be a line). And 11, 12.

Rationale: Students will learn to recognize components of systems of equations within word problems and be able to graphically model the data, leading to the ability to reason with the information.


 * Rationale: ** Students will learn to recognize components of systems of equations within word problems and be able to graphically model the data, leading to the ability to reason with the information.


 * Standard 8 - Instructional Strategies. The teacher understands and uses a variety of instructional strategies to encourage learners to develop deep understanding of content areas and their connections, and to build skills to apply knowledge in meaningful ways.**

determining goals, finding important variables, and setting up graphs.
 * MI Strategies: **
 * Verbal/Linguistic:**Discussion and small group work will allow students to verbally work through the processes of
 * Logical/Mathematical:** The step-by-step approach demonstrated by the teacher on the board will appeal to logically-inclined students
 * Visual/spacial:** Utilizing a graphic organizer will help visual students track the progress of their strategy.
 * Bodily/kinesthetic:** As a demonstration, students will use their bodies to create human graph models which will illustrate graphing in a kinesthetic manner.
 * Musical/rhythmic:** Music can be incorporated into the background during group work.
 * Interpersonal:** Students will be allowed to collaborate in groups to create their theories on possible solution methods, and there will be group OTR's during the second day's example walk-through.
 * Intrapersonal:** The pre-assessment at the beginning of the lesson will encourage students to assess their preexisting knowledge, and the "One Last Question" exit ticket will enable students to reflect on which parts of the material they are comfortable with, and which parts they would like more clarification on.
 * Naturalist:** The scenario of the sample word problem will be presented as a florist contemplating which flowers to buy.


 * Type II Technology: ** Online Graphing Application


 * Rationale: ** Students will be using FooPlot to represent a graphing example they receive in class. They will need to manipulate the picture of the graph to represent where functions intersect by using paint or a similar application.

__**NETS STANDARDS FOR TEACHERS**__ a. Promote, support, and model creative and innovative thinking and inventiveness Rationale Statement b. Engage students in exploring real-world issues and solving authentic problems using digital tools and resources
 * 1. Facilitates and Inspire Student Learning and Creativity. Teachers use their knowledge of subject matter, teaching and learning, and technology to facilitate experiences that advance student learning, creativity, and innovation in both face-to-face and virtual environments.**

c. Promote student reflection using collaborative tools to reveal and clarify students’ conceptual understanding and thinking, planning, and creative processes

d. Model collaborative knowledge construction by engaging in learning with students, colleagues, and others in face-to-face and virtual environments

a. Design or adapt relevant learning experiences that incorporate digital tools and resources to promote student learning and creativity
 * 2. Design and Develop Digital Age Learning Experiences and Assessments. Teachers design, develop, and evaluate authentic learning experiences and assessment incorporating contemporary tools and resources to maximize content learning in context and to develop knowledge, skills, and attitudes identified in the NETS-S.**

b. Develop technology-enriched learning environments that enable all students to pursue their individual curiosities and become active participants in setting their own educational goals, managing their own learning, and assessing their own progress

c. Customize and personalize learning activities to address students’ diverse learning styles, working strategies, and abilities using digital tools and resources

d. Provide students with multiple and varied formative and summative assessments aligned with content and technology standards and use resulting data to inform learning and teaching ||  ||   || About · Blog · [|Pricing] · Privacy · Terms · [|**Support**] · [|**Upgrade**] Contributions to http://edu221spring11class.wikispaces.com are licensed under a [|Creative Commons Attribution Share-Alike 3.0 License].
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