L1+Stoutamyer,+Mykayla

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

Teacher’s Name:** Ms. Mykayla Stoutamyer **Date of Lesson:** Lesson 1 (Explain)
 * Grade Level:** Grade 9 **Topic:** Equations and Inequalities

__**Objectives**__
Student will understand that equations have many ways for being solved. Student will know linear equations, constants, coefficients, ax+b, and what does the intersection of two graphs mean? Student will be able to show different ways of arriving at the same answer.

__**Maine Learning Results Alignment**__
a. Solve systems of linear equations and inequalities in two unknowns and interpret their graphs.
 * Maine Learning Results: Mathematics-D. Algebra**
 * Equations and Inequalities**
 * Grades 9-Diploma**
 * 2. Students solve families of equations and inequalities.**


 * Rationale:** Students will learn how to solve linear equations using a graphing calculator. They will start gaining a repertoire for how to solve equations.

__**Assessment**__
Students will be given a [|KWL chart] to fill out. They will fill out the know and want to know columns before the lecture starts. Periodically during the lesson, students will go to a group and add anything to the chart that they feel is necessary (even add to the learned column). For an in class activity students will complete the process 2 of an [|algebra webquest] to check their understanding of solving equations with calculators.
 * Formative (Assessment for Learning)**

Students will be asked to make a study guide using a wikispace. They will be able to add links to additional information that they found useful and also will be able to add their [|KWL charts]. Students will be assessed on their study guide with a check list type rubric to make sure everything I believe is important is covered on their wiki.
 * Summative (Assessment of Learning)**

__**Integration**__
Technology: Students will be creating a study guide for themselves covering the topics that were discussed in class. They will be providing links to additional sites that clarified the information and they will incorporate their [|KWL charts].

Geography:In the algebra webquest that the students will be completing in class, they will be dealing with geography and longitude and latitude.

__Groupings__
Use the [|3 minute review] during the lesson to have students get together and add knowledge that they didn't think of to their [|KWL charts]. This will provide students to confer with peers to see if they agree on aspects that they know or don't know. Students will be placed into groups as soon as they walk into the room. Each student will receive a different colored piece of paper and when the time comes to get into their groups, students will find the two other people that have the same colored paper. In these groups, one student will facilitate what they believe needs to be added to the already know column, one student will facilitate what needs to be added to the want to know column, and one student will facilitate what needs to be added to the learned column. The students will add the information to their charts in a different color so that I can see that they added. Then the facilitator will report out to the class one interesting or unique thing they added to their column. This enables everyone in the class to see if it applies to them as well. I will assess the participation taking place in the groups by walking around and observing.

__**Differentiated Instruction**__
__Verbal__: Discussion over why the mistake was made on the board problem. Why do they think they got it wrong? Why do they think they are right? __Logic__: Students will solve a variety of problems different ways in class. __Visual__: The equation about girls being evil will be done out with pictures or a handout given in pictures. __Kinesthetic__: After solving a problem on the board, students will move to various locations in the room with people who have the same answer (only works if two or more answers are found). Will discuss with their group how they arrived at their answer. __Naturalistic__: Students will be dealing with longitude and latitude in the webquest. __Intrapersonal__: Students will fill out the [|KWL chart] and will think about why they got a problem wrong. __Interpersonal__: Students will participate in the 3 minute review, work in groups to discuss their answer about a board problem, and talk in pairs about why they think a particular problem was marked wrong.
 * Strategies**

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

Absent students: Students who are absent from the class are going to fill out the [|KWL chart] before returning to school to talk to me. This will be made accessible through the class wiki, an e-mail from me, or if the student does not have the internet, a copy will be sent home with a responsible classmate. When returning to school, the student will set up a time to meet with me so that they will be able to receive the class notes, as well as get a brief run down over the algebra webquest that they will have to complete on their own time. I will then give them the checklist and the instructions for the study guide wikispace that they will complete like their peers.

Every student will complete a study guide using a wikispace. Using this technology will enable the student to bring in outside sources to help them remember the information better. This wikispace is a Type II technology because they have to use the knowledge they learned in class and then personalize that information so that they will remember. They get to use other internet sources so that they can accomplish this task. Videos, songs, pictures, etc. are highly encouraged to gain a full understanding.
 * Extensions**

__**Materials, Resources and Technology**__

 * different colored paper or index cards
 * [|KWL Charts]
 * colored pens or pencils
 * Laptop, laptop cart, or desktop access
 * Wikispace accounts
 * Wikispace artifact page with students' names for study guides
 * graphing calculators
 * chalkboard, whiteboard, or smartboard
 * handouts for practice problems
 * maps
 * globes
 * checklist handout for study guide
 * Study guide handout
 * webquest handout?
 * textbook
 * handout over [|girls=evil] equation?
 * Homework probelms
 * Answers to homework
 * Answer key to practice problems

__Source for Lesson Plan and Research__
[| Algebra Webquest]-This site provides an activity for my students to do using calculators to solve linear equations. I would shorten this task to just do the algrebra. [|Girls are evil equation]-This is simply a hook to get my students interested in equations before starting the lesson. [|KWL Charts] These next three sites all came from purplemath.com and provide a way for students to graph equations by hand in case they do not have a calculator. [| How to make a T-Chart]- [|How to plot points] [|Examples for graphing linear equations]

[|Graphing linear equations]-This is another site that students can get ideas for how to graph equations and examples of how to solve them. [|Basic Algebra Terms] - This site has simple, basic definitions for the common algebra terms (variable, coefficient, constant, etc.) [|Introduction to Algebra] - This website has definitions to some of the key algebra terms like variable, coefficient, constant, etc. [|Calculator] - this site has a great picture of a calculator so that the class will be able to follow along with instructions.

Practical Mathematics Sixth Edition. Palmer, Jarvis, Mrachek, Bibb. Copyright 1977 - This book is an older introduction to algebra and has some nice examples and explanations.

These sites are mostly beginning points for me to work from. It also gives me an idea of what I should include in my lesson about using calculators to solve equations.

__**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:** I will be asking my students to make a study guide for themselves. The beach balls of my class will enjoy the freedom that they have in designing their study guide because they can add anything they feel that they need and can personalize it in a way that will help them. This same activity will appeal to clipboards because they get to organize the information I have given them. Also all the instructions will be laid out so there will be no guess work as to what I want them to do. Even microscopes will like this activity. Then can go deeper into the information and decide what they need on their study guide. The details of the lesson will be the focus on their study guides and they can claim the product as their own. Puppies will love this lesson because they will be working with their peers and will be able to ask any question that they might have without being put down. I will constantly be helping students solve problems until they feel completely comfortable doing it on their own. Discussions will be held all class to make sure that students understand what is going on and what is being asked of them.


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

Rationale:** This lesson is a introduction to equations and inequalities. With this lesson students will begin to see ways to solve equations, focusing mainly on how to solve them with graphing and graphing calculators. My student will use this knowledge to being a study guide that will be applied to the first few lessons. In order to make an effective study guide for themselves, students must understand the material, and be able to explain it to themselves in terms that they understand. They will also find outside sources of information in order to supplement their thoughts. Since the goal of this lesson is to show equations can be solved in many ways, this lesson provides a couple of these techniques so that the students can come back to them later when trying to solve quadratic equations.


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

Rationale:** __Verbal__: Discussion over why the mistake was made on the board problem. Why do they think they got it wrong? Why do they think they are right? __Logic__: Students will solve a variety of problems different ways in class. __Visual__: The equation about girls being evil will be done out with pictures or a handout given in pictures. __Kinesthetic__: After solving a problem on the board, students will move to various locations in the room with people who have the same answer (only works if two or more answers are found). Will discuss with their group how they arrived at their answer. __Naturalistic__: Students will be dealing with longitude and latitude in the webquest. __Intrapersonal__: Students will fill out the [|KWL chart] and will think about why they got a problem wrong. __Interpersonal__: Students will participate in the 3 minute review, work in groups to discuss their answer about a board problem, and talk in pairs about why they think a particular problem was marked wrong.

Students will be using a Type II technology by creating a study guide on a wikispace. This will be considered a Type II because students will be incorporating different media types, videos, songs, pictures, etc., into their study guide in order to help them learn the material. Since every student is doing their own, they can specify the study guide to their preference and use the best technique to help them study the material.


 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//

Rationale:** Throughout the lesson students will be completing a series of informal assessments to show me what they understand and don't understand. [|KWL charts] will be used a a pre-assessment and as an indicator of learning during the lesson. Also, the 3 minute reviews that are conducted during class will help students collaborate with peers so that I can see what a common difficulty area is. Also students will complete process two of an [|algebra webquest] in class. With this I will be able to correct any common calculating errors in solving equations with calculators before they have to be formally assessed on it.

At the end of the lesson, students will begin a study guide for the lesson. They will create a wikispace in order to display this information and to add resources that will help them learn the material. A checklist will be used to evaluate these study guides.

__Teaching and Learning Sequence__
I feel as though setting the desks into a u shaped configuration would be the best for this lesson. Students will have to work in groups and desk would already be next to each other, so students wouldn't have to rearrange the room to do the 3 minute reviews. Also, since I plan on giving a lecture about how to use a calculator to solve equations, all the desks need to be facing the front of the room some how and the u shape provides a common focus for the desks.

Day 1: Day 2: Students will understand that equations have many different techniques for being solved and that they can use these techniques to find where a person has decided to stop on a vacation (algebra webquest) or to solve a budget. The lesson will be focused around getting the students able to pass the MLR "//**Students solve families of similar equations and inequalities**//." I plan on "hooking" my students by showing them a fun example of an equation proving girls are evil. (This will be made as a joke and introduced as not being derogatory in any manner). **(Where, What, Why, Hook, Tailor: Interpersonal, Intrapersonal, Naturalistic, Logical, Verbal, Visual).**
 * Students will enter the classroom, receive their colored paper, and get settled for class (3-5 minutes).
 * Students will receive KWL charts and fill them out (5-10 minutes).
 * Students will receive information on how to solve linear equations using a calculator or graph (15-20 minutes).
 * Students will get into groups based on their paper color and do a 3 minute review adding information to their KWL charts (3 minutes).
 * Groups will report out one thing that they added to each column (3-5 minutes).
 * Students will work on examples of solving equations using graphs. Students will also graph equations (20-30 minutes).
 * Will have a class discussion over problems that receive multiple answers. Students will explain how they arrived at that answer so I can see where the mistake is made (5-7 minutes)
 * Extra time will be allotted to ask me questions or to work on more examples.
 * Students will enter the classroom and get out any homework that was given (3-5 minutes).
 * We will discuss any problems with the homework examples and clear up any confusion (10-15 minutes).
 * Students will work on the algebra webquest dealing with solving equations (25-35 minutes).
 * I will introduce wikispaces and get the kids set up with accounts (5-10 minutes).
 * I will introduce the study guide assignment and handout the paper work that goes with it (study guide directions and checklist) (10-15 minutes).
 * Any extra time will be devoted to questions about the project and work time for the study guide.

Students will know linear equations, constants, coefficients, ax+b, and what does the intersection of two graphs mean? To provide the students I plan on giving a lecture with plenty of examples to show the difference reasons for wanting to know this information. In order to get all students to learn, the examples will be done individually and in groups. This will enable them to try to do it themselves and to ask me specific questions. Also, they will be able to bounce ideas off one another and get input of what they should do next. The [|algebra webquest] will provide a real life example dealing with longitude and latitude so that students can see an application of these equations in the real world. While they are working on these examples and real life application, I will constantly be asking questions and asking them if they have any questions. Also, if two different answers are found for the same problem, we will discuss how this could be caused and find the error so it doesn't happen again. See content notes below. **(Equip, Explore, Rethink, Tailors: Visual, Naturalistic, Logical, Interpersonal, Intrapersonal).**

Since this information will be new to a lot of students, they will record what they already know, what they want to know, and what they have learned throughout the lesson in a [|KWL chart]. Students tend to gain more ideas and knowledge from communicating with fellow peers about what each other knows and has learned. My students will use the [|3 minute review] to gain this knowledge from their classmates and to see that maybe they don't understand something as thoroughly as they thought. In these groups, chosen randomly by the color of their paper, each student will facilitate a column of the chart and lead the discussion about what they think should be added. This will turn into a discussion about what students still think I need to address better so that they fully understand what is going on. At the end of this lesson students will be able to show different ways for arriving at the same answer to a problem. At this point, they will show the different techniques simply through technology, but will add the algebraic portion in the next lesson. Since most of the lesson is examples, I will facilitate that they can accomplish this facet by forcing them to solve the problems one way and then having them check their solution another way. This will ensure me that they can solve the problem multiple ways. At the end of the lesson students will create a study guide for themselves with examples, outside resources, and explanations so that they have something to refer back to when we reach the algebraic portion of equations. Also, the examples in class, like the webquest, will enable me to see how the students are understanding what I have just taught them. Examples will be discussed and students will be able to work with peers and myself to figure out what they did wrong on a problem and then they will have the opportunity to redo the problem and try again. With this added assistance they will hopefully learn the material better because they will specifically see the mistakes that they are making and get a chance to fix them. **(Explore, Experience, Rethink, Revise, Refine, Tailors: Interpersonal, Intrapersonal, Logical, Verbal, Visual, Naturalistic).**

Students will fill in the [|KWL chart] as a self-assessment of what they already know and what they believe is new information. They they can hopefully pin point what they do not understand by looking at this chart. Also, when students are working on their study guides they will use the checklist to check off what they have already done so they can see what else they have left to do. All throughout the classes, I will be providing feedback on what they may be doing wrong with a problem and that is why there answer is not coming out right. This instantaneous feedback will enable students to not start getting into a flow of wrong practices. I will also look at their study guides as they are saving them on the wiki so that I can make comments if something is not right there as well. The study guide will be added to in the next lesson and they will be able to use the knowledge of how to solve equations with technology to check their work that they will be doing algebraically. **(Evaluate, Tailors: Intrapersonal, Logical)**

//__Basics of linear equations__// Coefficients are the numbers in front of the variable x. Instead of writing 3*x (3 times x) you can write it as 3x where [|3 is the coefficient of x.] In a linear equation a coefficient is the slope of the line. Slope is the steepness of the line, in other words how fast the line rises or falls. To find the slope of a line: rise/run. See practice examples below. Another part of equations is the variable. A [|variable is a letter or symbol], usually x, y, or t, that represents a number. Variables are used to [|show a relation] even though we may not know the exact numbers that we need. A common example of this is the area of a rectangle which is represented by A=lw. A is the area that we are trying to find, l is the length of the rectangle, and w is the width. This shows the relationship between the 3 variables even though we don't know the numbers. [|Constants are the numbers] that do not change in an equation. For example in the equation y=x+8, 8 is the constant because no matter what number is filled in for either x or y the 8 does not change. A constant in the equation is the y-intercept on the graph. A y-intercept is where the line crosses the y-axis. The coefficient or slope and the constant are very important when graphing an equation without a calculator.
 * content notes**

__Solving linear equations using a calculator__ Graphing calculators make solving equations relatively simple. First you have to make sure the equations is in a "y=" form. To do this get y by itself by doing the opposite of what is shown. For example, y-3x+2=0. To get y by itself we must do the opposite of all of the operations that are shown (-3x and +2). The opposite of +2 is -2, the only thing it if you do it to one side you must do it to the other side. Think of keeping the [|equation balanced]. Now our equation looks like y-3x=2. The last operations standing in the way of getting y by itself is -3x. To "undo" this operation we must do the opposite, ADDITION!. Add 3x to both sides and our equation is now a "y=" one, y=3x-2. Now that the equation is in the proper form for entering it into the [|calculator] go to the "y=" button on the upper left of the calculator. You will see a y= and this is where you enter the equation (3x-2). After this click the 2nd button (also in the upper left) and then the graph button in the upper right. You should see a table. To solve this equation for y= some number, simply find the number in question in the y column and then look in the corresponding row of the x column to obtain your answer. Simple enough. If you have an x term, do the exact opposite. Find that particular number in the x column and then find the corresponding number in the same row but in the y column. Now just hit the graph button by itself (again it is in the upper right hand corner of the calculator). A graph of your line should appear. There are a couple of ways to find a value in the graph setting. Lets say you know the x value. Simply type that number in and click enter (located in the bottom right hand corner) and see what corresponding y value it gives you, this is your answer. To find a value of x you will have to click the 2nd button and then the trace button (trace button is located next to the graph button). Scroll down till you find the word value and then hit enter (Usually value is the first on the list). Once you do this, type in your number and then hit enter again. The easiest way to find an x value when given a y value is to trace the line and that isn't the best way (or the way I recommend finding an answer for x). The numbers are not close enough but you can try. Click trace and then click the arrow either to the left or the right and watch the y value on the bottom. I would recommend using the table unless directed otherwise.

__Practice Examples__ For more examples of equations see book or sites from resources.
 * Basics of linear equations
 * 1) What is the coefficient and constant of this equation y=1/2x-9 (Answer: coefficient- 1/2 constant- -9)
 * 2) What is the slope of this equation 2y=2x+4 (make sure you put this in the correct form first). (Answer: coefficient - 1. You must divide by 2 on both sides and 2/2=1.)
 * Solving linear equations using a calculator
 * 1) Use the table to solve the equation y=(20x-16)/4 when a.) x=4 (Answer: 16) b.) y=-4 (Answer: 0)
 * 2) Use the graph to solve the equation y=(20x-16)/4 when a.) x=4 (Answer: 16) b.) give an estimate for when y=-4, get as close as you can ( approximately -.06)

[|KWL charts] Study guide checklist Study guide directions Webquest directions Practice problems Fun handout over [|girls being evil]
 * Handouts**