L5+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 5 (Self-Knowledge)
 * Grade Level:**Grade 9 **Topic:** Equations and Inequalities

__**Objectives**__
Students will understand that equations can be used to calculate some everyday situations. Students will know how to apply the equations to everyday problems. Students will be able to recognize everyday situations where equations can be used.

__**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:** This is making the students look at situations in our everyday lives and look at the equations that go along with these situations. After looking at these equations, students can determine which of the techniques that they have learned can be applied to this problem so that they can solve it.

__**Assessment**__
Students will be filling in a [|cluster/word web 3] with as many situations in everyday life that they can think of that uses equations. I will use this as an informal assessment and pre-assessment to see how many problems they already know that use equations. I will also use their small group discussion as a formative assessment. Students will be discussing their graphic organizers with one another, and I will be walking around and observing their discussions and making sure everyone participates. I would also like to use a informal class discussion to see if we can get any more situations that the students do not already have.
 * Formative (Assessment for Learning)**

I would like all of my students to create an e-folio with situations of everyday problems that arise that can be solved by equations. I want to assess these e-folios using a checklist. I feel a checklist is the best way to assess these e-folios because no situation is better than another. I just want my students to have a repertoire of problems that can be solved with equations so that if they get a word problem or encounter a situation that they want to solve, they can look back at this e-folio and see what equation they can use to solve it.
 * Summative (Assessment of Learning)**

__**Integration**__
Technology: Students are going to be making an e-folio using pictures, texts, and videos to explain situations in everyday life that can be solved with equations.

English/Life Studies: Students are going to be writing examples of everyday situations that equations can be used. Since these situations are from life in general, it can tie into a class about life and the situations that can happen.

__Groupings__
Students will be grouped into groups of 3 or 4 for a discussion over their [|cluster/word web 3]. I will group students by having them line up by shoe size without using words. Once they get in the line, I am going to count off by a number that will make my groups have 3 or 4 in each group and they will go with their assigned number. In these groups everyone is going to be a reporter and a recorder. I want everyone saying situations where they can use equations to solve them and I want everyone writing down ideas that they did not think of. As a group, they will nominate a class reporter who is going to report one really unique situation that they think the rest of the class did not think of. To come up with this one idea they are going to discuss which situation they believe is unique. I will assess these group discussions by walking around and observing the groups and making sure everyone is contributing and that they are staying on task.

__**Differentiated Instruction**__
Naturalistic: Students will go outside to find an object that they don't know the height of and try to figure out ways to find that height. Logic: Students will be trying to find ways to incorporate their knowledge of equations to everyday life and solving some of those examples. Verbal: We will have a class discussion over the ways that we could solve the height problem. Visual: Students will make visual representations of their examples for their E-folio. Interpersonal: Students will work in groups to compare examples and come up with more examples. Intrapersonal: Students will make their E-folios and will fill out the graphic organizer on their own
 * Strategies**

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

If a student misses this lesson, he or she will have to fill out the [|cluster/word web 3] and then come discuss his or her situations with me. This will allow me to make sure they do not have any situations that cannot be solved by equations. The absent student will then be given the e-folio instructions and be asked to complete the assignment like everyone else.

Students will be using an e-folio making program to combine text, pictures, and videos to explain situations that can be solved by using equations. This e-folio is a Type II technology because it combines text, pictures, and videos to show these situations that couldn't be done all together effectively without them. Students will be assessed using a checklist.
 * Extensions**

__**Materials, Resources and Technology**__

 * repertoire of situations to compare to
 * text book
 * chalkboard, whiteboard, or smartboard
 * instructions for e-folio
 * checklist for e-folio
 * [|cluster/word web 3]
 * laptops, laptop cart, desktop access

__Source for Lesson Plan and Research__
[|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. These first three sites are like lessons on how to solve those types of equations. It breaks the process down step by step. [|Solving one step linear equations] [|Solving multi-step linear equations] [|Solving equations with parentheses] [|Place to check answers] - This is a great tool for students on coolmath.com if they do not abuse it. Students can check their answers by typing them into the site. [|How to solve quadratic equations by factoring] - This site gives a simple explanation on how to solve a quadratic equation by factoring [|Tutorial on solving quadratic equations] - This tutorial gives a lesson on how to solve quadratic equations in a couple of different ways. [|Solving Quadratic equations] - This is a very brief explanation on solving quadratic equations, but this site includes a solver where students can check their work. [|Algebra skills] - This site has a lesson on almost every aspect of quadratic equations that may students may need assistance with. [|Quadratic equations] - This site is a simplistic explanation for solving quadratics. It also includes a quiz to test your knowledge. [|Quadratic formula] - This site is a simple explanation on using the quadratic formula to solve quadratic equations. [|Quadratic equation solver] - This solver will help students in correcting their answers and to see where they have made a mistake. [|Explanation of quadratic formula] [|Solving by factoring]- This purple math site provides explanations and examples for using a factored quadratic to solve quadratic equations. [|How to factor] [|Real world examples of linear equations] - This site provides some relevant real life examples of linear equations that students can relate to. [|Videos of real world examples]

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.

Students are going to be using a variety of techniques that they learned in the previous four lessons, so all of my sources are from those lessons.

__**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 feel this lesson is one of the best ways for me to incorporate all the the different leaning styles that my students may have (beach ball, puppy, clipboard, and microscope). Beach balls will love the freedom they have with this e-folio because I am not having super strict guidelines or grading aspects. My students will be given the opportunity to use their imagination and their creativity to show different situations where equations can be used to solve them. Beach balls get to have their own choices and use whatever media they feel can best express these problems. Clipboards will love the fact that this lesson ties all of their previous learning together in a sequential way. They will also enjoy that even though the e-folio has limited guidelines, there are guidelines for them to follow so that they know what they have to include in order to receive full credit. Microscopes should enjoy the concept of applying their solving techniques from lessons 1-4 and being able to see the the connection to this lesson 5. They can go in depth with situations in their lives where they could use an equation to solve their problem. This enables them to make real life connections and take ownership for their e-folio because it includes situations that they have seen or experienced in their everyday lives. Every lesson I plan to have a safe environment where my puppies can feel comfortable working and posing ideas and questions. This lesson is no different. I want my students to think really hard about ways in which they can use quadratic equations and linear equations to solve problems. This may mean that students do not come up with a situation that can be solved with one of these equations. I will make sure that they student does not feel dumb for mentioning it. Instead it will be used as a learning opportunity to show why it cannot be used as one of the situations and how to avoid the confusion when they continue thinking about these situations.


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

Rationale:** Students are going to be taking situations that they have experienced or witnessed in order to make their e-folios and see where equations can be used in their own life. My students and I will get a better understanding of the student's biases or tendencies because they will most likely think of the same type of situations that are similar. For example, if I was a student in my class for this lesson I would most likely come up with every single sports related situation that I could think of as my problems that can be solved by equations. As a teacher I would see that this student is very sports oriented. Knowing this, and using these biases, I can hopefully help students come up with more situations that will interest them so that the real life connections will be more relevant. This helps the students learn the material better and meet the standard more effectively because they are using some content that they know understand.


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

Rationale:** Naturalistic: Students will go outside to find an object that they don't know the height of and try to figure out ways to find that height. Logic: Students will be trying to find ways to incorporate their knowledge of equations to everyday life and solving some of those examples. Verbal: We will have a class discussion over the ways that we could solve the height problem. Visual: Students will make visual representations of their examples for their E-folio. Interpersonal: Students will work in groups to compare examples and come up with more examples. Intrapersonal: Students will make their E-folios and will fill out the graphic organizer on their own

Students will be using a Type II technology of e-folios in this lesson. These e-folios are Type II because they can incorporate many different types of medias and combine them in one place that could not be done in a traditional classroom. Students will really be able to simulate the situations that I am asking them to use and this will help them learn the connection easier and more effectively.


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

Rationale:** In this lesson I use a variety of formal and informal assessments to gauge my students' understanding. The [|cluster/word web 3] that I am having students fill out will act as a pre-assessment and a formative assessment. When they fill out the web on their own, it will be a pre-assessment to see how many situations they know of that they can solve using equations. When students get into groups to discuss more situations, the web will be acting as an informal assessment. I will also use the discussion of these everyday situations as an informal assessment. The formal assessment is the e-folio that my students will be creating. This is where I am going to assess that they actually know situations that can be solved with equations and I am going to expect them to solve some of those situations. This will be combining all the information and techniques from lessons 1-4 and forcing the students to use it with this lesson.

__Teaching and Learning Sequence__
I feel that for this lesson, my desks should be arranged in groups of 4. Normally I do not like groups because not all students can comfortably see the board. However, I am not using a board for this lesson and I believe it would be effective to have students in groups so that they do not have to rearrange the room when they have to get into these groups.

Day 1: Day 2: Students are going to see the direct connection of the equations and the techniques that they learned for solving these equations and the situations that they encounter in everyday life. Since they are solving equations, they are directly meeting the standard "//**Students solve families of equations and inequalities.**//" Every student sees these problems in their lives and now they will know how to solve them quickly and efficiently. I plan on hooking my students by bringing them on a field trip outside and asking them to find something that they do not know the height of. This will show them that equations can be used to solve for the height **(Where, Why, What, Hook, Tailors: Interpersonal, Intrapersonal, Logical, Verbal, Visual, Naturalistic).**
 * Students will enter class, get seated, and be ready to begin class (3-5 minutes).
 * I will give students the [|cluster/word web 3] and have them fill it out individually (10-15 minutes).
 * Students will line up by shoe size without talking (5-8 minutes).
 * After I count of by numbers to make sure I have groups of 4, students will get together with their same number and discuss the [|cluster/word web 3] more and add more situations (10-15 minutes).
 * We will have a class discussion over the many different types of situations that can be solved by using equations. (10-15 minutes).
 * I will bring the students outside and ask them to find an object they do not know the height of. I will then explain the process they would use to solve this problem with an equation (18-22 minutes).
 * Any extra time will be allotted to practice problems or questions.
 * Students will enter class, get seated, and have their [|cluster/word web 3] ready to go (3-5 minutes).
 * I will give out the instructions to the e-folio and the e-folio checklist. I will verbally explain both of these handouts (5-10 minutes).
 * Students will begin working on their e-folios using their [|cluster/word web 3]. Throughout this work session I will meet with students individually and answer any questions they have and see the work that they have so far (20-25 minutes).
 * Students will get back with their group of fours from the previous day and choose one person to peer review their work so far (20-25 minutes).
 * Remainder of class will be used to continue working on their e-folios (15 minutes).

For this lesson students need to know that equations can solve many of their real live situations. I plan on showing them this by having them fill in their web with problems that they think could be solved by using an equation. After they fill this web in, I am going to discuss these situations and show them how they can figure out if an equation will work or not. Then I want to bring the students outside and ask them to find an object that they do not know the height of. We will solve the problem together and use an equation to do so. I plan on using examples and discussions to explain these situations to students. I feel this is the best way for students to see the connection of equations to their everyday lives. I will check for understanding during the discussion and making sure that they actually grasp the connection. I hope that I will be able to observe my students' reactions and tell if they understand or not. (SEE CONTENT NOTES) **(Equip, Explore, Rethink, Tailors: Naturalistic, Verbal, Interpersonal, Logical).**

Students are going to be exploring and thinking more deeply about the equations they learned about in lessons 1-4. Students are going to be finding situations that they see in their lives and applying the equations to solve some of these problems. With this process, they will also have to figure out how to set up an equation using what they know about quadratic and linear equations to do so. This higher order thinking will take place in a class discussion or group discussion so students will be bouncing ideas of myself and each other to hopefully grasp the idea better. In this lesson students are going to be able to recognize situations that can be solved using either linear or quadratic equations. I will help guide them to this information, but I really want them to discover these connections on their own. I will be using a [|cluster/word web 3] so that students can organize their thoughts. I will also be using groups of four so that students can bounce ideas off of one another about situations that they think can be solved with these equations. I will also have a class discussion after students have worked independently and in their cooperative learning groups. After this discussion, I will bring them outside and give them a real life example where they can use a linear equation to solve for the height of an object. Students will be grouped by counting off and getting together with the people who have the same number. Every student is going to be a recorder and a reporter. I want all students mentioning situations and I want all of my students to write down the situations that they didn't think of. As a group they will nominate a class reporter who will report a unique situation that their group thought of. Students will show evidence of all their learning with the discussions, the [|cluster/word web 3], and their e-folios. Students are going to be revising and refining their [|cluster/word web 3]after they fill it out individually, have their group discussion, and after our class discussion. Thei e-folios will be looked over by me and I will give them feedback and they will also go through a peer feedback stage so that they have some ideas on how to make it better **(Explore, Experience, Rethink, Revise, Refine, Tailors: Interpersonal, Intrapersonal, Logical, Visual, Verbal, Natural).**

Students will self-assess by completing the e-folio checklist before submitting their final e-folio. This will ensure that students have completed the project the way that I would like them to and students will see if they have to add anything or not. I will have a class discussion over their [|cluster/word web 3] so that any situations that cannot be solved using equations get eliminated and do not get used for their e-folios. I will also be providing feedback in class over their work-in-progress e-folios so that they have ideas to consider before completing them. This connects directly to the previous 4 lessons that dealt with solving linear and quadratic equations. It also connects to the next lesson because lesson 6 also deals with real life applications of these equations. **(Evaluate, Tailors: Intrapersonal, Interpersonal, Logical, Verbal, Visual).**

//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. __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. [|One step linear equations] are those equations that you only have to do one thing in order to solve them. Examples are x+3=9 or 3x=9. To solve these equations you have to do the opposite of the operation being done to x. However, you have to do this operation to both sides. So for x+3=9, the opposite of the operation +3 is -3. When you do this to both sides you get x+3-3=9-3. Since x+3-3 is the same as saying x+0, we have x=9-3. 9-3 is 6 so the answer is x=6. You can check your solution by inputting 6 for x. This gives you 6+3=9 which is true. [|Multi-step linear equations] are like the name implies; they are equations that require more than one step in order to solve. Examples of these are 3x-3=9 and (x/2)+7=11. These can sometimes confuse students because they want to use the order of operations to solve. However, this is not the case. To solve these equations you have to solve the operation you would do last in the order of operations and work your way backwards. Once you isolate which operation you are starting with, you do the same thing you would do for one step linear equations; do the opposite of the operation and make sure you do this to both sides. In the example 3x-3=9, the last operation you would do in the order of operations is the -3, so when solving this equation it is the first thing you do. The opposite operation of -3 is +3 so you have to add 3 to both sides. This leaves you with the equation 3x=12. Now you are left with one operation multiplying by 3. The opposite of multiplication is division, so you have to divide each side by 3. This leaves you with x=12/3 so x=4. Again to check your solution substitute 4 for x. You'll get 3(4)-3=9, 13-3=9 which checks out. Other multi-step equations deal with x being on both sides of the equation like 4x-3=-2x+9. To solve these we first must get the x's on the same side of the equation. You do this just like you would do with numbers. If you have a -2x, you +2x. Once you do this you get 6x-3=9. This type of problem looks just like the one above and is solved the same way. [|Equations with parentheses] only have one extra step and this is applying the distributive property first before solving for x. An example is 3(x+2)=12. To apply the distributive property you have to multiply 3 by everything inside the parentheses. This means you need to multiply 3 by x to get 3x AND you have to multiply 3 by +2 which gives you +6. Now you have the equation 3x+6=12. This is solved just like the multi-step equations above. // 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. (These are in case I need to remind students of some aspects of linear equations.)
 * Content Notes**

//Quadratic Equations://

I will use a combination of the following resources to explain that roots are the x-values where the y-value would equal zero. I will also explain that this is the value(s) that we are trying to find when we solve quadratic equations. I will show my students what a quadratic typically looks like with examples. I will also show them the general form that I will use for a quadratic equation.

I will be using a combination of the following resources to teach my students how to factor simpler quadratic equations and also what the quadratic formula is and how to use it properly. These resources will also be a place my students can reference for a different examples or explanations. In [|order to factor], you are going to have to find numbers to fill in for the spaces (x+/- _)(x+/- ). For example x2+5x+6=0 can be factored down into (x+2)(x+3). In order to factor this you need to find factors of 6 that can be added up to equal a positive 5. Those factors are 3 and 4. The operation in front of the constant (the addition in front of the 6) tells us that the signs of the factors are the same and the operation in from of the 5x tells us the signs of the factors are positive like the addition sign. If the sign in front of the constant is a negative or subtraction it tells us the factors are of opposite signs. One is negative and one is positive. Once you know the factors and the signs of the factors, you simply plug them into the equation (x+/- _)(x+/- ). Factoring can only be done for more simple quadratic equations. If they are not simple enough to factor, you have to use the quadratic formula. The quadratic formula is this:. In order to find the roots and solve complicated quadratics you simply have to fill in the corresponding a, b, and c values and solve. To find those values you have to look at the general quadratic formula (ax2+bx+c=y) and find the corresponding numbers that match the a, b, and c values. For example, 5x2+6x+8=0, the a value is 5, the b value is 6 and the c value is 8. Fill those numbers into the equation and solve. I am not going to solve it out because it gets really messy on a computer. There is one thing to remember though when solving with the quadratic formula, the quadratic must be set equal to 0. Resources: [|Boys singing quadratic formula] - This video will help some of my students with remembering the quadratic formula because it is put to a beat. [|Quadratic formula] - This site is a simple explanation on using the quadratic formula to solve quadratic equations. [|Quadratic equation solver] - This solver will help students in correcting their answers and to see where they have made a mistake. [|Algebra skills] - This site has a lesson on almost every aspect of quadratic equations that may students may need assistance with. [|Quadratic equations] - This site is a simplistic explanation for solving quadratics. It also includes a quiz to test your knowledge. [|Explanation of quadratic formula] [|Solving by factoring]- This purple math site provides explanations and examples for using a factored quadratic to solve quadratic equations. [|How to factor]

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.


 * Handouts**
 * instructions for e-folio
 * checklist for e-folio
 * [|cluster/word web 3]