L6+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 6 (Interpret)
 * 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 use equations in everyday life. Students will be able to make sense of the information gained from using equations in everyday life.

__**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 are going to be using their knowledge of linear and quadratic equations to solve everyday problems that they see in their lives.

__**Assessment**__
Students are going to be filling out a chart about what information in the performance task they know and what information that they don't understand or that they don't remember learning. I will use these charts to make sure that students completely understand the performance task before letting them start working on them.
 * Formative (Assessment for Learning)**

The wikispace that the students will be creating for the WebQuest is the summative assessment for this lesson. This will show me that students can set-up equations, solve them, and graph them. I will assess this product using a rubric. Students will also be asked to present their wiki and explain it. I will also grade the presentation using a rubric.
 * Summative (Assessment of Learning)**

__**Integration**__
Technology: Students will be using wikis to show all of their equations, graphs, and examples. They will also be incorporating a commercial.

Drama: Students are going to be acting in their commercial and be using other techniques such as lighting and directing to make their commercial.

__Groupings__
Students are going to be working on their WebQuest in groups of four. I would like to put students in groups with people who they work well with and will be able to work outside of class with. However, letting students pick their own groups results with people being left out. So I would like to give students a survey asking who they would like to work with and why and also who it would be easier for them to meet up with outside of class and why. I am hoping that I will be able to use these surveys and make the groups as I see fit by using these surveys. Each student within these groups will have to set-up and solve their own equation for one item of the WebQuest. If the group only has 3 members, each person will get one item and they they will have to collaboratively solve the last item. Each student will also have to graph their equation and provide the necessary explanations that are asked of them. Students will be assessed on their group work by their final product and by their presentation.

__**Differentiated Instruction**__
__Verbal__: Students will get a verbal instruction from the teacher about the project they will be doing. __Kinesthetic__: Students will get to make a commercial for their project. __Logic__: Students will make equations that fit for their choices and will then solve those equations to make sure that it stays under budget. __Interpersonal__: Students will work in groups to complete the project. __Intrapersonal__: Students will be responsible for their own equation for their choice of the uniform for the project. __Visual__: Students will use pictures and graphs to enhance their wikispaces and to explain their choices to the audience
 * Strategies**

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

Students who are absent from the whole lesson are going to have to do bits and pieces of the WebQuest that I feel are the most important. If they are only absent for a day, they will simply have to work on their part of the assignment at home and bring what they have completed done to class.

Every group of students are going to make a wiki and a commercial for the WebQuest. This Type II technologu enables students to combine their work neatly and efficiently and also be able to include the commercial in the same location as the rest of the work.
 * Extensions**

__**Materials, Resources and Technology**__

 * laptops, laptop cart, or desktop access
 * rubrics for WebQuest
 * charts for knowledge
 * surveys for groups
 * WebQuest
 * graphing calculator

__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]

[|WebQuest]

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.

__**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:** This lesson provides beach balls with the opportunity to be creative because they get to make a commercial and they also get to design a uniform for the Boston Celtics. They get to manipulate equations and make them work for what they need. Puppies will love the idea of being able to work with their peers and creating something without the pressure to do all the work. The safe environment will still be there because students will be encouraged to work with one another and ask questions so that they can do the best possible on this project. Clipboards will have two rubrics that they will be able to follow in completing the project. Also, the WebQuest is set up to walk them through a sequential process that they follow in order to complete the project. Clipboards will love all of this structure and guidance. Microscopes will enjoy applying their knowledge from the previous 5 lessons to this final product. They will have to set-up and equation, solve it, and then graph it using every thinking skill they have learned in this unit.


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

Rationale:** Students are going to be interpreting their equations and graphs and explaining to the Boston Celtics what it all means in relation to their uniforms. Students are really going to have to put their knowledge of equations and graphs to the test to be able to adequately explain this information to someone who has never seen them before. Each student gets to explain in their own unique way as long as they have an explanation. This means that my students can play off of their strengths to explain the subject matter. Students are going to be tying directly into the learning result of solving equations because they will be solving the equations that they have just created.


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

Rationale:** __Verbal__: Students will get a verbal instruction from the teacher about the project they will be doing. __Kinesthetic__: Students will get to make a commercial for their project. __Logic__: Students will make equations that fit for their choices and will then solve those equations to make sure that it stays under budget. __Interpersonal__: Students will work in groups to complete the project. __Intrapersonal__: Students will be responsible for their own equation for their choice of the uniform for the project. __Visual__: Students will use pictures and graphs to enhance their wikispaces and to explain their choices to the audience

Students will be using the Type II technology of wikis to complete the WebQuest. Wikis are a Type II in this case because they are going to be able to combine explanations, pictures, and a commercial in one location that could not be done with any other form of technology.


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

Rationale:** This lesson does not use very many informal assignments because the whole lesson revolves around the formal assessment. The only informal assessment that I use in this lesson is the chart that I am having students fill out about what they know/understand about the performance task and what they don't know/don't understand about the performance task. This enables me to address main questions and concerns early and accurately because I answer them before they start working on the task. The formal assessment that I am using is the WebQuests final product of their wiki. This wiki will show me that the students can set-up an equation, solve it, graph it, and also explain it to someone who does not understand equations. With this knowledge I will know that they have met the learning result for this unit. I will be assessing these wikis using a rubric.

__Teaching and Learning Sequence__
The arrangement of the room will be the same as lesson 5; arranged in groups of 4. Students need to be able to work easily with their group and the most effective way to accomplish this is to be set up with your group by grouping the desk in that configuration.

Day 1: Day 2: Day 3: Students are going to be able to complete meet the learning result, "**//Students solve families of equations and inequalities//,**" because they will be able to set-up, graph, and solve the equations they are using for this performance task. Also, by completing this project students will be able to explain their equations and graphs to someone who does not necessarily understand them. The entire WebQuest is a far fetched real life example of budgets. I plan on hooking students by simply telling them about this cool project! **(Where, Why, What, Hook, Tailors: Logical, Visual, Interpersonal, Intrapersonal, Kinesthetic, Verbal).**
 * Students will enter class and be seated (3-5 minutes).
 * I will give the students the survey and have them fill it out (10-15 minutes).
 * I will give students the chart and have them read the WebQuest and fill out the chart (10-15 minutes).
 * Students will ask any questions that they may have with the WebQuest (5-10 minutes).
 * I will put students into their groups and they will start working (35 minutes).
 * Students will enter class and get ready to begin working on their projects (3-5 minutes).
 * Students will work on their projects while I meet individually with each group and give them feedback on what they have completed thus far (75 minutes).
 * Students will enter class and get ready to begin working on their projects (3-5 minutes).
 * I will match groups up and students will peer review and give feedback for each others work so far (40-45 minutes).
 * Students will work on their projects (30 minutes).

I will not have to equip the students with any knowledge because they are using knowledge that I have already taught them in the previous five lessons of the unit. I may have to remind them of the material, but I will not have to teach them anything new. The only interaction I will be having with students is answering their questions over the performance task and providing them with feedback over their work up to a certain point. I will check for their understanding of the project by using their responses to the chart of knowledge. With this I will be able to clarify any misconceptions or questions before they actually start working so when they actually get started they will not be bogged down by confusion. I will also check for understanding when I assess their final products and presentations because this will truly show me that the students have grasped the material from this unit. SEE CONTENT NOTES!! **(Equip, Explore, Rethink, Tailors: Interpersonal, Intrapersonal, Logical, Verbal, Visual, Kinesthetic).**

My students are going to be using all of the information from the unit to complete this task so they will be using a lot of higher order thinking. In order to be able to complete this assignment students are going to have to use what they know about equations and graphs to explain them to someone who does not understand equations and graphs. This will really get my students thinking about what they have learned and how they can apply what they know to form their explanations. These explanations tie directly into what I expect students to be able to do for this lesson which is be able to make sense of the information gained from using equations in everyday life. Since they have to explain how their equations pertain to the uniforms, students must know what the information from these equations represents in this real life example. I will group students by taking into account their preference to who they work best with. I will decide the groups with these considerations in mind. Each student in the group will have to set-up, solve, graph, and explain their equation on the wiki in some fashion. I will have them show evidence of learning by completing the assignment and earning a high score. Students will have a teacher conference and a peer review session to be able to rethink, revise, and refine their work based upon the feedback that they receive **(Explore, Experience, Rethink, Revise, Refine, Tailors: Interpersonal, Intrapersonal, Visual, Verbal, Logical, Kinesthetic).**

Students will self assess by using the rubric to finish the product and get the best possible scores. I would also like to have students grade their own products using the rubric. I will hold in class conferences with the groups and give them feedback over their work at that point in time. This does not connect to any future assignments, but it ties into the other lessons of the unit and also to their real lives in a fictional kind of way **(Evaluate, Tailors: Interpersonal, Logical, Verbal, Visual, Intrapersonal).**

//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: x. 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**
 * rubrics for WebQuest
 * charts for knowledge
 * surveys for groups