L3+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 3 (Perspective)
 * Grade Level:** Grade 9 **Topic:** Equations and Inequalities

__**Objectives**__
Students will understand that quadratic equations have different methods for solving. Student will know quadratic equations, ax²+bx+c, and what the roots of the quadratic equation represent. Student will be able to compare quadratic equations with linear equations.

__**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 begin solving more complicated equations called quadratic equations. Though this does not address the solving of quadratic equations, it enables students to begin thinking and get ready for the next lesson in which they actually begin solving.

__**Assessment**__
Students will be using a [|venn diagram] to compare and contrast the new quadratic equations that they are learning about to the linear equations that they have already learned about. This [|diagram] will enable students to begin thinking about ways to figure out to solve the quadratic equations. Students will be completing many practice problems to show their understanding as well.
 * Formative (Assessment for Learning)**

For a more fun approach to comparing and contrasting, the students will use their [|venn diagrams] make a creative comic life about the similarities and differences. This will enable the students to be creative and still explain the information. To assess these comics, I will use a rubric that students will have in their possession while completing their comic.
 * Summative (Assessment of Learning)**

__**Integration**__
Technology: Students will be using a program called Comic Life to make a comic about the similarities and differences between linear and quadratic equations. This creative assignments allows students to learn the material in a technology based setting.

Art: All though students are not drawing or painting, I believe that they are using art by creating the comic. They have to be creative and create something unique and their own.

__Groupings__
This lesson does not involve cooperative groups. Instead the entire class will have a discussion about the similarities and differences between linear and quadratic equations. Each student will be asked to contribute one thing that they put on their individual [|venn diagram] and this will help the class construct a class diagram. This discussion will enable me to evaluate what the students are thinking and enable me to get common misconceptions out of the way early. This discussion will also allow me to show them why their ideas may be wrong and also to show them the correct way to solve it. Since there are no small groups, I will not have to worry about how they are grouped. I will assess the students contribution to the class diagram as their group assessment.

__**Differentiated Instruction**__
__Verbal__: The class discussion about the venn diagram. __Visual__: Students filling in the venn diagram and making the comic. __Intrapersonal__: Students filling out the venn diagram and making the comic life alone. __Interpersonal__: The class discussion about the venn diagram and the peer feedback reviews. __Kinesthetic__: Students making the comic life. __Musical:__ Make up a rhyme for the quadratic equation. ax²+bx+c= the quadratic equation for you and me.(**Tailor**)
 * Strategies**

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

Students will be given directions on how to fill out a venn diagram about the linear equations and quadratic equations. Since a venn diagram is easy to make on one's own, the absent student will not be in need of one exactly like their classmates. After completing their diagram, the student will have to meet with me to see the class venn diagram and get directions for the comic. Also during this meeting, students will be given the class notes and we will have a mini discussion like the class discussion. After this meeting, students will have to complete the practice problems and homework if there is any.

Every student will be able to use Comic Life and make a comic creatively showing the similarities and differences between the equations. Comic Life is a Type II technology because students are using pictures, text, and dialogue to convey understanding of quadratic equations and linear equations.
 * Extensions**

__**Materials, Resources and Technology**__

 * huge class venn diagram
 * individual [|venn diagrams]
 * laptops, laptop cart, or desktop access
 * Comic Life program
 * chalkboard, whiteboard, or smartboard
 * handout of practice problems
 * comic instructions
 * comic rubric
 * textbook
 * graphing calculators
 * answer key to practice problems

__Source for Lesson Plan and Research__
[|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.

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 really addresses beach balls of my class because of the comic that they get to create in Comic Life. Beach balls get to be unique and make their own decisions about how to present the information in a comic style. As long as they meet the rubric they can be as creative as they would like. The rubric for the project appeals to my clipboards because it tells them exactly what they need to include in do well on the comic. Microscopes will enjoy the class discussion and the comic because they get to analyze linear equations and compare and contrast those with quadratic equations. Since this whole lesson is based on exploration and hypothesizing, no answer will be deemed wrong or stupid so the class will be safe for puppies to say what they think. I want my students to explore and try to figure things out on their own.


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

Rationale:** Students are going to use their own perspective and compare linear equations and what they know about quadratic equations. This will enable me to see what they know about quadratics but also get them thinking about what is to come in the next lesson. Since this is a pre-assessment for this lesson, students are not going to be graded, but I will inform them that the information that they learned about quadratics will come in handy later.


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

Rationale:** __Verbal__: The class discussion about the venn diagram. __Visual__: Students filling in the venn diagram and making the comic. __Intrapersonal__: Students filling out the venn diagram and making the comic life alone. __Interpersonal__: The class discussion about the venn diagram and the peer feedback reviews. __Kinesthetic__: Students making the comic life. __Musical:__ Make up a rhyme for the quadratic equation. ax²+bx+c= the quadratic equation for you and me.

Students will be using the Type II technology of comic life during this lesson. They are going to apply the knowledge from their venn diagram and use that to make a creative comic about the information. This is a Type II because they get to use pictures, text, and a story to explain the information.


 * //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 is all about self realization and trying to figure things out on one's own. Students will have a [|venn diagram] that they fill in on their own comparing and contrasting linear equations and quadratic equations. Then as a class they will complete a class diagram. This discussion will be assessed informally as well. Students will also be completing practice problems that will be assessed only so that they can see their mistakes and fix them.

Students are going to have to take the information from their [|venn diagrams] and use it to create a comic expressing all that information. This will be assessed using a rubric that all students will have from the beginning so that they can make sure that they meet every aspect.

__Teaching and Learning Sequence__
I believe that for this lesson desks should be arranged into a perimeter formation with the focus being the board. This is the best arrangement because of the class discussion. Students will be able to see the board and each other as they discuss the ways in which they think linear equations differ from quadratic equations.

Day 1:
 * Students will enter class and get settled at their seats (3-5 minutes).
 * Students will receive their [|venn diagram] and fill it out (8-12 minutes).
 * Students and I will have a discussion about their [|venn diagrams] and make a class venn diagram including everyone's ideas (8-12 minutes).
 * Students will complete some practice problems and be able to ask more questions (10-15 minutes).
 * Students will receive their comic assignment and rubric, be able to ask questions, and start working on their comic (15-20 minutes).
 * Students will get in get teacher feedback and student feedback about what they have completed on their homework thus far (12-16 minutes).
 * Extra time will be allotted to ask me questions or work through some more examples.

Students will be able to see the differences and similarities between linear equations and quadratic equations. I will explain to them where quadratics are used in everyday situations; how many of you have gotten so mad at your computer that you wanted to throw it off a building? Well I can tell how long it would take that computer to fall 100 feet before it would smash into millions of pieces. This lesson does not directly address how to solve equations or inequalities, but it is a prelude to a new type of equation, quadratics, so that students are thinking about them for the next lesson **(Where, Why, What, Hook, Tailors: Verbal, Visual, Intrapersonal, Interpersonal, Kinesthetic).**

Student will know quadratic equations, ax²+bx+c, and what the roots of the quadratic equation represent. I plan to introduce this knowledge while we are having a class discussion over their [|venn diagrams.] I believe they will see the connections better this way and it will lead into talking about how to solve these quadratic equations. I will provide lots of examples of why their theories may not work, but also why factoring does work. I will also give students plenty of practice problems that they can tune their factoring skills with and they will be able to ask me specific questions that they may still be having with this process. I will be trying to get students to solve the quadratics on their own with my guidance through a class discussion. SEE CLASS NOTES. **(Equip, Explore, Rethink, Tailors: Intrapersonal, Interpersonal, Verbal, Visual).**

Since students are going to be discussing ways that they believe are the ways to solve quadratic equations, they are going to be using knowledge that they previously know about linear equations and applying them to what they know about quadratic equations. This higher order thinking will hopefully allow them to see why factoring actually works. Students will also be using higher order thinking when they are filling in their [|venn diagrams]. They are going to be comparing and contrasting linear equations and quadratic equations. This whole diagram activity will show me that students will be able to compare quadratic equations with linear equations. Since we are filling out a class venn diagram, I will be able to correct misconceptions and add any knowledge that I believe that the students need to know in order to try to solve quadratic equations in the next lesson. For this lesson, I did not use small groups. Instead, I think a whole class discussion is the best way for every student to hear each others' ideas. Since there are no groups, there are also no separate roles. Students must be contributing members of the class discussion and at least mention one idea for the class diagram. Students will show understanding of linear equations and quadratic equations by filling in their [|venn diagrams] and by contributing to the class discussion about ways to solve the equations. They will also complete practice problems with deciphering between linear and quadratic equations and create a comic with the information from their diagrams. All of this will show me that they understand the differences between linear and quadratic equations. Students will be able to rethink their venn diagrams in the class discussion, but they will also be able to rethink and revise their comics after meeting with classmates and myself. After these conferences, students will take the feedback and improve their comics. **(Explore, Experience, Rethink, Revise, Refine, Tailors: Intrapersonal, Interpersonal, Verbal, Visual, Kinesthetic).**

Students will self-assess by filling out the venn diagram and also by filling out the rubric and grading themselves on their comics. By filling out the rubric, students will hopefully be able to catch aspects that they may have missed or that they can improve upon before turning in to me for grading. Students will receive prompt feedback from myself on their comics in the early stages since I will be meeting with each one of them individually and providing feedback for them to consider before finishing. Since they are just learning the concept of quadratic equations, it connects directly to lesson four where they are going to solve quadratics. **(Evaluate, Tailors: Interpersonal, Intrapersonal, Visual, Kinesthetic).**

//__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. Resources: [|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.

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**
 * practice problems
 * comic instructions
 * comic rubric
 * [|venn diagrams]