L2+Bartlett,+Kaitlyn

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

**LESSON PLAN FORMAT** Student will understand that there are many ways to solve equations and inequalities. Student will know various ways to solve equations and inequalities. Student will be able to consider different ways to solve equations and inequalities Maine Learning Results: Mathematics - D. Algebra Equations and Inequalities Grades 9-Diploma //**2 Students solve families of equations and inequalities**//
 * __Teacher’s Name__****:** Ms. Bartlett **__Lesson and Facet__:** 2 Empathy
 * __Grade Level__****:** 9 **__Topic__:** Solving equations and inequalities
 * __Objectives__**
 * __Maine Learning Results Alignment__**


 * Rationale:** In the lesson student will learn different approaches to solving equations and inequalities.


 * __Assessment__**

During the lesson, students will have many opportunities to explore and experience answering questions by using their knowledge of graphs to help solve problems. First, doing practice problems by themselves and in groups will test student’s knowledge. To begin students will use the step-by-step graphic organizer to record information about the different ways to solve equations and inequalities. This graphic organizer is set up in a fashion so to allow students to jot down a short description of how to use that technique and then record an example. Students will be allowed to continue to add to their step-by-step chart throughout the lesson. After we have reviewed several ways to solve equations and inequalities, they students will complete a work sheet in groups to be passed in for feedback.
 * Formative (Assessment for Learning)**

Garage Band/ iMovie: Students will work in groups using Garage Band/ iMovie to create a math rap/ song a specific approach to solving equations and inequalities. Students will present their final product to the class and be graded on a rubric.
 * Summative (Assessment of Learning)**

English: Students will need to include explanations of the process they chose to solve equations and inequalities. Music: Students will need to use their music skills to put together their songs.
 * __Integration__**
 * Technology:** Student will use Garage Band/ iMovie to create a math rap/song. Students will need to know the different approaches to solving equations and inequalities to be able to create their song the highlights one specific way.
 * Other Content Areas:**

Students will be placed randomly into groups of four using a random integer program on my calculator Students will then work in groups on the Jigsaw activity to solve equations and inequalities. Students will need to depend on others to completely solve their problems. Each student will hold a specific value to their group; the groups will use teamwork to present their group problem to the class.
 * __Groupings__**


 * __Differentiated Instruction__**

**Strategies:** **Verbal/ Linguistic-** Student will be able to create a rap and sing it. **Logical-** Student will use a step-by-step chart to sorts ideas. **Visual-** A graphic organized will be used to sort out ideas and thoughts of the different concepts of graphing equations and inequalities. **Interpersonal-** Students will have an opportunity to work in groups in class. **Intrapersonal-** Student will have the choice to work by themselves on a math rap. **Musical-** There is music in the rap video. **Naturalist-** Students can make a math song involving nature. **Kinesthetic-** These students will be able to make a video of their rap. **Modifications/Accommodations** I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.

Absence: If you are absent from school for any reason it is your responsibility the day you return back to school to pick up any work you may have missed in class. I realize that things happen unexpectedly time-to-time, so once something happens communicate with me immediately.

**Extensions** Students are creating a math rap/ song using Garage Band/ iMovie. Students will present their final product to the class and be graded on a rubric.

Step by Step Chart- [] [] iMovie tutorial: [] Garageband tutorial: http://www.youtube.com/watch?v=-WX_lV0nnx8 Completing the square: [] Factoring: []
 * __Materials, Resources and Technology__**
 * Laptops
 * Books
 * Pencil
 * Calculator
 * Projector
 * Paper
 * White Board
 * Step by Step Chart
 * __Source for Lesson Plan and Research__**


 * __Maine Standards for Initial Teacher Certification and Rationale__**

The clipboard leaner will like the aspect of this lesson that allows them to write their ideas down onto paper using a graphic organizer; these learners will also benefit from being able to visually see different approaches to solving equations and inequalities. Microscopes will also enjoy the graphic organizer and talking about different approaches to solving equations and inequalities because they will be able to analyze equations and inequalities in more ways to get a deeper understanding of the material. The beach ball learner will enjoy the option to choose how they solve a problem. This will allow them to better understand the use of inequalities and equations in the real world. The puppy learners will be able to hear the ideas of others and discuss problems.
 * //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://** Students will be learning different approaches to solving equations and inequalities.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * //Rationale://** Students will learn empathy when listening to songs produced by classmates and themselves about different approaches to solving equations and inequalities. Students will be able to recognize when to use certain types of ways to solve equations and inequalities, which will make it easier for them to learn how to solve word problems as well as graph them. Students will be able to brainstorm ideas by themselves, and then as a group by using a step-by-step chart.

equations and inequalities. **Interpersonal-** Students will have an opportunity to work in groups in class. **Intrapersonal-** Student will have the choice to work by themselves on a math rap. **Musical-** There is music in the rap video. **Naturalist-** Students can make a math song involving nature. **Kinesthetic-** These students will be able to make a video of their rap.
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**
 * //Rationale://**
 * Verbal/ Linguistic-** Student will be able to create a rap and sing it.
 * Logical-** Student will use a step-by-step chart to sort ideas.
 * Visual-** A graphic organized will be used to sort out ideas and thoughts of the different concepts of graphing

Students will create their own songs using Garage Band/ iMovie to test their abilities explain how to solve equations and inequalities. They will create examples and justify when to use the specific way they chose to teach solving equations and inequalities to the class. They will then present their product to the class.


 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * //Rationale://**
 * Formative:** During the lesson, students will have many opportunities to explore and experience answering questions by using their knowledge of graphs to help solve problems. First, doing practice problems by themselves and in groups will assess student’s knowledge. To begin students will use the step-by-step graphic organizer to record information about the different ways to solve equations and inequalities. This graphic organizer is set up in a fashion so to allow students to jot down a short description of how to use that technique and then record an example. Students will be allowed to continue to add to their step-by-step chart throughout the lesson. After we have reviewed several ways to solve equations and inequalities, they students will complete a work sheet in groups to be passed in for feedback.

When the students arrive to class the desks will be set up into groups of four. Agendas:
 * Summative:** Students will work in groups using Garage Band/ iMovie to create a math rap/ song a specific approach to solving equations and inequalities. Students will present their final product to the class and be graded on a rubric.
 * __Teaching and Learning Sequence__****:**
 * Day 1: (80mins) **
 * Check homework: (8) **
 * Video: (10) **
 * Review: (30) Explain various ways to solve problems, focus on factoring **
 * Break: (10) **
 * Worksheet: (17) Factoring **
 * Assign HW: (5) **


 * Day 2:(80mins) **
 * Problem of the day: (7) **
 * Check homework: (8) **
 * Go over work sheet: (15) **
 * Review: (30) Factoring, completing the square, and the quadratic formula **
 * Break: (10) **
 * Explain project: (5) **
 * Put groups together: (5) **


 * Day 3:(80mins) **
 * Problem of the day:(10) **
 * Check homework: (8) **
 * Tutorials: (15) **
 * Work in groups: (47) **


 * Day 4: (80mins) **
 * Problem of the day: (10) **
 * Finish up projects: (30) **
 * Break: (10) **
 * Presentations: (30) **

During this lesson, students will understand that there are many ways to solve equations and inequalities. They will find out that there are different approaches to tackling problems anywhere in the world. In this lesson, I will introduce 3 ways to solve problems, but put a main focus on factoring. I will play a math rap about factoring to introduce and get students excited about what they will be doing. The MLR is //**students solve families of equations and inequalities.**//
 * __Teaching and Learning Sequence__:**
 * Where, Why, What, Hook, Tailors: Visual, Intrapersonal, Musical, Logical and Verbal**

During this lesson students learn how to factor, completing the square, and the quadratic formula. I will provide this information through individual, group, formative and summative assessment, discussion, and traditional instructional time. To start class, students will be put into groups of 4 to 6 by alphabetical order. Each student in the group will be given a specific part of a simple equation and the groups will have to work together to put the pieces of the equation together without talking. After this activity, the students will stay in their groups and take note on their step-by-step chart on the three main ways to factor and solve equations. After we have gone over the 3 techniques with a focus on factoring polynomials, students will work together on a worksheet practicing their factoring techniques. After every group has finish, their worksheet they will be given a 10-minute break. After their break, we will go over the worksheet as a class so I can evaluate how people are grasping the content. The students will then be given some homework to do for next class. The next day we will start class with a problem of the day, which will be about relating solving equations to graphs. As they work on their problem of the day, I will go around and check to see who has attempted their homework. After I have gone over the problem of the day, we will go over homework and do the problem that students had trouble with.
 * Equip, Explore Rethink, Revise Tailors: Verbal, Visual, Intrapersonal, Logical, and Interpersonal**

During the lesson, students will have many opportunities to explore and experience answering questions by using their factoring skills. Formative assessments will be used to assess student’s progress with the material. These will include various practice problems worked on individually and with partners. To begin students will use the step-by-step graphic organizer to take notes about the different ways to solve equations and inequalities. This graphic organizer is set up in a way that allows students to take down notes of how to use the three specific techniques and then record an example of each. During class, we will go into depth about 3 specific techniques to solving equations. After this, I will assign students into 3 groups and explain their project to them. Students will work in groups using Garage Band/ iMovie to create a math rap/ song about a specific approach to solving equations. Students will present their final product to the class and be graded on a rubric. (See Content Notes and attachments) At the beginning of this class, students will once again be given a problem of the day. They will be given 3 equations and will need to use all three techniques they’ve learned to solve equations. During this lesson student will have an opportunity to watch a tutorial on GarageBand and iMovie to help make their projects. Then students will continue either work by themselves or in groups to create a math rap/ song about solving equations and inequalities. Then they will be graded on a rubric. The students will also self asses themselves on the same rubric so that I can compare what they think they deserve to the grade that I have given them. Students will then present their project next class. The videos will help teach and reinforce techniques that the will need in future lessons.
 * Explore, Experience, Rethink, Revise, Refine, Tailors: Visual, Intrapersonal, Interpersonal, Logical, Bodily/ Kinesthetic, and Verbal**
 * Evaluate, Tailors: Visual, Intrapersonal, Interpersonal, Logical, Kinesthetic, and Verbal**

Factoring: **1.)** (x-7)^2= (x-7)(x-7)=  x^2-7x-7x+49=  x^2-14x+49  **2.)** (x+2)(x+3) x^2+3x+2x+6= x^2+5x+6 **3.)** (2x-1)(2x+1)= 4x^2+2x-2x-1=  4x^2-1  **4.)** 3x^2(x+5) 3x^3+15x^2
 * __Content Notes__**
 * Brainteaser:**
 * GCF: Greatest Common Factor**
 * FOIL: First, Outer, Inner, Last**
 * Factoring:**
 * x^2+5x+6**
 * (x+3)(x+2)**


 * x^2-8x+15**
 * (x-3)(x-5)**


 * x^2 +4x-12**
 * (x+6)(x-2)**

Example: x^3-3x^2-16x+48= (x^3-3x^2)-(16x+48)= x^2(x-3)-16(x-3)= (x^2-16)(x-3)= (x+4)(x-4)(x-3) I need to find factors of 6 that add up to 5. Since 6 can be written as the product of 2 and 3, and since 2 + 3 = 5 , then I'll use 2 and 3. This is the answer: // x // 2 + 5//x// + 6 = ** (//x// + 2)(//x// + 3) ** This is how all of the "easy" quadratics will work: you will find factors of the constant term that add up to the middle term, and use these factors to fill in your parentheses. Quadratic Formula: This one doesn't f actor. // // ** The solution is ** Completing the square: Given any quadratic of the form it is possible to form a square that has the same first two terms:  This square differs from the original quadratic only in the value of the constant term. Therefore, we can write where //k// is a constant. 
 * Factor by grouping:**
 * ** Factor ****// x //**** 2 **** + 5//x// + 6. **
 * Note that you can always check your work by multiplying back to get the original answer. In this case: ||  || [[image:file:///Users/kaitlynbartlett/Library/Caches/TemporaryItems/msoclip/0/clip_image004.gif width="73" height="109" caption="x + 2)(x + 3) = x^2 + 5x + 6"]] ||
 * ** Solve ****// x //**** 2 **** + //x// – 4 = 0 **** . **

Step-by Step Graphic Organizer Rubric Worksheets
 * __Handouts__**