L3+Bowden,+Scott

**COLLEGE OF EDUCATION, HEALTH AND REHABILITATION **  **LESSON PLAN FORMAT **  
 * UNIVERSITY OF MAINE AT FARMINGTON **
 * Teacher’s Name: ** Mr. Bowden **Lesson:** Application
 * Grade Level: 9** **Topic:** Graphing Linear Equations

**__Objectives__**
 * Student will understand that ** algebraic equations of one degree can be represented as lines.
 * Student will know** independent variable, dependent variable, graphing methods, slope intercept form, standard form, point slope form, parallel lines, perpendicular lines.
 * Student will be able to** create the graph of a line.

**__Maine Learning Results Alignment__**  Maine Learning Results - Mathematics D. Algebra Equations and Inequalities Grades 9-Diploma 2. Students solve families of equations and inequalities


 * Rationale:** In this lesson, students will be learning how to graph equations of lines by isolating variables, relating values of points, and working with 2-variable equations. This will require them to solve equations for one variable in terms of another.

**__Assessment __** The roof model will have an accompanying lab that poses the mathematical questions for building the roof. The students will complete the mathematics and hand the lab worksheet in to the teacher for feedback before beginning to build the model for a score which will be used as a summative assessment. Homework will be handed in to the teacher so that lessons can be modified to match the process and content gaps of students. This homework assignment will be unscored and students will have the opportunity to view the answers before handing in the piece. The students will have an ice-cream graphic organizer that they can use to gather the presented material in a segmented fashion as there are many techniques to in this section. Students will not hand these in, but will be able to call upon it later as study material. At the end of the lesson, the teacher will review valuable information that should be included. Students will write journal or blog entries that are reflective of their thoughts on the lesson. The teacher will check them at the end of the lesson to modify the lesson structure for future classes.
 * Formative (Assessment for Learning) **

In this lesson, the teacher will hand out a lab worksheet that will require students to build a model roof using slope specifications. The lab worksheet will have all the mathematics completed and the students will be required to build this model using a scale that converts values on the x and y axes into a measurable unit. They will also graph out what their roof should look like and figure out the equation of the line that is represented by each half of the structure. Additionally, the students will take a low-stakes quiz relating to the material covered in the lesson.
 * Summative (Assessment of Learning)**

Technology: Students at the end of the lesson will use online software to reinforce how slope and points affect a graph.
 * __Integration__**

Art: Students will be required to build the roof model using materials that are not paper (like popsicle sticks, wood, cardboard). It will not be graded for artistic form, but students will be required to decorate it in some way, shape, or form.

__Groupings__ Before this lesson, the teacher will have students pull a roof slope at random. Students who have the same slope parameters will work in groups. These will be the Quick-Play groups for this lesson. These groups will have no more than 4 but no less than 2 students in each. Within each group, students will work together to complete the appropriate mathematics for their model and compare answers with other groups with the same slope. All students will be responsible for handing in their own lab worksheet and building their own model.


 * __Differentiated Instruction __**<span style="font-family: "Times New Roman","serif";">
 * <span style="font-family: "Times New Roman","serif";">Strategies **<span style="font-family: "Times New Roman","serif";">


 * Kinesthetic** - Students can build their model using the given parameters.
 * Logical** - Students do the computations of the project.
 * Musical** - Finding slopes and points in octaves of music.
 * Verbal** - Students discuss graphs and listen to instruction
 * Visual** - Students picture graphs
 * Interpersonal** - Students discuss plans for the roof with others.
 * Intrapersonal** - Students work with the online software individually.

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

Absent Students: The teacher will provide office hours for the students' use. It is up to the student to either contact a classmate to review the material or to contact the teacher before the next period. If the absence is for an extended period, the teacher can assign or obtain a tutor for the student. The assignments and the notes for the class will be available on the teacher/class wikispace page. If students have internet access, they can use a video conference software such as skype to be a virtual participant if they are willing or able to do so. Additionally, students who are absent during this lesson will need to complete the roof building lab. Students will meet with the teacher to discuss the assignment, determine the student's slope parameters and an acceptable time for the model to be handed in/completed.

After the design is complete, students will need to determine how long their roof will be on both ends by using the distance formula. At that point, they can determine how many square shingles of an arbitrary length would be required to cover the roof lengthwise, not taking the 2 dimensional nature of shingles or a roof into consideration. They may also have the choice to abstractly compare the designs and building of their own roof to another slope specification.
 * Extensions**

**__<span style="font-family: "Times New Roman","serif";">Materials, Resources and Technology __**<span style="font-family: "Times New Roman","serif";"> <span style="font-family: "Times New Roman","serif";">Teacher computer Projector/TV Screen for the computer Build A Roof Lab worksheet Model Roof Lab rubric Graphing Calculators for students who don't already have them. Stuff to write on the whiteboard/chalkboard with Graphic Organizers - Ice Cream. Lesson 3 Quiz Textbook and teacher notes Graph Paper for student work on graphing Some kind of food Scored itineraries from Lesson 2 Computers for students if they don't already have them.

**__Source for Lesson Plan and Research__** <span style="font-family: "Times New Roman","serif";">A discussion of independent and dependent variables with real examples: [] A definition of independent variable: [] A definition of dependent variable: [] An explanation for finding the equation of a line with different methods: [] An explanation of forms of linear equations: [|http://cs.selu.edu/~rbyrd/math/equations/] Terragon's explanation of finding the equations of parallel lines: [] Terragon's explanation of finding the equation of a perpendicular line: [] The location of the online graphing software is on this site under "Line Plotter": [] Slope-intercept graphing tutorial: [] Standard form / intercept graphing: [] A tutorial on horizontal and vertical lines: [] <span style="font-family: "Times New Roman","serif";">An Ice Cream Graphic Organizer: [] **__<span style="font-family: "Times New Roman","serif";">Maine Standards for Initial Teacher Certification and Rationale __**<span style="font-family: "Times New Roman","serif";"> Rationale: **<span style="font-family: "Times New Roman","serif";"> Beach Ball: Students will have the choice of how they construct their roof model. They will have the opportunity to try many different slopes and consider many different options and methods of building the roof and finding the equations for the roof. Clipboards: Students will be guided in a step-by-step process when learning the material and have structure as far as what steps to do and in what order for their lab. Microscopes: Students will use their lab to explore the material in a different and unique way and will have the opportunity to explore it with several different conditions. Puppy: Students will have the opportunity to receive help and support with practice problems and the roof lab both from other students and from the teacher. Students will be able to give answers to questions without the fear of looking stupid or being brought down for their comments.
 * //<span style="font-family: "Times New Roman","serif";">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. //****<span style="font-family: "Times New Roman","serif";">

Rationale:** This lesson was based around the fact that students will understand that algebraic equations of one degree are represented as lines. This was discussed when students were using slopes and heights to build a model roof with a specific slope and top height. This lesson acts as a way for students to solve families of equations and inequalities when they isolate variables prior to graphing equations as discussed in the Maine Learning Result for this lesson. Students learn concepts relating to lines, equations of lines, parallel and perpendicular lines, independent and dependent variables, and forms of linear equations. When the lesson is complete, students will be able to create the graph of a line.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** The following instructional strategies will be used in this lesson:
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//

Multiple Intelligences:
 * Kinesthetic** - Students can build their model using the given parameters.
 * Logical** - Students do the computations of the project.
 * Musical** - Finding slopes and points in octaves of music.
 * Verbal** - Students discuss graphs and listen to instruction
 * Visual** - Students picture graphs
 * Interpersonal** - Students discuss plans for the roof with others.
 * Intrapersonal** - Students work with the online software individually.

Technology: Students at the end of the lesson will use online software to reinforce how slope and points affect a graph.

Rationale:** In this lesson, students will be able to determine what they have learned while doing it.The roof model will have an accompanying lab that poses the mathematical questions for building the roof. The students will complete the mathematics and hand the lab worksheet in to the teacher for feedback before beginning to build the model for a score which will be used as a summative assessment. Homework will be handed in to the teacher so that lessons can be modified to match the process and content gaps of students. This homework assignment will be unscored and students will have the opportunity to view the answers before handing in the piece. The students will have an ice-cream graphic organizer that they can use to gather the presented material in a segmented fashion as there are many techniques to in this section. Students will not hand these in, but will be able to call upon it later as study material. At the end of the lesson, the teacher will review valuable information that should be included. Students will write journal or blog entries that are reflective of their thoughts on the lesson. The teacher will check them at the end of the lesson to modify the lesson structure for future classes. Additionally, students will show the teacher what they have learned. In this lesson, the teacher will hand out a lab worksheet that will require students to build a model roof using slope specifications. The lab worksheet will have all the mathematics completed and the students will be required to build this model using a scale that converts values on the x and y axes into a measurable unit. They will also graph out what their roof should look like and figure out the equation of the line that is represented by each half of the structure. Additionally, the students will take a low-stakes quiz relating to the material covered in the lesson.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//

**__Teaching and Learning Sequence__** <span style="font-family: "Times New Roman","serif";"> For this lesson, the desks will begin divided into "tables" having 4 desks each so 4 students can sit at one "table."

Agenda:

Day 1

Students take their seats and pick a slope (5 minutes) Instructor passes back scored itineraries and hands out Ice Cream organizer (5 minutes) Hook: Musical Math. How are musical octaves like parallel lines? (5 minutes) Teacher reviews slope and introduces slope-intercept form of a line and point-slope form of a line (10 minutes) Students work independently or in table groups on practice problems while teacher walks around to give help and support (5 minutes) Teacher introduces standard form of a line and how it's different from the other forms (10 minutes) Students have additional practice problems to work on with teacher and classmate support (5 minutes) Teacher introduces finding the equation of a line given two points (10 minutes) Students work on practice problems in groups or independently with teacher and classmate support (5 minutes) Teacher introduces the Roof Model Lab (10 minutes) Students divide into their "slope groups" and have time to work on the lab. (10 minutes)

Day 2

Students take their seats with their "slope groups" (5 minutes) Teacher begins discussing graphing lines in point-slope and slope-intercept form (10 minutes) Students have time to work on their Roof Model Lab worksheet during this time, students can have the teacher check their answers before they can build (45 minutes) Teacher assigns the model to be done for homework once the mathematics are cleared and introduces the model building portion of the Roof Model Lab and the parameters and introduces the rubric (10 minutes) Students have time to plan their model. (10 minutes)

Day 3

Students take their seats (5 minutes) Students hand their Model Roof Lab worksheet and their model roof in to the teacher. (10 minutes) Teacher introduces parallel and perpendicular lines (15 minutes) Students have time to work on problems independently or in table groups (10 minutes) Teacher introduces horizontal and vertical lines and assigns homework (10 minutes) Students reinforce their knowledge of graphing using the online Line Plotter (20 minutes) Students take the lesson 3 quiz.

Students will understand that algebraic equations of one degree can be represented as lines.. **//Students understand how to solve families of equations and inequalities.//** This material is useful across the disciplines like art and carpentry. At the beginning of the lesson, the teacher will talk briefly about music relating to math. Since octaves of musical notes like high and low C are like parallel lines that contain points (0,1) and (0,8), there is a connection between lines and music. **Where, What, Why, Hook, Tailor: Musical, Intrapersonal**

Students will know about independent variable, dependent variable, graphing methods, slope intercept form, standard form, point slope form, parallel lines, perpendicular lines. During instruction, the teacher will pose questions to the students at the end of each subtopic giving them time to try problems within that subtopic before moving on to the next subtopic. Different kinds of learning will be targeted here, the material will be visible on the board, discussed mathematically, and spoken about. The teacher will reference the graphic organizer by discussing different [|forms of equations] and [|how to find them], in addition to how to work with [|parallel] and [|perpendicular] lines and how to graph using [|standard form] and [|slope-intercept form]. The teacher will assess understanding of the material using the quiz at the end of the lesson, the homework assignment to be handed out, and the summative Roof Model lab. This lesson revolves around introducing the students forms of equations, how to graph a line, and what to do with perpendicular and parallel lines. **Equip, Explore, Tailor: Visual, Verbal, Intrapersonal, Logical**

The students will begin by handing their Roof Model Lab worksheet to the teacher. The teacher will give feedback on them and the students will have the opportunity to rework it and make changes before they begin to build the model. The ice cream map will be used for students to put examples of many different methods of graphing and forms of equations. The teacher will go over what material would be good to be on it. This will not be collected, but can be used as a study guide for homework or any quizzes. Students will build a model roof using the parameters set forth in the Roof Model Lab worksheet. In addition, at the end of the lesson, students will take a low stakes quiz over the material from the lesson to be scored. Students will be divided into Quick-Play groups for this lesson. These Quick-Play groups will be determined by every student when walking in the class will receive a slope. The students who have matching slopes will be in a group for the assignment. The groups will be no more than 4 but no less than 2 for the project. The entire group will work together to figure out the equations of the lines of their roof consistent with the slope they were given. At the end of the lesson, students will be able to create the graph of a line. **Experience, Revise, Refine, Rethink, Tailor: Logical, Interpersonal**, **Visual**, **Bodily Kinesthetic**

At the end of instruction for the lesson, students will complete a limited number of homework assignments from the textbook for the course. The answers for these problems will be located in the back of the textbook. Students will also do blogs or journal entries reflecting on their experience with the lesson, what they liked and thought worked, in addition to what they didn't like and how they think the teacher can make modifications. These will be checked and commented on by the teacher nightly, if they are blogs. If they are paper journals, they will be collected daily and the teacher will read them and comment on them. If homework comes from the book, the teacher will be responsible to assign problems that have answers in the back of the textbook. The model roof will be built at home and scored on the Model Roof Lab Rubric. This will connect to future lessons because the information may be called upon. The project will have students reflect upon this information in a unique lens that they might not have considered. It may also connect to students who are interested in carpentry or other hands-on work. Students will use this material on future assessments. **Evaluate, Tailor: Verbal, Logical, Intrapersonal**


 * __Content Notes__**

[|Independent] and [|Dependent] variables.

In this lesson, they will be referred to as x and y respectively. An independent variable is one that is freely changing and has values picked for it when a table of values is made. The dependent variable yields values based on the values picked for the independent variable. Example: y = 3x - 1. Since values for x can be picked and values of y are determined based on the values of x, y is dependent and x is independent. Some examples of real world variables can be found [|here].

[|Slope intercept form of a line].

Most often referred to y = mx + b form, it is an equation that can be used to graph lines based on picking values for x and for y. Variables: m is the slope, (0,b) is the y-intercept. Graphing lines like this can either be done using slope or by putting values into a table. Example y = (2/3)x + 1. For this, the slope is 2/3 and the y-int is (0,1). Start at the y-intercept. Graph points based on slope. Since slope is (rise/run), from (0,1), the next point will go up 2 and right 3. Then from that point, move up 2 and right 3. Connecting those points gives the graph of the line. NOTE: in this form, y is ALWAYS solved for beforehand. 2x = 6y + 2 is NOT slope intercept form!!

[|Standard form of a line].

Most often referred to as Ax + By = C, it is an equation that uses the x and y intercepts to graph lines. Let x = 0 to find the y intercept. If x = 0, By = C, so y = (B/C), so the y-intercept is (0,B/C). To find the x-intercept, solve the equation for x when y = 0. So Ax = C, so x = (A/C). Thus the x-intercept is (A/C,0). Then connect the two intercepts and extend to have the graph of the line. NOTE: in this form A, B, and C are integers. Not fractions. (2/3)x - (1/2)y = 5 is NOT standard form. A, B, and C must also be relatively prime, so 3x + 9y = 12 is NOT standard form.

[|Parallel lines].

2 lines are parallel if their slopes are the same. y = mx + b is parallel to y = 5x - 1 if m = 5. They can differ in the y-intercept, but they must have the same slope. The y-intercepts will be determined by the point given in the original equation, but at all y-intercepts, the slopes must be the same. Graphing these lines is the same as any other line in y = mx + b form.

[|Perpendicular lines]

2 lines are perpendicular if their slopes are opposite reciprocals. So y = mx + b is perpendicular to y = 5x - 1 if m = (-1/5). The y-intercepts will be determined by the point given in the original equation, but at all y-intercepts, the slopes must be opposite reciprocals. Graphing these lines is the same as any other line in y = mx + b form.

[|Horizontal and vertical lines].

A line is horizontal if it's in the form y = b. This is so because in a horizontal line, all the y values are the same regardless of how we change x. Given y = 4. a table of x and y values shows (-1,4) (0,4) (1,4). Vertical lines are written as x = a. No matter what y we choose, the x will always be equal to a. So, (1,-1), (1,0), and (1,1) are points on x = 1.

Model Roof Lab worksheet Model Roof Lab rubric Lesson 3 Quiz Ice Cream Map
 * __Handouts__**