L1+Bowden,+Scott


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

**LESSON PLAN FORMAT**


 * __Teacher’s Name__****:** Mr. Bowden **__Date of Lesson__:** Interpret
 * __Grade Level__****: 9** **__Topic__:** Coordinate Plane and Ordered Pairs


 * __Objectives__**
 * Student will understand that** the coordinate plane relates to ordered values in space.
 * Student will know** coordinate plane, ordered pairs, the x and y axes, slope, the slope formula, midpoints.
 * Student will be able to** illustrate the location of a point based on its ordered pair.


 * __Maine Learning Results Alignment__**

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


 * Rationale:** In this lesson, the teacher will explain aspects such as the coordinate plane, ordered pairs, the x and y axes, slopes, and midpoints to prepare the students to graph lines and solve equations and inequalities which are part of the Maine learning result.


 * __Assessment__**


 * Formative (Assessment for Learning):** Google Earth worksheet will be handed in to the teacher who will give students feedback, the students will continue to refine the worksheet and correct errors before handing it in 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. Students have a spider map (hyperlink) graphic organizer that they can use to gather the presented material. 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.


 * Summative (Assessment of Learning):** The teacher will give a worksheet to examine proficiency using Google Earth to determine points on the globe by Latitude and Longitude values. This worksheet will be two-fold, the first part will involve the students using Google Earth to find latitude and longitude points of specific cities, locations, and landmarks. The second will be how they can relate them to the subject matter and that the world can be talked about like a large coordinate plane. Students will also complete a low-stakes quiz at the end of the lesson. This quiz will encompass all the materials learned throughout the lesson.


 * __Integration__**
 * Technology:** Students will use the program Google Earth to determine ordered pairs of cities, landmarks, etc using the Latitude and Longitude lines on the globe.

Geography: Students use Google Earth to explore the surface of the Earth and using the concepts of latitude and longitude for their worksheet.
 * Other Content Areas:**

Students will be divided into groups and each member will get a number 1 to 3 or 1 to 4. After 2-3 minutes to consider and discuss answers, each group will have one member respond based on a random number draw. Students will be randomly divided by numbers the students drew at some point during the class. Depending on how large each group needs to be, the random numbers will be from 1-4 or 1-5. Each student will complete a role. One student will be the "reporting out" person and that will be picked randomly, the other members will discuss and consider ideas for the question posed by the teacher.
 * __Groupings__**


 * __Differentiated Instruction__**


 * Strategies:**
 * Kinesthetic**: Have floor represent a coordinate plane. Students will stand on specific "points" as directed by the teacher.
 * Interpersonal**: Students will work in small groups during the Google Earth activity.
 * Verbal**: Class discussion about material and discussing answers in the cooperative learning.
 * Visual**: Students use pictures to illustrate points and the coordinate plane.
 * Logical**: Use the coordinate plane to determine where the points are on it.
 * Intrapersonal**: Students will individually consider answers during cooperative learning and on their Google Earth Worksheet.

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. Students will also need to contact the teacher to make arrangements to use the Google Earth software if they don't have access to the software or internet at home. The teacher and the student will work out when the project is to be completed.

Students will use the program Google Earth to determine ordered pairs of cities, landmarks, etc using the Latitude and Longitude lines on the globe and then be challenged to do the same with a world map and atlas where the numbers aren't given exactly, but will be indicated somewhere and it will be up to the student to make an estimate.
 * Extensions**

Laptops/Computers for students that have Google Earth on them Teacher computer Projector/TV Screen for the computer Google Earth Worksheet. Graphing Calculators for students who don't already have them. Stuff to write on the whiteboard/chalkboard with Graphic Organizers - Spiderweb. Duct tape to make axes on the floor Pre-Assessment tests KWL charts for unit Textbook and teacher notes Quiz Graph Paper for student work on graphing Some kind of food
 * __Materials, Resources and Technology__**

This site by education world shows where the hook originates from: [] A graph paper making site: [] A short mini-lesson and discussion on coordinate planes and points: [] Purple Math's discussion of midpoints and the midpoint formula: [] Purple Math's discussion of slope and the slope formula: [] This is an explanation of using latitude and longitude on Google Earth: [] This is a written explanation of marking locations on Google Earth: [] Here is the template for the KWL Chart: [] Here is the template for the Spider Chart: []
 * __Source for Lesson Plan and Research__**


 * __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:** Beach Ball: Students will have the flexibility to work either alone or with others during the Google Earth activity. Additionally, they will be able to go beyond what is expected of them by thinking about the activity by using other methods, like a flat map or an atlas. Clipboard: Students will be instructed and discussions will ensue. Everything discussed in class will be available to read on the wiki or from their own notes and graphic organizer. Microscope: Students will use the Google Earth activity to think about the material in a different way and have the chance to play with it on their own. Those students can use the human geometry exercise to act out their learning. Puppy: Students have the right to give answers and ask questions. The teacher and others will be open to listening and learning and teaching one another in a non-judgmental way. The teacher and other students will offer advice when needed.


 * Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.**
 * Rationale:** This lesson was based around the fact that students will understand different facets of the coordinate plane and use them. This was brought in when the students were asked to perform different tasks based around ordered pairs using a real example, the planet Earth using the software Google Earth. This lesson acts as a precursor to students being able to solve families of equations as discussed in the Maine Learning Result for this unit. Students are learning the concepts relating to slopes, points, midpoints, and the coordinate plane. Upon completing this lesson, students will be able to identify a point on a plane based on it's ordered pair and identify the ordered pair for a point on the plane.


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


 * Kinesthetic**: Have floor represent a coordinate plane. Students will stand on specific "points" as directed by the teacher.
 * Interpersonal**: Students will work in small groups during the Google Earth activity.
 * Verbal**: Class discussion about material and discussing answers in the cooperative learning.
 * Visual**: Students use pictures to illustrate points and the coordinate plane.
 * Logical**: Use the coordinate plane to determine where the points are on it.
 * Intrapersonal**: Students will individually consider answers during cooperative learning and on their Google Earth Worksheet.

Technology will be used in the following way in this lesson: Students will use the program Google Earth to determine ordered pairs of cities, landmarks, etc using the Latitude and Longitude lines on the globe.


 * Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.**
 * Rationale:** Students will be assessed in class both formatively, as non-scored pieces of work in addition to summatively, pieces that are scored as benchmarks for student achievement. Students will be assessed formatively in the following ways. Students will complete a Google Earth worksheet to be handed in to the teacher who will give students feedback, the students will continue to refine the worksheet and correct errors before handing it in 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. Students have a spider map (hyperlink) graphic organizer that they can use to gather the presented material. 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. Students will be assessed summatively in the following ways. The teacher will give a worksheet to examine proficiency using Google Earth to determine points on the globe by Latitude and Longitude values. This worksheet will be two-fold, the first part will involve the students using Google Earth to find latitude and longitude points of specific cities, locations, and landmarks. The second will be how they can relate them to the subject matter and that the world can be talked about like a large coordinate plane. Students will also complete a low-stakes quiz at the end of the lesson. This quiz will encompass all the materials learned throughout the lesson.


 * __Teaching and Learning Sequence__****:**

The classroom will be set up in the perimeter format with the tables facing the center of the classroom. The floor will be divided into quadrants before the class begins. The desks will be the endpoint of the quadrants.

Day 1: Students will take their seats (3 minutes) The class begins by taking a pre-test of the unit material. (15 minutes) The teacher will present the syllabus for the unit (7 minutes) The teacher will divide the class into pairs by their table group and discuss the Battleship game. (10 minutes) Students will play the Battleship game. While this is going on, teacher will score the pre-tests and hand out the unit KWL chart. (15 minutes) Teacher will begin discussing the coordinate plane and ordered pairs. Students will record the information on their spider map. (10 minutes) Students will play Human Geometry - a reinforcement game for ordered pairs. (10 minutes) Teacher will begin discussing midpoints and slopes. Students will continue to record on their spider map. The teacher will assign homework at this point. (10 minutes)

Total - 80 minutes

Day 2: Students will take their seats and a random number from the teacher. (3 minutes) The teacher will hand back the pre-test from the last class and collect and homework from the night before (4 minutes) The teacher will continue discussing or review any information from the previous class (10 minutes) After discussion, students will get into their Quick-Play groups (as discussed below) (3 minutes) At this point, the teacher will pose review questions to the groups. Groups will have 2-3 minutes per question to think of an answer. The teacher will then call one student number which was given/picked by each student in each group before the activity, and the student from each group with that number will will give their response. If all groups don't agree on an answer, the students will discuss with teacher facilitation if needed until a concensus is found (15 minutes). Students will begin working on their Google Earth worksheet. The teacher will explain the assignment. (5 minutes) The students will work on Google Earth for the worksheet question answers. They may work individually or in pairs at their tables. The teacher will be available to help any student. Students may hand in their worksheet to the teacher during this time. The teacher will check it and the student will be able to make any modifications and resubmit for a score. Also, in this period, anyone who finishes early will be able to complete the extension listed above. Any worksheets not turned in for score during the period can be brought home for homework. (25 minutes) The teacher will assign any homework. The students will work on a quiz for the remainder of the period which will be scored. (15 minutes)

Students will understand that the coordinate plane relates to ordered values in space. **Students understand how to solve families of equations and inequalities.** This material is useful across the disciplines like geography. At the beginning of the lesson, students will play a variation of Battleship to experience introductions to the coordinate plane. Each student will divide their paper in half and draw a 10 by 10 grid and set "ships" within the spaces of the grid. They will then attempt to guess each other's ship locations. The teacher, afterwards, will discuss how Battleship is a game that works with using ordered pairs on a graph but instead of B8, they are named (x,y). This game will be played in pairs. **Where, What, Why, Hook, Tailor: Intrapersonal, Interpersonal**, **Logical**, **Visual**

Students will know about the coordinate plane, ordered pairs, the x and y axes, slope, the slope formula, midpoints. During instruction, the teacher will pose questions to the students at the end of each 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. Th e teacher will reference the graphic organizer using the central topic in the center with each arm being dedicated to the four individual subtopics: the [|coordinate plane, ordered pairs], [|midpoint], and [|slope]. 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 Google Earth project. This lesson revolves around introducing the students to the Cartesian Coordinate Plane, how to graph ordered pairs, what the slope of a line is and how to find it, and how to find the midpoint of any two given points. **Equip, Explore, Tailor: Visual, Verbal, Intrapersonal, Logical**

Students will hand in Google Earth worksheet to be looked at by the teacher. The teacher will hand it back with feedback for students to modify. Students will make changes and retool the worksheet for an official score. Students will also work on information on their spider map. At the end of the lesson, they will modify their spider map based on the suggestions of the teacher. The students can use these modifications to study for later and call upon them when needed. During in-class problem solving, students will be divided into groups and each member will get a number 1 to 3 or 1 to 4. These are called Quick-Play groups and are only in place for this activity After 2-3 minutes to consider and discuss answers, each group will have one member respond based on a random number draw. Students will be randomly divided by numbers the students drew at some point during the class. Depending on how large each group needs to be, the random numbers will be from 1-4 or 1-5. In these groups, one student will be the "reporting out" person and that will be picked randomly, the other members will discuss and consider ideas for the question posed by the teacher. To reinforce the material, students will play "Human Geometry," a game devised by the teacher where the students will in turn go to the point named by the teacher. Students will be able to illustrate the location of a point based on its ordered pair. Students will receive a score on their Google Earth worksheet after having feedback by the teacher. They will also be taking a low-stakes scored quiz at the beginning of the second class. **Experience, Rethink, Revise, Refine, Tailor: Interpersonal, Logical, Verbal**, **Bodily-Kinesthetic**

At the end of instruction and discussion for the lesson, students will complete a limited number of homework problems from their textbook. These problems will be left unscored by the teacher, and merely checked for completion. Students will also be responsible for journal or blog entries at the end of each lesson describing what they have learned, how they might use it, and what they feel the teacher has done inadequately or how the teacher could improve. These will also contain the positive aspects of the lesson in the minds of the students. To provide feedback, the teacher will check blog entries on a daily basis, and if the journals are submitted on paper, feedback will be available by the next class period. If homework is assigned from the textbook, it will be the responsibility of the teacher to ensure that the problems required have answers in the back of the book. If the homework takes the form of a worksheet, the teacher will provide the correct answers on their class wikispace page. This will connect to the next lesson because every lesson builds upon the last. The next lesson integrates techniques and ideas that require the knowledge of the ideas presented in this lesson. This will connect to future assessments for the same reason. Since this material builds and goes in succession, students will need to know this information in order to be successful in later lessons and assessments. **Evaluate, Tailor: Intrapersonal**, **Verbal, Logical**

[|The coordinate plane.] The coordinate plane is a set of conjoined number lines that can be used to represent locations in space. This is similar to a regular number line, with the difference that now travel in either direction, the x-axis for traveling horizontally and the y-axis for traveling vertically, can be achieved. These locations in space are known as ordered pairs.
 * __Content Notes__**

Ordered pairs These are points mapped out on a coordinate plane. An ordered pair is found by traveling in the x direction, then in the y direction. This need not be on the x or y axes, but along their direction. All mapping starts at the center of the axes, a point called the origin, and moving in the x and y directions to the point. For example, the point (3,4) would require moving 3 in the positive x direction (to the right) from the origin and then moving 4 in the positive y direction (up) from the origin. A point of (5,-3) would be mapped by traveling 5 in the positive x direction from the origin and then 3 in the negative y direction (down) from the origin. The point (-7,6) would be mapped by traveling 7 in the negative x direction (to the left) from the origin and then 6 in the positive y direction from the origin. The point (-1,-2) would require traveling 1 in the negative x direction from the origin and then traveling 2 in the negative y direction from the origin. For ease, we denote the origin as the point (0,0) since we travel nowhere in the x direction to get to it and nowhere in the y direction to get to it.

[|Midpoints] The midpoint of two points is exactly that, the middle point. The midpoint of two points is used when the intent is to know exactly what point lays in the middle of them. Consider the points (3,1) and (5, 7). (3,1) is mapped by going to the right 3 and then up 1 from the origin. (5,7) is mapped by going to the right 5 and up 7 from the origin. Now the point that lies in the middle is very simply found. First, the x-value that lies between them is found by adding the two x-values together and dividing by 2. So, it is (3+5)/2 = 8/2 = 4. Then the y-value that lies in the middle is found by adding the two y-values together and dividing that by 2. So, it's (1+7)/2 = 8/2 = 4. So, the midpoint of these two points is (4,4). In another example, finding the midpoint of (-11,8) and (15,-12). First, the x-values are added together and divided by 2, so (-11+15)/2 = 4/2 = 2. Then the same is done with the y-values, so (8+-12)/2 = -4/2 = -2. So the midpoint is (2,-2). In general, any midpoint can be found by this formula: Mdpt = ((x-a)/2, (y-b)/2) where two points (x,y) and (a,b) are given.

[|Slope.] The slope represents how steep a line that goes through two points would be. Consider the points (11,7) and (3,-1). The first is found by traveling 11 to the right and 7 up from the origin. The second is found by traveling 3 to the right and 1 down from the origin. Now to find the slope, the change in x and change in y values must be found. These may be found by subtracting the x and y values of each point. But stay consistent. If one point is selected for (x,y) and the other (a,b), then don't switch them before hand. In this case, (11,7) will be (x,y) and (3,-1) will be (a,b). Now the difference in x-values is determined, so 11 - 3 = 8. Then the difference in the y-values is determined, so 7 - (-1) = 8. Now, to find slope, consider the old phrase: rise over run. This means that slope is the y-value distance "rise" from one slope to the other divided by the x-value difference "run". So, the slope will be the "rise" of 8 divided by the "run" of 8 for 8/8 = 1. Now, if the order of subtraction changed, that wouldn't change the slope. So, if (3,-1) was (x,y) and (11,7) was (a,b), it makes no difference for the new "rise" will be -1 - 7 = -8 and the new "run" is 3 - 11 = -8. So the slope is -8/-8 which still equals 1.

[|Google Earth.] The tutorial listed above will discuss how to use latitude and longitude on Google Earth. Students will watch this before starting the worksheet. The teacher will be available to answer questions that the students may have. Students can find the coordinates by either mousing over the point on the map or by clicking the button that looks like a thumbtack with a + on it. This will add a place-mark. They will have the best results if they start by searching using the "fly to" tab in the search panel which is off to the left hand side. They can select the placemark button and put their placemark on the result and that will tell them the exact latitude and longitude of the points. If in the "fly to" tab, they input a latitude and longitude value, Google Earth will travel to it automatically. The [|marking] values are to be entered like this 18 15'16" N 19 21'23" W.

Pre-test Graphic Organizer KWL charts Graph Paper Quiz Google Earth Worksheet
 * __Handouts__**