L6+O'Halloran,Erin+Marissa


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


 * Teacher’s Name: Ms. Erin O'Halloran** **Lesson: 6 (Empathy)**
 * Grade Level: 10** **Topic: Transformations of Polygons**

__**Objectives**__

 * Student will understand that** problems can be solved using geometric properties.
 * Student will know** translation, reflection, rotation, dilation, x-axis, y-axis, degrees, radians.
 * Student will be able to** imagine what a shape would look like after a transformation.

__**Maine Learning Results Alignment**__
//Maine Learning Results: Mathematics- C. Geometry// //Geometric Figures// //Grades 9 - Diploma// //Students justify statements about polygons and solve problems//


 * Rationale:** Once a students knows about transformations, they will be able to picture rotations, dilations, and translations of polygons. This will ensure that students will learn all the properties of polygons.

__**Assessment**__
Students will be able to make graphic organizers in class that will reflect how they organize important information. Using the Cluster/Web graphic organizer, students will be able to categorize the transformations. Once students have categorized the transformations and they have had practice problems to work on in their groups, students will be given a quiz. The quiz will not be graded, but it will indicate whether or not students are ready for the summative assessment.
 * Formative (Assessment for Learning)**

Students will create a Geogebra file that shows polygons before and after certain transformations. There are transformation functions on the Geogebra program, but students will have to manually translate, rotate, dilate, or any combination of the transformation. Students will be given a handout with the polygons and the transformation needed to be performed on it. The original polygon and the final polygon should be represented in the file. Students will work on this individually- they cannot collaborate with other students. The project is worth 10% of students' grades and will be graded out of 100 points with a checklist.
 * Summative (Assessment of Learning)**

__**Integration**__

 * Technology**: Students will find all that they need in the Geogebra program. They will not need to use Paint or pictures from the internet to create the images of the polygons. Students will need to know how to show labels, however, using the Geogebra settings. It is important to label the points and polygons so that the final transformation is clear. It is also important to use Check Boxes in the file so that problems can be easily viewed by the teacher. All of these features will be discussed during class time.


 * Engineering**: It is extremely important for machines to function with the use of transformations. In Mechanical Engineering, machines do things that humans can't such as melt metal, shave metal, etc. It is important for the machine to know how far to translate the tool so that the engineer gets exactly what he or she wants. Most movements are based off of axises: the x, y, and z axis.

__Groupings__
The RoundRobin Brainstorming grouping will be applied to the class. Groups of 4 to 6 students will be formed and they will have to answer a question presented in class. Each member will do the problem separately and then once the "think time" has ended, they will share their answers or ideas with the rest of the group. A recorded in the group will write down everyone's answers and compare them to see if everyone in the group understands the problem. The job of the recorder will change each question.

__**Differentiated Instruction**__

 * Strategies:**
 * Logical:** Assign numbers or coordinates to the polygons. This way, it might be easier to visualize the transformations based on a scale. It would also be easier to determine which side of the new transformation collaborates with the original polygon.
 * Spatial:** Color coordinate the transformations so it is easier to follow. Label each polygons similarly like ABC and A'B'C' so that it does not confuse the reader. Using color and different style lines will help the students and the reader identify which is the original and which is the new transformation.
 * Interpersonal:** Students cannot work on the problems in the project together, but they can certainly collaborate with other students if they are not clear on the assignment or the process. Geogebra can be a tricky program so they can also ask for help if they are unclear about a certain tool.
 * Intrapersonal:** The project itself is interpersonal because students will be doing the final project themselves. They will each have to create separate file and then will upload them to the class wiki.
 * Linguistic:** Before putting the polygons and transformations on the Geogebra file, draw out the polygons and then the transformations. This way, students can compare the ones in the file to the ones students have drawn.
 * Bodily:** Show transformations of human shapes. Like move from one side of the room to another for translation, shrink to knees for dilation, etc.

**Absent:** If students are absent, then they will need to get the notes listing the transformations from another student in the class. Should the absent student have a question, they can email the teacher and set up an appointment. If the student is absent during the explanation of the project, they should schedule a meeting with the teacher for a quick tutorial on Geogebra. Because this assignment will not be presented in class, an extension could be made for the absent student.
 * Modifications/Accommodations**

**Extensions:** Students will be able to perform more than one transformation on a polygon. For example they could do a glide transformation which includes a translation and dilation. Students can further expand on the fact that there are certain transformations that will undo the previous transformation. Which transformation relate to each other in a way that they send the image to its original state? How would students represent and test that theory?

__Materials, Resources and Technology__

 * LCD Projector
 * Computer to show software and slides
 * Text book
 * Hand outs
 * Graphic organizer
 * Web that lists the transformations and the properties of the transformation
 * Checklist
 * Geogebra Tutorial

__Source for Lesson Plan and Research__
Translations: [] ; dilation, reflection, rotation, and translation Slide show: [] ; shows examples of dilation, reflection, rotation, and translation Axis: [] ; shows the x any y axis, and even goes into the third dimension Degrees and Radians: [] ; shows the difference between degrees and radians and how to convert from one to the other

__**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 have the liberty to style the the Geogebra file. It is advised that students make the new transformation different from the original polygon. They can do this by changing the lines, colors, labels, etc. Students will learn how to do this from a short tutorial in class.
 * Clipboard:** Students will have a hand out that fully explains the problem and which transformation to do. They will need to use the Check Box option Geogebra has in order to hid other problems from being shown. Because the hand out is essentially the checklist they will be graded with, if students follow the instructions carefully, then they will gain the knowledge needed to receive a good grade.
 * Microscope:** Students will have the option as a bonus to undo a transformation. This is better detailed in the Extensions section. By doing the bonus, students will be focusing in details and analyzing concepts.
 * Puppy:** Students will have time to work on this project in class so they will be able to ask the teacher questions. They will also be able to ask the teacher about how to create graphics.

Refer to content notes. // Students will be able to imagine what a shape would look like after a transformation. // It might be hard for some students to see a specific transformation before preforming it. It is important for students to be able to do this because they need to make sure they are doing the transformation properly. In order to picture the transformation, students need to practice the process and see many examples. By doing the process step-by-step it should be easier to picture the specific transformation. This is an example of empathy in a way that the students need to see the transformations before actually performing them.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * Rationale:**


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

**Logical:** Assign numbers or coordinates to the polygons. This way, it might be easier to visualize the transformations based on a scale. It would also be easier to determine which side of the new transformation collaborates with the original polygon. **Spatial:** Color coordinate the transformations so it is easier to follow. Label each polygons similarly like ABC and A'B'C' so that it does not confuse the reader. Using color and different style lines will help the students and the reader identify which is the original and which is the new transformation. **Interpersonal:** Students cannot work on the problems in the project together, but they can certainly collaborate with other students if they are not clear on the assignment or the process. Geogebra can be a tricky program so they can also ask for help if they are unclear about a certain tool. **Intrapersonal:** The project itself is interpersonal because students will be doing the final project themselves. They will each have to create separate file and then will upload them to the class wiki. **Linguistic:** Before putting the polygons and transformations on the Geogebra file, draw out the polygons and then the transformations. This way, students can compare the ones in the file to the ones students have drawn. **Bodily:** Show transformations of human shapes. Like move from one side of the room to another for translation, shrink to knees for dilation, etc.


 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * Rationale:** Using both the formative and summative assessments assigned for this lesson, the teacher can determine if the students fully understand the different polygons and their properties. Because the formative and summative assessments are using two different sides of the brain, students with different learning styles will be able to learn the way they want to.

**Formative (Assessment for Learning)** Students will be able to make graphic organizers in class that will reflect how they organize important information. Using the Cluster/Web graphic organizer, students will be able to categorize the transformations. Once students have categorized the transformations and they have had practice problems to work on in their groups, students will be given a quiz. The quiz will not be graded, but it will indicate whether or not students are ready for the summative assessment.

**Summative (Assessment of Learning)** Students will create a Geogebra file that shows polygons before and after certain transformations. There are transformation functions on the Geogebra program, but students will have to manually translate, rotate, dilate, or any combination of the transformation. Students will be given a handout with the polygons and the transformation needed to be performed on it. The original polygon and the final polygon should be represented in the file. Students will work on this individually- they cannot collaborate with other students. The project is worth 10% of students' grades and will be graded out of 100 points with a checklist.

__Teaching and Learning Sequence__
For classroom arrangement, I will have students sit in a perimeter so they everyone can see the screen without other peoples' heads in the way. It is vital to see which polygon is being discussed during the lecture to minimize confusion. The notes for my class will be displayed from a computer using an LCD projector.

Day 1: translation, reflection, rotation, dilation, x-axis, y-axis, degrees, radians.

Introduce x and y axis (5 minutes) Introduce degrees and radians and how to convert them from one to the other (10 minutes) Introduce translations (10 minutes) Introduce reflection (10 minutes) Introduce rotation (10 minutes) Introduce dilation (10 minutes) Break (5 minutes) RoundRobin Brainstorming exercise (20 minutes)

HOMEWORK: Work on graphic organizers alone.

Day 2: Ungraded quiz on the transformations (20 minutes) Go over Geogebra assignment and have students work on it in class (60 minutes)

Students will understand that problems can be solved using geometric properties. **//Students justify statements about polygons and solve problems//.** It is important to know about translations because they are used in many engineering professions. Machines are programmed to know transformations because they need to perform tasks that others cannot. To get students interested in the topic, the will be shown a video of a series called [|Orbit High]. This episode takes place in the future where they show examples of several transformations such as translation and rotation. After the hook, students will have to map out how they are using transformations just by walking, turning around, etc. **Where, Why, What, Hook Tailors: Visual, Kinesthetics, Interpersonal, Intrapersonal**

Student will know translation, reflection, rotation, dilation, x-axis, y-axis, degrees, radians. They will organize these terms using a Word/Cluster Web graphic organizer. Unlike the other lessons in this unit, students will complete these graphic organizers themselves. They should have the ability to identify important terms and procedures on their own at this point in the unit. The teacher will check for understanding by giving them an ungraded quiz. This way, the teacher can determine whether or not students understand the material or how to identify important details about the lesson. **Equip, Explore, Rethink, Revise, Tailors: Linguistic, Intrapersonal**

In the final assignment, there will be an bonus where students get to analyze the idea of transformations and make general ideas. Students will be able to imagine what a shape would look like after a transformation. The RoundRobin Brainstorming grouping will be applied to the class. Groups of 4 to 6 students will be formed and they will have to answer a question presented in class. Each member will do the problem separately and then once the "think time" has ended, they will share their answers or ideas with the rest of the group. A recorded in the group will write down everyone's answers and compare them to see if everyone in the group understands the problem. The job of the recorder will change each question.**Explore, Experience, Revise, Refine, Tailors: Visual, Linguistic, Interpersonal, Intrapersonal, Logical**

Students will be given feedback on both the quiz and the final Geogebra product. The grade will reflect on what they have learned and how they represented their work. Because this is one assignment where students are not allowed to work together, they will have to fill out an evaluation form for themselves on how comfortable they felt with the topic. They will also evaluate themselves on the time management tactic they used to complete the project, seeing as though they didn't rely on other people to finish some of the work for them. **Evaluate, Tailors: Intrapersonal, Linguistic**


 * Content Notes**

 **The -axis is the horizontal axis of a two-dimensional plot in [|Cartesian coordinates] that is conventionally oriented to point to the right (left figure). In three dimensions, the -, -, and are usually arranged so as to form a [|right-handed coordinate system] .** **Physicists and astronomers sometimes call this axis the [|abscissa], although that term is more commonly used to refer to coordinates along the -axis.**

Converting radians to degrees:
To convert radians to degrees, we make use of the fact that p radians equals one half circle, or 180º. This means that if we divide radians by p, the answer is the number of half circles. Multiplying this by 180º will tell us the answer in degrees. So, to convert radians to degrees, multiply by 180/ p, like this:

Converting degrees to radians:
To convert degrees to radians, first find the number of half circles in the answer by dividing by 180 º. But each half circle equals p radians, so multiply the number of half circles by p. So, to convert degrees to radians, multiply by p/180, like this:


 * ==Transformations == ||

Triangle //ABC// and its **reflection** //A'B'C'// have the same size and shape, that is they are [|congruent]. === ===
 * [|Plane] figures and solids can be changed (or transformed) by [|translation], [|reflection] and [|dilation]. The symmetry of shapes is related to translation, reflection and [|rotation].=== Reflection ===

<span style="color: #fb0000; font-family: 'Times New Roman'; font-size: 16pt; font-style: normal; font-weight: normal;"> Translation
A **translation** is defined by specifying the distance and the direction of a movement. For example, triangle //ABC// is translated by 2 units to the right. Triangle //ABC// and its image //A'B'C'// have the same size and shape. That is, they are [|congruent].

<span style="color: #fb0000; font-family: 'Times New Roman'; font-size: 16pt; font-style: normal; font-weight: normal;"> Rotation
Triangle //ABC// and its image //A'B'C'// have the same size and shape, that is they are [|congruent].
 * Rotation** is defined by stating the centre of rotation, amount of turning in degrees and the direction of rotation (clockwise or anticlockwise). For example, triangle //ABC// is rotated about //O// through 90º in an anticlockwise direction.

**We notice that:**
The [|reflection], [|translation] and [|rotation] are **congruent transformations**.

<span style="color: #fb0000; font-family: 'Times New Roman'; font-size: 16pt; font-style: normal; font-weight: normal;"> Dilation
If a figure is enlarged or reduced and retains its shape, then it is said to be **dilated**. This is an aspect of **similarity** as shown below. Note that the stretching (or shrinking) of a shape is called a **dilation**. It is clear that dilation is not a [|congruent] transformation, because the size of the shape is changed.

**In general:**

 * Lengths and areas are not preserved under dilation.
 * If the dilation factor is the same for each side of the figure, then the figures are similar.

**Key Terms**
[|transformation], [|reflection], [|translation], [|rotation], [|centre of rotation], [|amount of turning], [|direction of rotation], [|dilation], [|dilated], [|similarity] ||


 * Handouts**
 * Hand outs **
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Graphic organizer
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Web that lists the transformations and the properties of the transformation
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Checklist
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Geogebra Tutorial