L1+O'Halloran,Erin+Marissa


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


 * Teacher’s Name:** Ms. O'Halloran **Lesson 1:** Self-Knowledge
 * Grade Level:** 10 **Topic:** Shapes and sizes of polygons

__**Objectives**__
Student will understand that measurements are based on shape and size. Student will know properties of right triangles, triangles, squares, rectangles, parallelograms, trapezoids, circles, rhombi, cubes, regular prisms, irregular prisms, cylinders, pyramids, cones, and spheres. Student will be able to do recognize measurements of objects and their names.

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


 * Rationale:** By classifying polygons by name and measurement, we can later determine the properties that will help solve problems.

__**Assessment**__
Making the Cluster/Word Web 3 for the Glogster poster for each shape to make sure they have all the elements. Which elements are based on other elements? Have teacher collect the Web and see if students truly understand the shapes and its properties. Teacher will pass back the Web with notes identifying if they have truly understood the properties of the five polygons the students have selected.
 * Formative (Assessment for Learning)**

Students will create a Glogster web page about shapes and their properties. This is meant to get the students' creative juices flowing. Individually, students will create a web page on Glogster defining the polygons mentioned during the lesson and all of its properties. Throughout the lesson, polygons and their properties will be mentioned and discussed. Students will be given a number 1-3. That number determines which group of 5 polygons they will have to present on their Glogster. Use all the features Glogster offers to make the website memorable. Students will need to include all of the properties of the polygons they choose to represent. All the links of the Glogsters will be added to the class wiki so students can be displayed. The grade will be determined out of 100 points. This assignment is worth 10% of the student's final grade.
 * Summative (Assessment of Learning)**

__**Integration**__

 * Technology**: Glogster will be used to display polygons in a way where they will remember key terms and properties such as congruent sides, congruent angles, right angles. perpendicular sides, and parallel sides. In order to make the shapes, students will use Geogebra, Geometer's Sketch Pad, or Paint to create the shapes digitally.


 * Art**: Students will learn about art with the different types of polygons in famous works of art. Find artists who use geometric shapes in their works and discuss what the students found in their research. These works of art can be sculptures, paintings, installments, etc.

__Groupings__
Students will be split up into groups of four or six and they will use the Think-Pair-Share strategy. The strategy involves a three step cooperative structure. During the first step individuals think silently about a what they want to include on their Glogster website. Individuals pair up during the second step and exchange thoughts to compare and contrast what they think is important to include in the final product. In the third step, the pairs share their responses to the entire group.

__**Differentiated Instruction**__

 * Strategies**
 * Linguistic**: Have students present project and write out a script about the properties of the shapes and how they are going to represent the information. The Web could be assigned as homework, graded, and handed back so that students have clear guidelines as to how they are going to make their Glogster.
 * Intrapersonal**: Have students choose the format of the poster using what they have learned to correctly space out the poster.
 * Interpersonal**: Students can work in a group to discuss format and which shapes they want to focus on. After students have had time to look through the features of Glogster on their own, have them discuss their plan or theme of the site they are going to make. Brainstorming about ideas can really help someone stuck. Also, new features could be brought up that one student did not know about until they talked in the group.
 * Bodily/Kinesthetics**: Students can use their bodies to make the shapes displayed on the poster. Have students take pictures of themselves as the shapes they are displaying. In groups, create a square, circle, parallelogram, etc. using their hands, feet, and bodies instead of creating them in Geogebra or finding a picture of the polygon online.
 * Musical**: Have students find a song that lists the shapes and properties and incorporate that into the Glogster by adding audio.
 * Spatial**: Put all of the finished Glogsters on the class wiki. Because there are 15 polygons being discussed in the lesson and the students get to choose 5, they will only master understanding the properties of a third of the polygons presented in the lesson. Since the rest of the Glogsters will have the 10 other polygons they need to know, they can refer to their classmate's sites to learn about the other polygons.

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


 * Absent:** If students are absent, then they will need to get the notes listing the polygons and their properties from another student in the class. Should the absent student have a question, they can email the teacher and set up an appointment. If student is absent when the numbers (1-3) determining which polygons they have to represent are given out, then they will email receive an email saying which of the 15 polygons they will need to represent.


 * Extensions:** Glogster will be used to design the different types of polygons and display them in a way where they will remember key terms. In order to make the shapes, students will use Geogebra, Geometer's Sketch Pad, or Paint to create the shapes digitally. Where can the students find real life examples of these shapes? Have students become so familiar with their surroundings and environments that they do not recognize polygons all around them? Just sitting where you are, how many different polygons can you name looking around? Using this [|website], students can explore the world of fractals and how polygons relate to recursive functions.

__**Materials, Resources and Technology**__

 * LCD Projector
 * Computer to show software and slides
 * Text book
 * Hand outs
 * Graphic organizer
 * Web that lists the polygons and students have to list the properties of that polygon
 * Rubric

__Source for Lesson Plan and Research__
Graphic Organizer: [|Word/Cluster Web 3] where students will classify the properties of certain polygons. Cooperative Learning: [|Think-Pair-Share]

[|Properties of regular and irregular prisms];cross sections, examples of regular and irregular prisms [|Properties of polygons]; parts of polygons, convex, concave, names. [|Properties of right triangles]; trigonometric angles [|Properties of triangles]; this site explains interior angles of a triangle, relationship between side length and angles, and triangle inequality theorem. [|Properties of quadrilaterals]; this site includes the properties of squares, rectangles, rhombus, trapezoid, parallelogram. [|Properties of circles] circumference, origin, radius, center, chord, arc [|Properties of cylinders] properties, volumes, area, and surface area [|Properties of cones]; bases, sides, volume, area, surface area [|Properties of spheres]; symmetry, examples, volume, area, balloon example

__**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 can use whatever resources they want related to Glogsters. They can add audio, pictures, examples of he polygons in real life. They can choose how to create the polygons in which program they want to use to create them.
 * Clipboard**: Having students create the Web with the polygons and their properties will create structure and direction to the project.
 * Microscope**: The expectations of this project is very clear that this Glogster will be used as a resource throughout the unit. The teacher should expect students to be very creative with all the features of Glogster.
 * Puppy**: Students will get to explain their ideas of the theme of their Glogster with the rest of their Think-Pair-Share group. This will create a safe environment where the students can share their ideas and give feedback.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter//****//, students, curriculum goals//****//, and learning and development theory.//**
 * Rationale:** Refer to the content notes. //Students will be able to recognize measurements of objects and their names.// In this lesson, students will learn a basic list of polygons and their properties. At the end of the lesson, students will be able to identify congruent angles, congruent sides, parallel sides, perpendicular sides, and right angles using the fact of self-knowledge. Because this content is legitimately memorizing, students will have covered a broad array of strategies that could help them determine what assists them in memorization. Using the Web will help students who need to recopy their notes to fully understand. Displaying the content in a creative way can also help students remember easily. Depending on the student's thought process, students will be able to determine after this lesson how they are going to learn to understand the material in the rest of the unit.


 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**
 * Rationale:**
 * Linguistic**: Have students present project and write out a script about the properties of the shapes and how they are going to represent the information. The Web could be assigned as homework, graded, and handed back so that students have clear guidelines as to how they are going to make their Glogster.
 * Intrapersonal**: Have students choose the format of the poster using what they have learned to correctly space out the poster.
 * Interpersonal**: Students can work in a group to discuss format and which shapes they want to focus on. After students have had time to look through the features of Glogster on their own, have them discuss their plan or theme of the site they are going to make. Brainstorming about ideas can really help someone stuck. Also, new features could be brought up that one student did not know about until they talked in the group.
 * Bodily/Kinesthetics**: Students can use their bodies to make the shapes displayed on the poster. Have students take pictures of themselves as the shapes they are displaying. In groups, create a square, circle, parallelogram, etc. using their hands, feet, and bodies instead of creating them in Geogebra or finding a picture of the polygon online.
 * Musical**: Have students find a song that lists the shapes and properties and incorporate that into the Glogster by adding audio.
 * Spatial**: Put all of the finished Glogsters on the class wiki. Because there are 15 polygons being discussed in the lesson and the students get to choose 5, they will only master understanding the properties of a third of the polygons presented in the lesson. Since the rest of the Glogsters will have the 10 other polygons they need to know, they can refer to their classmate's sites to learn about the other polygons.


 * //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.

Making a Web for the Glogster poster for each shape to make sure they have all the elements. Which elements are based on other elements? Have teacher collect the Web and see if students truly understand the shapes and its properties. Teacher will pass back the Web with notes identifying if they have truly understood the properties of the five polygons the students have selected.
 * Formative (Assessment for Learning)**

Students will create a Glogster web page about shapes and their properties. This is meant to get the students' creative juices flowing. Individually, students will create a web page on Glogster defining the polygons mentioned during the lesson and all of its properties. Throughout the lesson, polygons and their properties will be mentioned and discussed. Students will be given a number 1-3. That number determines which group of 5 polygons they will have to present on their Glogster. Use all the features Glogster offers to make the website memorable. Students will need to include all of the properties of the polygons they choose to represent. All the links of the Glogsters will be added to the class wiki so students can be displayed. The grade will be determined out of 100 points. This assignment is worth 10% of the student's final grade.
 * Summative (Assessment of Learning)**

__Teaching and Learning Sequence__
Paragraph 1: 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: Pre-assess students on the definition of a polygon. Have students write out their definition or draw pictures. (5 minutes) Have students share what they thought a polygon was with the rest of the class. (10 minutes) Define a polygon by showing examples on the overhead. (5 minutes) Introduce right angles on the overhead. (10 minutes) Introduce congruent angles on the overhead. (3 minutes) Introduce congruent sides. Have students point out congruent sides or lines in the classroom. (5 minutes) Introduce parallel sides on the overhead. (5 minutes) Introduce perpendicular sides on the overhead. (5 minutes) Introduce squares on the overhead. (5 minutes) Introduce rectangles on the overhead. (5 minutes) Introduce triangles on overhead. (20 minutes) Assign homework from text. (1 minute)

Day 2: Introduce parallelograms on overhead. (10 minutes) Introduce trapezoids on overhead. (10 minutes) Introduce circles on overhead. (15 minutes) Introduce rhombus on overhead. (10 minutes) Introduce cubes on overhead. Show website from sources in class. .(10 minutes) Introduce regular prisms (20 minutes) Introduce quadrilaterals by using the website in sources. Have students manipulate the figure to the parallelograms, rhombus, trapezoids, etc. (10 minutes) Assign homework in text (1 minute)

Day 3: Pass out assignment about Glogster so students have an idea about what they will need to do for the assessment and pass out the rubric. (2 minutes) Introduce irregular prisms (30 minutes) Introduce cylinders (10 minutes) Introduce cones (10 minutes) Introduce spheres (10 minutes) Do the Think-Share-Pair exercise for the rest of the class (20 minutes) Pass out Web students will have to do for homework (2 minutes)

Day 4: Have students work on Glogsters in class and have them ask questions. (80 minutes)

Students will understand that measurements are based on shape and size.**//Students justify statements about polygons and solve problems//.** Knowing shape and size can help when determining space. Shape and size are mainly what make a figure unique. These unique shapes have other elements such as dimension, length, and width that can essentially determine how much room that unique figure requires. Determining the different properties of the different shapes segues into determining area and volume. Students will get interested in topic of properties by watching this [|video] that introduces students to the idea of three dimensional shapes. **Where, Why, What, Hook, Tailors: Visual, Interpersonal, Musical**

Paragraph 2: Students will know the properties of right triangles, triangles, squares, rectangles, parallelograms, trapezoids, circles, rhombi, cubes, regular prisms, irregular prisms, cylinders, pyramids, cones, and spheres. Using a Cluster/Word Web, students will differentiate between shapes' properties by listing them. This will display the information in a compare and contrast way so students can make connections between polygons. By collecting the Web after the students have them for homework, the teacher will give feedback to assure the students of their knowledge. **Equip, Explore, Tailors: Intrapersonal, Loical**

Paragraph 3: After given the Cluster/Word Web, students will be able to easily classify the different polygons based on shape and congruence. With this new knowledge, students should be able to easily identify different polygons in the real world. From looking around the classroom they should be able to identify many different shapes based on measurements. In class, I will ask students to locate shapes around their rooms, outside, in the classroom, etc. so they they get the big picture of geometry in the world. Students will be split up into Think-Share-Pair groups where they will think about their Glogster project, share their idea with a partner, then share their idea with several other people in a group. Each student will be paired with one other student and that couple will be paired with another couple. Each student will get the role of listener and sharer. To show evidence of learning, the teacher will have students complete a Word/Cluster Web that will be passed in to the teacher who will give prompt feedback. At this point the teacher will decide whether or not the student gets the idea of polygons having their own properties. **Explore, Experience, Rethink, Revise, Refine, Tailor: Interpersonal, Intrapersonal**

Paragraph 4: Once students receive their grade from the summative assessment, they will have to write a self-analysis about which method helped them remember the properties the most. Was it the graphic organizer which mapped out the information in an organized way, or the creativeness of the Glogster that helped you remember the properties in a more fun way? From there, students can determine which method would be best when studying a lesson geared more toward geometry. Knowing the properties of polygons relates directly to area and volumes that will be discussed in further lessons. **Evaluate Tailor: Intrapersonal, Linguistic**


 * Content Notes**

**Polygons**

 * Regular** - all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral.
 * Equiangular** - all angles are equal.
 * Equilateral** - all sides are the same length.


 * [[image:http://www.math.com/tables/art/geometry/convexpolygon.gif width="78" height="73"]] || **Convex** - a straight line drawn through a convex polygon **crosses at most two sides**. Every interior angle is less than 180°. ||
 * [[image:http://www.math.com/tables/art/geometry/concavepolygon.gif width="78" height="73"]] || **Concave** - you can draw at least one straight line through a concave polygon that **crosses** **more than two sides**. At least one interior angle is more than 180°. ||

Polygon Parts A [|polygon] is a [|plane] shape (two-dimensional) with straight sides. Examples include triangles, quadrilaterals, pentagons, hexagons and so on. A "Regular Polygon" has:
 * [[image:http://www.math.com/tables/art/geometry/polygonparts.gif]] || ** Side ** - one of the line segments that make up the polygon.
 * Vertex ** - point where two sides meet. Two or more of these points are called vertices.
 * Diagonal ** - a line connecting two vertices that isn't a side.
 * Interior Angle ** - Angle formed by two adjacent sides inside the polygon.
 * Exterior Angle ** - Angle formed by two adjacent sides outside the polygon. ||

Otherwise it is **irregular**.
 * all **sides** equal and
 * all **angles** equal.
 * [[image:http://www.mathsisfun.com/geometry/images/pentagon-regular.gif width="110" height="100"]] || [[image:http://www.mathsisfun.com/geometry/images/pentagon-irregular.gif width="110" height="100"]] ||
 * Regular Pentagon || Irregular Pentagon ||

Important Properties

 * congruent sides - sides with the same length
 * congruent angles - angles with the same angle measure
 * right angles - angle with 90 degrees
 * perpendicular sides - when a right angle is formed where two sides meet
 * parallel sides - sides that have the same slope. If extended, they will never cross.

Square:
A square has equal sides and every angle is a right angle (90°) Also opposite sides are parallel.
 * [[image:http://www.mathsisfun.com/images/quadrilateral-square.gif width="138" height="133" caption="Square"]] ||  ||   ||
 * ^  || [[image:http://www.mathsisfun.com/images/quadrilateral-right-key.gif width="19" height="22"]] || //means "right angle"// ||
 * ^  || [[image:http://www.mathsisfun.com/images/quadrilateral-equal-key.gif width="19" height="19"]] || //show equal sides// ||

Rectangle
A **rectangle** is a four-sided shape where every angle is a [|right angle] (90°). Also **opposite sides** are [|parallel] and of equal length.
 * [[image:http://www.mathsisfun.com/images/quadrilateral-rectangle.gif width="193" height="132" caption="Rectangle"]] ||  ||   ||
 * ^  || [[image:http://www.mathsisfun.com/images/quadrilateral-right-key.gif width="19" height="22"]] || //means "right angle"// ||
 * ^  || [[image:http://www.mathsisfun.com/images/quadrilateral-equal-key.gif width="11" height="19"]]and[[image:http://www.mathsisfun.com/images/quadrilateral-equal-key2.gif width="19" height="19"]] || //show equal sides// ||

Triangles:
Triangles are one of the most fundamental geometric shapes and have a variety of often studied properties relating to their
 * [|(1)interior angles](angles on the inside) sum up to 180° ([|more])
 * [|(2) Triangle Inequality Theorem] : This theorem states that the sum of the lengths of any 2 sides of a triangle must be greater than the third side ([|more])
 * [|(3)Relationship between measurement of the sides and angles in a Triangle]: The largest interior angle and side are opposite each other. The same rule applies to the smallest sized angle and side and the middle sized angle and side. ([|more])

Right triangles


The sides of the triangle are related to each other by the trigonometric functions:

sin = opposite / hypothenuse sin a = a / c sin b = b / c

cos = adjacent / hypothenuse cos a = b / c cos b = a / c

tan = opposite / adjacent tan a = a / b tan b = b / a

Parallelograms


Opposite sides are parallel and equal in length, and opposite angles are equal (angles "a" are the same, and angles "b" are the same) NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Example:

 * [[image:http://www.mathsisfun.com/geometry/images/regular-quadrilateral-sm.gif width="40" height="40" caption="square"]] || A parallelogram with all sides equal and angles "a" and "b" as right angles is a square. ||

Trapezoids
A trapezoid (called a trapezium in the UK) has one pair of opposite sides parallel. It is called an **Isosceles** trapezoid if the sides that aren't parallel are equal in length and both angles coming from a parallel side are equal, as shown. A trapezoid is **not** a parallelogram because only one pair of sides is parallel.
 * [[image:http://www.mathsisfun.com/images/quadrilateral-trapezium.gif width="394" height="87" caption="Trapezoid (or Trapezium)"]] ||
 * Trapezoid ||  Isosceles Trapezoid  ||

Circles

 * Arc:** A continuous piece of a circle is called an arc. In other words, any portion of the circumference of a circle is called an arc.
 * Chord:** A straight line joining any two points on the circumference of a circle is called a chord.
 * Circumference:** The perimeter of a circle is called its circumference
 * Diameter:** Any straight line drawn through the center and terminating at both ways by the circumference is called a diameter.
 * Origin:** Origin refers to the center of a circle
 * Pi ( [[image:http://www.ricksmath.com/images/pi.gif]] ):** An approximate value of [[image:http://www.ricksmath.com/images/pi.gif]] is 22/7 which is correct to two decimal places. A more accurate value of [[image:http://www.ricksmath.com/images/pi.gif]] is 3.14159 which is correct to five decimal places.
 * Radius:** The constant distance of every point on the circle from its center is called the radius of the circle. It is half of the diameter.
 * Sector:** A sector is that part of a circle, which lies between an arc and two radii joining the extremities of the center. The most important sector is a quadrant, which is one-fourth of the circle.
 * Tangent of a circle:** It is a line perpendicular to the radius that touches only one point on the circle.

Rhombus

A **rhombus** is a four-sided shape where all sides have equal length. Also opposite sides are parallel //and// opposite angles are equal. Another interesting thing is that the diagonals (dashed lines in second figure) of a rhombus bisect each other at right angles.

Prisms
All the previous examples are **Regular** Prisms, because the cross section is regular (in other words it is a shape with equal edge lengths) Here is an example of an **Irregular Prism**: Pentagon is not "regular"in shape) ||
 * Irregular Pentagonal Prism: || Cross-Section: ||
 * [[image:http://www.mathsisfun.com/geometry/images/irr-pentagonal-prism.png width="181" height="119"]] || [[image:http://www.mathsisfun.com/geometry/images/irregular-pentagon.png width="141" height="110"]] ||
 * (It is "irregular" because the

(using straight lines!), Then imagine it extending up from the sheet of paper, - that's a prism ! || || A prism is a [|polyhedron], which means the cross section will be a [|polygon] (a straight-edged figure) ... so all sides will be flat! No curved sides. For example, **a [|cylinder] is not a prism**, because it has curved sides. ||
 * Try drawing a **shape** on a piece of paper
 * [[image:http://www.mathsisfun.com/geometry/images/prism-not-cylinder.jpg width="138" height="202" caption="Prism not cylinder"]] ||  || ==No Curves!==

These are all Prisms:
|| || all along its length) (Also see [|Rectangular Prisms] ) || || ||
 * Square Prism: || Cross-Section: ||
 * [[image:http://www.mathsisfun.com/geometry/images/square-prism.png width="182" height="122"]] || [[image:http://www.mathsisfun.com/geometry/images/square.png width="102" height="102"]] ||
 * Cube: || Cross-Section: ||
 * [[image:http://www.mathsisfun.com/geometry/images/cube.png width="155" height="166"]] || [[image:http://www.mathsisfun.com/geometry/images/square.png width="102" height="102"]] ||
 * (yes, a cube is a prism, because it is a square
 * Triangular Prism: || Cross-Section: ||
 * [[image:http://www.mathsisfun.com/geometry/images/triangular-prism.png width="180" height="122"]] || [[image:http://www.mathsisfun.com/geometry/images/triangle.png width="116" height="100"]] ||
 * Pentagonal Prism: || Cross-Section: ||
 * [[image:http://www.mathsisfun.com/geometry/images/pentagonal-prism.png width="175" height="106"]] || [[image:http://www.mathsisfun.com/geometry/images/pentagon.png width="114" height="108"]] ||

Cylinder:

 * ~ Cylinder Facts ||
 * **Notice these interesting things:** ||
 * || It has a flat base and a flat top ||
 * || The base is the same as the top, and also in-between ||
 * || It has one curved side ||
 * || Because it has a curved surface it is not a polyhedron. ||

Cones


 * ~ Cone Facts ||
 * **Notice these interesting things:** ||
 * || It has a flat base ||
 * || It has one curved side ||
 * || Because it has a curved surface it is not a polyhedron. ||

Sphere



 * ~ Sphere Facts ||
 * **Notice these interesting things:** ||
 * || It is perfectly symmetrical ||
 * || It has no edges or vertices ||
 * || It is **not** a polyhedron ||
 * || All points on the surface are the same distance from the center ||


 * Handouts**