L2+O'Halloran,Erin+Marissa

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

**Teacher’s Name:** Ms. Erin O'Halloran **Lesson 2:** Interpretation **Grade Level:** 10 **Topic:** Areas and Volumes

**__Objectives__** **Student will understand that** measurements are based on shapes. **Student will know** areas of the polygons covered in the previous lesson: right triangles, triangles, squares, rectangles, parallelograms, trapezoids, circles, rhombi, cubes, regular prisms, irregular prisms, cylinders, pyramids, cones, and spheres. **Student will be able to** analogies area and volume values when given the shape and measurements.

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

**Rationale:** Using the previously learned properties of polygons, students can determine area and volumes when given the formulas.

**__Assessment__** **Formative (Assessment for Learning)** In groups, students will determine what real life situations would use area and volume. They will be given a certain amount of time to come up with jobs, scenarios, or any situations that use area and volume. When the time is up, the group share some of the ideas they came up with with the rest of the class. Based on the explanations and the different situations, the teacher will make a note of which groups really though through the exercise and which groups did not.

**Summative (Assessment of Learning)** Students will play a game on Smart Board where they to figure out the area of a shape by using the definitions. Using a pre-made template by the teacher, students will be able to go up to the board and solve one problem each. If the student gets stuck, they have 2 lives where they can ask anyone in the class for help if they get stuck. The teacher will grade the student at the board on whether they complete the problem, how many lives they use, and if the answer is correct. Students will need to study all the areas and volumes because they will not know which problem they might get.

**__Integration__** **Technology**: SmartBoard will be used as an instrument to get the students excited to be "assessed" for this topic. This way, the rest of the class can interact with the student doing the problem easily because the problem will be displayed on the board. The pictures will be made by the teacher using Geogrbra or Paint.

**History**: Geometry has been around for centuries and so have areas and volumes. Students can research when some of the area and volume formulas were derived and who they were derived by. After the research, students can write a report or make a presentation on the information they found. **__Groupings__** In class, students will be split up into groups to perform a three step interview. Teacher provides interview questions or may assign character roles for interview process. In pairs, student A interviews student B, practicing listening and questioning skills. Students reverse roles and B interviews A. Pairs team up with another pair to form groups of four. Each member of the group introduces the partner interviewed, sharing interesting points. This relates to the formative assessment topic. Students will ask what jobs would be important to know area and volumes. Once the interview is done, they will share their findings with the rest of the class.

**__Differentiated Instruction__** **Strategies:** **Linguistic**: Have students write their own answers to the problems presented in class even if they are not called to the board. This way, students can have examples of all the different polygons and their areas and volumes. **Intrapersonal**: Have the students answer the questions on their own at their desks and then call on someone who has answered the question to go up to the board and do it. **Interpersonal**: Have students work in a group then call on a group to answer the question after a certain amount of time. **Bodily**/**Kinesthetics**: Have students walking up to the board and having a different environment where they are working rather than their desks. **Spatial**: Have some slides have directions where the student has to draw the object first, then solve the area or volume problem. **Logical**: Have students write out the steps that helped them determine what shape is on the screen.

**Modifications/Accommodations** **//I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and 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 the student is absent during the testing day, a make up testing day will be scheduled at the end of the week. Using a time a common time, the teacher will have students perform the test either after class or during a study hall. Students should still email the teacher when they know they are going to be absent.

**Extensions:** In order to get students interested in the subject, students will have to think of examples in life where the knowledge of area and volume would be useful. It may be easier to view three dimensional objects using this [|website] rather than using a two dimensional surface. Students can use this website to count the sides of the three dimensional object and identify the height easier.

**__Materials, Resources and Technology__** [] ; area of squares, rectangles, parallelograms, trapezoids, circles, and triangles, regular polygons [] ; area of a rhombus [] ; volumes of cubes, regular prisms, irregular prisms, cylinder, pyramid, cones, spheres

**__Source for Lesson Plan and Research__**
 * LCD Projector
 * Computer to show software and slides
 * Text book
 * Hand outs
 * Graphic organizer
 * Web that lists the area and volume formulas

**__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 not know when they are going up to the board because the teacher will be selecting them randomly. This adds spontaneity to the assessment. The environment will be different because the students will be working out problems at the board rather than at their desk with paper and pencil. They can use whatever tools they want that the Smart Board offers. **Clipboard:** Students who show how to solve the problem step by step will better show that they know how to do the problem. The explanation is as easy as they want it to be. Students can choose to do the problem at their desk before stepping up to the board and presenting the problem in front of the class. **Microscope:** Students at the board will be given the option of discussing the problem with their peers. Through this process, students can dive deeper into the problem and get people's different points of view. **Puppy:** Some students might feel that being in front of the class will be uncomfortable; however, the rest of the class is able to help the students at the board. This way creates a more comfortable atmosphere because the class is not sitting there judging the student at the board.

**//Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//** **Rationale:** Refer to the content notes to see what students will know. //Students will be able to analogies area and volume values when given the shape and measurements.// In this lesson, students will learn the area and volume formulas. At the end of the lesson, students will be able to compute volumes and areas based on the polygon and its properties. Interpreting the different properties and determining if they are needed to solve for area or volume is essential to this lesson. Images are another essential to this lesson. It would be extremely difficult to explain the topics of area and volume without showing pictures of the polygons. Students will discuss the importance of area and volume in groups during the lesson.

**//Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//** **Rationale:** **Linguistic**: Have students write their own answers to the problems presented in class even if they are not called to the board. This way, students can have examples of all the different polygons and their areas and volumes. **Intrapersonal**: Have the students answer the questions on their own at their desks and then call on someone who has answered the question to go up to the board and do it. **Interpersonal**: Have students work in a group then call on a group to answer the question after a certain amount of time. **Bodily**/**Kinesthetics**: Have students walking up to the board and having a different environment where they are working rather than their desks. **Spatial**: Have some slides have directions where the student has to draw the object first, then solve the area or volume problem. **Logical**: Have students write out the steps that helped them determine what shape is on the screen.

**//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 areas and volumes. 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)** In groups, students will determine what real life situations would use area and volume. They will be given a certain amount of time to come up with jobs, scenarios, or any situations that use area and volume. When the time is up, the group share some of the ideas they came up with with the rest of the class. Based on the explanations and the different situations, the teacher will make a note of which groups really though through the exercise and which groups did not.

**Summative (Assessment of Learning)** Students will play a game on Smart Board where they to figure out the area of a shape by using the definitions. Using a pre-made template by the teacher, students will be able to go up to the board and solve one problem each. If the student gets stuck, they have 2 lives where they can ask anyone in the class for help if they get stuck. The teacher will grade the student at the board on whether they complete the problem, how many lives they use, and if the answer is correct. Students will need to study all the areas and volumes because they will not know which problem they might get.

**__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: Introduce area of a right triangle (10 minutes) Introduce area of a regular triangle (5 minutes) Introduce area of a square (5 minutes) Introduce area of rectangles (5 minutes) Introduce area of parallelograms (10 minutes) Introduce area of trapezoids (10 minutes) Introduce area of circles and circumference (10 minutes) Introduce area of rhombus (5 minutes) Split up class into groups and have them discuss the importance of areas in everyday life (20 minutes) Day 2: Introduce volume of cubes (10 minutes) Introduce volume of regular prisms (10 minutes) Introduce volume of irregular prisms (10 minutes) Introduce volume of cylinders (10 minutes) Introduce volume of pyramids (10 minutes) Introduce volume of cones (5 minutes) Introduce volume of spheres (5 minutes) For the rest of class, pass out the Word Cluster Web and show students how they will organize all the different volumes and areas on that sheet. Day 3: SmartBoard assessment (80 minutes)

Student will understand that measurements are based on shapes. //**Students justify statements about polygons and solve problems**//**.** ** Learning about areas and volumes is very beneficial to solve real life problems. Students will discuss these topics during class in their interview groups. Using the following video, [], students will see how area problems can be solved in real life. The video shows examples of different types of area problems where more than on equation needs to be used. At the end of the lesson, students will learn how to do this. Where, Why, What, Hook Tailors: Visual, Logical**

Students will need to know areas of the polygons covered in the previous lesson: right triangles, triangles, squares, rectangles, parallelograms, trapezoids, circles, rhombi, cubes, regular prisms, irregular prisms, cylinders, pyramids, cones, and spheres, height, base, and units. It is important for students to find the connections between the polygons’ areas rather than memorizing the formula. Using the Web Cluster Organizer, students can easily see the connections between the polygons rather than looking back and forth in their notes. After the groups in the three interview have finished brainstorming, students will present their ideas. This way, the teacher can determine if the students in that group put a lot of thought into the lesson or did not. **Equip, Explore, Rethink, Revise, Tailors: Linguistic, Interpersonal, Intrapersonal**

Given the Cluster Word Web, students will be able to make the connections between the polygons rather than memorizing the formulas. Going through the Cluster Word Web will assure the teacher that the students are understanding the material at a higher level. By listening to the examples of area and volume in the classroom, the teacher will be able to assess if the students are understanding the content. The rest of the class will also be able to listen to other ideas the rest of the groups had, and they can reflect on those ideas as well as their own. **Explore, Experience, Revise, Refine, Tailors: Linguistic, Logical, Visual**

Students will be given a self assessment sheet where they will have to list the new processes they learned by watching their peers perform area and volume problems. Did they learn new methods? New properties? The teacher will assess the students for the Smart Board assessment and they will know their final grade the next day in class. This lesson relates to the next lessons because students can relate area and volume to transformations and similarities in polygons. **Evaluate, Tailors: Intrapersonal**

** Content Notes ** **square** = a 2 **rectangle** = ab  **parallelogram** = bh   **trapezoid** = h/2 (b1 + b2) **circle** = //pi// r 2 **ellipse** = //pi// r1 r2


 * **triangle** **=** || [[image:http://www.math.com/images/tables/gareatri.gif width="49" height="47"]] || [[image:http://www.math.com/tables/geometry/triangle.gif align="baseline"]] || one half times the base length times the height of the triangle ||


 * **equilateral triangle =** || [[image:http://www.math.com/images/tables/garea1.gif]] ||
 * Area of a rhombus**

1. The "base times height" method First pick one side to be the base. Any one will do, they are all the same length. Then determine the altitude - the perpendicular distance from the chosen base to the opposite side. The area is the product of these two, or, as a formula: //**b**// is the length of the base //**a**// is the altitude (height). ||  ||
 * [[image:http://www.mathopenref.com/images/rhombusarea/ba.gif width="72" height="18"]] || where

2. The "diagonals" method Another simple formula for the area of a rhombus when you know the lengths of the diagonals. The area is half the product of the diagonals. As a formula: //**d1**// is the length of a diagonal //**d2**// is the length of the other diagonal ||  ||
 * [[image:http://www.mathopenref.com/images/rhombusarea/d1d2.gif width="82" height="42"]] || where
 * Volumes**

cube = a 3 rectangular prism = a b c irregular prism = **b** h cylinder = **b** h = //pi// r 2 h pyramid = (1/3) **b** h cone = (1/3) **b** h = 1/3 //pi// r 2 h sphere = (4/3) //pi// r 3 ellipsoid = (4/3) //pi// r1 r2 r3