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Galin Ma 7th Grade Math Devotion Elementary February 2009 Ms. Jennifer Jordan Math 1 Hour 1. Content Area: Geometry Students learn the relationships between shapes, both two dimensional and three dimensional. Specifically in this lesson, I will describe the relationships between the surface area and volume of rectangular objects, prisms, and cylinders. 2. Topic: I will be going over the basic formulations of three dimensional rectangles, rectangular prisms, and cylinders. Students will also learn how to approximate the surface area and volume of different objects without using any tools for measurement. They will also learn how to calculate surface area and volume given only the dimensions of the object. 3. Goals: To understand the relative volumes of objects in real life compared to theoretical calculations. Students should be able to calculate the dimensions of objects and have a general idea of the formulas needed to find the volume and surface areas of objects. They should differentiate between the properties of cylindrical and non-cylindrical shapes. 4. Objectives: My students will be able to o calculate the volume and surface area of a cylinders, three dimensional rectangles, and prisms o estimate the volume and surface area of objects by sight and without any calculations o Understand the formulas length times width times height, r^2pi times height o Identity real life objects, such as buildings, balls, and soda cans as specific three dimensional objects o Measure objects to find their surface area and volume based on the dimensions 5. Technology, materials and aids: I will use my laptop and a borrowed electronic projector to project a PowerPoint presentation on shapes and objects. I will also supply materials and objects such as coke cans, books, and people for students to measure. There will also be worksheets copied for each student in the class focusing on group activities. Students will also need: Calculators for calculating volume and surface area Meter sticks to measure objects Foot-long rulers to measure smaller objects Pen and pencil to work on handouts 6. Procedures/methods: a. Overview: My lesson will review concepts taught by Ms. Jordan from previous lessons, but also add a constructivist approach to it. I will integrate media, group activities and real life connections to concepts already learned by the students. My job will be to make the math concepts more relatable and personal to their everyday lives. I will do so by first starting with an activity about identifying and estimating certain objects’ volumes and surface area and then moving on to a PowerPoint review session of the concepts. Also I will then show videos online of interesting comparisons of stars and planets to show aspects of volume and surface area. I will wrap up by facilitating a group discussion and listening to the students’ responses to questions I pose at the end to make sure the class understands. b. Introduction: I will begin by introducing the topic by an activity involving estimating the actual volumes of different buildings and objects. These exhibits will be shown on PowerPoint. The objects will consist of a small office building, a book, and large living room. The students will discuss as in groups to what they think the correct volume is and each winning group will get candy as a reward. There will be 5 different objects so that there will be an opportunity for each team to receive a reward. c. Activities: 1. The first activity will be the activity mentioned in the introduction. This will serve as an icebreaker to the rest of the lesson. The activity will shift the students’ focus to thinking about how concepts about surface area and volume relate to real life and its applications. 2. The second activity will be an overview of the concepts taught beforehand by Ms. Jordan. Slides of the different formulas will be shown on the slide as well as a few practice questions to make sure the material is understood by the class. 3. Next I will pull up the website I made with Dreamweaver, which will have more material specifically about rectangular prisms, cylinders and rectangular prisms. 4. On the website there will be videos of the largest rectangular prisms in the world (Skyscrapers). The videos will have information about their dimensions. 5. Given the dimensions of the Prudential Center, what will the volume be? 6. The class will separate into groups of three or four to work on a worksheet to compare which object is bigger given certain dimensions. 7. Discuss the answers as a class. 8. End with a video on the sizes of planets and stars in the universe located on the Dreamweaver so that the students can have an idea of how big some planets are. d. Follow-up: Give out a worksheet that they would take home and complete that is a comprehensive overview of shapes, volume and surface areas. The questions will focus more on real-life scenarios and applications. The worksheet will be collected the next day by Ms. Jordan. 7. Technology Frameworks: 1.14 Use various number formats (e.g., scientific notation, percentages, exponents) as appropriate. Use a variety of technology tools (e.g., dictionary, thesaurus, grammar-checker, calculator) to maximize the accuracy of work. Plan, design, and develop a multimedia product to present research findings and creative ideas effectively, citing sources. 8. Assessment: After reviewing concepts about pyramids, rectangular prisms, and spheres, students should be able to solve for volumes and surface areas given certain dimensions of the objects. They should also intuitively find certain dimensions of objects given incomplete information about its measurements. Students should also have an understanding about the relative size of real-life objects; they should be able to estimate the areas and have a general understanding of the relative sizes of different objects, especially skyscrapers and planets. The teacher will test the students’ knowledge by orally asking the students to estimate the size of different objects, for example, skyscrapers, cars, books, and planets. Students should understand that a books’ volume will vastly different from that of a car, skyscraper, and a planet. Also, the teacher should test the students’ conceptual knowledge of the mathematical content of finding surface areas and volumes. Having the students work individually, in groups or as a class on the quiz provided will give a general assessment of the class’s progress. The quiz has both questions that test basic understanding of the topic and advanced understanding that requires intuitive thinking and problem solving. The quiz is provided below and correct answers are in bold. There are also additional practice problems on the website that test students’ understanding as they move along in the web page. Calculate the missing information for the following of a rectangular prism: 1) l = 9 m, w = 2 m, h = 3 m, V =? a) 54 m^3 b) 64 m^3 c) 128 m^3 d) 54pi m^3 2) l = 6.8 m, w = 5.4 m, h = 2 m, V= ? a) 74.44 m^3 b) 146.88 m^3 c) 73.44 m^3 d) 146.88pi m^3 3) V = 30 cm^3, w = 5 cm, h = 2 cm, l = ? a) 3 cm b) 5 cm c) 2 cm d) sqrt(12) cm 4) A = 48 mm^2, l = 6 mm, h = 4 mm, w =? a) 4 mm b) 8.5 mm c) 1 mm d) 2.4 mm Calculate the missing information for the following of a sphere given the following dimensions: 1) r = 6cm, V = ? a) 506.22 cm^3 b) 506.22 cm^2 c) 904.32 cm^3 d 904.32 cm^2 2) Circumference = 25.24 in, V = ? a) 60 in^3 b) 52.86 in^3 c) 54.32 in^3 d) 54.32 in^2 3) V = 225 in^3, Diameter = ? a) 5.23 in b) 69.22 in c) 3.77 in d) 2.33 in 4) A = 64pi cm^2, r = ? a) 4 cm b) 5 cm c) 3.8 cm d) 2.2 cm Calculate the missing information for the following of a pyramid given the following dimensions: 1) b = 9m, h = 3m, S = sqrt(90), V = ? a) 81m^3 b) 9 m^3 c) 162 m^3 d) 25 m^3 2) b = 9.70m, h = 2.43m, S = 10m, V = ? a) 76.21 m^3 b) 43.29 m^3 c) 32.57 m^3 d) 26.84 m^3 3) S = ?, h = 3 cm, b = 8 cm V = ? a) S = 6.54 cm^2, V = 64 cm^3 b) S = 8.54 cm^2, V = 64 cm^3 c) S = 8.54 cm^2, V = 96 cm^3 d) S = 6.54 cm^2, V = 96 cm^3 4) A = 48 in^2, S = 3 b = ? a) 8 in b) 4 in c) 6 in d) 10 in