Algebra/Geometry Institute Summer 2010
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1 Algebra/Geometry Institute Summer 2010 Faculty Name: Diana Sanders School: John F. Kennedy Memorial High School Mound Bayou, MS Grade Level: 7 th Grade Investigating Surface Area 1. Teaching objective(s) Students will solve real-world and mathematical problems involving the surface area of three-dimensional figures. (Institute s Objective) MS 3b. Construct two-dimensional representations of three-dimensional objects. (DOK 2) MS 4c. Develop and justify geometric formulas for volume and surface area of cylinders, pyramids, and prisms. (DOK 3) 2. Instructional Activities Introduction: Teacher will give each student a cylinder to observe. Students will discuss their observations made of the cylinder. Students will cut the tape on the cylinder, open it up, and lay it flat on the table/desk. Teacher will ask students to observe the cylinder again and describe what they see (2 circles and 1 rectangle). Teacher will point out that the rectangular part of the cylinder is called the lateral face and the circles are called the circular bases. Teacher will provide guided practice on calculating the surface area of cylinders and rectangular prisms using teacher created worksheets. Students will use the formulas for a circle and rectangle to find the areas. Teacher will have students to add all the areas of the cylinder to find the sum (surface area). The class will discuss steps taken to find the surface area of a cylinder. Teacher will provide feedback. Students will complete the hands-on activity involving finding the surface area of a cylinder. Activity: 1. Students will work in groups and use manipulatives (cylinders) to calculate the surface area. 2. Students will use prepared data and models of cylinders to calculate the surface area. 3. Students will write collected data on index cards (optional).
2 Teacher will observe students while working and provide immediate feedback. After students have completed the activity, students will explain how to find the surface area of a cylinder. Teacher will give each student a rectangular prism to observe. Students will discuss observations made of the rectangular prism. Students will cut the tape on the rectangular prism, open it up, and lay it flat on the table/desk. Teacher ask students to observe the cylinder again and describe what they see [6 rectangles (a square is a type of rectangle)]. Students will use the formula for a rectangle to find all the areas of the faces of the rectangular prism. Teacher will have students to add the areas of all the faces of the rectangular prism to find the sum (surface area). The class will discuss steps taken to find the surface area of a rectangular prism. Students will complete hands-on activity involving finding the surface area of a rectangular prism. Activity: 1. Students will work in groups and use manipulatives (building unit cubes) to calculate the surface area. 2. Students will use prepared data and models of rectangular prism to calculate the surface area. 3. Students will write collected data on index cards (optional). Teacher will observe students and provide immediate feedback. After students have completed the activity, have students to explain how to find the surface area of a rectangular prism. The class will discuss the characteristics of cylinders and rectangular prisms and how to find the surface area. Cylinders are made up of three different surfaces two congruent circular bases and a rectangular surface that wraps around the bases (lateral face). Rectangular Prisms are prisms in the shape of rectangles that have six faces; all of which are rectangles. To calculate the surface area for cylinders use the formula Surface Area = 2r (r + h), where r = radius and h = height. To calculate the surface area for rectangular prisms use the formula Surface Area = 2(lw + lh + wh), where l = length, w = width and h = height.
3 3. Materials and Resources Teacher created worksheets Pencil Rectangular Prisms (nets) Building Unit Cubes Cylinders (nets) Index Cards (optional) Overhead Projector Transparencies Transparencies markers Rulers Calculators Scissors Resources Enright, Brian; Fox, Joan; and Gyles, Robert; Breakaway Math: From Practice to Performance, Options Publishing CO, Merrimack, NH, Level H, pp Enright, Brian; Fox, Joan; and Gyles, Robert; Breakaway Math: From Practice to Performance, Options Publishing CO, Merrimack, NH, Level G, pp Assessment Teacher will observe students, listen to oral responses, and have students complete Working with Surface Area Activity (Cylinder) and Using Unit Cubes to find the Surface Area (Rectangular Prism) activities.
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5 I. Let Do It! (Make a list if necessary) A. Finding the area of the circular base B. Finding the area of the rectangular surface (lateral face). IV. Now Let s Find the Surface Area of the Cylinder!!! + + = area of base 1 area of base 2 area of lateral face surface area GREAT JOB!!!!!
6 I. Let s Do It!!! A. Finding the area of the top and bottom faces. Total 1= B. Find the area of the front and back faces. Total 2 = C. Find the area of the left and right faces. Total 3 = II. Now Let s Find the Surface Area of the Rectangular Prism!!! + + = Total 1 Total 2 Total 3 Surface Area GREAT JOB!!!!!
7 Directions: Using the unit cubes, build a 4 by 3 three story rectangular prism. (Each cube = 1 inch) It s your turn to answer questions! 1. What are the dimensions of each rectangular face? List each. 2. What is the surface area of the rectangular prism constructed? 3. What method did you use to find the surface area of the rectangular prism? Use pictures/words to represent your answer.
8 I. The dimensions of a given cylinder are: h = d = II. Use the data in #I to sketch and label the 2-dimensional and 3-dimensional diagram of this cylinder. III. Find the surface area of the cylinder: Work Area Circular Base Work Area Lateral Face IV. What is the surface area of the cylinder? V. How do you find the surface area of a cylinder?
9 A. Finding the area of the top and bottom faces. Total 1= Top: x = Bottom: x = length width area length width area B. Find the area of the front and back faces. Total 2 = Front: x = Back: x = length width area length width area C. Find the area of the left and right faces. Total 3 = Left: x = Right: x = length width area length width area
10 I. Let Do It! (Make a list if necessary) A. Finding the area of the circular base 1. Let = Find the radius (1/2 the diameter) = Square the radius (2.55) 2 = Multiply steps 1 and 3 (this is the area) A=r 2 A=(3.14)(2.55) 2 A=(3.14)(6.5025) A= cm 2 Height = 8.5 cm Diameter = 5.1 cm B. Finding the area of the rectangular surface (lateral face). 1. Find the height 2. Find the circumference 3. Multiply height x circumference A=2rh A=(2)(3.14)(2.55)(8.5) A= IV. Now Let s Find the Surface Area of the Cylinder!!! cm cm cm 2 = cm 2 area of base 1 area of base 2 area of lateral face surface area GREAT JOB!!!!!
11 I. Let s Do It!!! A. Finding the area of the top and bottom faces. Total 1= 67.5 cm 2 Top: 7.5 cm x 4.5 cm = cm 2 Bottom: 7.5 cm x 4.5 cm = cm 2 B. Find the area of the front and back faces. Total 2 = 67.5 cm 2 Front: 7.5 cm x 4.5 cm = cm 2 Back: 7.5 cm x 4.5 cm = cm 2 C. Find the area of the left and right faces. Total 3 = 40.5 cm 2 Left: 4.5 cm x 4.5 cm = cm 2 Right: 4.5 cm x 4.5 cm = cm 2 II. Now Let s Find the Surface Area of the Rectangular Prism!!! 67.5 cm cm cm 2 = cm 2 Total 1 Total 2 Total 3 Surface Area GREAT JOB!!!!!
12 A. Finding the area of the top and bottom faces. Total 1= 67.5 cm 2 Top: 7.5 cm x 4.5 cm = cm 2 Bottom: 7.5 cm x 4.5 cm = cm 2 length width area length width area B. Find the area of the front and back faces. Total 2 = 67.5 cm 2 Front: 7.5 cm x 4.5 cm = cm 2 Back: 7.5 cm x 4.5 cm = cm 2 length width area length width area C. Find the area of the left and right faces. Total 3 = 40.5 cm 2 Left: 4.5 cm x 4.5 cm = cm 2 Right: 4.5 cm x 4.5 cm = cm 2 length width area length width area
13 J. The dimensions of a given cylinder are: h = cm d = 4.5 cm II. Use the data in #I to sketch and label the 2-dimensional and 3-dimensional diagram of this cylinder. Answers will vary III. Find the surface area of the cylinder: Work Area Circular Base A=r 2 A=(3.14)(2.25) 2 A=(3.14)(5.0625) A= cm 2 Work Area Lateral Face A=2rh A=(2)(3.14)(2.25)(11.2) A= IV. What is the surface area of the cylinder? cm 2 V. How do you find the surface area of a cylinder? (answers will vary) 1. Find the area of the circular base. 2. Find the area of lateral face. 3. Add all the areas to find the sum.
14 Directions: Using the unit cubes, build a 4 by 3 three story rectangular prism. (Each cube = 1 inch) It s your turn to answer questions! 1. What are the dimensions of each rectangular face? List each. Top: 4 in x 3 in = 12 in 2 Bottom: 4 in x 3 in = 12 in 2 Front: 4 in x 3 in = 12 in 2 Back: 4 in x 3 in = 12 in 2 Left: 3 in x 3 in = 9 in 2 Right: 3 in x 3 in = 9 in 2 2. What is the surface area of the rectangular prism constructed? 66 in 2 24 in in in 2 = 66 in 2 3. What method did you use to find the surface area of the rectangular prism? Use pictures/words to represent your answer. (anwers will vary) 1. Find the areas of the top and bottom faces. Add the areas and get a total. 2. Find the areas of the front and back faces. Add the areas and get a total. 3. Find the areas of the left and right faces. Add the areas and get a total. 4. To find the surface area, add all the totals.
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Someone else might choose to describe the closet by determining how many square tiles it would take to cover the floor. 6 ft.
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