Learning by Logic - Total Surface Area

Boyd, Carolyne Bennett Elementary

Objectives: 1. The student will calculate the area of plane surfaces using the formulas for the area of a square, rectangle and triangle. 2. The student will develop the formula for calculating the total surface area of two geometric solids, the cube and rectangular prism. 3. The student will calculate the total surface area of cubes and rectangular prisms. 4. The student will apply concepts to determine the total surface area of a variety of classroom and household materials. Apparatus Needed geoboard rubber bands overhead projector transparency film (clear, green, yellow) markers small boxes from household materials yardstick shoebox kit consisting of:
plastic pieces of various sizes (poster board may be used)
4 squares
4 rectangles
centimeter grid paper
centimeter grid ruler
wooden cube*
wooden rectangular prism*
construction paper
small boxes from household products
small plastic ziplock bags
duplicated sheets
scissors * milk cartons can be used to
tape construct a cube or rectangular prism

Recommended Strategy Using a geoboard and overhead projector, lead students in a discussion of square units. Develop the concept that squares are quadrilaterals with four equal sides, opposite sides parallel and each angle measuring 90 degrees. Develop the concept that rectangles are quadrilaterals with opposite sides parallel and each angle measures 90 degrees, the opposite sides are of equal length. Develop the concept that a triangle is one-half of a quadrilateral. Write formulas for each geometric figure discussed: Square........ A = s x s or A = s2 Rectangle..... A = l x w Triangle...... A = 1/2 (b x h) Students will work in groups of four or five. Each group will receive a kit containing the above listed materials. Students will take from a plastic bag varied pieces of plastic. Examine each and look for similarities that would allow the pieces to be grouped. Next arrange them into similar stacks. Draw them onto the centimeter grid paper, arranging from largest to smallest. Be sure to begin each figure even with a line on the grid paper. Calculate the area of each plane figure, using the three formulas listed on the board. Given a duplicated sheet containing a variety of shapes, students are asked to divide and conquer. Determine the surface area of the eight planar shapes. The student will find the area of each planar region by adding the sum of the areas of its parts. Given a cube and rectangular prism, each student will wrap the geometric solid, to develop the concept that surface area means to surround. Draw straight lines, cut out the six sections. Tape the sections to a sheet of paper, look for similarities. Develop a method for determining the total surface area of the cube. Do the same for the rectangular prism. Use this information to develop a formula for finding the Total Surface Area of a cube and rectangular prism. The Total Surface Area of the cube is equal to the sum of the area of six equal sides: Cube....................T. S. A. = 6 (s x s) or 6 s2 The Total Surface Area of the rectangular prism is equal to the sum of six surfaces........ the front and back... (h x l) both ends............ (h x w) top and bottom..... ..(w x l) Rectangular Prism.......T. S. A. = 2 (h x l) + 2 (h x w) + 2 (w x l) or....T. S. A. = 2 [ (hl) + (hw) + (wl) ] Use the formulas developed to determine the T. S. A. of other cubes, rectangular prisms, a paper house, the floor and ceiling of the classroom, the painted surfaces of the classroom, household items and drawings on a worksheet. A centimeter ruler and yardstick are provided for convenience. Calculators may be used for this activity. Make sure each answer contains the appropriate unit squared. Resources... Lund, Charles. Dot paper Geometry with or Without a Geoboard Oregon State Math. Resource Project. Geometry and Visualization Stokes, William T. Gems of Geometry
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