```Learning by Logic - Total Surface AreaBoyd, Carolyne                              Bennett Elementary                                            821-2680                           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
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 pencils wooden cube* wooden rectangular prism*  construction paper small boxes from household products small plastic ziplock bags paper duplicated sheets scissors                     * milk cartons can be used to  tape                           construct a cube or rectangular prismRecommended Strategy
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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