```Counting TrianglesMamie P. Scott                    Coles School                                          8440 South Phillips                                  Chicago, Illinois 60617                                  312-933-6550                           Objectives:  The sixth grade student will:  1.  Organize, summarize, and record information.  2.  Discover a rule or formula that will find the total number of triangles in       a figure.        Equipment and Materials:    1. Overhead projector, transparencies, and marker.   2. Transparency displaying one large triangle divided into six small      triangles.  Make a 1-part triangle, a 2-part triangle and a 3-part triangle      to be used as overlays on the large triangle.     3. Teacher-prepared worksheet with six triangles arranged in numerical order      from 1 to 6.  Each triangle should be equally divided to represent the      number to be counted.                                                     Recommended Strategies:    A. Establish a meaningful definition of a triangle.  B. Form small groups and distribute worksheets.  C. Use overhead projector to demonstrate how to establish a counting      arrangement by writing a letter name starting clockwise in the triangle      (a, b, c, d, e, f).  Name all 1-part triangles, name all 2-part triangles      and name all 3-part triangles.   D. Summarize by organizing all the data into one table like this:                               Triangle Table
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Type of triangle       Listing by letter     Number of triangles
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1-part              a, b, c, d, e, f             6
2-part              bc, ed, af,                  3
3-part              abc, bcd, cde, fed           6
afe, fab
6-part              abcdef                       1
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Total number of triangles         16

E. Use the second worksheet to count total number of triangles numbered 1-6.
In counting the triangles, a pattern should be discovered by students. The
pattern is that the total number of triangles is the sum of all counting
numbers from 1 to the number of small triangles in the figure.
Example: A triangle equally divided into three small triangles is:
1 + 2 + 3 = 6

Evaluation:     Provide additional opportunities for reinforcement of this concept by using     worksheets.                                                              References:     Lenchner, George. Creative Problem Solving in School Mathematics. Boston:     Houghton Mifflin Company, 1983.          Seymour, Dale. Favorite Problems. Palo Alto, Calif.: Dale Seymour      Publications, 1982.```