Counting Triangles

Mamie P. Scott Coles School
8440 South Phillips
Chicago, Illinois 60617


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 __________________________________________________________________ Type of triangle Listing by letter Number of triangles ___________________________________________________________________ 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 ___________________________________________________________________ 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


Lenchner, George. Creative Problem Solving in School Mathematics. Boston:
Houghton Mifflin Company, 1983.

Seymour, Dale. Favorite Problems. Palo Alto, Calif.: Dale Seymour
Publications, 1982.

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