**Counting Triangles**

Mamie 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**
__________________________________________________________________
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

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.

Return to Mathematics Index