LESSON PLAN: GOLDEN TRIANGLES

Sara Burrus/Kris Hightshoe

Teacher Objectives:

To acquaint students with the "golden triangle"
To assist students with construction of the golden triangle
To encourage students to look for and identify patterns
To facilitate recognition of the Fibonacci numbers in a golden triangle

Student Objectives:

To be able to follow a sequence of written and verbal instructions
To be able to construct a golden triangle
To recognize the Fibonacci numbers/golden ratio inherent in this triangle

Teaching Strategies:

Discussion
Demonstration/Modeling
Individual work

Prerequisite Information:

Students should by now be very familiar with the Fibonacci numbers. They will be less familiar with the use of a compass and may need to review/practice using it to draw various lengths of line segments and arcs.

Anticipatory Set:

Show a picture/painting which incorporates the Golden Triangle. (eg. The Virgin Mary with her Child and St. John the Baptist by Raphael) Point out the use of the Golden Triangle within the painting. You might also ask if anyone knows what a pentagram is or if they could describe one.

Materials:

Pencil/Paper
compasses
rulers
(This lesson would lend itself quite well to use of Geometer Sketchpad or some other drawing program if it is available.)

Procedure:
1. Model for students the use of a compass to measure a specific length and how to draw an arc.
2. Distribute materials: worksheet, paper, compasses, rulers
3. Model first five steps and have students follow each step as you model it.
4. Have students answer the questions after step five then continue with the remaining steps as you assist with individual work.
5.Students should finish drawing and questions individually.
Assessment:

Successfully completed drawings should look like a pentagram--a regular hexagon with a star (3 golden triangles) inside it.

Enrichment:

Students may do any of the following for extra credit or as an enrichment activity:
1. Describe as many patterns as you can in the figure ( 5--or more.)
2.Find where the pentagonal shape occurs in nature. Give at least five examples--more if you find them.
3.Research the pentagram. Tell what groups through history have used this symbol. See if you can find out why it was used by each group.
4.Create a game using the pentagram. (Maybe you could divide it into shapes and make up figures or puzzles--like tangrams.)
5.Find examples of art work which incorporate the Golden Triangle.
6.Create a picture or drawing in which the golden Triangle is used as a focal point or is implied within the scene. (That means you don't actually draw a triangle, but the subject of the picture is somewhat in the shape of the triangle.)

Connections:

This lesson links to the following Illinois State Goals for Math :

7B.3b: Select and apply instruments and units of measure to the degree of accuracy required in a particular situation.
8: Make generalizations based on observed patterns, and communicate findings...
9A.3a: Draw or construct two- and three-dimensional figures including prisms, pyramids, cylinders and cones.
9C.3b: Develop and solve problems using geometric relationships and models, with and without the use of technology.

The lesson also links to the following NCTM Standards:

Mathematics as connections
Mathematics as reasoning

Click here to see student pages.

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