Geometric figures are very much a part of our environment and help
define the ways in which we view and interpret our world. Everywhere
we look we see the influences of pattern, symmetry, and design. A
football field has numerous figures that a young student can easily
distinguish and others, which can be rotated or embedded, that may call
on spatial skills of a more challenging nature.
Reproduce a copy of the Figuring in Football Activity Sheet for each student.
Figuring in Football Activity Sheet
Then, proceed with the lesson as follows:
- Discuss with the class the fact that geometric figures are common
in the world in which we live. Sports often use items of both two- and
three-dimensional shapes, from the equipment used, such as balls and
nets, to the playing fields on which the sports take place. In
particular, football fields often include many geometric figures.
- Have each student locate the geometric figures in Questions 1
through 3 on the activity sheet. You might want to have students
outline the figures with colored markers.
- Have the students study the diagram of the football field to answer Questions 4 through 6.
After students have completed the activity sheet, conduct a class
discussion about the shapes that they found. For instance, ask them to
describe the effects of flips (reflections), turns (rotations), and
slides (translations) on the shapes. Is a shape different just because
it is moved? Also discuss the difference between congruent and similar
figures. [Congruent figures are exactly the same size and shape;
similar figures have the same shape but a different size.]
- J David Keller, Daniel J. Brahier, and William R. Speer. The Arithmetic Teacher. January 1993, 40, 5. p. 264–77.
Have students make the same type of drawings for different sports
fields, such as baseball, soccer, basketball, and tennis. Then, have
them identify the different geometric figures that occur on each field.
- Have students make the same type of drawings for different sports fields, such as baseball, soccer, basketball, and tennis.
- Have students collect from newspapers and magazines
information about the Super Bowl that includes references to geometry
(e.g., "the 10-yard line" or "two teams squared off").
- The activity sheet can be enlarged and the figures that
students are asked to locate can be cut out. These cutouts can then be
used as "figure finders" by placing them on the activity sheet and
sliding, turning, or flipping them until they cover a congruent (or
similar) figure on the field.
Question for Students
What different geometric figures can you identify on the football field?
[Answers will vary, and there are many. Some of the obvious answers are
lines, circles, squares (diamonds), triangles, rectangles, and
parallelograms. Less common items include "bow ties" (two triangles that
meet at a vertex), "home plate" (consisting of three triangles and a
diamond; these occur in the top and bottom of each end zone), and
hexagons (made from two diamonds and two triangles).]