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Figuring In Football

  • Lesson
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In this primary grades lesson, students identify figures on a football field. They look for both congruent and similar figures, and they consider figures that are the same but that occur in a different orientation because of translation, rotation, or reflection.

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.

866 football field

Reproduce a copy of the Figuring in Football Activity Sheet for each student.

pdficonFiguring in Football Activity Sheet

Then, proceed with the lesson as follows:

  1. 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.
  2. 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.
  3. 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.

Assessment Option

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.


  1. Have students make the same type of drawings for different sports fields, such as baseball, soccer, basketball, and tennis.
  2. 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").
  3. 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).]

Learning Objectives

Students will:

  • Identify and visualize congruent and similar two-dimensional geometric figures.
  • Recognize that rotations, translations, and reflections do not change geometric figures.

NCTM Standards and Expectations

  • Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes.
  • Recognize and create shapes that have symmetry.
  • Create mental images of geometric shapes using spatial memory and spatial visualization.