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Unforgivable Blackness: A Film Directed by Ken Burns

About the Film Rebel of the Progressive Era Sparring The Fight of the Century Knockout Ghost in the House For Teachers
For TeachersCircling the Square: Boxing Ring Math
Introduction

Lesson Plans

Resources
Download the Educator's Guide (PDF)



For additional classroom content, please visit PBS TeacherSource.

Subject:

Mathematics

Objectives:

Students will:

  • be introduced to modern specifications and construction of boxing rings

  • apply various methods for finding area of circles, rectangles, trapezoids, and complex area coverings

  • compare and contrast areas and overlaps for attack and defense in the ring

Estimated Time for Completion:

One or more 50-minute periods

Materials:

  • Computers with Internet access

  • Episode one of Unforgivable Blackness: The Rise and Fall of Jack Johnson (available from ShopPBS)

  • Compass and straightedge

  • Graph paper models of the boxing ring

  • Internet resources listed below

Procedure:

Watch segments of the Ken Burns film Unforgivable Blackness: The Rise and Fall of Jack Johnson showing Johnson in the ring, particularly his fights against Tommy Burns (starting approximately 45 minutes and 40 seconds into Episode One, and continuing for 6 minutes) and Jim Jeffries (starting approximately one hour, 30 minutes and 40 seconds into Episode One, and continuing for 5 minutes 45 seconds). Ask the students to note the restrictions of movement the boxers have because of the ring size and the roped off areas in which they fight. Can they see a pattern as to how the boxers move along the ropes or how they take a stand in the center? Are there certain ways that they move toward one another or how they move to avoid each other? Then continue with the lesson.

Jack Johnson was known for his ability to land punches (offense) as well as his ability to avoid being punched (defense). He was compared to the great John L. Sullivan for his punching prowess, and he was compared to the great "Gentleman" Jim Corbett for his defensive finesse. All of the fine techniques for getting in close to punch and for staying away to avoid being punched take place in a small area, officially required to be between 18 and 22 feet (or 5.4 to 6.7 meters).

For purposes of this activity, assume the area of the boxing ring is 20 ft. x 20 ft. = 400 sq ft., and that all boxers are six feet tall with an arm reach that is a circle with a three foot radius.

  • Map out that part (area) of the ring that would be reachable by a boxer moving around the center of the ring with his feet on the center, moving in a circle of radius = reach = 3 feet as in the picture below. What is this area as a percent of the whole?

  • Graph of boxing ring

  • Next, map out that part (area) of the ring that would be reachable by a boxer moving around the perimeter of the ring with his back against the ropes. Find this area three different ways: a) using rectangles, b) using trapezoids, c) using the difference of two squares. What is this area as a percent of the whole?

  • Graph of boxing ring

  • At this point one boxer is against the ropes and the other is on the center of the ring. This situation would leave how much uncovered area between them in "no-man's-land"? What is this area as a percent of the whole?

  • Graph of boxing ring

  • If the boxer in the center takes one step forward, his reach can extended three feet forward and backward to cover how much area? What is this area as a percent of the whole?

  • Graph of boxing ring

  • If the boxer against the ropes takes one step forward, his reach can go three feet forward or backward to cover how much area? What is this area as a percent of the whole?

  • Graph of boxing ring

  • At this point one boxer has taken one step from against the ropes and the other has taken one step from the center of the ring. This situation would leave an overlapping battle area between them of what area? What is this battle area as a percent of the whole?

  • Graph of boxing ring

Answers to Questions:

  • Area = 3.14 x 3 x 3 = 28.26 sq ft.
    area as a percent of the whole = 28.26 sq ft / 400 sq ft = 7.1/100 = 7%

  • Area by (a) = (3x20 sq ft top + 3x20 sq ft bottom +3x14 sq ft left +3x14 sq ft right
    = Area by (b) = four equal trapezoids at 4x1/2 x (20+14) x3 sq ft
    = Area by (c) = difference of two squares at 20x20 -14x14 sq ft = 204 sq ft.
    area as a percent of the whole = 204 sq ft / 400 sq ft = 51/100 =51%

  • Area = 14 x 14 sq ft - Pi x 3 x 3 sq ft = 196 - 28.26 sq ft = 139.48 sq ft
    area as a percent of the whole = 139.48 / 400 = 35%
  • Extended Area = Pi x 6 ft x 6 ft = 113.04 sq ft.
    area as a percent of the whole113 sq ft / 400 sq ft = 28%
  • Area equal to the difference of two squares 20 ft x 20 ft - 8 ft x 8 ft = 336 sq ft, and now subtract the four corners of the ring = 6 ft x 6 ft - Pi x 3 ft x 3 ft = approximately 7.74 sq ft. This would yield 336 sq ft - 7.74 sq ft = 328.26 sq ft.
    area as a percent of the whole = 328.26 sq ft / 400 sq ft = 82%

  • Overlapping area = Pi x 6 ft x 6 ft - 8 ft x 8 ft = 113.04 sq ft - 64 sq ft = 49 sq ft
    battle area as a percent of the whole = 49 sq ft / 400 sq ft = 12%

Extension Activities:

Students can write up their own responses or they may work in collaborative groups to submit a best response for whole class presentation and consideration.

What would be some advantages and or disadvantages of these extremes?

  • Defending the center or attacking from the center

  • Defending from the ropes or attacking from the ropes

  • What does entering either the no-mans-land or common battleground do to the area to defend or to attack from these extremes?

  • What area would 3 steps from center cover?

  • How would that area overlap with the area of a boxer against the ropes?

Categorize different attack strategies for taking 1-2-3 steps from the center. Categorize different defense strategies for taking 2-3 steps from attackers.

What other geometries for this Ring exist? Consider possibilities such as 1) circle overlap circle away from the ropes, 2) circle areas partially restricted by the ropes, and 3) specific area overlap constrictions in the corners.

Investigate how reach changes with height. Have students make a class graph with Height on the X-axis and Reach on the Y-axis. Is there a strong correlation in the scatter plot generated in this way? How would a shorter or taller pair of boxers (or those of different heights and reaches) effect the results of these geometries? Do some Boxing Ring Math based upon your students' own heights and reaches.

How would the activity change by using the minimum size ring of 18 feet by 18 feet? What would be the effect by using the maximum size ring of 22 feet by 22 feet?

For something completely different.... a fun review of math addition and multiplication facts in a timed competition, sporting an added element of hand-eye coordination with the computer mouse... go to this website and "knock 'em out"!

Online Resources:

AIBA Rules
The rules of the Association International de Boxe Amateur specify, among other things, the size, shape and materials used for boxing rings used in international competition.

California Business and Professions Code Section 18700-18748
This section of the California legal code enumerates regulations for boxing contests in the state, including required physical specifications for the ring.

Boxing
This article by noted boxing historian Bert Sugar describes the history and rules of amateur and professional boxing.

Standards:

NCTM Curriculum Standards and Expectations for Grades 9-12:

Algebra
  • Identify essential quantitative relationships and determine the class or classes of functions that might model the relationships.

  • Draw reasonable conclusions about a situation being modeled.

Geometry
  • Analyze properties and determine attributes of two- and three-dimensional objects.

  • Use geometric models to gain insights into, and answer questions in, other areas of math.

  • Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest.

Measurement
  • Understand and use formulas for area.

Problem Solving
  • Solve problems that arise in mathematics and in other contexts.

  • Apply and adapt a variety of appropriate strategies to solve problems.

Communication
  • Communicate mathematical thinking coherently and clearly to peers, teachers, others.

  • Analyze and evaluate the mathematical thinking and strategies of others.

Connections
  • Recognize and apply mathematics in contexts outside of mathematics.

About the Author:

Author Steve Crandall has taught secondary mathematics and science since 1979. An amateur entomologist and astronomer, this National Board Certified Teacher has presented lessons at state and national conferences for math, science, middle school.