Gold Seal Lesson:
Football Field

Copernicus Education Gateway

 

Subject:

 

Mathematics

Grade:

 

 

9-12

 

 

 

ICLE Standards:

 

 

Interpersonal -  work with others

Resources -   identify, organize, and plan

Systems -   understand complex interrelationships

Basic Skills -   read, write, and perform mathematical operations

Thinking Skills -  solve problems

 

 

 

Performance Task:

 

 

During the summer, Richard worked in a summer recreation program. His duties included lining off athletic fields and courts. This proved to be a challenge to him until he learned how to use the Pythagorean Theorem. This theorem was helpful in establishing a right angle at the corner of a field. He used the 6-8-10 method to establish a square corner for an athletic field.  First, Richard would stake where he wanted one corner of the playing area. He would carefully measure 6 feet in the direction from the stake to establish the end line of the field.  Next, he would measure 8 feet from the stake in the direction of the sideline being careful to form a right triangle. Finally, Richard would measure the distance (hypotenuse) from the ends of the two sides.  The desired result Richard was seeking was 10 feet.  If the hypotenuse was not 10 feet, he would need to move one line (end or side) in or out so the hypotenuse was exactly 10 feet. When this was established, Richard knew that he had a right angle. Then, he would extend the end line and sideline the desired distance and repeat the procedure to establish the next corner.

The purpose of this activity is to direct students toward thinking of ways to use the Pythagorean Theorem to solve practical problems. Students will use the scale 1-yard equals 1-foot to establish the corners of a scaled football field. They will also establish goal lines, sidelines, and the lines surrounding the end zone.

Procedure:

  1. With a partner, select the general area for your football field, remembering that you are using the scale of 1-foot equals 1-yard. The dimensions for a full-size field are:
    Playing field: 300 feet by 160 feet
    End zone: 30 feet by 160 feet

  2. After deciding how the field is going to lay, establish the first corner by driving a stake in the ground.

  3. Measure 6 feet in the direction you want the goal line and drive a stake in the ground.  Stretch a string between the two stakes.

  4. As near as possible to a right angle to the goal line string, measure 8 feet in the direction you want the sideline and drive a stake in the ground to mark the spot.  Stretch a string between the corner stake and the side line stake.

  5. Measure the distance between the goal line stake and the side line stake.  According to the Pythagorean Theorem if the two strings are at right angles, the distance should be 10 feet (6 squared plus 8 squared equals 100). The square root of 100 is 10.

  6. If the hypotenuse is not exactly 10 feet, then the angle you formed is not square.  Move either the sideline string or the goal line string until the hypotenuse is exactly 10 feet.

  7. Extend the side line string the appropriate distance (according to scale) to establish the next corner.  Repeat the procedure above to establish the second corner that is a right angle.

  8. Extend the original goal line string the appropriate distance (according to scale) to establish the next corner. Repeat the procedure above to create a corner that is a right angle.

  9. Extend the second goal line string the appropriate distance according to scale to establish the fourth corner. Extend the second side line string the appropriate distance to intersect with the second goal line string.  Using the 6-8-10 method, check to make sure the fourth corner is a right angle.

  10. Devise a method to establish the corner for the end zone.

  11. Discuss with your partner and research other ways in which the corners could be established at right angles and write a short paper describing alternative methods for laying out a football field. Include other ways that the Pythagorean Theorem can have a practical application.

 

 

 

Knowledge / Skills:

 

 

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions.   M.1

Use the Pythagorean theorem to compute side lengths of right triangles.  M.21

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min).  Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis.  M.33

Follow written directions carefully and accurately.  ELA.6

Write a report on a topic that uses several sources of information and correctly document those sources.  ELA.36A

 

 

 

Rubric:

 

 

4 POINTS:  Excellent: The student worked above minimum requirements of the assignment and demonstrated mastery of the subject, topic, or principle with little or no help or coaching.

 

 

3  POINTS:  Very good: The student worked above minimum requirements of the assignment and demonstrated mastery of the subject, topic, or principle with some coaching and help.

 

 

2 POINTS:   Good but needs improvement: The student met only the minimum requirements of the assignment.  He or she did not demonstrate mastery of the subject, topic, or principle and needed considerable coaching and help.

 

 

1 POINT:  Poor: The student did not meet the minimum requirements for the assignment even with considerable coaching and extra help.

The student was able to follow directions and complete a layout of the perimeters of a scaled football field with 100 percent accuracy.  

The student demonstrated knowledge of the Pythagorean Theorem through application.         

The student was able to acquire the materials and supplies necessary for this activity and used them efficiently.      

The student was able to work with a partner and contributed equally in effort to complete the activity.       

The student recognized a problem, such as a corner not being square, and devised a way to correct it.       

The student was able to work with his or her partner to discover other uses of the Pythagorean Theorem and to communicate these ideas in written form effectively.        

 

 

 

Keywords:

 

 

GEOMETRY
PYTHAGOREAN THEORY
TRIANGLES STATISTICS
MEASUREMENT
PROBLEM SOLVING
COMPUTATION
TEAMWORK  
RATIOS

 

 

 

Grades:

 

 

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [x] - 10 [x] - 11 [x] - 12 [x]

 

 

 

ICLE Application:

 

 

D

 

 

 

 

 

© 2000 International Center for Leadership in Education
1587 Route 146 - Rexford - NY - 12148
518.399.2776 Fax: 518.399.7607
19