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Bernie’s Field at Schroeder Stadium

(Download as Microsoft Word Document: Instructional Plan)

 

 

          You are helping to build the new baseball field at Schroeder Stadium.  Your goal is to calculate how much sod you will need for all the grassy areas of the playing field.

 

Given Facts:   

·       Base cutouts have a radius of 5 feet. (Dirt area)

·       Home cutout has a radius of 8 feet. (Dirt area)

·       Pitcher’s mound has a diameter of 16 feet. (Dirt area)

 

 

Read the questions and consider Diagram 1 carefully.  Use the properties of geometric figures to answer each of the following questions.  Give answers to 3 decimal places.

 

Part I:  Finding the Areas

1.  Determine the surface area of the combined dirt regions. Explain how you arrived at your answer.

 

 

 

 

2.  Find the amount of sod needed in the infield.  Explain how you arrived at your answer.

 

 

 

3.  Find the amount of sod needed for the outfield.  Explain how you arrived at your answer.

 

 

 

 

Part II:  Find How Much Sod You Need to Order

 

The sod company suggests that you need to allow for a 7% waste when determining the amount of sod you need.  What would be the minimum amount of sod that you need to order to include this waste factor?  Show all computations below.

 

 

 

 

 

 

 

 

 

 

 

Part III: Covering First

 

The pitching rubber is 60 feet 6 inches from home plate.  How far must the pitcher run to get to first base?  (Hint:  the pitching rubber is not in the center of the diamond.)  Explain how you arrived at your answer, including a diagram.

 

 

 

 

 

 

 

 

 

 

 

Part IV:  Probability

Assume that when the batter hits the ball, it lands randomly in the field of play.  Showing all work, determine the probability of:

 

a)     The ball landing in left field.

 

 

 

 

    

b)     The ball landing in the dirt region.

 

 

 

 

 

c)      The ball not landing in the infield.

 

Extensions:

 

1.     Using the internet, find out the cost of sod in your area and determine the total cost (including tax and delivery charges) for the sod needed for Schroeder’s Stadium.  Please cite your internet sites.

 

 

 

 

 

 

2.     Now consider Diagram 2.  Assume that you have 100,000 square feet of sod and will have no waste.  Keep the infield the same as the original diagram.  You are trying to create the largest outfield possible.  What is the maximum distance from home plate that you could place a new fence if the fence was an arc of a circle? (Hint: You will be finding the radius of a circle.)

 

 

 

Diagram 1

 

 

AT
 
Schroeder Field

Bernie’s Ballpark

Text Box: 338 feetText Box: 20 feet

 

 

 

 

 

 

 

Diagram 2

 

Bernie’s Arcpark

 

Text Box: ? feetText Box: 20 feet

 

 

 

 

 

Mathematics Governor’s Institute 2006

 

Names of group members:  John Bradica, Rodney Hart, Carol Wengerd, Eugene Wengerd, Craig Yoder

 

Topic/Theme:  Areas, Probabilities

 

Level:  Geometry

 

Time Element:  45 minutes

 

NCTM Standards Addressed:  Geometry and Measurement

 

PA Math Standards Addressed:  Geometry and Measurement

 

Math Assessment Anchors Addressed:  M11.C.1.1, M11.C.1.2, M11.C.1.4,  M11.B.2, M11.D.2.1.3

 

Objectives:  Student will be able to:

                                   1.)  identify and/or use parts of circles and segments associated

                                         with circles .

                                   2.)  recognize and/or apply properties of angles, triangles and

                                        quadrilaterals.

                                   3.)  solve problems involving right triangles using the Pythagorean

                                         Theorem.

                                   4.)  apply appropriate techniques, tools and formulas to determine

                                         measurements.

                                   5.)  write, solve and/or apply a linear equation (including problem

                                         situations).

 

Instructional Strategies and Plan:  The teacher will introduce the problem to the students, hand out a diagram of the problem and let them ‘wrestle’ with the mathematics involved, providing support when necessary.

 

Materials/Resources:  scientific or graphing calculator, paper and pencil

 

Assessment Strategies:  Formative—teacher observation

                                         Summative—collect student work

 

Correctives/Remediation:  The teacher will check each aspect of the students’ work to determine the area of difficulty and discuss with them the changes that need to be made.

 

Extensions/Enrichment: The student will be provided with variations on the problem and suggestions for research on the internet.

 

Special Accommodations:   A certain student is visually impaired, total loss of vision in one eye and diminished vision in the other.  We will be enlarging the diagram and the questions thus giving the student more room to do his work.

 

 

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