Circling the Bases:
Baseball & Geometry

I. Introduction
II. Objectives
III. Preparing the Students
IV. Presentation
V. Enrichment and Assessment Activities
VI. Additional Resources
VII. Relevant Learning Standards
VIII. Planning a Videoconference?




I. Introduction - rationale, goals, target audience
One of the great features of baseball stadiums and fields is that no two are alike - anymore. Maybe there's a big hill in centerfield, as in Houston's Minute Maid Park, or maybe there's a 37-foot tall "Green Monster" forming Boston's left field wall. Outfielders need to know the dimensions and special characteristics of the fields in which they play to help them decide how to field the ball - do they play the fly ball off the wall or try to jump and catch it for an out? Make an informed decision in a dugout full of shapes, area, perimeter, diameter, Pythagorean theorems and other aspects of geometry while learning about some of the "angles" of playing baseball. Will you hit a single, double, triple or home run? It depends on the hitter's math skills in this interactive game where circling the bases means more than just hitting a home run. Batter up!

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II. Objectives - in completing this lesson, students will:
A. Examine how everyday geometric concepts, such as circumference, area, perimeter, diameter, etc., apply to baseball and the real world.

B. Analyze characteristics of the baseball playing field and interpret data in terms of fundamental geometric operations.

C. Understand the characteristics of shapes in baseball and how they can be applied using basic geometric principles.

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III. Preparing the Students
A. Background
On-deck circles, batter's boxes, pitching mounds, foul lines - all of these standard elements appear on baseball fields of all shapes and sizes throughout baseball's history. From Yankee Stadium's short right field fence to Boston's Green Monster, players know details of the fields they play on and use them during the game, while executives will sign certain players to fit the unique elements of their home field. Just as in science and math, students can use baseball to learn key geometric concepts. Finding triangles in the stadium and areas of the outfield is a hidden part of the game, but one that is important in the classroom, as well.

B. Vocabulary
Angle
Area
Batter's box*
Circumference
Diameter
Hypotenuse
Intersecting
Line
Parallel
Parallelogram
Perimeter
Pi
Pitching rubber*
Polygon
Pythagorean Theorem
Quadrilateral
Radius
Rectangle
Rhombus
Right angle
Segment
Symmetry
Volume
*Baseball terms

C. Suggested Pre-Program Activities
1) Ask students to create an overhead diagram of their favorite team's baseball field. Have them compare distances to the fences between ballparks.

2) Go to Ballparks.com and have students compare the distance of outfield fences throughout the history of some of the legendary ballparks (Yankee Stadium, Fenway Park, Wrigley Field, etc…). How do they compare with newer versions of those parks, or the newest ballparks in Major League Baseball?

3) Ask students to compare and contrast how the dimensions of baseball fields differ from basketball courts, football fields, hockey rinks and soccer fields.

4) Have students design their own baseball stadium, complete with notations and distances and simulate a baseball game on the students' products.


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IV. Presentation
If you are participating in a school visit or videoconference please do not review this section with your students. It will be taught as part of the presentation.

A. Opening
1) Explain how geometry defines and describes many important concepts in baseball, especially the playing field. Knowing geometry can help us understand the game of baseball better.

2) Pass out the diagram of the official playing field from the Major League Baseball rulebook, and explain that this applies only to Major League Baseball (American League & National League), and not softball or Little League. What do you see? You can see lines, angles, rectangles, circles, squares - just like in a math book.

B. Lesson
1) Begin a discussion about the elements of a Major League field. What do you call the point where the foul lines meet? How many degrees are in that angle? What do the numbers on the outfield wall mean? How many bases are there, and what is the distance between them? What shapes do they make? Discuss other standard elements, like the pitcher's mound, the pitching rubber, batter's boxes and on-deck circles.

2) Begin preparation for "Circling the Bases" game:
How do you find the perimeter of a 10" x 4" rectangle? Since we know a rectangle has opposite sides of equal distance, we can simply add 10" + 4" + 10" + 4" = 28"
(or 2 x (10" + 4") = 28"
What about finding the circumference of a circle six feet in diameter? Circumference is the diameter multiplied by pi (estimated at 3.14). So C = 3.14 x 6' = 18.84'

How do you find the area of a 10" x 4" rectangle? To get the area of a rectangle, area equals length multiplied by width. So 10" x 4" = 40 square inches. The "square" is necessary.
How do you find the area of a circle six feet in diameter? To find the area of a circle, multiply pi by the squared radius. And remember the radius is half the diameter of a circle. Let's keep pi at 3.14, so we have A = 3.14 x 3², which means A = 3.14 x 9 or A = 28.26 square feet.

3) Discuss the Pythagorean Theorem (a² + b² = c²). How do we find the length of the hypotenuse of a right triangle, if we know two sides are 3" and 4"? Using the Pythagorean Theorem, 3² + 4² = c², making 9 + 16 = c². c² would then be 25 and c = 5.

4) Using the Batter Up! game guidelines, play a simulated game where batters (students) complete math problems of varying difficulty. Students should be organized into teams with lineups. Correct answers result in singles, doubles, triples or home runs depending on their degree of challenge. Incorrect answers result in outs.

C. Conclusion
1) Review with students what has been learned today, including the various mathematical concepts that were used in the game.

2) Ask students what they have learned about baseball while playing this game. If you are participating in a school visit or videoconference please do not review this section with your students. It will be taught as part of the presentation.

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V. Enrichment and Assessment Activities
A. Print and distribute this list of Mark McGwire's 70 home runs in 1998. Discuss the various ballparks listed in the linked box scores and their outfield dimensions. What if Mark McGwire played on a different team with a different home stadium? Which home runs potentially would have been caught in the outfield?

B. Have students find examples of triangles, circles, rectangles and other polygons in a baseball stadium.

C. Ask students to hypothesize how changing distances in ballpark dimensions and baseball rules would affect statistics and player performance. These changes might encompass the distance to the outfield fence, distances between bases or the distance between the pitcher's mound and home plate.


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VI. Additional Resources
A. Literature
Bench, Johnny. The Complete Idiot's Guide to Baseball. Alpha Books, 1999.

Buckley Jr., James. The Visual Dictionary of Baseball. Dorling Kindersley, 2001.


B. Web Links
Official Diagram of a Major League Baseball Field

Mark McGwire's home run list - 1998

Ballparks.com
Official site of Major League Baseball
Baseball and the Pythagorean Theorem (University of Illinois)

D. Multi-Media Gallery
Coming soon!

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VII. Relevant Learning Standards

Click here for appropriate learning standards.
This link provides .pdf versions of national education standards and also standards by select states and grades met by this program.

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VIII. Planning a Videoconference?
A. Videoconference Checklist (PDF)

B. Guidelines for Batter Up! Game
This provides clarification and elaboration of the rules for the Batter Up! game. These are written for the teacher and should be reviewed with the class prior to the videoconference.

C. Rosters